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Data Mining and Time Series Analysis of Brain Dynamical Behavior with Applications in Epilepsy

Permanent Link: http://ufdc.ufl.edu/UFE0022059/00001

Material Information

Title: Data Mining and Time Series Analysis of Brain Dynamical Behavior with Applications in Epilepsy
Physical Description: 1 online resource (247 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: analysis, approximate, biclustering, correlation, data, detection, dynamics, eeg, entropy, epilepsy, logistic, lyapunov, machines, mining, nerve, nonlinear, quantitative, regression, seizure, stimulation, sum, support, surrogate, vagus, vector
Biomedical Engineering -- Dissertations, Academic -- UF
Genre: Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Epilepsy is a neurological disorder characterized by recurrent seizures. Approximately 30% of patients with epilepsy have seizures that are resistant to anti-epileptic drug (AED) therapy. If these patients are unable to undergo epilepsy surgery, they may choose to utilize the Vagus Nerve Stimulator (VNS) implant. The VNS therapy(R) system has been approved by the FDA to electrically stimulate the left vagus nerve for epilepsy treatment. Patients with newly implanted VNS systems undergo an adjustment period of several months involving numerous medical check-ups to fine tune the electrical stimulation parameters based on clinical response. This sub-optimal adjustment method leaves the patient at risk of seizures and imposes financial burden. Identification of a marker of desired VNS operation would greatly expedite this adjustment process. The utility of non-invasive electroencephalogram (EEG), success of neural state classification research for diagnosis and treatment of neurological disorders, and the potential for real-time application due to advances of computer technology motivate this study. This dissertation outlines data mining approaches involving biclustering, logistic regression, and support vector machines as well as statistical comparisons of a range of relevant EEG dynamical measures for the characterization of electroencephalographic patterns associated with VNS therapy. The preliminary results are consistent with biological processes and clinical observations. One explanation for the electroencephalographic behavior is that VNS mimics a theorized therapeutic seizure effect where a seizure 'resets' the brain from an unfavorable preictal state to a more favorable interictal state. The preliminary results suggest a connection between the EEG patterns and the stimulation parameters which may require a range of linear and nonlinear measures for adequate characterization. In addition, support vector machines are utilized to create a seizure detection and stratification algorithm in patients with generalized absence epilepsy. The algorithm utilizes dynamic time warping distance and Teager-Kaiser energy as the representative EEG features. The algorithm performed slightly better at seizure onset detection than for seizure offset. This is likely due to increased waveform consistency shortly after onset compared to offset. Such an algorithm may benefit clinicians and researchers by providing a means to rapidly annotate EEG signals as well as a means to provide a clinically interesting measure of therapeutic efficacy for drug evaluation studies (e.g., distribution of seizure durations may vary before and after drug therapy, and thus a measure of this distribution may find clinically relevant information which a raw seizure count would miss). A future direction of this project is to test additional EEG feature inputs and assess how the algorithm copes with the challenges presented in online EEG analysis.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Pardalos, Panagote M.
Local: Co-adviser: Ding, Mingzhou.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022059:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022059/00001

Material Information

Title: Data Mining and Time Series Analysis of Brain Dynamical Behavior with Applications in Epilepsy
Physical Description: 1 online resource (247 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: analysis, approximate, biclustering, correlation, data, detection, dynamics, eeg, entropy, epilepsy, logistic, lyapunov, machines, mining, nerve, nonlinear, quantitative, regression, seizure, stimulation, sum, support, surrogate, vagus, vector
Biomedical Engineering -- Dissertations, Academic -- UF
Genre: Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Epilepsy is a neurological disorder characterized by recurrent seizures. Approximately 30% of patients with epilepsy have seizures that are resistant to anti-epileptic drug (AED) therapy. If these patients are unable to undergo epilepsy surgery, they may choose to utilize the Vagus Nerve Stimulator (VNS) implant. The VNS therapy(R) system has been approved by the FDA to electrically stimulate the left vagus nerve for epilepsy treatment. Patients with newly implanted VNS systems undergo an adjustment period of several months involving numerous medical check-ups to fine tune the electrical stimulation parameters based on clinical response. This sub-optimal adjustment method leaves the patient at risk of seizures and imposes financial burden. Identification of a marker of desired VNS operation would greatly expedite this adjustment process. The utility of non-invasive electroencephalogram (EEG), success of neural state classification research for diagnosis and treatment of neurological disorders, and the potential for real-time application due to advances of computer technology motivate this study. This dissertation outlines data mining approaches involving biclustering, logistic regression, and support vector machines as well as statistical comparisons of a range of relevant EEG dynamical measures for the characterization of electroencephalographic patterns associated with VNS therapy. The preliminary results are consistent with biological processes and clinical observations. One explanation for the electroencephalographic behavior is that VNS mimics a theorized therapeutic seizure effect where a seizure 'resets' the brain from an unfavorable preictal state to a more favorable interictal state. The preliminary results suggest a connection between the EEG patterns and the stimulation parameters which may require a range of linear and nonlinear measures for adequate characterization. In addition, support vector machines are utilized to create a seizure detection and stratification algorithm in patients with generalized absence epilepsy. The algorithm utilizes dynamic time warping distance and Teager-Kaiser energy as the representative EEG features. The algorithm performed slightly better at seizure onset detection than for seizure offset. This is likely due to increased waveform consistency shortly after onset compared to offset. Such an algorithm may benefit clinicians and researchers by providing a means to rapidly annotate EEG signals as well as a means to provide a clinically interesting measure of therapeutic efficacy for drug evaluation studies (e.g., distribution of seizure durations may vary before and after drug therapy, and thus a measure of this distribution may find clinically relevant information which a raw seizure count would miss). A future direction of this project is to test additional EEG feature inputs and assess how the algorithm copes with the challenges presented in online EEG analysis.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Pardalos, Panagote M.
Local: Co-adviser: Ding, Mingzhou.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022059:00001


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DATA MINING AND TIME SERIES ANALYSIS OF BRAIN DYNAMICAL BEHAVIOR
WITH APPLICATIONS IN EPILEPSY




















By

MICHAEL ANDREW BEWERNITZ


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008

































2008 Michael A. Bewernitz

































To my family, my loving fiancee Teddi, and all those whom have helped me along the way of
this challenging journey.









ACKNOWLEDGMENTS

I would first like to thank Panos Pardalos for his guidance, wisdom, and his persistent

drive towards excellence which helped me and numerous students to think big, aim high, and

repeatedly achieve great feats throughout the years. Most of all, I thank Dr. Pardalos for the

effort he exerted to assist me during a difficult portion of my graduate schooling. I would also

like to thank Dr. Basim Uthman for teaming up with me to share his brilliant ideas, time, energy,

and financial support. The benefits of his impact on my graduate experience are beyond

measure. I'm very grateful for opportunity to work with Dr. Georges Ghacibeh and for the large

positive impact he has had on my career as a Ph.D. student. I would also like to thank Dr.

Mingzhou Ding, Dr. Steven Roper, and Dr. Hans Van Oostrom for serving on my graduate

committee and providing valuable feedback.

I thank Dr. J. Chris Sackellares for his guidance and support throughout the years,

especially when we worked together at the Brain Dynamics Laboratory at the University of

Florida. In addition, I commend Dr. Deng-Shan Shiau for his continual assistance in all areas of

my graduate career for the last five years. I'm also grateful for the guidance of my BDL

labmates, Dr. Wanpracha Chaovalitwongse, Linda Dance, Chang-Chia Liu, Dr. Sandeep Nair,

and Wichai Suharitdamrong as well as Dr. Wendy Norman for their assistance with work and

just keeping my bearings during this challenging chapter of my life.

I would also like to thank Dr. Paul Carney for his guidance throughout the years during

meetings, conferences, seminars, or just in passing on campus. He has helped me in numerous

ways and I extend sincere thanks. I am also grateful for Dr. Kevin Kelly for providing me the

privilege of a fruitful and engaging experience working at his facility. I thoroughly enjoyed the

summer of 2005 working in his Pittsburgh lab on our challenging task. I am grateful to have









made the acquaintance of Peter Jukkola, Dr. Elena Kharlamov, Kathy Schmitt, and all the

Allegheny-Singer Research Institute staff that helped me along the way.

I'm very grateful for my most recent group of friends in the Center for Applied

Optimization at the University of Florida. The broad spectrum of research experience available

my CAO colleagues such as Ashwin Arulselvan, Dr. Vladimir Boginski, Nikita Boyko, Dr.

Stanislav Busygin, Dr. Altannar Chinchuluun, Alla Kammerdiner, O. Erhun Kundakcioglu, Dr.

Antonio Mucherino, Dr. Oleg Prokopyev, Steffen Rebennack, Dr. Onur Seref, Oleg Shylo, and

Petros Xanthopoulos helped provide me with rapid answers to many research questions,

numerous perspectives to attacking a problem, as well some tasty ethnic food, drink and insider

information for world travel! Short of becoming a United Nations ambassador, I doubt I will

ever work with such a unique and diverse group of friends ever again.

I also appreciate the efforts of Scott Bearden, David Juras, and all the staff at the Malcom

Randall VA Medical Center of the North Florida/South Georgia Veterans Health System who

have collaborated with our University of Florida research team and provided invaluable support

for my Ph.D. studies.

I would also like to thank Professor Jens Timmer, Professor Andreas Schulze-Bonhage,

Dr. Bjorn Schelter, Dr. Michael Jachan, Hinnerk Feldwisch, Armin Brandt, Jakob Nawrath,

Raimar Sandner, Johannes Wohlmuth, Thomas Maiwald, Christiane Lehmann, Carolin

Gierschner, Dr. Matthias Winterhalder, Dipl. Ing. Richard Aschenbrenner-Scheibe, Dr. Henning

Voss of the Freiburg Center for Data Analysis and Modeling, University of Freiburg, Germany,

for providing publicly available de-identified EEG signals for research purposes. Their

generosity has greatly benefited my studies. In addition, General Clinical Research Center,









Grant # MO 1-RR00082 has provided the means to conduct a portion of the research conducted

in this dissertation.

I would like to acknowledge the efforts of April-Lane Derfinyak, Anide Pierre-Louis,

Laura Studstill, Kristi Wagner, Kathryn Whitesides, as well as Tifiny Dyer, Michelle Griffin,

Danielle Wise, and Cindy Hansen for helping keep me on schedule with graduate school

deadlines and comply with all the university guidelines that were a challenge to keep track of.

Outside of my professional contacts, I would like to thank all my friends and my entire

family, Howard, Noreen, Julie, and Mark Bewernitz for countless hours of encouragement in

good and bad times. They have shared my ups and downs and maintained a steady supply of

loving support throughout it all. I thank my loving fiancee, Teddi, for her continued support

throughout the various phases of my graduate career. You mean everything to me Teddi.

Above all, I thank The Father, The Son, and The Holy Spirit for the grace and blessings to

persevere throughout the greatest challenge of my life thus far.









TABLE OF CONTENTS

page

ACKNOWLEDGMENT S .........4.... ...............4
A C K N O W L E D G M E N T S ............................................................................................................... 4

L IST O F T A B L E S ......... .... .............. ..................................... ...........................10

LIST OF FIGURES .................................. .. .... ..... ................. 12

LIST OF ABBREVIATION S ........................... ........................... .... .................. 17

A B S T R A C T ......... ....................... ............................................................ 18

1 INTRODUCTION ............... .......................................................... 20

Computational Therapeutic Approaches: a New Frontier in Medical Treatment ..................21
Establishm ent of N eural States in Epilepsy....................................... ......................... 24
D ynam ical D isorders in N eurology ............................................... ............................ 25
Objectives and Contributions of this Dissertation......................................................27
Organization of Chapters ................................................. ...... ................. 28

2 AN OVERVIEW OF EPILEPTIC DISORDERS AND EPILEPSY RESEARCH
D IR E C T IO N S ...................................... .................................................... 32

In tro d u c tio n ...................... .....................................................................................3 2
C classification of Seizure Types ........................................... .................. ............... 34
P partial S eizu res ................................................................ 34
G en eraliz ed S eizu re s ................................................................................................. 3 5
A absence seizures ....................... ......................... .. .. ................ 35
S tatu s ep ilep ticu s ................................................................................ 3 6
E p ilep sy T reatm ent ............... ........................ .................................... ................... 3 7
The Electroencephalogram as a Diagnostic Tool................................. ...... ............ ...38
Antiepileptic Drugs ......................... ........... .. .. .......... ..... ..... 39
Sodium channel blockers .............. ................................................................40
GABA agonists, reuptake inhibitors, and transaminase inhibitors ........................40
G lutam ate blockers ................... .. ................ ................ .. ...... .. ........ .... 41
Pharmacologically-resistant epileptic seizures..................................................41
E p ilep sy Su rg ery ....................................................... ................ 4 2
G ene T therapy ............................................................................ 42
Electrical Stim ulation Therapy ............................................. .............................. 42
D eep brain stimulation .......................... ........... ........ ............ 44
C e reb e llu m ...............................................................................................................4 5
Subcortical structures ........................ ................ ................... .. ...... 46
C au date nu cleu s............................................................................... ............... 4 6
T h alam u s ............................................................................ 4 6
Centrom edian nucleus ............................................. .......... ............... 47
A interior thalam ic nu cleu s ............................................................. .....................47









Subthalam ic nucleus.............................................................. ...........................48
H ip p o cam p u s ........................................... ....................................4 8
V agus nerve stim ulation ................................................. .............................. 48
Future Therapeutic D directions ................................................... ........................ 51
Complex nature of epileptic dynamics .............. .............................................. 52
Dynamical diseases and disorders...................................................................... 52
Epilepsy as a dynamical disorder of brain systems...............................................54
Compensating for impaired neural control mechanisms: system control therapy ...54

3 TIME SERIES ANALYSIS AND DATA MINING TECHNIQUES: THEORY AND
A P P L IC A T IO N .......................................................................................................5 6

Glossary of Term s ...................... ... .............................................56
Tim e Series A analysis ............... .. ........................................................... .. .... 57
Methods Applied in the Time Domain....................... ......................... 58
Autoregressive moving average modeling............................................................58
Autoregressive integrated moving average modeling............................................59
C ross correlation ............................................ ....... ................. 59
M methods Applied in the Frequency Domain ....................................... ............... 61
C oherence .............................................................................................................6 1
D iscrete Fourier transform ............................................... ............................ 62
W av e let a n aly sis ................................................................................................. 6 4
Inform action B asked M methods ......................................................................... ....................65
A pproxim ate Entropy ................................................. .. .... ........ ........ 65
Pattern M atch R egularity Statistic.............................................................................. ...66
M mutual Inform action ......................... ........... .. .. ......... ..... ..... 67
Chaotic System A analysis Techniques.......................................................... ............... 68
Phase Space M apping ................................................. ...... .. .............. .. 70
The M ethod of D elays .................. .................................... .. ...... .... 71
F ractal D im en sion ................ ............................................ ................ .......... ...... 72
B ox counting dim ension (D O) ........................................................ ............... 74
Inform ation dim ension (D )........................................... .............................. 74
Correlation dim ension (D2) .................................. .....................................75
The Lyapunov Exponent ............................................................. ............... 75
Computing Short-Term Maximum Lyapunov Exponents.............................................77
M ean Angular Frequency in Phase Space................................................. ............... 85
D ata M in in g ...............................86.............................
C lu stern g ................................................................8 7
K -m ean s clu sterin g ............................................................................................. 8 7
B iclu steering ................................................................... 87
C on sistent b iclu sterin g ....................................................................................... 89
Data Classification..........................................................92
Machine learning ................... ..............................92
Mahalanobis distance classification ...................................... 93
Support vector m machines ............................................................... ............. 94




8









4 INVESTIGATION OF EEG BIOMARKER EXISTENCE FOR VAGUS NERVE
STIMULATION THERAPY: A DATA MINING APPROACH ........................................102

M motivation for VN S Therapy Improvement .......... ..... ....... ...... .. .... .................... 103
EEG Markers for Treatment of Neurological Diseases and Disorders .......................103
M odeling Brain D disorder D ynam ics .......................... .............. ................. .... 104
Biclustering Analysis of EEG Dynamics in Patients undergoing VNS Therapy for
E pilep sy ....... ..........................................................107
D ata D description ................................................... ............... ........... 107
STLm ax Feature Extraction ................................................ .............................. 109
Experim mental Setup .................. ...................................... ................ 110
R e su lts .............................................................. ................................................1 1 1
D iscu ssion ..... .......... ............. ....... ................. ............ ...............112
SVM Analysis of EEG Phase Space Patterns in Patients undergoing VNS Therapy for
E p ilep sy ....... ..........................................................1 13
D ata D e scrip tio n ...................................................................................................... 1 14
SVM Application D description ......................................................... .............. 114
Experim mental D design .................. ...................................... ................. 115
R e su lts ................... ...................1...................1.........7
Discussion............................ ........ ....... ...... ...... ...............117
Data Mining Analysis of EEG Dynamics Patients undergoing VNS Therapy for
E epilepsy ...... ..........................................................120
D ata D e scrip tio n ...................................................................................................... 12 0
Feature Extraction .............................................. .. .. .... ........ ......... 121
SVM Analysis of EEG Dynamics ...... .......................... .............................. ....... 121
Logistic Regression Analysis of EEG Dynamics.......... ...................................122
Experim mental Setup .......................... ...................... ... .... ......... ......... 124
R e su lts ........................................................................12 4
D discussion ............................................. 125
C onclusions.....................................................................127

5 ANALYSIS OF INTERSTIMULATION BRAIN DYNAMICS IN VAGUS NERVE
STIM U L A TIO N TH ER A PY .......................................................................................... 142

Further Characterizations/Investigations of EEG-Effects in VNS Therapy .........................142
Dynamical EEG Measures as Markers for Neurological Diseases and Disorders........ 143
Data Description ......................................145
The Surrogate Analysis Method ..........................................146
The Role of Surrogate Data Analysis in EEG studies ....... ..........................148
Nonlinearity Analysis of Interstimulation EEG ...................................................149
C choosing a T est Statistic ............................................................150
E xperim mental D design ...............................................................15 1
R e su lts ........................................................................1 5 2
D isc u ssio n ................................. ........ ................................................ ............... 1 5 3
Temporal Evolution of Interstimulation EEG Dynamics ..... ......... .... ...............156
D ata D e scrip tio n ............. .. ............. ...................................................................... 1 5 6
E E G D ynam ical M measures ...................................................................................... 157


9









A pproxim ate entropy ............................................ ....................................... 157
C correlation sum ..................................... ..................... .. ........ .... 158
M ean angular frequency in phase space............... .............................................. 159
Short-term maximum Lyapunov exponent .................................... ............... 159
Experim mental D design ........................ ...................... ... .... ......... ......... 160
R e su lts ........................................................................1 6 2
D discussion ............................................. 163
C onclusions.....................................................................166

6 A NOVEL GENERALIZED ABSENCE SEIZURE DETECTION ALGORITHM ........... 199

M e th o d s .......................................................................................................................... 2 0 0
Energy M ethod for SW D Detection ................................ ...................... ....... 200
Fanselow M ethod for SW D D election ....................................................... 201
Westerhuis Method for SWD Detection............................... ..... ........ 201
Dynamic Time W arping .................................... ............... ...................202
Teager-Kaiser Energy ......... .......................................................203
E m p iric al S tu d y .............................................................................................................. 2 0 4
E E G D ata A acquisition ..............................................................204
Data Sampling and Feature Extraction ........................... .............. 205
SVM Training and Testing ................................. .......................... ... ....... 206
Detector Performance Evaluation............................................................207
R e su lts ................... ...................2.............................8
D iscu ssion .......... ..........................................................208

7 DISCUSSION AND CONCLUDING REMARKS .................................... ....217

Towards Real-Time EEG Analysis Tools for the Bedside and Implantation ...................217
Data Mining Approaches to Characterizing EEG Patterns .............................................218
Analysis of Interstimulation Dynamics ............... .............. ... ..... ........ 222
R em arks on V N S R results ...............................................................225
Seizure D election and Stratification ............................................. ............... 226
F in al R em ark s ................................................................................ 22 7

L IST O F R E F E R E N C E S ...................................................................................................229

BIO GRA PH ICA L SK ETCH ...............................................................247

LIST OF TABLES

Table page

T able 4-1. V N S stim ulation param eters................................................................................. 133

Table 4-2. Patient information for epilepsy patients with the VNS implant. .............................136

Table 4-3. SVM separation accuracy and seizure information................ ....... ........... 136



10









Table 4-4. Mean SVM and LR separation accuracy and patient seizure information................. 141

Table 5-1. Surrogate analysis results summary for all six patients with the VNS implant.........176

Table 5-2. Control patient surrogate analysis results summary .............................................177

Table 5-3. Approximate entropy analysis results for VNS patients. Results are expressed as
the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt
m measure ........................................................ .................................187

Table 5-4. Approximate entropy analysis results for the control patient. Results are
expressed as the fraction of epochs in each channel which rejected hypothesis H1
using the A pE nt m measure. ....................................................................... ...................188

Table 5-5. Correlation sum analysis results for VNS patients. Results are expressed as the
fraction of epochs in each channel which rejected hypothesis H2 using the
correlation sum m measure. ........................................................................ ................... 189

Table 5-6. Correlation sum analysis results for the control patient. Results are expressed as
the fraction of epochs in each channel which rejected hypothesis H2 using the
correlation sum m measure. ...................................................................... ..................... 190

Table 5-7. Mean angular frequency in phase space analysis results for VNS patients. Results
are expressed as the fraction of epochs in each channel which rejected hypothesis H3
using the Q measure. ................................... .. .. ........ .. ............191

Table 5-8. Mean angular frequency in phase space analysis results for control patient.
Results are expressed as the fraction of epochs in each channel which rejected
hypothesis H3 using the Q m measure. ........................................................................193

Table 5-9. Short-term maximum Lyapunov exponent analysis results for VNS patients.
Results are expressed as the fraction of epochs in each channel which rejected
hypothesis H4 using the STLmax measure.............. ............................... ...............194

Table 5-10. Short-term maximum Lyapunov exponent analysis results for the control
patient. Results are expressed as the fraction of epochs in each channel which
rejected hypothesis H4 using the STLmax measure............... ......... ................. 196

Table 6-1. Classification performance using the first second of each seizure.............................213

Table 6-1. Classification performance using the last second of each seizure..............................213









LIST OF FIGURES


Figure page

Figure 2-1. Seizure classification ruling as designated by the Epilepsy Foundation (2008).........34

F figure 2-2. V N S pulse sequence ................................................................................. .......... 49

Figure 2-3. Closed-loop seizure control device using electroencephalogram or
electrocorticogram signals as an input to a feature extraction algorithm, which
supplies the extracted features to a controller which makes a decision regarding the
action of a stim ulator. .......................... ...... ..................... .... ............... 55

Figure 3-1. A 15 second segment depicting the 200 Hz EEG of an absence seizure viewed
from channel F p l-F 7............. ....................................................................... .......... ... 98

Figure 3-2. A 15 second segment depicting the spectrogram of an absence seizure viewed
from channel Fpl-F7. The vertical lines represent the onset and offset of the seizure. ....99

Figure 3-3. Example angular frequency evolution in phase space. ...........................................100

Figure 3-4. Biclustering result of a toy dataset. The dataset produced three distinct classes.....100

Figure 4-1. Rationale for studying EEG patterns which may be associated with the effect of
V N S o n th e b ra in ............................................................................................................13 1

Figure 4-2. Conceptual EEG dynamics model in three-dimensional feature space for testing
stimulation parameter configurations in newly-implanted VNS patients. Adjusting
the stimulation parameters results in an altered dynamical 'state' of the brain denoted
by the coordinates in three-dimensional feature space. The model's colored regions
relate the EEG dynamical state to its predicted clinical outcome..................................132

Figure 4-3. EEG electrode placement. Electrodes were positioned according to the 10-20
electrode placement system which assigns locations proportionally spaced locations
(e.g. 10%-20%) with respect to the size of the patient's head............... ... .................133

Figure 4-4. STLmax class designation for biclustering analysis..........................................134

Figure 4-5. Biclustering heatmap of STLmax from A) patient A and B) patient B ..................135

Figure 4-6. Mean SVM separation accuracy value across the stimulations for each individual
intra-stim ulation w window ....................................................................... ....................137

Figure 4-7. VNS output current and the corresponding mean SVM separation accuracy over
2 4 h ou rs......... ....... .. ........... .............. ...............................................13 7

Figure 4-8. VNS pulse width and the corresponding mean SVM separation accuracy over 24
h o u rs ................... ........................................................................... 13 8









Figure 4-9. VNS signal frequency and the corresponding mean SVM separation accuracy
o v er 2 4 h o u rs....................................................................... 13 8

Figure 4-10. SVM Separation accuracy throughout the VNS epoch, averaged across all
epochs. Stimulation begins at t=0 seconds. ........................................ ............... 139

Figure 4-11. Overall mean SVM separation averaged across intra-epoch time points and all
epoch s ......................................................... ..................................139

Figure 4-12. LR separation quality throughout the VNS epoch, averaged across all epochs.
Stimulation begins at t=0 seconds. ...........................................................................140

Figure 4-13. Overall mean LR AUC averaged across intra-epoch time points and all epochs...140

Figure 5-1. Map of EEG electrode location for the VNS patients. The electrodes were
positioned according to the 10-20 electrode placement system which assigns
locations proportionally spaced locations (e.g. 10%-20%) with respect to the size of
the patient's head. ............... ........... ..................................................... 171

Figure 5-2. Electrode positions for the control patient from A) an inferior and right view and
B) axial slice view of the brain. Red circles indicate focal electrodes (TBa4, TBb6,
HR7), blue circles indicate non-focal electrodes (TLb2, TLb3, TLc2). Images
provided for this publication courtesy of the Freiburg Center for Data Analysis and
Modeling at the Albert-Ludwigs Universitat Freiburg (University of Freiburg),
Freiburg, G erm any .................. .................................................... ... ......... 171

Figure 5-3. Comparison of pulse width parameter to the fraction of epochs displaying a
nonlinear signature in the six patients treated with VNS. The fraction of epochs
displaying a nonlinear signature in control patient using the 3-minute and 5-minute
off pseudo stimulation times are represented by the column of six triangles (3 minute
off times) and six squares (5 minute off times). ................................... ............... 172

Figure 5-4. Patient A surrogate data analysis results over 24 hours during the
interstimulation epoch. Yellow indicates that particular interstimulation epoch
abscissaa) for the channel of interest ordinatee) rejected the null hypothesis................172

Figure 5-5. Patient B surrogate data analysis results over 24 hours during the
interstimulation epoch. Yellow indicates that particular interstimulation epoch
abscissaa) for the channel of interest ordinatee) rejected the null hypothesis. The red
lines indicate seizures ........................................................ 173

Figure 5-6. Patient C surrogate data analysis results over 24 hours during the
interstimulation epoch. Yellow indicates that particular interstimulation epoch
abscissaa) for the channel of interest ordinatee) rejected the null hypothesis................173

Figure 5-7. Patient D surrogate data analysis results over 24 hours during the
interstimulation epoch. Yellow indicates that particular interstimulation epoch
abscissaa) for the channel of interest ordinatee) rejected the null hypothesis................174









Figure 5-8. Patient E surrogate data analysis results over 24 hours during the
interstimulation epoch. Yellow indicates that particular interstimulation epoch
abscissaa) for the channel of interest ordinatee) rejected the null hypothesis................174

Figure 5-9. Patient F surrogate data analysis results over 24 hours during the interstimulation
epoch. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis. .............................................174

Figure 5-10. The fraction of all interstimulation epochs per channel which rejected the null
hypothesis HO using ApEnt for A) patient A, B) patient B, C) patient C, D) patient
D E ) patient E F ) patient F ............................................................................... .... 175

Figure 5-11. Control patient (with 5-minute artificial stimulation times) surrogate data
analysis results over 24 hours for all artificial interstimulation epochs. Yellow
indicates that particular interstimulation epoch abscissaa) for the channel of interest
ordinatee) rejected the null hypothesis........... ........ ...... .. ............. ............... 177

Figure 5-12. Control patient (with 3-minute artificial stimulation times) surrogate data
analysis results over 24 hours for all artificial interstimulation epochs. Yellow
indicates that particular interstimulation epoch abscissaa) for the channel of interest
ordinatee) rejected the null hypothesis........... ........ ...... .. ............. ............... 177

Figure 5-13. Experimental setup for characterizing the temporal evolution EEG dynamics
during interstimulation intervals in patients undergoing VNS therapy for epilepsy.
The double head arrows indicate a statistical comparison is made between the EEG
feature segments represented by the shaded rectangles...............................178

Figure 5-14. Patient A temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis. ......................................................................... 179

Figure 5-15. Patient B temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis. The red lines indicate seizures .......................................... .................180

Figure 5-16. Patient C temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis. ......................................................................... 18 1

Figure 5-17. Patient D temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis. ......................................................................... 182









Figure 5-18. Patient E temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis. ......................................................................... 183

Figure 5-19. Patient F temporal evolution of dynamics analysis results for A) ApEnt, B)
correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis. ......................................................................... 184

Figure 5-20. Control patient (with 5-minute artificial stimulation times) temporal evolution
of dynamics analysis results for A) ApEnt, B) correlation sum, C) 0, and D)
STLmax. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis. .....................................185

Figure 5-21. Control patient (with 3-minute artificial stimulation times) temporal evolution
of dynamics analysis results for A) ApEnt, B) correlation sum, C) 0, and D)
STLmax. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis. .....................................186

Figure 5-22. Approximate entropy analysis results for VNS patients. Results are expressed
as the fraction of epochs in each channel which rejected hypothesis H1 using the
A pE nt m easure............................................................................................ . 188

Figure 5-23. Correlation sum analysis results for VNS patients. Results are expressed as the
fraction of epochs in each channel which rejected hypothesis H2 using the
correlation sum m measure. ........................................................................ ................... 190

Figure 5-24. Mean angular frequency in phase space analysis results for VNS patients.
Results are expressed as the fraction of epochs in each channel which rejected
hypothesis H3 using the Q m measure. ........................................................................192

Figure 5-25. Short-term maximum Lyapunov exponent analysis results for VNS patients.
Results are expressed as the fraction of epochs in each channel which rejected
hypothesis H4 using the STLmax measure............................................. ...............195

Figure 5-26. ApEnt results and the corresponding output current setting. Results are
expressed as the fraction of interstimulation epochs showing significant temporal
variation ........................................................ ................................ 196

Figure 5-27. Correlation sum results and the corresponding output current setting. Results
are expressed as the fraction of interstimulation epochs showing significant temporal
variation ........................................................ ................................ 197

Figure 5-28. Q results and the corresponding output current setting. Results are expressed
as the fraction of interstimulation epochs showing significant temporal variation. ........197









Figure 5-29. STLmax results and the corresponding output current setting. Results are
expressed as the fraction of interstimulation epochs showing significant temporal
variation ........................................................................................ 198

Figure 6-1. Approximately 6 seconds of scalp-EEG demonstrating the 2.5-3.5 Hz spike-
wave discharge that defines an electrographic absence seizure (data provided
courtesy of D r. Gregory H olm es). ............................................ ........................... 210

Figure 6-2. DTW comparison of two different SWD segments. The top signal is a 300 ms
SWD segment. Bottom signal is a 300 ms segment of a different SWD. The DTW
distance is about 2.4 x 10................... ................ ..... ............ 211

Figure 6-3. DTW comparison of a SWD segment with a random interictal segment. Top
signal is a 300 ms EEG segment of a SWD. Bottom signal is 300 ms of interictal
EEG. The DTW distance is about 5.1 x 10 ...................................... ............... 212

Figure 6-4. Seizure classification evaluation framework. ................................ ..................212

Figure 6-5. Seizure detection performance for RBF parameter sigma=20 using the first
second of each seizure. ............................................. .. .. ............... ....... 214

Figure 6-6. Seizure detection performance for RBF parameter sigma=40 using the first
second of each seizure. ............................................. .. .. ............... ....... 214

Figure 6-7. Seizure detection performance for RBF parameter sigma=80 using the first
second of each seizure. ............................................. .. .. ............... ....... 215

Figure 6-8. Seizure detection performance for RBF parameter sigma=20 using the last
second of each seizure. ............................................. .. .. ............... ....... 215

Figure 6-9. Seizure detection performance for RBF parameter sigma=40 using the last
second of each seizure. ............................................. .. .. ............... ....... 216

Figure 6-10. Seizure detection performance for RBF parameter sigma=80 using the last
second of each seizure. ............................................. .. .. ............... ....... 216









LIST OF ABBREVIATIONS

AED Anti-epileptic drug

ApEnt Approximate entropy

DNA Deoxyribonucleic acid

DTW Dynamic time warping

EEG Electroencephalogram

FN False negative

FP False positive

GCRC General Clinical Research Center

IID Independent and identically distributed

IRB Institutional Review Board

LR Logistic regression

PLED Periodic lateralized epileptiform discharge

STLmax Short-term maximum Lyapunov exponent

SVM Support vector machine

SWD Spike-and-wave discharge

TN True negative

TP True positive

VNS Vagus nerve stimulation

Q Mean angular frequency in phase space









Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

DATA MINING AND TIME SERIES ANALYSIS OF BRAIN DYNAMICAL BEHAVIOR
WITH APPLICATIONS IN EPILEPSY

By

Michael Andrew Bewernitz

May 2008

Chair: Panagote M. Pardalos
Major: Biomedical Engineering

Epilepsy is a neurological disorder characterized by recurrent seizures. Approximately

30% of patients with epilepsy have seizures that are resistant to anti-epileptic drug (AED)

therapy. If these patients are unable to undergo epilepsy surgery, they may choose to utilize the

Vagus Nerve Stimulator (VNS) implant. The VNS therapy system has been approved by the

FDA to electrically stimulate the left vagus nerve for epilepsy treatment. Patients with newly

implanted VNS systems undergo an adjustment period of several months involving numerous

medical check-ups to fine tune the electrical stimulation parameters based on clinical response.

This sub-optimal adjustment method leaves the patient at risk of seizures and imposes financial

burden. Identification of a marker of desired VNS operation would greatly expedite this

adjustment process. The utility of non-invasive electroencephalogram (EEG), success of neural

state classification research for diagnosis and treatment of neurological disorders, and the

potential for real-time application due to advances of computer technology motivate this study.

This dissertation outlines data mining approaches involving biclustering, logistic regression, and

support vector machines as well as statistical comparisons of a range of relevant EEG dynamical

measures for the characterization of electroencephalographic patterns associated with VNS

therapy. The preliminary results are consistent with biological processes and clinical









observations. One explanation for the electroencephalographic behavior is that VNS mimics a

theorized therapeutic seizure effect where a seizure "resets" the brain from an unfavorable

preictal state to a more favorable interictal state. The preliminary results suggest a connection

between the EEG patterns and the stimulation parameters which may require a range of linear

and nonlinear measures for adequate characterization.

In addition, support vector machines are utilized to create a seizure detection and

stratification algorithm in patients with generalized absence epilepsy. The algorithm utilizes

dynamic time warping distance and Teager-Kaiser energy as the representative EEG features.

The algorithm performed slightly better at seizure onset detection than for seizure offset. This is

likely due to increased waveform consistency shortly after onset compared to offset. Such an

algorithm may benefit clinicians and researchers by providing a means to rapidly annotate EEG

signals as well as a means to provide a clinically interesting measure of therapeutic efficacy for

drug evaluation studies (e.g. distribution of seizure durations may vary before and after drug

therapy, and thus a measure of this distribution may find clinically relevant information which a

raw seizure count would miss). A future direction of this project is to test additional EEG feature

inputs and assess how the algorithm copes with the challenges presented in online EEG analysis.









CHAPTER 1
INTRODUCTION

Recent advances in mathematics provide new tactics for the analysis of complex datasets.

These advances provide new options for analyzing and modeling seemingly complex system

behavior such as that seen in biological systems. In addition, the rapid growth of computational

capabilities in the modern computer provides the possibility for real-time computational analysis

of biological datasets. Such scientific milestones have revolutionized the direction of scientific

research in many disciplines, among them, the study of epilepsy. In recent decades, a growing

body of evidence has surfaced in research reports suggesting the existence of a pre-ictal state has

resulted in a great interest in quantitatively characterizing this theorized "seizure imminent"

state. Due to the superior time resolution and large availability of the electroencephalographs,

much research has been devoted to characterizing the preictal state in terms of

electroencephalogram (EEG) datasets.

Advances in the understanding of non-linear system dynamics have lead to massive

breakthroughs for the challenging task of characterizing the dynamics governing the behavior of

complex systems. In many instances, these novel system modeling approaches can achieve

better results than were previously attainable with standard linear approaches.

One major premise for the characterization of neural states is that the dynamics directing

brain function are often best examined within a nonlinear deterministic framework (Savit et al.,

2003). Such a framework can provide a useful means to analyze systems that that exhibit

adaptive behavior and are non-autonomous (both of which are traits of biological systems). For

the example of seizure prediction, this method bypasses the explicit underlying

neurophysiological processes involved in seizure generation and instead focuses on predicting

"undesirable" neural states (e.g. seizures) by measuring and modeling the temporal progression









of various observable features of brain behavior. Whether predicting seizure or other neural state

changes, such features may currently include brain electrical or magnetic field fluctuations,

blood flow, neurochemical concentration profiles. Of these measures, electrical activity as

measured in EEG data sets is the most commonly used feature for describing neural state in

epilepsy.

Computational Therapeutic Approaches: a New Frontier in Medical Treatment

The computational power and memory storage abilities of modern computational age

have revolutionized the way that scientists and engineers approach problems. One of the most

exciting achievements of the 20th century is the invention of the semiconductor transistor, which

was followed by a cascade of computational advances throughout the last 50 years. Moore's Law

is a famous model of the observed growth rate of computational abilities and has remained

astonishingly accurate for several decades (Intel Corporation, 2005). The state of modern

technology provides modern researchers the ability to not only solve problems that could be not

practically be solved a few decades ago, but now we are in a unique position to solve many such

problems in real-time applications.

While the benefits of such technology are manifesting at an almost alarming pace in

every aspect of life, the fields of biology and medicine have capitalized in ways that may have

seemed inconceivable only decades ago.

Necessity is the mother of invention, and such is the driving force for many of the

numerous serendipitous medical discoveries. One prime example is a solution to the many

problems plaguing the functionality of hospital bedside cardiac regulation devices. The original

device utilized an external bedside machine which regulated the cardiac pacing. Among the

many difficulties included impeded patient mobility due to the size and mass of the equipment,

alternating current power requirement, as well as skin burns at electrode sites (Nelson, 1993).









The advent of implantable devices forever revolutionized the field of medical treatment when a

Swedish group first implemented the previously unheard-of idea of utilizing an implantable

device for cardiac pacing (Nelson, 1993). The success of cardiac pacemakers opened the eyes of

physicians and engineers alike that were seeking new solutions to the challenge of improving the

state of medical treatment.

The cardiac pacemaker was highly sophisticated solution to the treatment of damaged and

diseased hearts and helped pave the way for a revolution in medicine; the use of computational

devices (implantable or bedside) to help regulate the physiology of patients afflicted with some

chronic condition. This new engineering direction added numerous challenges such a

biocompatibility and safety issues, as well as new concepts (e.g. designing implantable devices

with the expectation that the treatment device is likely to or guaranteed to fail in lifetime of the

patient).

In recent years, microelectromechanical devices (MEMs) have been able to strongly

capitalize on the advancements of computers. As computers became smaller, faster, and more

efficient, savvy engineers were able to capitalize on the new options available to them. For

example, the combination of MEM sound sensors, processors, and transcutaneous transmitters

provides the possibility of mimicking the role of the cochlea in patients with a specific cause of

hearing impairment (Chapin and Moxon, 2001). While the device is far from being as precise or

accurate as the original brain tissue, such a device helped pioneer a new research direction for

augmenting impaired brain function.

Additionally, retinal implants are being heavily researched to compensate for certain

types of blindness (Schanze et al., 2007). The device is able to mimic some of the tasks of a









function retinal including photo detection and the directing preprocessing phase output to the

optic nerve.

Despite the astonishing milestones of progress in these brain machine interfaces (BMI),

these two implantation devices are still being heavily researched. Another intensely researched

field of BMI aims to integrate the state of the art computational technology combined with the

modern marvels of neuroscience in order to overcome certain types of paralysis (Nicolelis et al.,

2001; Kim et al., 2007). Such an apparatus provides the ability of the brains muscle movement

signals to execute actions in a prosthetic limb.

The above BMIs face numerous challenges which must be overcome before such devices

can become a mainstay of treatment. For one, adequate input data acquisition is massive

challenge in and of itself. All such devices assume that obtaining samples of the brain's

electrical signals can serve as sufficient inputs (as the specific knowledge of neurotransmitter

chemistry and exact neuronal connectivity cannot currently be obtained as successfully as the

electrical signals can be recorded). Also, while our understanding of the roles of the secondary

and primary motor cortices in the planning and execution of motor movements have sufficed to

provide exciting preliminary results for such BMIs, the time and spatial resolution of such

recordings required for optimal external limb control remains uncertain. In addition, one

massive challenge of itself is to extract useful features from such signals in order to serve as the

proper inputs to the underlying model governing the action of such a device. Furthermore, the

proper choice of model is a field of heavy research in and of itself. As is expected, the available

models of brain function have numerous advantages and disadvantages compared one another

that can depend on the particular states of the brain to be modeled, the range of brain states

considered, quality of recordings, feature extraction methods and so on.









While the state of the art of neuroscience has made progress relevant to the development

of BMIs, there is still much room for improvement in understanding the basic and advanced

mechanisms of normal brain function as well as impaired brain function in various neurological

disorders. While the impaired neural functions of interest in the previously described BMI

applications may in some cases seem rather straight forward, the specific neural impairment

processes of some other neurological disorders are at the present moment less explicitly

understood. For such disorders, such as epilepsy, the extraction of suitable biomarkers for any

type of advanced therapeutic scheme is hampered by the apparent mysterious nature of the

disorder. Epilepsy is a disorder that not only has symptoms that are not fully understood (e.g. the

specific cause and purpose of an epileptic seizure), but also the occurrence of seizures often does

not appear to follow any known behavioral pattern with a sufficient degree of accuracy. There is

much room for improvement.

Establishment of Neural States in Epilepsy

Extensive research has been conducted in the last four decades with the focus of

unveiling and modeling the mechanisms that lead up to a seizure. It has been said that only

approximately 3% of epilepsy cases present seizures that are initiated by some external stimulus

whereas for the vast majority of patients there are no such clear events associated with seizure

initiation (Le Van Quyen et al., 2001). However, there is a large body of clinical evidence

suggesting that seizures are preceded by a physiologic state change that occurs prior to seizure

onset.

Documented clinical changes preceding a seizure include increase in heart rate

(Delamont et al., 1999; Novak et al., 1999; Kerem and Geva, 2005), cerebral blood flow

(Weinand et al., 1997; Baumgartner et al., 1998), the availability of oxygen (Adelson et al.,

1999), magnetic resonance imaging of the blood oxygen-level-dependent signal (Federico et al.,









2005) as well as changes visible in single photon emission computed tomographic patterns

(Baumgartner et al., 1998).

Thus, one of the most profound discoveries in this field of research is postulation of a

physiologic "preseizure" state (Mormann et al., 2007). This theory is supported by a large

volume of documented physiologic changes occurring prior to seizure onset within and outside

of the brain. This transition from a "normal" state into a preseizure or "preictal" state is one of

the major theories regarding seizure initiation that has affected the direction of epilepsy research.

On a neuronal level, the preictal state results in an abnormal synchronized "bursting" involving

large populations of neurons in various brain structures. Depending on the type of epilepsy,

these discharges can begin locally and possibly spread to various regions of the brain or can

begin multiple regions nearly simultaneously.

Dynamical Disorders in Neurology

The epileptic disorder exhibits traits similar to a class of diseases termed "dynamic diseases"

which demonstrate particular complex behavior patterns that evolve over time. Specifically,

these "dynamic diseases" have been broadly described as a class of diseases which undergo a

temporal disruption of underlying physiological control mechanisms leading to period of

abnormal dynamical behavior (Mackey and Glass, 1977; Mackey and an der Heiden, 1982;

Milton and Mackey, 1989; Belair et al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da

Silva et al., 2003; Colijn and Mackey, 2005). Examples of these phenomena include the

oscillation of blood cell populations in hematological diseases (Colijn et al., 2006), tremor in

Parkinson's Disease (Beuter and Vasilakos, 1994), as well as several neurological disorders such

as epilepsy, migraine, and multiple sclerosis (Milton and Black, 1995). Within the perspective of

control mechanisms (e.g. feedback or feed forward control systems), dynamical diseases can be

viewed as an undesirable alteration of a standard biological control scheme (Mackey and Glass,









1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et al., 1995; Milton

and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003). Such dynamical disorders often

undergo state transitions that bear resemblances to bifurcations in mathematical systems, for

example. The overall significance of identifying dynamic diseases is that it may be possible to

develop therapeutic approaches based on the manipulation of the identified critical control

parameters (Mackey and an der Heiden, 1982; Milton and Black, 1995). Numerous studies

present models utilizing linear and nonlinear dynamical EEG time series analysis measures to

model the transition into a seizure (lasemidis and Sackellares, 1991; lasemidis et al., 1993;

Lehnertz and Elger, 1995; Casdagli et al., 1996; Lehnertz, 1999; Le Van Quyen et al., 2001;

Osorio et al., 2001; lasemidis et al., 2003, 2004; Chaovalitwongse et al., 2005). Often the long-

term goal is to utilize these measures to serve as inputs for a dynamical disease model used in a

closed-loop therapeutic control device (lasemidis et al., 2003; Good et al., 2004, 2005; Fountas

and Smith, 2007). Thus, if a seizure represents a period of aberration in a dynamical epileptic

disorder which is characterized by nonlinear EEG measures such as STLmax (lasemidis et al.,

2000), then nonlinear dynamical measures (such as STLmax) could conceivably provide a useful

framework for characterizing the effect of therapeutic intervention (Good et al., 2004, 2005;

Ghacibeh et al., 2005).

Aside from such practical applications, quantitative EEG analysis from a non-linear

dynamical framework has also helped provide some novel insight towards defining a

physiological role of seizures in epileptic disorders. For example, one theory states that a seizure

is the manifestation of the brain's mechanism for "resetting" the brain when it enters an

undesirable state. Such a state has been characterized by an unhealthy similarity in the rate of

information production among critical brain sites, a process referred to as dynamicall









entrainment" (lasemidis et al., 2004). Physiologically, such a resetting effect may follow a

proposed therapeutic mechanism similar to that of ECT induced seizures (Fink, 2000; Gwinn et

al., 2002; Taylor, 2007).

The theorized existence of neural states that are indicative of the current status of the

epileptic disorder forms the basis for many model-based seizure control therapy research

projects. A common belief of researchers in this field is that a therapeutic dosage of drug or

electrical stimulation can be applied at the proper location of the central nervous system and at

the proper time to mitigate and possibly prevent seizure occurrence. In essence, this line of

therapy embraces a philosophy that a well-timed, "minor" therapeutic action in the proper

location will abort a seizure by means of fulfilling the therapeutic action for which the seizure

was intended.

Much like the cardiac pace maker described earlier, a "brain pacemaker" is becoming more

of a realistic possibility (Savit, 2003) for providing a means to dispense localized electrical

stimulation or drug dispensing treatment "on demand" when preictal transition state changes are

detected (Stein et al., 2000; Theodore and Fisher, 2004; Good et al., 2004, 2005; Morell, 2006).

Objectives and Contributions of this Dissertation

A team of leading scientists, health care providers, and leaders of voluntary health

organizations came together to discuss what it would take to find a cure for epilepsy in March,

2000. The milestone White-House initiated conference, "Curing Epilepsy: Focus on the Future,"

was sponsored by the National Institute of Neurological Disorders and Stroke in collaboration

with the American Epilepsy Society, Citizens United for Research in Epilepsy, Epilepsy

Foundation, as well as the National Association of Epilepsy Centers. The conference stressed

the importance of scientists throughout the nation to investigate methods of studying and treating









seizures. The conference produced a national agenda for epilepsy research which has served as a

community guide towards a cure.

Since then, the epilepsy research community has progressed substantially in updating the

research benchmarks to be aligned with current research developments. As a result, a primary

goal of the 2007 conference was to assess the original benchmarks and discuss new research

directions. The attendees voted on which areas were most promising, as well as those in need of

attention. The Epilepsy Benchmark Stewards gathered in October 2007 to finalize a hierarchy of

epilepsy research benchmarks. Of particular interest to this dissertation are the following

specific benchmarks:

* Develop valid screening strategies and biomarkers and surrogate markers (e.g., genetic,
pharmacogenomic, electrophysiologic, imaging, biochemical) to identify patients who are
likely to respond to, or develop adverse effects from specific therapies.

* Develop higher-throughput cost-effective models for screening pharmacotherapies for
specific types of epilepsy.

* Optimize existing therapies

The main goal of this dissertation is to extract useful features from the EEG signal of

patients afflicted with epilepsy in order to further the understanding of the disorder and work

towards improvements to existing therapies. The first portion of this research addresses the

desire to identify EEG markers of optimal VNS therapy for the purpose of expediting the

parameter adjustment phase in newly-implanted patients. The final chapter introduces a novel

approach to seizure detection and stratification algorithm which may provide a useful tool for

evaluation drug efficacy.

Organization of Chapters

The research presented in this dissertation is organized into seven chapters. Chapter one

provides an overview of the document. The overview consists of a brief introduction to the field









of quantitative EEG analysis in epilepsy as well as the scope of research presented in this

dissertation from the context of federally-established epilepsy research guidelines.

Chapter two describes an extensive overview of various epileptic disorders, symptoms,

diagnosis, and a range of relevant clinical and biological information. In addition, an overview of

diagnostic tools and current treatment modalities is presented as well the direction of future

treatment research.

Chapter three overviews the broad range of methods utilized in quantitative EEG analysis.

The described methods are broadly classified as time series analysis and data mining methods.

Relevant mathematical theory is and biological interpretations in experimental situations are

explained.

Chapter four begins with a description of epilepsy from a dynamical disorder perspective

and outlines some key EEG data mining analysis methods applied within this framework. Based

on these observations from scientific literature, the aforementioned dynamical EEG analysis

methods are employed to study the effect of vagus nerve electrical stimulation therapy in order to

characterize the relationship of the stimulation parameters with the EEG behavior in terms of

dynamical measures. The results are discussed in terms of their relationship to relevant clinical

research observations and the underlying biological processes. The work described in chapter

four is has been published in three journal articles:

* "Biclustering EEG data from epileptic patients treated with vagus nerve stimulation",
authored by Stanislav Busygin, Nikita Boyko, Panos Pardalos, Michael Bewemitz, and
Georges Ghacibeh (Busygin, 2007).

* "Quantification of the Impact of Vagus Nerve Stimulation Parameters on
electroencephalographic Measures" with authors Michael Bewemitz, Georges Ghacibeh,
Onur Seref, Panos Pardalos, Chang-Chia Liu, Basim Uthman (Bewemitz, 2007).

* "A Data Mining Approach to the Investigation of EEG Biomarker Existence for Vagus
Nerve Stimulation Therapy Patients", with authors Nikita Boyko, Michael Bewemitz,









Vitaliy Yatsenko, Panos Pardalos, Georges Ghacibeh, Basim Uthman, submitted to
Computing and Optimization in Medicine and Life Sciences Vol. 3, (Boyko et al., 2008).

Chapter five provides additional quantitative EEG analysis in patients undergoing VNS

therapy for epilepsy. This chapter closely examines the interstimulation EEG dynamics using

numerous EEG dynamical measures commonly applied in neural state classification studies.

Specifically, this chapter assesses the nonlinearity of EEG dynamics and characterizes time-

dependent dynamical behavior and compares these features to stimulation parameters.

The results are discussed in the context relevant clinical research findings as well as

relevant physiologic processes. The potential application of such results for use in real-time

seizure control applications and rapid parameter tuning apparatus is presented. A paper related

to these interstimulation dynamics studies was published under the title "Optimization of

epilepsy treatment with vagus nerve stimulation" with authors Basim Uthman, Michael

Bewernitz, Chang-Chia Liu, and Georges Ghacibeh (Uthman et al., 2007).

Chapter six begins with an introduction into generalized absence epilepsy. A novel seizure

detection and stratification algorithm is presented as a means to help physicians and researchers

rapidly annotate EEG signals as well as provide online diagnostic tools. In particular, such a

seizure stratification algorithm may provide a clinically interesting measure of therapeutic

efficacy for drug evaluation studies (e.g. the distribution of seizure duration distribution before

and after drug therapy may provide clinically relevant information which a raw seizure count

would miss). A manuscript related to this work was published under the title "Support vector

machines in neuroscience" with authors Onur Seref, O. Erhun Kundakcioglu, and Michael

Bewernitz (Seref et al., 2007).









Chapter seven summarizes the findings of this dissertation. Concluding remarks regarding

the overall significance of the findings are discussed. Future research directions in light of these

results are presented.









CHAPTER 2
AN OVERVIEW OF EPILEPTIC DISORDERS AND EPILEPSY RESEARCH DIRECTIONS

Introduction

The term epilepsy is derived from the Greek word epilamvanein which means "to be

seized", "to be attacked", "to be taken hold of". This disorder has been well documented

throughout historical texts for thousands of years in numerous civilizations. Ancient Greeks

referred to people "being seized" and "having an attack" as if the person were under the

influence of a supernatural force. This idea comes from the ancient notion that disease was a

form of punishment from the gods or evil spirits (Engel, 1989). These descriptions likely refer to

the abrupt, complex timing of seizure onset and how the symptoms could be described as almost

a supernatural "seizing" of the individual for certain types of seizure. Hippocrates was the first

person documented as having suggested that epilepsy was a disorder of the brain around 400

B.C. (Parker and Parker, 2003).

Epilepsy is not a disease, though, but rather a symptom of a disorder of the brain.

Normally, the tens of billions of brain cells making up the brain communicate with one another

via small bursts of electrical activity. An unexpected, erratic electrical discharge of a group of

brain cells is referred to as a seizure. A seizure can be brought on by a variety of insults such as

toxins, drugs, metabolic disturbances, or trauma, flashing lights, or hyperventilation (Wilner,

2003). Such a provoked seizure is separate from Epilepsy, which is a disorder distinguished by

recurrent seizures (Lothman et al., 1991).

The epileptic condition can arise from numerous causes. Typically, the common element

in all causes of epilepsy are events that result in a disturbance of neuronal functionality such as

extreme illness, chemical or physical brain damage, or abnormal brain development resulting

from genetic or other triggers (Parker and Parker, 2003). Specific brain features resulting from









such brain alterations that could be responsible for epilepsy include altered neuronal

connectivity, excessive levels of excitatory neurotransmitters, deficiencies of inhibitory

neurotransmitters, or possibly a combination thereof. It has also been observed that the brain's

attempts to repair itself after injury can lead to irregular nerve connectivity patterns which

eventually lead to epilepsy (Parker and Parker, 2003). Recent estimates of world-wide epilepsy

prevalence for a wide range of age groups indicated between 3 and 8 reported cases of epilepsy

per 1000 people (Shorvon et al., 2004).

The hallmark of epilepsy is recurrent seizures caused by the sudden development of

synchronous neuronal firing. Seizure symptoms can include uncontrollable shaking, loss of

awareness, visual and aural hallucinations, phantom odors, and other sensory disturbances

depending on the location and spread of electrical activity in the brain (Weaver, 2001; Wilner,

2003).

Electroencephalogram (EEG) recordings show that these discharges begin either locally in

one or more portions of a cerebral hemisphere or simultaneously in both cerebral hemispheres

(Binnie et al., 1997; Niedermeyer et al., 1993). These seemingly unpredictable seizures can cause

a variety of motor symptoms and have a major effect on the patient's quality of life by imposing

restricted driving privileges, adverse effects on social and career opportunities, self-esteem,

education, and psychiatric issues (Goldstein and Harden, 2001; Manford, 2003; Wilner, 2006).

In addition, recurrent seizures may cause progressive neuronal damage, leading to impaired

memory and cognition. A 1995 study estimated that epilepsy imposed an economic burden of

$12.5 billion in associated health care costs and losses in employment, wages, and productivity

in the U.S. (Begley et al., 2000).









Classification of Seizure Types

All types of seizures are broadly classified depending on whether the seizure arises in a

restricted portion of the brain within one hemisphere or if the onset involves both hemispheres

(Shorvon et al., 2004). Seizures that do not fit into these categories are referred to as unclassified.

Figure 2-1 outlines a basic framework for seizure classification as designated by the Epilepsy

Foundation (2008).


Epileptic Seizure Types




S Partial Status Epilepticus Generalized




Infantile
Tonic Clonic Spasms

Complex Simple Absence Myoclonic Atonic


Figure 2-1. Seizure classification ruling as designated by the Epilepsy Foundation (2008).

Partial Seizures

Partial seizures are those that occur in a localized region of the brain known as a "focus".

Partial seizures can be roughly broken down into simple partial, complex partial, and secondary

generalized seizures.

A simple partial seizure may materialize with rhythmic twitching of a limb, cessation of

speed, strange sensations in the body, or hallucinations (Shorvon et al., 2004). The particular

symptoms vary from patient to patient and depend on the region of the brain in which the seizure









is occurring. Simple partial seizures begin suddenly, cease quickly, and do not involve an

impairment of consciousness.

In a complex partial seizure a person will temporarily undergo an impairment of

consciousness are often preceded by a premonitory sensory or psychic aura (Shorvon et al.,

2004). During the seizure the person appears unresponsive and may make purposeless limb

movements called "automatisms". Automatisms can include such behavior as eye blinks,

twitches, chewing motions of the mouth, and possibly walking in a circular pattern (Parker and

Parker, 2003). Patients can often be amnesic about the events occurring in complex partial

seizures.

Some partial seizures can spread to both hemispheres resulting in tonic (muscle tensing)

and clonic (rhythmic muscle twitching) symptoms. This type of spreading of seizure activity

after focal onset is referred to as secondary generalization. These seizures were once referred to

as "grand mal" seizures, though this terminology is now discouraged. Conversely, atonic

seizures produce a sudden reduction in muscle tone.

Generalized Seizures

Generalized seizures refer to seizures initiate in both brain hemispheres simultaneously.

These seizures are often accompanied with impaired consciousness. Two important types of

generalized absence seizures are absence seizures and status epilepticus.

Absence seizures

Absence seizures are a type of generalized seizure where seizures are initiated by an abrupt

rapid onset as well as an abrupt rapid offset. These seizures have an off and on nature where the

duration of the seizure is rarely longer than 30 seconds in duration and most often less than 5

seconds in duration (Shorvon et al., 2004). Often the patient will not provide explicit symptoms

of having experienced a seizure, but rather may continue the behavior or movement pattern that









was active at seizure onset. The impaired consciousness combined with a general amnesia about

the experience means that absence seizures can interfere with schooling and may even be

misinterpreted as daydreaming.

Status epilepticus

Status epilepticus is a serious, potentially fatal condition in which seizures persevere for

significantly longer durations than other seizure types. One of the challenges in diagnosing

status epilepticus is to provide a definition that is theoretically sound as well as useful in the

emergency room as neuronal damage can occur after sufficient time (Costello and Cole, 2007).

In addition to the brain, prolonged seizures can damage to numerous body systems including

heart, lung, and kidney tissue (Wilner, 2003). A recent review article suggests a hybrid of

operational definitions including 5 minutes of persistent, generalized, convulsive seizure activity

or two or more distinct seizures between which there is incomplete recovery of consciousness

(Lowenstein et al., 1999) where the seizure activity also persists after sequential administration

of appropriate doses of appropriate first and second line-AEDs (Costello and Cole, 2007).

Nonconulsive status epilepticus (NCSE) refers to the cases of status epilepticus associated

with ictal EEG activity yet without convulsive motor activity (Uthman and Bearden, 2008).

Patients in the NCSE state may appear to be in a confused stuporous state or a comatose-like

state (Costello and Cole, 2007). While status epilepticus can take on many

electroencephalographic characteristics, "clear cut" nonconvulsive status epileptic cases will

present the following properties:

* Frequent or continuous focal electroencephalographic seizures demonstrating changes in
amplitude, frequency, or localization

* Frequency or continuous generalized spike and wave discharges (SWDs) in patients whom
do not have a history of epilepsy









* Frequent or continuous generalized SWDs which show significant amplitude or frequency
differences in relation to previous SWDs (in patients with a history of epileptic
encephalopathy)

* Periodic lateralized epileptiform discharges (PLEDs) in patients which have become
comatose after convulsive status epilepticus

(Korff and Nordli, 2007).

The challenge of treating NCSE cases is that both the electroencephalographic

characteristics and the clinical symptoms can appear very similar to those exhibited by metabolic

disorders. For example, cases of positive NCSE diagnosis have been reported where patients

initially demonstrated extended periods of diffuse rhythmic delta activity before any ictal

waveforms were presented (Uthman and Bearden, 2008).

Triphasic waves can be present in both NCSE as well as the non-epileptic

encephalopathies such as metabolic encephalopathies, though triphasic-like waves must be

highly persistent to be considered as possibly arising from NCSE (Kaplan and Birbeck, 2006).

Currently, one of the most reliable diagnostic strategies is to administer a dosage of a

benzodiazepine class drug and to observe any changes in the EEG signal. Though a small

portion of patients (-15%) will be resistant to benzodiazepine therapy, the drug will often result

in improved mental status and suppression of ictal waveforms in patients that were undergoing

NCSE (Shneker and Fountain, 2003). The absence of clinical improvement after benzodiazepine

dosage does not necessary rule out NCSE.

Epilepsy Treatment

Surprising as it may be the plethora of modem medical imaging technologies that have

developed in the recent decades, though useful for supplementing available information about

the brain, are no substitute for a medical imaging modality invented over 80 years ago. EEG









recordings are relatively cheap to acquire, relatively safe, are often noninvasive (except in more

severe epilepsy cases), and provide exceptional time resolution.

The Electroencephalogram as a Diagnostic Tool

EEG recordings as well as other related electrophysiological measures are the most

commonly used diagnostic tools for the treatment of epilepsy. Though numerous people made

significant technological contributions, Richard Caton is established as the first physician to

observe the brain's continuous spontaneous electrical activity in 1875 (Goldensohn, 1997). Hans

Berger is credited as the father of electroencephalography due to his 1932 report containing four

photographic EEG segments of a patient's postictal recovery (Goldensohn, 1997).

The measurement of the brain's electrical field potentials via EEG is the cornerstone for

epileptic diagnosis and classification of epileptic seizures (Speckmann et al., 1997). Field

potentials are detectable in the space surrounding nervous system tissue. Field potentials arise

from the changes in membrane potential of neurons and glial cells. An excitatory post synaptic

potential (EPSP) occurs when an excitatory afferent fiber is stimulated and the resulting inflow

of cations (e.g. sodium) lead to a membrane depolarization. The spread of the membrane

depolarization results in an intracellular current as well as an extracellular current. The

extracellular current induces the field potential which is perceived by a nearby electrode as a

negative charge (due to the influx of cations) and a distant electrode perceives a positive charge

(due to the out flux of cations) (Speckmann et al., 1997). A similar yet opposing process occurs

for an inhibitory post synaptic potential (IPSP), where the stimulation of an inhibitory afferent

fiber induces an outflow of cations perceived by a nearby electrode as a local positive charge.

Field potentials generated by epileptic processes exceed the potentials generated by

nonepileptic processes because the epileptic activity is highly synchronized (and thus have

relatively elevated amplitude due to a summation effect). Furthermore, experiments have









demonstrated a close temporal relationship between the paroxysmal depolarization of a neuron in

superficial cortex and EEG sharp waves (an indicator of epileptic activity) during the

development of an epileptic focus in a seizure model (Speckmann et al., 1997). Due to the large

degree of synchrony in epileptic outbursts the behavior of this neuron can be extrapolated to

provide a suitable representation of the epileptic neuronal network. Though sharp waves have

an important role in epilepsy diagnosis, there are numerous types of epilepsy with differing

characteristic EEG patterns. For example, absence seizures are often associated with 3-hz

generalized spike and wave patterns yet tonic-clonic seizures are often associated with a variety

of rhythms of generalized spiking and polyspike bursting (Chabolla and Cascino, 1997). Beyond

the handful of examples of epileptiform EEG patterns listed here, there are numerous EEG

properties that the trained electroencephalographer takes into consideration before arriving at a

diagnosis. Such diagnostic details are beyond the scope of this dissertation, however, an

excellent overview can be found in Chabolla and Cascino (1997).

Once the proper diagnosis is made, there are numerous methods used to treat epilepsy.

The methods are treating a specific cause (if one can be identified), avoiding precipitants of

seizures (if any can be identified), antiepileptic drugs (AED), behavior modification, surgery,

electrical stimulation, and diet control (Oxley and Smith, 1991). Use of AEDs is the most

common form of treatment.

Antiepileptic Drugs

AEDs can treat seizures in numerous ways. Some AEDs make brain cells less excitable.

Others make brain cells less likely to pass messages. Still other AEDs increase the amount of a

inhibitory neurotransmitters such as gamma amino butyric acid (GABA) (Oxley and Smith,

1991). One way to classify AEDs is by their main therapeutic mechanism (though there are

some drugs that utilize numerous mechanisms and others may even have unknown mechanisms).









From this organizational framework, the main groups include sodium channel blockers, calcium

current inhibitors, gamma-aminobutyric acid (GABA) enhancers, glutamate blockers, carbonic

anhydrase inhibitors, hormones, and drugs with unknown mechanisms of action (Ochoa and

Riche, 2007). While an in-depth review of antiepileptic drugs is beyond the scope of this

dissertation, an executive summary of some of the basic antiepileptic drug categories will be

outlined.

Sodium channel blockers

This class of drug is well characterized. As the name implies, sodium channel blocking

drugs inhibit sodium channel operation which prevents the affected neuron from depolarizing

and thus inhibits neuronal firing (Ochoa and Riche, 2007). Prominent examples of sodium

channel blockers include carbamazepine, lamotrigine and zonisimide. Lamotrigine is a drug

commonly used to treat absence seizures.

GABA agonists, reuptake inhibitors, and transaminase inhibitors

y-aminobutyric acid (GABA) is an inhibitory neurotransmitter and popular target for

antiepileptic drug action. This is because there are numerous ways to enhance the functionality

of the GABA system, many of which demonstrate a clinically useful antiepileptic effect. GABA-

A receptors control the influx of Cl- ions and GABA-B receptors are connected with potassium

channel function (Ochoa and Riche, 2007). The effect of GABA can be enhanced several ways:

* direct binding to GABA-A receptors,

* blocking presynaptic GABA uptake,

* inhibiting the metabolism of GABA by GABA transaminase,

* increasing the synthesis of GABA

(Ochoa and Riche, 2007). Benzodiazepines (BZDs) are an important class of short-acting

drugs whose anticonvulsant effect is due to binding with GABA-A receptors, where they then









enhance inhibitory neurotransmission (Shorvon et al., 2004). BZDs are commonly used in

epilepsy treatment as well as anesthetic applications. They are most often used for treating status

epilepticus and clusters of seizures rather than long term treatment. For example, the BZD

midazolam has demonstrated effectiveness the treatment of convulsive status epilepticus in

patients for whom phenytoin, and/or phenobarbital had failed (Kumar and Bleck, 1992). One

difficulty in with this drug class is the sedative effects which are a major factor limiting the use

of benzodiazepines in long term seizure therapy. Thus, benzodiazepines tend to be used most

often for acute seizure treatment.

Glutamate blockers

Glutamate is more of the most important excitatory neurotransmitters in the brain (along

with aspartate). The glutamate neurotransmission system is highly intricate and the major

classification scheme for ionotropic glutamate receptors is to name them after the agonist that

activates the binding site (e.g. AMPA, kainite, and NMDA). AMPA and kainite sites control

channels that pass sodium and a small amount of calcium. NMDA sites control channels that

pass large amounts of calcium in addition to sodium (Ochoa and Riche, 2007). Felbamate and

Topiramate are examples of antiepileptic drugs that mitigate glutamate excitatory transmission.

Pharmacologically-resistant epileptic seizures

AED therapy can be very effective in preventing seizures. Primary generalized epilepsy

and benign partial epilepsy are two classes of epilepsy that respond well to AEDs. Patients with

temporal lobe epilepsy are not so fortunate, though. These unfortunate people can usually expect

to take AEDs their entire life. The odds of gaining complete control over temporal lobe epilepsy

seizures are not as good as primary generalized or benign partial epilepsy (Oxley and Smith,

1991). Approximately 30% of patients with epilepsy have seizures that are resistant to AED

therapy, and must resort to alternative therapies (Theodore and Fisher, 2004).









Epilepsy Surgery

Surgical treatment may be considered in extreme cases where the patient does not achieve

adequate benefit from AED therapy (Engel et al., 1993). The mean duration of in-patient

hospital stay for pre-surgical EEG monitoring ranges from 4.7 to 5.8 days and costs over $200

million each year (Begley et al., 2000). In order to be a candidate for surgery, the first criterion is

that the patient must have seizures arising from a single seizure focus in the brain. In addition,

the excision procedure cannot be performed on brain regions that are essential for normal

functioning of the patient (Roper, et al., 1993; Velasco et al., 2000; Durand and Bikson, 2001).

Even if as many as 50% of these patients were to benefit from surgical resection (an optimistic

estimate), many patients still require new therapeutic approaches (Theodore et al., 2004).

Gene Therapy

Gene therapy is an innovative approach to providing antiepileptic therapy to patients with

pharmacologically resistant seizures. From the perspective of treating epilepsy by correcting an

imbalance in excitatory and inhibitory neuronal transmission, a vector can be used to insert

neuropeptide genes in certain brains which lead to intracranial creation of therapeutic peptides.

For example, the neuropeptide Y gene inserted into rat hippocampus with adeno-associated viral

vectors resulted in reduced generalization, delayed seizure initiation, and provided

neuroprotection in a rat seizure model (Noe' et al., 2007). Additionally, the lentivirus may be

used as a vector, or to graft genetically engineered cells which produce therapeutic substances

(Vezzani, 2004). Though these as well as other results are very promising, gene therapy for

epilepsy treatment is still at the pre-clinical research stage.

Electrical Stimulation Therapy

Brain stimulation is becoming one of the main alternative therapeutic approaches for

patients whom are suffering for pharmacologically intractable epilepsy and are not surgical









candidates. While the force can have a strong influence on the weak-minded (Kenobi, 1977),

conventional electrical stimulation therapy remains a more widely-used form of brain

stimulation. Numerous forms of electrical stimulation therapy have been utilized for the

treatment of epilepsy. One such method of brain stimulation is membrane polarization by

uniform direct current (DC) electric fields.

This form of stimulation comes from the basic principle that electrical current can generate

an electric field when then results in generation of electric current. Specifically, electric fields

generated by the nervous system can directly modulate the activity of neurons and often can

recruit neighboring cells. DC electric fields have a unique property compared to other

stimulation paradigm in that they can cause either excitation or inhibition of neuronal activity

depending on the orientation of the field with respect to dendrite. (Durand and Bikson, 2001).

While DC field stimulation utilizes a relatively low current amplitude (only a few

microamperes), there are several drawbacks to this method: 1) irreversible chemical reactions

can result the dc field which often result in tissue and/or electrode damage; 2) the efficacy of

stimulation is highly sensitive on DC field orientation; 3) either excitation or inhibition can be

induced depending cell location and orientation (thus, improper DC field orientation can induce

the "opposite" of the intended effect); 4) the termination of the DC pulse induces an excitation

which results in a rebound of spontaneous activity; and 5) DC fields application must typically

be applied for the entire duration of an ictal event for desired efficacy and thus may require long

pulses (Durand and Bikson, 2001).

Low frequency stimulation paradigms (e.g. stimulation frequencies less than 10 Hz)

provide robustness over DC electric field stimulation. Unlike DC field stimulation, low

frequency stimulation is not orientation dependent and thus its effects are less variable. In









addition, low-frequency and single pulse stimulation have long-lasting effects which remain long

after the duration of the pulse. This after effect helps minimize the electrochemical damage as

well as the amount of energy required for stimulus.

Periodic low frequency stimulation applied via transcranial magnetic stimulation (TMS) is

a noninvasive method to induce electric fields in the brain. A study investigating the

susceptibility of amygdala for kindling in rats demonstrated a 55% higher threshold for the

induction of epileptic after discharges two weeks after a single TMS train (120A/Ls, 20 Hz for 3

s) (Ebert, 1999). The mechanism underlying this type of antiepileptic effect for low-frequency

stimulation is unknown, but suspected to be long-term depression (LTD). LTD is a persistent

decrease in synaptic strength caused by low frequency (e.g. 1 Hz) stimulation (Purves et al.,

2004). Low-frequency stimulation paradigms for establishing LTD could decrease neuronal

firing rate which may in an antiepileptic effect (Durand and Bikson, 2001).

Deep brain stimulation

Deep brain stimulation (DBS) attracted great attention in 1996 for its use in the treatment

of tremor related to Parkinson's disease and essential tremor (Gross, 1994). DBS offers several

advantages over PNS (e.g. vagus nerve) stimulation. Specifically, electrodes implanted in the

brain can directly stimulate the targeted structure with far greater accuracy than PNS stimulation.

Also, the coarse action of PNS stimulation risks activation of afferent (such as pain or sensory)

and efferent fibers (such as those modulating cardiovascular and abdominal visceral functions)

(Durand and Bikson, 2001). Naturally, a major DBS disadvantage is that the implantation of

intracranial electrodes has a greater extent of invasiveness and associated risk than PNS

stimulation.

There are presently four general hypotheses explaining the therapeutic mechanism of DBS:

1) stimulation-induced alterations in the activation of voltage-gated currents block neural output









near the stimulating electrode; 2) indirect inhibition of neuronal output by means of activation of

axon terminals that make synaptic connections with neurons near the stimulating electrode; 3)

synaptic transmission failure of the efferent output of stimulated neurons as a result of

transmitter depletion; 4) stimulation-induced disruption of pathologic network activity (McIntyre

et. al, 2004). Additional research utilizing microdialysis, neural recordings, modeling, and

functional imaging will likely need to be conducted in order to fully characterize the effects of

DBS (McIntyre et. al, 2004).

Since DBS therapy relies on accurate positioning of electrodes, surgical implantation is

assisted with several guiding tools. DBS electrodes are implanted into the brain using stereotaxic

methods, MRI targeting, recording of extracellular unit activity, and electroencephalographic

monitoring. Some typical stimulation parameters are 1-10 volts, 90 gts pulses in trains of 100-

165 Hz, running either continuously or in intervals of 1 minute on and 5 minutes off (Theodore

and Fisher, 2004). Clinically useful and tolerable stimulation parameters can vary from patient

to patient as well as across different sections of the brain. Thus, a common strategy of DBS is to

exploit the natural behavior of various brain structures in a manner to most effectively produce

an anti-seizure effect.

Cerebellum

Cerebellar stimulation can be performed to capitalize on the inhibitory outflow which is

present in nearly all patients. Anterior stimulation decreased hippocampal formation discharges.

However, cerebellar stimulation has had variable effects in animal models, which may have been

related to variable stimulation parameters (Theodore and Fisher, 2004). An interesting

phenomenon discovered in controlled DBS studies is the placebo effect. For example, in a

controlled study of cerebellar DBS involving 14 control patients, 2 of the 14 patients showed

improvements in seizure frequency (Hodaie et al., 2002). This placebo effect, defined as a









reduction (or abolition) of symptoms with insertion of DBS alone, might be due to an initial

lesioning resulting from the implantation procedure.

Subcortical structures

Interest in subcortical stimulation comes from its widespread, non-specific, anterior and

intralaminar nuclear connections to the mesial frontal, temporal, and limbic structures. In

addition, it demonstrates progressive recruitment of substantial nigra, subthalamic nucleus, and

midline thalamic nuclei in animal models of epilepsy. Stimulation of the subthalamic nucleus,

anterior, thalamus, and substantial nigra have been shown to inhibit limbic seizures in animal

models of epilepsy (Theodore and Fisher, 2004). In addition, stimulation of the basal ganglia

structure may modify propagation of seizures (Deransart et al., 1998). Some of the most

important subcortical structures will now be discussed.

Caudate nucleus

The effect of caudate nucleus stimulation has demonstrated antiepileptic effects in an

aluminum-hydroxide seizure focus model, though the efficacy is highly dependent on stimulation

frequency (Theodore and Fisher, 2004). An inhibitory seizure protection effect was

demonstrated for stimulation at 10-100 Hz, whereas 100 Hz stimulation increased seizure

frequency. The anti-seizure effects of the caudate-nucleus are hypothesized to be due to

activation of the substantial nigra under the presumption that low-frequency stimulation is

excitatory and high frequency stimulation is inhibitory (Theodore and Fisher, 2004). Since these

results are from uncontrolled studies, it is uncertain if "micro ablation" resulting from electrode

implantation is contributing to the anti-seizure effect.

Thalamus

The thalamus is seen as a strategic stimulation site on the basis that it is the pacemaker of

the cortex, with widespread connections between the two structures. There is electrophysical









and anatomical evidence suggesting that midline thalamic nuclei may participate in modulation

and spread of limbic seizures. Experimentally, thalamic stimulation has been shown to terminate

seizures in a primate epilepsy model. Studies of human thalamic stimulation have been

published with favorable results (Theodore and Fisher, 2004).

Centromedian nucleus

The centromedian nucleus (CN) has been classified as part of the non-specific thalamus.

The CN's major difference from the thalamus in terms of stimulation for epileptic seizures is that

the CN's output is more strongly related with the caudate nucleus than with the cortex (Theodore

and Fisher, 2004). In a placebo-controlled double-blind study involving 7 patients, CN

stimulation resulted in a 30% decrease with respect to baseline when the stimulator was on

versus an 8% decrease when the stimulator was off (Fisher et al., 1992). CN stimulation

appeared safe and well tolerated by the patients.

Anterior thalamic nucleus

The anterior nucleus of the thalamus (ATN) may help influence the propensity of seizures

due on its connectivity and functional relations with the cortex and limbic structures. High

frequency stimulation of the ATN leads to EEG desynchronization, which is believed to render

the cortex less susceptible to seizures (Hodaie et al., 2002). Specifically, 100 Hz had an anti-

seizure effect whereas stimulation at 10-50 Hz lowered the seizure threshold. A controlled study

of 5 patients resulted in a mean seizure reduction of 54%. An interesting observation was that

the results did not differ from the stimulation on and stimulation off periods (Theodore and

Fisher, 2004). This is thought to be due to a "microthalamotomy" placebo-effect. This

phenomenon of a reduction or abolition of symptoms due to insertion of DBS electrodes alone

has been seen in over 53% of DBS electrode implantations for tremor, and can last up to a year

in some cases (Hodaie et al., 2002).









Subthalamic nucleus

The subthalamic nucleus (STN) was chosen based on encouraging responses in patients

with movement disorders as well as high-frequency stimulation in animal epilepsy models. In a

study utilizing STN high frequency stimulation in 5 patients, 3 patients showed reduction in

seizure frequency of 67-80%, one patient had approximately 50% seizure reduction, and the fifth

showed no improvement. In this study, the recording of epileptiform activity in the STN

suggests that it is part of a cortico-subcortical network involved in the epileptogenic process

(Chabardes et al., 2002).

Hippocampus

Human studies of hippocampal stimulation have demonstrated that high-frequency

stimulation, rather than low frequency, can be inhibitory. This is contradictory to several

preclinical investigations of hippocampal stimulation. One theory for this phenomenon is that

the anti-seizure effect is due to the activation or inhibition of downstream structures (as opposed

to the hippocampus itself). Nevertheless, 7 patients that participated in a hippocampal

stimulation study involving 2-3 weeks of 130 Hz electrical stimulation for 23 hours per day

responded very well. Stimulation halted clinical seizures and decreased the number of interictal

EEG spikes at the focus after 5-6 days. However, no observable antiepileptic effects (or no

effects at all) were found in three patients when stimulation was either interrupted or given

elsewhere just outside of the hippocampus (Theodore and Fisher, 2004).

Vagus nerve stimulation

VNS therapy has been the subject of many studies before and after its approval for

treatment of intractable seizures in 1997 (Uthman et al., 1993; Ben-Menachem et al., 1994;

Theodore et al., 1997; Schachter et al., 2002; Cyberonics, 2006; Ardesch et al., 2007; Ramani,

2008). VNS is licensed in several countries as an adjunctive epilepsy therapy with a rare









occurrence of serious side effects. Studies suggest that VNS treatment results in a much lower

incidence of adverse cognitive, neurological, and systemic effects than AED treatments (George,

2001). Over 40,000 epilepsy patients have VNS therapy implants (Cyberonics, 2008). VNS

is a useful therapy for patients with medically refractory and localization-related epilepsy

characterized by complex partial and secondary generalized seizures (Theodore and Fisher,

2004). The apparatus consists of an electric stimulator which is implanted subcutaneously in the

left side of the chest and connected to the left cervical vagus nerve using subcutaneous electrical

wires. The device is programmed to provide neurostimulation at a set duration, frequency,

intensity, and pulse width for the treatment of epilepsy. Figure 2-2 provides an example of the

VNS pulse sequence.


On time

1
Ramp up Ramp down
(2 sec) (2 sec)
mA
Output mA
Current



1/frequency Pulse Width

Figure 2-2. VNS pulse sequence.

The vagus nerve was chosen as the site for stimulation because of its diffuse and

widespread projections to the thalamus, amygdala, and forebrain through the nucleus tractus

solitarius and to other cortical areas via the medullary reticular formation.

Though VNS therapy has demonstrated seizure treatment efficacy, the therapeutic

mechanism is still uncertain (Ben-Menachem et al., 1994; Fisher et al., 1999; Groves, 2005;

Ramani, 2008). However, a physiologic framework for the VNS therapy mechanism has been









described (Upton et al., 1991; Ramani, 2008). The vagus nerve is the 10th cranial nerve and is

comprised of approximately 80% afferent fibers, which carry sensory information to the brain.

The vagus nerve is highly involved in the regulations of numerous autonomic systems such as

the heart, the intestines, and provides and integral role in respiration.

Studies suggest that the metabolic activation of thalamic, brainstem, and limbic regions

may be integral in the mediation of VNS effects (Fisher et al., 1999). It has been shown that

depletion of norepinephrine in the locus coeruleus attenuates the AED-like effect of VNS (Krahl

et al., 1998). Recent studies also suggest that the VNS may exert its effect through the locus

coeruleus (Groves, 2005; Ramani, 2008).

Experiments in which cat vagus afferent neurons were stimulated were able to produce

either cortical synchronization or desynchronization, depending on the fibers' conduction

velocity (Upton, 1991). Recent studies have determined that vagus A and B fiber activation can

lead to EEG synchronization whereas vagus C fiber activation results in EEG desynchronization

(Groves, 2005). Electrical stimulation of the vagus nerve resulted in a reduction of interictal

epileptiform spike frequency during and up to three minutes after stimulation in a rat seizure

model (McLachlan, 1993). Overall, in lieu of these and other reported VNS effects there is no

consensus as to how these empirical effects relate to epilepsy. Though studies have examined

how vagus A, B, and C fiber stimulation affects synchronization, the overall VNS-induced

effects of these fibers and other relevant brain structures on EEG, reports suggest that these

effects not explicitly visible in the time domain (Fisher et al., 1999) or in frequency domain

(Salinsky et al., 1993). Numerous studies report little success in quantifying immediate EEG

effects corresponding with VNS (Hammond et al., 1992; Salinsky et al., 1993; Koo, 2001; Rizzo

et al., 2004; Marrosu et al., 2005). The only reported scalp-EEG effects of VNS are reported to









occur numerous months after VNS implantation. Studies involving long-term EEG monitoring

have shown that long-term VNS produces a delay in interspiking activity and a reduction in the

occurrence of epileptic interictal spikes (Koo, 2001; Olejniczak et al., 2001). Marrosu et al.

reported no noticeable changes after one month but an increase in gamma activity and

desynchronization one year after VNS implantation compared to baseline recordings (2005).

Studies have demonstrated VNS effects on interictal epileptiform discharges (Santiago-

Rodriguez and Alonso-Vanegas, 2006) and that the absence of bilateral interictal epileptiform

discharges may be an electroencephalographic predictor of seizure freedom (Janszky et al.,

2005). In addition, long-term VNS effects have been reported on the spectral content of sleep

EEG after 10-18 months of VNS compared to a baseline at 3 months prior to implantation (Rizzo

et al., 2004).

Future Therapeutic Directions

One major epilepsy research direction is to enhance therapeutic effectiveness of electrical

stimulation or drug therapy though the application of implantable controlled therapy systems.

For patients which are currently undergoing therapy from the available electrical stimulation

implants (such as the vagus nerve stimulator), research in this direction may help to enhance

efficacy, mitigate side effects, reduce therapeutic tolerance, and prolong battery life. Along

these lines, such a framework could be adapted to an implantable drug delivery system that

would dispense drug at "right" and the right place (e.g. in proximity of a seizure focus or in a

location to rapidly circulate medication such as the ventricles).

One framework from which this strategy can be visualized is from a system control

perspective. Thus, the basic theory behind this strategy is that the transition from a normal

interictal state into a preictal state can be conceptualized as a deviation of a control parameter

from its set point. Numerous researchers have invested in this idea using EEG signals as









controlled measure (Osorio et al., 2001; lasemidis, 2003; lasemidis et al., 2003; Osorio et al.,

2005).

While the basic example of deviation from a set point does not do justice to the enormous

complexity of the brain's electrical activity, recent advances in mathematical theory of complex

nonlinear dynamical systems provide an interesting perspective from which to examine and

interpret EEG signals.

Complex nature of epileptic dynamics

One of the most challenging aspects of epilepsy treatment is that despite the major

milestones in biological research, there is still an inadequate knowledge of the underlying

biological processes governing the epileptic condition that describes how, where, when, and for

what purpose a seizure will occur. One perspective is that the epileptic brain is exposed to at

least two states, a normal (interictal) state and a seizure imminent (preictal state).

A natural approach for studying any aspect of brain behavior is to create mathematical

model of some brain function using measurable quantities, such as electrical signals. Such

models allow predictions to be made about the behavior of sections of the brain. Due to the

massive complexity of the interacting neurons in the brain, direct models are most often achieved

for small groups of neurons and small brain structures (Hodgkin and Huxley, 1952; Breakspear,

2001; Chauvet and Berger, 2002). The enormous complexity of electrical brain signals often

means exact modeling approaches are insufficient. However, despite the observed dynamical

complexity of the epileptic brain there certain behavioral characteristics it possess which can

provide analytical guidance.

Dynamical diseases and disorders

One important diagnostic aspect of many diseases and disorders is the physiologic

behavior in the temporal dimension. In the 1980's many studies addressed the temporal behavior









of biological systems with and without a disease state. Experts within this field often focused

their attention on the time scales involved in the clinical aspects of the disorder. This includes

characterization of the disease or disorder onset (acute or subacute) as well the succeeding

clinical course (self-limiting, relapsing-remitting, cyclic, or chronic progressive) (Belair et al.,

1995).

The term Dynamical Disease or Dynamical Disorder refers to the general class of diseases

and disorders that are characterized by sudden changes in physiological dynamics that lead to

state of morbidity characterized by abnormal dynamics (Belair et al., 1995). Such dynamical

disorders arise as a result of abnormalities in underlying physiological control mechanisms.

There are many instances of disease and disorder models where the apparent shift of control

parameters to region results in pathological behavior of an observable which bears a resemblance

to experimental data. Mackey and Glass demonstrated adaptive respiratory disease behavior that

displayed a wide range of behaviors such as limit cycle oscillations with periodic chaotic

solutions (Mackey and Glass, 1977). This particular example exhibited a bifurcation in the

systems dynamics that was associated with disease onset. The unstable dynamical realm

achieved by altering a "normal" hematopoiesis model bears qualitative similarities to actual

hematopoietic data from a leukemia patient (Mackey and Glass, 1977). Thus, there are

biological examples to support the claim that mathematical models of physiologic systems may

be able to predict the existence of dynamical regimes corresponding to the status of a dynamical

disease. Whether the dynamical behavior is periodic, irregular, or apparently random, the

significance of dynamical disease identification is that it may be possible to develop therapeutic

strategies based on manipulation of critical control parameters (Milton and Black, 1995).

Taking into account the temporal rhythm of the disorder as well as an understanding that certain









dynamical rhythms may respond better to some treatments rather than others can help provide a

foundation for a suitable therapy (Belair et al., 1995).

Epilepsy as a dynamical disorder of brain systems

Neurological disorders can take on a wide range of complex and abnormal rhythmic

behavior over time (Milton et al., 1989). Milton and Black reported observations of recurring

sets of symptoms and oscillatory behavior in 32 "periodic" diseases of the nervous system

including, ankle clonus in corticospinal tract disease, movement disorders such as essential

tremor and Parkinson's disease, as well as paroxysmal oscillations in neuronal discharges in

epileptic seizures (Milton and Black, 1995). The cluster of symptoms occurring with a distinct

temporal pattern could represent the clinical manifestation of dynamical state changes in these

patients. In the context of neural tissue, one view of the abnormal dynamical behavior in

neurological patients may arise because of altered control parameters (e.g. nerve conduction

time, number of receptors, etc.) and/or alterations in neuronal network structure (Milton et al.,

1989).

Compensating for impaired neural control mechanisms: system control therapy

Currently, the biological mechanisms driving transitions into and out of dynamical

rhythms (e.g. oscillatory behavior) in neurological disorders are in general poorly understood. A

study examining a tremor simulation by inducing delay and amplification in a visual motor task

suggests there tremor could be an alteration of numerous interacting control loops or possibly a

time-delay state-dependent control system (Milton et al., 1989). One major difficultly whether

dealing with tremor or other neurological disorders is to uncover the complex interactions of

various interconnected control loops and determine how each contributes to the observed

dynamical behavior. Understanding the origins of the dynamical behaviors seen in neurological









disorders can provide a foundation for designing any type of patient-specific therapeutic control

system. An example of such a device is shown in figure 2-3.

ECoG
Stimulator / EEG Feature
extraction
algorithm

Closed loop
Controller <



Figure 2-3. Closed-loop seizure control device using electroencephalogram or electrocorticogram
signals as an input to a feature extraction algorithm, which supplies the extracted
features to a controller which makes a decision regarding the action of a stimulator.

One of the major themes of quantitative EEG analysis in epilepsy as well as other

neurological disorders is the identification of signal features that are sensitive to neural state

changes. Chapter 3 provides an overview of the rich spectrum of feature extraction strategies

employed for quantification of brain dynamics in neurological disorders such as epilepsy.









CHAPTER 3
TIME SERIES ANALYSIS AND DATA MINING TECHNIQUES: THEORY AND
APPLICATION

The wealth of epilepsy research conducted via quantitative analysis of EEG signals

comprises a rich history. Numerous mathematical models have been applied for the purpose of

modeling the progression of disease and inferring the biological significance of the underlying

the observed EEG signal patterns. The EEG is a time series of voltage measurements acquired

between a scalp or intracranial location of interest and a reference electrode point (e.g. an

electrode placed on the ear). Naturally, time series analysis techniques were among the first

methods applied for quantifying brain dynamics and constitute a significant portion of

quantitative EEG research. In addition, data mining tools are becoming increasingly popular for

the extraction and classification of patterns in biological datasets such as EEG signals. The

following literature review provides a general overview of the tools used in quantitative EEG

research.

Glossary of Terms

Attractor. An attractor is defined as a set of points mapped into a phase space representation

which is a target region which adjacent states within a neighborhood (see: basin of attraction)

will converge towards as the system evolves towards infinity. An attractor is established to be

the smallest region for which the entire volume cannot be further split into two or more attractors

having corresponding basins of attraction (as a system may have multiple attractors each with a

basin of attraction).

Basin of Attraction. A set of points in phase space such that initial conditions existing in this set

evolve over time into a corresponding attractor.









Bifurcation. A bifurcation is defined as a sudden appearance of a qualitative change in dynamics

resulting from an alteration in a parameter of a nonlinear system. Bifurcations can occur in both

continuous systems as well as discrete systems.

Degrees of Freedom. The dimensions of a phase space mapping.

Limit Cycle. In a phase space, a limit-cycle is a closed trajectory which possesses the

characteristic that at least one other trajectory will traverse into it as time approaches infinity.

Phase Space. Phase space is the group of potential states for a dynamical system. Phase space is

typically identified with a topological manifold. Each point in the phase space represent an

instantaneous and unique state of the system.

Strange Attractor. Strange attractors have a non-integer dimension. The descriptive term

'strange' refers to the geometrical structure of the attractor, whereas the term 'chaotic' refers to

the dynamics on the attractor (Grebogi, 1984).

Trajectory. The trajectory of a dynamical system is the orbit connecting points in chronological

order in the phase space that is traversed by a solution of an initial value problem. If the state

variables are within a real-valued continuum, then the orbit of a continuous time system is a

curve. Discreet system trajectories consist of a sequence of points.


Time Series Analysis

Time series analysis is the field of study that aims to extract useful information from time

series datasets. A time series is a series of measurements that are acquired at successive times

often with a constant time interval. Many aspects of our universe can be represented and studied

as time series datasets. This field of study has been extensively applied to financial decision

making as well as numerous scientific disciplines. One major goal of time series analysis is to

extract useful information about the system that generated the time series dataset. An additional









aim of time series analysis is to model the system dynamics in order to make predictions about

future behavior.

Methods Applied in the Time Domain

Numerous linear EEG processing techniques have been implemented in the history of

quantitative analysis. This section reviews some of the most utilized measures for the analysis of

discrete time series data within the time domain.

Autoregressive moving average modeling

The autoregressive moving average model (ARMA) is standard time series analysis tool

used to model univariate datasets. This method is also known as the Box-Jenkins model as the

iterative Box-Jenkins procedure it often used to estimate model coefficients (Box and Jenkins,

1976). The model is comprised of two parts, an autoregressive component and a moving average

component. For a univariate time series dataset Xt, autoregressive component at time t is defined

as:

P
X, =C+ ,Xt + E, (3-1)


where C is a constant, .. p are the parameters of the model of order p and c, is the error term.

The moving average component is defined as:

q
Xt = Oit-1 +- t
i=1 (3-2)

where O0...Op are the parameters of the model of order q, and E, and E, are the previous and

current error terms, respectively. Combining the autoregressive term with the moving average

term produces the ARMA model of order p (autoregressive terms), and q (moving average

terms):









P q

=1 =1 (3-3)

Such methods have been utilized in modeling functional brain network organization using

spectral analysis of local field potentials (Bressler et al., 2007).

Autoregressive integrated moving average modeling

The autoregressive integrated moving average (ARIMA) process is a well-known method

for making predictions in nonstationary time series datasets (Box and Jenkins, 1976). As the

name implies, this measure is a generalization of the ARMA process. The ARIMA approach to

working with nonstationary time series works by utilizing the dth difference to convert the

nonstationary time series to a stationary ARMA process. Naturally, the ARIMA method assumes

that a time series can be reduced to a stationary time series through the process of differencing.

The statistical properties of the stationary time series remain constant in time, and residuals

(errors between the original time series and the ARIMA model) are assumed to be the result of

noise.

Let {y, } be an ARIMA process of order p,d,q where the dth difference of y, is a

stationary ARMA process of order p,q. The model ARIMA model is then expressed as:

D(B)(1- B)d t = (B)zt (3-4)

where D and 0 are polynomials of degree p and q (respectively) having roots outside the unit

circle, B is the backward shift operator, and zt is white noise.

Cross correlation

Cross-correlation analysis is one of the oldest and most standard time series analysis

techniques (Bendat and Piersol, 1986). This method measures the linear coupling between two

signals.









Let X be some represent an identically distributed stationary stochastic process where

X(t) is the value of X at time t. Cross-correlation function representing the coupling between

two time series functions X(t) and Y(t) is defined with a time lag, T, as follows:


(r) = x(t + r)y(t)dt. (3-5)


Cross-correlation is often applied to data from a physical system which typically takes on a

discrete form. Let xo,...,xM and 0,...,_ Y represent two simultaneously acquired stationary

time series of length M, zero mean, and unit standard deviation. The discrete unbiased estimate

of the cross correlation function is then defined as a function of time lag ,

r = -M ),...,,...,M las follows:


x C r<0
<(r)= (3-6)



The normalized cross-correlation function outputs values within the range of negative one

(maximum anti-synchronization) to one (complete synchronization). The maximum T of

equation 3.5 is understood to be an estimation of the delay between two signals (assuming this

signals have a linear relationship to one another). The cross-correlation of a function to itself is

called autocorrelation.

As the cross-correlation value approaches zero, the signals of interest are increasingly

linearly independent. Often a significance threshold is applied to prevent the possible occurrence

of a non-zero cross-correlation value for two linearly independent systems (Box and Jenkins,

1976).









Methods Applied in the Frequency Domain

Frequency representation is a standard format for visualizing signal characteristics. This

perspective provides a clear visualization of a signal's periodic behavior which may not be

evident in the time domain. Thus, frequency domain analysis can help uncover important

properties of the system of interest.

Coherence

Coherence is a measure of coupling between two signals as a function of frequency. The

signal coherence can take on values between zero and one that provide a relative indicator of

how well the signal X corresponds to signal Y at each frequency. The Fourier transform is

performed on each signal to convert the signal into the frequency domain (calculate the power

spectral density). The cross power spectral density is calculated by multiplying one signal by the

complex conjugate of the other signal. The coherence measure is a function of the power spectral

density of the individual signals and the cross power spectral density. This measure is typically

expressed in terms of its square magnitude and is derived by normalizing the cross power density

by the product of power spectral density for the two signals,


c (f)= p. (f (3-7)
c() P(f)P ( f )

where P1 and P, represent the power spectral densities for signals X and Y respectively and

P1 is the cross power spectral density (Fuller, 1976). A coherence of zero indicates no coupling

between the two signals at the particular frequency whereas a coherence of one implies linear

relationship with constant phase shifts between each frequency component. Coherence has been

implemented in electrophysiology experiments for several years and more information can be

found in literature (Shaw, 1984; Leocani, 1999).









Discrete Fourier transform

The Fourier transform has been implemented in extensively in numerous fields such as

mathematics, physics and natural sciences. The Fourier transform is an especially attractive

algorithm due to the development of the streamlined Fast Fourier Transform (FFT) (Cooley and

Tukey, 1965). In recent years, additional developments have been implemented in the FFTW

subroutine library developed by a team of MIT researchers (Frigo and Jonhnson, 2005). This

free software package provides a means to optimize the FFT algorithm using various heuristic

approaches for each unique problem and platform combination. This subroutine library has been

utilized by many researchers and is even implemented in the Matlab function library.

Fourier analysis decomposes a signal into linear component parts. The analysis involves to

concepts:

* Linear combination of different waveforms.

* A time series of any shape can be sufficiently represented by the summation of ample
simple sine waves of different frequencies, phases, and amplitudes.

Given a signal x(t), Fourier analysis models the signal as a linear combination of sine and

cosine waves for frequency f where:


x(t)= X(f)e2'*df (3-8)

and


X(f)= x(t)e '22'dt. (3-9)


Equation (3-8) is the continuous Fourier transform which is comprised of the complex

coefficients representing the contributions of each frequency, f, to the overall representation of

the original time series x(t). Equation (3-7) is often referred to as the inverse Fourier transform.









For a discrete signal,

x = txo,..., x',_}, (3-10)

where x, is sampled at the time t, = to + jA, the discrete Fourier transform (DFT) is

represented as:

N 1 -z 2,*n
X(k)= x(n)e N (3-11)
n-0

for the discrete frequencies

k
fk =N (3-12)

where the inverse Fourier transform is expressed as:

i N-_1 Ni2kn
x(n)= 1 X(k)e N (3-13)


While Fourier analysis is useful for capturing periodic waveforms in non-transient signals,

this measure is not suited for extracting transient features. This is because time information is no

longer available in the frequency domain as the DFT coefficients are representative of the entire

signal duration.

The Fourier transform has been extensively applied to the analysis of EEG waveforms in

epileptic patients. Diagnostically, it can help determine the presence of specific brain wave

rhythms which may be indicative of certain types of epileptic behavior. Often the time series of

interest is broken down into non-overlapping segments in which the Fourier transform is

calculated to give a rough estimate of the frequency behavior over time. An example of an a

single channel of EEG acquired during an absence seizure and its corresponding windowed

Fourier transform is shown in figures 3-1 and 3-2, respectively.









In figure 3-2, the absence seizure onset is characterized by a sudden energy increase in the

0-30 Hz frequency band with the strongest effect around 3 Hz (which is the typical rhythm of

spike wave discharges in absence seizures).

Wavelet analysis

Wavelet analysis is a signal processing tool which models a times series signal in terms of

shifted and scaled "mother" wavelet. Wavelet analysis is similar in some aspects to Fourier

analysis, which models a signal using sinusoids. Instead of sinusoids, wavelet analysis models a

signal using an application-specific waveform called a wavelet which has an effectively limited

duration and a mean value of zero (Misiti et al., 1996). Wavelet analysis is very useful for

performing localized analysis in a subregion of a larger signal. In addition, wavelet analysis is

capable of revealing aspects of data that traditional signal analysis techniques may miss such as

trends, breakdown points, discontinuities in higher derivatives, and self-similarity (Misiti et al.,

1996). For a particular mother wavelet function Y(t), the subspace at time t for a scale, a, and a

position, b is represented by


,bt) W= I tb. (3-14)
C^a I

If x(t) represents the time series signal, then the continuous wavelet transformation at scale, a,

and position b is defined as:

1 (t-b
Cb = x(t) I a dt, (3-15)


where Y denotes the complex conjugate of the wavelet and a,b e R,a # 0. For low values of

the scaling factor a, the wavelet becomes compressed and becomes sensitive to rapidly-changing

details and high frequency waveforms. For high values of a, the wavelet becomes stretched and









is more sensitive to coarse slowly-changing features and low frequency waveforms. The

parameter b localizes the wavelet function in time. Wavelet analysis has demonstrated utility for

the analysis of nonstationary signals such as EEG (Geva et al., 1998, Giler and Ubeyli, 2005;

Glassman et al., 2005).

Information Based Methods

Information theory is based on the 1948 publication by Claude Shannon which was the

first paper to quantify the concepts involved in communication. Information quantified in units

of bits and concepts such as entropy and mutual information were used to describe the transfer of

information (Shannon, 1948). Information theory concepts have been extended to time series

analysis in biological series such as the EEG. Under the proper statistical conditions, these

measures provide useful information about the behavior of the brain.

Approximate Entropy

Approximate entropy (ApEnt) is a statistical measure used to quantify system

regularity/complexity from a time series dataset. This measure has been extensively utilized in

physiological time series data (Pincus, 1995). The ApEnt measure has been utilized to study the

EEG signals acquired from Alzheimer's disease patients (Abasolo et al., 2005), as a measure of

anesthetic depth (Bruhn et al., 2000, 2001, 2003), epileptic seizures detection (Abasolo et al.,

2007; Srinivasan, 2007), and studies characterizing EEG nonlinearity patterns (Thomasson et al.,

2000; Burioka et al., 2003,2005; Ferenets et al., 2006).

The ApEnt measure has demonstrated the ability to quantify system complexity using as

few as 1000 data points based on theoretical analyses of stochastic and deterministic chaotic

processes (Pincus, et al., 1991; Pincus and Keef, 1992) as well as clinical and clinical

applications (Pincus 1995; Bruhn et al., 2000). In this dissertation, ApEnt is used as a measure

for quantifying the VNS effect on EEG recordings.









Let U be a signal oflengthN. For positive integer m and a positive real number rf.,

extract N-m+1 create vectors xm(i)= u(i),u(i + ),...,u(i+m-1)}. For all i, 1
the quantity Cm is computed as follows: number ofj such that

c (r)= number of j such that d[x (i), (j)] r (3-16)
N-m+1

where d is the maximum absolute difference between the respective scalar components of the

two vectors xm (i), x () defined as :

d(xm(i),xm(j))= max mx,(i + k-1)- (j + k -1)) (3-17)

Using these results, the value of Om can be calculated as:

m N- 1 N-m+l
O ry )logCM
N-m+ ,= (3-18)

ApEnt is calculated as:

ApEn(m, r,N)= Dm(r )- ml (r). (3-19)

In this manner, the value of the positive real number rf corresponds distance between the

neighboring point that is often designated as some fraction of the signal's standard deviation. For

this reason, the positive real number rf can be thought of as a filtering level for the process. The

parameter m is the dimension at which the signal is embedded for calculation.

Pattern Match Regularity Statistic

Pattern match regularity statistic (PMRS) is a method used to extract the nonlinear

characteristics (complexity) of a time series over time. This measure has been for the

quantifying the complexity of an input EEG signal and further detecting EEG state changes such

as seizure onset (Shiau, 2001; Shiau et al., 2004). This measure estimates the likelihood of









pattern similarity for a given time series. PMRS has the attractive feature that it can be

interpreted in both stochastic and chaotic models. The steps to calculate PMRS include

reconstruction of the state space, searching for the pattern matched state vectors, and the

estimation of pattern match probabilities. Specially, given an EEG signal U = {ul,u2,..., u }, let

(^ be the sample standard deviation for U. For an integer m (embedding dimension), phase

space vectors U are reconstructed as

x, ={u,,u 1,...,u,+}, lKiin-m+l (3-20)

then for a given positive rf x, and x, are considered pattern match to each other if:

I u, -u, 1
(3-21)

where rf corresponds distance between the neighboring point that is often designated as some

fraction of the signal's standard deviation. PMRS can then be calculated as:


PMRS = In(p) (3-22)
n m =

where

p, = Pr ob {sign (u ,m u ,+) = sign (u +, -u j,,) | x, and x, are pattern matched }

(3-23)

Mutual Information

Information theory measures such as mutual information have shown utility for estimating

high order statistical dependencies between signals. In contrast to linear coupling measures (e.g.

cross-correlation), mutual information is sensitive to nonlinear dependencies.








For continuous variables X and Y with probability density function of f(x) and f(y),

respectively, and f(x, y) is the joint density function, mutual information can be calculated as

follows:

I(X,Y)= f(x,y)log f(x,) dxd (3-24)
r x f (x)f (y)

Mutual information between two discrete random variables having marginal probabilities

p (x) = prob(X=x) and p, (y) = prob(Y=y) and joint probability p (x)= prob(X = x,Y = y) is

defined as:

I(X,Y)= p(x, y)log p(xy) (3-25)
x,y PX(x p (y)

A common approach to calculating mutual information is to first partition X and Y into

bins (e.g. a histogram). An estimation of I(X,Y) Ibn(X,Y) is obtained by replacing the

probability functions f(x), f(y), and f(x,y) with an approximations based on the histogram.

Thus, if bx and by are the number of points from X within the x-th bin and number of points from Y

within the y-th bin, respectively, and b is the number of points in the intersection of the two bins,

then px(x),b /N, p,(y)G by/N, and p(x,y)= b I/N.

Mutual information has been successfully used to quantify statistical couplings in biological

applications such as sleep studies (Na et al., 2006) Alzheimer's disease (Abasolo et al., 2007) and

epileptic seizures (Varma et al., 1997; Palus et al., 2001; Netoff et al., 2002).

Chaotic System Analysis Techniques

One approach for quantifying the behavior of a complex system such as the brain is to

create a mathematical model of the system behavior using measurable quantities. Electrical

signal measurements are often used to model the brain modeling the brain's behavior. Such









models allow predictions to be made about the behavior of sections of the brain. Due to the

massive complexity of the interacting neurons in the brain, direct models have only been

achieved for small groups of neurons and small brain structures (Breakspear et al., 2001;

Chauvet and Berger, 2002; Hodgkin and Huxley, 1952). The enormous complexity of electrical

brain signals often means exact modeling approaches are insufficient.

Edward Lorenz is often credited as the discoverer of chaos for the fruits of his efforts to

devise a long-term weather prediction scheme (Lorenz, 1963). Though Lorenz's model did not

turn out to aid in forecasting weather, his results directed his attention to research which helped

give rise to research in the area of chaos theory.

Chaotic systems have the interesting property of displaying apparent random behavior but

are actually governed by deterministic laws. Specifically, chaotic systems demonstrate a large

degree of sensitivity to initial conditions to the point at which minor fluctuations in initial

parameters give rise to extremely altered outcomes (to the extent that prediction of such events

may even be hampered by sensitivity to computer precision rounding). Since chaotic systems

have characteristic similar to noise as well as a broad range of frequency components, linear

measures may fail to provide meaningful results.

When exact knowledge of the system governing dynamics is unknown, such as in the

brain, an alternative method is a macroscopic modeling approach based on empirical measures of

the system as a whole (lasemidis et al., 1996). After such information is extracted, it may be

possible to derive useful empirical models of the global behavior of the system as a whole.

A well-known method to study complex system behavior is to observe the system from a phase

space representation (Hively et al., 2005; lasemidis et al., 1996). Phase space mapping is a

process of applying some transformation on a dataset, often into a higher dimensional space,









from which system behavior characteristics can be quantified. Some classic transformations

applied in EEG analysis include time delay mapping, (Breakspear, 2001; Hively et al., 2005;

lasemidis et al., 1996; Da Silva et al., 2003; Marino et al., 2003) derivative mapping (Aksenova

et al., 1999, 2003; Letellier et al., 1998; Sceller et al., 1999; Tetko et al., 1999). Phase space

mapping provides a means to help distinguish random, noisy signals from signals generated from

a system governed by deterministic chaos.

Phase Space Mapping

Generate of a time-delay phase space portrait of the system is one of the most established

methods for visualizing the dynamical behavior of a multivariable system such as the brain

(lasemidis et al., 1996; Hively et al., 2005). Time-delay phase space maps are a particularly

useful phase space mapping variant and are often used for the study of nonlinear deterministic

systems. The phase space portrait is created by assigning each time-dependent variable of the

observed from the system as a vector element in a multidimensional phase space. Each vector

mapped into the phase space represents a unique and instantaneous state of the system. By

plotting the phase space vectors in chronological order a representation of the temporal evolution

of a discrete system can be visualized.

In principle, the analysis of an individual measured variable can provide dynamical

information about other system variables which are related to the measured variable (lasemidis et

al., 2003). A relevant example of this concept is that EEG recorded from one electrode can be

related to the activities located at distant electrode sites. Thus, important features of a dynamical

system can often be quantified through analysis of a single variable's behavior over time in terms

of geometrical attractor properties.

From the reconstructed phase space, measurements can be made to extract useful system

information from a single variable (lasemidis et al., 1996; Pardalos et al., 2003; Chaovalitwongse









et al., 2006). Such information can often be used in data classification algorithms for determining

neural state (Tetko et al., 1999, Hively et al., 2005). The method of quantifying phase space

properties has been extensively applied to EEG signals analysis for the purpose of studying

neurological disorders (Chaovalitwongse et al., 2006; Hively et. all, 2000, 2005; lasemidis et al.,

1996, 2004, 2005; Pardalos et al., 2003, 2004).

The Method of Delays

Time-delay embedding is performed as follows:

x(tn)
x(tn r)
x(t, 2r)

x > (3-26)


x(, (m- 2)r)
x(tf (m 1)r)

where r is the time delay and m is the embedding dimension (Takens, 1981). For a

discrete system, every instantaneous state of the system is represented by the vector x, in m

dimensional phase space.

Numerous studies have addressed the problem of determining proper parameters for the

embedding dimension m and r. The first zero of the autocorrelation function (Rapp et al., 1988)

or the first minimum of the mean automutual information (Fraser et al., 1986) are two of the

most common approaches to obtain the time delay, r. Takens recommended a minimum

embedding dimension m = (2D+1) to ensure complete unfolding of the attractor, where D is the

fractal dimension (Takens, 1981).









Fractal Dimension

The term "fractal" was coined by Benoit Mandelbrot in 1975 to describe self-similarity

characterized as a jagged geometric shape which can be split into parts which are approximately

reduced-size copies of a whole (Mandelbrot et al., 1983). The fractal dimension is a statistical

measure of the extent to which a fractal appears to fill space. A non-integer fractal dimension is

said to originate from fractal geometry. Strange attractors often have a complex structure with

fractal-like properties. Thus, the fractal dimension is a logical measure to use for quantifying

strange attractor dimension.

Determining the dimension of an attractor is an important step in the characterization of a

system's properties. A proper dimensionality estimate can enhance the accuracy at which the

location of a point on an attractor can be specified. Furthermore, the dimension value provides a

lower bound on the number of variables required to model the system dynamics.

A standard technique for estimating attractor dimension is from the framework of

measuring the changes in the number of points occupying a sphere of radius r as it approaches

zero (Grassberger and Procaccia, 1983a; 1983b). Geometrically, the relevance of this observation

is that volume occupied by a sphere of radius r in dimension dbehaves as rd For most

attractors the dimension d would be the dimension of the attractor, regardless of the origin of the

sphere.

For a chaotic attractor, however, the dimension will vary depending on which point is

selected for the estimation. If the particular system's dynamics do not result in dimensional

variation, then the mean of the surrounding points can be used. Obtaining the dimension in this

method can be obtained by determining the number of point y(k) within a sphere positioned at

the phase space location x as follows:









1 N
n(x,r)= (r- y(k)-x), (3-27)
N k=1
Nk1

where 0 represents the Heaviside Step Function where:

O(n)= n (3-28)
1, n>0

Equation (3-26) returns a counts of all the points on the orbit y(k) located within a radius r

from point x and normalizes this quantity by N, the number of points in the dataset. The point

density, p(x), on an attractor does not need to be uniform to utilize this method (for a strange

attractor). If equation (3-27) is raised to the power of q-1, the function C(q,r) is established in

terms of q and r and the mean of n(x, r)1 over the attractor weighted with the natural density

p(x) as:


C(q,r)= dxxp(x)n(x,r)q1 =_ I (r y(n)- y(ki) (3-29)
M k=1 M n=1,n.k

This quantity is referred to as the correlation function or correlation integral. This function

estimates the probability that two points on the attractor lie within a distance r of each other. M

and K are large in value (but not infinite). Though this function is invariant on the attractor, it is

conventional to only look at the variation of C(q, r) when r is small. At that scale, it is assumed

that:

C(q,r) r(q 1)Dq, (3-30)

which defines the fractal dimension Dq. The quantity Dq is estimated in the case of small r as:


Sli log[C(q, r) (3-31)
r-o (q -1)log(r)









Using this method, C(q,r) needs to be calculated over a small range of r in order to achieve a

near-linear range for selection of the slope of log[C(q,r)] over log(r).

Box counting dimension (DO)

Box counting dimension (DO) is the title given to the measure when q=O. DO can be

estimated as the amount of spheres of radius r or the number of "boxes" required to envelop all

points in the dataset. If N(r) represent the amount of D-dimensional spheres needed to cover the

attractor for relatively small values of r, then the box counting dimension can be estimated as:

S log[N(r)] lmlog[N(r)] (32)
r-o> (q- )log(r) r-o log(r)

Equation (3-31) is often represented as:

D,= limD,. (3-33)
q-0O

Information dimension (Dl)

Information dimension (Dl) is the name of the measure when q=l. Dl is a generalization

of the box counting dimension that takes into account the relative probability of cubes used to

cover the dataset. Let I represent the information function:

N
I -~P,(r)log[P,(r)] (3-34)
1=1

and P(r) represent the probability that an element i is populated, normalized such that:

N
(r)= 1. (3-35)


Information dimension is thus defined as:

N = P(r)log[P(r] (3-36)
S log(r)-36)
1 log(r)









Correlation dimension (D2)

Correlation dimension (D2) is title of the measure when q=2 (Grassberger and Procaccia,

1983a, 1983b; Kantz and Schreiber 1997). Under this condition, Dq takes on special form which

tends towards reliable computation. Correlation dimension is estimated as the slope of the log-

log plot generated by:


D2 =lim lg[C(2r (3-37)
r-O log(r)

The correlation dimension can be challenging to quantify in time series data as it can result in

highly nonlinear slopes for small r. Correlation dimension has been extensively utilized for

neural state classification studies using EEG (Tirsch et al., 2000; 2004) and has been utilized

extensively in analysis of physiological data (Kantz and Schreiber, 1995) such as seizure

prediction applications (Elger et al., 1998; Martinerie et al., 1998). As correlation sum can

demonstrate a high sensitivity to EEG amplitude when using a fixed radius (Osorio, 2001), many

authors have implemented a relative radius (with respect to the dataset diameter in vector space)

to strengthen their findings (Casdagli et al., 1996, 1997, Merkwirth et al., 2002).

The Lyapunov Exponent

The Lyapunov exponent is an important measure for the quantification of dynamical

systems. This measure quantifies the degree of system chaoticity by quantifying the rate of

divergence or convergence between two points initially in close proximity (lasemidis et al.,

1999). Lyapunov exponents provide a generalization of linear stability analysis due to steady-

state solution perturbation to time-dependent solution perturbations. The measure also provides

a meaningful characterization of asymptotic behavior in nonlinear dynamical systems.

Lyapunov exponents are a collection of invariant geometric measures that characterize

describe a system's dynamics. Specifically, they provide a measure of predictability for the









particular system. Lyapunov exponents provide a global measure of the rate of convergence or

divergence or of two trajectories initially in close proximity to one another for a dynamical

system. Positive Lyapunov exponents measure represent the mean exponential divergence rate of

two trajectories, whereas negative Lyapunov exponents measure represent the mean exponential

convergence of two trajectories. As Lyapunov exponents becomes more positive, trajectories

move apart more rapidly. Similarly, as Lyapunov exponents become more negative, the

trajectories move together more rapidly. A system with positive exponents has positive entropy

as trajectories that are initially in close proximity to one another separate over time.

If a discrete nonlinear system is dissipative then the sum of all the Lyapunov exponents is

zero. A system with both a positive and negative Lyapunov exponents is said to be chaotic. Thus,

Lyapunov exponents provide a measure of linear stability (or instability) of the attractor or an

asymptotically long orbit for a dynamical system.

For a chaotic system with initial conditions a and b which are initially in close proximity,

the distance between these two trajectories at successive time points will exponentially increase

over time. If this is written as e"' for a time duration ofn iterations, then A is the Lyapunov

exponent. For a system to be chaotic, at least one Lyapunov exponent needs to be positive. Thus,

at each point in the series the derivative of the time-advanced equation is evaluated. The

Lyapunov exponent is expressed as the mean value of the log of the derivative. If the Lyapunov

exponent is negative, the iteration is stable. It is important to note that by summing the logs of

the derivatives the result corresponds to multiplying the derivatives. Thus, if the product of the

derivatives has magnitude less than 1, points will attract together as they go through the iteration.

Though an n-dimensional system will produce n Lyapunov exponents, the maximum

exponent is usually most important. The maximum Lyapunov exponent represents the time









constant, ,, in the expression for the change in distance between the two initial orbits, e" If, is

negative, then the orbits converge over time, and thus the dynamical system is insensitive to the

choice of initial conditions. However, if, is positive, then the distance between the initial orbits

increases exponentially over time and the system displays sensitivity to initial conditions.

Calculation of the spectrum of Lyapunov exponents can be derived analytically for

systems in which process dynamical equations are known aprioi (Shimada et al., 1979).

Numerous algorithms have been developed which compute this measure on experimental

datasets. One of the most well-known algorithms was developed by Wolf et al. (1985), though

other algorithms have been established (Eckman et al., 1986; Ellner et al., 1991).

Short comings of the Wolf algorithm have been identified as sensitivities to the number of

observations as well as measurement noise. Numerous researchers have proposed updated

versions of Wolf s algorithm with increased robustness to the number of observations (Ellner et

al., 1991; lasemidis et al., 1991; lasemidis and Sackellares, 1992; Abarbanel, 1996). The

following section will provide an executive overview of the Lyapunov exponent estimation.

Additional details can be found in (lasemidis et al., 1991, 2000; Wolf et al., 1985).

Computing Short-Term Maximum Lyapunov Exponents

A phase space mapping is performed by embedding a signal x(t) of duration T using the

method of delays (3-26). The phase space representation provides the proper perspective for

measuring the degree of chaoticity of the attractor. An attractor is chaotic if on average the two

trajectories with similar initial conditions (two points in close proximity in phase space) diverge

at an exponential rate (expansion process). If these trajectories are members of a finite attractor,

they will fold back into the attractor as time progresses (folding process). A result of these two

processes may be the generation of a stable and topologically layered attractor. If the expansion








process outweighs the folding process in some of the attractor's eigen-directions, the attractor is

said to be chaotic. If the phase space is D-dimensional then theoretically up to D Lyapunov

exponents can be estimated. However, as expected, only (D +1) of them will be real (Abarbanel,

1996).

If L represents the short term largest Lyapunov exponent estimate STLmax, then:

1 No HX, (At
L = N- 1lg, A (3-38)
NAt 9A, (0)|
where
,,(0)= X(t,)- X(t), (3-39)
X, (At) = X(t, + At)- X(tJ + At) (3-40)
for the following conditions:
1. X(t) is the point of the fiducial trajectory ([X(t()] having
t = t X(tQ) = [x(tQ),..., x(tQ + (D- 1)r) (, T denotes the transverse, and X(t ) is a properly
chosen vector adjacent to X(t,) in the phase space.
2. 5XJ (0) = X(t,)- X(t) is the displacement vector t, i.e., a perturbation of the fiducial
order at t, and X,J (At) = X(t, + At)- X(tJ + At) is the evolution of this perturbation
after time At.
3. t, = to + (i- 1)At and t, = t, + (j- )At, where i e [1,N] and j e [1,N] for j > i.
4. At is the evolution time for 5XAJ (the time provided for 5XJ to evolve in phase space).
If the evolution time At is given in seconds, then the Lyapunov exponent is measured in
bits/sec.
5. t, is the initial time point of the fiducial trajectory and coincides with the time point of
the first data in the data segment of analysis. In the estimation of L, for a complete scan
of the attractor, to should move within [0, At].
6. N, is the number of local Lmax 's that will be estimated within a duration T data segment.
Therefore, if t, is the sampling period of the time domain data, then
T = (N )t, = N At +(D ) .

The method proposed by Iasemidis et al. (Iasemidis et al., 1999) was used to estimate the

short term maximum Lyapunov exponent (STLmax). This method is a modification of Wolf s

algorithm (Wolf et al., 1985). The measure is denoted as "short term" to distinguish it from the

variants used to study autonomous dynamical systems. Modification of Wolf s algorithm is









necessary to enhance STLmax estimate robustness to transients in small data segments such as

interictal spikes. The main modification is in the replacement vector searching procedure along

the fiducial trajectory. One of the most crucial parameters affecting STLmax's ability to

distinguish interictal from preictal states is the adaptive estimation in time and phase space of the

magnitude bounds of the candidate displacement vector (lasemidis 1999), though evolution time

At, and the angular separation V,,, between the evolved displacement vector 6X,i,,(At) and the

candidate displacement vector 6X,1,,(0) are important components as well (Frank et al., 2005).

The modifications proposed by lasemidis and Sackellares (1991) can be summarized as

follows:

1. To help ensure that L is a reliable estimate of STLmax, the candidate vector X(t) should
be chosen such that the previously evolved displacement vector 56X_,_ (At) is nearly
parallel to the candidate displacement vector 6X,,(0), that is,
V = (,XJ (0), Xj 1, (At) < Vmax (3-41)
where Vmax should be relatively a small value and (y,0) denotes the absolute value of
the angular separation between two vectors y and 0 in phase space.
2. Also, 6X,,(0) should also be relatively small in magnitude. This constraint helps avoid
computer overflow in the future evolution within very chaotic regions and also reduces
the probability of starting up with points on separatrices (Wolf et al., 1986).
Mathematically, this corresponds to,
'(XJ (0) = X(t| ) X() < Am (3-42)
where Ama takes on a small value.
Thus, the parameters involved in the estimation of L are:
(i) The embedding dimension p and the time lag T for the reconstruction of the phase
space
(ii) The evolution time At
(iii) The constraint parameters for selecting X(t,; Vmax and Amax )
(iv) The duration of the data segment T

It is worth nothing that since only vector differences are involved in the estimation of L,

any direct current (DC) present in analyzed data segment does not influence the value of L. In

addition, only vector difference ratios participate in the estimation ofL. Thus, L is not influenced

by data scaling (provided the parameters involved in the estimation procedure, i. e. Ama are









expressed in values relative to the scale of each analyzed data segment). Both of the above points

are consistent with the fact that L is related to the entropy rate of the data (Palus et al., 1993).

Selecting D and T. The selection of the embedding dimension D is such that the dimension

of the epileptic attractor in phase space is clearly defined. For an epileptic attractor, v z3

(lasemidis et al., 1988, 1990; lasemidis, 1991). Thus, according to Takens theorem a value of D

> (2 3 + 1) = 7 can be viewed as adequate for the embedding of the epileptic attractor in the

phase space. This value of D may not provide a large enough phase space to embed all interictal

brain states, but has demonstrated success in detecting the transition of the brain toward the ictal

stage (lasemidis and Sackellares, 1991).

The parameter T should be small enough to characterize the shortest signal changes (i.e.,

highest frequency component) in the data. However, T should be large enough to result in the

maximum feasible independence between the vectors components in the phase space (with the

method of delays). These two conditions are typically addressed by selecting T to be the first

minimum of the mutual information or as the first zero of the time domain autocorrelation

function of the data (Abarbanel, 1996). Since the time span (D-l) T of each vector in the phase

space theoretically represents the duration of a system state, (D-l) T has been recommended to be

(at the greatest) equal to the period of the maximum (or dominant) frequency component in the

data (Abarbanel, 1996). As an example, a sine wave (or a limit cycle) has v = 1, then D = 2 1 +

1 = 3 is required the phase space embedding and (D-l) T = 2 T should equal the sine wave's

period. In such a case, the value of T would then correspond to the Nyquist frequency of the sine

wave. In addition, for the epileptic attractor the highest frequency considered is 70 Hz (as EEG

data are often low-pass filtered at 70Hz) which would require a maximum T of about 7 ms

according to the above rationale for D = 3. However, since a typical epileptic attractor (i.e.,









during the ictal period) in temporal lobe epilepsy has described to have a maximum dominant

frequency of about 12 Hz (lasemidis and Sackellares, 1991), according to the above rationale, an

adequate T value for phase space reconstruction of the epileptic attractor is (7 1) T 84 ms, and

thus, T should be about 14 ms (for additional details see lasemidis and Sackellares, 1991).

Selecting At. If the evolution time At is too large, the folding process within the attractor

distorts L. If At is too small, 6Xi,j(0) may not follow the direction of the maximum rate of

information change. One option is to obtain At as a fraction of time-delay mapping of the

maximum frequency component of interest in the data, fo. Specifically, the At is usually chosen

to correspond to 0.5*fo (lasemidis and Sackellares, 1991). Therefore, according to the previous

discussions about the selection of D and T At z ((D 1) T)/2, which results in At z 42 ms which

is within a range that can distinguish the ictal state from the pre-ictal state (lasemidis and

Sackellares (1991).

Selecting Amax. In Wolfs algorithm (1986), Amax is selected as

Amax = max3Xgk (0O (3-43)


where j = 1,...,N and i = 1,...,Na

Thus, Amax represents the global maximum distance between any two phase space vectors

in a segment of data. This value suffices as long as the data is stationary and distributed

relatively uniformly in phase space. Rarely is this the case with real data, especially with the

brain's electrical activity which is strongly nonstationary and nonuniform (Barlow et. al, 1985;

Feber et. al, 1987; Jansen and Cheng, 1988). Such statistical fluctuations combined with noise

may adversely influence the predictive power of STLmax (Lai et al., 2003, 2004). Thus it is

essential to perform a searching procedure modification in order to locate the proper X(tj). The

first step is obtain an adaptive estimation of Amax for each point X(ti) as









Amax =max XJ (0), (3-44)

where j = 1,...,N. Estimating Amax in this manner can help compensate for the nonuniformity of

phase space (Amax is now a spatially local quantity of the phase space at a point X(t,) ). Another

technique for managing nonstationary data is to estimate Amax with a temporal constraint on top

of the spatial constraint. From this perspective, Amax is

A ,max max gX, (0); j # i (3-45)
IDIST1
for which

IDIST, = (3-46)

IDIST2 = (D- )r (3-47)

where IDISTI and IDIST2 upper and lower bounds fort t-t which help enforce temporal

constraints when searching for a maximum spatial distance. In other words, these parameters

establish a neighborhood in time around each point in the fiducial trajectory for the estimation of

the parameter Ai,max, which establishes a spatial search neighborhood around this point in the

phase space. Thus, the search for Ai,max is always made temporally about the state X(ti) and its

changes within a period of the time span (D 1) z of a state. According to the previous formulae,

the values for the parameters involved in the adaptive estimation of Ai,max for the neural state

classification studies are: IDIST = T = 14 msec and IDIST2= (D 1) T 84 msec.

Selecting Vmax. Starting with an initial Vmax,initia = 0.1 rad, if a replacement vector X(t) is

not found with 0 < V < Vmax,initial and X,, (0) < 0.1*Amax, the bound is relaxed for X,, (o0.

At this point the process is repeated with bounds up to 0.5* Amax. If it is not successful, we relax

the bounds for VJ by doubling Vmax and then repeat the process with bounds for Vmax up to 1









rad. It should be noted that values of Vmax larger than 0.8 rad did not occur in the reported results

(lasemidis and Sackellares, 1991). If Vmax does grow this large, the replacement procedure halts,

a local L(ti) is not estimated at time ti the entire procedure beings again at the next point in the

fiducial trajectory.

Selecting X(tj). It is important that the replacement vector X(tj) should be spatially close to

X(ti) in phase space (with respect to angle deviation and magnitude), yet with sufficient temporal

distance from X(ti) to allow selecting X(tj) from a nearby (but not the same) trajectory.

Otherwise, by replacing one state with one that shares "too many" common components would

lead to a false underestimation of L. The arguments described above are represented by the

following expressions:

0 < V, < V,, ,zl = 0. rad (3-48)

bA max < SX, (0)< cA, max (3-49)


t, t > IDIST, (D- l)r (3-50)

The parameter c at a value of 0.1 and increases with a step of 0.1 up to 0.5 in order to

locate a replacement vector X(tj) satisfying (3-48) through (3-50). The parameter b (which must

be less than parameter c) is used to account for possible noise contamination of the data. Thus, b

is the distance below which the estimation of L is considered to be inaccurate. A value ofb =

0.05 provided is recommended (Wolf et al., 1985; lasemidis and Sackellares, 1991). To clarify,

the temporal bound IDIST2 should not be confused with the temporal bound IDIST3. The

variable IDIST2 places an upper temporal bound for locating an appropriate Ai,max at each point

X(ti), whereas IDIST3 is a lower temporal bound for locating an appropriate X(tj) within a Ai,max

spatial distance from X(ti).









Selecting T. For data obtained from a stationary system state, the time duration T of the

analyzed data segment may be large for estimating of L. For nonstationary data, there are two

competing requirements: T is desired to be as small as possible to provide local dynamic

information yet the algorithm requires a minimum length of the data segment to stabilize the

STLmax estimate. Previous studies have deemed that for 200 Hz, a window of 2048 points

(corresponding to 10.24 seconds) is a sufficient length for the algorithm to converge and yet is

able to distinguish the two extreme cases (pre-ictal and ictal) (lasemidis, 1991; lasemidis and

Sackellares, 1991; lasemidis et al., 2000). These studies also point to the IDIST2 parameter as

being the most critical parameter in the above algorithm.

The STLmax seizure prediction algorithm identifies progressively increasing similarity in

the information production rate (termed dynamicall entrainment") between critical electrode

sites prior to seizures. In other words, long before the onset of an epileptic seizure, critical brain

sites begin to display similar dynamics. The progressive STLmax convergence prior to a seizure

is thought to reflect dynamical dependence because 1) the critical sites share direct or indirect

anatomical connections that are conducive to physiologic interaction, and 2) occurrence of the

progressive STLmax entrainment prior to a seizure (lasemidis et al., 2004). This concept is

indirectly supported by the therapeutic effect of neurostimulation therapies such as ECT-induced

seizures and the potential long-term anticonvulsant effect (for a recent review of ECT therapy

see Taylor, 2007). A potential physiologic basis for brain resetting could be a release of

neuromodulators after seizures (Gwinn et al., 2002). In addition, lasemidis et al. (2004) suggest

that the lack of an observed time-reverse of the resetting phenomenon is consistent with

hysteresis, a characteristic observed in epilepsy as well as other dynamical disorders (Lopes Da

Silva et al., 2003).









Mean Angular Frequency in Phase Space

One modification of the Lyapunov exponent was proposed by lasemidis to measure a

quantity related to the STLmax measure (lasemidis et al., 2002, 2003). The mean angular

frequency in phase space ( ) measure quantifies the angular frequency of the phase space

evolution of two nearest neighbor points relative to a reference point. Conceptually, this

measure quantifies the rate of change in stability of a dynamical system. The measure is related

to the Lyapunov exponent, which measures the local stability of a system. Consider the vectors

X(t ) and X(t, + At) as two states in phase space separated by the time delay At. The difference

in phase between these two states in phase space is AO( (lasemidis et al., 2002). The mean

(AO) of the local phase changes AO( in state space is denoted as:

1 NT
A = -- -YAD (3-51)
N, -

where N, is the total number of phase differences calculated from the evolution of X(tj) to

X(t + At) in state space, according to:


A = arccos (tX(t, +At) (3-52)
\X(tj X(t, +At\

The mean angular frequency in phase space Q can then be defined as:

1= AO. (3-53)
At

If the units of At are seconds, Q has units of radians per second (an alternative is to divide by

2n resulting in units of sec-1 or Hz for expression of rate of system state change). Figure 3-3

illustrates the concept of the phase change measure as it is applied to data with the same phase









space mapping with STLmax where At = k x dt is the evolution time allowed for the vector

X(t ) to evolve to X(t, + At) where dt is the sampling period of the original time series.

Data Mining

Data mining refers to the application of algorithms to extracting patterns from and

modeling large databases (Flexer et al., 2000) and provides reasonable tools for extracting useful

patterns in datasets from complex systems. Data mining techniques have demonstrated

successful detection of scalp EEG patterns which may be difficult for the human eye to visualize

(Acir et al., 2005; Chaovalitwongse et al., 2006; Thulasidas et al., 2006). Often such algorithms

or the patterns they reveal can be utilized in real time applications, providing a basis for real-time

EEG analysis tools (Chaovalitwongse et al., 2005; lasemidis et al., 2005; Sackellares et al., 2006;

Thulasidas et al., 2006).

Typical data mining tasks are described by the following categories:

* Dimensionality reduction: the process of mapping of a high-dimensional data set into a
lower-dimensional space in order to facilitate data exploration

* Reduction of noise: correction or removal of measurement artifacts and significantly
atypical samples from the data set.

* Clustering: creation of a partition of a given set of samples into classes according to
similarities that are relevant to the particular analysis

One of the more important instances of dimensionality reduction is called feature selection.

This process results in the generation of a lower-dimensional space by eliminating a subset of

dimensions from the original space. Feature selection is an important process for reducing

computation time as well potentially improving accuracy. Reduction of noise is an important

procedure which is universally applied in applications spanning numerous disciplines. Finally,

clustering refers to a broad class of data mining applications which are highly relevant to the

work done in this dissertation.









Clustering

Clustering problems can be subdivided into unsupervised or supervised clustering.

Unsupervised learning methods divide data into natural groupings. Supervised clustering

methods are also referred to as classification, which is described later in this chapter. The

following represents a non-exhaustive listing of some basic clustering techniques.

K-means clustering

The k-means algorithm is one of the most basic and commonly applied cluster algorithms.

The method clusters a set of N data points into K partitions based on the similarity between the

pattern and the cluster centers, where K< N (Jain et al., 1999). A random initial partition is

selected after which the patterns are repeatedly reassigned some convergence (e.g. squared error

threshold) is achieved.

The k-means algorithm is especially attractive due to its O(n) complexity as well as its ease

of implementation (Jain et al., 1999). One deficit of this method is a high sensitivity to initial

conditions, which can result in convergence at local minima.

Biclustering

Biclustering is a data mining technique which provides the ability to not only cluster data

samples, but also the data features. The procedure is performed in a manner that each class of

data features created within the biclustering is related to a class of data samples by a particular

property that distinguishes it from samples in other classes and is said to be the "cause" of its

creation. In other words, the biclusters are subsets of samples which exhibit similar

characteristics across a subset of features, or vice versa.

The biclustering methodology has been used extensively in numerous biomedical research

applications such as DNA microarray analysis and drug design as well as others (Madeira and

Oliveira, 2004; Shamir et al., 2005; Busygin et al., 2006). The output of biclustering algorithms









is especially useful for feature extraction, a crucial procedure in many biomedical studies.

Analogous to the ability of biclustering to reveal up regulation and down regulation of genes in

dna microarray datasets, biclustering is a data mining tool well-suited for revealing spatial and

temporal subsets of EEG features that are indicative of neural states (Busygin, 2007).

A dataset containing m features and n samples is arranged as a rectangular

matrix A = (a )m n, where a,, represents the i-th feature of thej-th sample. Consider the

assignment of the samples into classes as follows

S ,S2,...,S,,Sk c {1,...n},k =1,...,r,
S, S2 U...uS, = {1,...,n},
Sk nS, =0,k,l= ,...,r,k l

This method intends to assign samples such that samples from the same class share specific

common properties. Similarly, a feature i may be assigned to one of the features classes

F,,F2,..., Fr, Fk {1,...,m},k = 1,...,r,
F uF2 ... u F, = (,...,m,
Fk rF, = 0,k,l = l,...,r,k l

in such a manner that the features of class Fk are "responsible" for the creation of the class of

samples Sk. Such a simultaneous classification of samples and features is termed biclustering.



Definition 1: A biclustering of a dataset is a group of sample /feature pair subsets

B= ((S,,IF1), (S2F2),F),... SF) such that the group (S ,,S2,,Sr) forms a partition of the set of


samples, and the collection (F F2 ., F) forms a partition of the set offeatures. A pair (Sk Fk

will be called a bicluster.

Various criteria may be used for relating sample clusters to feature clusters. Most

commonly, it is required that the subset corresponding to a bicluster is either includes a certain









amount of values above the mean of the dataset, or has a lower variance than that of the dataset.

In general, it is acceptable for biclustering to rely on any type of common pattern among the

elements of the bicluster.

Consistent biclustering: The following biclustering framework utilizes feature selection based

on 0-1 fractional programming (Busygin, 2005). Let each sample be arbitrarily assigned to one

of the classes S, S,,..., S,. A 0-1 matrix S = (sjk), r is introduced such that sjk = 1 if j e Sk and

sjk = 0 otherwise. The sample class centroids are represented by the matrix C = (ck )m :

C = AS(STS) (3-54)

whose k-th column represents the centroid of class Sk.

Consider a row i of the matrix C. Each element in the row is the mean expression of the i-

th feature in one of the sample classes. Each feature is then assigned to the class where it is

among the largest number of features with a similar value as is shown in figure 3-4. Let the i-th

feature be classified as a member of the class k with the maximal value ck

i E F :> Vk = 1,...,r,k k:cki> ck (3-55)


Using the acquired feature classification (F F2,' 2' F ), let a classification of samples be

constructed using the same principle of maximal average expression and test whether this arrives

at the same classification as when using features. This is performed by constructing a 0-1 matrix

F = (fk )mr such that fk =1 if i e Fk and fk = 0 otherwise. The feature class centroids can be

represented by a matrix D = (djk )n


D= A'F(F F)1, (3-56)









whose k-th column represents the centroid of the class Fk. The requirement for sample

classification is

j S> Vk = 1,...,r,k # k: d > d, (3-57)

The feature selection and supervised biclustering framework proposed in (Busygin, 2005)

is grounded in the following definition.



Definition 2: A biclustering B will be called consistent if both relations (3-55) and (3-57) hold,

where the matrices C and D are defined as in (3-54) and (3-56).



Unlike other biclustering schemes, this definition of consistent biclustering is justified by

the fact that consistent biclustering implies class separability with convex cones (Busygin, 2005).

Theorem 1: Let B be a consistent biclustering. Accordingly, there exist convex cones

P1, P,,..., PI c 9" such that every sample from Sk belongs to the cone P. and no other sample

belongs to it, k = ,...,r.

Similarly, there exist convex cones Q1, ,,..., Qr C 9" such that every feature from

Fk belongs to the cone Qk and no other feature belongs to it, k = ,..., r.



It follows from the theorem of conic separability that convex hulls of the classes are

separated and thus do not intersect. The term biclustering-admitting is used to describe a dataset

for which some consistent biclustering exists. In addition, the data set will be called

conditionally biclustering-admitting with respect to a given (partial) classification of certain










samples and / or features if a consistent biclustering exists which preserves the given (partial)

classification.


Given a training set A = (aJ) where the samples are assigned to classes (SS.;.,S )


the corresponding classification of features can be constructed according to expression (3-55). If

the obtained biclustering is not consistent, features are then excluded from the dataset so that the

biclustering with respect to the cropped feature set is consistent.

Let a vector of 0-1 variables x = (x, )=, be introduced where the i-th feature is selected


if x, =1 and is not selected otherwise. When only the selected features are applied, the condition

of biclustering consistency in expression (3-57) becomes

m m
I a, fkx Zafkx
1-1 > Vj S,,k = ,...,r,k # k (3-58)

=1 1

The expressions in (3-58) are utilized as constraints of a feature set optimization problem.

Though the objective function may take on various functions of x depending on the desirable

properties of the features, a general choice is to aim for the maximal number of features. This

formulation helps minimize the amount of lost information provided during training. In this

scenario, the objective function is expressed as

m
max X, (3-59)
i=1

Expressions (3-58) and (3-59) comprise a specific type of fractional 0-1 programming problem

which can be solved using the approach laid out in (Busygin et al., 2005).









Data Classification

Classification can be described as the process of categorizing an unknown dataset. First, a

so-called training set of samples wherein sample classes are known a priori is provided to the

algorithm. The pre-classified training data is used to train the algorithm to recognize the

specified patterns. Training is typically an iterative process where the parameters affecting

classification are systematically adjusted until the classification error bound is decreased below a

specified threshold. This specific process is referred to as machine learning.

Machine learning

Machine learning refers to a collective group of methods which are utilized to enable

computers to "leam". There have been very successful implementations such as finding genes in

a DNA sequence, filtering email, financial analysis, detecting or recognizing objects in machine

vision, language processing, and medical diagnosis (Cristianini and Shawe-Taylor, 2000). Many

of these applications rely on pattern recognition which is essentially concerned with object

classification based on characteristics. An object's characteristics or features can be described as

the qualitative and quantitative measures which can distinguish it from other objects. The amount

of similarity between two objects can be quantified as a function of the differences in the objects'

set of features. Object similarity can be used as a basis for grouping objects into classes. Please

note, while the content of a person's character may be a useful feature of a person, the color of a

person's skin is not a good feature for classification. Classes may be represented in various ways

such as approximation functions or functions that define borders between classes. Arranging

objects into classes based on their location relative to these functions is referred to as

classification.

Machine learning from the classification perspective can be organized into two main

categories. Supervised learning refers to the process where a system learns from an example data









set in the form of input/output pairs. In such an example dataset, the input is typically a vector of

representing an object's features and the output is the object's class label. A set of objects each

with a corresponding feature vector and class label is more formally referred to as a training set.

The training set is used to derive a classification function. Once trained, a classification function

is capable of predicting an object's label. The term "supervised" stems from the nature of the

training scheme where the training set's object labels are determined by an outside source and

provided as an input. Therefore, this training method requires supervisory guidance to train the

classifier. Unsupervised learning is the other machine learning category where objects are not

labeled with any class information a priori. Thus, unsupervised learning forms object classes

based on inherent feature similarities determined during training.

Supervised learning systems applications have found extensive use in biological

applications (see Tarca et al., 2007 for a review). Briefly, some biological and medicinal

applications include detection of cancer prone tissues, mapping tissue gene expression profiles to

disease groups, and protein folding based on the DNA sequence. In addition, a broad range of

machine learning algorithms have provided a means for successful neural state classification and

neurological disorder diagnosis using EEG signal features (Flexer, 2000; Lotte et al., 2007; Seref

et al., 2007).

There are several well-known machine learning algorithms, including decision trees, neural

networks, and support vector machines. These base algorithms can be used in combination with

other algorithms for improved accuracy often at the cost of hindered performance. One of the

most widely used measures in classification problems is the Mahalanobis distance metric.

Mahalanobis distance classification

Mahalanobis distance is a statistical distance measure which factors in correlations

between variables. The mahalanobis distance is a useful method of quantifying similarity of an









unknown sample set to a known sample set. The square of the mahalanobis distance measure

has been applied to the classification of neural states using EEG signal patterns (Scher et al.,

2003; Le Van Quyen et al., 2005; Piccini et al., 2005). The squared mahalanobis distance, D2ref,t,

between a 25-dimensional EEG data point vector X(t) where

X(t)= (Xl,,t, Xh2z,, Xh3,t,..., Xchs,t (3-60)

and the centroid of the reference class [ref where

"ref = ( ohl, cch2, ch3 ..., ch25 )T (3-61)

is equal to:

D2ef, = X(t)- ef C (X(t)- / f,) (3-62).

The Cref term is the covariance matrix for the reference class.

The mahalanobis distance measure D2comparison,t refers to distance between the same EEG

data point, X(t), and the centroid of the comparison class, Pcomparison The EEG data point X(t) is

assigned to the class with the closest centroid (e.g. the class from which the point is at the

minimum Mahalanobis distance) to X(t) (Le Van Quyen et al., 2005). If the EEG data point is

equidistant between the two classes, the point is considered misclassified. The accuracy of the

minimum Mahalanobis distance classifier is equal to the number of correctly classified points

divided by the total number of points.

Support vector machines

Support Vector Machines (SVMs) are a class of data classification algorithms first

introduced by Vapnik and Lerner (1963) which are used to model and classify large volumes of

multivariate data. The SVM algorithm determines the optimal separating hyper surface between

two multidimensional datasets (Burgess et al., 1998). SVMs have been demonstrated success in

numerous biomedical applications such as magnetic resonance imaging (MRI), functional MRI









(fMRI), positron emission tomography (PET), and Single-photon emission computed

tomography (SPECT) (Seref et al., 2007) in addition to applications where neural states were

classified from EEG data (Acir et al., 2005; Chaovalitwongse et al., 2006; Lehmann et al., 2007;

Thulasidas et al., 2006).

The SVM formulation for linearly separable data quantifies the distance from the hyper

surface for each data point in the positive class and each data point in the negative class. In this

context, the term "margin" will refer to the distance between the separating hyper surface and the

nearest point for a class. The margin of the function output is referred to as the functional

margin. The geometric margin is the functional margin of a normalized weight vector. Hence

the geometric margin can be optimized by fixing the functional margin to be equal to one and

then minimizing the norm of the weight vector (Cristianini and Shawe-Taylor, 2000). If w is the

weight vector for a functional margin of distance equal to one from a positive (reference) class

point, x+ and a distance equal to one from a negative (comparison) class point, x-, then the

geometric margin can be determined as follows. For a functional margin equal to one:

iw, x+ +b= +1 (3-63)

(w,x +b =-1 (3-64).

To calculate the geometric margin, w must be normalized. The geometric margin, y, is then

the functional margin of the resulting classifier

1 w w



1I (WX w, ) (3-65)
1~
iI









Thus, the interclass margin is maximized by

min w (3-66)
w,b

subject to y ((w,x)+ b)>1 Vi =1,--,n (3-67)

where the constraints are that all points are properly classified for positive and negative

classes, as stated in (3-67). For non-separable data, the objective function (3-68) combines the

term for maximizing interclass margin with a term for minimizing misclassification error

(Cristianini and Shawe-Taylor, 2000).

n
minll II: + i=,2,...,n (3-68)


y,((w-x,)+b )>- Vi=l,-.,n (3-69)

S> 0 Vi = 1,...,n (3-70)

The cost term, C, in (3-68) is the weight assigned to the error. Expressions (3-69) and (3-

70) represent the constraints that each misclassified point is assigned a linear penalty (slack

variable) and that all slack variables are non-negative, respectively. An example of such a soft

margin classifier is shown in figure 3-5.

The SVM formulation in equations (3-68), (3-69), and (3-70) utilizes a linear hyper surface

for discrimination. A common practice for improving separation accuracy is to perform a

transformation to remap the data from input space into feature space using a kernel function.

The inner product is then performed on the transformed feature space data (see equation (3-71)).

K(x,,x )= (x, ), (x )) (3-71)

The concept of a kernel function is identical to that of phase space mapping. The purpose

is to view the data in a transformed space to unmask patterns which may have been hidden in








input space. The radial basis function (RBF) is a standard choice as a kernel function in

neuroscience applications (Acir and Giizelis, 2005; Bewernitz et. al., 2006; Lehmann et. al.,

2007; Thulasidas et. al., 2006; Seref et al., 2006). The RBF function is expressed as


K(x,,x )= exp x, J (3-72)


The SVM is trained using a set of data features with a known classification. The SVM's

performance is measured in terms of the accuracy at which it is able to classify a test data set.












300
I o I
200



100-
a-io




E -100
2

LU -200


-300 -

I 00
0 5 10 15
seconds

Figure 3-1. A 15 second segment depicting the 200 Hz EEG of an absence seizure viewed from
channel Fpl-F7.











70 I0
70
60 60

o I I
50 | |

:- 40 40
CD
30 -.I
/ It

20

10
10 .


5 10 15
0 5 10 15
seconds

Figure 3-2. A 15 second segment depicting the spectrogram of an absence seizure viewed from
channel Fpl-F7. The vertical lines represent the onset and offset of the seizure.

















(0) kodt= t t2
xo to







A(D2





Figure 3-3. Example angular frequency evolution in phase space.



















VI"Y'-U'-;- --;" o'."lXUUrullI~~"E~-"; s~u---------------r~ e~i~E--; L-" U"" r"F

Figure 3-4. Biclustering result of a toy dataset. The dataset produced three distinct classes.












100










Ma.lli>l \ I
i-\


\ N


/ii i
/Iw 0
l1w||


0 *


Figure 3-5. Linear hyperplane classifier applied to non-separable data.


Origin









CHAPTER 4
INVESTIGATION OF EEG BIOMARKER EXISTENCE FOR VAGUS NERVE
STIMULATION THERAPY: A DATA MINING APPROACH

Patients with newly implanted vagus nerve stimulation (VNS) systems in VNS therapy

undergo a calibration period of several months. With little knowledge of the mechanism of

action (see chapter 2) or a rapid measure of efficacy, the current process of tuning VNS

stimulation parameters in newly implanted patients is essentially based on the physician's

experience and trial-and-error. This process consists of setting initial stimulation parameters

then iteratively adjusting stimulation parameters based on patient reports of clinical efficacy

(seizure frequency) and tolerability since the previous visit to the doctor. It is known that "high"

settings for stimulation parameters (such as output current, frequency, and pulse width) are

shown to result in greater seizure reduction than "low" settings (Ben-Menachem et. al, 1994), but

there is no available means for determining the proper set of stimulation parameters for a

particular patient without numerous visits to the neurologist. This period involves numerous

medical check-ups to fine tune the electrical stimulation parameters based on clinical response.

This sub-optimal adjustment method leaves the patient at risk of seizures and imposes financial

burden. The purpose of this study is to address this problem using data mining analysis.

This chapter is organized as follows. First, the rationale for this study is introduced in

terms of clinical relevance. Next, the experimental strategy is outlined and justified with

examples from the literature. Afterwards, the four experiments comprising this chapter are

presented in the following format: introduction, data description, experimental setup, results, and

discussion. Finally, an overall conclusion is presented which comments on all the findings as a

whole.









Motivation for VNS Therapy Improvement

It is desirable to establish a method to rapidly predict the efficacy of the various

combinations of VNS parameters newly-implanted patients in order to mitigate doctor's visits

and perhaps expedite the process of optimizing therapeutic efficacy. A first step towards this

goal is to investigate the existence of a physiologic metric that is sensitive to the EEG

stimulation parameters and then the patient's clinical response to VNS therapy. Such an effect

could be present in the EEG signal.

EEG Markers for Treatment of Neurological Diseases and Disorders

The utility of electroencephalogram (EEG) markers in treatment of neurological disorders

motivates the examination of this treatment modality in terms of EEG effect (see chapters 2 and

3 for additional details). Electroencephalographic markers have demonstrated robust utility for

the diagnosis, treatment, and evaluation of treatment for epilepsy (lasemidis et al.,1996; Pardalos

et. al, 2003, 2004; Chaovalitwongse et al., 2005, 2006; Ding et al., 2007; Schevon et al., 2007) as

well as other neurological disorders (Krystal et al., 1996, 1997, 2000; Asyali et al., 2007; Ding et

al., 2007; Quintana et al., 2007). Specifically, there is has been an interest in the application of

such analysis to the EEG signals of VNS patients to provide a better understanding of the therapy

(Uthman et al., 2007). Recent studies have produced interesting findings of long-term VNS

effects on epileptic interictal spikes (Koo, 2001), epileptiform sharp waves in the hippocampus

(Olejniczak et al., 2001), interictal epileptiform discharges (Janszky et al., 2005; Santiago-

Rodriguez and Alonso-Vanegas, 2006), gamma activity and desynchronization (Marrosu et al.,

2005), and spectral content of sleep (Rizzo et al., 2004).

The effects on interictal epileptiform discharges such as the studies by Koo and

Olejniczak et al. suggest the presence of brain dynamical changes and further motivate the desire

to examine VNS-induced EEG changes from the perspective of nonlinear dynamics since the









existence dynamical changes are implied by changes in spiking patterns. In addition, no studies

could be located which aimed to relate the EEG effects of VNS to the stimulation parameters.

Aside from long-term epileptiform effect (Koo, 2001) or effects observed in hippocampal

depth electrodes (Olejniczak et al., 2001), the lack of readily-available short-term scalp

electroencephalographic VNS effects reported in the literature (Hammond, 1992; Salinsky et al.,

1993; Fisher et al., 1999; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005), the benign non-

invasiveness of scalp-EEG, state of the art techniques of modem knowledge discovery in

database techniques (Flexer, 2000), and the potential for real-time application due to modern

computer technology make EEG data mining analysis a desirable approach to studying VNS

effect. These reasons motivate the current study which aims to identify electroencephalographic

markers which are sensitive to VNS stimulation parameter configuration. If such

electroencephalographic markers are identified, and if the electrographic markers are found to

correlate with clinical efficacy then these findings could be applied to determine optimal VNS

stimulation parameters on a patient-by-patient basis.

Modeling Brain Disorder Dynamics

One approach for studying the brain's behavior is to generate a mathematical model of

some subset the brain's activity using observable quantities, such as EEG recordings. Such

models provide a means to make predictions about the behavior of one or more sections of the

brain in response to various inputs. Due to the high degree of complex neuronal interaction in the

brain, direct models have only been achieved for small neuronal networks small brain structures

(Breakspear, 2001; Chauvet and Berger, 2002). The enormous complexity of electrical brain

signals often means exact modeling approaches are insufficient. The challenge of direct

modeling is compounded by the fact that no consistent immediate or short-term VNS-induced

effects have been identified in the raw EEG or its time-frequency profile (Salinsky et al., 1993;









Fisher, et al., 1999; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005). However, suppression

of epileptiform sharp waves in the hippocampus has been observed (Olejniczak et al., 2001).

This provides motivation for searching for dynamical scalp-EEG effects of VNS.

However, in a complex system such as the brain, it is often difficult if not impossible to

obtain exact knowledge of system governing the observed dynamical behavior. In such a case, an

alternative method to exact modeling is to develop a macroscopic modeling approach based on

observable measures of the system in its entirety, such as EEG signals (lasemidis et al., 1996).

Upon extraction of such information, it may be possible to generate useful empirical models of

the system's global behavior.

One such modeling scheme treats epilepsy as a dynamic disorder which is a class of

disorders characterized by a sudden qualitative change in dynamics in response to an endogenous

factor or a clinical maneuver (Milton, 2000). From this perspective, epileptic symptoms occur as

a result of modifications to underlying physiologic control system parameters (Mackey and

Glass, 1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et al., 1995;

Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003). Such changes may

manifest, for example, as a qualitative change in dynamics corresponding to bifurcations in

mathematical systems. The importance of identifying a dynamic disorder is that a treatment

possibility can focus on manipulating underlying control parameters back into a range of healthy

dynamics (Milton, 2000). An example of this is the epileptic seizure control strategy of

lasemidis et al. where the control focuses on maintaining a "healthy" range of STLmax t-index

values (associated with seizure transition) by therapeutic intervention (lasemidis et al., 2003;

Good et al., 2004, 2005). An analogous scenario may apply to VNS calibration in newly-

implanted patients where the VNS parameters are adjusted in order to elucidate a brain









dynamical response or "state" that has been previously established as indicative of desired and

even optimal seizure protection. Thus, the achieved neural state as described by dynamical EEG

responses associated with different stimulation parameters over time may serve as "marker" for

VNS treatment and facilitate rapid determination of optimal VNS parameters. See figure 4-2 for

a three-dimensional conceptual example of such a model.

The example in 4-2 utilizes three measures only for the sake of example. In actuality, a

real model may utilize dozens or even hundreds of such EEG features. Determining which EEG

measures should be used in such model is a challenging task indeed.

A common approach for revealing complex relationships among the features and samples

from large a multidimensional dataset (such as an EEG recording) is to employ data mining

methods. Data mining refers to the application of algorithms in order to extract patterns from

complex databases (Flexer, 2000) and provides a means for identifying EEG features which may

be sensitive to neural stimulation as well as neural stimulation parameters in the VNS implant.

Previous work employing data mining techniques has demonstrated successful pattern detection

from scalp EEG signals which is often difficult for the human eye to visualize (lasemidis et al.,

1996; Pardalos et al., 2003; lasemidis et al., 2004; Acir et al., 2005; lasemidis et al., 2005;

Chaovalitwongse et al., 2006; Sackellares et al., 2006; Thulasidas et al., 2006). Thus, such an

algorithm may be useful in the case of VNS therapy where short-term stimulation scalp EEG

effects are not explicitly visible in the time or frequency domain (Hammond et al., 1992;

Salinsky et al., 1993; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005). Often such algorithms

can be run in real time, providing a basis for an online EEG analysis tool (Sackellares et al.,

1997; Chaovalitwongse et al., 2005; lasemidis et al., 2005; Thulasidas et al., 2006).









The overall goal of this work is to investigate the existence of EEG feature patterns

which may be related to clinical and biological aspects of a patient's VNS therapy. The

underlying hypothesis of this work (stated as null) is "electroencephalographic effects in patients

undergoing VNS therapy for epilepsy do not vary with differing VNS parameters". Expressing

VNS-related effects in terms of scalp-EEG recordings is desirable considering its wide

availability at medical facilities and utility in epilepsy diagnosis. Such EEG measures may one

day find use as markers to help determine optimal VNS parameters more rapidly in newly-

implanted patients.

Biclustering Analysis of EEG Dynamics in Patients undergoing VNS Therapy for Epilepsy

Biclustering is a useful method for determining the existence of supervised binary

classifications in multivariate datasets. The outputs of biclustering are particularly valuable for

feature extraction purposes which are a significant concern in many biomedical studies. One of

the most common applications is establishing connections between syndromes (e.g., signs and

symptoms in cancer) and their corresponding gene expression patterns (Cheng et al. 2000;

Kluger et al., 2003; Yoon et al., 2005). The biclustering algorithm's ability to distinguish two

predefined states makes it a potentially useful tool for characterizing EEG dynamical alterations

associated with VNS activation using EEG features (such as STLmax ) as an input.

Data Description

The scalp-EEG recordings utilized in this study were obtained from patients with

functioning VNS implants for the treatment of epilepsy. The recordings were performed at the

General Clinical Research Center (GCRC) in Shand's Hospital at The University of Florida.

EEG was acquired under GCRC protocol # 614, Institutional Review Board (IRB) protocol

#617-2004, "Neurophysiologic Measures of Vagus Nerve Stimulation". EEG data were

obtained at 512 Hz sampling rate using 16-bit precision with a 0.16 Hz high pass filter and 105









Hz low pass filter hardwired into the amplifier. The dataset contained 25 scalp-EEG channels

arranged in the standard international 10-20 system (see Fig. 4-3).

EEG channels included in the study were: Fpl, Fp2, F3, F4, C3, C4, P3, P4, 01, 02, F7,

F8, T3, T4, T5, T6, Al, A2, Fz, Cz, Pz, Leye, Reye, Lmn, and Rmn ("mn" refers to an electrode

placed on the mandibular notch positioned between the jaw bone and the skull, which provides

information about the temporal lobe).

The CPz electrode, which is positioned between Cz and Pz, is used as the reference for the

25 EEG channels and electrocardiogram (ECG). The ECG electrode was placed near the VNS

pulse generator for two reasons. While this position provides a sufficient ECG signal, it is also

close enough to the pulse generator to introduce a unique artifact in the ECG channel which

corresponds to the pulse generator activation. This explicit VNS signature provides a means to

determine stimulation times. Once stimulation times were obtained, the ECG channel was

excluded the further study.

This study included two patients. The VNS paradigm is configured to deliver stimulation

for 30 seconds and halt stimulation for 5 minutes, a cycle which repeated regularly throughout

the entire recording for both Patient A and Patient B. Patient A's VNS parameters were 1.75 mA

output current, 30 Hz signal frequency, 500 tsec pulse width, 30 second signal duration, and a 5

minute VNS deactivation duration. Patient B's VNS stimulation parameters were 1.5 mA output

current, 20 Hz signal frequency, 250 tsec pulse width, 30 second signal duration and 5 minutes

VNS deactivation duration. The VNS implants allow manual activation of the device should the

patient require an immediate stimulation (e.g. if the patient senses an imminent seizure). Patient

A's manual stimulation parameters were 2 mA output current, 30 Hz signal frequency, 500 [tsec

pulse width, and a 60 second stimulation duration. Patient A did not experience any seizures









during the recording session, and did not initiate manual stimulations. Patient B's manual

stimulation parameters were 1.75 mA output current, 20 Hz signal frequency, 500 [isec pulse

width, and a 60 second signal duration. Patient B underwent 14 seizures during the recording

session and manually activated the stimulator between 20 to 40 seconds after onset of each

seizure (a total of 14 manual activations). Additional information on the patient's clinical status

can be found in tables 4-1 and 4-2.

Each patient underwent continuous scalp-EEG recordings approximately 24 hours in

duration. For Patient A, a total of 255 VNS were analyzed in this study. For Patient B, a total of

237 VNS cycles were used in the analysis. Some of Patient B's VNS cycles were excluded from

the study due to their disruption by a manually-activated stimulation and/or occurrence during a

seizure. Finally, the last VNS cycle was excluded from analysis for both patients because it was

not a complete cycle (it began closer than a full cycle length to the end of the recording).

STLmax Feature Extraction

Modeling brain activity using chaos measures has been shown to be useful for providing

dynamical information about the neural state of the epileptic brain. Studies involving human

patients (lasemidis and Sackellares, 1990; lasemidis and Shiau et al., 1999; lasemidis et al.,

2001; lasemidis and Pardalos et al. 2003; lasemidis and Shiau et al., 2003) and animal models of

epilepsy (Nair et al., 2004, 2005, 2006; Talathi et al., 2008) suggest that occurrence of

spontaneous seizures correlates with the evolution of the brain to a state of greater spatio-

temporal order. This phenomenon manifests as a progressive increase in intra-channel similarity

as measured by Lyapunov exponents calculated from multichannel EEG recordings. The

reported sensitivity of STLmax to neural state changes in epilepsy make the measure a

reasonable choice for attempting to characterize the VNS effects. Additional information can be

found on the STLmax measure in chapter 3.









Briefly, as was described in chapter 3, the window duration for calculating STLmax needs

to be short to provide temporally local information about the brain's dynamics yet contain

enough points for the algorithm to converge. A window length of 2048 points (corresponding to

4 seconds) was selected as it was sufficient for providing a stabilized STLmax estimate in

previous neural state classification studies in epilepsy (lasemidis and Sackellares, 1999). In

addition, it is desirable to utilize the shortest window length possible for STLmax estimation in

order to provide locally dynamic information. As such, while maintaining a window length of

the recommended number of data points for algorithm convergence, the 512 Hz sampling

frequency provides improved time resolution over previous studies (which utilized a 200 Hz

frequency). Additional parameters for STLmax estimation were selected based on the successful

neural state classification studies that utilized them (lasemidis and Sackallares, 1999):

reconstructed dimension D = 7, phase space reconstruction delay T = 14 msec (7 samples),

evolution time AT = 41 msec (21 samples).

Experimental Setup

The STLmax time series for 25 EEG channels were analyzed using a consistent

biclustering framework to determine separability of EEG fragments corresponding to stimulation

times versus VNS deactivation. Since stimulation duration was set to 30 second and a four

second time window was used to estimate each STLmax value, each stimulation provided seven

data points. In order to help compensate for EEG pattern changes over the recording session

which may not be related to VNS, each point in the stimulation class was averaged with the

corresponding samples across all other stimulation cycles. This procedure reduces the amount of

features to seven STLmax values for each channel to represent the stimulation class.

The non-stimulation class was comprised often STLmax points starting 250 seconds after

each stimulation to represent the portion of the non-stimulation temporally furthest from the end









of stimulation. This class size was utilized capture as much information about the non-

stimulation periods as possible while keep class sizes reasonably close to one another (<50% size

difference in classes). Each STLmax point in the non-stimulation class was averaged across all

VNS epochs (where an epoch consists of one stimulation and one non-stimulation period). Thus,

the non-stimulation class consists often averaged STLmax samples from non-stimulation time

intervals (see figure 4-4).

Thus, with 25 EEG channels, there total dimensionality of the biclustering input is 25 x 17.

This particular input size this problem could be solved without any relaxation using CPLEX

(ILOG Inc., 2004). Cross-validation by the leave-one-out method was performed for each

sample.

Results

Patient A's data were conditionally biclustering-admitting into a binary supervised

classification for the designated non-stimulation and stimulation classes with inclusion of all

features (see figure 4-5).

All but one feature (channel P3) were classified into the non-stimulation class. The

heatmap indicates that STLmax indicates during the stimulation with respect to non-stimulation

for all but the P3 channel. The leave-one-out cross-validation method resulted in consistent

classification of all 17 samples for Patient A.

Only five features in patient B were able to fulfill the supervised biclustering-admitting

sample class designation with respect to given stimulation and non-stimulation classes. Channels

F7 and T6 were designated as belonging to the non-stimulation class, while channels T3, Leye

and Reye were classified into the stimulation class. Thus, there is less similarity among the

channels during stimulation and non-stimulation, and a less clear distinction between stimulation

and non-stimulation in Patient B than Patient A.









Patient A's stimulation parameters (1.75 mA, 30 Hz, and 500 t[s pulse width) were all

greater than Patient B's (1.5 mA, 20 Hz, and 250 [ts pulse width) except for the 30 second on

time and 5 minute off time, which were the same for both patients.

Discussion

The successful application of biclustering with Lyapunov exponents demonstrates the

potential to distinguish during VNS stimulation from VNS deactivation epochs using the

dynamical scalp-EEG measure STLmax.

There is a greater spatial-temporal similarity in EEG dynamics during stimulation in

patient A than during non-stimulation. However, this phenomenon was not nearly as well-

defined in patient B. It should be noted that Patient A had no seizures during the recording,

whereas Patient B underwent seizures which were accompanied by a manually-initiated VNS

stimulation. Though epochs containing seizures or manual stimulations were excluded from the

analysis, it is possible that the seizures may have affected the results. Studies have demonstrated

EEG dynamical transitions (in terms of the STLmax measure) preceding seizures minutes to

hours (lasemidis et al., 1988; lasemidis, 1991; lasemidis et al., 1994, 1996, 1997). It may be that

EEG dynamical changes leading up to a seizure and/or persisting after the seizure lead to such a

small amount of features selected in Patient B.

Despite the seizures and manual stimulations, the signals arising from the frontal lobe (f7,

leye, and reye) and temporal lobe (t3 and t6) of the brain were sufficiently altered between

stimulation and non-stimulation to allow a biclustering of the during the stimulation class (from

t3, leye and reye channels) and non-stimulation class (from f7 and t6 channels) for Patient B.

This could mean that the EEG effects of VNS are most pronounced in the frontal and temporal

lobes. Patient B has a right frontal lobe focus.









The biological significance of these results may be related to study which discovered that

VNS-induced acute suppression of epileptiform activity in a hippocampal depth electrode

(Olejniczak et al., 2001). While the study by Olejniczak et al. utilized depth electrodes, its

possible that scalp EEG recordings may display some manifestation of such an EEG effect

observed at a hippocampal depth electrode. From this perspective, perhaps the STLmax

behavioral differences between patients A and B are associated with enhanced suppression of

epileptiform activity in patient A compared to patient B. Patient A's stimulation parameters

were all higher than patient B's parameters, with the exception of stimulation duration and off

time, which were 30 seconds and 5 minutes for both patients, respectively. In general, "high"

stimulation parameters are associated with a greater clinical response than "low" settings (Ben-

Menachem et al., 1994). Thus, any enhancement to epileptiform activity suppression in patient A

over patient B is likely attributed to patient A's higher stimulation parameter settings.

This work was published in the paper "Biclustering EEG data from epileptic patients

treated with vagus nerve stimulation", authored by Stanislav Busygin, Nikita Boyko, Panos

Pardalos, Michael Bewernitz, and Georges Ghacibeh (Busygin, 2007).

SVM Analysis of EEG Phase Space Patterns in Patients undergoing VNS Therapy for
Epilepsy

In light of the numerous successful neural state classification applications, often in real

time (Chaovalitwongse et al., 2006; Thulasidas et al., 2006) it is possible that SVMs may be able

to provide a computationally inexpensive yet robust similarity measure for quantifying

stimulation-induced EEG effects. As was stated chapter 3, experimental evidence supports the

idea of a therapeutic resetting effect of epileptic seizures in terms of preictal convergence and

postictal divergence of the STLmax measure among critical EEG electrodes (lasemidis et al.,

2004). Furthermore, recent experimental evidence suggests that therapeutic interventions such









as neurostimulation and AEDs can mimics the electroencephalographic resetting effect of a

seizure (Good et al., 2004, 2005; Ghacibeh et al., 2005). Thus, a reasonable approach for

examining VNS therapy is from the framework that it mimics the effect of a seizure by

comparing stimulation "artificial seizures" to non-stimulation ("post-ictal" or "interictal"). Thus,

the EEG phase space of an EEG segment during VNS stimulation was compared to successive

windows spanning the full stimulation / non-stimulation epoch with the intent of comparing the

degree of separability to the stimulation parameters and the clinical status of the patient.

The application of support vector machines for obtaining an estimate of EEG similarity

during stimulation compared to subsequent EEG segments may provide a rapid means to

investigate and quantify electroencephalographic effects of VNS. The goal of this study is to

extract EEG patterns which could be used as an electroencephalographic marker of optimal VNS

stimulation parameters.

Data Description

Approximately 24 hours of scalp-EEG was recorded and analyzed from six epileptic

patients being treated undergoing AEDs and VNS therapy and the control patient. The recording

electrode placement scheme is described in figure 4-2. The VNS Patient information is

summarized in tables 4-1 and 4-2.

SVM Application Description

SVM training and testing were performed using LIBSVM software package designed for

Matlab (Chang et al., 2001). The RBF kernel transform (equation 3-72) is a useful feature space

mapping technique successfully utilized in numerous neurophysiological studies (Acir et al.,

2005; Lehmann et al., 2007; Thulasidas et al., 2006).The RBF kernel with C=39 was utilized for

the feature space transformation and a cost parameter of C=1000 were employed based on

studies utilizing RBF SVMs to classify neural states using scalp EEG data (Kaper et al., 2004;









Acir et al., 2005; Lotte et al. 2007). Thus, In contrast to the traditional SVM application where a

typical goal is to obtain maximal separation basis by adapting all parameters, this study fixes the

a and C parameters in order to mitigate subjectivity when comparing stimulation epochs to the

non-stimulation epochs. An SVM classification accuracy of 50% implies minimal separation

between the reference class and comparison class whereas 100% separation implies maximal

separation between the reference and comparison class. These two extremes are interpreted as

maximal and minimal similarity, respectively.

Experimental Design

The progression of EEG pattern evolution was quantified as the amount of separation

achieved with support vector machines between two EEG segments both mapped into feature

space using the radial basis function kernel. This exploratory study aims to examine how the

EEG feature space patterns evolve throughout VNS stimulation and to identify potential

relationships to stimulation parameters. In addition, the results will be compared to the clinical

status of the patient.

The ECG electrode was positioned on the skin over the VNS pulse generator so that VNS

stimulation waveform is introduced into the ECG channel (see figure 4-3). The VNS stimulation

times were then obtained by examining the ECG channel, which was excluded from further

analysis. The following experimental procedure was applied to each stimulation epoch (an epoch

defined as a VNS "on" cycle and one "off cycle) in the continuous EEG recording for each

patient (with the exclusion of the final stimulation epoch which began less than one full cycle

before the EEG acquisition was deactivated). An EEG segment occurring from 10 seconds to 20

seconds after the start of the VNS stimulation is selected as the positive class (from here on this

class will be referred to as the "reference class"). The duration of each class was set at 10

seconds because this time frame is suggested to be long enough to be able to quantify brain









dynamics yet short enough to be sufficiently stationary (Casdagli et al., 1995, 1996, 1997). The

reference class segment was selected to start at one full window length after the start of

stimulation because that allows the stimulator to have finished the ramp-up phase and be at the

steady-state stimulation phase. The first successive EEG window (the segment ranging from 20

seconds to 30 seconds) was selected as the first negative class (from here on this class will be

referred to as the "comparison class"). The first preprocessing step was to down sample both

classes by calculating the mean value of a moving-average non-overlapping window, a step

which decreases SVM classification time often without a significant effect of results (Thulasidas

et al., 2006). The smoothing window was set at 10 points in duration based on prior experience.

Next, each data point is converted to a z-score by normalizing to zero mean and unit standard

deviation. This procedure prevents channels with greater mean amplitudes from dominating the

classification decision (Acir et al., 2005).

The trained SVM was tested with a v-fold cross validation scheme, as described in (Hsu et

al., 2003). This process applied a resampling technique in which the two classes are first

randomly shuffled then divided into v equally-sized subsets. The SVM is trained using v-1

segments and is tested using the remaining subset V. This process is repeated until all v subsets

have been tested. The accuracy is the percentage of properly classified points from each of the v

trials. Based on prior experience, v=2 folds were utilized for SVM training and testing in this

study. Once the training accuracy is obtained for the particular reference class and comparison

class combination, the comparison class advances one full window length and the process

repeats. The process of calculating SVM accuracy then advancing the comparison class is

repeated for all comparison segments which occur within one window length from the next

stimulation (into the next VNS epoch). This process is performed for each VNS epoch in the









approximately 24 hour continuous EEG recording for each patient (with the exception for the

final stimulation epoch during which the EEG recording ended).

Results

The results for the six patients are shown in figures 4-6 through 4-9 and table 4-3. The

vertical line at 30 seconds in figure 4-6 represents the time when the VNS stimulator deactivates.

Patients D and F have fewer comparison segments due to their off time of 3 minutes (thus the

time between stimuli is less than the rest of the patients, which have a 5 minute off time).

Patients E and F are seizure free.

Discussion

The results suggest a correlation may exist between pulse width and SVM separation

accuracy (figure 4-8) as well as between stimulation frequency and SVM separation accuracy

(figure 4-9). Furthermore, less similarity (greater SVM separation accuracy) is observed between

the reference class (10 second EEG segment during stimulation) and all subsequent comparison

classes (all non-overlapping 10 second EEG segments prior to the next stimulation) for higher

values of pulse width and stimulation frequency than is observed with lower values of pulse

width and stimulation frequency.

The biological significance of these results may be related to studies demonstrating

differences in cerebral blood flow related to stimulation parameters. Specifically, a study

demonstrated that the 250 pts VNS pulse width caused reduced blood flow in significantly more

brain regions (e.g. hippocampus and superior temporal lobe) than a 500 ps pulse width (Mu et

al., 2004). It is possible that pulse-width-induced blood flow changes in these brain regions may

have altered neuronal activity and thus be responsible for covariation of EEG feature space

dispersion with pulse width. Another study reported that a 20 Hz stimulation frequency produced

significant blood flow increase over 5 Hz in numerous brain regions such as the orbitofrontal









cortex, hypothalamus, and thalamus in VNS patients (Lomarev et al., 2002). These regions may

brain regions may be responsible for observed covariation of EEG feature space dispersion with

stimulation frequency.

It may seem counterintuitive that output current (figure 4-7) did not appear to demonstrate

a trend with the SVM separation measure as a study demonstrated that "higher" stimulation

settings (such as output current, frequency, and pulse width) can result in greater seizure

reduction than "lower" (Ben-Menachem et al., 1994). However, the output current increase in

(Ben-Menachem, et al., 1994) was also accompanied by increases in frequency and pulse width

parameters. Thus the outcomes of that study can not be attributed to changes in a single

parameter. Fortunately, the other two parameters (frequency and pulse width) mentioned in

(Ben-Menachem et al., 1994) may correlate with EEG pattern changes, though more patients are

needed to verify such a claim.

It is possible that VNS mimics the seizure effect of "resetting" the brain from an

unfavorable preictal state to a more favorable interictal state (Sackellares et al., 1997; lasemidis

et al., 2004) in which case the decrease in EEG similarity (signified by higher SVM separation

accuracy) between the reference class and all subsequent comparison classes in an epoch may be

an multidimensional analog to the brain dynamical resetting effect. The original effect was

described as statistical convergence and divergence of STLmax values among critical electrode

pairs (lasemidis et al., 2004). Thus, one explanation for the observed feature space similarity

phenomenon is these measures are electroencephalographic evidence that VNS is in some

manner "resetting" the brain more effectively (as denoted by the lower similarity measures after

stimulation) in the patients with fewer seizures per month. Perhaps therapies such VNS provide









ongoing gradual therapeutic action which suppresses the need for a large scale brain dynamical

transition such as a seizure.

It is worth stating that the time of each patient's last seizure prior to the EEG recording

session for this study is not documented. The timing of the last seizure could prove to be

important for patients who are not seizure-free (A, C and D). This is because there is a period of

heightened seizure resistance during the period immediately following a generalized tonic-clonic

seizure. If patients A, C, and D had undergone a generalized tonic clonic seizure shortly before

the EEG data were recorded for this study, then they may still have been under the influence of

the reduced seizure susceptibility phenomenon. This may explain why they did not experience

any seizures during this study. If Patient B had not experienced a generalized tonic clonic seizure

recently, then reduced seizure susceptibility phenomenon may have been partially responsible for

the large number of seizures reported this patient underwent during the study. These results

should be viewed in the context that all six VNS patients are considered responders to the

therapy defined as having at least 50% seizure reduction after one year of VNS therapy (Morell

et al., 2006).

Drug medication differences could also have an effect on the results. For example, patient

D (whom demonstrated the lowest average similarity) is the only patient using either

carbamazepine or zonisamide. On the other hand, Patient B (whom demonstrated the highest

average similarity) is the only patient taking phenobarbital. Perhaps these differences in

antiepileptic medications could have altered the observed electroencephalographic effects.

As all patients have undergone VNS therapy for >1 year it may be regions of their nervous

system such as the vagus nerve and/or brain may have adapted to VNS to such an extent that

they do not demonstrate a significant acute EEG response to individual stimulations. However, it









is premature to arrive at such a conclusion. The SVM training parameters utilized, though

successful in similar studies, are not optimized for this particular application. In addition to non-

optimized SVM parameters, it is likely that improvements can be made in terms of feature

selection for exposing VNS EEG effects.

This study is published in an article titled "Quantification of the Impact of Vagus Nerve

Stimulation Parameters on electroencephalographic Measures" with authors Michael Bewemitz,

Georges Ghacibeh, Onur Seref, Panos Pardalos, Chang-Chia Liu, Basim Uthman (Bewernitz,

2007).

Data Mining Analysis of EEG Dynamics Patients undergoing VNS Therapy for Epilepsy

The fact that the resetting effect is described in terms of the STLmax feature motivates

the use of the STLmax measure for investigating EEG patterns potentially associated with VNS

and VNS stimulation parameters. Inspired by the notion that therapeutic interventions may

replicate the therapeutic seizure resetting effect of a seizure without adverse symptoms, the

following study computes and compares STLmax values before VNS to values during VNS and

utilizes SVMs as well as logistic regression to provide measures of STLmax pattern evolution.

The evolution of STLmax values among the EEG channels is one method to track global EEG

dynamics over time.

Data Description

This study involved six patients undergoing VNS therapy for intractable epilepsy. The

continuous scalp-EEG recordings are -24 hour in duration and were obtained at the Shands

Hospital GCRC protocol # 614, IRB protocol #617-2004, "Neurophysiologic Measures of Vagus

Nerve Stimulation" at the University of Florida, Gainesville. Clinical information for all six

patients used in this study is summarized in tables 4-1 and 4-2. The electrode placement scheme

is illustrated in figure 4-2.The stimulation times were obtained from the ECG channel, which









was recorded in close proximity to the VNS pulse generator. The ECG channel was excluded

from the EEG analysis.

Feature Extraction

The behavior of STLmax values calculated from EEG signals for seizure prediction has

been extensively researched (see chapter 3). The embedded dimension of the reconstructed

space D=7, lag step T=7 (14 msec), evolution time AT=21 (41 msec), and a window size N=2048

(4 sec) have provided useful neural state classification estimates (lasemidis and Sackellares,

1991; Casdaglil996; Casdaglil997; lasemidis et al., 1999). The interested reader may find the

detailed explanation and justification of the algorithm and parameters in (lasemidis, 1991),

(lasemidis and Sackellares, 1999) and (Wolf et al., 1985).

STLmax was calculated for all 25 channels for the full EEG recording duration (- 24

hours) for all six patients.

SVM Analysis of EEG Dynamics

The LIBSVM software package for the Matlab environment was used for SVM training

and testing (Chang et al., 2001). An RBF kernel with o=39 and a cost parameter of C=1000 were

utilized based on studies utilizing RBF SVM to classifying neural states from scalp EEG data

(Kaper et al., 2004; Acir et al., 2005; Lotte et al., 2007). The SVM parameters C and sigma are

held constant in an effort to provide objectivity to this measure which can be used to study EEG

signal evolution over time in feature space for all the patients. This study fixes the C and C

parameters in order to mitigate subjectivity when comparing stimulation epochs to the non-

stimulation epochs.

An SVM separation accuracy of 50% is interpreted as maximum measureable dynamical

feature space similarity between reference class and comparison class features. An SVM









separation accuracy of 100% is interpreted as the minimum dynamical feature space similarity

between the reference class and comparison class features.

Results are validated using a v-fold cross validation scheme, as described in (Hsu et al.,

2003) using 10 folds. This process applied a resampling technique in which the two classes are

first randomly shuffled then divided into v equally-sized subsets. The SVM is trained using v-1

segments and is tested using the remaining subset V. This process is repeated until all v subsets

have been tested. The accuracy is the percentage of properly classified points from each of the v

trials.

Logistic Regression Analysis of EEG Dynamics

Logistic regression (LR) has seen number applications for the diagnosis of neurological

diseases and disorders. Examples include Parkinson's Disease diagnosis using various clinical

diagnostic measures (Leentjens et. al, 2002), diagnosis of Alzheimer's Disease (Lehmann et al.,

2007), cognitive decline (Prichep et al., 2006), and Schizophrenia using electrophysiological

features (Price et al., 2006), and epilepsy using EEG features (Alkan et al., 2005; Subasi et al.,

2005). Thus, LR analysis is a suitable candidate for further characterizing the brain dynamics in

patients undergoing VNS.

LR is a statistical modeling technique utilized for probabilistic binary classification. As

described in Subasi et al., 2005, the probability, Pt,ref, of a binary outcome event (EEG point at

time "t" belonging to the reference class) is related to EEG value of channel "ch" at time "t", Xch,t

in the form:

P1,1f 25 (4-1)
LOGIT(P,)= In r = P, +xhl, +...+ /25X ch25,t + ch(), (4-1)
1 (,ref ch=1









1 1
1 1 =(4-2)
t.,refK ) t -LOGIT(P,(X,))2(4
1+e ch 1

In equation (4-1), 30 is the intercept of the model and 31, 32, ..., 325 represent the

coefficients for EEG channels one through 25. Once the logistic regression model is trained, the

probability Pt,ref of an EEG data point Xt belonging to the reference class can be calculated in

equation (4-2).

The performance of the logistic regression model is measured using the area under the

curve (AUC) approach (Komaraek, et al., 2005). The AUC is equal to the area under the

receiver operating characteristics (ROC) curve. The AUC metric is simply the ratio of the area

of an ROC curve to the area under a perfect ROC curve.

Let "NR" be the number of points in the reference class, and "NC" be the number of points

in the comparison class. NR = NC for this study, but do not have to be equal. The ROC curve is

generated by first calculating Pt,ref for each EEG data point Xt in both the reference class and the

comparison class. Then, the Pt,ref values are sorted in decreasing order. The ROC curve creation

begins at the lower left hand corner of a blank curve plot. Each point with Pt,ref > 0.5 (most

likely that the EEG point is from the reference class) results in the creation of an upward line

segment of length one unit. Each point with Pt,ref < 0.5 (most likely that the EEG point is from

the comparison class) in the creation of a line segment of length one unit to the right. The AUC

metric is the ratio of the area under the generated ROC curve divided by the area under a perfect

ROC curve (which climbs from (0,0) to (0, NR), then moves laterally from (0, NR) to (NC, NR)

and is equal to one in this case).









An AUC=0.5 (or ROC=0.5) is equivalent negligible dynamical feature space similarity

between the reference class and comparison class. AUC=1.0 (or ROC=0) refers to the maximum

measurable dynamical feature space similarity between the reference class and comparison class.

Experimental Setup

The following procedure was applied to each stimulation epoch (an epoch defined as a

VNS "on" cycle and one "off" cycle) for each patient using SVMs and then repeated for LR.

The EEG segment occurring 8 seconds (two window lengths) prior to stimulation start is selected

as the "reference class". The reference class was represented as an n x m array of STLmax

values where n is the number of channels and m is one less than the total number of stimulations

occurring during the EEG recording. Setting m as one less than the total number of detected

stimulations ensures that only complete VNS epochs are included in the analysis (as the last

stimulation intersected with the end of the recording for all six patients). For each patient, the

reference class utilized STLmax estimates from all n=25 channels from the time period of 8

seconds (two full window lengths) prior to stimulation start, for all m stimulations. The

"comparison class" was initially established as an n x m array of STLmax values occurring at the

start of the stimulation for all m stimulations included for each patient. The SVM and LR

classifiers are trained and tested for separation of the reference and comparison class

combination. Once the accuracies are obtained, the reference class is advanced 4 seconds (one

full window length) and the process is repeated throughout the epoch with the last comparison

class occurring 200 seconds after stimulation start. The end point corresponds to the end of the 3

minute interstimulation cycle, which is the final endpoint which

Results

Figures 4-10, 4-11, 4-12, and 4-13 as well as table 4-4 demonstrate a similar performance

between the LR and SVM results. Using both methods, the same two patients which produced









the greatest STLmax feature separation between non-stimulation and stimulation epochs

(patients A and D) also possessed the greatest stimulation frequency, 30 Hz, whereas the patient

with the lowest separation (patient B) also possessed the lowest stimulation frequency, 20 Hz. In

addition, patient D produced the second greatest separation while possessing highest stimulation

frequency of 30 Hz. On the other hand, Patient F also had the greatest stimulation frequency of

30 Hz yet only achieved an intermediate separation value compared to the other patients (though

patient F is seizure-free whereas patients A, B, and D are not). The final noteworthy observation

the width was the lowest (250 microseconds) and Patient B who demonstrated the least

separation. There was no apparent trend regarding the degree of separation using either LR or

SVM and output current.

One interesting connection with the clinical status was that the patients whom experienced

the greatest amount of separation (patients A and D) were also taking more types of AED

medications (patients A and D each were on four medications, patient B was on three

medications, all other patients were only taking two medications). Another interesting

connection to the clinical status is that the patient with the largest number of monthly seizures

(patient B) also demonstrated the least amount of STLmax feature separation between non-

stimulation and stimulation.

Discussion

The LR and SVM classification results suggest that EEG dynamical pattern changes (in

terms of the STLmax measure) between stimulation and non-stimulation may be related to the

stimulation frequency parameter. Lomarev et al. reported that a 20 Hz stimulation frequency

produced significant blood flow increase over 5 Hz in numerous brain regions such as the

orbitofrontal cortex, hypothalamus, and thalamus in VNS patients (2002). These regions may









brain regions may be responsible for observed covariation of STLmax dispersion with

stimulation frequency.

At a first glance it seems counterintuitive that the output current did not appear to

demonstrate a similar LR or SVM classification accuracy trend as pulse width and stimulation

frequency, as a study demonstrated that "higher" stimulation parameter settings (such as

frequency, output current, and pulse width) are associated with greater seizure reduction than

"lower" settings (Ben-Menachem et al., 1994). However, the output current increase mentioned

in (Ben-Menachem et al., 1994) was accompanied by increases in frequency and pulse width and

thus the observed therapeutic effect in that study can not be attributed to changes in an individual

parameter. Furthermore, the values of the other two parameters mentioned in the study by Ben-

Menachem et al. (frequency and pulse width) did show indications of a connection with EEG

dynamical changes, which is encouraging.

Patient B's large amount of seizures accompanying the lowest LR and SVM separation is

an interesting observation. It is difficult to draw preliminary conclusions about clinical

connections to the brain dynamical behavior as Patient B's stimulator was set at the lowest pulse

width and the lowest stimulation frequency of all six patients. However, a potential connection

between this patient's clinical behavior and the observed EEG patterns can be viewed from an

interesting perspective first described in seizure prediction research studies. Considering the

electroencephalographic and clinical effects observed during seizures, it is possible that the VNS

therapeutic effect is enacted by artificially replicating the theorized therapeutic seizure

mechanism first suggested by lasemidis et al. (2004).

By adopting this perspective, patient B's seizures could be seen as the result of the VNS

failing to replicate the resetting function of a real seizure. Thus, the brain is then "permitted" to









seize in order to reset itself. This observation is congruent with the notion that patient B has the

lowest STLmax feature separation for both LR and SVM between the VNS on (which could be

considered a VNS 'artificial' seizure) and VNS off class (which from an 'artificial' seizure

perspective could be viewed as a 'post-ictal' period for the 'artificial' seizure). It is worth

mentioning that all six patients are considered as responders to VNS therapy by a definition of

experiencing at least a 50% seizure frequency reduction following one year of VNS therapy

(Morell et al., 2006).

The observation that patients A and D were taking the most types of AEDs and

demonstrated the highest STLmax feature separation between non-stimulation and stimulation is

reasonable. Again, from the view of a seizure's "resetting" mechanism described in the previous

paragraph, the two additional AEDs could possibly be enhancing effectiveness of the VNS

resetting phenomenon as characterized by increased STLmax separation between VNS on and

VNS off.

This study was submitted to Computing and Optimization in Medicine and Life Sciences

Vol. 3, under the title "A Data Mining Approach to the Investigation of EEG Biomarker

Existence for Vagus Nerve Stimulation Therapy Patients", with authors Nikita Boyko, Michael

Bewernitz, Vitaliy Yatsenko, Panos Pardalos, Georges Ghacibeh, Basim Uthman (Boyko et al.,

2008).

Conclusions

The interesting results of these studies may be indicative of EEG dynamical effects of

VNS and suggest the LR, SVM and biclustering may serve as useful data classification tools for

use in an online real-time seizure control application. Biologically, these results may be related

to the trait pointed in a study by Olejniczak et al. which discovered a short-term suppression of

epileptiform sharp waves following VNS from a hippocampal depth-electrode (2001). While the









scalp electrodes used to collect the EEG data for this chapter cannot achieve the fidelity of

hippocampal depth electrodes, it is possible that the scalp EEG data mining analysis results may

reflect the same therapeutic effect as observed in the hippocampus by Olejniczak et al. (2001).

The biological significance of the potential covariation of the EEG patterns with the pulse

width and stimulation frequency parameters may be related to studies which demonstrated

cerebral blood flow patterns corresponding to the pulse width (Mu et al., 2004) and stimulation

frequency (Lomarev et al., 2002) parameters in VNS patients.

Additional patients are needed to validate such claims against possible type 1 error.

However, additional patients would also provide the opportunity to potentially uncover any

VNS-induced EEG dynamical changes which may have been missed in this small sample (thus

reducing the chance of type 2 error).

A difficulty for this type of clinical research is recruiting patients with similar clinical

situations (e.g. similar stimulation parameter configurations) in order to strengthen any observed

connections between EEG behavior and stimulation parameters. For example, if numerous

patients with similar stimulation parameters could be recruited, the patients may be taking

different medications in different doses, etc. While it may be tempting to consider altering drug

paradigms to mitigate inter-subject variability, practical and ethical concerns must be kept in

mind at all times when attempting to alter patient treatment regimes for research purposes.

In addition, the impact of epileptic seizures on these EEG features and classification

techniques is important for generating a robust stimulation-response model. Thus, as the clinical

circumstances such seizure occurrence can affect observed EEG dynamical patterns, it is worth

mentioning that each patient's last seizure time prior to this study's EEG recording session is

unknown. The time at which the last seizure occurred may be important factor for the patients









which are not seizure free (patients A, B, C, and D) as there exists a period of reduced seizure

susceptibility for a period of time following a generalized tonic-clonic seizure. Thus, patients A,

C, and D could have experienced generalized tonic clonic seizures prior to the study recording

session and thus been influenced by this period of reduced seizure susceptibility. Such an

scenario could have contributed to the lack of seizures occurring during the recording session

and also influenced seizure dynamics. In addition, if patient B had not experience a generalized

tonic-clonic seizure prior to the study recording session then this patient's large number of

seizures may have been partially induced due to the lack of said "seizure protection" phenomena

following a seizure.

Despite exclusion of stimulation epochs containing seizure activity from analysis, patient

B's seizures during the recording session still may have altered the observed EEG patterns. The

rationale for such as claim is the observation of dynamical EEG shifts (in terms of the STLmax

measure) identified from minutes to hours prior to epileptic seizures (lasemidis et al., 1988;

lasemidis, 1991; lasemidis et al., 1994, 1996, 1997). Thus, conclusions about patient B must be

carefully considered as the seizures themselves could affect the observed EEG classification

results. There is also a possibility of error in the monthly seizure rate as described by the

patients. A 2007 study by Hoppe et al. demonstrated documentation inaccuracies in patient

seizure counts (Hoppe et al., 2007). Thus, caution must be exercised in any epilepsy study which

incorporates seizure information that was documented by patients.

Thus, in an ideal study, additional consideration should focus on recruiting a group of

patients with similar epilepsy cases (e.g. similar focus locations). By studying multiple patient

groups each with similar variants of epilepsy, experimental findings are strengthened and the

findings may help tailor resulting VNS therapy devices.









In order further the understanding of EEG effects accompanying VNS it is important to

track EEG feature patterns in patients before, immediately after, and for at least six months after

implantation. A longitudinal study starting before VNS implantation and ending 6-12 months

after implantation would provide insight into the evolution of EEG dynamical patterns before

and after VNS parameter adjustment. In addition, such an analysis would help determine the

presence of EEG characteristics present prior to VNS implantation for each individual patient.

Thus, such a study design would add strength to post-implantation EEG patterns which are not

observed prior to VNS implantation.

In the case that pre-VNS data is not available for a particular patient of interest, patients

whom are receiving VNS for depression treatment may serve as useful control subjects. Such

patients could help determine how brain dynamics in VNS patients are influenced by epilepsy

and seizures. The potential knowledge gained from these suggested studies could lead us one

step closer to the creation of an EEG marker for optimal VNS parameters.

In addition, as the relationship of EEG patterns stimulation parameters and clinical

outcome in VNS patients is not clearly defined, then it is possible that the EEG measure

parameters or perhaps the measures used in data classifiers are suboptimal. Thus, additional EEG

features should be utilized for possible improvements in EEG dynamical comparisons.

Complexity measures entropy measures have demonstrated success as data mining features for

extracting brain dynamical information and classifying neural states (Chaovalitwongse et al.,

2006).













Clinical Literature
Review / Future
Experiments


Stimulation
parameters


Experimental
objective


-' Ultimate
A" goal


EEG
measures


Figure 4-1. Rationale for studying EEG patterns which may be associated with the effect of VNS
on the brain.


Clinical
effect










OC = 0.75mA
PW= 250
SF = 20 Hz
On = 30 sec
Off =5 min


1-a- _--- '


0.4 -
0.2

0.2

-0-2 .8 ......
-0.4 .--
-0-G6 -------'
-0.8 -------


OC= 1.0mA OC = 1.25mA OC = 1.25mA
PW= 250 PW = 250 PW= 500
SF = 20Hz SF = 20Hz SF = 20 Hz
On = 30 sec On = 30 sec On = 30 sec
Off= 5 min Off= 5 min Off 5 min




_. -
. -.-..


0.8 1
0.6


2 0.4
0.2


Figure 4-2. Conceptual EEG dynamics model in three-dimensional feature space for testing
stimulation parameter configurations in newly-implanted VNS patients. Adjusting the
stimulation parameters results in an altered dynamical 'state' of the brain denoted by
the coordinates in three-dimensional feature space. The model's colored regions
relate the EEG dynamical state to its predicted clinical outcome.















132


4i i




i i iil









Table 4-1. VNS stimulation parameters
Patient A
Output Current (mA) 1.75
Stimulation Frequency (Hz) 30
Pulse Width (ps) 500
On Time (seconds) 30
Off Time (minutes) 5
Magnet Output Current (mA) 2
Magnet On Time (seconds) 60
Magnet Pulse width (ps) 500


20% Vertex


B
1.5
20
250
30
5
1.75
60
500


C
2.5
25
500
30
5
2.75
60
500


D
2
30
500
30
3
2
30
500


E
1.25
20
500
30
5
1.5
60
500


F
0.75
30
750
30
3
0.75
60
750


Front


S 20%


) P ""


10% :
Nasioi


Right
side


Back


Figure 4-3. EEG electrode placement. Electrodes were positioned according to the 10-20
electrode placement system which assigns locations proportionally spaced locations
(e.g. 10%-20%) with respect to the size of the patient's head.
















40 sec, 10 samples


250 sec ,.








St

F5min


Figure 4-4. STLmax class designation for biclustering analysis.


28 sec, 7 samples
28 sec, 7 samples










A
ZZZZZZZZZZcmmmcnfmw


B
ZZZZZZZzz00trnioA


NAME
f7
ts
t3
leye
reye


Figure 4-5. Biclustering heatmap of STLmax from A) patient A and B) patient B.


NAME
fpl
fp2
f3
f4
c3
c4
p4
ol
o2
f7
fB
t3
t4
t5
t6
al
a2
fz
12
PZ
leye

Imn
rnn
p3










Table 4-2. Patient information for epilepsy patients with the VNS implant.


Patient
Age
Focus


Mean
seizures per
month
# of seizures
during
recording
Seizure Type





Duration of
VNS therapy
(years)
Medications*


A
38
Right
frontal
Left
frontal
3


C. Partial
with
infrequent
secondary
gen.
> 1 year


Gab
Lam
Lev
Preg


*Gab = Gabapentin, I
Phenobarbital, Top =


B
53
Right
frontal



30


14


C. Partial
with
infrequent
secondary
gen.
> 1 year


Lev
Phen
Top


Lam = Lamotrigine, Lev
Topiramate, Carb = Carl


C
54
Right
temporal


C. Partial
with
infrequent
secondary
gen.
> 1 year


Gab
Top


D
29
Left frontal


C. Partial
with
infrequent
secondary
gen.
> 1 year


Carb
Lam
Lev


Levetiracetam, Preg


E
54
unknown


C. Partial
with
infrequent
secondary
gen.
> 1 year


Chlor
Gab


F
54
Right
temporal
Left
temporal
0


0


C. Partial
with
infrequent
secondary
gen.
> 1 year


Preg
Lev


Pregabalin, Phen


bamazepine, Chlor = Chlorazepate


Table 4-3. SVM separation accuracy and seizure information.
Patient Mean SVM Average monthly seizure Seizures during recording
separation rate
A .9284 3 0
B .7788 30 14
C .8359 2 0
D .9807 3 0
E .9454 0 0
F .8982 0 0
*Average monthly seizure rate of zero indicates seizure freedom.




































0 50 100 150 200 250 300
Time after reference segment (seconds)


Figure 4-6. Mean SVM separation accuracy value across the stimulations for each individual
intra-stimulation window.



2.68
C


2.4

2.2

2

1.8

1.6

1.4

1.2

1 -

0.8

0 75


0.8 0.85 0 9
SVM accuracy (%)


Figure 4-7. VNS output current and the corresponding mean SVM separation accuracy over 24
hours.














750

700

650

600

550

500

450

400

350

300

250 _


A E


0 75 0.8 0.85 0 9 0.95 1
SVM accuracy (%)



Figure 4-8. VNS pulse width and the corresponding mean SVM separation accuracy over 24
hours.


30



o 28



V26
n

C 24
g-





22


20


0 75




Figure 4-9


F A


0.8 0.85 09 0.95 1
SVM accuracy (%)



VNS signal frequency and the corresponding mean SVM separation accuracy over 24
hours.















0.


0.g
Patients


-- B
C
D
F
-----__------------------------ -w----
------- 9--------------------------------F
01
i0 i i i i


time, sec


Figure 4-10. SVM Separation accuracy throughout the VNS epoch, averaged across all epochs.
Stimulation begins at t=0 seconds.


0.9

0.8

0.7
~06-
>,0.6
-
, 0.5

> 0.4
~0-
C)

S0.3

0.2
0

0.1

0
0-


D E F


Patients


Figure 4-11. Overall mean SVM separation averaged across intra-epoch time points and all
epochs.


-C



















Patients

-6- A
--- B
---C
-- -D

)I E
--S-- F


0 20 40 60
time, sec


Figure 4-12. LR separation quality throughout the
Stimulation begins at t=0 seconds.


1



0.8



0.6



0.4


VNS epoch, averaged across all epochs.


0.2



0 --


--r-


r


r


Patients


Figure 4-13. Overall mean LR AUC averaged across intra-epoch time points and all epochs.


I -r-









Table 4-4. Mean SVM and LR separation accuracy and patient seizure information.
Overall mean SVM Overall mean LR Seizures per Seizures during
Patient separation separation month recording
A 0.8082 0.9701 3 0
B 0.4746 0.5104 30 14
C 0.6171 0.7571 2 0
D 0.7536 0.9658 3 0
E 0.7210 0.8878 0 0
F 0.6885 0.8319 0 0









CHAPTER 5
ANALYSIS OF INTERSTIMULATION BRAIN DYNAMICS IN VAGUS NERVE
STIMULATION THERAPY

The Identification of a marker of desired VNS operation would greatly expedite the VNS

parameter adjustment process in newly-implanted patients. This study faces two significant

challenges: 1) the underlying therapeutic mechanism of VNS is still poorly understood, and 2)

despite some interesting results reported in innovative research studies, the

electroencephalographic effects of vagus nerve stimulation are not clearly defined. From the

perspective of dynamical disorder (see chapter 2), there is reason to believe any such potential

stimulation-induced EEG effects are likely to be elucidated from dynamical EEG analysis

(Uthman et al., 2007).

Further Characterizations/Investigations of EEG-Effects in VNS Therapy

Preliminary data mining results described in chapter four present interesting EEG

dynamical phenomena with biological interpretations that are consistent with the theory about

the physiological "resetting" role of a seizure. Of additional interest is the behavior of the brain

between VNS stimulations. Viewing inter-stimulation brain behavior provides a means to

determine how the brain recovers after VNS therapy (or 'artificial seizures'). In addition, this

analysis duration also provides information about the brain while is not being actively influenced

by a therapeutic action (e.g. VNS or the therapeutic effect of a seizure). Thus, as non-ictal EEG

can help provide information about the seizure imminent state, so to may the inter-stimulation

EEG intervals provide information additional information about the brain's response to VNS

which may not be available while the VNS is active. This chapter focuses on characterizing the

temporal dynamical behavior of the EEG signals during the periods when the VNS is inactive.









Building on the successes of the data mining approaches in chapter four, this chapter

aims to further characterize EEG patterns which may be related to VNS. The brain's behavior

will be characterized during all periods of respite from VNS.

Dynamical EEG Measures as Markers for Neurological Diseases and Disorders

The success of EEG markers for the treatment of neurological disorders is the primary

motivation for this study. Such "signature" observations of pathological activity have greatly

boosted diagnosis, treatment, and therapeutic evaluation of a range of neurological disorders

(Krystal et al., 1996, 1997, 2000; Asyali et al., 2007; Ding et al., 2007; Quintana et al., 2007)

including epilepsy (lasemidis et al., 1996; Pardalos et. al, 2003, 2004; Chaovalitwongse et al.,

2005, 2006; Ding et al., 2007; Schevon et al., 2007). Additional details can be found in chapters

2 and 3.

Despite reported interest in the application of such a technique to the EEG signals for

improving VNS epilepsy therapy (Uthman et al., 2007), studies have been published which do

not support the presence of VNS-induced EEG effects (Hammond et al., 1992; Salinsky et al.,

1993; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005).

Though long-term VNS-induced EEG changes on epileptic interictal spikes (Koo, 2001)

epileptiform sharp waves in the hippocampus (Olejniczak et al., 2001), interictal epileptiform

discharges (Janszky et al., 2005; Santiago-Rodriguez and Alonso-Vanegas, 2006), gamma

activity and desynchronization (Marrosu et al., 2005), and spectral content of sleep (Rizzo et al.,

2004) have been reported, the time frame for observing such an effect renders it less useful the

current task of expediting VNS parameter calibration in newly-implanted patients.

Physiological behavior such as alterations in the interitical spiking rate is congruent with

the characteristics dynamical diseases and disorders. The class of disorders termed "dynamic

disorders" demonstrates complex behavior patterns which evolve over time. Specifically, these









disorders have been broadly described as undergoing a temporal disruption in the underlying

physiological control mechanisms which results in a period of abnormal dynamical behavior

(Mackey and Glass, 1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et

al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003; Colijn and

Mackey, 2005). Thus, studying epilepsy therapy from the vantage point of a dynamical disorder

is a rational approach.

Koo's observation of the VNS effect on interictal spiking rate (2001) demonstrates that

relatively short-term EEG effects (such as interictal spikes) are the manifestation of long-term

modulatory VNS effects (e.g. after several months). Thus, this observation raises the possibility

of less obvious short-term manifestations of VNS modulatory effects existing in the EEG. Such

EEG effects may be detectable using EEG measures that have demonstrated successful neural

state characterization such as preictal transitions in seizure prediction studies (Casdagli et al.,

1996; Chaovalitwongse et al., 2005; lasemidis and Sackellares, 1991; lasemidis et al., 1993;

lasemidis et al., 2003, 2004; Le Van Quyen et al., 2001; Lehnertz, 1999; Lehnertz and Elger,

1995; Osorio et al., 2001).

The purpose of identifying dynamic disorders is that successful treatment may result from

manipulation of some physiologic control parameter into a range associated with healthy

dynamics of the observed variables (Milton, 2000). One example of this is a seizure control

strategy where the"healthy" range of STLmax t-index values (associated with seizure transition)

in maintained by therapeutic intervention (lasemidis et al., 2003; Good et al., 2004, 2005). An

analogous scenario may apply to VNS parameter adjustment in newly-implanted patients where

the VNS parameters may be adjusted in order to elucidate a brain dynamical response or "state"

that has been previously established as indicative of desired or even optimal seizure protection.









Thus, the achieved neural state as described by dynamical EEG responses associated with

different stimulation parameters over time may serve as "marker" for VNS treatment and

facilitate rapid determination of optimal VNS parameters.

An example of this concept is illustrated for a brain dynamics model involving three

dynamical measures in chapter 4, figure 4-2. Realistically, mapping the clinical outcome to

subregions of a multidimensional feature space will likely be very complex and require

numerous additional features for adequate characterization. While determining the proper

features to best represent the brain behavior and its relationship to stimulation parameters in

VNS is a daunting task, this study aims to provide an in-depth evaluation of a number of EEG

measures which have demonstrated sensitivity to neural state changes in other studies. For these

reasons, the current study aims to identify electroencephalographic markers which are sensitive

to the stimulation parameter configuration in patients with the VNS implant. If such

electroencephalographic markers are identified, and if the electrographic markers are found to

correlate with clinical efficacy then these findings could be applied to determine optimal VNS

stimulation parameters on a patient-by-patient basis.

Data Description

This study utilized EEG data from six patients undergoing VNS therapy for epilepsy.

Extensive patient information can be found in chapter four. The recordings were acquired under

GCRC protocol # 614 / IRB protocol #617-2004, "Neurophysiologic Measures of Vagus Nerve

Stimulation" GCRC in Shand's Hospital at The University of Florida. EEG data was acquired

from channels Fpl, Fp2, F3, F4, C3, C4, P3, P4, 01, 02, F7, F8, T3, T4, T5, T6, Al, A2, Fz, Cz,

Pz, Leye, Reye, Lmn, and Rmn using CPz (located between Cz and Pz) as a reference. The data

were acquired at 512 Hz sampling rate using 16-bit precision from an amplifier with 0.16 Hz

high pass filter and 105 Hz low pass hardwired filters. The mandibular notch channel near the









location where the jaw and skull contact one another provides information about the nearby

temporal lobe. See figure 5-1 for electrode locations.

The ECG electrode was placed near the pulse generator to introduce the VNS waveform in

the ECG channel when the stimulator is active. Thus, the VNS signature waveform was

introduced into the ECG (see figure 4-4) to provide an effective means to identify stimulation

times by modifying a channel that is not used in the quantitative analysis. A summary of patient

clinical information can be found in tables 4-1 and 4-2.

Ideally, the baseline recording from each involved patient should be compared to their

own EEG after implantation in order to strengthen claims that observed EEG patterns are the

result of VNS and thus were not present prior to implantation. However, baseline EEG data was

not available for this set of patients. As no baseline data was available for the VNS study, an

interictal EEG recording from a temporal lobe epilepsy patient of -24 hours in duration

provided courtesy of the Freiburg Center for Data Analysis and Modeling at the Albert-Ludwigs

Universitat Freiburg (University of Freiburg), Freiburg, Germany (Winterhalder et al., 2006) was

utilized as a control dataset. The interictal EEG data came from patient p012 and was acquired

at 512 Hz. The data were acquired from three focal channels (TBa4, TBb6, HR7) and three non-

focal channels (TLb2, TLb3, TLc2).

The patient has a right hippocampal seizure focus which gives rise to simple partial,

complex partial, and generalized tonic-clonic seizures. The control dataset was utilized with

artificial stimulation times based on both a 5 minute interstimulation interval and a 3 minute

interstimulation interval.

The Surrogate Analysis Method

The surrogate data analysis method is a statistical approach for identifying nonlinearity in a

time series. The best expression of the surrogate data method is from a statistical hypothesis









testing framework (Theiler et al., 1992). This formulation requires a null hypothesis to test

against and some test statistic. The null hypothesis is a possible description of system output

which is tested to determine how well it models the observed data. The test statistic is a quantity

calculated from the sample data to determine whether or not to reject the null hypothesis.

Surrogate data analysis typically defines the null hypothesis such that the time series data

are described by a specific process belonging to a broader class of processes (Schreiber and

Schmitz, 2000). A common null hypothesis asserts that the time series data are generated by a

general Gaussian linear stochastic process (Theiler et al, 1992). However, different realizations

that fit within this broad category can result in surrogates with different power spectra and

distributions. This scenario and may cause the test statistic may mistake such variations for

deviations from the null hypothesis and falsely reject the null hypothesis (Schreiber and Schmitz,

2002). The can be approach using pivotal statistics or using constrained realizations (Theiler and

Prichard, 1996). Pivotal statistics are measure created such that do not depend on mean or

standard deviation under the null hypothesis. The "constrained realization" method enforces a

requirement that all surrogates display the same power spectrum and distribution of values as the

original data (Theiler and Prichard, 1996; Schreiber and Schmitz, 2000). Under the constrained

realization approach the randomization method covers the "pivotal" requirement and thus opens

up the possibility to use numerous non-pivotal test statistics for testing the null hypothesis.

While the surrogate method is useful for suggesting the presence of nonlinear signal

components, this technique cannot be used to characterize the specific type of observed nonlinear

behavior. For example, while it is valid to utilize a Lyapunov exponent to test the null

hypothesis, surrogate analysis cannot indicate that an observed nonlinear signal is the result of

low-dimensional chaos (Pritchard et al., 1995; Palus, 1997; Schreiber and Schmitz, 2000).









Surrogate data sets were generated using the algorithm proposed by Schreiber and Schmitz

to produce same power spectrum and amplitude distribution as the original dataset (1996). The

algorithm runs as follows. Let {s, } represent an EEG signal of length n. Store sorted list of the

raw EEG values, (s ,,, ), and the absolute value of the amplitudes of the discrete Fourier

transform (equation 3-11) of {s, which is denoted as {Sk First the original data {s, are

randomly shuffled {s ()}. Each iteration consists of two actions. At iteration step i, the signal

from the previous iteration {s ('j1) is brought to the desired power spectrum by computing the

Fourier transform and replacing the amplitudes {Sk (1) with those of the original signal {Sk }, and

performing the inverse Fourier transform. The original complex Fourier phase values of the

signal from the previous iteration {s( 1)} remain unchanged when reconstructing the signal

s ('} having the desired power spectrum. While this step enforces the correct power spectrum, it

usually disrupts the signal amplitude distribution. Thus, the second step in an iteration is to rank

order the resulting time series {s(') and replace the ranked indices with the ranked amplitudes

from the original signal {s,;st }. Performing the rank ordering will thus alter the power spectrum

calculate in step i+1, thus requiring the entire procedure to repeat. After each iteration, the

deviation from the original power spectrum is checked and the process repeats until a given

accuracy is achieved.

The Role of Surrogate Data Analysis in EEG studies

Nonlinear measures such as complexity, chaoticity, and information-based measures can

be useful in the analysis of the output of complex systems such as the brain (Lehnertz and Elger,

1995; Pincus, 1995; Lehnertz, 1999; Le Van Quyen et al., 2001; Osorio et al., 2001; lasemidis et

al., 2003, 2004). However, analysis of less complex systems may not require the application of

148









nonlinear methods as they may provide the same (or perhaps less) information about the system

at hand while often resulting in increased computational cost. Thus, an original application of

surrogate analysis was to provide partial justification for the use of nonlinear analysis methods in

EEG studies. Surrogate data analysis has provided support for the presence of nonlinear

components of EEG signal in various types of epilepsy (Casdagli et al., 1995; 1996, 1997; Lopes

Da Silva et al., 1999; Jung et al., 2003; Liu et al., 2007). Additionally, observations have been

made regarding the different neural states in epilepsy such as interictal, preictal, ictal, and

postictal the corresponding occurrence of significant nonlinearity (Pijn et al., 1997; Jung et al.,

2003) as well as a measure of the "amount" of nonlinearity (e.g. the magnitude of the p-value

when comparing original to surrogate data) (Liu et al., 2007). In addition, surrogate data

analysis has demonstrated changes in nonlinear signal component expression following various

brain stimuli such as transcranial magnetic stimulation (Jing and Takigawa, 2002), drug

treatment (Ferenets et al., 2006) compared to baseline EEG. As any similar studies regarding

VNS was could not be located, such an analysis may provide a means for quantifying EEG

effects related to VNS parameters and perhaps clinical outcome. In addition the following

analysis may provide an improved understanding of the brain's EEG response to VNS and

potentially provide insight into how it delivers its therapy.

Nonlinearity Analysis of Interstimulation EEG

The following study is motivated by a desire to characterize the interstimulation EEG

dynamics in VNS patients and identify potential covariation with stimulation parameters using

surrogate EEG analysis. The underlying hypothesis (stated as null) which motivates this study is

"EEG dynamics during the interstimulation period are unrelated to the stimulation parameters in

VNS patients". The interstimulation period is targeted in order to track the brain's post









stimulation response which may contain useful EEG dynamical information relating to the

stimulation parameter configuration.

Under this experimental setup, it is logical to compare to the results to a control patient

which utilizes artificial stimulation times. Resulting EEG dynamical differences between the

VNS patient interstimulation epochs and the control patient artificial interstimulation epochs

could provide convincing support for the existence of VNS-induced EEG effects which may be

related to the VNS parameters.

Choosing a Test Statistic

By utilizing the "constrained realization" approach to surrogate data analysis, the options

for a test statistic become more plentiful as the requirement for a pivotal test statistic is now

relinquished (Theiler and Prichard, 1996). Based on the successful application of entropy

measures in EEG nonlinearity test studies (Thomasson et al., 2000; Burioka et al., 2003,2005;

Ferenets et al., 2006), as well as the general success in classifying neural states from EEG

(Bruhn, 2000; Bruhn, 2001; Bruhn, 2003; Abasolo, 2005; Ferenets et al., 2006), the approximate

entropy (ApEnt) measure will serve as the test statistic.

The ApEnt measure was calculated within non-overlapping windows of size 2048 points (4

seconds). A window of this size falls within a reasonable range utilized for computing ApEnt in

terms of clinical and theoretical relevance (Pincus, 1995). The noise threshold r=0.2*std was

selected as a result of studies which successfully correlated the ApEnt EEG measure to clinical

drug anesthesiology levels (Bruhn, 2000; Bruhn, 2001; Bruhn, 2003; Ferenets et al., 2006), as

well as a study which used ApEnt to characterize background EEG in patients with Alzheimer's

Disease (Abasolo, 2005). The phase space mapping process utilized an embedding dimension of

7 is used based on previous EEG complexity studies quantifying neural state transitions in

patients with mesial temporal lobe epilepsy (lasemidis et al. 1988; lasemidis et al., 1990;









lasemidis et al., 1999). The time delay embedding process utilized a delay T=7 corresponding

tol4 ms (lasemidis et al., 1990; Zaveri et al., 1993; lasemidis et al., 1996).

Experimental Design

The amount of surrogates were selected based on a model proposed by Schreiber and

Schmitz which considers a residual probability a of a false rejection by random chance with a

corresponding significance level of ( a) x 100 % (2000) The proposal suggests creating an

amount of surrogates M=2*K/a -1 such that the probability that the data will reject the null

hypothesis by chance is a for a two-tailed test (Schreiber and Schmitz, 2000). Due to the

intensive computational complexity of this procedure, this preliminary analysis utilizes K=l and

a=0.1 for the purposes of selecting the amount of surrogate data copies. Thus, this study uses 19

surrogates.

EEG surrogates were calculated in non-overlapping windows of length 2048 points (4

seconds). This window size is considered to be within a reasonable range for surrogate data

generation (Schreiber and Schmitz, 1996). This is also used as the window length utilized in the

calculation of the ApEnt measure used as the test statistic.

The mean value of each ApEnt point across all 19 surrogates is computed to the surrogate

datasets to a single time series which is then compared to the original signal (Casdagli et al.,

1996; 1997; Liu et al., 2007). For patients with a 5 minute interstimulation time a window of 73

points represented the interstimulation period. For patients with a 5 minute interstimulation time

a window of 73 points represented the interstimulation period. For patients with a 3-minute

interstimulation time, a 43 point window represented the interstimulation time. Statistical testing

was performed using a two-tailed paired-t test. For 95% certainty and 72 degrees of freedom and

42 degrees of freedom the critical t-values are t= 1.993 and t=2.018, respectively.









This preliminary study assesses the dynamical structure of EEG signals during VNS

interstimulation periods. The dynamical structure is evaluated by testing each interstimulation

epoch against a null hypothesis of a Gaussian linear process using surrogate datasets for all

epochs for all six patients. The hypothesis, stated as null is:

S HO: EEG dynamics during an interstimulation epoch are described by a Gaussian linear
stochastic process.

Results

For each patient and for each channel, the hypothesis was tested using approximate

entropy of the EEG of VNS deactivation epoch (see figure 5-3 through 5-12 and tables 5-1

through 5-3). Patients A and B showed a notable increase in the amount of interstimulation

epochs demonstrating a nonlinear signature occurring across most channels occurring between

11 pm until 7 am. The control patient showed a decrease in a nonlinear fingerprint occurrence in

non-focal channels during the same time of day.

The fraction of epochs across the entire recording and all channels which displayed a

nonlinear signature (could reject HO at the given significance) displayed a potential negative

correlation with the pulse width parameter for all six patients.

In addition, patient F showed nonlinear signatures in fewer epochs than any other patient

(35.1% of all epochs could reject HO at the given significance), followed by patient E (39.0%).

Both of these patients are seizure free. Patient B's EEG showed the most nonlinear fingerprints

having 52.3% of the epochs rejecting HO at the given significance level. While patient F showed

the most nonlinearity, patient F had the greatest stimulation frequency (30 Hz) and the greatest

pulse width (750 us). Patient B had the lowest stimulation frequency (20 Hz) and the shortest

pulse width (250 [ts). The fraction of epochs which displayed nonlinear signatures for the









control patient with 5-minute and 3-minute interstimulation times were 42.5% and 37.2%,

respectively.

In general, the lower the monthly seizure rate, the less nonlinear signatures were

observed. According figure 5-3, patient F (seizure-free) produced a smaller fraction of nonlinear

interstimulation epochs than the 3-minute control whereas patient D (-3 seizures per month)

produced a larger fraction of nonlinear epochs than the 3-minute control. A similar trend was

observed in the patients with the 5-minute interstimulation time. Patients C and E (seizure free

and seizures per month, respectively) generated a smaller fraction of nonlinear epochs than the

5-minute control whereas patients A and B (-3 seizures per month and -30 seizures per month,

respectively) displayed a larger fraction of nonlinear epochs than the 5-minute control.

Patients A, B, D, and F showed noticeably higher expressions of nonlinearity in channels

located near foci than non-focal channels. The control patient demonstrated a high density of

nonlinear behavior in non-focal channels during waking hours which is diminished around 11

pm 7 am, except for the TLc2 channel which shows a greater fraction of epochs demonstrating

nonlinear signatures than other channels.

Discussion

In regards to the connection of EEG patterns stimulation parameters, the most obvious

observation was the potential relationship between the fraction of epochs which displayed

nonlinearity and the pulse width parameter. In addition, Patient F produced the smallest

fraction of epochs presenting a nonlinear signature (35.1% of epochs could reject HO at the given

significance level) and patient had the highest stimulation frequency (30 Hz) and the highest

pulse width (750 ks) of all six VNS patients. Patient B's EEG presented the greatest fraction of

epochs presenting a nonlinear fingerprint (52.3% of epochs could reject HO) whereas the patient









had the lowest stimulation frequency (20 Hz) and the lowest pulse width (250 [ts) of all six VNS

patients.

The underlying biology driving this EEG behavior could be related to a study which

demonstrated an acute suppression of epileptiform activity in the hippocampus during VNS

(Olejniczak et al., 2001). Perhaps enhanced suppression of epileptiform activity is responsible

for the diminished nonlinearity in patients with fewer seizures.

Also, a study has demonstrated that the 250 [ts pulse width parameter results in blood

flow mitigation to significantly more brain regions (e.g. hippocampus, sup. temp. lobe) than a

500 [ts pulse width in VNS patients (Mu et al., 2004). Perhaps pulse width related blood-flow

reductions reported by Mu et al. are responsible for any such changes in epileptiform activity

suppression which may have been detected by the surrogate data analysis.

In addition, patients E and F demonstrated the lowest fraction of epochs presenting a

nonlinear signature (39% and 35.1%) and also happen to be the only two patients which are

seizure-free. This may be aligned with the clinical observation that the absence of bilateral

interictal epileptiform discharges was the only EEG predictor of seizure freedom (Janszky et al.,

2005). Future studies should include characterizing the profile of interictal epileptiform

discharges for relationship to linear and nonlinear measures.

In patients A and B there was a notable increase in the amount of interstimulation epochs

demonstrating a nonlinear signature occurring across most channels at times around 11 pm until

7 am. The increase in the occurrence of nonlinear signature may have been partially resulted

from the patient being drowsy or asleep. A surrogate analysis study by Shen et al. demonstrated

a considerable number of EEG segments displaying a nonlinear signature during stage 2 sleep

and may be the result of K-complexes (Shen et al., 2003).









The control patient demonstrated a high density of nonlinear behavior in non-focal

channels during waking hours which is diminished around 11 pm 7 am, except for the TLc2

channel which shows a greater fraction of epochs demonstrating nonlinear signatures than other

channels.

Patients A, B, D, and F showed a greater fraction of epochs presenting nonlinear

signatures in channels located near foci than non-focal channels. This observation is aligned

with the literature where focal electrodes demonstrated higher nonlinearity than non-focal

electrodes (Casdagli et al., 1995, 1996, 1997).

While the control patient provides information from a patient with a similar epileptic

condition and recorded at the same frequency as the VNS patients, the depth electrode recordings

from the control patient provide limits to what can be suggested to conclusions about VNS-

induced scalp-EEG patterns. The ideal control would be use baseline from each patient using an

identical electrode setup.

The fraction of epochs rejected the null hypothesis is a necessary condition for nonlinear

dynamical, however, these results are not sufficient to suggest a particular type of nonlinearity

(e.g. surrogate analysis cannot prove the existence of low-dimensional chaos). Changing

parameters (e.g. the dimensionality or noise threshold) for ApEnt may improve sensitivity to

potential VNS-induced EEG effects and thus provide the possibility to relate said effects to

stimulation parameters and ultimately to the clinical outcome. The results, combined with studies

documenting the ability of various nonlinear measures to quantify neural states motivates the

usage of nonlinear as well as linear measures to examine EEG dynamical behavior which could

be associated with VNS stimulation.









Temporal Evolution of Interstimulation EEG Dynamics

The results of the previous experiment characterized the presence of nonlinear EEG signal

components throughout each of the interstimulation epochs for each of the six patients

undergoing VNS therapy for epilepsy. However, as surrogate analysis does not provide

characterization of nonlinear signal components, it is possible that the properties of the detected

nonlinear components may distinguish the control patient from the VNS patient. Thus,

additional characterization signal dynamics would enhance the findings from the surrogate

analysis.

This experimental perspective aims to analyze the observed nonlinear signal components

and further characterize how brain dynamical patterns behave during the period between

stimulations. This study is motivated by an underlying hypothesis (stated as null) "HO:

Interstimulation EEG dynamics are time invariant in patients undergoing VNS therapy for

epilepsy". While VNS is believed to induce its therapeutic effect via long-term modulation (Koo,

2001), this long-term effect may manifest as changes in short-term temporal dynamical behavior

compared to baseline which would be consistent with the traits of a dynamical disorder such as

epilepsy (Mackey and Glass, 1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989;

Belair et al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003).

Thus, it is possible that the brain dynamics during the interstimulation epochs in VNS

patients will be distinguishable from a control patient, which would provide support for the use

of EEG dynamical analysis for the study of VNS effects. Furthermore, EEG dynamical behavior

during the interstimulation period may be related to stimulation parameters.

Data Description

Six patients undergoing VNS therapy for intractable epilepsy were analyzed in this study.

The continuous scalp-EEG recordings are approximately 24 hours in duration and were obtained









at the Shands Hospital GCRC protocol # 614, IRB protocol #617-2004, "Neurophysiologic

Measures of Vagus Nerve Stimulation" at the University of Florida, Gainesville. Available

clinical information for the six patients is summarized in tables 4-1 and 4-2. The electrode

positions are described in figure 5-1. VNS activation times were obtained from the ECG channel,

which was recorded from an electrode placed in close proximity to the VNS pulse generator.

The ECG channel was otherwise excluded from this study.

EEG Dynamical Measures

Quantitative EEG analysis is a broad field incorporating numerous methods for

quantifying various properties of EEG signals (see chapter 3). In order to improve the

characterization of the dynamical evolution, this study utilized multiple EEG measures. Each of

the EEG analysis techniques first applies a phase space transformation after which the relevant

information is extracted. The phase space mapping procedure of Takens (1981) was applied

using an embedding dimension of 7 is used based on previous studies in which the epileptic

attractor was characterized from EEG recordings of patients with mesial temporal lobe epilepsy

(lasemidis et al. 1988; lasemidis et al., 1990; lasemidis et al., 1999). For an embedding

dimension of 7, a time delay of T=7 samples corresponding tol4 ms is applied. This time delay

value has demonstrated success in characterizing the rhythm of a typical seizure in temporal lobe

epilepsy (lasemidis et al., 1990; Zaveri et al., 1993; lasemidis et al., 1996;).

Approximate entropy

This ApEnt measure (see equations 3-16 to 3-19) has been utilized to study EEG patterns

in Alzheimer's disease patients (Abasolo, 2005), as a surrogate marker for anesthesia depth

(Bruhn 2000, Bruhn 2001, Bruhn 2003), detecting epileptic seizures (Abasolo 2007; Srinivasan,

2007), and as a test statistic for characterizing EEG nonlinearity (Thomasson et al., 2000;









Burioka et al., 2003,2005; Ferenets et al., 2006). Thus, it may be useful for characterizing brain

dynamics during interstimulation intervals.

The noise threshold was set at 20% of the signal's standard deviation r=0.2*std was

applied based on studies which successfully correlated ApEnt with drug anesthesia levels

(Bruhn, 2000; Bruhn, 2001; Bruhn, 2003; Ferenets et al., 2006) and a study characterizing

background EEG in patients with Alzheimer's Disease (Abasolo, 2005). The 2048 point (4

second) window selected for this study is within a range that has been described as being

clinically and theoretically appropriate (Pincus, 1995).

Correlation sum

For a collection of points in some vector space, the correlation sum is the fraction of all

possible vector pairs which are closer than a given distance r for a particular norm distance norm

(see equation 3-2). The correlation sum is estimated after mapping the EEG into phase space.

The correlation sum is often used to estimate the correlation dimension (equation 3-27) which

has been extensively utilized in physiological data (Kantz and Schreiber, 1995) such as neural

state classification studies using EEG (Tirsch et al., 2000, 2004), as well as seizure prediction

(Elger et al., 1998; Martinerie et al., 1998). However, since use of an absolute radius can result

in a heavy EEG amplitude sensitivity (Osorio et al., 2001), this study utilizes a relative radius

measure (with respect to the diameter of the dataset in phase space) for brain dynamics

characterization (Casdagli et al., 1996, 1997, Merkwirth et al., 2002).

Correlation sum was estimated using the TSTOOL package (Merkwirth, 2002) for

Matlab. Theiler recommends application of an exclusionary window to a range of points

surrounding each reference point in order to avoid embedding vectors on the same trajectory

(Theiler et al., 1986). Based on the results of similar studies, a 250 ms (128-point) exclusion









window around reference points and a search radius r=0.2 (10% of attractor diameter) were

implemented (Casdagli et al., 1996, 1997).

Mean angular frequency in phase space

A modification to the Lyapunov exponent measures, the mean angular frequency in phase

space measure (0) quantifies the angular frequency of the phase space evolution of two nearest

neighbor points relative to a reference point (lasemidis et al., 2001, 2002, 2003). Conceptually,

this measures the average rate of change of a system state. The measure is related to the

Lyapunov exponent, which measures the local stability of a system. A study quantifying neural

states in epilepsy found that preictal, ictal, and postictal states corresponded with medium, high,

and lower values of 0, respectively (lasemidis et al., 2002, 2003). In addition, the dynamic

entrainment / disentrainment and seizure resetting phenomena observed before and after epileptic

seizures using the STLmax measure has also been described with Q (lasemidis et al., 2003).

Thus, the sensitivity of Q to changes in neural state makes it a candidate for quantifying any

EEG dynamics changes which may be associated with VNS. The window length selected for

this study, 2048 points, is the same window length as was used in lasemidis et al. (2001, 2002,

2003).

Short-term maximum Lyapunov exponent

The STLmax measure has been shown to be useful for providing dynamical information

about the neural state of the epileptic brain. Studies performed on EEG from human patients

(lasemidis and Sackellares, 1990; lasemidis and Shiau et al., 1999; lasemidis et al., 2001;

lasemidis and Pardalos et al. 2003; lasemidis and Shiau et al., 2003) and animal models of

epilepsy (Nair et al., 2004, 2005, 2006; Talathi et al., 2008) imply that the evolution of the brain

to a state of greater spatio-temporal order correlates with spontaneous seizures. This









phenomenon is presented as a temporally progressive increase in the similarity among so-called

critical channels measured by STLmax calculated from multichannel EEG recordings. Thus,

sensitivity of STLmax to neural state changes in epilepsy indicated by the above studies makes

the measure a reasonable candidate for identification and characterization of potential VNS-

induced EEG effects.

The window duration for calculating STLmax needs to be short to provide temporally local

information about the brain's dynamics yet contain enough points for the algorithm to converge

(additional information about this can be found in chapter 3). The 2048 point (4 second) window

size chosen for this study is suggested to provide a sufficiently stable STLmax estimate in

previous neural state classification studies in epilepsy (lasemidis and Sackellares, 1999). Also,

use of the shortest window length possible for STLmax estimation can help provide a stationary

segment for estimating local dynamical information. As such, while maintaining a window

length of the recommended number of data points for algorithmic convergence, the 512 Hz

sampling frequency provides improved time resolution over previous studies (which utilized a

200 Hz frequency). The evolution time parameter was set to AT = 41 msec (21 samples) based

on successful neural state classification studies that utilized them (lasemidis and Sackallares,

1999).

Experimental Design

This preliminary investigation into the temporal evolution of the EEG between

stimulations will start searching for coarse dynamics transitions between the first and second

halves of each epoch where the VNS is deactivated. The rationale for this class designation is to

assess the existence of any short-term transitions, to characterize the temporal evolution where it

exists, compare with a similar experimental setup in a control patient and determine any

correlation to clinical parameters. The underlying hypothesis (stated as null) which motivates









this study is "EEG dynamics during the interstimulation period are unrelated to the stimulation

parameters in VNS patients". Figure 5-13 shows an illustration indicating how the measures

were grouped to examine the temporal evolution of these dynamical measures during VNS-OFF.

As shown in figure 5-13, EEG measures corresponding to the first half of an epoch are

compared to EEG measures corresponding to the second half of an epoch for each channel, for

all channels (except ECG). Using 4 second windows to calculate the various EEG measures, the

The preliminary hypotheses (stated as null) are formulated for the purpose of

characterizing the EEG behavior associated with stimulation in the VNS patients:

* HI: The EEG dynamics as quantified by approximate entropy are time invariant while
VNS is deactivated.

* H2: The EEG dynamics as quantified by correlation sum are time invariant while VNS is
deactivated.

* H3: The EEG dynamics as quantified by mean angular frequency in phase space are time
invariant while VNS is deactivated.

* H4: The EEG dynamics as quantified by short-term maximum Lyapunov exponent are
time invariant while VNS is deactivated.

These hypotheses aim to answer the question of how the dynamical brain behavior as described

by these four nonlinear EEG measures evolves over time between stimulations. Such an analysis

may identify EEG patterns which are sensitive to particular stimulation parameter configurations

as well as the candidate measures for detecting such patterns.

The control patient underwent two similar tests; one which utilized stimulation times with

a 3 minute 'off duration, and a second test which utilized stimulation times with a 5 minute 'off

duration. The hypotheses were tested with a two-tailed unpooled two-sample t-test with a=0.05

using the Matlab Statistics Toolbox. The tests were performed assuming unequal variances and

utilized Satterthwaite's approximation for the effective degrees of freedom. For a measure

window size of 2048 points (4 seconds), the first and second halves of the interstimulation epoch









each contain 36 values of each measure for patients A,B,C,E (whom have a 5 minute

interstimulation duration) and 21 values of each measure for patients D and F (whom have a 3

minute interstimulation duration). The same statistical testing method was used to test the

control patient. The control patient was tested with artificial stimulation times using 3-minute

and 5-minute interstimulation duration.

Results

As figures 5-22 and 5-24 show, for all patients the ApEnt and Q measures resulted in a

larger fraction of epochs rejecting H1 and H3 (respectively) than the control patient for the

majority of the 25 EEG channels. When using the correlation sum measure, the majority of

electrodes had a greater fraction of epochs reject H2 for patient A than the control patient.

However, the correlation sum did not show any such trend for any other patients. For all four

measures, patient C rejected the four hypotheses in 2-3 times more interstimulation epochs than

the control patient. For all four measures, patient F produced the fewest amount of

interstimulation epochs that rejected the null hypothesis than any other patient.

Numerous observations can be made regarding focal and non-focal electrode behavior

according to tables 5-3, 5-5, 5-7, 5-9. In terms of the ApEnt measure, the focuses of patients

A,B,C, and F produced significant dynamical complexity fluctuations during more

interstimulation epochs than their corresponding non-focal areas, and greater than the control

focus. This phenomenon could be related to studies where electrodes in the vicinity of an

epileptogenic focus displayed more prominent nonlinear behavior (Casdagli et al., 1995, 1996,

1997). The correlation sum measure suggested that the focus and non-focus of patient A

demonstrated significant time varying dynamics in more interstimulation epochs than the control.

For all six patients, the Q showed significant temporal dynamics variation in more epochs than









the corresponding control patient. With regards to the spatial comparison of focal and non-focal

electrodes, the STLmax measure did not show any obvious trends.

The main finding in regards to the dynamical behavior throughout the day (see figures 5-

14 through 5-21) is the overall trend of diminished dynamical variance between approximately

11 pm and 7 am for all four measures in patients A (-epoch 130) and C (-epoch 140). Patient

B's seizures were accompanied by significant temporal fluctuation in the Q dynamical measure

before and after seizures. As stimulation epochs which overlapped with seizures were excluded

from the study, these dynamical alterations occurred within about 10 minutes of the seizure.

Discussion

This study aimed to characterize the interstimulation EEG periods using a range of

dynamical EEG measures which have demonstrated sensitivity to neural state changes such as

those observed in epilepsy.

Patient C had highest output current (2.5 mA) as well as the greatest amount of epochs

(45.6%, 36.8%, 36.1%, and 21.8%) showing time varying dynamics of all the patients as

measured by the ApEnt, correlation sum, Q, and STLmax measures, respectively (see figures

5-26 through 5-29). Patient A showed similar ApEnt and Q behavior (35.7% and 31.0% of

interstimulation epochs demonstrated significant temporal variance for both measures, whereas

control values were 21.8%, 10.5%, respectively) compared to patient C and had the second

highest output current (1.75 mA). Patient F showed an opposite trend having the lowest output

current (0.75 mA) where ApEnt, 0, and STLmax produced the smallest fraction epochs

rejecting H1, H3, and H4 (23.8%, 20.2% and 14.3% whereas control values produced 16.9%,

7.9%, and 19.4%, respectively). The ApEnt measure quantifies the regularity in a time series

(Pincus, 1995; Abasolo et al., 2007), the Q measure provides an estimate of the stability of the









reconstructed attractor in phase space (lasemidis et al., 2002, 2003), and STLmax provides a

measure of chaoticity of a signal (lasemidis et al., 1991). Thus, the similar behavior of these

three measures implies the EEG could be undergoing fewer changes in the regularity, stability

and observed chaoticity in patient F than patients A and C. Overall, the ApEnt and Q measures

demonstrated the greatest deviation from the control patient, the broadest range of the fraction of

epochs showing time varying dynamics, and a potential covariation with output current. For

these reasons, the ApEnt and Q measures may potentially find use as EEG biomarkers for VNS.

Biologically, these results may be related to the findings of studies which identified a

current threshold for suppression of chemically induced seizure models. For example, seizures

induced in a low Ca2+ model could be suppressed with currents greater than 1 tA (Warren and

Durand, 1998). In addition, seizures induced in a high K+ model could be suppressed with

currents greater than 4tA (Nakagawa and Durand, 1991). Yet patient F has been seizure free for

at least one year at the time of recording, while patients A and C have mean seizure rates of 3

and 2 seizures per month (respectively). In general, higher values of VNS parameters are

associated with improved seizure protection (Ben-Menachem et al., 1994). So while at first it

may seem counterintuitive that the patient with the lowest output current (patient F) is seizure

free, keep in mind that the aforementioned study is referring to collective impact of output

current, pulse width, and stimulation frequency. So even though patient F's output current (0.75

mA) is less than patient A's (1.75 mA) and patient C's (2.5 mA), patient F has higher pulse

width (750 [ts) than patients A and C (both 500 [as). In addition, patients A and F have the

greatest stimulation frequency of all the patients in the study (30 Hz) whereas patient C has a 25

Hz stimulation frequency.









In addition, patient F has a shorter interstimulation interval (3 minutes) compared to

patients A and C (both 5 minutes). It is tempting to attribute patient F's seizure freedom to this

patient having a greater amount of stimulation cycles over time, however patient E is also seizure

free and has a 5 minute interval.

It is interesting that all four measures behaved in a similar manner for patient F whom

had the lowest output current and was seizure free. Perhaps when the output current raises above

a particular threshold value the neuronal activity is affected in such a manner that it becomes

more erratic and thus results in more rapid dynamical transitions. The minimum current

threshold for suppression of epileptiform activity in seizure observed by Nakagawa and Durand

(1991) as well as Warren and Durand (1998) may be responsible for this. This could explain why

patients A, B, C, D and E whom had greater output currents than patient F produced results less

consistent with the other dynamical measures than for patient F.

Regarding the relationship to the time of day to EEG dynamical effects, the most obvious

trend was the period corresponding to 11 pm and about 7 am (see figures 5-14 and 5-16). The

reduced dynamical temporal variance for all four measures in A (-epoch 130) and C (-140)

during this period compared to other times of day is likely related to the fact that the patients are

drowsy or asleep. A recent study by Rizzo et al. (2004) demonstrated that an overall increase in

EEG total power both in sleep and wakefulness after long-term VNS treatment compared to pre-

treatment EEG, so it is plausible that the dynamical measures during sleep were influenced by

the VNS. However, EEG sleep studies have demonstrated a decrease in the mean and standard

deviation of the ApEnt measure (Acharya et al., 2005; He et al., 2005) during sleep compared to

wakefulness, which is aligned with the observation of diminished variation of the ApEnt measure

during times when the patient is presumed to be asleep. In addition, a study by Acharya et al.









showed an increase in mean and a decrease in standard deviation for most sleep stages (2005).

Thus, the observation of STLmax behavior during sleep is aligned with the literature. Therefore,

while VNS has been shown to affect the sleep EEG signal (Rizzo et al., 2004), the behavior of

the nonlinear measures during a period when the patient is drowsy or asleep is consistent with

sleep patterns in people without VNS implants.

Conclusions

The results from the surrogate EEG analysis show a potential between the fraction of

epochs which displayed nonlinearity and the pulse width parameter. In addition, Patient F

produced the smallest fraction of epochs presenting a nonlinear signature (35.1% of epochs could

reject HO at the given significance level) and patient had the highest stimulation frequency (30

Hz) as well as highest pulse width (750 ts) of all six VNS patients. Patient B's EEG presented

the greatest fraction of epochs presenting a nonlinear fingerprint (52.3% of epochs could reject

HO) whereas the patient's stimulator was programmed with the lowest stimulation frequency (20

Hz) and the lowest pulse width (250 [ts) of all six VNS patients. In addition, patient B

demonstrated the greatest amount of monthly seizures. It is possible that neuronal modulation

may be sensitive to the duration of the individual pulses in a manner which may manifest as

increased linearity of neuronal output. For example, Mu et al. (2004) demonstrated that 250 ts

showed blood flow reduction to significantly more brain regions than 500 [as. However, such an

observation requires additional patients for verification. Also, patients E and F demonstrated the

lowest fraction of epochs presenting a nonlinear signature (39% and 35.1%) and are also the only

two patients which are seizure-free. This observation may be aligned with the clinical

observation that the absence of bilateral interictal epileptiform discharges was the only EEG

predictor of seizure freedom (Janszky et al., 2005). While interictal epileptiform discharge

detection was not included in this study, future studies should include the spatio-temporal









distribution of interictal epileptiform discharges in the characterization process. Comparison with

linear and nonlinear EEG measures may provide additional information relevant to the

connection between stimulation parameters and EEG patterns.

The results from the temporal analysis of interstimulation dynamics demonstrate a

potential manifestation of the VNS long-term modulation effect in terms of the interstimulation

dynamics behavior. In particular, the ApEnt and Q measures displayed a potential covariation

the output current parameter, demonstrated the greatest deviation from the control patient, the

broadest range of the fraction of epochs showing time varying dynamics. For these reasons, the

ApEnt,and Q measures could serve as EEG biomarkers for VNS. In light of this result, its

possible that when the current reaches a threshold level the neuronal activity intensifies such

that the summed output (the EEG) behaves more erratically (in terms of more rapidly fluctuating

dynamical measures such as ApEnt and Q,). This phenomena could be related to the

observation of minimum stimulation current thresholds were needed to suppress epileptiform

activity in low Ca2+ (Warren and Durand, 1998) and high K+ (Nakagawa and Durand, 1991)

seizure models.

Overall, the two interstimulation analysis experiments (analysis of nonlinearity and

analysis of temporal variation) showed potential connections EEG covariation with the pulse

width, output current, and signal frequency parameters. Such effects may be useful as an EEG

biomarker of optimal VNS settings. Additional studies should be performed on a larger sample

of patients in order to validate these claims. In addition, baseline EEG recordings obtained prior

to VNS implantation are crucial for determining which EEG effects in the VNS patient could be

associated with VNS and which effects appeared to be present in the EEG prior to VNS

implantation.









The EEG measures were likely suboptimal as they were selected based on similar studies.

Though it is difficult to select the proper parameters in measures used in an expeditionary study

such as this one, a good place to start may be to calibrate the measures such that they are able to

capture and unfold an epileptic attractor in phase space. From this perspective, future VNS

studies which utilize phase space embedding transformations should utilize a patient's own

seizures to determine the dimension and delay for embedding signals.

In addition, study of the VNS in this setup is limited by the fact that the stimulator is

programmed for chronic regular stimulation. Thus, though these studies aim to characterize the

short-term EEG effects after stimulation, the short-term affect is produced by the cumulative

effect of a large number of stimulations. Thus, an interesting study to help truly elucidate the

effects of an individual stimulation or a group of stimulations would be to record prestimulation

baseline for a group of patients, perform a single VNS stimulation, and perform an additional

EEG recording while keeping output current at zero milliamps to examine any post-stimulation

effects. Such an analysis may be one of the best ways to provide the most objective insight into

the EEG effects of VNS without concern of any long-term modulatory effects. In addition,

tracking the progression of such measures over time (e.g. 3 months, 6 months, 12 months after

implantation) and comparing with the patients own baseline EEG recording are a desirable

approach to examining EEG dynamics in patients with VNS.

The seizures that patient B underwent during the recording session could likely have had

a far reaching impact on the observed dynamics patterns, as EEG dynamical transitions have

been documented as occurring several minutes to several hours prior to seizures (lasemidis et

al., 2004). One potential improvement to this study is to record multiple days of recordings in

order to compare a sufficient amount of 'interictal' data, which has been defined as being at least









8 hours away from a seizure (Pardalos et al., 2003; Hively et al., 2005; Chaovalitwongse et al.,

2006). This would eliminate pre-seizure dynamical transitions as an additional variable to

influence results. If this were not possible, one other possibility would be to examine only the

EEG data that occurs at least 8 hours away from any detected seizure in a patient. One

challenging aspect this approach is that the amount of EEG that would be allowed in the study

would be diminished significantly (e.g. two-thirds of a single day would be excluded due to a

single seizure), and with only a handful of seizures at the 'wrong' time would render this

approach infeasible.

Though sleep staging was not included in this research protocol obtaining the precise

sleep times with manual and/or computer automated sleep staging for each patient should be

included in future work. This would help to further examine the observation that the four EEG

measures underwent less variation over time during the periods between about 11 pm and about

8 am.

The preliminary study of temporal evolution of dynamics used a two tailed test to

determine the means are different or not. A future study should look at the direction of the two

way test to determine if regularity, stability, or chaoticity are increasing or decreasing throughout

the duration of the interstimulation interval. Such information may provide additional insight

into the dynamical behavior and the stimulation parameters (e.g. a trend of decreasing or

increasing the dynamical measures may be related to the stimulation parameters, the clinical

status of the patient, or even the time of day).

Ultimately this study may lead to a method of surgical VNS testing, e.g. surgically

exposing the left vagus nerve so a diagnostic vagus nerve stimulation device could be

temporarily attached to the patient, stimulations could be applied in the operating room and the









EEG signal can be analyzed. If this setup were to prove successful, it may provide a method to

prescreen patients for responsiveness to VNS therapy prior to undergoing the implantation

process.

An article related to these studies was published under the title "Optimization of epilepsy

treatment with vagus nerve stimulation" with authors Basim Uthman, Michael Bewernitz,

Chang-Chia Liu, and Georges Ghacibeh (Uthman et al., 2007).









20% Vertex
F ----------- C ,.
-C '20%


C D Z


10% i
Nasio!


Front


Right
side


Back


Figure 5-1. Map of EEG electrode location for the VNS patients. The electrodes were positioned
according to the 10-20 electrode placement system which assigns locations
proportionally spaced locations (e.g. 10%-20%) with respect to the size of the
patient's head.


Figure 5-2. Electrode positions for the control patient from A) an inferior and right view and B)
axial slice view of the brain. Red circles indicate focal electrodes (TBa4, TBb6,
HR7), blue circles indicate non-focal electrodes (TLb2, TLb3, TLc2). Images
provided for this publication courtesy of the Freiburg Center for Data Analysis and
Modeling at the Albert-Ludwigs Universitat Freiburg (University of Freiburg),
Freiburg, Germany.















800

700
600
S500

| 400
01
' 300
200
100
0


0.3


* Patients 5 min off
A Patients 3 min off
* Control 5 min off
A Control 3 min off


0.35 0.4 0.45 0.5
Fraction of interstimulation epochs displaying a nonlinear signature
(rejecting HO at 95% significance)


Figure 5-3. Comparison of pulse width parameter to the fraction of epochs displaying a nonlinear
signature in the six patients treated with VNS. The fraction of epochs displaying a
nonlinear signature in control patient using the 3-minute and 5-minute off pseudo
stimulation times are represented by the column of six triangles (3 minute off times)
and six squares (5 minute off times).


100 150 200 250
Interstimulation Epoch


Figure 5-4. Patient A surrogate data analysis results over 24 hours during the interstimulation
epoch. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis.


A
F
E

D, C A
B

A m
------A---- ---------





















2601

20 40 60 80 100 120 140 160 180 200 220
Interstimulation Epoch


Figure 5-5. Patient B surrogate data analysis results over 24 hours during the interstimulation
epoch. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis. The red lines indicate
seizures.


o 15


Interstimulation Epoch


Figure 5-6. Patient C surrogate data analysis results over 24 hours during the interstimulation
epoch. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis.


200
Interstimulation Epoch


5 15










Figure 5-7. Patient D surrogate data analysis results over 24 hours during the interstimulation
epoch. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis.


o 15

20

25


50 100 150 200
Interstimulation Epoch


Figure 5-8. Patient E surrogate data analysis results over 24 hours during the interstimulation
epoch. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis.


20

25


Interstimulation Epoch


Figure 5-9. Patient F surrogate data analysis results over 24 hours during the interstimulation
epoch. Yellow indicates that particular interstimulation epoch abscissaa) for the
channel of interest ordinatee) rejected the null hypothesis.











A -








D


E
02
F 01






Figure 5-10. The fraction of all interstimulation epochs per channel which rejected the null
hypothesis HO using ApEnt for A) patient A, B) patient B, C) patient C, D) patient D,
E) patient E, F) patient F.










Table 5-1. Surrogate analysis results summary for all six patients with the VNS implant.
% of epochs where the ApEnt measure rejected HO


channel
fpl-CPz
fp2-CPz
f3-CPz
f4-CPz
c3-CPz
c4-CPz
p3-CPz
p4-CPz
ol-CPz
o2-CPz
f7-CPz
f8-CPz
t3-CPz
t4-CPz
t5-CPz
t6-CPz
al-CPz
a2-CPz
fz-CPz
cz-CPz
pz-CPz
leye-CPz
reye-CPz
Imn-CPz
rmn-CPz
# epochs


A
* 58.27%
* 61.42%
* 56.30%
* 44.49%
27.56%
29.92%
38.98%
28.35%
27.17%
28.74%
* 57.09%
*66.14%
46.46%
42.13%
24.02%
24.80%
53.54%
44.49%
* 71.65%
60.63%
61.81%
51.97%
53.54%
56.30%
43.70%
254


* denotes focal EEG channel


B
42.37%
* 38.56%
62.71%
* 60.17%
31.36%
77.54%
24.58%
50.00%
39.41%
36.02%
85.17%
* 78.39%
48.31%
78.81%
48.73%
46.19%
56.78%
47.88%
30.08%
51.69%
47.88%
43.64%
61.44%
59.75%
61.02%
236


C
42.15%
40.61%
57.85%
49.04%
52.11%
50.57%
48.66%
41.76%
47.89%
51.34%
35.25%
35.25%
32.95%
* 44.83%
36.78%
* 45.98%
37.16%
51.34%
36.78%
27.59%
21.46%
33.33%
30.65%
25.29%
23.37%
261


150
Interstimulation Epoch


D
* 29.31%
32.76%
* 64.53%
42.12%
30.05%
38.18%
31.53%
39.66%
42.86%
55.17%
* 36.45%
33.50%
39.16%
43.10%
38.42%
50.25%
34.24%
35.22%
44.33%
34.98%
41.63%
41.38%
61.08%
30.79%
27.83%
406


E
38.89%
36.90%
30.95%
36.11%
37.70%
49.21%
32.94%
34.92%
36.11%
44.05%
27.38%
37.70%
39.29%
42.06%
31.35%
33.33%
42.86%
40.87%
40.48%
47.62%
56.35%
42.06%
44.84%
30.16%
39.68%
252


F
36.27%
31.62%
31.13%
35.05%
34.80%
27.45%
19.61%
22.55%
33.33%
33.82%
39.95%
41.67%
* 55.64%
* 54.66%
* 48.77%
* 35.05%
32.60%
32.60%
27.94%
26.72%
22.30%
47.79%
34.31%
42.16%
30.15%
408









Figure 5-11. Control patient (with 5-minute artificial stimulation times) surrogate data analysis
results over 24 hours for all artificial interstimulation epochs. Yellow indicates that
particular interstimulation epoch abscissaa) for the channel of interest ordinatee)
rejected the null hypothesis.


300 350


Figure 5-12. Control patient (with 3-minute artificial stimulation times) surrogate data analysis
results over 24 hours for all artificial interstimulation epochs. Yellow indicates that
particular interstimulation epoch abscissaa) for the channel of interest ordinatee)
rejected the null hypothesis.

Table 5-2. Control patient surrogate analysis results summary.
% of epochs where the ApEnt measure rejected HO
channel Control 5 minute 'off time Control 3 minute 'off time
TBA4 *22.65% 19.41%
TBB6 29.27% 22.85%
HR7 *27.18% *26.54%
TLB2 43.21% 40.05%
TLB3 51.57% 44.72%
TLC2 81.53% 70.02%
# epochs 261 406
denotes focal EEG channel












Ep
VN
on/
EE
fea
cha

EE
fea
cha


EE
fea
cha


och I 1 I
S
off
G
ture for
nnel 1 I
I I
G
ture for
annel 2

I


G
ture for
nnel 26


SEpoch "n"


Second half of an
interstimulation
period
........................


First half of an
interstimulation
period


For the purposes of this study, a full stimulation epoch consists of 30
seconds of stimulation and either a 3 or 5 minute 'off period.

Figure 5-13. Experimental setup for characterizing the temporal evolution EEG dynamics during
interstimulation intervals in patients undergoing VNS therapy for epilepsy. The
double head arrows indicate a statistical comparison is made between the EEG feature
segments represented by the shaded rectangles.

















2UU


A







B







C







D


50 100


Interstimulation Epoch


Figure 5-14. Patient A temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis.


5
10
15
20
25
50 100 150 200 250














A 10

20
25
20 40 60 80 100 120 140 160 180 200 220

5

B 10

20
25
20 40 60 80 100 120 140 160 180 200 220


5
2 10
C
g 15
20
25
20 40 60 80 100 120 140 160 180 200 220





S20

25
20 40 60 80 100 120 140 160 180 200 220
Interstimulation Epoch


Figure 5-15. Patient B temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) Q and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis. The red lines indicate seizures.
















20
25
50 100 150 200 250


6
B 10
15
20
26
50 100 160 200 250



C 10

20
25
50 100 150 200 250



D 10
6
20
26
50 100 160 200 250
Interstimulation Epoch


Figure 5-16. Patient C temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) Q and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis.






























181














A io
15
20
25
50 100 150 200 250 300 350 400


5
B ~10
2 15
20
25
50 100 150 200 250 300 350 400


5

C 10

20
25


5
S10
D
15
20
25
50 100 150 200 250 300 350 400
Interstimulation Epoch


Figure 5-17. Patient D temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis.














5 10
~ 16
20
25
50 100 150 200 250


6
B 10

20


5
50 100 150 200 250



C

20
25
50 100 150 200 250


5
10
D
15
20
25
50 100 150 200 250
Interstimulation Epoch


Figure 5-18. Patient E temporal evolution of dynamics analysis results over 24 hours for A)
ApEnt, B) correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis.














S10
A
5 15
20
25
50 100 150 200 250 300 350 400


6
10
B
c 15
20
26
60 100 160 200 260 300 360 400


6
C 10
15
20
25
50 100 150 200 250 300 350 400


6
2 10

20
25
50 100 150 200 250 300 350 400
Interstimulation Epoch


Figure 5-19. Patient F temporal evolution of dynamics analysis results for A) ApEnt, B)
correlation sum, C) 0, and D) STLmax. Yellow indicates that particular
interstimulation epoch abscissaa) for the channel of interest ordinatee) rejected the
null hypothesis.












2
A 4

6


50 100 150


CB
c


250


CD
u


2UU


25U


D J4
C)


150
Interstimulation Epoch


250


Figure 5-20. Control patient (with 5-minute artificial stimulation times) temporal evolution of
dynamics analysis results for A) ApEnt, B) correlation sum, C) 0, and D) STLmax.
Yellow indicates that particular interstimulation epoch abscissaa) for the channel of
interest ordinatee) rejected the null hypothesis.


I
A 11 1 1 11''110













A


50 100 150 200 250 300 350 400


2
B
4


50 100 150 200 250 300 350 400


2

C 4


50 100 150 200 250 300 350 400


2




50 100 150 200 250 300 350 400
Interstimulation Epoch


Figure 5-21. Control patient (with 3-minute artificial stimulation times) temporal evolution of
dynamics analysis results for A) ApEnt, B) correlation sum, C) 0, and D) STLmax.
Yellow indicates that particular interstimulation epoch abscissaa) for the channel of
interest ordinatee) rejected the null hypothesis.










Table 5-3. Approximate entropy analysis results for VNS patients. Results are expressed as the
fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt
measure.
% of epochs rejecting H1


channel
fpl-CPz
fp2-CPz
f3-CPz
f4-CPz
c3-CPz
c4-CPz
p3-CPz
p4-CPz
ol-CPz
o2-CPz
f7-CPz
f8-CPz
t3-CPz
t4-CPz
t5-CPz
t6-CPz
al-CPz
a2-CPz
fz-CPz
cz-CPz
pz-CPz
leye-CPz
reye-CPz
lmn-CPz
rmn-CPz
# epochs


Patient A
* 40.94%
* 40.94%
* 44.09%
* 40.55%
42.13%
29.53%
27.17%
26.38%
38.98%
38.58%
* 36.22%
* 38.98%
42.91%
33.46%
33.86%
37.80%
40.55%
35.43%
37.40%
29.92%
20.47%
37.40%
32.68%
37.80%
29.92%
254


* denotes focal EEG channel


Patient B
31.78%
* 43.64%
49.58%
* 41.53%
38.14%
33.47%
35.59%
25.42%
41.53%
37.29%
54.24%
* 54.24%
50.85%
43.22%
52.54%
41.10%
50.42%
50.00%
34.32%
23.31%
26.69%
29.24%
37.71%
46.61%
47.88%
236


Patient C
47.13%
43.30%
52.11%
49.43%
42.53%
50.57%
47.89%
50.57%
47.51%
49.81%
50.96%
47.89%
43.30%
* 40.23%
39.08%
* 41.38%
34.10%
41.00%
46.74%
48.28%
36.78%
50.19%
50.96%
44.83%
44.06%
261


Patient D
* 18.23%
20.20%
* 21.67%
24.14%
20.44%
24.14%
22.41%
22.41%
24.14%
22.91%
27.34%
* 25.37%
29.80%
23.65%
20.94%
25.86%
31.53%
28.08%
19.21%
17.49%
21.67%
24.38%
24.88%
24.38%
21.43%
406


Patient E
34.92%
32.94%
31.75%
30.95%
28.57%
29.37%
24.60%
26.59%
24.21%
30.16%
38.49%
37.70%
34.92%
37.70%
32.14%
35.32%
35.71%
36.11%
28.97%
25.40%
18.65%
34.92%
35.71%
40.48%
36.90%
252


Patient F
24.75%
24.26%
25.00%
29.90%
23.53%
26.72%
19.36%
20.59%
22.55%
22.79%
24.51%
28.43%
* 30.39%
* 30.88%
*30.15%
* 28.43%
24.75%
23.28%
21.08%
18.87%
17.65%
17.40%
18.87%
19.85%
21.81%
408











A 05


B


S03


D
02




F
--- I [ '




Figure 5-22. Approximate entropy analysis results for VNS patients. Results are expressed as the
fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt
measure.

Table 5-4. Approximate entropy analysis results for the control patient. Results are expressed as
the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt
measure.
% of epochs rejecting H1
channel Control 5 minute 'off time Control 3 minute 'off time
TBA4 22.65% 18.18%
TBB6 25.44% 17.94%
HR7 23.34% 15.23%
TLB2 20.91% 17.69%
TLB3 23.69% 19.66%
TLC2 14.63% 13.02%
TBA4 261 406
* denotes focal EEG channel










Table 5-5. Correlation sum analysis results for VNS patients. Results are expressed as the
fraction of epochs in each channel which rejected hypothesis H2 using the correlation
sum measure.
% of epochs rejecting H2


channel
fpl-CPz
fp2-CPz
f3-CPz
f4-CPz
c3-CPz
c4-CPz
p3-CPz
p4-CPz
ol-CPz
o2-CPz
f7-CPz
f8-CPz
t3-CPz
t4-CPz
t5-CPz
t6-CPz
al-CPz
a2-CPz
fz-CPz
cz-CPz
pz-CPz
leye-CPz
reye-CPz
Imn-CPz
rmn-CPz
# epochs


Patient A
* 25.98%
* 26.38%
* 19.29%
* 18.11%
19.29%
15.75%
13.39%
12.99%
15.35%
17.32%
* 16.93%
* 16.14%
22.44%
16.54%
15.35%
11.81%
11.81%
16.54%
22.05%
17.32%
14.57%
14.96%
16.54%
13.78%
12.60%
254


Patient B
18.64%
* 16.10%
12.71%
* 10.17%
13.98%
15.25%
11.86%
8.47%
8.90%
8.47%
9.75%
* 9.32%
10.59%
6.78%
10.17%
9.32%
13.56%
13.56%
12.71%
8.05%
7.63%
13.56%
12.71%
7.20%
8.47%
236


* denotes focal EEG channel


Patient C
34.10%
29.12%
24.90%
26.05%
21.84%
19.92%
14.94%
13.79%
13.03%
13.79%
31.80%
29.50%
22.22%
* 21.07%
13.41%
* 17.24%
23.37%
22.22%
25.67%
11.11%
9.96%
27.97%
32.57%
21.84%
24.90%


Patient D
* 12.07%
12.81%
* 9.85%
12.81%
10.59%
12.07%
11.58%
12.32%
11.82%
14.29%
* 11.82%
12.32%
11.08%
13.30%
9.85%
12.07%
11.08%
15.27%
11.33%
9.61%
11.33%
10.10%
13.55%
9.36%
11.58%
406


Patient E
20.24%
19.84%
18.65%
18.25%
17.86%
18.25%
15.48%
15.87%
13.49%
11.90%
21.43%
18.65%
18.65%
21.83%
12.30%
21.83%
21.03%
18.25%
17.46%
18.65%
15.08%
17.06%
17.06%
17.46%
16.27%
252


Patient F
10.54%
8.82%
11.52%
11.52%
10.54%
9.31%
9.80%
9.31%
10.29%
13.73%
10.54%
10.29%
* 12.25%
* 11.52%
*9.31%
* 8.33%
10.29%
11.03%
12.01%
12.25%
6.13%
10.05%
8.33%
11.03%
9.56%
408













B


C


D


E


F

0^ 0^ 0^ 0^ 0< C, C, j 0 j 0 j 0 0 C) C) cj C, C 1


Figure 5-23. Correlation sum analysis results for VNS patients. Results are expressed as the
fraction of epochs in each channel which rejected hypothesis H2 using the correlation
sum measure.

Table 5-6. Correlation sum analysis results for the control patient. Results are expressed as the
fraction of epochs in each channel which rejected hypothesis H2 using the correlation
sum measure.
% of epochs rejecting H2
channel Control 5 minute 'off time Control 3 minute 'off time
TBA4 *11.50% *8.60%
TBB6 10.80% 8.85%
HR7 *8.71% *8.11%
TLB2 9.76% 7.13%
TLB3 8.71% 8.35%
TLC2 5.57% 7.37%
# epochs 261 406
denotes focal EEG channel









Table 5-7. Mean angular frequency in phase space analysis results for VNS patients. Results are
expressed as the fraction of epochs in each channel which rejected hypothesis H3 using the 0
measure.
% of epochs rejecting H3
channel Patient A Patient B Patient C Patient D Patient E Patient F
fpl-CPz *38.19% 30.51% 37.93% 23.89% 39.68% 20.10%
fp2-CPz 35.83% 22.46% 38.70% 22.66% 32.94% 24.02%
f3-CPz 29.53% 26.27% 41.00% 24.88% 34.92% 19.36%
f4-CPz 27.95% 27.12% 41.76% 23.65% 33.73% 21.32%
c3-CPz 30.31% 26.27% 38.70% 22.17% 36.51% 18.38%
c4-CPz 34.25% 35.17% 31.80% 26.11% 41.67% 19.61%
p3-CPz 31.89% 27.54% 35.25% 27.83% 33.33% 17.89%
p4-CPz 26.38% 22.88% 32.95% 22.91% 33.73% 18.14%
ol-CPz 29.53% 23.73% 39.46% 25.62% 28.97% 19.12%
o2-CPz 29.92% 20.34% 34.87% 26.85% 33.33% 21.81%
f7-CPz 34.25% 25.00% 43.68% 24.38% 33.73% 19.12%
f8-CPz *31.10% 23.73% 39.46% 27.34% 35.32% 20.10%
t3-CPz 39.37% 24.58% 41.00% 23.40% 38.10% 19.85%
t4-CPz 29.92% 22.46% 31.42% 27.59% 34.13% *21.08%
t5-CPz 28.74% 25.00% 31.42% 26.35% 26.59% *21.08%
t6-CPz 25.59% 21.61% 31.42% 22.41% 37.30% 20.098%
al-CPz 24.80% 19.92% 31.03% 26.60% 31.35% 18.87%
a2-CPz 27.56% 22.03% 31.80% 30.30% 32.54% 18.38%
fz-CPz 27.95% 36.02% 39.46% 23.40% 34.52% 20.83%
cz-CPz 29.53% 23.73% 40.61% 20.94% 30.16% 21.57%
pz-CPz 31.10% 24.58% 34.48% 25.37% 29.37% 19.61%
leye-CPz 37.80% 29.66% 42.53% 26.60% 34.92% 20.83%
reye-CPz 32.68% 28.81% 37.93% 26.85% 31.35% 21.57%
Imn-CPz 32.68% 23.31% 34.10% 19.70% 34.92% 18.38%
rmn-CPz 29.13% 22.88% 37.93% 25.12% 30.16% 23.77%
# epochs 254 236 261 406 252 408
denotes focal EEG channel











A -


B





D
02










Figure 5-24. Mean angular frequency in phase space analysis results for VNS patients. Results
are expressed as the fraction of epochs in each channel which rejected hypothesis H3
using the Q measure.









Table 5-8. Mean angular frequency in phase space analysis results for control patient. Results are
expressed as the fraction of epochs in each channel which rejected hypothesis H3
using the Q measure.
% of epochs rejecting H3
channel Control 5 minute 'off time Control 3 minute 'off time
TBA4 12.20% *7.13%
TBB6 13.59% 8.60%
HR7 9.41% 8.85%
TLB2 8.01% 7.13%
TLB3 8.36% 6.88%
TLC2 11.50% 9.09%
# epochs 261 406
denotes focal EEG channel










Table 5-9. Short-term maximum Lyapunov exponent analysis results for VNS patients. Results
are expressed as the fraction of epochs in each channel which rejected hypothesis H4
using the STLmax measure.
% of epochs rejecting H4


channel
fpl-CPz
fp2-CPz
f3-CPz
f4-CPz
c3-CPz
c4-CPz
p3-CPz
p4-CPz
ol-CPz
o2-CPz
f7-CPz
f8-CPz
t3-CPz
t4-CPz
t5-CPz
t6-CPz
al-CPz
a2-CPz
fz-CPz
cz-CPz
pz-CPz
leye-CPz
reye-CPz
Imn-CPz
rmn-CPz
# epochs


Patient A
*29.13%
* 28.35%
*29.13%
* 24.41%
24.80%
21.26%
19.69%
17.72%
23.23%
20.47%
* 24.41%
* 26.77%
40.94%
29.53%
25.20%
17.32%
24.41%
30.71%
24.41%
15.75%
21.65%
26.38%
23.23%
16.93%
20.08%
254


Patient B
30.08%
* 32.20%
27.54%
* 15.25%
15.25%
14.41%
16.10%
15.25%
19.07%
16.95%
22.88%
* 30.51%
27.12%
15.25%
19.92%
15.68%
31.78%
28.81%
19.07%
15.25%
15.25%
23.73%
19.07%
17.80%
20.76%
236


Patient C
40.23%
33.72%
35.25%
37.55%
44.06%
39.85%
35.63%
37.55%
35.25%
31.80%
42.53%
37.16%
43.68%
* 40.61%
32.95%
* 38.70%
32.95%
38.31%
25.29%
26.44%
25.67%
44.83%
38.31%
34.87%
30.27%
261


Patient D
* 18.23%
16.50%
* 17.49%
15.52%
14.78%
16.75%
16.26%
16.01%
15.52%
17.00%
* 17.73%
17.00%
24.88%
20.94%
17.49%
16.26%
24.88%
21.18%
18.97%
11.82%
14.04%
14.29%
18.97%
12.81%
14.04%
406


Patient E
31.35%
29.37%
28.97%
22.22%
26.98%
23.81%
19.84%
19.84%
21.43%
25.40%
28.17%
19.84%
26.98%
27.78%
23.41%
22.62%
30.16%
17.06%
26.19%
21.83%
25.79%
25.40%
19.05%
19.84%
15.87%
252


Patient F
17.65%
17.89%
15.93%
19.12%
18.63%
12.50%
10.54%
11.27%
13.48%
11.76%
13.97%
15.69%
* 14.95%
* 21.57%
* 20.34%
* 15.93%
13.24%
12.25%
10.54%
10.78%
11.52%
15.20%
12.50%
12.01%
9.56%
408


* denotes focal EEG channel











A 0-

B







E

F





Figure 5-25. Short-term maximum Lyapunov exponent analysis results for VNS patients. Results
are expressed as the fraction of epochs in each channel which rejected hypothesis H4
using the STLmax measure.












Table 5-10. Short-term maximum Lyapunov exponent analysis results for the control patient.
Results are expressed as the fraction of epochs in each channel which rejected
hypothesis H4 using the STLmax measure.
% of epochs rejecting H4
channel Control 5 minute 'off time Control 3 minute 'off time
TBA4 *26.13% 20.88%
TBB6 32.06% 26.78%
HR7 *27.87% *22.11%
TLB2 21.60% 14.25%
TLB3 19.86% 16.95%
TLC2 15.68% 15.72%
# epochs 261 406
denotes focal EEG channel

3
-A C
S2.5 A
SA D
S2 A *A m Patients 5 min off
A 0 U B A Patients 3 min off
1.5 -A Control 5 min off
F A Control 3 min off
= 1
O E
A 0 A E
0.5 A I
0 0.1 0.2 0.3 0.4 0.5
Fraction of epochs showing significant temporal
variation


Figure 5-26. ApEnt results and the corresponding output current setting. Results are expressed as
the fraction of interstimulation epochs showing significant temporal variation.















* Patients 5 min off
A Patients 3 min off
* Control 5 min off
A Control 3 min off


Fraction of epochs showing significant temporal
variation


Figure 5-27. Correlation sum results and the corresponding output current setting. Results are
expressed as the fraction of interstimulation epochs showing significant temporal
variation.


AU C


A A


A F B E

A A

0 0.1 0.2 0.3 0.4 0.

Fraction of epochs showing significant temporal variation


m Patients 5 min off
A Patients 3 min off
* Control 5 min off
A Control 3 min off


Figure 5-28. Q results and the corresponding output current setting. Results are expressed as the
fraction of interstimulation epochs showing significant temporal variation.


C
AU
A D A
A U AF


A B UE



A 0
A












A C
< 2.5 A -
D A
2 A Patients 5 min off
A A Patients 3 min off
1.5 A Control- 5 min off
A B E A Control 3 min off
0 1 A
F A
0.5 A,
0.1 0.2 0.3 0.4 0.5
Fraction of epochs showing significant temporal variation


Figure 5-29. STLmax results and the corresponding output current setting. Results are expressed
as the fraction of interstimulation epochs showing significant temporal variation.








































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CHAPTER 6
A NOVEL GENERALIZED ABSENCE SEIZURE DETECTION ALGORITHM

Absence epilepsy makes up about 8% of child epilepsy cases with peak occurrence

between 6-7 years of age (Berkovic, 1996). Absence seizures are clinically characterized by

brief, transient loss of awareness, responsiveness, and memory. These paraxoysmal discharges

have a sudden onset, are often less than 5 seconds in duration, cease abruptly without postictal

effects and can occur multiple times per day. Absence seizures are generalized with regular and

symmetrical 2.5-3.5 Hz SWDs (Panayiotopoulos et al., 1994). Figure 6-1 shows an example of

an electrographic absence seizure.

The antiepileptic drugs valproic acid and ethosuximide are the most commonly-used drugs

for treating absence epilepsy. For additional information on absence epilepsy, see chapter 2.

Seizure detection is an important procedure for the treatment of epilepsy. In particular,

there are areas wherein seizure detection can benefit epilepsy treatment; rapid seizure annotation

and online real-time EEG analysis. Seizure detection algorithms can greatly improve the rate at

which physicians analyze EEG recordings by providing a tool to help point out EEG waveforms

which are likely to be epileptiform discharges. Such an algorithm can improve the efficiency of

health care for epilepsy treatment.

The other popular application of seizure detection algorithms is for online real-time

analysis. Such analysis is useful in the research field for enhancing the understanding of how

EEG activity correlates to the clinical status of the patient or for cognitive testing in animal

models of epilepsy. For some epilepsy variants, such as mesial temporal lobe epilepsy, seizure

detection may provide a basis for an implantable seizure control device (e.g. utilizing a drug

pump and/or neural stimulation apparatus). For generalized absence epilepsy, it is possible that









someday an online real-time absence seizure detection algorithm may be integrated with scalp-

EEG recordings as part of medical checkups in patients with generalized absence epilepsy.

In addition to seizure detection, such an algorithm can be extended to perform seizure

stratification and provide a histogram of seizure count versus seizure duration. The ability to

automatically stratify seizures may provide additional useful information for evaluating

therapeutic effect (e.g. compare the seizure stratification histogram profile before and after

therapeutic intervention).

For these reasons, the purpose of this study is examine a novel method for expediting

detection and stratification of SWDs such as those found in generalized absence epilepsy.

Methods

Previous automated SWD detection algorithms typically relied on thresholding methods

and performed well in animal seizure models (Westerhuis et al. 1996; Fanselow et al., 2000; Van

Hese et al., 2003).

Energy Method for SWD Detection

One method calculates the signal energy (Van Hese et al., 2003) and establishes a

threshold energy level which designates spike and wave activity or non-spike and wave activity.

In each window, the signal energy is calculated as

L-1
E(k)= x (n + (k- )S) (6-1)
n=0

where a detection is signified if the calculated energy exceeds a chosen threshold value for four

consecutive windows.


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Fanselow Method for SWD Detection

The Fanselow method (Fanselow et al., 2000) establishes a voltage threshold which allows

classification of SWDs. The method is based on the maximum absolute value of the EEG

amplitude within a window

A(k)= max x(n + (k i)S). (6-2)
n=0, ,L-1

A threshold is set for each subject. If three consecutive windows are above the threshold, a

SWD detection is made.

Westerhuis Method for SWD Detection

The Westerhuis method (Westerhuis et al., 1996) estimates the first derivative of the EEG

signal which is referred to as the steepness of signal. The maximum value of this steepness in

consecutive, non-overlapping windows is evaluated as

D(k)= max d(n+(k-1)S) (6-3)
n=0, ,L-1

where

d(n) x(n+)- x(n) (6-4)

A positive detection is made if D exceeds a certain threshold value in four consecutive windows.

The threshold is automatically determined on the basis of the EEG during wakefulness. This

method showed strong performance in Genetic Absence Epilepsy Rats from Strasbourg

(GAERS).

This study aims to address improvements in the following areas; minimize detection lag

(which is critical for online utilization of such a seizure detection device), decreasing window

size (to help increase detection time resolution), increasing robustness to noise, and simplified

detection calibration. For these reasons, supervised machine learning algorithms were utilized









with the intention of providing a robust seizure detector. The two features selected for this

algorithm are Teager-Kaiser energy and dynamic time warping distance.

Dynamic Time Warping

Dynamic time warping (DTW) is one of the most well-studied temporal pattern similarity

measures (Rabiner et al., 1978). This method utilizes a dynamic programming approach to align

a test time series to a template time series and provides an alignment distortion measure to

ascertain pattern similarity.

For two time series X and Y of equal length X = Y = n, pattern similarity is established

by aligning time series X with time series Y using the minimum computed alignment

distortion Dag, (X, Y). The distortion path is obtained by warping time for each signal such that

the minimum alignment distance between the two signals is achieved. This study applies the

DTW measure to two EEG signals of equal length though the signals do not need to be the same

length.

DTW has been used extensively in biological applications such as ECG analysis (Jen and

Hwang, 2007; Kotas, 2008), EEG spiking pattern recognition (Chi et al., 2007), analysis of

event-related potentials (Casarotto et al., 2005), fingerprint recognition (Kovacs-Vajna, 2000),

and medical imaging reconstruction (Okumura et al., 2007). The DTW measure has

demonstrated utility as a kernel function for support vector machine based seizure prediction

algorithms in temporal lobe epilepsy (Chaovalitwongse and Pardalos, 2008).

The minimum DTW distance can be obtained using the following dynamic programming

technique. First, an n x n alignment array is generated where each element of the array represents

a distance metric for all combinations of points between the two signals. In this array the (i,j)th

element is the distance between points x, and y. Euclidean distance d(x,,y )= ( y )2 is


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typically used as the distance measure. A warp path W = w,,..., wK is then constructed where K

is the length of the warp path for which max(XI, Y)<< K < X + YI. Element k of the warping

path represents Element k of the warp path represents a matching point w = (i, j) of the two

time series, where (i,j) corresponds to index i of time series X and index of time series Y. A

warping path must begin at the first sample of both time series, w, = (1,1) and must finish at the

last sample of both time series, w, = (n,n). An additional constraint requires the warping path

indices i andj to increase monotonically. That is, wk = (i,j) and wk = (',j), where

i < i < i +1 and j < j < j +1. The optimal warp path possesses the minimum warping cost

defined as

1 K)
DIg, (X, Y)= minm d(w,, k). (6-5)

This problem can be approached from a dynamic programming perspective where the path

is advanced by one unit on the i axis, one unit on thej axis, or both. Thus, this approach only

requires evaluation of cumulative distance found in adjacent elements,


D(i,j)= d(x,,x,)+min, D(i-1, j) (6-6)
D(i 1, 1)

Teager-Kaiser Energy

In 1990, Kaiser first derived Teager's nonlinear energy algorithm in discrete time domain

to calculate the energy of a sound (Kaiser, 1990). The Teager-Kaiser energy (TKE) operator has

demonstrated sensitive to both amplitude and frequency changes in time series signals. This

measure has demonstrated utility feature for the detection of seizures and high frequency


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epileptiform activity (Zaveri et. al., 1993; Smart et. al., 2005; Gardner et. al., 2006). This study

utilizes the mean value of the TKE operator across a window,

1 N1[
TKE(X) = [x(k)2 X(k- 1)X(k +1) (6-7)
N k=2

where N is the length of the window of interest.

Empirical Study

In order to investigate the possibility of seizure detection and stratification, two

experiments are presented, each classifying a different subset of the seizure:

* Separate the beginning of each seizure from randomly-selected non-seizure segments

* Separate the end of each seizure from randomly-selected non-seizure segments.

Separating the beginning of the seizure from non-seizure segments (experiment one) tests

the seizure detection abilities of the detector whereas distinguishing the end of a seizure from

non-seizure segments (experiment two) is a critical task in seizure stratification. These two

experiments provide an initial framework for testing the SVM classifier's ability to stratify

generalized SWDs.

This empirical study is motivated by an underlying hypothesis that SVM's are capable of

distinguishing neural states (seizure and non-seizure) in a newly-diagnosed patient with typical

absence seizures. The signal features consist of the DTW distances between a template SWD

signal the test window to be classified, both of which are 0.3 seconds in duration. This section

describes the EEG data acquisition, data sampling and feature extraction, SVM training and

testing, and results.

EEG Data Acquisition

Approximately 24 hours of scalp EEG data were acquired from a SleepMed DigiTrace

ambulatory EEG recording device. The data were acquired at 200 Hz with an input range of 0.6


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mV with built-in filter of 0.5-70 Hz. A bipolar, longitudinal, chain electrode recording montage

was employed to provide 16 EEG channels (Fpl-F3, F3-C3, C3-P3, P3-01, Fp2-F4, F4-C4, C4-

P4, P4-02, Fpl-F7, F7-T3, T3-T5, T5-01, Fp2-F8, F8-T4, T4-T6, T6-02) as well as two

auxiliary channels which were not utilized. This EEG study utilized the F3-C3 and F4-C4

channels because provide high-quality representations of the SWDs yet are located reasonably

far away from facial muscles. The patient underwent 93 seizures during the -24 hour

continuous EEG recording. Seizure times were verified by a board-certified clinical

electroencephalographer.

Data Sampling and Feature Extraction

Each data sample consists of extracted features from an EEG window one second in

duration. Within the one-second data sample window, a sub-window of 0.3 seconds in duration

is advanced with 50% overlap from the start of the data sample window to the end of the data

sample window (providing 5 sub-windows and thus 5 features per data sample window per EEG

channel). Thus for channels F3-C3 and F4-C4 there are ten features representing each data

sample window.

For each sub-window within the data sample, the DTW similarity feature is obtained via

comparison with an archetypical SWD template. Figures 6-2 and 6-3 illustrate the DTW

distance metric in this application.

The study uses 93 SWD templates (one selected from each seizure) which are centered on

the spike and 0.3 seconds in duration. SWD templates are reassigned randomly such that no

seizure uses its own template for feature extraction.

The seizure class consists of data sample windows from all 93 seizures. The non-seizure

class consists of a total of 93 non-seizure data sample windows randomly selected from -24 hour

continuous EEG recording with the following constraints:


205









* Must be at least 60 seconds away from any seizure onset or offset

* Must be at least 0.1 seconds away from another non-seizure sample

The training dataset consists of the 93 seizure and 93 non-seizure data sample windows.

SVM Training and Testing

The soft-margin SVM classifier with a RBF kernel is applied to this problem based on

success in other neural state classification problems (Kaper et. al., 2004; Acir and Giizelis, 2005;

Bewernitz et. al., 2006; Lehmann et. al., 2007; Seref et al., 2006). A range of SVM parameters

which demonstrated satisfactory results in similar EEG classification studies were applied to this

study. Thus, each SVM cycle was performed for all nine combinations of cost=10,100,1000

(Kaper et al., 2004; Acir and Giizelis, 2005) and the RBF parameter sigma=20,40,60 (Kaper et.

al., 2004; Lehmann et al., 2007).

SVM training is performed using a 10-fold cross validation scheme. This scheme employs

a resampling technique in which the seizure and non-seizure classes are first randomly shuffled.

Next, 10 % (-9 samples) of the shuffled seizure class and 10% (-9 samples) of the shuffled non-

seizure class are extracted (individually for each class) and combined to form the test set. In

general, SVM training is optimal for training datasets with equal numbers of data points from

each class. Otherwise, the classifier can be biased towards the class which had more training

points.

The remaining 90% of each class is used to train the SVM classifier which is then tested on

the extracted testing dataset. Upon testing the SVM, the test dataset is replaced in the shuffled

training data and the succeeding 10% block of each shuffled class is extracted to form the next

test set. This validation scheme repeats until the last 10% block of each shuffled class is

extracted and tested. This study repeats the sampling, feature extraction, resampling, training

and testing cycle 1000 times.


206









Detector Performance Evaluation

The detection sensitivity and specificity are used to evaluate the performance of the SVM

seizure detector. This involves categorizing the classification results into one of four possible

outcomes:

* True positives (TPs) refer to the correct classification of seizure segment

* True negatives (TNs) refer to the correct classification of a non-seizure segment

* False positives (FPs) refer to the incorrect classification of a non-seizure segment as a
seizure

* False negatives (FNs) refer to the incorrect classification of seizure segment as a non-
seizure

The four possible detection outcomes may be illustrated in the context of figure 6-4. A

classification result is considered a TP if a seizure EEG sample is classified as a seizure sample.

A classification result is considered a TN if a non-seizure EEG sample is classified as a non-

seizure sample. A classification result is considered a FP if a non-seizure EEG sample is

classified as a seizure sample. Finally, a classification result is considered a FN if a seizure EEG

sample is classified as a non-seizure sample.

The sensitivity and specificity measures often used for evaluating detector performance

can be derived from these four outcome quantities. Sensitivity is the fraction of positive samples

that are classified as positive:

TP
Sensitivity = (6-8)
TP + FN

where 'positive' refers to the seizure class. Specificity refers to the fraction of negative samples

that are classified as negative:

TN
Specificity = (6-9)
TN + FP


207









where 'negative' refers to the non-seizure class.

Results

The mean value of sensitivity and specificity are reported for 100 SVM detection trials,

where each trial underwent 10-fold cross validation for one of the nine combinations of SVM

parameters. The results for experiment one, seizure detection of the first second of each seizure

are shown in table 6-1. Results from experiment two, seizure stratification experiment

performing detection on the last second of each seizure are summarized in table 6-2.

Discussion

As is shown in table 6-1 and figures 6-5, 6-6, 6-7, the SVM classifier's overall best

performance is experiment one's application where the SVM is function as a seizure-onset

detector (classifying the first second of each seizure). This result makes sense in comparison

with experiment two where the last second of the seizure is classified as a first step towards a

seizure stratification application (figures 6-8, 6-9, 6-10). The beginnings of the seizures appear

more visually similar to one another than the ends of the seizures. Even still, the performance of

the classifier in the experiment two setup demonstrated high sensitivity and specificity for

numerous parameter combinations.

The observation that classification is less affected by SVM parameters in experiment one

compared to experiment two is a reasonable phenomena. Due to stronger

electroencephalographic similarity among various seizures at onset compared to offset, then the

beginning of the seizures may be more regular in feature space than the seizure offset. Thus, the

alterations in SVM parameters do not seem to have as large of an effect on the results of

experiment one as with experiment two. In particular, the classifier varied more with changes in

cost for experiment two than experiment one, which could be due to a loss of generality resulting

from "over fitting" the more variant seizure offset period.


208









These results show promise for the SVM application to seizure detection and stratification.

Such a tool may provide benefit to clinicians and researchers by providing a means to rapidly

annotate as well as provide a clinically interesting measure of drug effect on a histogram of

seizure durations. Thus, this line of work may lead to a greater understanding of the therapeutic

effects of AEDs.

Future studies will provide a more comprehensive evaluation of features. While the DTW

measure performed well, other similarity measures (such as similarity index) may be worth

implementing. In addition, adding more EEG channels may improve classification performance

though channel addition imposes a computational burden increase. These results should be

validated in additional patients. Finally, an important future step is to implement this algorithm

in a pseudo-online fashion to assess the robustness to noise. While SVMs provide exceptional

generalization abilities, a sliding window classifier will provide an interesting assessment of how

the classifier copes with the challenges of real-time EEG acquisition.

An expansive review article regarding support vector machines in neuroscience

applications was accepted for publication under the title "support vector machines in

neuroscience" with authors Onur Seref, O. Erhun Kundakcioglu, and Michael Bewemitz (Seref

et al., 2007).


209




































Figure 6-1. Approximately 6 seconds of scalp-EEG demonstrating the 2.5-3.5 Hz spike-wave
discharge that defines an electrographic absence seizure (data provided courtesy of
Dr. Gregory Holmes).


210































0 10 20 30 40 50 60

Figure 6-2. DTW comparison of two different SWD segments. The top signal is a 300 ms SWD
segment. Bottom signal is a 300 ms segment of a different SWD. The DTW distance
is about 2.4 x 107.

































0 10 20 30 40 50 60



Figure 6-3. DTW comparison of a SWD segment with a random interictal segment. Top signal is
a 300 ms EEG segment of a SWD. Bottom signal is 300 ms of interictal EEG. The
DTW distance is about 5.1 x 107.


Reality
/---~A--


Seizure


Non-seizure


Prediction


Seizure

Non-seizure


Figure 6-4. Seizure classification evaluation framework.


212










Table 6-1. Classification performance using the first second of each seizure.


Sigma
20
20
20
40
40
40
80
80
80


Cost
10
100
1000
10
100
1000
10
100
1000


Sensitivity
97.11%
96.45%
96.37%
97.18%
96.56%
96.19%
97.10%
96.82%
96.04%


Specificity
96.94%
96.46%
96.43%
97.04%
96.49%
96.37%
97.04%
96.62%
96.31%


Mean
97.02%
96.45%
96.40%
97.11%
96.53%
96.28%
97.07%
96.72%
96.18%


Table 6-1. Classification performance using the last second of each seizure.


Sigma
20
20
20
40
40
40
80
80
80


Cost
10
100
1000
10
100
1000
10
100
1000


Sensitivity
94.85%
91.98%
90.25%
95.04%
93.03%
89.91%
94.93%
93.86%
90.74%


Specificity
93.46%
93.10%
92.07%
93.34%
93.27%
92.13%
93.29%
93.29%
92.63%


Mean
94.16%
92.54%
91.16%
94.19%
93.15%
91.02%
94.11%
93.58%
91.69%


213









Sigma = 20
Cost= 10


Sigma = 20
Cost= 100


Sigma = 20
Cost= 1000


100.00%
90.00%
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%


Figure 6-5. Seizure detection performance for RBF
each seizure.


* Sz Detection
* NSz Detection


parameter sigma=20 using the first second of


Sigma = 40
Cost= 10


Sigma = 40
Cost= 100


Sigma = 40
Cost= 1000


Sz NSz Sz NSz Sz NSz


* Sz Detection
* NSz Detection


Figure 6-6. Seizure detection performance for RBF parameter sigma=40 using the first second
of each seizure.


214


Sz NSz Sz NSz Sz NSz


100.00%
90.00%
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%










Sigma = 80
Cost = 10


Sigma = 80
Cost = 100


Sigma = 80
Cost = 1000


100.00%
90.00%
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%


Sz NSz Sz NSz Sz NSz


Figure 6-7. Seizure detection performance for RBF
each seizure.


* Sz Detection
* NSz Detection


parameter sigma=80 using the first second of


Sigma = 20
Cost= 10


Sigma = 20
Cost= 100


Sigma = 20
Cost= 1000


100.00%
90.00%
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%


Sz NSz Sz NSz


Figure 6-8. Seizure detection performance for RBF
each seizure.


NSz
NSz


* Sz Detection
* NSz Detection


parameter sigma=20 using the last second of


215









Sigma = 40
Cost = 10


Sigma = 40
Cost= 100


Sigma = 40
Cost = 1000


100.00%
90.00%
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
fn nno/-


Sz NSz Sz NSz

Figure 6-9. Seizure detection performance for RBF
each seizure.

Sigma = 40 Sigma =40
Cost = 10 C.nst = 100


* Sz Detection
* NSz Detection


S NSz


parameter sigma=40 using the last second of


Sigma = 40
Cost = 1000


100.00%
90.00%
80.00%
70.00%
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%


Sz NSz Sz NSz


S NSz


Figure 6-10. Seizure detection performance for RBF parameter sigma
of each seizure.


* Sz Detection
* NSz Detection









=80 using the last second


216


L h -i


V 10 m = 1









CHAPTER 7
DISCUSSION AND CONCLUDING REMARKS

Epilepsy is a disorder of the brain which is characterized by intermittent synchronized

discharges of large populations of neurons. This disorder can greatly impact a patient's life in

numerous ways including financial, social, professional, and psychiatric effects. While AED

therapy may help keep seizures at bay in some patients others are not so fortunate. In the last few

decades, savvy researchers have taken advantage of the rapid progression of computer

technology, biomaterials, signal analysis advances and medical knowledge advancement to

extract relevant EEG features in order to enhance epilepsy treatment.

Computational neuroscience is an exciting frontier which is providing numerous options

for addressing neurological disorders which may have been inconceivable decades ago. The

ability to map the brain's states in terms of the status of a dynamic neurologic disorder will likely

be a highly sought-after research goal for years to come. This dissertation has helped provide

preliminary data mining and dynamical EEG analyses to help uncover patterns which may be

related to stimulation parameters and ultimately improve our understanding of the mechanisms

that produce the VNS therapeutic effect. In addition, a study outlining a novel generalized spike

wave detection algorithm was outlined here as well. These projects aim towards creation of

bedside and/or implantable real-time seizure control devices.

Towards Real-Time EEG Analysis Tools for the Bedside and Implantation

The exciting progress made in the characterization of sophisticated disease and disorders

modeling schemes is part of the driving force this research. The characteristics of the class of

disorders known as dynamic disorders provide an interesting framework to approach the problem

of improving existing and creating new therapeutic approaches. This perspective treats such

disorders as deviations from a range of healthy dynamics in the underlying physiologic control


217









systems. Such a perspective implies therapeutic approaches which involve a fusion of medicine,

biology, and engineering. Numerous researchers are investigating the possibility of applying a

systems control approach to the epileptic brain in order to reduce the burden of epileptic seizures.

Some of the studies presented in this dissertation are geared towards such an approach and aim to

improve the VNS therapy modality.

Patients with newly-implanted VNS systems undergo a period often lasting several months

of sub-optimal therapy. During this period, patients may need to undergo numerous visits to the

doctor's office in order to fine-tune the stimulation parameters for clinical efficacy and tolerance.

Such a process results in increased medical treatment costs and all the while the patients may be

at a higher risk to seizures due to sub-optimal stimulation parameters. One of the goals of the

work presented it to examine the possibility of an EEG marker of optimal VNS therapeutic

efficacy to help expedite the process of tuning parameters in newly-implanted patients. The

main focus of the research on the VNS data is to characterize EEG characteristics in numerous

VNS patients in order to assess any relationships to stimulation parameters. If such a relationship

can be established and if the effects could then be geared towards a final outcome, then such

EEG characteristics may find use in a bedside device for rapid VNS calibration or even in an

implantable control system for optimal VNS therapy. The studies presented in chapter four

represent data mining approaches to characterizing such EEG effects.

Data Mining Approaches to Characterizing EEG Patterns

Data mining tools have demonstrated an extensive capacity to discover patterns in

biological datasets including EEG signals. Data mining is the process of applying algorithms to

extract patterns in large datasets. While the human eye is often the best pattern detector of all,

data mining algorithms can work on exceedingly large datasets and examine complex

multidimensional datasets. One of the most attractive features of data mining tools are their


218









ability to perform clustering data subsets according to inherent similarities or in a supervised

manner. For the purpose of characterizing EEG patterns in patients undergoing VNS therapy for

epilepsy, data mining methods provide a useful tool for elucidating preliminary patterns which

incorporate an expansive representation of features from all channels.

The biclustering experiment provided a characterization of the EEG patterns which may be

related to VNS therapy. The observations were based on patterns of the STLmax measure, which

assumes a chaotic framework and provides a measure of the sensitivity of the signal to initial

conditions. Though the brain's behavior may not always be consistent with a low-dimensional

chaos model, the chaoticity measure has provided an ability to classify neural states in epilepsy

(e.g. interictal or far from a seizure, preictal or seizure imminent, ictal or during a seizure, and

postictal or the period of altered consciousness following a seizure). Thus, the measure was

selected as a candidate for detecting EEG patterns which may be related to VNS therapy. The

study demonstrated separability between the VNS on and off states for which all of patient A's

electrodes contributed to and only a few frontal and temporal electrodes in patient B contributed

to. The biological relevance of these results may be related to study which discovered that

VNS-induced acute suppression of epileptiform activity in a hippocampal depth electrode

(Olejniczak et al., 2001). Though the study by Olejniczak et al. utilized depth electrodes, it is

possible that scalp EEG recordings may display some manifestation of such an EEG effect

observed at a hippocampal depth electrode. From this perspective, perhaps the STLmax

behavioral differences between patients A and B are associated with enhanced suppression of

epileptiform activity in patient A compared to patient B. An interesting future application of

biclustering would be to examine the EEG effects during non-stimulation in an unsupervised

manner. Such an experiment would provide a highly objective method to determine spatio-


219









temporal patterns of EEG features. Based on the results of chapter 5, future experiments should

include both linear and nonlinear features to help ensure proper characterization of the wide

range of EEG dynamical behavior patterns observed during these studies. This work was

published in the paper "Biclustering EEG data from epileptic patients treated with vagus nerve

stimulation", authored by Stanislav Busygin, Nikita Boyko, Panos Pardalos, Michael Bewernitz,

and Georges Ghacibeh (Busygin, 2007).

The next experiment examined the patterns of the raw EEG behavior in feature space using

support vector machines. The accuracy at which the SVM's could separate the raw EEG between

two adjacent EEG segments, a reference segment during stimulation and successive non-

overlapping windows was interpreted as a robust measure of EEG similarity (or dissimilarity)

and compared with stimulation parameters. The study determined observed a potential

covariation between the EEG and the pulse width and stimulation frequency parameters.

A study by Mu et al. showed that a 250 ps VNS pulse width caused reduced blood flow in

significantly more brain regions (e.g. hippocampus, sup. temp. lobe) than 500 pts (2004).

Perhaps these regions may be responsible for covariation of EEG feature space dispersion with

pulse width parameter. Furthermore, a recent study demonstrated that a 20 Hz stimulation

frequency produced significant cerebral blood flow increases (e.g. in the orbitofrontal cortex,

hypothalamus, and thalamus) compared to 5 Hz in VNS patients (Lomarev et al., 2002). It is

possible that the altered blood flow in these regions may be responsible for the observed

covariation of EEG feature space dispersion with stimulation frequency.

In addition, patients where seizure free and patients which experienced a small number of

seizures per month resulted in greater separation accuracy between the reference class and all

subsequent comparison classes in a VNS epoch. The patient with the most seizures per month


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resulted in the poorest separation between the reference class and all adjacent classes. This

phenomenon could be the multichannel analog of the dynamic resetting effect between two EEG

channels postulated by lasemidis et al. which states that a seizure resets the brain from an

unfavorable state to a more favorable state (Sackellares and lasemidis, 1997; lasemidis et al.,

2004). Thus, the results were interpreted as electroencephalographic evidence that the VNS

mimics the therapeutic resetting effect of a seizure. Future studies involving SVM would apply

the algorithm in an unsupervised manner to help provide unbiased information about patterns in

the data. Also, modification of the support vector machine algorithm, such as adaptive feature

scaling (Grandvalet et. al., 2003) can help provide insight into the relevance of each input feature

for SVM classification. This study is published in an article titled "Quantification of the Impact

of Vagus Nerve Stimulation Parameters on electroencephalographic Measures" with authors

Michael Bewernitz, Georges Ghacibeh, Onur Seref, Panos Pardalos, Chang-Chia Liu, Basim

Uthman (Bewernitz, 2007).

The final study utilized SVMs and LR to analyze the time-varying feature space separation

of the STLmax dynamical measure in patients undergoing VNS therapy. With an eye towards

the VNS replicating the resetting effect of a seizure, this study aimed to characterize potential

relationships between the EEG and stimulation parameters using an experimental setup similar to

lasemidis et al. (2004). Thus, a reference class was selected at 8 seconds prior to the stimulation

onset and was comprised of the STLmax value of all channels for all stimulations combined.

Similarly, each succeeding non-overlapping window for all channels for all epochs was

compared with the reference class. The study demonstrated that the observed pattern changes

may be related to the stimulation frequency parameter. Lomarev et al. demonstrated that a 20 Hz

stimulation frequency produced significant cerebral blood flow increases (e.g. in the









orbitofrontal cortex, hypothalamus, and thalamus) compared with the 5 Hz stimulation frequency

in VNS patients (Lomarev et al., 2002). The brain regions which showed a pulse-width

dependent blood flow in the study by Lomarev et al. may be the source of the observed

covariation of EEG feature space dispersion with stimulation frequency.

Also, it was speculated that the poor STLmax separation between VNS on (which may be

considered as a VNS 'artificial' seizure) and VNS off in patient B combined with patient B's

high seizure frequency (compared with the other patients) is aligned with the dynamic seizure

resetting effect described by lasemidis et al. (2004). In addition, this experiment demonstrated

the concept previously observed by Bewemitz et al. (2007) except while using the STLmax

measure. Thus, the connection between the observed effect and the observations of lasemidis et

al (2004) are stronger. This study was submitted to Computing and Optimization in Medicine

and Life Sciences Vol. 3, under the title "A Data Mining Approach to the Investigation of EEG

Biomarker Existence for Vagus Nerve Stimulation Therapy Patients", with authors Nikita

Boyko, Michael Bewemitz, Vitaliy Yatsenko, Panos Pardalos, Georges Ghacibeh, Basim

Uthman (Boyko et al., 2008).

In regards to the biological impact, these results may be related to the phenomenon

discovered in a study by Olejniczak et al. where a short-term suppression of epileptiform sharp

waves was observed following VNS from a hippocampal depth-electrode (2001). While the

scalp electrodes used to collect the data in these analyses cannot achieve the recording quality of

hippocampal depth electrodes, it is possible that the scalp EEG data mining analysis results may

reflect the same therapeutic effect as observed in the hippocampus by Olejniczak et al. (2001).

Analysis of Interstimulation Dynamics

The studies described in chapter 5 focus analysis on the EEG dynamics occurring during

interstimulation epochs. While the comparisons of stimulation to non-stimulation epochs


222









provided interesting results with clinical significance, the advantage of this experimental setup is

that the possibility of direct neural modulation is eliminated. Thus, the results are more likely to

be due to an "after-effect" of stimulation rather than due to immediate neuronal modulation.

The first experiment performed an extensive nonlinearity characterization using surrogate

EEG analysis. Each epoch was compared to 19 surrogate datasets using the ApEnt measure. The

most obvious connection of the EEG with the stimulation parameters was a covariation with the

pulse width. In addition, the two seizure-free patients (E and F) produced the lowest fraction of

epochs which displayed a nonlinear fingerprint (e.g. rejected the null hypothesis at the given

significance level). These results may be related to a study by Olejniczak et al. which reported

an acute VNS-induced suppression of epileptiform activity in the hippocampus (2001). Though

the effect was observed from a hippocampal depth electrode in the study by Olejniczak et al., it

is possible that some manifestation of the effect is present in the scalp-EEG signal analyzed in

the present study. The VNS-enhanced suppression of epileptiform activity reported in the

literature may be responsible for the diminished nonlinearity in patients with fewer seizures. The

cause of any epileptiform activity suppression may be related to a pulse-width dependency of

blood flow to various brain regions (e.g. hippocampus and superior temporal lobe) reported by

Mu et al., 2001. The observation that the seizure-free patients expressed the least amount of

nonlinearity may be congruent with the findings of Janszky et al. where the absence of bilateral

interictal epileptiform discharges was the only EEG predictor of seizure freedom (2005). Thus,

future studies should include epileptiform discharges in order to help further characterize the

EEG effect associated with VNS.

Shen et al. demonstrated that K-complex expression patterns can affect nonlinearity in

surrogate analysis of sleep EEG (2003). The observed nonlinearity increases in patients A and B


223









during late night (-11pm until -7am) may be the result of altered k-complex expression during

sleep (though other patients did not show this trend). The VNS is known to cause an increase in

the overall EEG power during sleep (Rizzo et al., 2004).

The nature of surrogate data analysis is to provide a yes/no answer to the question of

nonlinearity, but does not provide information on what type of nonlinearity is observed. All in

all, these results suggest that nonlinear measures may someday demonstrate sensitivity to the

outcome of VNS effect. In addition, this study motivates the usage of linear and nonlinear

measures in conjunction with one another as well as specific waveforms such as epileptiform

discharges in order to characterize the complex signal patterns present in EEG.

The second study in chapter five aimed to characterize any time dependence of the EEG

dynamics during the interstimulation epochs. This preliminary study was executed by performing

a statistical comparison of the first half of each interstimulation epoch to the second half. The

study utilized four measures which have demonstrated success in classifying neural state changes

in epilepsy; ApEnt, correlation sum, Q, and STLmax. The study showed that the patient with

the greatest amount of interstimulation epochs demonstrating significant time variation (for

Apent, correlation sum, and Q ) also had the highest output current (2.5 mA for patient C).

Patient A showed a similar trend and had the second highest output current (1.75 mA). Patient F

showed an opposing trend with 0.75 mA output current and the smallest fraction of

interstimulation epochs showing time variation. The ApEnt and Q measures demonstrated a

noticeably larger deviation from the control in all six patients than the other two measures, as

well as sensitivity to the output current. These two observations suggest that the ApEnt and Q

measures may be good candidates for EEG biomarkers in VNS patients. Biologically, these

results may be related two studies which demonstrated an electrical current threshold for


224









epileptiform activity suppression when stimulating the hippocampus in a low Ca2+ seizure

model (Warren and Durand, 1998) and a high K+ seizure model (Nakagawa and Durand, 1991).

A paper related to these interstimulation dynamics studies was published under the title

"Optimization of epilepsy treatment with vagus nerve stimulation" with authors Basim Uthman,

Michael Bewernitz, Chang-Chia Liu, and Georges Ghacibeh (Uthman et al., 2007).

Remarks on VNS Results

The variation in observed sensitivity in these measures to the various VNS parameters

suggest that different EEG measures are better suited for providing different information about

the EEG signal than other measures. Intuitively, it seems logical that a complex system such as

the epileptic brain may require several EEG measures for adequate characterization for

therapeutic intervention purposes. This observation is underscored in light of the intermittent

expression of nonlinear signatures in various interstimulation epochs. Future studies should

address the characterization task using a blend of linear and nonlinear measures.

In addition, future studies require additional patients to validate the interpretation of these

results. Baseline EEG recordings would provide additional support for the existence of EEG-

induced VNS effects by providing an opportunity to demonstrate the absence of such patterns

prior to implantation. After acquisition of the necessary baseline data, an interesting study

would be to examine the changes induced by the first stimulation. Thus, after the first

stimulation, a subsequent VNS deactivation and EEG acquisition may be applied. This would

provide a highly objective experimental setup possible for identifying short-term VNS effects.

Subsequent follow-up recording sessions may provide additional characterization of the summed

modulatory effect of chronic VNS.

The time of the last seizure should be obtained from the patient for all such studies. The

reason for this is that the patient undergoes a brief period of increased seizure protection after


225









some seizures (e.g. generalized tonic-clonic seizures). Thus, if the patient is under the influence

of this particular neural state, then that would provide a reduced chance of seizure which is not

consistent with the patient's standard behavior. This information would be helpful for

interpreting results. In addition, caution must be exercised when interpreting the results of

patients whom undergo seizures. As dynamical transitions can occur several minutes to several

hours prior to a seizure, many researchers operationally define the interictal period as being a

minimum of 8 hours away from a seizure (Pardalos et al., 2003; Hively et al., 2005;

Chaovalitwongse et al., 2006). Thus, the occurrence of a handful of seizures may produce an

unknown amount of influence on EEG dynamics. For this reason, future studies may withhold

analysis of EEG signals occurring within 8 hours of a seizure.

Seizure Detection and Stratification

The final project of this dissertation applied SVM classification in a preliminary

experiment geared towards a seizure detection and stratification system in patients with

generalized absence epilepsy. The seizure detection system utilized DTW distance with a

reference vector centered on a spike as the extracted feature. As spike and wave discharges in

absence epilepsy are generalized and often have a highly characteristic pattern. The first

experiment in this study performed SVM training and testing for the detection of the first second

of the seizure versus randomly selected non-seizure EEG which was located at least one minute

away from a seizure and at least 0.1 second away from another non-seizure segment. Though

both experiments present high sensitivity and specificity, the SVM classifier performed better at

classifying the first second of the seizure than final second o the seizure. This is likely due to

stronger electroencephalographic similarity among the different seizures at onset compared to

offset. Alteration of the RBF kernel bandwidth did not appear to appear the results much.

Variation of the cost parameter produced a greater effect on accuracy in experiment two than


226









experiment one. This is likely due to a loss of generality resulting from rigid "over fit" models

which may occur when the cost is sufficiently high.

Such an algorithm may benefit clinicians and researchers by providing a means to rapidly

annotate EEG signals as well as a means to provide a clinically interesting measure of

therapeutic efficacy (e.g. distribution of seizure durations may vary before and after drug

therapy, and thus a measure of this distribution may find clinically relevant information which a

raw seizure count would miss). A future direction of this project is to implement the classifier in

a real-time situation to test how the algorithm deals with the challenges presented in real-time

EEG analysis.

This study was submitted to a 2008 volume of the "Optimization and Its Applications"

book series under the title "A Novel Algorithm for the Detection and Stratification of

Generalized Absence Seizures" with authors Michael Bewernitz, Onur Seref, Basim Uthman,

and Panos M. Pardalos. In relation to this work, a review article regarding support vector

machines in neuroscience applications was accepted for publication under the title "support

vector machines in neuroscience" with authors Onur Seref, O. Erhun Kundakcioglu, and Michael

Bewernitz (Seref et al., 2007).

Final Remarks

The collection of studies presented address preliminary challenges involved with

development of online real-time EEG analysis systems for bedside and/or implantable therapy or

diagnosis enhancement tools. The choice of EEG source and extracted features for such a tool is

one of the greatest challenges presented to researchers in this field. Brain activity can be

measured on numerous scales from individual neurons up to macroscopic field potentials

representing large regions of the cerebral cortex. In addition, ensuring high-fidelity recordings is

an additional challenge requiring careful consideration for preprocessing tasks such as artifact


227









rejection and filtering. In addition to the complex nature of EEG analysis, the EEG data source

itself is limited in what it can tell a person about the brain. As technology improves and

electronic components become smaller, faster, and more efficient, future implantable therapeutic

control prostheses may also implement chemical sensors for quantifying neurotransmitter

concentrations, for example. Inclusion of additional information related to brain function could

greatly enhance the characterization of brain's behavior and potentially augment the performance

of implantable therapeutic control devices.


228









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BIOGRAPHICAL SKETCH

Michael Andrew Bewernitz was born and raised in the state of Michigan in the United

States of America. Michael received his Bachelor of Science degree in chemical engineering

with a biochemical engineering option from Michigan State University in 2002. He enrolled the

Ph.D. program of the J. Crayton Pruitt Family Department of Biomedical Engineering in 2003

under the guidance of Dr. J. Chris Sackellares in the Brain Dynamics Lab. After three

productive years, Michael joined Dr. Panos Pardalos in the Center for Applied Optimization in

the summer of 2006. In summer of 2007, Michael earned his Master of Engineering degree

from the J. Crayton Pruitt Family Department of Biomedical Engineering. He went on to

complete his Doctor of Philosophy in spring of 2008. Michael has written and presented three

conference talks, produced four journal publications, one book chapter, participated in the

creation of a patent, helped create four IRB medical research protocols on which he served as a

sub-investigator, participated in the creation of a bioengineering research fellowship grant, as

well as an NIH R21 grant. He has worked as a visiting researcher at the Allegheny-Singer

Research Institute in Pittsburgh, PA under the guidance of Dr. Kevin Kelly for two months

during the summer of 2005. Michael's research interests include data mining biomedical time-

series datasets and neural state classification using electroencephalographic recordings obtained

from patients or animal models of neurological disorders.





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DATA MINING AND TIME SERIES ANALYSIS OF BRAIN DYNAMICAL BEHAVIOR WITH APPLICATIONS IN EPILEPSY By MICHAEL ANDREW BEWERNITZ A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 1

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2008 Michael A. Bewernitz 2

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To my family, my loving fiance Teddi, and all those whom have helped me along the way of this challenging journey. 3

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ACKNOWLEDGMENTS I would first like to thank Panos Pardalos for his guidance, wisdom, and his persistent drive towards excellence which helped me and numerous students to think big, aim high, and repeatedly achieve great feats throughout the years. Most of all, I thank Dr. Pardalos for the effort he exerted to assist me during a difficult portion of my graduate schooling. I would also like to thank Dr. Basim Uthman for teaming up with me to share his brilliant ideas, time, energy, and financial support. The benefits of his impact on my graduate experience are beyond measure. Im very grateful for opportunity to work with Dr. Georges Ghacibeh and for the large positive impact he has had on my career as a Ph.D. student. I would also like to thank Dr. Mingzhou Ding, Dr. Steven Roper, and Dr. Hans Van Oostrom for serving on my graduate committee and providing valuable feedback. I thank Dr. J. Chris Sackellares for his guidance and support throughout the years, especially when we worked together at the Brain Dynamics Laboratory at the University of Florida. In addition, I commend Dr. Deng-Shan Shiau for his continual assistance in all areas of my graduate career for the last five years. Im also grateful for the guidance of my BDL labmates, Dr. Wanpracha Chaovalitwongse, Linda Dance, Chang-Chia Liu, Dr. Sandeep Nair, and Wichai Suharitdamrong as well as Dr. Wendy Norman for their assistance with work and just keeping my bearings during this challenging chapter of my life. I would also like to thank Dr. Paul Carney for his guidance throughout the years during meetings, conferences, seminars, or just in passing on campus. He has helped me in numerous ways and I extend sincere thanks. I am also grateful for Dr. Kevin Kelly for providing me the privilege of a fruitful and engaging experience working at his facility. I thoroughly enjoyed the summer of 2005 working in his Pittsburgh lab on our challenging task. I am grateful to have 4

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made the acquaintance of Peter Jukkola, Dr. Elena Kharlamov, Kathy Schmitt, and all the Allegheny-Singer Research Institute staff that helped me along the way. Im very grateful for my most recent group of friends in the Center for Applied Optimization at the University of Florida. The broad spectrum of research experience available my CAO colleagues such as Ashwin Arulselvan, Dr. Vladimir Boginski, Nikita Boyko, Dr. Stanislav Busygin, Dr. Altannar Chinchuluun, Alla Kammerdiner, O. Erhun Kundakcioglu, Dr. Antonio Mucherino, Dr. Oleg Prokopyev, Steffen Rebennack, Dr. Onur Seref, Oleg Shylo, and Petros Xanthopoulos helped provide me with rapid answers to many research questions, numerous perspectives to attacking a problem, as well some tasty ethnic food, drink and insider information for world travel! Short of becoming a United Nations ambassador, I doubt I will ever work with such a unique and diverse group of friends ever again. I also appreciate the efforts of Scott Bearden, David Juras, and all the staff at the Malcom Randall VA Medical Center of the North Florida/South Georgia Veterans Health System who have collaborated with our University of Florida research team and provided invaluable support for my Ph.D. studies. I would also like to thank Professor Jens Timmer, Professor Andreas Schulze-Bonhage, Dr. Bjrn Schelter, Dr. Michael Jachan, Hinnerk Feldwisch, Armin Brandt, Jakob Nawrath, Raimar Sandner, Johannes Wohlmuth, Thomas Maiwald, Christiane Lehmann, Carolin Gierschner, Dr. Matthias Winterhalder, Dipl. Ing. Richard Aschenbrenner-Scheibe, Dr. Henning Voss of the Freiburg Center for Data Analysis and Modeling, University of Freiburg, Germany, for providing publicly available de-identified EEG signals for research purposes. Their generosity has greatly benefited my studies. In addition, General Clinical Research Center, 5

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Grant # MO1-RR00082 has provided the means to conduct a portion of the research conducted in this dissertation. I would like to acknowledge the efforts of April-Lane Derfinyak, Anide Pierre-Louis, Laura Studstill, Kristi Wagner, Kathryn Whitesides, as well as Tifiny Dyer, Michelle Griffin, Danielle Wise, and Cindy Hansen for helping keep me on schedule with graduate school deadlines and comply with all the university guidelines that were a challenge to keep track of. Outside of my professional contacts, I would like to thank all my friends and my entire family, Howard, Noreen, Julie, and Mark Bewernitz for countless hours of encouragement in good and bad times. They have shared my ups and downs and maintained a steady supply of loving support throughout it all. I thank my loving fiancee, Teddi, for her continued support throughout the various phases of my graduate career. You mean everything to me Teddi. Above all, I thank The Father, The Son, and The Holy Spirit for the grace and blessings to persevere throughout the greatest challenge of my life thus far. 6

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES .........................................................................................................................10 LIST OF FIGURES .......................................................................................................................12 LIST OF ABBREVIATIONS ........................................................................................................17 ABSTRACT ...................................................................................................................................18 1 INTRODUCTION..................................................................................................................20 Computational Therapeutic Approaches: a New Frontier in Medical Treatment ..................21 Establishment of Neural States in Epilepsy ............................................................................24 Dynamical Disorders in Neurology ........................................................................................25 Objectives and Contributions of this Dissertation ..................................................................27 Organization of Chapters ........................................................................................................28 2 AN OVERVIEW OF EPILEPTIC DISORDERS AND EPILEPSY RESEARCH DIRECTIONS.........................................................................................................................32 Introduction .............................................................................................................................32 Classification of Seizure Types ..............................................................................................34 Partial Seizures ................................................................................................................34 Generalized Seizures .......................................................................................................35 Absence seizures ......................................................................................................35 Status epilepticus ......................................................................................................36 Epilepsy Treatment .................................................................................................................37 The Electroencephalogram as a Diagnostic Tool ............................................................38 Antiepileptic Drugs .........................................................................................................39 Sodium channel blockers .........................................................................................40 GABA agonists, reuptake inhibitors, and transaminase inhibitors ..........................40 Glutamate blockers ...................................................................................................41 Pharmacologically-resistant epileptic seizures .........................................................41 Epilepsy Surgery .............................................................................................................42 Gene Therapy ..................................................................................................................42 Electrical Stimulation Therapy ........................................................................................42 Deep brain stimulation .............................................................................................44 Cerebellum ...............................................................................................................45 Subcortical structures ...............................................................................................46 Caudate nucleus ........................................................................................................46 Thalamus ..................................................................................................................46 Centromedian nucleus ..............................................................................................47 Anterior thalamic nucleus ........................................................................................47 7

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Subthalamic nucleus .................................................................................................48 Hippocampus ............................................................................................................48 Vagus nerve stimulation ...........................................................................................48 Future Therapeutic Directions .........................................................................................51 Complex nature of epileptic dynamics .....................................................................52 Dynamical diseases and disorders ............................................................................52 Epilepsy as a dynamical disorder of brain systems ..................................................54 Compensating for impaired neural control mechanisms: system control therapy ...54 3 TIME SERIES ANALYSIS AND DATA MINING TECHNIQUES: THEORY AND APPLICATION......................................................................................................................56 Glossary of Terms ...................................................................................................................56 Time Series Analysis ..............................................................................................................57 Methods Applied in the Time Domain ............................................................................58 Autoregressive moving average modeling ...............................................................58 Autoregressive integrated moving average modeling ..............................................59 Cross correlation ......................................................................................................59 Methods Applied in the Frequency Domain ...................................................................61 Coherence .................................................................................................................61 Discrete Fourier transform .......................................................................................62 Wavelet analysis .......................................................................................................64 Information Based Methods ...................................................................................................65 Approximate Entropy ......................................................................................................65 Pattern Match Regularity Statistic ...................................................................................66 Mutual Information .........................................................................................................67 Chaotic System Analysis Techniques .....................................................................................68 Phase Space Mapping ......................................................................................................70 The Method of Delays .....................................................................................................71 Fractal Dimension ...........................................................................................................72 Box counting dimension (D0) ..................................................................................74 Information dimension (D1) .....................................................................................74 Correlation dimension (D2) .....................................................................................75 The Lyapunov Exponent ..........................................................................................75 Computing Short-Term Maximum Lyapunov Exponents ...............................................77 Mean Angular Frequency in Phase Space .......................................................................85 Data Mining ............................................................................................................................86 Clustering ........................................................................................................................87 K-means clustering ...................................................................................................87 Biclustering ..............................................................................................................87 Consistent biclustering .............................................................................................89 Data Classification ...........................................................................................................92 Machine learning ......................................................................................................92 Mahalanobis distance classification .........................................................................93 Support vector machines ..........................................................................................94 8

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4 INVESTIGATION OF EEG BIOMARKER EXISTENCE FOR VAGUS NERVE STIMULATION THERAPY: A DATA MINING APPROACH........................................102 Motivation for VNS Therapy Improvement .........................................................................103 EEG Markers for Treatment of Neurological Diseases and Disorders .........................103 Modeling Brain Disorder Dynamics .............................................................................104 Biclustering Analysis of EEG Dynamics in Patients undergoing VNS Therapy for Epilepsy .............................................................................................................................107 Data Description ............................................................................................................107 STLmax Feature Extraction ..........................................................................................109 Experimental Setup .......................................................................................................110 Results ...........................................................................................................................111 Discussion ......................................................................................................................112 SVM Analysis of EEG Phase Space Patterns in Patients undergoing VNS Therapy for Epilepsy .............................................................................................................................113 Data Description ............................................................................................................114 SVM Application Description .......................................................................................114 Experimental Design .....................................................................................................115 Results ...........................................................................................................................117 Discussion ......................................................................................................................117 Data Mining Analysis of EEG Dynamics Patients undergoing VNS Therapy for Epilepsy .............................................................................................................................120 Data Description ............................................................................................................120 Feature Extraction .........................................................................................................121 SVM Analysis of EEG Dynamics .................................................................................121 Logistic Regression Analysis of EEG Dynamics ..........................................................122 Experimental Setup .......................................................................................................124 Results ...........................................................................................................................124 Discussion ......................................................................................................................125 Conclusions ...........................................................................................................................127 5 ANALYSIS OF INTERSTIMULATION BRAIN DYNAMICS IN VAGUS NERVE STIMULATION THERAPY................................................................................................142 Further Characterizations/Investigations of EEG-Effects in VNS Therapy .........................142 Dynamical EEG Measures as Markers for Neurological Diseases and Disorders ........143 Data Description ............................................................................................................145 The Surrogate Analysis Method ....................................................................................146 The Role of Surrogate Data Analysis in EEG studies ...................................................148 Nonlinearity Analysis of Interstimulation EEG ...................................................................149 Choosing a Test Statistic ...............................................................................................150 Experimental Design .....................................................................................................151 Results ...........................................................................................................................152 Discussion ......................................................................................................................153 Temporal Evolution of Interstimulation EEG Dynamics .....................................................156 Data Description ............................................................................................................156 EEG Dynamical Measures ............................................................................................157 9

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Approximate entropy ..............................................................................................157 Correlation sum ......................................................................................................158 Mean angular frequency in phase space .................................................................159 Short-term maximum Lyapunov exponent ............................................................159 Experimental Design .....................................................................................................160 Results ...........................................................................................................................162 Discussion ......................................................................................................................163 Conclusions ...........................................................................................................................166 6 A NOVEL GENERALIZED ABSENCE SEIZURE DETECTION ALGORITHM...........199 Methods ................................................................................................................................200 Energy Method for SWD Detection ..............................................................................200 Fanselow Method for SWD Detection ..........................................................................201 Westerhuis Method for SWD Detection ........................................................................201 Dynamic Time Warping ................................................................................................202 Teager-Kaiser Energy ....................................................................................................203 Empirical Study ....................................................................................................................204 EEG Data Acquisition ...................................................................................................204 Data Sampling and Feature Extraction ..........................................................................205 SVM Training and Testing ............................................................................................206 Detector Performance Evaluation ..................................................................................207 Results ...................................................................................................................................208 Discussion .............................................................................................................................208 7 DISCUSSION AND CONCLUDING REMARKS.............................................................217 Towards Real-Time EEG Analysis Tools for the Bedside and Implantation .......................217 Data Mining Approaches to Characterizing EEG Patterns ...................................................218 Analysis of Interstimulation Dynamics ................................................................................222 Remarks on VNS Results .....................................................................................................225 Seizure Detection and Stratification .....................................................................................226 Final Remarks .......................................................................................................................227 LIST OF REFERENCES .............................................................................................................229 BIOGRAPHICAL SKETCH .......................................................................................................247 LIST OF TABLES Table page Table 4-1. VNS stimulation parameters .......................................................................................133 Table 4-2. Patient information for epilepsy patients with the VNS implant. ..............................136 Table 4-3. SVM separation accuracy and seizure information. ...................................................136 10

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Table 4-4. Mean SVM and LR separation accuracy and patient seizure information. ................141 Table 5-1. Surrogate analysis results summary for all six patients with the VNS implant. ........176 Table 5-2. Control patient surrogate analysis results summary. ..................................................177 Table 5-3. Approximate entropy analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt measure. ...........................................................................................................................187 Table 5-4. Approximate entropy analysis results for the control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt measure. ................................................................................................188 Table 5-5. Correlation sum analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H2 using the correlation sum measure. .................................................................................................189 Table 5-6. Correlation sum analysis results for the control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H2 using the correlation sum measure. .................................................................................................190 Table 5-7. Mean angular frequency in phase space analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H3 using the measure. ......................................................................................................191 Table 5-8. Mean angular frequency in phase space analysis results for control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H3 using the measure. ..............................................................................193 Table 5-9. Short-term maximum Lyapunov exponent analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H4 using the STLmax measure. .....................................................................194 Table 5-10. Short-term maximum Lyapunov exponent analysis results for the control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H4 using the STLmax measure. .......................................................196 Table 6-1. Classification performance using the first second of each seizure. ............................213 Table 6-1. Classification performance using the last second of each seizure. .............................213 11

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LIST OF FIGURES Figure page Figure 2-1. Seizure classification ruling as designated by the Epilepsy Foundation (2008). ........34 Figure 2-2. VNS pulse sequence. ...................................................................................................49 Figure 2-3. Closed-loop seizure control device using electroencephalogram or electrocorticogram signals as an input to a feature extraction algorithm, which supplies the extracted features to a controller which makes a decision regarding the action of a stimulator. ........................................................................................................55 Figure 3-1. A 15 second segment depicting the 200 Hz EEG of an absence seizure viewed from channel Fp1-F7. .........................................................................................................98 Figure 3-2. A 15 second segment depicting the spectrogram of an absence seizure viewed from channel Fp1-F7. The vertical lines represent the onset and offset of the seizure. ....99 Figure 3-3. Example angular frequency evolution in phase space. .............................................100 Figure 3-4. Biclustering result of a toy dataset. The dataset produced three distinct classes. ....100 Figure 4-1. Rationale for studying EEG patterns which may be associated with the effect of VNS on the brain. ............................................................................................................131 Figure 4-2. Conceptual EEG dynamics model in three-dimensional feature space for testing stimulation parameter configurations in newly-implanted VNS patients. Adjusting the stimulation parameters results in an altered dynamical state of the brain denoted by the coordinates in three-dimensional feature space. The models colored regions relate the EEG dynamical state to its predicted clinical outcome. ...................................132 Figure 4-3. EEG electrode placement. Electrodes were positioned according to the 10-20 electrode placement system which assigns locations proportionally spaced locations (e.g. 10%-20%) with respect to the size of the patients head. ........................................133 Figure 4-4. STLmax class designation for biclustering analysis. ................................................134 Figure 4-5. Biclustering heatmap of STLmax from A) patient A and B) patient B. ...................135 Figure 4-6. Mean SVM separation accuracy value across the stimulations for each individual intra-stimulation window. ................................................................................................137 Figure 4-7. VNS output current and the corresponding mean SVM separation accuracy over 24 hours. ...........................................................................................................................137 Figure 4-8. VNS pulse width and the corresponding mean SVM separation accuracy over 24 hours. ................................................................................................................................138 12

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Figure 4-9. VNS signal frequency and the corresponding mean SVM separation accuracy over 24 hours. ...................................................................................................................138 Figure 4-10. SVM Separation accuracy throughout the VNS epoch, averaged across all epochs. Stimulation begins at t=0 seconds. .....................................................................139 Figure 4-11. Overall mean SVM separation averaged across intra-epoch time points and all epochs. .............................................................................................................................139 Figure 4-12. LR separation quality throughout the VNS epoch, averaged across all epochs. Stimulation begins at t=0 seconds. ..................................................................................140 Figure 4-13. Overall mean LR AUC averaged across intra-epoch time points and all epochs. ..140 Figure 5-1. Map of EEG electrode location for the VNS patients. The electrodes were positioned according to the 10-20 electrode placement system which assigns locations proportionally spaced locations (e.g. 10%-20%) with respect to the size of the patients head. ............................................................................................................171 Figure 5-2. Electrode positions for the control patient from A) an inferior and right view and B) axial slice view of the brain. Red circles indicate focal electrodes (TBa4, TBb6, HR7), blue circles indicate non-focal electrodes (TLb2, TLb3, TLc2). Images provided for this publication courtesy of the Freiburg Center for Data Analysis and Modeling at the Albert-Ludwigs Universitt Freiburg (University of Freiburg), Freiburg, Germany. ..........................................................................................................171 Figure 5-3. Comparison of pulse width parameter to the fraction of epochs displaying a nonlinear signature in the six patients treated with VNS. The fraction of epochs displaying a nonlinear signature in control patient using the 3-minute and 5-minute off pseudo stimulation times are represented by the column of six triangles (3 minute off times) and six squares (5 minute off times). ..............................................................172 Figure 5-4. Patient A surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. .................172 Figure 5-5. Patient B surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. The red lines indicate seizures. .....................................................................................................173 Figure 5-6. Patient C surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. .................173 Figure 5-7. Patient D surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. .................174 13

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Figure 5-8. Patient E surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. .................174 Figure 5-9. Patient F surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. .............................................174 Figure 5-10. The fraction of all interstimulation epochs per channel which rejected the null hypothesis H0 using ApEnt for A) patient A, B) patient B, C) patient C, D) patient D, E) patient E, F) patient F. ............................................................................................175 Figure 5-11. Control patient (with 5-minute artificial stimulation times) surrogate data analysis results over 24 hours for all artificial interstimulation epochs. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. ............................................................................177 Figure 5-12. Control patient (with 3-minute artificial stimulation times) surrogate data analysis results over 24 hours for all artificial interstimulation epochs. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. ............................................................................177 Figure 5-13. Experimental setup for characterizing the temporal evolution EEG dynamics during interstimulation intervals in patients undergoing VNS therapy for epilepsy. The double head arrows indicate a statistical comparison is made between the EEG feature segments represented by the shaded rectangles. ..................................................178 Figure 5-14. Patient A temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. ................................................................................................................179 Figure 5-15. Patient B temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. The red lines indicate seizures. .............................................................180 Figure 5-16. Patient C temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. ................................................................................................................181 Figure 5-17. Patient D temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. ................................................................................................................182 14

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Figure 5-18. Patient E temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. ................................................................................................................183 Figure 5-19. Patient F temporal evolution of dynamics analysis results for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. ................................................................................................................184 Figure 5-20. Control patient (with 5-minute artificial stimulation times) temporal evolution of dynamics analysis results for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. .............................................185 Figure 5-21. Control patient (with 3-minute artificial stimulation times) temporal evolution of dynamics analysis results for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. .............................................186 Figure 5-22. Approximate entropy analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt measure. ................................................................................................................188 Figure 5-23. Correlation sum analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H2 using the correlation sum measure. .................................................................................................190 Figure 5-24. Mean angular frequency in phase space analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H3 using the measure. ..............................................................................192 Figure 5-25. Short-term maximum Lyapunov exponent analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H4 using the STLmax measure. .....................................................................195 Figure 5-26. ApEnt results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. ..........................................................................................................................196 Figure 5-27. Correlation sum results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. ..........................................................................................................................197 Figure 5-28. results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. ........197 15

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Figure 5-29. STLmax results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. ..........................................................................................................................198 Figure 6-1. Approximately 6 seconds of scalp-EEG demonstrating the 2.5-3.5 Hz spike-wave discharge that defines an electrographic absence seizure (data provided courtesy of Dr. Gregory Holmes). ...................................................................................210 Figure 6-2. DTW comparison of two different SWD segments. The top signal is a 300 ms SWD segment. Bottom signal is a 300 ms segment of a different SWD. The DTW distance is about 2.4 x 10. 7 ...............................................................................................211 Figure 6-3. DTW comparison of a SWD segment with a random interictal segment. Top signal is a 300 ms EEG segment of a SWD. Bottom signal is 300 ms of interictal EEG. The DTW distance is about 5.1 x 10. 7 ...................................................................212 Figure 6-4. Seizure classification evaluation framework. ...........................................................212 Figure 6-5. Seizure detection performance for RBF parameter sigma=20 using the first second of each seizure. ....................................................................................................214 Figure 6-6. Seizure detection performance for RBF parameter sigma=40 using the first second of each seizure. ....................................................................................................214 Figure 6-7. Seizure detection performance for RBF parameter sigma=80 using the first second of each seizure. ....................................................................................................215 Figure 6-8. Seizure detection performance for RBF parameter sigma=20 using the last second of each seizure. ....................................................................................................215 Figure 6-9. Seizure detection performance for RBF parameter sigma=40 using the last second of each seizure. ....................................................................................................216 Figure 6-10. Seizure detection performance for RBF parameter sigma=80 using the last second of each seizure. ....................................................................................................216 16

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LIST OF ABBREVIATIONS AED Anti-epileptic drug ApEnt Approximate entropy DNA Deoxyribonucleic acid DTW Dynamic time warping EEG Electroencephalogram FN False negative FP False positive GCRC General Clinical Research Center IID Independent and identically distributed IRB Institutional Review Board LR Logistic regression PLED Periodic lateralized epileptiform discharge STL max Short-term maximum Lyapunov exponent SVM Support vector machine SWD Spike-and-wave discharge TN True negative TP True positive VNS Vagus nerve stimulation Mean angular frequency in phase space 17

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DATA MINING AND TIME SERIES ANALYSIS OF BRAIN DYNAMICAL BEHAVIOR WITH APPLICATIONS IN EPILEPSY By Michael Andrew Bewernitz May 2008 Chair: Panagote M. Pardalos Major: Biomedical Engineering Epilepsy is a neurological disorder characterized by recurrent seizures. Approximately 30% of patients with epilepsy have seizures that are resistant to anti-epileptic drug (AED) therapy. If these patients are unable to undergo epilepsy surgery, they may choose to utilize the Vagus Nerve Stimulator (VNS) implant. The VNS therapy system has been approved by the FDA to electrically stimulate the left vagus nerve for epilepsy treatment. Patients with newly implanted VNS systems undergo an adjustment period of several months involving numerous medical check-ups to fine tune the electrical stimulation parameters based on clinical response. This sub-optimal adjustment method leaves the patient at risk of seizures and imposes financial burden. Identification of a marker of desired VNS operation would greatly expedite this adjustment process. The utility of non-invasive electroencephalogram (EEG), success of neural state classification research for diagnosis and treatment of neurological disorders, and the potential for real-time application due to advances of computer technology motivate this study. This dissertation outlines data mining approaches involving biclustering, logistic regression, and support vector machines as well as statistical comparisons of a range of relevant EEG dynamical measures for the characterization of electroencephalographic patterns associated with VNS therapy. The preliminary results are consistent with biological processes and clinical 18

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observations. One explanation for the electroencephalographic behavior is that VNS mimics a theorized therapeutic seizure effect where a seizure resets the brain from an unfavorable preictal state to a more favorable interictal state. The preliminary results suggest a connection between the EEG patterns and the stimulation parameters which may require a range of linear and nonlinear measures for adequate characterization. In addition, support vector machines are utilized to create a seizure detection and stratification algorithm in patients with generalized absence epilepsy. The algorithm utilizes dynamic time warping distance and Teager-Kaiser energy as the representative EEG features. The algorithm performed slightly better at seizure onset detection than for seizure offset. This is likely due to increased waveform consistency shortly after onset compared to offset. Such an algorithm may benefit clinicians and researchers by providing a means to rapidly annotate EEG signals as well as a means to provide a clinically interesting measure of therapeutic efficacy for drug evaluation studies (e.g. distribution of seizure durations may vary before and after drug therapy, and thus a measure of this distribution may find clinically relevant information which a raw seizure count would miss). A future direction of this project is to test additional EEG feature inputs and assess how the algorithm copes with the challenges presented in online EEG analysis. 19

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CHAPTER 1 INTRODUCTION Recent advances in mathematics provide new tactics for the analysis of complex datasets. These advances provide new options for analyzing and modeling seemingly complex system behavior such as that seen in biological systems. In addition, the rapid growth of computational capabilities in the modern computer provides the possibility for real-time computational analysis of biological datasets. Such scientific milestones have revolutionized the direction of scientific research in many disciplines, among them, the study of epilepsy. In recent decades, a growing body of evidence has surfaced in research reports suggesting the existence of a pre-ictal state has resulted in a great interest in quantitatively characterizing this theorized seizure imminent state. Due to the superior time resolution and large availability of the electroencephalographs, much research has been devoted to characterizing the preictal state in terms of electroencephalogram (EEG) datasets. Advances in the understanding of non-linear system dynamics have lead to massive breakthroughs for the challenging task of characterizing the dynamics governing the behavior of complex systems. In many instances, these novel system modeling approaches can achieve better results than were previously attainable with standard linear approaches. One major premise for the characterization of neural states is that the dynamics directing brain function are often best examined within a nonlinear deterministic framework (Savit et al., 2003). Such a framework can provide a useful means to analyze systems that that exhibit adaptive behavior and are non-autonomous (both of which are traits of biological systems). For the example of seizure prediction, this method bypasses the explicit underlying neurophysiological processes involved in seizure generation and instead focuses on predicting undesirable neural states (e.g. seizures) by measuring and modeling the temporal progression 20

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of various observable features of brain behavior. Whether predicting seizure or other neural state changes, such features may currently include brain electrical or magnetic field fluctuations, blood flow, neurochemical concentration profiles. Of these measures, electrical activity as measured in EEG data sets is the most commonly used feature for describing neural state in epilepsy. Computational Therapeutic Approaches: a New Frontier in Medical Treatment The computational power and memory storage abilities of modern computational age have revolutionized the way that scientists and engineers approach problems. One of the most exciting achievements of the 20 th century is the invention of the semiconductor transistor, which was followed by a cascade of computational advances throughout the last 50 years. Moores Law is a famous model of the observed growth rate of computational abilities and has remained astonishingly accurate for several decades (Intel Corporation, 2005). The state of modern technology provides modern researchers the ability to not only solve problems that could be not practically be solved a few decades ago, but now we are in a unique position to solve many such problems in real-time applications. While the benefits of such technology are manifesting at an almost alarming pace in every aspect of life, the fields of biology and medicine have capitalized in ways that may have seemed inconceivable only decades ago. Necessity is the mother of invention, and such is the driving force for many of the numerous serendipitous medical discoveries. One prime example is a solution to the many problems plaguing the functionality of hospital bedside cardiac regulation devices. The original device utilized an external bedside machine which regulated the cardiac pacing. Among the many difficulties included impeded patient mobility due to the size and mass of the equipment, alternating current power requirement, as well as skin burns at electrode sites (Nelson, 1993). 21

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The advent of implantable devices forever revolutionized the field of medical treatment when a Swedish group first implemented the previously unheard-of idea of utilizing an implantable device for cardiac pacing (Nelson, 1993). The success of cardiac pacemakers opened the eyes of physicians and engineers alike that were seeking new solutions to the challenge of improving the state of medical treatment. The cardiac pacemaker was highly sophisticated solution to the treatment of damaged and diseased hearts and helped pave the way for a revolution in medicine; the use of computational devices (implantable or bedside) to help regulate the physiology of patients afflicted with some chronic condition. This new engineering direction added numerous challenges such a biocompatibility and safety issues, as well as new concepts (e.g. designing implantable devices with the expectation that the treatment device is likely to or guaranteed to fail in lifetime of the patient). In recent years, microelectromechanical devices (MEMs) have been able to strongly capitalize on the advancements of computers. As computers became smaller, faster, and more efficient, savvy engineers were able to capitalize on the new options available to them. For example, the combination of MEM sound sensors, processors, and transcutaneous transmitters provides the possibility of mimicking the role of the cochlea in patients with a specific cause of hearing impairment (Chapin and Moxon, 2001). While the device is far from being as precise or accurate as the original brain tissue, such a device helped pioneer a new research direction for augmenting impaired brain function. Additionally, retinal implants are being heavily researched to compensate for certain types of blindness (Schanze et al., 2007). The device is able to mimic some of the tasks of a 22

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function retinal including photo detection and the directing preprocessing phase output to the optic nerve. Despite the astonishing milestones of progress in these brain machine interfaces (BMI), these two implantation devices are still being heavily researched. Another intensely researched field of BMI aims to integrate the state of the art computational technology combined with the modern marvels of neuroscience in order to overcome certain types of paralysis (Nicolelis et al., 2001; Kim et al., 2007). Such an apparatus provides the ability of the brains muscle movement signals to execute actions in a prosthetic limb. The above BMIs face numerous challenges which must be overcome before such devices can become a mainstay of treatment. For one, adequate input data acquisition is massive challenge in and of itself. All such devices assume that obtaining samples of the brains electrical signals can serve as sufficient inputs (as the specific knowledge of neurotransmitter chemistry and exact neuronal connectivity cannot currently be obtained as successfully as the electrical signals can be recorded). Also, while our understanding of the roles of the secondary and primary motor cortices in the planning and execution of motor movements have sufficed to provide exciting preliminary results for such BMIs, the time and spatial resolution of such recordings required for optimal external limb control remains uncertain. In addition, one massive challenge of itself is to extract useful features from such signals in order to serve as the proper inputs to the underlying model governing the action of such a device. Furthermore, the proper choice of model is a field of heavy research in and of itself. As is expected, the available models of brain function have numerous advantages and disadvantages compared one another that can depend on the particular states of the brain to be modeled, the range of brain states considered, quality of recordings, feature extraction methods and so on. 23

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While the state of the art of neuroscience has made progress relevant to the development of BMIs, there is still much room for improvement in understanding the basic and advanced mechanisms of normal brain function as well as impaired brain function in various neurological disorders. While the impaired neural functions of interest in the previously described BMI applications may in some cases seem rather straight forward, the specific neural impairment processes of some other neurological disorders are at the present moment less explicitly understood. For such disorders, such as epilepsy, the extraction of suitable biomarkers for any type of advanced therapeutic scheme is hampered by the apparent mysterious nature of the disorder. Epilepsy is a disorder that not only has symptoms that are not fully understood (e.g. the specific cause and purpose of an epileptic seizure), but also the occurrence of seizures often does not appear to follow any known behavioral pattern with a sufficient degree of accuracy. There is much room for improvement. Establishment of Neural States in Epilepsy Extensive research has been conducted in the last four decades with the focus of unveiling and modeling the mechanisms that lead up to a seizure. It has been said that only approximately 3% of epilepsy cases present seizures that are initiated by some external stimulus whereas for the vast majority of patients there are no such clear events associated with seizure initiation (Le Van Quyen et al., 2001). However, there is a large body of clinical evidence suggesting that seizures are preceded by a physiologic state change that occurs prior to seizure onset. Documented clinical changes preceding a seizure include increase in heart rate (Delamont et al., 1999; Novak et al., 1999; Kerem and Geva, 2005), cerebral blood flow (Weinand et al., 1997; Baumgartner et al., 1998), the availability of oxygen (Adelson et al., 1999), magnetic resonance imaging of the blood oxygen-level-dependent signal (Federico et al., 24

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2005) as well as changes visible in single photon emission computed tomographic patterns (Baumgartner et al., 1998). Thus, one of the most profound discoveries in this field of research is postulation of a physiologic preseizure state (Mormann et al., 2007). This theory is supported by a large volume of documented physiologic changes occurring prior to seizure onset within and outside of the brain. This transition from a normal state into a preseizure or preictal state is one of the major theories regarding seizure initiation that has affected the direction of epilepsy research. On a neuronal level, the preictal state results in an abnormal synchronized bursting involving large populations of neurons in various brain structures. Depending on the type of epilepsy, these discharges can begin locally and possibly spread to various regions of the brain or can begin multiple regions nearly simultaneously. Dynamical Disorders in Neurology The epileptic disorder exhibits traits similar to a class of diseases termed dynamic diseases which demonstrate particular complex behavior patterns that evolve over time. Specifically, these dynamic diseases have been broadly described as a class of diseases which undergo a temporal disruption of underlying physiological control mechanisms leading to period of abnormal dynamical behavior (Mackey and Glass, 1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003; Colijn and Mackey, 2005). Examples of these phenomena include the oscillation of blood cell populations in hematological diseases (Colijn et al., 2006), tremor in Parkinsons Disease (Beuter and Vasilakos, 1994), as well as several neurological disorders such as epilepsy, migraine, and multiple sclerosis (Milton and Black, 1995). Within the perspective of control mechanisms (e.g. feedback or feed forward control systems), dynamical diseases can be viewed as an undesirable alteration of a standard biological control scheme (Mackey and Glass, 25

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1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003). Such dynamical disorders often undergo state transitions that bear resemblances to bifurcations in mathematical systems, for example. The overall significance of identifying dynamic diseases is that it may be possible to develop therapeutic approaches based on the manipulation of the identified critical control parameters (Mackey and an der Heiden, 1982; Milton and Black, 1995). Numerous studies present models utilizing linear and nonlinear dynamical EEG time series analysis measures to model the transition into a seizure (Iasemidis and Sackellares, 1991; Iasemidis et al., 1993; Lehnertz and Elger, 1995; Casdagli et al., 1996; Lehnertz, 1999; Le Van Quyen et al., 2001; Osorio et al., 2001; Iasemidis et al., 2003, 2004; Chaovalitwongse et al., 2005). Often the long-term goal is to utilize these measures to serve as inputs for a dynamical disease model used in a closed-loop therapeutic control device (Iasemidis et al., 2003; Good et al., 2004, 2005; Fountas and Smith, 2007). Thus, if a seizure represents a period of aberration in a dynamical epileptic disorder which is characterized by nonlinear EEG measures such as STLmax (Iasemidis et al., 2000), then nonlinear dynamical measures (such as STLmax) could conceivably provide a useful framework for characterizing the effect of therapeutic intervention (Good et al., 2004, 2005; Ghacibeh et al., 2005). Aside from such practical applications, quantitative EEG analysis from a non-linear dynamical framework has also helped provide some novel insight towards defining a physiological role of seizures in epileptic disorders. For example, one theory states that a seizure is the manifestation of the brains mechanism for resetting the brain when it enters an undesirable state. Such a state has been characterized by an unhealthy similarity in the rate of information production among critical brain sites, a process referred to as dynamical 26

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entrainment (Iasemidis et al., 2004). Physiologically, such a resetting effect may follow a proposed therapeutic mechanism similar to that of ECT induced seizures (Fink, 2000; Gwinn et al., 2002; Taylor, 2007). The theorized existence of neural states that are indicative of the current status of the epileptic disorder forms the basis for many model-based seizure control therapy research projects. A common belief of researchers in this field is that a therapeutic dosage of drug or electrical stimulation can be applied at the proper location of the central nervous system and at the proper time to mitigate and possibly prevent seizure occurrence. In essence, this line of therapy embraces a philosophy that a well-timed, minor therapeutic action in the proper location will abort a seizure by means of fulfilling the therapeutic action for which the seizure was intended. Much like the cardiac pace maker described earlier, a brain pacemaker is becoming more of a realistic possibility (Savit, 2003) for providing a means to dispense localized electrical stimulation or drug dispensing treatment on demand when preictal transition state changes are detected (Stein et al., 2000; Theodore and Fisher, 2004; Good et al., 2004, 2005; Morell, 2006). Objectives and Contributions of this Dissertation A team of leading scientists, health care providers, and leaders of voluntary health organizations came together to discuss what it would take to find a cure for epilepsy in March, 2000. The milestone White-House initiated conference, "Curing Epilepsy: Focus on the Future," was sponsored by the National Institute of Neurological Disorders and Stroke in collaboration with the American Epilepsy Society, Citizens United for Research in Epilepsy, Epilepsy Foundation, as well as the National Association of Epilepsy Centers. The conference stressed the importance of scientists throughout the nation to investigate methods of studying and treating 27

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seizures. The conference produced a national agenda for epilepsy research which has served as a community guide towards a cure. Since then, the epilepsy research community has progressed substantially in updating the research benchmarks to be aligned with current research developments. As a result, a primary goal of the 2007 conference was to assess the original benchmarks and discuss new research directions. The attendees voted on which areas were most promising, as well as those in need of attention. The Epilepsy Benchmark Stewards gathered in October 2007 to finalize a hierarchy of epilepsy research benchmarks. Of particular interest to this dissertation are the following specific benchmarks: Develop valid screening strategies and biomarkers and surrogate markers (e.g., genetic, pharmacogenomic, electrophysiologic, imaging, biochemical) to identify patients who are likely to respond to, or develop adverse effects from specific therapies. Develop higher-throughput cost-effective models for screening pharmacotherapies for specific types of epilepsy. Optimize existing therapies The main goal of this dissertation is to extract useful features from the EEG signal of patients afflicted with epilepsy in order to further the understanding of the disorder and work towards improvements to existing therapies. The first portion of this research addresses the desire to identify EEG markers of optimal VNS therapy for the purpose of expediting the parameter adjustment phase in newly-implanted patients. The final chapter introduces a novel approach to seizure detection and stratification algorithm which may provide a useful tool for evaluation drug efficacy. Organization of Chapters The research presented in this dissertation is organized into seven chapters. Chapter one provides an overview of the document. The overview consists of a brief introduction to the field 28

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of quantitative EEG analysis in epilepsy as well as the scope of research presented in this dissertation from the context of federally-established epilepsy research guidelines. Chapter two describes an extensive overview of various epileptic disorders, symptoms, diagnosis, and a range of relevant clinical and biological information. In addition, an overview of diagnostic tools and current treatment modalities is presented as well the direction of future treatment research. Chapter three overviews the broad range of methods utilized in quantitative EEG analysis. The described methods are broadly classified as time series analysis and data mining methods. Relevant mathematical theory is and biological interpretations in experimental situations are explained. Chapter four begins with a description of epilepsy from a dynamical disorder perspective and outlines some key EEG data mining analysis methods applied within this framework. Based on these observations from scientific literature, the aforementioned dynamical EEG analysis methods are employed to study the effect of vagus nerve electrical stimulation therapy in order to characterize the relationship of the stimulation parameters with the EEG behavior in terms of dynamical measures. The results are discussed in terms of their relationship to relevant clinical research observations and the underlying biological processes. The work described in chapter four is has been published in three journal articles: Biclustering EEG data from epileptic patients treated with vagus nerve stimulation, authored by Stanislav Busygin, Nikita Boyko, Panos Pardalos, Michael Bewernitz, and Georges Ghacibeh (Busygin, 2007). Quantification of the Impact of Vagus Nerve Stimulation Parameters on electroencephalographic Measures with authors Michael Bewernitz, Georges Ghacibeh, Onur Seref, Panos Pardalos, Chang-Chia Liu, Basim Uthman (Bewernitz, 2007). "A Data Mining Approach to the Investigation of EEG Biomarker Existence for Vagus Nerve Stimulation Therapy Patients", with authors Nikita Boyko, Michael Bewernitz, 29

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Vitaliy Yatsenko, Panos Pardalos, Georges Ghacibeh, Basim Uthman, submitted to Computing and Optimization in Medicine and Life Sciences Vol. 3, (Boyko et al., 2008). Chapter five provides additional quantitative EEG analysis in patients undergoing VNS therapy for epilepsy. This chapter closely examines the interstimulation EEG dynamics using numerous EEG dynamical measures commonly applied in neural state classification studies. Specifically, this chapter assesses the nonlinearity of EEG dynamics and characterizes time-dependent dynamical behavior and compares these features to stimulation parameters. The results are discussed in the context relevant clinical research findings as well as relevant physiologic processes. The potential application of such results for use in real-time seizure control applications and rapid parameter tuning apparatus is presented. A paper related to these interstimulation dynamics studies was published under the title Optimization of epilepsy treatment with vagus nerve stimulation with authors Basim Uthman, Michael Bewernitz, Chang-Chia Liu, and Georges Ghacibeh (Uthman et al., 2007). Chapter six begins with an introduction into generalized absence epilepsy. A novel seizure detection and stratification algorithm is presented as a means to help physicians and researchers rapidly annotate EEG signals as well as provide online diagnostic tools. In particular, such a seizure stratification algorithm may provide a clinically interesting measure of therapeutic efficacy for drug evaluation studies (e.g. the distribution of seizure duration distribution before and after drug therapy may provide clinically relevant information which a raw seizure count would miss). A manuscript related to this work was published under the title Support vector machines in neuroscience with authors Onur Seref, O. Erhun Kundakcioglu, and Michael Bewernitz (Seref et al., 2007). 30

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Chapter seven summarizes the findings of this dissertation. Concluding remarks regarding the overall significance of the findings are discussed. Future research directions in light of these results are presented. 31

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CHAPTER 2 AN OVERVIEW OF EPILEPTIC DISORDERS AND EPILEPSY RESEARCH DIRECTIONS Introduction The term epilepsy is derived from the Greek word epilamvanein which means to be seized, to be attacked, to be taken hold of. This disorder has been well documented throughout historical texts for thousands of years in numerous civilizations. Ancient Greeks referred to people being seized and having an attack as if the person were under the influence of a supernatural force. This idea comes from the ancient notion that disease was a form of punishment from the gods or evil spirits (Engel, 1989). These descriptions likely refer to the abrupt, complex timing of seizure onset and how the symptoms could be described as almost a supernatural seizing of the individual for certain types of seizure. Hippocrates was the first person documented as having suggested that epilepsy was a disorder of the brain around 400 B.C. (Parker and Parker, 2003). Epilepsy is not a disease, though, but rather a symptom of a disorder of the brain. Normally, the tens of billions of brain cells making up the brain communicate with one another via small bursts of electrical activity. An unexpected, erratic electrical discharge of a group of brain cells is referred to as a seizure. A seizure can be brought on by a variety of insults such as toxins, drugs, metabolic disturbances, or trauma, flashing lights, or hyperventilation (Wilner, 2003). Such a provoked seizure is separate from Epilepsy, which is a disorder distinguished by recurrent seizures (Lothman et al., 1991). The epileptic condition can arise from numerous causes. Typically, the common element in all causes of epilepsy are events that result in a disturbance of neuronal functionality such as extreme illness, chemical or physical brain damage, or abnormal brain development resulting from genetic or other triggers (Parker and Parker, 2003). Specific brain features resulting from 32

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such brain alterations that could be responsible for epilepsy include altered neuronal connectivity, excessive levels of excitatory neurotransmitters, deficiencies of inhibitory neurotransmitters, or possibly a combination thereof. It has also been observed that the brains attempts to repair itself after injury can lead to irregular nerve connectivity patterns which eventually lead to epilepsy (Parker and Parker, 2003). Recent estimates of world-wide epilepsy prevalence for a wide range of age groups indicated between 3 and 8 reported cases of epilepsy per 1000 people (Shorvon et al., 2004). The hallmark of epilepsy is recurrent seizures caused by the sudden development of synchronous neuronal firing. Seizure symptoms can include uncontrollable shaking, loss of awareness, visual and aural hallucinations, phantom odors, and other sensory disturbances depending on the location and spread of electrical activity in the brain (Weaver, 2001; Wilner, 2003). Electroencephalogram (EEG) recordings show that these discharges begin either locally in one or more portions of a cerebral hemisphere or simultaneously in both cerebral hemispheres (Binnie et al., 1997; Niedermeyer et al., 1993). These seemingly unpredictable seizures can cause a variety of motor symptoms and have a major effect on the patients quality of life by imposing restricted driving privileges, adverse effects on social and career opportunities, self-esteem, education, and psychiatric issues (Goldstein and Harden, 2001; Manford, 2003; Wilner, 2006). In addition, recurrent seizures may cause progressive neuronal damage, leading to impaired memory and cognition. A 1995 study estimated that epilepsy imposed an economic burden of $12.5 billion in associated health care costs and losses in employment, wages, and productivity in the U.S. (Begley et al., 2000). 33

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Classification of Seizure Types All types of seizures are broadly classified depending on whether the seizure arises in a restricted portion of the brain within one hemisphere or if the onset involves both hemispheres (Shorvon et al., 2004). Seizures that do not fit into these categories are referred to as unclassified. Figure 2-1 outlines a basic framework for seizure classification as designated by the Epilepsy Foundation (2008). Figure 2-1. Seizure classification ruling as designated by the Epilepsy Foundation (2008). Partial Seizures Partial seizures are those that occur in a localized region of the brain known as a focus. Partial seizures can be roughly broken down into simple partial, complex partial, and secondary generalized seizures. A simple partial seizure may materialize with rhythmic twitching of a limb, cessation of speed, strange sensations in the body, or hallucinations (Shorvon et al., 2004). The particular symptoms vary from patient to patient and depend on the region of the brain in which the seizure 34

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is occurring. Simple partial seizures begin suddenly, cease quickly, and do not involve an impairment of consciousness. In a complex partial seizure a person will temporarily undergo an impairment of consciousness are often preceded by a premonitory sensory or psychic aura (Shorvon et al., 2004). During the seizure the person appears unresponsive and may make purposeless limb movements called automatisms. Automatisms can include such behavior as eye blinks, twitches, chewing motions of the mouth, and possibly walking in a circular pattern (Parker and Parker, 2003). Patients can often be amnesic about the events occurring in complex partial seizures. Some partial seizures can spread to both hemispheres resulting in tonic (muscle tensing) and clonic (rhythmic muscle twitching) symptoms. This type of spreading of seizure activity after focal onset is referred to as secondary generalization. These seizures were once referred to as grand mal seizures, though this terminology is now discouraged. Conversely, atonic seizures produce a sudden reduction in muscle tone. Generalized Seizures Generalized seizures refer to seizures initiate in both brain hemispheres simultaneously. These seizures are often accompanied with impaired consciousness. Two important types of generalized absence seizures are absence seizures and status epilepticus. Absence seizures Absence seizures are a type of generalized seizure where seizures are initiated by an abrupt rapid onset as well as an abrupt rapid offset. These seizures have an off and on nature where the duration of the seizure is rarely longer than 30 seconds in duration and most often less than 5 seconds in duration (Shorvon et al., 2004). Often the patient will not provide explicit symptoms of having experienced a seizure, but rather may continue the behavior or movement pattern that 35

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was active at seizure onset. The impaired consciousness combined with a general amnesia about the experience means that absence seizures can interfere with schooling and may even be misinterpreted as daydreaming. Status epilepticus Status epilepticus is a serious, potentially fatal condition in which seizures persevere for significantly longer durations than other seizure types. One of the challenges in diagnosing status epilepticus is to provide a definition that is theoretically sound as well as useful in the emergency room as neuronal damage can occur after sufficient time (Costello and Cole, 2007). In addition to the brain, prolonged seizures can damage to numerous body systems including heart, lung, and kidney tissue (Wilner, 2003). A recent review article suggests a hybrid of operational definitions including 5 minutes of persistent, generalized, convulsive seizure activity or two or more distinct seizures between which there is incomplete recovery of consciousness (Lowenstein et al., 1999) where the seizure activity also persists after sequential administration of appropriate doses of appropriate first and second line-AEDs (Costello and Cole, 2007). Nonconulsive status epilepticus (NCSE) refers to the cases of status epilepticus associated with ictal EEG activity yet without convulsive motor activity (Uthman and Bearden, 2008). Patients in the NCSE state may appear to be in a confused stuporous state or a comatose-like state (Costello and Cole, 2007). While status epilepticus can take on many electroencephalographic characteristics, clear cut nonconvulsive status epileptic cases will present the following properties: Frequent or continuous focal electroencephalographic seizures demonstrating changes in amplitude, frequency, or localization Frequency or continuous generalized spike and wave discharges (SWDs) in patients whom do not have a history of epilepsy 36

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Frequent or continuous generalized SWDs which show significant amplitude or frequency differences in relation to previous SWDs (in patients with a history of epileptic encephalopathy) Periodic lateralized epileptiform discharges (PLEDs) in patients which have become comatose after convulsive status epilepticus (Korff and Nordli, 2007). The challenge of treating NCSE cases is that both the electroencephalographic characteristics and the clinical symptoms can appear very similar to those exhibited by metabolic disorders. For example, cases of positive NCSE diagnosis have been reported where patients initially demonstrated extended periods of diffuse rhythmic delta activity before any ictal waveforms were presented (Uthman and Bearden, 2008). Triphasic waves can be present in both NCSE as well as the non-epileptic encephalopathies such as metabolic encephalopathies, though triphasic-like waves must be highly persistent to be considered as possibly arising from NCSE (Kaplan and Birbeck, 2006). Currently, one of the most reliable diagnostic strategies is to administer a dosage of a benzodiazepine class drug and to observe any changes in the EEG signal. Though a small portion of patients (~15%) will be resistant to benzodiazepine therapy, the drug will often result in improved mental status and suppression of ictal waveforms in patients that were undergoing NCSE (Shneker and Fountain, 2003). The absence of clinical improvement after benzodiazepine dosage does not necessary rule out NCSE. Epilepsy Treatment Surprising as it may be the plethora of modern medical imaging technologies that have developed in the recent decades, though useful for supplementing available information about the brain, are no substitute for a medical imaging modality invented over 80 years ago. EEG 37

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recordings are relatively cheap to acquire, relatively safe, are often noninvasive (except in more severe epilepsy cases), and provide exceptional time resolution. The Electroencephalogram as a Diagnostic Tool EEG recordings as well as other related electrophysiological measures are the most commonly used diagnostic tools for the treatment of epilepsy. Though numerous people made significant technological contributions, Richard Caton is established as the first physician to observe the brains continuous spontaneous electrical activity in 1875 (Goldensohn, 1997). Hans Berger is credited as the father of electroencephalography due to his 1932 report containing four photographic EEG segments of a patients postictal recovery (Goldensohn, 1997). The measurement of the brains electrical field potentials via EEG is the cornerstone for epileptic diagnosis and classification of epileptic seizures (Speckmann et al., 1997). Field potentials are detectable in the space surrounding nervous system tissue. Field potentials arise from the changes in membrane potential of neurons and glial cells. An excitatory post synaptic potential (EPSP) occurs when an excitatory afferent fiber is stimulated and the resulting inflow of cations (e.g. sodium) lead to a membrane depolarization. The spread of the membrane depolarization results in an intracellular current as well as an extracellular current. The extracellular current induces the field potential which is perceived by a nearby electrode as a negative charge (due to the influx of cations) and a distant electrode perceives a positive charge (due to the out flux of cations) (Speckmann et al., 1997). A similar yet opposing process occurs for an inhibitory post synaptic potential (IPSP), where the stimulation of an inhibitory afferent fiber induces an outflow of cations perceived by a nearby electrode as a local positive charge. Field potentials generated by epileptic processes exceed the potentials generated by nonepileptic processes because the epileptic activity is highly synchronized (and thus have relatively elevated amplitude due to a summation effect). Furthermore, experiments have 38

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demonstrated a close temporal relationship between the paroxysmal depolarization of a neuron in superficial cortex and EEG sharp waves (an indicator of epileptic activity) during the development of an epileptic focus in a seizure model (Speckmann et al., 1997). Due to the large degree of synchrony in epileptic outbursts the behavior of this neuron can be extrapolated to provide a suitable representation of the epileptic neuronal network. Though sharp waves have an important role in epilepsy diagnosis, there are numerous types of epilepsy with differing characteristic EEG patterns. For example, absence seizures are often associated with 3-hz generalized spike and wave patterns yet tonic-clonic seizures are often associated with a variety of rhythms of generalized spiking and polyspike bursting (Chabolla and Cascino, 1997). Beyond the handful of examples of epileptiform EEG patterns listed here, there are numerous EEG properties that the trained electroencephalographer takes into consideration before arriving at a diagnosis. Such diagnostic details are beyond the scope of this dissertation, however, an excellent overview can be found in Chabolla and Cascino (1997). Once the proper diagnosis is made, there are numerous methods used to treat epilepsy. The methods are treating a specific cause (if one can be identified), avoiding precipitants of seizures (if any can be identified), antiepileptic drugs (AED), behavior modification, surgery, electrical stimulation, and diet control (Oxley and Smith, 1991). Use of AEDs is the most common form of treatment. Antiepileptic Drugs AEDs can treat seizures in numerous ways. Some AEDs make brain cells less excitable. Others make brain cells less likely to pass messages. Still other AEDs increase the amount of a inhibitory neurotransmitters such as gamma amino butyric acid (GABA) (Oxley and Smith, 1991). One way to classify AEDs is by their main therapeutic mechanism (though there are some drugs that utilize numerous mechanisms and others may even have unknown mechanisms). 39

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From this organizational framework, the main groups include sodium channel blockers, calcium current inhibitors, gamma-aminobutyric acid (GABA) enhancers, glutamate blockers, carbonic anhydrase inhibitors, hormones, and drugs with unknown mechanisms of action (Ochoa and Riche, 2007). While an in-depth review of antiepileptic drugs is beyond the scope of this dissertation, an executive summary of some of the basic antiepileptic drug categories will be outlined. Sodium channel blockers This class of drug is well characterized. As the name implies, sodium channel blocking drugs inhibit sodium channel operation which prevents the affected neuron from depolarizing and thus inhibits neuronal firing (Ochoa and Riche, 2007). Prominent examples of sodium channel blockers include carbamazepine, lamotrigine and zonisimide. Lamotrigine is a drug commonly used to treat absence seizures. GABA agonists, reuptake inhibitors, and transaminase inhibitors -aminobutyric acid (GABA) is an inhibitory neurotransmitter and popular target for antiepileptic drug action. This is because there are numerous ways to enhance the functionality of the GABA system, many of which demonstrate a clinically useful antiepileptic effect. GABA-A receptors control the influx of Clions and GABA-B receptors are connected with potassium channel function (Ochoa and Riche, 2007). The effect of GABA can be enhanced several ways: direct binding to GABA-A receptors, blocking presynaptic GABA uptake, inhibiting the metabolism of GABA by GABA transaminase, increasing the synthesis of GABA (Ochoa and Riche, 2007). Benzodiazepines (BZDs) are an important class of short-acting drugs whose anticonvulsant effect is due to binding with GABA-A receptors, where they then 40

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enhance inhibitory neurotransmission (Shorvon et al., 2004). BZDs are commonly used in epilepsy treatment as well as anesthetic applications. They are most often used for treating status epilepticus and clusters of seizures rather than long term treatment. For example, the BZD midazolam has demonstrated effectiveness the treatment of convulsive status epilepticus in patients for whom phenytoin, and/or phenobarbital had failed (Kumar and Bleck, 1992). One difficulty in with this drug class is the sedative effects which are a major factor limiting the use of benzodiazepines in long term seizure therapy. Thus, benzodiazepines tend to be used most often for acute seizure treatment. Glutamate blockers Glutamate is more of the most important excitatory neurotransmitters in the brain (along with aspartate). The glutamate neurotransmission system is highly intricate and the major classification scheme for ionotropic glutamate receptors is to name them after the agonist that activates the binding site (e.g. AMPA, kainite, and NMDA). AMPA and kainite sites control channels that pass sodium and a small amount of calcium. NMDA sites control channels that pass large amounts of calcium in addition to sodium (Ochoa and Riche, 2007). Felbamate and Topiramate are examples of antiepileptic drugs that mitigate glutamate excitatory transmission. Pharmacologically-resistant epileptic seizures AED therapy can be very effective in preventing seizures. Primary generalized epilepsy and benign partial epilepsy are two classes of epilepsy that respond well to AEDs. Patients with temporal lobe epilepsy are not so fortunate, though. These unfortunate people can usually expect to take AEDs their entire life. The odds of gaining complete control over temporal lobe epilepsy seizures are not as good as primary generalized or benign partial epilepsy (Oxley and Smith, 1991). Approximately 30% of patients with epilepsy have seizures that are resistant to AED therapy, and must resort to alternative therapies (Theodore and Fisher, 2004). 41

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Epilepsy Surgery Surgical treatment may be considered in extreme cases where the patient does not achieve adequate benefit from AED therapy (Engel et al., 1993). The mean duration of in-patient hospital stay for pre-surgical EEG monitoring ranges from 4.7 to 5.8 days and costs over $200 million each year (Begley et al., 2000). In order to be a candidate for surgery, the first criterion is that the patient must have seizures arising from a single seizure focus in the brain. In addition, the excision procedure cannot be performed on brain regions that are essential for normal functioning of the patient (Roper, et al., 1993; Velasco et al., 2000; Durand and Bikson, 2001). Even if as many as 50% of these patients were to benefit from surgical resection (an optimistic estimate), many patients still require new therapeutic approaches (Theodore et al., 2004). Gene Therapy Gene therapy is an innovative approach to providing antiepileptic therapy to patients with pharmacologically resistant seizures. From the perspective of treating epilepsy by correcting an imbalance in excitatory and inhibitory neuronal transmission, a vector can be used to insert neuropeptide genes in certain brains which lead to intracranial creation of therapeutic peptides. For example, the neuropeptide Y gene inserted into rat hippocampus with adeno-associated viral vectors resulted in reduced generalization, delayed seizure initiation, and provided neuroprotection in a rat seizure model (Noe et al., 2007). Additionally, the lentivirus may be used as a vector, or to graft genetically engineered cells which produce therapeutic substances (Vezzani, 2004). Though these as well as other results are very promising, gene therapy for epilepsy treatment is still at the pre-clinical research stage. Electrical Stimulation Therapy Brain stimulation is becoming one of the main alternative therapeutic approaches for patients whom are suffering for pharmacologically intractable epilepsy and are not surgical 42

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candidates. While the force can have a strong influence on the weak-minded (Kenobi, 1977), conventional electrical stimulation therapy remains a more widely-used form of brain stimulation. Numerous forms of electrical stimulation therapy have been utilized for the treatment of epilepsy. One such method of brain stimulation is membrane polarization by uniform direct current (DC) electric fields. This form of stimulation comes from the basic principle that electrical current can generate an electric field when then results in generation of electric current. Specifically, electric fields generated by the nervous system can directly modulate the activity of neurons and often can recruit neighboring cells. DC electric fields have a unique property compared to other stimulation paradigm in that they can cause either excitation or inhibition of neuronal activity depending on the orientation of the field with respect to dendrite. (Durand and Bikson, 2001). While DC field stimulation utilizes a relatively low current amplitude (only a few microamperes), there are several drawbacks to this method: 1) irreversible chemical reactions can result the dc field which often result in tissue and/or electrode damage; 2) the efficacy of stimulation is highly sensitive on DC field orientation; 3) either excitation or inhibition can be induced depending cell location and orientation (thus, improper DC field orientation can induce the opposite of the intended effect); 4) the termination of the DC pulse induces an excitation which results in a rebound of spontaneous activity; and 5) DC fields application must typically be applied for the entire duration of an ictal event for desired efficacy and thus may require long pulses (Durand and Bikson, 2001). Low frequency stimulation paradigms (e.g. stimulation frequencies less than 10 Hz) provide robustness over DC electric field stimulation. Unlike DC field stimulation, low frequency stimulation is not orientation dependent and thus its effects are less variable. In 43

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addition, low-frequency and single pulse stimulation have long-lasting effects which remain long after the duration of the pulse. This after effect helps minimize the electrochemical damage as well as the amount of energy required for stimulus. Periodic low frequency stimulation applied via transcranial magnetic stimulation (TMS) is a noninvasive method to induce electric fields in the brain. A study investigating the susceptibility of amygdala for kindling in rats demonstrated a 55% higher threshold for the induction of epileptic after discharges two weeks after a single TMS train (120A/s, 20 Hz for 3 s) (Ebert, 1999). The mechanism underlying this type of antiepileptic effect for low-frequency stimulation is unknown, but suspected to be long-term depression (LTD). LTD is a persistent decrease in synaptic strength caused by low frequency (e.g. 1 Hz) stimulation (Purves et al., 2004). Low-frequency stimulation paradigms for establishing LTD could decrease neuronal firing rate which may in an antiepileptic effect (Durand and Bikson, 2001). Deep brain stimulation Deep brain stimulation (DBS) attracted great attention in 1996 for its use in the treatment of tremor related to Parkinsons disease and essential tremor (Gross, 1994). DBS offers several advantages over PNS (e.g. vagus nerve) stimulation. Specifically, electrodes implanted in the brain can directly stimulate the targeted structure with far greater accuracy than PNS stimulation. Also, the coarse action of PNS stimulation risks activation of afferent (such as pain or sensory) and efferent fibers (such as those modulating cardiovascular and abdominal visceral functions) (Durand and Bikson, 2001). Naturally, a major DBS disadvantage is that the implantation of intracranial electrodes has a greater extent of invasiveness and associated risk than PNS stimulation. There are presently four general hypotheses explaining the therapeutic mechanism of DBS: 1) stimulation-induced alterations in the activation of voltage-gated currents block neural output 44

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near the stimulating electrode; 2) indirect inhibition of neuronal output by means of activation of axon terminals that make synaptic connections with neurons near the stimulating electrode; 3) synaptic transmission failure of the efferent output of stimulated neurons as a result of transmitter depletion; 4) stimulation-induced disruption of pathologic network activity (McIntyre et. al, 2004). Additional research utilizing microdialysis, neural recordings, modeling, and functional imaging will likely need to be conducted in order to fully characterize the effects of DBS (McIntyre et. al, 2004). Since DBS therapy relies on accurate positioning of electrodes, surgical implantation is assisted with several guiding tools. DBS electrodes are implanted into the brain using stereotaxic methods, MRI targeting, recording of extracellular unit activity, and electroencephalographic monitoring. Some typical stimulation parameters are 1-10 volts, 90 s pulses in trains of 100-165 Hz, running either continuously or in intervals of 1 minute on and 5 minutes off (Theodore and Fisher, 2004). Clinically useful and tolerable stimulation parameters can vary from patient to patient as well as across different sections of the brain. Thus, a common strategy of DBS is to exploit the natural behavior of various brain structures in a manner to most effectively produce an anti-seizure effect. Cerebellum Cerebellar stimulation can be performed to capitalize on the inhibitory outflow which is present in nearly all patients. Anterior stimulation decreased hippocampal formation discharges. However, cerebellar stimulation has had variable effects in animal models, which may have been related to variable stimulation parameters (Theodore and Fisher, 2004). An interesting phenomenon discovered in controlled DBS studies is the placebo effect. For example, in a controlled study of cerebellar DBS involving 14 control patients, 2 of the 14 patients showed improvements in seizure frequency (Hodaie et al., 2002). This placebo effect, defined as a 45

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reduction (or abolition) of symptoms with insertion of DBS alone, might be due to an initial lesioning resulting from the implantation procedure. Subcortical structures Interest in subcortical stimulation comes from its widespread, non-specific, anterior and intralaminar nuclear connections to the mesial frontal, temporal, and limbic structures. In addition, it demonstrates progressive recruitment of substantia nigra, subthalamic nucleus, and midline thalamic nuclei in animal models of epilepsy. Stimulation of the subthalamic nucleus, anterior, thalamus, and substantia nigra have been shown to inhibit limbic seizures in animal models of epilepsy (Theodore and Fisher, 2004). In addition, stimulation of the basal ganglia structure may modify propagation of seizures (Deransart et al., 1998). Some of the most important subcortical structures will now be discussed. Caudate nucleus The effect of caudate nucleus stimulation has demonstrated antiepileptic effects in an aluminum-hydroxide seizure focus model, though the efficacy is highly dependent on stimulation frequency (Theodore and Fisher, 2004). An inhibitory seizure protection effect was demonstrated for stimulation at 10-100 Hz, whereas 100 Hz stimulation increased seizure frequency. The anti-seizure effects of the caudate-nucleus are hypothesized to be due to activation of the substantia nigra under the presumption that low-frequency stimulation is excitatory and high frequency stimulation is inhibitory (Theodore and Fisher, 2004). Since these results are from uncontrolled studies, it is uncertain if micro ablation resulting from electrode implantation is contributing to the anti-seizure effect. Thalamus The thalamus is seen as a strategic stimulation site on the basis that it is the pacemaker of the cortex, with widespread connections between the two structures. There is electrophysical 46

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and anatomical evidence suggesting that midline thalamic nuclei may participate in modulation and spread of limbic seizures. Experimentally, thalamic stimulation has been shown to terminate seizures in a primate epilepsy model. Studies of human thalamic stimulation have been published with favorable results (Theodore and Fisher, 2004). Centromedian nucleus The centromedian nucleus (CN) has been classified as part of the non-specific thalamus. The CNs major difference from the thalamus in terms of stimulation for epileptic seizures is that the CNs output is more strongly related with the caudate nucleus than with the cortex (Theodore and Fisher, 2004). In a placebo-controlled double-blind study involving 7 patients, CN stimulation resulted in a 30% decrease with respect to baseline when the stimulator was on versus an 8% decrease when the stimulator was off (Fisher et al., 1992). CN stimulation appeared safe and well tolerated by the patients. Anterior thalamic nucleus The anterior nucleus of the thalamus (ATN) may help influence the propensity of seizures due on its connectivity and functional relations with the cortex and limbic structures. High frequency stimulation of the ATN leads to EEG desynchronization, which is believed to render the cortex less susceptible to seizures (Hodaie et al., 2002). Specifically, 100 Hz had an anti-seizure effect whereas stimulation at 10-50 Hz lowered the seizure threshold. A controlled study of 5 patients resulted in a mean seizure reduction of 54%. An interesting observation was that the results did not differ from the stimulation on and stimulation off periods (Theodore and Fisher, 2004). This is thought to be due to a microthalamotomy placebo-effect. This phenomenon of a reduction or abolition of symptoms due to insertion of DBS electrodes alone has been seen in over 53% of DBS electrode implantations for tremor, and can last up to a year in some cases (Hodaie et al., 2002). 47

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Subthalamic nucleus The subthalamic nucleus (STN) was chosen based on encouraging responses in patients with movement disorders as well as high-frequency stimulation in animal epilepsy models. In a study utilizing STN high frequency stimulation in 5 patients, 3 patients showed reduction in seizure frequency of 67-80%, one patient had approximately 50% seizure reduction, and the fifth showed no improvement. In this study, the recording of epileptiform activity in the STN suggests that it is part of a cortico-subcortical network involved in the epileptogenic process (Chabardes et al., 2002). Hippocampus Human studies of hippocampal stimulation have demonstrated that high-frequency stimulation, rather than low frequency, can be inhibitory. This is contradictory to several preclinical investigations of hippocampal stimulation. One theory for this phenomenon is that the anti-seizure effect is due to the activation or inhibition of downstream structures (as opposed to the hippocampus itself). Nevertheless, 7 patients that participated in a hippocampal stimulation study involving 2-3 weeks of 130 Hz electrical stimulation for 23 hours per day responded very well. Stimulation halted clinical seizures and decreased the number of interictal EEG spikes at the focus after 5-6 days. However, no observable antiepileptic effects (or no effects at all) were found in three patients when stimulation was either interrupted or given elsewhere just outside of the hippocampus (Theodore and Fisher, 2004). Vagus nerve stimulation VNS therapy has been the subject of many studies before and after its approval for treatment of intractable seizures in 1997 (Uthman et al., 1993; Ben-Menachem et al., 1994; Theodore et al., 1997; Schachter et al., 2002; Cyberonics, 2006; Ardesch et al., 2007; Ramani, 2008). VNS is licensed in several countries as an adjunctive epilepsy therapy with a rare 48

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occurrence of serious side effects. Studies suggest that VNS treatment results in a much lower incidence of adverse cognitive, neurological, and systemic effects than AED treatments (George, 2001). Over 40,000 epilepsy patients have VNS therapy implants (Cyberonics, 2008). VNS is a useful therapy for patients with medically refractory and localization-related epilepsy characterized by complex partial and secondary generalized seizures (Theodore and Fisher, 2004). The apparatus consists of an electric stimulator which is implanted subcutaneously in the left side of the chest and connected to the left cervical vagus nerve using subcutaneous electrical wires. The device is programmed to provide neurostimulation at a set duration, frequency, intensity, and pulse width for the treatment of epilepsy. Figure 2-2 provides an example of the VNS pulse sequence. Figure 2-2. VNS pulse sequence. The vagus nerve was chosen as the site for stimulation because of its diffuse and widespread projections to the thalamus, amygdala, and forebrain through the nucleus tractus solitarius and to other cortical areas via the medullary reticular formation. Though VNS therapy has demonstrated seizure treatment efficacy, the therapeutic mechanism is still uncertain (Ben-Menachem et al., 1994; Fisher et al., 1999; Groves, 2005; Ramani, 2008). However, a physiologic framework for the VNS therapy mechanism has been 1 0 mA Output Current Pulse Width Ramp up (2 sec) 1/frequency Ramp down (2 sec) On time 49

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described (Upton et al., 1991; Ramani, 2008). The vagus nerve is the 10th cranial nerve and is comprised of approximately 80% afferent fibers, which carry sensory information to the brain. The vagus nerve is highly involved in the regulations of numerous autonomic systems such as the heart, the intestines, and provides and integral role in respiration. Studies suggest that the metabolic activation of thalamic, brainstem, and limbic regions may be integral in the mediation of VNS effects (Fisher et al., 1999). It has been shown that depletion of norepinephrine in the locus coeruleus attenuates the AED-like effect of VNS (Krahl et al., 1998). Recent studies also suggest that the VNS may exert its effect through the locus coeruleus (Groves, 2005; Ramani, 2008). Experiments in which cat vagus afferent neurons were stimulated were able to produce either cortical synchronization or desynchronization, depending on the fibers conduction velocity (Upton, 1991). Recent studies have determined that vagus A and B fiber activation can lead to EEG synchronization whereas vagus C fiber activation results in EEG desynchronization (Groves, 2005). Electrical stimulation of the vagus nerve resulted in a reduction of interictal epileptiform spike frequency during and up to three minutes after stimulation in a rat seizure model (McLachlan, 1993). Overall, in lieu of these and other reported VNS effects there is no consensus as to how these empirical effects relate to epilepsy. Though studies have examined how vagus A, B, and C fiber stimulation affects synchronization, the overall VNS-induced effects of these fibers and other relevant brain structures on EEG, reports suggest that these effects not explicitly visible in the time domain (Fisher et al., 1999) or in frequency domain (Salinsky et al., 1993). Numerous studies report little success in quantifying immediate EEG effects corresponding with VNS (Hammond et al., 1992; Salinsky et al., 1993; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005). The only reported scalp-EEG effects of VNS are reported to 50

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occur numerous months after VNS implantation. Studies involving long-term EEG monitoring have shown that long-term VNS produces a delay in interspiking activity and a reduction in the occurrence of epileptic interictal spikes (Koo, 2001; Olejniczak et al., 2001). Marrosu et al. reported no noticeable changes after one month but an increase in gamma activity and desynchronization one year after VNS implantation compared to baseline recordings (2005). Studies have demonstrated VNS effects on interictal epileptiform discharges (Santiago-Rodriguez and Alonso-Vanegas, 2006) and that the absence of bilateral interictal epileptiform discharges may be an electroencephalographic predictor of seizure freedom (Janszky et al., 2005). In addition, long-term VNS effects have been reported on the spectral content of sleep EEG after 10-18 months of VNS compared to a baseline at 3 months prior to implantation (Rizzo et al., 2004). Future Therapeutic Directions One major epilepsy research direction is to enhance therapeutic effectiveness of electrical stimulation or drug therapy though the application of implantable controlled therapy systems. For patients which are currently undergoing therapy from the available electrical stimulation implants (such as the vagus nerve stimulator), research in this direction may help to enhance efficacy, mitigate side effects, reduce therapeutic tolerance, and prolong battery life. Along these lines, such a framework could be adapted to an implantable drug delivery system that would dispense drug at right and the right place (e.g. in proximity of a seizure focus or in a location to rapidly circulate medication such as the ventricles). One framework from which this strategy can be visualized is from a system control perspective. Thus, the basic theory behind this strategy is that the transition from a normal interictal state into a preictal state can be conceptualized as a deviation of a control parameter from its set point. Numerous researchers have invested in this idea using EEG signals as 51

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controlled measure (Osorio et al., 2001; Iasemidis, 2003; Iasemidis et al., 2003; Osorio et al., 2005). While the basic example of deviation from a set point does not do justice to the enormous complexity of the brains electrical activity, recent advances in mathematical theory of complex nonlinear dynamical systems provide an interesting perspective from which to examine and interpret EEG signals. Complex nature of epileptic dynamics One of the most challenging aspects of epilepsy treatment is that despite the major milestones in biological research, there is still an inadequate knowledge of the underlying biological processes governing the epileptic condition that describes how, where, when, and for what purpose a seizure will occur. One perspective is that the epileptic brain is exposed to at least two states, a normal (interictal) state and a seizure imminent (preictal state). A natural approach for studying any aspect of brain behavior is to create mathematical model of some brain function using measurable quantities, such as electrical signals. Such models allow predictions to be made about the behavior of sections of the brain. Due to the massive complexity of the interacting neurons in the brain, direct models are most often achieved for small groups of neurons and small brain structures (Hodgkin and Huxley, 1952; Breakspear, 2001; Chauvet and Berger, 2002). The enormous complexity of electrical brain signals often means exact modeling approaches are insufficient. However, despite the observed dynamical complexity of the epileptic brain there certain behavioral characteristics it possess which can provide analytical guidance. Dynamical diseases and disorders One important diagnostic aspect of many diseases and disorders is the physiologic behavior in the temporal dimension. In the 1980s many studies addressed the temporal behavior 52

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of biological systems with and without a disease state. Experts within this field often focused their attention on the time scales involved in the clinical aspects of the disorder. This includes characterization of the disease or disorder onset (acute or subacute) as well the succeeding clinical course (self-limiting, relapsing-remitting, cyclic, or chronic progressive) (Belair et al., 1995). The term Dynamical Disease or Dynamical Disorder refers to the general class of diseases and disorders that are characterized by sudden changes in physiological dynamics that lead to state of morbidity characterized by abnormal dynamics (Belair et al., 1995). Such dynamical disorders arise as a result of abnormalities in underlying physiological control mechanisms. There are many instances of disease and disorder models where the apparent shift of control parameters to region results in pathological behavior of an observable which bears a resemblance to experimental data. Mackey and Glass demonstrated adaptive respiratory disease behavior that displayed a wide range of behaviors such as limit cycle oscillations with aperiodic chaotic solutions (Mackey and Glass, 1977). This particular example exhibited a bifurcation in the systems dynamics that was associated with disease onset. The unstable dynamical realm achieved by altering a normal hematopoiesis model bears qualitative similarities to actual hematopoietic data from a leukemia patient (Mackey and Glass, 1977). Thus, there are biological examples to support the claim that mathematical models of physiologic systems may be able to predict the existence of dynamical regimes corresponding to the status of a dynamical disease. Whether the dynamical behavior is periodic, irregular, or apparently random, the significance of dynamical disease identification is that it may be possible to develop therapeutic strategies based on manipulation of critical control parameters (Milton and Black, 1995). Taking into account the temporal rhythm of the disorder as well as an understanding that certain 53

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dynamical rhythms may respond better to some treatments rather than others can help provide a foundation for a suitable therapy (Belair et al., 1995). Epilepsy as a dynamical disorder of brain systems Neurological disorders can take on a wide range of complex and abnormal rhythmic behavior over time (Milton et al., 1989). Milton and Black reported observations of recurring sets of symptoms and oscillatory behavior in 32 periodic diseases of the nervous system including, ankle clonus in corticospinal tract disease, movement disorders such as essential tremor and Parkinsons disease, as well as paroxysmal oscillations in neuronal discharges in epileptic seizures (Milton and Black, 1995). The cluster of symptoms occurring with a distinct temporal pattern could represent the clinical manifestation of dynamical state changes in these patients. In the context of neural tissue, one view of the abnormal dynamical behavior in neurological patients may arise because of altered control parameters (e.g. nerve conduction time, number of receptors, etc.) and/or alterations in neuronal network structure (Milton et al., 1989). Compensating for impaired neural control mechanisms: system control therapy Currently, the biological mechanisms driving transitions into and out of dynamical rhythms (e.g. oscillatory behavior) in neurological disorders are in general poorly understood. A study examining a tremor simulation by inducing delay and amplification in a visual motor task suggests there tremor could be an alteration of numerous interacting control loops or possibly a time-delay state-dependent control system (Milton et al., 1989). One major difficultly whether dealing with tremor or other neurological disorders is to uncover the complex interactions of various interconnected control loops and determine how each contributes to the observed dynamical behavior. Understanding the origins of the dynamical behaviors seen in neurological 54

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disorders can provide a foundation for designing any type of patient-specific therapeutic control system. An example of such a device is shown in figure 2-3. ECoG / EEG Stimulator Feature extraction algorithm Closed loop Controller Figure 2-3. Closed-loop seizure control device using electroencephalogram or electrocorticogram signals as an input to a feature extraction algorithm, which supplies the extracted features to a controller which makes a decision regarding the action of a stimulator. One of the major themes of quantitative EEG analysis in epilepsy as well as other neurological disorders is the identification of signal features that are sensitive to neural state changes. Chapter 3 provides an overview of the rich spectrum of feature extraction strategies employed for quantification of brain dynamics in neurological disorders such as epilepsy. 55

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CHAPTER 3 TIME SERIES ANALYSIS AND DATA MINING TECHNIQUES: THEORY AND APPLICATION The wealth of epilepsy research conducted via quantitative analysis of EEG signals comprises a rich history. Numerous mathematical models have been applied for the purpose of modeling the progression of disease and inferring the biological significance of the underlying the observed EEG signal patterns. The EEG is a time series of voltage measurements acquired between a scalp or intracranial location of interest and a reference electrode point (e.g. an electrode placed on the ear). Naturally, time series analysis techniques were among the first methods applied for quantifying brain dynamics and constitute a significant portion of quantitative EEG research. In addition, data mining tools are becoming increasingly popular for the extraction and classification of patterns in biological datasets such as EEG signals. The following literature review provides a general overview of the tools used in quantitative EEG research. Glossary of Terms Attractor. An attractor is defined as a set of points mapped into a phase space representation which is a target region which adjacent states within a neighborhood (see: basin of attraction) will converge towards as the system evolves towards infinity. An attractor is established to be the smallest region for which the entire volume cannot be further split into two or more attractors having corresponding basins of attraction (as a system may have multiple attractors each with a basin of attraction). Basin of Attraction. A set of points in phase space such that initial conditions existing in this set evolve over time into a corresponding attractor. 56

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Bifurcation. A bifurcation is defined as a sudden appearance of a qualitative change in dynamics resulting from an alteration in a parameter of a nonlinear system. Bifurcations can occur in both continuous systems as well as discrete systems. Degrees of Freedom. The dimensions of a phase space mapping. Limit Cycle. In a phase space, a limit-cycle is a closed trajectory which possesses the characteristic that at least one other trajectory will traverse into it as time approaches infinity. Phase Space. Phase space is the group of potential states for a dynamical system. Phase space is typically identified with a topological manifold. Each point in the phase space represent an instantaneous and unique state of the system. Strange Attractor. Strange attractors have a non-integer dimension. The descriptive term strange refers to the geometrical structure of the attractor, whereas the term chaotic refers to the dynamics on the attractor (Grebogi, 1984). Trajectory. The trajectory of a dynamical system is the orbit connecting points in chronological order in the phase space that is traversed by a solution of an initial value problem. If the state variables are within a real-valued continuum, then the orbit of a continuous time system is a curve. Discreet system trajectories consist of a sequence of points. Time Series Analysis Time series analysis is the field of study that aims to extract useful information from time series datasets. A time series is a series of measurements that are acquired at successive times often with a constant time interval. Many aspects of our universe can be represented and studied as time series datasets. This field of study has been extensively applied to financial decision making as well as numerous scientific disciplines. One major goal of time series analysis is to extract useful information about the system that generated the time series dataset. An additional 57

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aim of time series analysis is to model the system dynamics in order to make predictions about future behavior. Methods Applied in the Time Domain Numerous linear EEG processing techniques have been implemented in the history of quantitative analysis. This section reviews some of the most utilized measures for the analysis of discrete time series data within the time domain. Autoregressive moving average modeling The autoregressive moving average model (ARMA) is standard time series analysis tool used to model univariate datasets. This method is also known as the Box-Jenkins model as the iterative Box-Jenkins procedure it often used to estimate model coefficients (Box and Jenkins, 1976). The model is comprised of two parts, an autoregressive component and a moving average component. For a univariate time series dataset X t autoregressive component at time t is defined as: tpiititXCX1 (3-1) where C is a constant, pi ... are the parameters of the model of order p and t is the error term. The moving average component is defined as: tqititX11 (3-2) where pi ... are the parameters of the model of order q, and 1t and t are the previous and current error terms, respectively. Combining the autoregressive term with the moving average term produces the ARMA model of order p (autoregressive terms), and q (moving average terms): 58

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tqitipiititXX111 (3-3) Such methods have been utilized in modeling functional brain network organization using spectral analysis of local field potentials (Bressler et al., 2007). Autoregressive integrated moving average modeling The autoregressive integrated moving average (ARIMA) process is a well-known method for making predictions in nonstationary time series datasets (Box and Jenkins, 1976). As the name implies, this measure is a generalization of the ARMA process. The ARIMA approach to working with nonstationary time series works by utilizing the d th difference to convert the nonstationary time series to a stationary ARMA process. Naturally, the ARIMA method assumes that a time series can be reduced to a stationary time series through the process of differencing. The statistical properties of the stationary time series remain constant in time, and residuals (errors between the original time series and the ARIMA model) are assumed to be the result of noise. Let be an ARIMA process of order p,d,q where the d ty th difference of is a stationary ARMA process of order p,q. The model ARIMA model is then expressed as: ty ttdzByBB1 (3-4) where and are polynomials of degree p and q (respectively) having roots outside the unit circle, B is the backward shift operator, and z t is white noise. Cross correlation Cross-correlation analysis is one of the oldest and most standard time series analysis techniques (Bendat and Piersol, 1986). This method measures the linear coupling between two signals. 59

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Let X be some represent an identically distributed stationary stochastic process where is the value of tX X at time t. Cross-correlation function representing the coupling between two time series functions and tX tY is defined with a time lag, as follows: dttytxCxy (3-5) Cross-correlation is often applied to data from a physical system which typically takes on a discrete form. Let and represent two simultaneously acquired stationary time series of length M, zero mean, and unit standard deviation. The discrete unbiased estimate of the cross correlation function is then defined as a function of time lag 10,...,Mxx 10,...,Myy 1,...,0,...,1MM as follows: 0,0,11xyNiiixyCyxNC (3-6) The normalized cross-correlation function outputs values within the range of negative one (maximum anti-synchronization) to one (complete synchronization). The maximum of equation 3.5 is understood to be an estimation of the delay between two signals (assuming this signals have a linear relationship to one another). The cross-correlation of a function to itself is called autocorrelation. As the cross-correlation value approaches zero, the signals of interest are increasingly linearly independent. Often a significance threshold is applied to prevent the possible occurrence of a non-zero cross-correlation value for two linearly independent systems (Box and Jenkins, 1976). 60

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Methods Applied in the Frequency Domain Frequency representation is a standard format for visualizing signal characteristics. This perspective provides a clear visualization of a signals periodic behavior which may not be evident in the time domain. Thus, frequency domain analysis can help uncover important properties of the system of interest. Coherence Coherence is a measure of coupling between two signals as a function of frequency. The signal coherence can take on values between zero and one that provide a relative indicator of how well the signal X corresponds to signal Y at each frequency. The Fourier transform is performed on each signal to convert the signal into the frequency domain (calculate the power spectral density). The cross power spectral density is calculated by multiplying one signal by the complex conjugate of the other signal. The coherence measure is a function of the power spectral density of the individual signals and the cross power spectral density. This measure is typically expressed in terms of its square magnitude and is derived by normalizing the cross power density by the product of power spectral density for the two signals, fPfPfPfCyyxxxyxy22 (3-7) where and represent the power spectral densities for signals X and Y respectively and is the cross power spectral density (Fuller, 1976). A coherence of zero indicates no coupling between the two signals at the particular frequency whereas a coherence of one implies linear relationship with constant phase shifts between each frequency component. Coherence has been implemented in electrophysiology experiments for several years and more information can be found in literature (Shaw, 1984; Leocani, 1999). xxP yyP xyP 61

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Discrete Fourier transform The Fourier transform has been implemented in extensively in numerous fields such as mathematics, physics and natural sciences. The Fourier transform is an especially attractive algorithm due to the development of the streamlined Fast Fourier Transform (FFT) (Cooley and Tukey, 1965). In recent years, additional developments have been implemented in the FFTW subroutine library developed by a team of MIT researchers (Frigo and Jonhnson, 2005). This free software package provides a means to optimize the FFT algorithm using various heuristic approaches for each unique problem and platform combination. This subroutine library has been utilized by many researchers and is even implemented in the Matlab function library. Fourier analysis decomposes a signal into linear component parts. The analysis involves to concepts: Linear combination of different waveforms. A time series of any shape can be sufficiently represented by the summation of ample simple sine waves of different frequencies, phases, and amplitudes. Given a signal Fourier analysis models the signal as a linear combination of sine and cosine waves for frequency where: tx f dfefXtxfti2 (3-8) and dtetxfXfti2 (3-9) Equation (3-8) is the continuous Fourier transform which is comprised of the complex coefficients representing the contributions of each frequency, to the overall representation of the original time series Equation (3-7) is often referred to as the inverse Fourier transform. f tx 62

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For a discrete signal, (3-10) 10,...,Nxxx where is sampled at the time nx jttn0 the discrete Fourier transform (DFT) is represented as: 102NnNknienxkX (3-11) for the discrete frequencies Nkfk (3-12) where the inverse Fourier transform is expressed as: 1021NkNkniekXNnx (3-13) While Fourier analysis is useful for capturing periodic waveforms in non-transient signals, this measure is not suited for extracting transient features. This is because time information is no longer available in the frequency domain as the DFT coefficients are representative of the entire signal duration. The Fourier transform has been extensively applied to the analysis of EEG waveforms in epileptic patients. Diagnostically, it can help determine the presence of specific brain wave rhythms which may be indicative of certain types of epileptic behavior. Often the time series of interest is broken down into non-overlapping segments in which the Fourier transform is calculated to give a rough estimate of the frequency behavior over time. An example of an a single channel of EEG acquired during an absence seizure and its corresponding windowed Fourier transform is shown in figures 3-1 and 3-2, respectively. 63

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In figure 3-2, the absence seizure onset is characterized by a sudden energy increase in the 0-30 Hz frequency band with the strongest effect around 3 Hz (which is the typical rhythm of spike wave discharges in absence seizures). Wavelet analysis Wavelet analysis is a signal processing tool which models a times series signal in terms of shifted and scaled mother wavelet. Wavelet analysis is similar in some aspects to Fourier analysis, which models a signal using sinusoids. Instead of sinusoids, wavelet analysis models a signal using an application-specific waveform called a wavelet which has an effectively limited duration and a mean value of zero (Misiti et al., 1996). Wavelet analysis is very useful for performing localized analysis in a subregion of a larger signal. In addition, wavelet analysis is capable of revealing aspects of data that traditional signal analysis techniques may miss such as trends, breakdown points, discontinuities in higher derivatives, and self-similarity (Misiti et al., 1996). For a particular mother wavelet function t the subspace at time t for a scale, a, and a position, b is represented by abtatba1, (3-14) If represents the time series signal, then the continuous wavelet transformation at scale, a, and position b is defined as: tx dtabtatxCba1, (3-15) where denotes the complex conjugate of the wavelet and 0,, aRba For low values of the scaling factor a, the wavelet becomes compressed and becomes sensitive to rapidly-changing details and high frequency waveforms. For high values of a, the wavelet becomes stretched and 64

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is more sensitive to coarse slowly-changing features and low frequency waveforms. The parameter b localizes the wavelet function in time. Wavelet analysis has demonstrated utility for the analysis of nonstationary signals such as EEG (Geva et al., 1998, Gler and Ubeyli, 2005; Glassman et al., 2005). Information Based Methods Information theory is based on the 1948 publication by Claude Shannon which was the first paper to quantify the concepts involved in communication. Information quantified in units of bits and concepts such as entropy and mutual information were used to describe the transfer of information (Shannon, 1948). Information theory concepts have been extended to time series analysis in biological series such as the EEG. Under the proper statistical conditions, these measures provide useful information about the behavior of the brain. Approximate Entropy Approximate entropy (ApEnt) is a statistical measure used to quantify system regularity/complexity from a time series dataset. This measure has been extensively utilized in physiological time series data (Pincus, 1995). The ApEnt measure has been utilized to study the EEG signals acquired from Alzheimers disease patients (Absolo et al., 2005), as a measure of anesthetic depth (Bruhn et al., 2000, 2001, 2003), epileptic seizures detection (Absolo et al., 2007; Srinivasan, 2007), and studies characterizing EEG nonlinearity patterns (Thomasson et al., 2000; Burioka et al., 2003,2005; Ferenets et al., 2006). The ApEnt measure has demonstrated the ability to quantify system complexity using as few as 1000 data points based on theoretical analyses of stochastic and deterministic chaotic processes (Pincus, et al., 1991; Pincus and Keef, 1992) as well as clinical and clinical applications (Pincus 1995; Bruhn et al., 2000). In this dissertation, ApEnt is used as a measure for quantifying the VNS effect on EEG recordings. 65

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Let Ube a signal of length. For positive integer and a positive real number extract create vectors N m fr 1 m N 1,...,1, miuiuiuixm For all i, 11 mNi the quantity is computed as follows: number of j such that miC 1,dsuch that j ofnumber mNrjxixrCfmmfmi (3-16) where d is the maximum absolute difference between the respective scalar components of the two vectors defined as : ixm jxm 11max,,...,1kjxkixjxixdmmmkmm (3-17) Using these results, the value of can be calculated as: m 11log11mNimifmCmNr (3-18) ApEnt is calculated as: fmfmfrrNrmApEn1,, (3-19) In this manner, the value of the positive real number corresponds distance between the neighboring point that is often designated as some fraction of the signals standard deviation. For this reason, the positive real number can be thought of as a filtering level for the process. The parameter mis the dimension at which the signal is embedded for calculation. fr fr Pattern Match Regularity Statistic Pattern match regularity statistic (PMRS) is a method used to extract the nonlinear characteristics (complexity) of a time series over time. This measure has been for the quantifying the complexity of an input EEG signal and further detecting EEG state changes such as seizure onset (Shiau, 2001; Shiau et al., 2004). This measure estimates the likelihood of 66

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pattern similarity for a given time series. PMRS has the attractive feature that it can be interpreted in both stochastic and chaotic models. The steps to calculate PMRS include reconstruction of the state space, searching for the pattern matched state vectors, and the estimation of pattern match probabilities. Specially, given an EEG signal let },,,{21nuuuU u be the sample standard deviation for U. For an integer m (embedding dimension), phase space vectors U are reconstructed as 11},,,,{11 mniuuuxmiiii (3-20) then for a given positive x fr i and x j are considered pattern match to each other if: 11)()(,||,||1111 mkforuusignuusignandruuruukjkjkikimjmiji (3-21) where corresponds distance between the neighboring point that is often designated as some fraction of the signals standard deviation. PMRS can then be calculated as: fr mniipmnPMRS1)ln(1 (3-22) where }|)()({Pr11matchedpatternarexandxuusignuusignobpjimjmjmimii (3-23) Mutual Information Information theory measures such as mutual information have shown utility for estimating high order statistical dependencies between signals. In contrast to linear coupling measures (e.g. cross-correlation), mutual information is sensitive to nonlinear dependencies. 67

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For continuous variables X and Y with probability density function of and respectively, and is the joint density function, mutual information can be calculated as follows: xf yf yxf, dxdyyfxfyxfyxfYXIXY,log,, (3-24) Mutual information between two discrete random variables having marginal probabilities = prob(X=x) and = prob(Y=y) and joint probability xpX ypY ),(yYxXprobxpX is defined as: ypxpyxpyxpYXIYxyx,log,,, (3-25) A common approach to calculating mutual information is to first partition X and Y into bins (e.g. a histogram). An estimation of YXIYXIbin,, is obtained by replacing the probability functions, and xf yf yxf, with an approximations based on the histogram. Thus, if and are the number of points from X within the x-th bin and number of points from Y within the y-th bin, respectively, and is the number of points in the intersection of the two bins, then and xb yb xyb Nbxpxx/ NbypyY/ Nbyxpxy/, Mutual information has been successfully used to quantify statistical couplings in biological applications such as sleep studies (Na et al., 2006) Alzheimers disease (Absolo et al., 2007) and epileptic seizures (Varma et al., 1997; Palus et al., 2001; Netoff et al., 2002). Chaotic System Analysis Techniques One approach for quantifying the behavior of a complex system such as the brain is to create a mathematical model of the system behavior using measurable quantities. Electrical signal measurements are often used to model the brain modeling the brains behavior. Such 68

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models allow predictions to be made about the behavior of sections of the brain. Due to the massive complexity of the interacting neurons in the brain, direct models have only been achieved for small groups of neurons and small brain structures (Breakspear et al., 2001; Chauvet and Berger, 2002; Hodgkin and Huxley, 1952). The enormous complexity of electrical brain signals often means exact modeling approaches are insufficient. Edward Lorenz is often credited as the discoverer of chaos for the fruits of his efforts to devise a long-term weather prediction scheme (Lorenz, 1963). Though Lorenzs model did not turn out to aid in forecasting weather, his results directed his attention to research which helped give rise to research in the area of chaos theory. Chaotic systems have the interesting property of displaying apparent random behavior but are actually governed by deterministic laws. Specifically, chaotic systems demonstrate a large degree of sensitivity to initial conditions to the point at which minor fluctuations in initial parameters give rise to extremely altered outcomes (to the extent that prediction of such events may even be hampered by sensitivity to computer precision rounding). Since chaotic systems have characteristic similar to noise as well as a broad range of frequency components, linear measures may fail to provide meaningful results. When exact knowledge of the system governing dynamics is unknown, such as in the brain, an alternative method is a macroscopic modeling approach based on empirical measures of the system as a whole (Iasemidis et al., 1996). After such information is extracted, it may be possible to derive useful empirical models of the global behavior of the system as a whole. A well-known method to study complex system behavior is to observe the system from a phase space representation (Hively et al., 2005; Iasemidis et al., 1996). Phase space mapping is a process of applying some transformation on a dataset, often into a higher dimensional space, 69

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from which system behavior characteristics can be quantified. Some classic transformations applied in EEG analysis include time delay mapping, (Breakspear, 2001; Hively et al., 2005; Iasemidis et al., 1996; Da Silva et al., 2003; Marino et al., 2003) derivative mapping (Aksenova et al., 1999, 2003; Letellier et al., 1998; Sceller et al., 1999; Tetko et al., 1999). Phase space mapping provides a means to help distinguish random, noisy signals from signals generated from a system governed by deterministic chaos. Phase Space Mapping Generate of a time-delay phase space portrait of the system is one of the most established methods for visualizing the dynamical behavior of a multivariable system such as the brain (Iasemidis et al., 1996; Hively et al., 2005). Time-delay phase space maps are a particularly useful phase space mapping variant and are often used for the study of nonlinear deterministic systems. The phase space portrait is created by assigning each time-dependent variable of the observed from the system as a vector element in a multidimensional phase space. Each vector mapped into the phase space represents a unique and instantaneous state of the system. By plotting the phase space vectors in chronological order a representation of the temporal evolution of a discrete system can be visualized. In principle, the analysis of an individual measured variable can provide dynamical information about other system variables which are related to the measured variable (Iasemidis et al., 2003). A relevant example of this concept is that EEG recorded from one electrode can be related to the activities located at distant electrode sites. Thus, important features of a dynamical system can often be quantified through analysis of a single variables behavior over time in terms of geometrical attractor properties. From the reconstructed phase space, measurements can be made to extract useful system information from a single variable (Iasemidis et al., 1996; Pardalos et al., 2003; Chaovalitwongse 70

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et al., 2006). Such information can often be used in data classification algorithms for determining neural state (Tetko et al., 1999, Hively et al., 2005). The method of quantifying phase space properties has been extensively applied to EEG signals analysis for the purpose of studying neurological disorders (Chaovalitwongse et al., 2006; Hively et. all, 2000, 2005; Iasemidis et al., 1996, 2004, 2005; Pardalos et al., 2003, 2004). The Method of Delays Time-delay embedding is performed as follows: 12...2mtxmtxtxtxtxxnnnnnn (3-26) where is the time delay and m is the embedding dimension (Takens, 1981). For a discrete system, every instantaneous state of the system is represented by the vector in m dimensional phase space. nx Numerous studies have addressed the problem of determining proper parameters for the embedding dimension m and The first zero of the autocorrelation function (Rapp et al., 1988) or the first minimum of the mean automutual information (Fraser et al., 1986) are two of the most common approaches to obtain the time delay, Takens recommended a minimum embedding dimension m = (2D+1) to ensure complete unfolding of the attractor, where D is the fractal dimension (Takens, 1981). 71

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Fractal Dimension The term "fractal" was coined by Benoit Mandelbrot in 1975 to describe self-similarity characterized as a jagged geometric shape which can be split into parts which are approximately reduced-size copies of a whole (Mandelbrot et al., 1983). The fractal dimension is a statistical measure of the extent to which a fractal appears to fill space. A non-integer fractal dimension is said to originate from fractal geometry. Strange attractors often have a complex structure with fractal-like properties. Thus, the fractal dimension is a logical measure to use for quantifying strange attractor dimension. Determining the dimension of an attractor is an important step in the characterization of a systems properties. A proper dimensionality estimate can enhance the accuracy at which the location of a point on an attractor can be specified. Furthermore, the dimension value provides a lower bound on the number of variables required to model the system dynamics. A standard technique for estimating attractor dimension is from the framework of measuring the changes in the number of points occupying a sphere of radius r as it approaches zero (Grassberger and Procaccia, 1983a; 1983b). Geometrically, the relevance of this observation is that volume occupied by a sphere of radius r in dimension d behaves as d r For most attractors the dimension d would be the dimension of the attractor, regardless of the origin of the sphere. For a chaotic attractor, however, the dimension will vary depending on which point is selected for the estimation. If the particular systems dynamics do not result in dimensional variation, then the mean of the surrounding points can be used. Obtaining the dimension in this method can be obtained by determining the number of point y(k) within a sphere positioned at the phase space location x as follows: 72

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NkxkyrNrxn11, (3-27) where represents the Heaviside Step Function where: 0,10,0nnn (3-28) Equation (3-26) returns a counts of all the points on the orbit y(k) located within a radius r from point x and normalizes this quantity by N, the number of points in the dataset. The point density, (x), on an attractor does not need to be uniform to utilize this method (for a strange attractor). If equation (3-27) is raised to the power of q-1, the function C(q,r) is established in terms of q and r and the mean of n(x, r) q-1 over the attractor weighted with the natural density (x) as: 11,1111,,qMkMknnqxkynyrMMrxnxxdrqC (3-29) This quantity is referred to as the correlation function or correlation integral. This function estimates the probability that two points on the attractor lie within a distance r of each other. M and K are large in value (but not infinite). Though this function is invariant on the attractor, it is conventional to only look at the variation of rqC, when r is small. At that scale, it is assumed that: qDqrrqC1, (3-30) which defines the fractal dimension The quantity is estimated in the case of small r as: qD qD rqrqCDrqlog1,loglim0 (3-31) 73

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Using this method, needs to be calculated over a small range of r in order to achieve a near-linear range for selection of the slope of rqC, rqC,log over rlog Box counting dimension (D0) Box counting dimension (D0) is the title given to the measure when q=0. D0 can be estimated as the amount of spheres of radius r or the number of boxes required to envelop all points in the dataset. If N(r) represent the amount of D-dimensional spheres needed to cover the attractor for relatively small values of r, then the box counting dimension can be estimated as: rrNrqrNDrrlogloglimlog1loglim000 (3-32) Equation (3-31) is often represented as: qqDD00lim (3-33) Information dimension (D1) Information dimension (D1) is the name of the measure when q=1. D1 is a generalization of the box counting dimension that takes into account the relative probability of cubes used to cover the dataset. Let I represent the information function: rPrPIiNiilog1 (3-34) and represent the probability that an element i is populated, normalized such that: rPi 11NiirP (3-35) Information dimension is thus defined as: NiiirrPrPD11loglog (3-36) 74

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Correlation dimension (D2) Correlation dimension (D2) is title of the measure when q=2 (Grassberger and Procaccia, 1983a, 1983b; Kantz and Schreiber 1997). Under this condition, Dq takes on special form which tends towards reliable computation. Correlation dimension is estimated as the slope of the log-log plot generated by: rrCDrlog,2loglim02 (3-37) The correlation dimension can be challenging to quantify in time series data as it can result in highly nonlinear slopes for small r. Correlation dimension has been extensively utilized for neural state classification studies using EEG (Tirsch et al., 2000; 2004) and has been utilized extensively in analysis of physiological data (Kantz and Schreiber, 1995) such as seizure prediction applications (Elger et al., 1998; Martinerie et al., 1998). As correlation sum can demonstrate a high sensitivity to EEG amplitude when using a fixed radius (Osorio, 2001), many authors have implemented a relative radius (with respect to the dataset diameter in vector space) to strengthen their findings (Casdagli et al., 1996, 1997, Merkwirth et al., 2002). The Lyapunov Exponent The Lyapunov exponent is an important measure for the quantification of dynamical systems. This measure quantifies the degree of system chaoticity by quantifying the rate of divergence or convergence between two points initially in close proximity (Iasemidis et al., 1999). Lyapunov exponents provide a generalization of linear stability analysis due to steady-state solution perturbation to time-dependent solution perturbations. The measure also provides a meaningful characterization of asymptotic behavior in nonlinear dynamical systems. Lyapunov exponents are a collection of invariant geometric measures that characterize describe a systems dynamics. Specifically, they provide a measure of predictability for the 75

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particular system. Lyapunov exponents provide a global measure of the rate of convergence or divergence or of two trajectories initially in close proximity to one another for a dynamical system. Positive Lyapunov exponents measure represent the mean exponential divergence rate of two trajectories, whereas negative Lyapunov exponents measure represent the mean exponential convergence of two trajectories. As Lyapunov exponents becomes more positive, trajectories move apart more rapidly. Similarly, as Lyapunov exponents become more negative, the trajectories move together more rapidly. A system with positive exponents has positive entropy as trajectories that are initially in close proximity to one another separate over time. If a discrete nonlinear system is dissipative then the sum of all the Lyapunov exponents is zero. A system with both a positive and negative Lyapunov exponents is said to be chaotic. Thus, Lyapunov exponents provide a measure of linear stability (or instability) of the attractor or an asymptotically long orbit for a dynamical system. For a chaotic system with initial conditions a and b which are initially in close proximity, the distance between these two trajectories at successive time points will exponentially increase over time. If this is written as for a time duration of n iterations, then ne is the Lyapunov exponent. For a system to be chaotic, at least one Lyapunov exponent needs to be positive. Thus, at each point in the series the derivative of the time-advanced equation is evaluated. The Lyapunov exponent is expressed as the mean value of the log of the derivative. If the Lyapunov exponent is negative, the iteration is stable. It is important to note that by summing the logs of the derivatives the result corresponds to multiplying the derivatives. Thus, if the product of the derivatives has magnitude less than 1, points will attract together as they go through the iteration. Though an n-dimensional system will produce n Lyapunov exponents, the maximum exponent is usually most important. The maximum Lyapunov exponent represents the time 76

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constant, in the expression for the change in distance between the two initial orbits, If is negative, then the orbits converge over time, and thus the dynamical system is insensitive to the choice of initial conditions. However, if is positive, then the distance between the initial orbits increases exponentially over time and the system displays sensitivity to initial conditions. ne Calculation of the spectrum of Lyapunov exponents can be derived analytically for systems in which process dynamical equations are known aprioi (Shimada et al., 1979). Numerous algorithms have been developed which compute this measure on experimental datasets. One of the most well-known algorithms was developed by Wolf et al. (1985), though other algorithms have been established (Eckman et al., 1986; Ellner et al., 1991). Short comings of the Wolf algorithm have been identified as sensitivities to the number of observations as well as measurement noise. Numerous researchers have proposed updated versions of Wolfs algorithm with increased robustness to the number of observations (Ellner et al., 1991; Iasemidis et al., 1991; Iasemidis and Sackellares, 1992; Abarbanel, 1996). The following section will provide an executive overview of the Lyapunov exponent estimation. Additional details can be found in (Iasemidis et al., 1991, 2000; Wolf et al., 1985). Computing Short-Term Maximum Lyapunov Exponents A phase space mapping is performed by embedding a signal x(t) of duration T using the method of delays (3-26). The phase space representation provides the proper perspective for measuring the degree of chaoticity of the attractor. An attractor is chaotic if on average the two trajectories with similar initial conditions (two points in close proximity in phase space) diverge at an exponential rate (expansion process). If these trajectories are members of a finite attractor, they will fold back into the attractor as time progresses (folding process). A result of these two processes may be the generation of a stable and topologically layered attractor. If the expansion 77

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process outweighs the folding process in some of the attractors eigen-directions, the attractor is said to be chaotic. If the phase space is D-dimensional then theoretically up to D Lyapunov exponents can be estimated. However, as expected, only (D +1) of them will be real (Abarbanel, 1996). If L represents the short term largest Lyapunov exponent estimate STLmax, then: aNijijiaXtXtNL1,,20log1 (3-38) where jijitXtXX0, (3-39) ttXttXtXjiji (3-40) for the following conditions: 1. is the point of the fiducial trajectory itX ittX' having ,, T denotes the transverse, and itt TDtxtxtX1,...,000 jtX is a properly chosen vector adjacent to in the phase space. itX 2. jijitXtXX0, is the displacement vector i.e., a perturbation of the fiducial order at and it it ttXttXtXjiji is the evolution of this perturbation after time t 3. and titti10 tjttj 10 where Ni,1 and Nj,1 for ij 4. is the evolution time for t jiX, (the time provided for jiX, to evolve in phase space). If the evolution time is given in seconds, then the Lyapunov exponent is measured in bits/sec. t 5. 0 is the initial time point of the fiducial trajectory and coincides with the time point of the first data in the data segment of analysis. In the estimation of L, for a complete scan of the attractor, should move within t 0t t ,0 6. is the number of local s that will be estimated within a duration T data segment. Therefore, if is the sampling period of the time domain data, then aN maxL st 11DtNtNTas The method proposed by Iasemidis et al. (Iasemidis et al., 1999) was used to estimate the short term maximum Lyapunov exponent (STLmax). This method is a modification of Wolfs algorithm (Wolf et al., 1985). The measure is denoted as short term to distinguish it from the variants used to study autonomous dynamical systems. Modification of Wolf's algorithm is 78

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necessary to enhance STLmax estimate robustness to transients in small data segments such as interictal spikes. The main modification is in the replacement vector searching procedure along the fiducial trajectory. One of the most crucial parameters affecting STLmaxs ability to distinguish interictal from preictal states is the adaptive estimation in time and phase space of the magnitude bounds of the candidate displacement vector (Iasemidis 1999), though evolution time t, and the angular separation V i,j between the evolved displacement vector X i-1,j (t) and the candidate displacement vector X i-1,j (0) are important components as well (Frank et al., 2005). The modifications proposed by Iasemidis and Sackellares (1991) can be summarized as follows: 1. To help ensure that L is a reliable estimate of STLmax, the candidate vector X(t j ) should be chosen such that the previously evolved displacement vector X i-1,j-1 (t) is nearly parallel to the candidate displacement vector X i,j (0), that is, max1,1,,,0VtXXVjijiji (3-41) where Vmax should be relatively a small value and denotes the absolute value of the angular separation between two vectors and in phase space. 2. Also, X i,j (0) should also be relatively small in magnitude. This constraint helps avoid computer overflow in the future evolution within very chaotic regions and also reduces the probability of starting up with points on separatrices (Wolf et al., 1986). Mathematically, this corresponds to, max,0jijitXtXX (3-42) where takes on a small value. Thus, the parameters involved in the estimation of L are: (i) The embedding dimension p and the time lag for the reconstruction of the phase space (ii) The evolution time t (iii) The constraint parameters for selecting X(t max j ; V max and max ) (iv) The duration of the data segment T It is worth nothing that since only vector differences are involved in the estimation of L, any direct current (DC) present in analyzed data segment does not influence the value of L. In addition, only vector difference ratios participate in the estimation of L. Thus, L is not influenced by data scaling (provided the parameters involved in the estimation procedure, i. e. are max 79

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expressed in values relative to the scale of each analyzed data segment). Both of the above points are consistent with the fact that L is related to the entropy rate of the data (Palus et al., 1993). Selecting D and The selection of the embedding dimension D is such that the dimension of the epileptic attractor in phase space is clearly defined. For an epileptic attractor, v 3 (Iasemidis et al., 1988, 1990; Iasemidis, 1991). Thus, according to Takens theorem a value of D (2 3 + 1) = 7 can be viewed as adequate for the embedding of the epileptic attractor in the phase space. This value of D may not provide a large enough phase space to embed all interictal brain states, but has demonstrated success in detecting the transition of the brain toward the ictal stage (Iasemidis and Sackellares, 1991). The parameter should be small enough to characterize the shortest signal changes (i.e., highest frequency component) in the data. However, should be large enough to result in the maximum feasible independence between the vectors components in the phase space (with the method of delays). These two conditions are typically addressed by selecting to be the first minimum of the mutual information or as the first zero of the time domain autocorrelation function of the data (Abarbanel, 1996). Since the time span (D-1) of each vector in the phase space theoretically represents the duration of a system state, (D-1) has been recommended to be (at the greatest) equal to the period of the maximum (or dominant) frequency component in the data (Abarbanel, 1996). As an example, a sine wave (or a limit cycle) has v = 1, then D = 2 1 + 1 = 3 is required the phase space embedding and (D-1) = 2 should equal the sine waves period. In such a case, the value of would then correspond to the Nyquist frequency of the sine wave. In addition, for the epileptic attractor the highest frequency considered is 70 Hz (as EEG data are often low-pass filtered at 70Hz) which would require a maximum of about 7 ms according to the above rationale for D = 3. However, since a typical epileptic attractor (i.e., 80

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during the ictal period) in temporal lobe epilepsy has described to have a maximum dominant frequency of about 12 Hz (Iasemidis and Sackellares, 1991), according to the above rationale, an adequate value for phase space reconstruction of the epileptic attractor is (7 1) 84 ms, and thus, should be about 14 ms (for additional details see Iasemidis and Sackellares, 1991). Selecting t. If the evolution time t is too large, the folding process within the attractor distorts L. If t is too small, Xi,j(0) may not follow the direction of the maximum rate of information change. One option is to obtain t as a fraction of time-delay mapping of the maximum frequency component of interest in the data, f 0 Specifically, the t is usually chosen to correspond to 0.5*f 0 (Iasemidis and Sackellares, 1991). Therefore, according to the previous discussions about the selection of D and t ((D 1) )/2, which results in t 42 ms which is within a range that can distinguish the ictal state from the pre-ictal state (Iasemidis and Sackellares (1991). Selecting max In Wolf's algorithm (1986), max is selected as 0max,,maxjijiX (3-43) where j = 1,,N and i = 1,,N a Thus, max represents the global maximum distance between any two phase space vectors in a segment of data. This value suffices as long as the data is stationary and distributed relatively uniformly in phase space. Rarely is this the case with real data, especially with the brains electrical activity which is strongly nonstationary and nonuniform (Barlow et. al, 1985; Feber et. al, 1987; Jansen and Cheng, 1988). Such statistical fluctuations combined with noise may adversely influence the predictive power of STLmax (Lai et al., 2003, 2004). Thus it is essential to perform a searching procedure modification in order to locate the proper X(t j ). The first step is obtain an adaptive estimation of max for each point X(t i ) as 81

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0max,max,jijiX (3-44) where j = 1,,N. Estimating max in this manner can help compensate for the nonuniformity of phase space ( max is now a spatially local quantity of the phase space at a point X(t i ) ). Another technique for managing nonstationary data is to estimate max with a temporal constraint on top of the spatial constraint. From this perspective, max is ijXjiIDISTttIDISTiji;0max,max,21 (3-45) for which 1IDIST (3-46) 12DIDIST (3-47) where and upper and lower bounds for 1IDIST 2IDIST jitt which help enforce temporal constraints when searching for a maximum spatial distance. In other words, these parameters establish a neighborhood in time around each point in the fiducial trajectory for the estimation of the parameter i,max which establishes a spatial search neighborhood around this point in the phase space. Thus, the search for i,max is always made temporally about the state X(t i ) and its changes within a period of the time span (D 1) of a state. According to the previous formulae, the values for the parameters involved in the adaptive estimation of i,max for the neural state classification studies are: = = 14 msec and = (D 1) 84 msec. 1IDIST 2IDIST Selecting V max Starting with an initial V max,initial = 0.1 rad, if a replacement vector X(t j ) is not found with 0 jiV, < V max,initial and 0,jiX < 0.1* max the bound is relaxed for 0,jiX At this point the process is repeated with bounds up to 0.5* max If it is not successful, we relax the bounds for jiV, by doubling V max and then repeat the process with bounds for V max up to 1 82

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rad. It should be noted that values of V max larger than 0.8 rad did not occur in the reported results (Iasemidis and Sackellares, 1991). If V max does grow this large, the replacement procedure halts, a local L(t i ) is not estimated at time t i the entire procedure beings again at the next point in the fiducial trajectory. Selecting X(t j ). It is important that the replacement vector X(t j ) should be spatially close to X(ti) in phase space (with respect to angle deviation and magnitude), yet with sufficient temporal distance from X(t i ) to allow selecting X(t j ) from a nearby (but not the same) trajectory. Otherwise, by replacing one state with one that shares too many common components would lead to a false underestimation of L. The arguments described above are represented by the following expressions: radVVinitialjiji1.00,,, (3-48) max,,max,0ijiicXb (3-49) 13DIDISTttji (3-50) The parameter c at a value of 0.1 and increases with a step of 0.1 up to 0.5 in order to locate a replacement vector X(t j ) satisfying (3-48) through (3-50). The parameter b (which must be less than parameter c) is used to account for possible noise contamination of the data. Thus, b is the distance below which the estimation of L is considered to be inaccurate. A value of b = 0.05 provided is recommended (Wolf et al., 1985; Iasemidis and Sackellares, 1991). To clarify, the temporal bound IDIST2 should not be confused with the temporal bound IDIST3. The variable IDIST2 places an upper temporal bound for locating an appropriate i,max at each point X(t i ), whereas IDIST3 is a lower temporal bound for locating an appropriate X(t j ) within a i,max spatial distance from X(t i ). 83

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Selecting T. For data obtained from a stationary system state, the time duration T of the analyzed data segment may be large for estimating of L. For nonstationary data, there are two competing requirements: T is desired to be as small as possible to provide local dynamic information yet the algorithm requires a minimum length of the data segment to stabilize the STLmax estimate. Previous studies have deemed that for 200 Hz, a window of 2048 points (corresponding to 10.24 seconds) is a sufficient length for the algorithm to converge and yet is able to distinguish the two extreme cases (pre-ictal and ictal) (Iasemidis, 1991; Iasemidis and Sackellares, 1991; Iasemidis et al., 2000). These studies also point to the IDIST2 parameter as being the most critical parameter in the above algorithm. The STLmax seizure prediction algorithm identifies progressively increasing similarity in the information production rate (termed dynamical entrainment) between critical electrode sites prior to seizures. In other words, long before the onset of an epileptic seizure, critical brain sites begin to display similar dynamics. The progressive STLmax convergence prior to a seizure is thought to reflect dynamical dependence because 1) the critical sites share direct or indirect anatomical connections that are conducive to physiologic interaction, and 2) occurrence of the progressive STLmax entrainment prior to a seizure (Iasemidis et al., 2004). This concept is indirectly supported by the therapeutic effect of neurostimulation therapies such as ECT-induced seizures and the potential long-term anticonvulsant effect (for a recent review of ECT therapy see Taylor, 2007). A potential physiologic basis for brain resetting could be a release of neuromodulators after seizures (Gwinn et al., 2002). In addition, Iasemidis et al. (2004) suggest that the lack of an observed time-reverse of the resetting phenomenon is consistent with hysteresis, a characteristic observed in epilepsy as well as other dynamical disorders (Lopes Da Silva et al., 2003). 84

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Mean Angular Frequency in Phase Space One modification of the Lyapunov exponent was proposed by Iasemidis to measure a quantity related to the STLmax measure (Iasemidis et al., 2002, 2003). The mean angular frequency in phase space ( ) measure quantifies the angular frequency of the phase space evolution of two nearest neighbor points relative to a reference point. Conceptually, this measure quantifies the rate of change in stability of a dynamical system. The measure is related to the Lyapunov exponent, which measures the local stability of a system. Consider the vectors and as two states in phase space separated by the time delay. The difference in phase between these two states in phase space is itX ttXi t i (Iasemidis et al., 2002). The mean () of the local phase changes in state space is denoted as: i NiiN11 (3-51) where is the total number of phase differences calculated from the evolution of to in state space, according to: N itX ttXi ttXtXttXtXiiiiiarccos (3-52) The mean angular frequency in phase space can then be defined as: t1 (3-53) If the units of are seconds, t has units of radians per second (an alternative is to divide by 2 resulting in units of sec -1 or Hz for expression of rate of system state change). Figure 3-3 illustrates the concept of the phase change measure as it is applied to data with the same phase 85

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space mapping with STLmax where dtkt is the evolution time allowed for the vector to evolve to where dt is the sampling period of the original time series. itX ttXi Data Mining Data mining refers to the application of algorithms to extracting patterns from and modeling large databases (Flexer et al., 2000) and provides reasonable tools for extracting useful patterns in datasets from complex systems. Data mining techniques have demonstrated successful detection of scalp EEG patterns which may be difficult for the human eye to visualize (Acir et al., 2005; Chaovalitwongse et al., 2006; Thulasidas et al., 2006). Often such algorithms or the patterns they reveal can be utilized in real time applications, providing a basis for real-time EEG analysis tools (Chaovalitwongse et al., 2005; Iasemidis et al., 2005; Sackellares et al., 2006; Thulasidas et al., 2006). Typical data mining tasks are described by the following categories: Dimensionality reduction: the process of mapping of a high-dimensional data set into a lower-dimensional space in order to facilitate data exploration Reduction of noise: correction or removal of measurement artifacts and significantly atypical samples from the data set. Clustering: creation of a partition of a given set of samples into classes according to similarities that are relevant to the particular analysis One of the more important instances of dimensionality reduction is called feature selection. This process results in the generation of a lower-dimensional space by eliminating a subset of dimensions from the original space. Feature selection is an important process for reducing computation time as well potentially improving accuracy. Reduction of noise is an important procedure which is universally applied in applications spanning numerous disciplines. Finally, clustering refers to a broad class of data mining applications which are highly relevant to the work done in this dissertation. 86

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Clustering Clustering problems can be subdivided into unsupervised or supervised clustering. Unsupervised learning methods divide data into natural groupings. Supervised clustering methods are also referred to as classification, which is described later in this chapter. The following represents a non-exhaustive listing of some basic clustering techniques. K-means clustering The k-means algorithm is one of the most basic and commonly applied cluster algorithms. The method clusters a set of N data points into K partitions based on the similarity between the pattern and the cluster centers, where K< N (Jain et al., 1999). A random initial partition is selected after which the patterns are repeatedly reassigned some convergence (e.g. squared error threshold) is achieved. The k-means algorithm is especially attractive due to its O(n) complexity as well as its ease of implementation (Jain et al., 1999). One deficit of this method is a high sensitivity to initial conditions, which can result in convergence at local minima. Biclustering Biclustering is a data mining technique which provides the ability to not only cluster data samples, but also the data features. The procedure is performed in a manner that each class of data features created within the biclustering is related to a class of data samples by a particular property that distinguishes it from samples in other classes and is said to be the cause of its creation. In other words, the biclusters are subsets of samples which exhibit similar characteristics across a subset of features, or vice versa. The biclustering methodology has been used extensively in numerous biomedical research applications such as DNA microarray analysis and drug design as well as others (Madeira and Oliveira, 2004; Shamir et al., 2005; Busygin et al., 2006). The output of biclustering algorithms 87

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is especially useful for feature extraction, a crucial procedure in many biomedical studies. Analogous to the ability of biclustering to reveal up regulation and down regulation of genes in dna microarray datasets, biclustering is a data mining tool well-suited for revealing spatial and temporal subsets of EEG features that are indicative of neural states (Busygin, 2007). A dataset containing m features and n samples is arranged as a rectangular matrix nmijaA where a ij represents the i-th feature of the j-th sample. Consider the assignment of the samples into classes as follows lkrlkSSnSSSrknSSSSlkrkr,,...,1,,,,...,1...,,...,1,,...,1,,...,,2121 This method intends to assign samples such that samples from the same class share specific common properties. Similarly, a feature i may be assigned to one of the features classes lkrlkFFmFFFrkmFFFFlkrkr ,,...,1,,,,...,1...,,...,1,,...,1,,...,,2121 in such a manner that the features of class F k are responsible for the creation of the class of samples S k Such a simultaneous classification of samples and features is termed biclustering. Definition 1: A biclustering of a dataset is a group of sample / feature pair subsets such that the group rrFSFSFSB,,...,,,,2211 rSSS,...,,21 forms a partition of the set of samples, and the collection forms a partition of the set of features. A pair rFFF,...,,21 kkFS, will be called a bicluster. Various criteria may be used for relating sample clusters to feature clusters. Most commonly, it is required that the subset corresponding to a bicluster is either includes a certain 88

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amount of values above the mean of the dataset, or has a lower variance than that of the dataset. In general, it is acceptable for biclustering to rely on any type of common pattern among the elements of the bicluster. Consistent biclustering: The following biclustering framework utilizes feature selection based on 0-1 fractional programming (Busygin, 2005). Let each sample j be arbitrarily assigned to one of the classes. A 0-1 matrix rSSS,...,,21 rnjksS is introduced such that = 1 if and = 0 otherwise. The sample class centroids are represented by the matrix : jks kSj jks rmikcC 1SSASCT (3-54) whose k-th column represents the centroid of class kS Consider a row i of the matrix C. Each element in the row is the mean expression of the i-th feature in one of the sample classes. Each feature is then assigned to the class where it is among the largest number of features with a similar value as is shown in figure 3-4. Let the i-th feature be classified as a member of the class with the maximal value : k kic ikkikcckkrkFi:,,...,1 (3-55) Using the acquired feature classification rFFF,...,,21 let a classification of samples be constructed using the same principle of maximal average expression and test whether this arrives at the same classification as when using features. This is performed by constructing a 0-1 matrix such that if and rmikfF 1ikf kFi 0 ikf otherwise. The feature class centroids can be represented by a matrix rnjkdD : 1FFFADTT (3-56) 89

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whose k-th column represents the centroid of the class The requirement for sample classification is kF jkkjkddkkrkSj:,,...,1 (3-57) The feature selection and supervised biclustering framework proposed in (Busygin, 2005) is grounded in the following definition. Definition 2: A biclustering B will be called consistent if both relations (3-55) and (3-57) hold, where the matrices C and D are defined as in (3-54) and (3-56). Unlike other biclustering schemes, this definition of consistent biclustering is justified by the fact that consistent biclustering implies class separability with convex cones (Busygin, 2005). Theorem 1: Let B be a consistent biclustering. Accordingly, there exist convex cones such that every sample from belongs to the cone and no other sample belongs to it, nrPPP,...,,21 kS kP rk,...,1 Similarly, there exist convex cones such that every feature from belongs to the cone and no other feature belongs to it, nrQQQ,...,,21 kF kQ rk,...,1 It follows from the theorem of conic separability that convex hulls of the classes are separated and thus do not intersect. The term biclustering-admitting is used to describe a dataset for which some consistent biclustering exists. In addition, the data set will be called conditionally biclustering-admitting with respect to a given (partial) classification of certain 90

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samples and / or features if a consistent biclustering exists which preserves the given (partial) classification. Given a training set nmijaA where the samples are assigned to classes the corresponding classification of features can be constructed according to expression (3-55). If the obtained biclustering is not consistent, features are then excluded from the dataset so that the biclustering with respect to the cropped feature set is consistent. rSSS,...,,21 Let a vector of 0-1 variables miixx,...,1 be introduced where the i-th feature is selected if and is not selected otherwise. When only the selected features are applied, the condition of biclustering consistency in expression (3-57) becomes 1ix kkrkkSjxfxfaxfxfakmiiikmiiikijmiikimiikiij,,...,1,,,1111 (3-58) The expressions in (3-58) are utilized as constraints of a feature set optimization problem. Though the objective function may take on various functions of x depending on the desirable properties of the features, a general choice is to aim for the maximal number of features. This formulation helps minimize the amount of lost information provided during training. In this scenario, the objective function is expressed as miiX1max (3-59) Expressions (3-58) and (3-59) comprise a specific type of fractional 0-1 programming problem which can be solved using the approach laid out in (Busygin et al., 2005). 91

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Data Classification Classification can be described as the process of categorizing an unknown dataset. First, a so-called training set of samples wherein sample classes are known a priori is provided to the algorithm. The pre-classified training data is used to train the algorithm to recognize the specified patterns. Training is typically an iterative process where the parameters affecting classification are systematically adjusted until the classification error bound is decreased below a specified threshold. This specific process is referred to as machine learning. Machine learning Machine learning refers to a collective group of methods which are utilized to enable computers to learn. There have been very successful implementations such as finding genes in a DNA sequence, filtering email, financial analysis, detecting or recognizing objects in machine vision, language processing, and medical diagnosis (Cristianini and Shawe-Taylor, 2000). Many of these applications rely on pattern recognition which is essentially concerned with object classification based on characteristics. An objects characteristics or features can be described as the qualitative and quantitative measures which can distinguish it from other objects. The amount of similarity between two objects can be quantified as a function of the differences in the objects set of features. Object similarity can be used as a basis for grouping objects into classes. Please note, while the content of a persons character may be a useful feature of a person, the color of a persons skin is not a good feature for classification. Classes may be represented in various ways such as approximation functions or functions that define borders between classes. Arranging objects into classes based on their location relative to these functions is referred to as classification. Machine learning from the classification perspective can be organized into two main categories. Supervised learning refers to the process where a system learns from an example data 92

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set in the form of input/output pairs. In such an example dataset, the input is typically a vector of representing an objects features and the output is the objects class label. A set of objects each with a corresponding feature vector and class label is more formally referred to as a training set. The training set is used to derive a classification function. Once trained, a classification function is capable of predicting an objects label. The term supervised stems from the nature of the training scheme where the training sets object labels are determined by an outside source and provided as an input. Therefore, this training method requires supervisory guidance to train the classifier. Unsupervised learning is the other machine learning category where objects are not labeled with any class information a priori. Thus, unsupervised learning forms object classes based on inherent feature similarities determined during training. Supervised learning systems applications have found extensive use in biological applications (see Tarca et al., 2007 for a review). Briefly, some biological and medicinal applications include detection of cancer prone tissues, mapping tissue gene expression profiles to disease groups, and protein folding based on the DNA sequence. In addition, a broad range of machine learning algorithms have provided a means for successful neural state classification and neurological disorder diagnosis using EEG signal features (Flexer, 2000; Lotte et al., 2007; Seref et al., 2007). There are several well-known machine learning algorithms, including decision trees, neural networks, and support vector machines. These base algorithms can be used in combination with other algorithms for improved accuracy often at the cost of hindered performance. One of the most widely used measures in classification problems is the Mahalanobis distance metric. Mahalanobis distance classification Mahalanobis distance is a statistical distance measure which factors in correlations between variables. The mahalanobis distance is a useful method of quantifying similarity of an 93

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unknown sample set to a known sample set. The square of the mahalanobis distance measure has been applied to the classification of neural states using EEG signal patterns (Scher et al., 2003; Le Van Quyen et al., 2005; Piccini et al., 2005). The squared mahalanobis distance, D 2 ref,t between a 25-dimensional EEG data point vector X(t) where TtchtchtchtchXXXXtX,,...,,,,25,3,2,1 (3-60) and the centroid of the reference class ref where Tchchchchref25321,...,,, (3-61) is equal to: refrefTreftreftXCtXD1,2 (3-62). The C ref term is the covariance matrix for the reference class. The mahalanobis distance measure D 2 comparison,t refers to distance between the same EEG data point, X(t), and the centroid of the comparison class, comparison The EEG data point X(t) is assigned to the class with the closest centroid (e.g. the class from which the point is at the minimum Mahalanobis distance) to X(t) (Le Van Quyen et al., 2005). If the EEG data point is equidistant between the two classes, the point is considered misclassified. The accuracy of the minimum Mahalanobis distance classifier is equal to the number of correctly classified points divided by the total number of points. Support vector machines Support Vector Machines (SVMs) are a class of data classification algorithms first introduced by Vapnik and Lerner (1963) which are used to model and classify large volumes of multivariate data. The SVM algorithm determines the optimal separating hyper surface between two multidimensional datasets (Burgess et al., 1998). SVMs have been demonstrated success in numerous biomedical applications such as magnetic resonance imaging (MRI), functional MRI 94

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(fMRI), positron emission tomography (PET), and Single-photon emission computed tomography (SPECT) (Seref et al., 2007) in addition to applications where neural states were classified from EEG data (Acir et al., 2005; Chaovalitwongse et al., 2006; Lehmann et al., 2007; Thulasidas et al., 2006). The SVM formulation for linearly separable data quantifies the distance from the hyper surface for each data point in the positive class and each data point in the negative class. In this context, the term margin will refer to the distance between the separating hyper surface and the nearest point for a class. The margin of the function output is referred to as the functional margin. The geometric margin is the functional margin of a normalized weight vector. Hence the geometric margin can be optimized by fixing the functional margin to be equal to one and then minimizing the norm of the weight vector (Cristianini and Shawe-Taylor, 2000). If w is the weight vector for a functional margin of distance equal to one from a positive (reference) class point, x+ and a distance equal to one from a negative (comparison) class point, x-, then the geometric margin can be determined as follows. For a functional margin equal to one: 1,bxw (3-63) 1,bxw (3-64). To calculate the geometric margin, w must be normalized. The geometric margin, is then the functional margin of the resulting classifier 22221,,21,,21wxwxwwxwwxww (3-65). 95

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Thus, the interclass margin is maximized by 2,minwbw (3-66) subject to 1,bxwyi ni,,1 (3-67) where the constraints are that all points are properly classified for positive and negative classes, as stated in (3-67). For non-separable data, the objective function (3-68) combines the term for maximizing interclass margin with a term for minimizing misclassification error (Cristianini and Shawe-Taylor, 2000). niibwCw1,22,,min (3-68) ni,,1 iiibxwy1 (3-69) ni,,1 0i (3-70) ni,,1 The cost term, C, in (3-68) is the weight assigned to the error. Expressions (3-69) and (3-70) represent the constraints that each misclassified point is assigned a linear penalty (slack variable) and that all slack variables are non-negative, respectively. An example of such a soft margin classifier is shown in figure 3-5. The SVM formulation in equations (3-68), (3-69), and (3-70) utilizes a linear hyper surface for discrimination. A common practice for improving separation accuracy is to perform a transformation to remap the data from input space into feature space using a kernel function. The inner product is then performed on the transformed feature space data (see equation (3-71)). jijixxxxK,, (3-71) The concept of a kernel function is identical to that of phase space mapping. The purpose is to view the data in a transformed space to unmask patterns which may have been hidden in 96

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input space. The radial basis function (RBF) is a standard choice as a kernel function in neuroscience applications (Acir and Gzelis, 2005; Bewernitz et. al., 2006; Lehmann et. al., 2007; Thulasidas et. al., 2006; Seref et al., 2006). The RBF function is expressed as 2exp,jijixxxxK (3-72) The SVM is trained using a set of data features with a known classification. The SVMs performance is measured in terms of the accuracy at which it is able to classify a test data set. 97

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Figure 3-1. A 15 second segment depicting the 200 Hz EEG of an absence seizure viewed from channel Fp1-F7. 98

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Figure 3-2. A 15 second segment depicting the spectrogram of an absence seizure viewed from channel Fp1-F7. The vertical lines represent the onset and offset of the seizure. 99

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t 1 Figure 3-3. Example angular frequency evolution in phase space. Figure 3-4. Biclustering result of a toy dataset. The dataset produced three distinct classes. 2 1 t 2 t 0 )0(0x )1(0x )0(kx)1(kxtdtk 100

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Figure 3-5. Linear hyperplane classifier applied to non-separable data. 101

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CHAPTER 4 INVESTIGATION OF EEG BIOMARKER EXISTENCE FOR VAGUS NERVE STIMULATION THERAPY: A DATA MINING APPROACH Patients with newly implanted vagus nerve stimulation (VNS) systems in VNS therapy undergo a calibration period of several months. With little knowledge of the mechanism of action (see chapter 2) or a rapid measure of efficacy, the current process of tuning VNS stimulation parameters in newly implanted patients is essentially based on the physicians experience and trial-and-error. This process consists of setting initial stimulation parameters then iteratively adjusting stimulation parameters based on patient reports of clinical efficacy (seizure frequency) and tolerability since the previous visit to the doctor. It is known that high settings for stimulation parameters (such as output current, frequency, and pulse width) are shown to result in greater seizure reduction than low settings (Ben-Menachem et. al, 1994), but there is no available means for determining the proper set of stimulation parameters for a particular patient without numerous visits to the neurologist. This period involves numerous medical check-ups to fine tune the electrical stimulation parameters based on clinical response. This sub-optimal adjustment method leaves the patient at risk of seizures and imposes financial burden. The purpose of this study is to address this problem using data mining analysis. This chapter is organized as follows. First, the rationale for this study is introduced in terms of clinical relevance. Next, the experimental strategy is outlined and justified with examples from the literature. Afterwards, the four experiments comprising this chapter are presented in the following format: introduction, data description, experimental setup, results, and discussion. Finally, an overall conclusion is presented which comments on all the findings as a whole. 102

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Motivation for VNS Therapy Improvement It is desirable to establish a method to rapidly predict the efficacy of the various combinations of VNS parameters newly-implanted patients in order to mitigate doctors visits and perhaps expedite the process of optimizing therapeutic efficacy. A first step towards this goal is to investigate the existence of a physiologic metric that is sensitive to the EEG stimulation parameters and then the patient's clinical response to VNS therapy. Such an effect could be present in the EEG signal. EEG Markers for Treatment of Neurological Diseases and Disorders The utility of electroencephalogram (EEG) markers in treatment of neurological disorders motivates the examination of this treatment modality in terms of EEG effect (see chapters 2 and 3 for additional details). Electroencephalographic markers have demonstrated robust utility for the diagnosis, treatment, and evaluation of treatment for epilepsy (Iasemidis et al.,1996; Pardalos et. al, 2003, 2004; Chaovalitwongse et al., 2005, 2006; Ding et al., 2007; Schevon et al., 2007) as well as other neurological disorders (Krystal et al., 1996, 1997, 2000; Asyali et al., 2007; Ding et al., 2007; Quintana et al., 2007). Specifically, there is has been an interest in the application of such analysis to the EEG signals of VNS patients to provide a better understanding of the therapy (Uthman et al., 2007). Recent studies have produced interesting findings of long-term VNS effects on epileptic interictal spikes (Koo, 2001), epileptiform sharp waves in the hippocampus (Olejniczak et al., 2001), interictal epileptiform discharges (Janszky et al., 2005; Santiago-Rodriguez and Alonso-Vanegas, 2006), gamma activity and desynchronization (Marrosu et al., 2005), and spectral content of sleep (Rizzo et al., 2004). The effects on interictal epileptiform discharges such as the studies by Koo and Olejniczak et al. suggest the presence of brain dynamical changes and further motivate the desire to examine VNS-induced EEG changes from the perspective of nonlinear dynamics since the 103

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existence dynamical changes are implied by changes in spiking patterns. In addition, no studies could be located which aimed to relate the EEG effects of VNS to the stimulation parameters. Aside from long-term epileptiform effect (Koo, 2001) or effects observed in hippocampal depth electrodes (Olejniczak et al., 2001), the lack of readily-available short-term scalp electroencephalographic VNS effects reported in the literature (Hammond, 1992; Salinsky et al., 1993; Fisher et al., 1999; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005), the benign non-invasiveness of scalp-EEG, state of the art techniques of modern knowledge discovery in database techniques (Flexer, 2000), and the potential for real-time application due to modern computer technology make EEG data mining analysis a desirable approach to studying VNS effect. These reasons motivate the current study which aims to identify electroencephalographic markers which are sensitive to VNS stimulation parameter configuration. If such electroencephalographic markers are identified, and if the electrographic markers are found to correlate with clinical efficacy then these findings could be applied to determine optimal VNS stimulation parameters on a patient-by-patient basis. Modeling Brain Disorder Dynamics One approach for studying the brains behavior is to generate a mathematical model of some subset the brains activity using observable quantities, such as EEG recordings. Such models provide a means to make predictions about the behavior of one or more sections of the brain in response to various inputs. Due to the high degree of complex neuronal interaction in the brain, direct models have only been achieved for small neuronal networks small brain structures (Breakspear, 2001; Chauvet and Berger, 2002). The enormous complexity of electrical brain signals often means exact modeling approaches are insufficient. The challenge of direct modeling is compounded by the fact that no consistent immediate or short-term VNS-induced effects have been identified in the raw EEG or its time-frequency profile (Salinsky et al., 1993; 104

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Fisher, et al., 1999; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005). However, suppression of epileptiform sharp waves in the hippocampus has been observed (Olejniczak et al., 2001). This provides motivation for searching for dynamical scalp-EEG effects of VNS. However, in a complex system such as the brain, it is often difficult if not impossible to obtain exact knowledge of system governing the observed dynamical behavior. In such a case, an alternative method to exact modeling is to develop a macroscopic modeling approach based on observable measures of the system in its entirety, such as EEG signals (Iasemidis et al., 1996). Upon extraction of such information, it may be possible to generate useful empirical models of the systems global behavior. One such modeling scheme treats epilepsy as a dynamic disorder which is a class of disorders characterized by a sudden qualitative change in dynamics in response to an endogenous factor or a clinical maneuver (Milton, 2000). From this perspective, epileptic symptoms occur as a result of modifications to underlying physiologic control system parameters (Mackey and Glass, 1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003). Such changes may manifest, for example, as a qualitative change in dynamics corresponding to bifurcations in mathematical systems. The importance of identifying a dynamic disorder is that a treatment possibility can focus on manipulating underlying control parameters back into a range of healthy dynamics (Milton, 2000). An example of this is the epileptic seizure control strategy of Iasemidis et al. where the control focuses on maintaining a healthy range of STLmax t-index values (associated with seizure transition) by therapeutic intervention (Iasemidis et al., 2003; Good et al., 2004, 2005). An analogous scenario may apply to VNS calibration in newly-implanted patients where the VNS parameters are adjusted in order to elucidate a brain 105

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dynamical response or state that has been previously established as indicative of desired and even optimal seizure protection. Thus, the achieved neural state as described by dynamical EEG responses associated with different stimulation parameters over time may serve as marker for VNS treatment and facilitate rapid determination of optimal VNS parameters. See figure 4-2 for a three-dimensional conceptual example of such a model. The example in 4-2 utilizes three measures only for the sake of example. In actuality, a real model may utilize dozens or even hundreds of such EEG features. Determining which EEG measures should be used in such model is a challenging task indeed. A common approach for revealing complex relationships among the features and samples from large a multidimensional dataset (such as an EEG recording) is to employ data mining methods. Data mining refers to the application of algorithms in order to extract patterns from complex databases (Flexer, 2000) and provides a means for identifying EEG features which may be sensitive to neural stimulation as well as neural stimulation parameters in the VNS implant. Previous work employing data mining techniques has demonstrated successful pattern detection from scalp EEG signals which is often difficult for the human eye to visualize (Iasemidis et al., 1996; Pardalos et al., 2003; Iasemidis et al., 2004; Acir et al., 2005; Iasemidis et al., 2005; Chaovalitwongse et al., 2006; Sackellares et al., 2006; Thulasidas et al., 2006). Thus, such an algorithm may be useful in the case of VNS therapy where short-term stimulation scalp EEG effects are not explicitly visible in the time or frequency domain (Hammond et al., 1992; Salinsky et al., 1993; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005). Often such algorithms can be run in real time, providing a basis for an online EEG analysis tool (Sackellares et al., 1997; Chaovalitwongse et al., 2005; Iasemidis et al., 2005; Thulasidas et al., 2006). 106

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The overall goal of this work is to investigate the existence of EEG feature patterns which may be related to clinical and biological aspects of a patient's VNS therapy. The underlying hypothesis of this work (stated as null) is electroencephalographic effects in patients undergoing VNS therapy for epilepsy do not vary with differing VNS parameters. Expressing VNS-related effects in terms of scalp-EEG recordings is desirable considering its wide availability at medical facilities and utility in epilepsy diagnosis. Such EEG measures may one day find use as markers to help determine optimal VNS parameters more rapidly in newly-implanted patients. Biclustering Analysis of EEG Dynamics in Patients undergoing VNS Therapy for Epilepsy Biclustering is a useful method for determining the existence of supervised binary classifications in multivariate datasets. The outputs of biclustering are particularly valuable for feature extraction purposes which are a significant concern in many biomedical studies. One of the most common applications is establishing connections between syndromes (e.g., signs and symptoms in cancer) and their corresponding gene expression patterns (Cheng et al. 2000; Kluger et al., 2003; Yoon et al., 2005). The biclustering algorithms ability to distinguish two predefined states makes it a potentially useful tool for characterizing EEG dynamical alterations associated with VNS activation using EEG features (such as STLmax ) as an input. Data Description The scalp-EEG recordings utilized in this study were obtained from patients with functioning VNS implants for the treatment of epilepsy. The recordings were performed at the General Clinical Research Center (GCRC) in Shands Hospital at The University of Florida. EEG was acquired under GCRC protocol # 614, Institutional Review Board (IRB) protocol #617-2004, "Neurophysiologic Measures of Vagus Nerve Stimulation". EEG data were obtained at 512 Hz sampling rate using 16-bit precision with a 0.16 Hz high pass filter and 105 107

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Hz low pass filter hardwired into the amplifier. The dataset contained 25 scalp-EEG channels arranged in the standard international 10-20 system (see Fig. 4-3). EEG channels included in the study were: Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, T6, A1, A2, Fz, Cz, Pz, Leye, Reye, Lmn, and Rmn ("mn" refers to an electrode placed on the mandibular notch positioned between the jaw bone and the skull, which provides information about the temporal lobe). The CPz electrode, which is positioned between Cz and Pz, is used as the reference for the 25 EEG channels and electrocardiogram (ECG). The ECG electrode was placed near the VNS pulse generator for two reasons. While this position provides a sufficient ECG signal, it is also close enough to the pulse generator to introduce a unique artifact in the ECG channel which corresponds to the pulse generator activation. This explicit VNS signature provides a means to determine stimulation times. Once stimulation times were obtained, the ECG channel was excluded the further study. This study included two patients. The VNS paradigm is configured to deliver stimulation for 30 seconds and halt stimulation for 5 minutes, a cycle which repeated regularly throughout the entire recording for both Patient A and Patient B. Patient A's VNS parameters were 1.75 mA output current, 30 Hz signal frequency, 500 sec pulse width, 30 second signal duration, and a 5 minute VNS deactivation duration. Patient B's VNS stimulation parameters were 1.5 mA output current, 20 Hz signal frequency, 250 sec pulse width, 30 second signal duration and 5 minutes VNS deactivation duration. The VNS implants allow manual activation of the device should the patient require an immediate stimulation (e.g. if the patient senses an imminent seizure). Patient A's manual stimulation parameters were 2 mA output current, 30 Hz signal frequency, 500 sec pulse width, and a 60 second stimulation duration. Patient A did not experience any seizures 108

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during the recording session, and did not initiate manual stimulations. Patient B's manual stimulation parameters were 1.75 mA output current, 20 Hz signal frequency, 500 sec pulse width, and a 60 second signal duration. Patient B underwent 14 seizures during the recording session and manually activated the stimulator between 20 to 40 seconds after onset of each seizure (a total of 14 manual activations). Additional information on the patients clinical status can be found in tables 4-1 and 4-2. Each patient underwent continuous scalp-EEG recordings approximately 24 hours in duration. For Patient A, a total of 255 VNS were analyzed in this study. For Patient B, a total of 237 VNS cycles were used in the analysis. Some of Patient Bs VNS cycles were excluded from the study due to their disruption by a manually-activated stimulation and/or occurrence during a seizure. Finally, the last VNS cycle was excluded from analysis for both patients because it was not a complete cycle (it began closer than a full cycle length to the end of the recording). STLmax Feature Extraction Modeling brain activity using chaos measures has been shown to be useful for providing dynamical information about the neural state of the epileptic brain. Studies involving human patients (Iasemidis and Sackellares, 1990; Iasemidis and Shiau et al., 1999; Iasemidis et al., 2001; Iasemidis and Pardalos et al. 2003; Iasemidis and Shiau et al., 2003) and animal models of epilepsy (Nair et al., 2004, 2005, 2006; Talathi et al., 2008) suggest that occurrence of spontaneous seizures correlates with the evolution of the brain to a state of greater spatio-temporal order. This phenomenon manifests as a progressive increase in intra-channel similarity as measured by Lyapunov exponents calculated from multichannel EEG recordings. The reported sensitivity of STLmax to neural state changes in epilepsy make the measure a reasonable choice for attempting to characterize the VNS effects. Additional information can be found on the STLmax measure in chapter 3. 109

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Briefly, as was described in chapter 3, the window duration for calculating STLmax needs to be short to provide temporally local information about the brains dynamics yet contain enough points for the algorithm to converge. A window length of 2048 points (corresponding to 4 seconds) was selected as it was sufficient for providing a stabilized STLmax estimate in previous neural state classification studies in epilepsy (Iasemidis and Sackellares, 1999). In addition, it is desirable to utilize the shortest window length possible for STLmax estimation in order to provide locally dynamic information. As such, while maintaining a window length of the recommended number of data points for algorithm convergence, the 512 Hz sampling frequency provides improved time resolution over previous studies (which utilized a 200 Hz frequency). Additional parameters for STLmax estimation were selected based on the successful neural state classification studies that utilized them (Iasemidis and Sackallares, 1999): reconstructed dimension D = 7, phase space reconstruction delay = 14 msec (7 samples), evolution time T = 41 msec (21 samples). Experimental Setup The STLmax time series for 25 EEG channels were analyzed using a consistent biclustering framework to determine separability of EEG fragments corresponding to stimulation times versus VNS deactivation. Since stimulation duration was set to 30 second and a four second time window was used to estimate each STLmax value, each stimulation provided seven data points. In order to help compensate for EEG pattern changes over the recording session which may not be related to VNS, each point in the stimulation class was averaged with the corresponding samples across all other stimulation cycles. This procedure reduces the amount of features to seven STLmax values for each channel to represent the stimulation class. The non-stimulation class was comprised of ten STLmax points starting 250 seconds after each stimulation to represent the portion of the non-stimulation temporally furthest from the end 110

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of stimulation. This class size was utilized capture as much information about the non-stimulation periods as possible while keep class sizes reasonably close to one another (<50% size difference in classes). Each STLmax point in the non-stimulation class was averaged across all VNS epochs (where an epoch consists of one stimulation and one non-stimulation period). Thus, the non-stimulation class consists of ten averaged STLmax samples from non-stimulation time intervals (see figure 4-4). Thus, with 25 EEG channels, there total dimensionality of the biclustering input is 25 x 17. This particular input size this problem could be solved without any relaxation using CPLEX (ILOG Inc., 2004). Cross-validation by the leave-one-out method was performed for each sample. Results Patient As data were conditionally biclustering-admitting into a binary supervised classification for the designated non-stimulation and stimulation classes with inclusion of all features (see figure 4-5). All but one feature (channel P3) were classified into the non-stimulation class. The heatmap indicates that STLmax indicates during the stimulation with respect to non-stimulation for all but the P3 channel. The leave-one-out cross-validation method resulted in consistent classification of all 17 samples for Patient A. Only five features in patient B were able to fulfill the supervised biclustering-admitting sample class designation with respect to given stimulation and non-stimulation classes. Channels F7 and T6 were designated as belonging to the non-stimulation class, while channels T3, Leye and Reye were classified into the stimulation class. Thus, there is less similarity among the channels during stimulation and non-stimulation, and a less clear distinction between stimulation and non-stimulation in Patient B than Patient A. 111

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Patient As stimulation parameters (1.75 mA, 30 Hz, and 500 s pulse width) were all greater than Patient Bs (1.5 mA, 20 Hz, and 250 s pulse width) except for the 30 second on time and 5 minute off time, which were the same for both patients. Discussion The successful application of biclustering with Lyapunov exponents demonstrates the potential to distinguish during VNS stimulation from VNS deactivation epochs using the dynamical scalp-EEG measure STLmax. There is a greater spatial-temporal similarity in EEG dynamics during stimulation in patient A than during non-stimulation. However, this phenomenon was not nearly as well-defined in patient B. It should be noted that Patient A had no seizures during the recording, whereas Patient B underwent seizures which were accompanied by a manually-initiated VNS stimulation. Though epochs containing seizures or manual stimulations were excluded from the analysis, it is possible that the seizures may have affected the results. Studies have demonstrated EEG dynamical transitions (in terms of the STLmax measure) preceding seizures minutes to hours (Iasemidis et al., 1988; Iasemidis, 1991; Iasemidis et al., 1994, 1996, 1997). It may be that EEG dynamical changes leading up to a seizure and/or persisting after the seizure lead to such a small amount of features selected in Patient B. Despite the seizures and manual stimulations, the signals arising from the frontal lobe (f7, leye, and reye) and temporal lobe (t3 and t6) of the brain were sufficiently altered between stimulation and non-stimulation to allow a biclustering of the during the stimulation class (from t3, leye and reye channels) and non-stimulation class (from f7 and t6 channels) for Patient B. This could mean that the EEG effects of VNS are most pronounced in the frontal and temporal lobes. Patient B has a right frontal lobe focus. 112

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The biological significance of these results may be related to study which discovered that VNS-induced acute suppression of epileptiform activity in a hippocampal depth electrode (Olejniczak et al., 2001). While the study by Olejniczak et al. utilized depth electrodes, its possible that scalp EEG recordings may display some manifestation of such an EEG effect observed at a hippocampal depth electrode. From this perspective, perhaps the STLmax behavioral differences between patients A and B are associated with enhanced suppression of epileptiform activity in patient A compared to patient B. Patient As stimulation parameters were all higher than patient Bs parameters, with the exception of stimulation duration and off time, which were 30 seconds and 5 minutes for both patients, respectively. In general, high stimulation parameters are associated with a greater clinical response than low settings (Ben-Menachem et al., 1994). Thus, any enhancement to epileptiform activity suppression in patient A over patient B is likely attributed to patient As higher stimulation parameter settings. This work was published in the paper Biclustering EEG data from epileptic patients treated with vagus nerve stimulation, authored by Stanislav Busygin, Nikita Boyko, Panos Pardalos, Michael Bewernitz, and Georges Ghacibeh (Busygin, 2007). SVM Analysis of EEG Phase Space Patterns in Patients undergoing VNS Therapy for Epilepsy In light of the numerous successful neural state classification applications, often in real time (Chaovalitwongse et al., 2006; Thulasidas et al., 2006) it is possible that SVMs may be able to provide a computationally inexpensive yet robust similarity measure for quantifying stimulation-induced EEG effects. As was stated chapter 3, experimental evidence supports the idea of a therapeutic resetting effect of epileptic seizures in terms of preictal convergence and postictal divergence of the STLmax measure among critical EEG electrodes (Iasemidis et al., 2004). Furthermore, recent experimental evidence suggests that therapeutic interventions such 113

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as neurostimulation and AEDs can mimics the electroencephalographic resetting effect of a seizure (Good et al., 2004, 2005; Ghacibeh et al., 2005). Thus, a reasonable approach for examining VNS therapy is from the framework that it mimics the effect of a seizure by comparing stimulation artificial seizures to non-stimulation (post-ictal or interictal). Thus, the EEG phase space of an EEG segment during VNS stimulation was compared to successive windows spanning the full stimulation / non-stimulation epoch with the intent of comparing the degree of separability to the stimulation parameters and the clinical status of the patient. The application of support vector machines for obtaining an estimate of EEG similarity during stimulation compared to subsequent EEG segments may provide a rapid means to investigate and quantify electroencephalographic effects of VNS. The goal of this study is to extract EEG patterns which could be used as an electroencephalographic marker of optimal VNS stimulation parameters. Data Description Approximately 24 hours of scalp-EEG was recorded and analyzed from six epileptic patients being treated undergoing AEDs and VNS therapy and the control patient. The recording electrode placement scheme is described in figure 4-2. The VNS Patient information is summarized in tables 4-1 and 4-2. SVM Application Description SVM training and testing were performed using LIBSVM software package designed for Matlab (Chang et al., 2001). The RBF kernel transform (equation 3-72) is a useful feature space mapping technique successfully utilized in numerous neurophysiological studies (Acir et al., 2005; Lehmann et al., 2007; Thulasidas et al., 2006).The RBF kernel with =39 was utilized for the feature space transformation and a cost parameter of C=1000 were employed based on studies utilizing RBF SVMs to classify neural states using scalp EEG data (Kaper et al., 2004; 114

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Acir et al., 2005; Lotte et al. 2007). Thus, In contrast to the traditional SVM application where a typical goal is to obtain maximal separation basis by adapting all parameters, this study fixes the and C parameters in order to mitigate subjectivity when comparing stimulation epochs to the non-stimulation epochs. An SVM classification accuracy of 50% implies minimal separation between the reference class and comparison class whereas 100% separation implies maximal separation between the reference and comparison class. These two extremes are interpreted as maximal and minimal similarity, respectively. Experimental Design The progression of EEG pattern evolution was quantified as the amount of separation achieved with support vector machines between two EEG segments both mapped into feature space using the radial basis function kernel. This exploratory study aims to examine how the EEG feature space patterns evolve throughout VNS stimulation and to identify potential relationships to stimulation parameters. In addition, the results will be compared to the clinical status of the patient. The ECG electrode was positioned on the skin over the VNS pulse generator so that VNS stimulation waveform is introduced into the ECG channel (see figure 4-3). The VNS stimulation times were then obtained by examining the ECG channel, which was excluded from further analysis. The following experimental procedure was applied to each stimulation epoch (an epoch defined as a VNS "on" cycle and one "off' cycle) in the continuous EEG recording for each patient (with the exclusion of the final stimulation epoch which began less than one full cycle before the EEG acquisition was deactivated). An EEG segment occurring from 10 seconds to 20 seconds after the start of the VNS stimulation is selected as the positive class (from here on this class will be referred to as the reference class). The duration of each class was set at 10 seconds because this time frame is suggested to be long enough to be able to quantify brain 115

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dynamics yet short enough to be sufficiently stationary (Casdagli et al., 1995, 1996, 1997). The reference class segment was selected to start at one full window length after the start of stimulation because that allows the stimulator to have finished the ramp-up phase and be at the steady-state stimulation phase. The first successive EEG window (the segment ranging from 20 seconds to 30 seconds) was selected as the first negative class (from here on this class will be referred to as the "comparison class"). The first preprocessing step was to down sample both classes by calculating the mean value of a moving-average non-overlapping window, a step which decreases SVM classification time often without a significant effect of results (Thulasidas et al., 2006). The smoothing window was set at 10 points in duration based on prior experience. Next, each data point is converted to a z-score by normalizing to zero mean and unit standard deviation. This procedure prevents channels with greater mean amplitudes from dominating the classification decision (Acir et al., 2005). The trained SVM was tested with a v-fold cross validation scheme, as described in (Hsu et al., 2003). This process applied a resampling technique in which the two classes are first randomly shuffled then divided into v equally-sized subsets. The SVM is trained using v-1 segments and is tested using the remaining subset V. This process is repeated until all v subsets have been tested. The accuracy is the percentage of properly classified points from each of the v trials. Based on prior experience, v=2 folds were utilized for SVM training and testing in this study. Once the training accuracy is obtained for the particular reference class and comparison class combination, the comparison class advances one full window length and the process repeats. The process of calculating SVM accuracy then advancing the comparison class is repeated for all comparison segments which occur within one window length from the next stimulation (into the next VNS epoch). This process is performed for each VNS epoch in the 116

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approximately 24 hour continuous EEG recording for each patient (with the exception for the final stimulation epoch during which the EEG recording ended). Results The results for the six patients are shown in figures 4-6 through 4-9 and table 4-3. The vertical line at 30 seconds in figure 4-6 represents the time when the VNS stimulator deactivates. Patients D and F have fewer comparison segments due to their off time of 3 minutes (thus the time between stimuli is less than the rest of the patients, which have a 5 minute off time). Patients E and F are seizure free. Discussion The results suggest a correlation may exist between pulse width and SVM separation accuracy (figure 4-8) as well as between stimulation frequency and SVM separation accuracy (figure 4-9). Furthermore, less similarity (greater SVM separation accuracy) is observed between the reference class (10 second EEG segment during stimulation) and all subsequent comparison classes (all non-overlapping 10 second EEG segments prior to the next stimulation) for higher values of pulse width and stimulation frequency than is observed with lower values of pulse width and stimulation frequency. The biological significance of these results may be related to studies demonstrating differences in cerebral blood flow related to stimulation parameters. Specifically, a study demonstrated that the 250 s VNS pulse width caused reduced blood flow in significantly more brain regions (e.g. hippocampus and superior temporal lobe) than a 500 s pulse width (Mu et al., 2004). It is possible that pulse-width-induced blood flow changes in these brain regions may have altered neuronal activity and thus be responsible for covariation of EEG feature space dispersion with pulse width. Another study reported that a 20 Hz stimulation frequency produced significant blood flow increase over 5 Hz in numerous brain regions such as the orbitofrontal 117

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cortex, hypothalamus, and thalamus in VNS patients (Lomarev et al., 2002). These regions may brain regions may be responsible for observed covariation of EEG feature space dispersion with stimulation frequency. It may seem counterintuitive that output current (figure 4-7) did not appear to demonstrate a trend with the SVM separation measure as a study demonstrated that higher stimulation settings (such as output current, frequency, and pulse width) can result in greater seizure reduction than lower (Ben-Menachem et al., 1994). However, the output current increase in (Ben-Menachem, et al., 1994) was also accompanied by increases in frequency and pulse width parameters. Thus the outcomes of that study can not be attributed to changes in a single parameter. Fortunately, the other two parameters (frequency and pulse width) mentioned in (Ben-Menachem et al., 1994) may correlate with EEG pattern changes, though more patients are needed to verify such a claim. It is possible that VNS mimics the seizure effect of "resetting" the brain from an unfavorable preictal state to a more favorable interictal state (Sackellares et al., 1997; Iasemidis et al., 2004) in which case the decrease in EEG similarity (signified by higher SVM separation accuracy) between the reference class and all subsequent comparison classes in an epoch may be an multidimensional analog to the brain dynamical resetting effect. The original effect was described as statistical convergence and divergence of STLmax values among critical electrode pairs (Iasemidis et al., 2004). Thus, one explanation for the observed feature space similarity phenomenon is these measures are electroencephalographic evidence that VNS is in some manner resetting the brain more effectively (as denoted by the lower similarity measures after stimulation) in the patients with fewer seizures per month. Perhaps therapies such VNS provide 118

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ongoing gradual therapeutic action which suppresses the need for a large scale brain dynamical transition such as a seizure. It is worth stating that the time of each patient's last seizure prior to the EEG recording session for this study is not documented. The timing of the last seizure could prove to be important for patients who are not seizure-free (A, C and D). This is because there is a period of heightened seizure resistance during the period immediately following a generalized tonic-clonic seizure. If patients A, C, and D had undergone a generalized tonic clonic seizure shortly before the EEG data were recorded for this study, then they may still have been under the influence of the reduced seizure susceptibility phenomenon. This may explain why they did not experience any seizures during this study. If Patient B had not experienced a generalized tonic clonic seizure recently, then reduced seizure susceptibility phenomenon may have been partially responsible for the large number of seizures reported this patient underwent during the study. These results should be viewed in the context that all six VNS patients are considered responders to the therapy defined as having at least 50% seizure reduction after one year of VNS therapy (Morell et al., 2006). Drug medication differences could also have an effect on the results. For example, patient D (whom demonstrated the lowest average similarity) is the only patient using either carbamazepine or zonisamide. On the other hand, Patient B (whom demonstrated the highest average similarity) is the only patient taking phenobarbital. Perhaps these differences in antiepileptic medications could have altered the observed electroencephalographic effects. As all patients have undergone VNS therapy for >1 year it may be regions of their nervous system such as the vagus nerve and/or brain may have adapted to VNS to such an extent that they do not demonstrate a significant acute EEG response to individual stimulations. However, it 119

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is premature to arrive at such a conclusion. The SVM training parameters utilized, though successful in similar studies, are not optimized for this particular application. In addition to non-optimized SVM parameters, it is likely that improvements can be made in terms of feature selection for exposing VNS EEG effects. This study is published in an article titled Quantification of the Impact of Vagus Nerve Stimulation Parameters on electroencephalographic Measures with authors Michael Bewernitz, Georges Ghacibeh, Onur Seref, Panos Pardalos, Chang-Chia Liu, Basim Uthman (Bewernitz, 2007). Data Mining Analysis of EEG Dynamics Patients undergoing VNS Therapy for Epilepsy The fact that the resetting effect is described in terms of the STLmax feature motivates the use of the STLmax measure for investigating EEG patterns potentially associated with VNS and VNS stimulation parameters. Inspired by the notion that therapeutic interventions may replicate the therapeutic seizure resetting effect of a seizure without adverse symptoms, the following study computes and compares STLmax values before VNS to values during VNS and utilizes SVMs as well as logistic regression to provide measures of STLmax pattern evolution. The evolution of STLmax values among the EEG channels is one method to track global EEG dynamics over time. Data Description This study involved six patients undergoing VNS therapy for intractable epilepsy. The continuous scalp-EEG recordings are ~24 hour in duration and were obtained at the Shands Hospital GCRC protocol # 614, IRB protocol #617-2004, Neurophysiologic Measures of Vagus Nerve Stimulation at the University of Florida, Gainesville. Clinical information for all six patients used in this study is summarized in tables 4-1 and 4-2. The electrode placement scheme is illustrated in figure 4-2.The stimulation times were obtained from the ECG channel, which 120

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was recorded in close proximity to the VNS pulse generator. The ECG channel was excluded from the EEG analysis. Feature Extraction The behavior of STLmax values calculated from EEG signals for seizure prediction has been extensively researched (see chapter 3). The embedded dimension of the reconstructed space D=7, lag step =7 (14 msec), evolution time T=21 (41 msec), and a window size N=2048 (4 sec) have provided useful neural state classification estimates (Iasemidis and Sackellares, 1991; Casdagli1996; Casdagli1997; Iasemidis et al., 1999). The interested reader may find the detailed explanation and justification of the algorithm and parameters in (Iasemidis, 1991), (Iasemidis and Sackellares, 1999) and (Wolf et al., 1985). STLmax was calculated for all 25 channels for the full EEG recording duration (~ 24 hours) for all six patients. SVM Analysis of EEG Dynamics The LIBSVM software package for the Matlab environment was used for SVM training and testing (Chang et al., 2001). An RBF kernel with =39 and a cost parameter of C=1000 were utilized based on studies utilizing RBF SVM to classifying neural states from scalp EEG data (Kaper et al., 2004; Acir et al., 2005; Lotte et al., 2007). The SVM parameters C and sigma are held constant in an effort to provide objectivity to this measure which can be used to study EEG signal evolution over time in feature space for all the patients. This study fixes the and C parameters in order to mitigate subjectivity when comparing stimulation epochs to the non-stimulation epochs. An SVM separation accuracy of 50% is interpreted as maximum measureable dynamical feature space similarity between reference class and comparison class features. An SVM 121

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separation accuracy of 100% is interpreted as the minimum dynamical feature space similarity between the reference class and comparison class features. Results are validated using a v-fold cross validation scheme, as described in (Hsu et al., 2003) using 10 folds. This process applied a resampling technique in which the two classes are first randomly shuffled then divided into v equally-sized subsets. The SVM is trained using v-1 segments and is tested using the remaining subset V. This process is repeated until all v subsets have been tested. The accuracy is the percentage of properly classified points from each of the v trials. Logistic Regression Analysis of EEG Dynamics Logistic regression (LR) has seen number applications for the diagnosis of neurological diseases and disorders. Examples include Parkinson's Disease diagnosis using various clinical diagnostic measures (Leentjens et. al, 2002), diagnosis of Alzheimer's Disease (Lehmann et al., 2007), cognitive decline (Prichep et al., 2006), and Schizophrenia using electrophysiological features (Price et al., 2006), and epilepsy using EEG features (Alkan et al., 2005; Subasi et al., 2005). Thus, LR analysis is a suitable candidate for further characterizing the brain dynamics in patients undergoing VNS. LR is a statistical modeling technique utilized for probabilistic binary classification. As described in Subasi et al., 2005, the probability, P t,ref of a binary outcome event (EEG point at time t belonging to the reference class) is related to EEG value of channel ch at time t, x ch,t in the form: 251,0,2525,110,,,...1lnchtichitchtchreftreftreftxxxPPPLOGIT (4-1) 122

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251,0,1111,chtichtreftxXPLOGITtrefteeXP (4-2) In equation (4-1), 0 is the intercept of the model and 1, 2, 25 represent the coefficients for EEG channels one through 25. Once the logistic regression model is trained, the probability P t,ref of an EEG data point X t belonging to the reference class can be calculated in equation (4-2). The performance of the logistic regression model is measured using the area under the curve (AUC) approach (Komaraek, et al., 2005). The AUC is equal to the area under the receiver operating characteristics (ROC) curve. The AUC metric is simply the ratio of the area of an ROC curve to the area under a perfect ROC curve. Let NR be the number of points in the reference class, and NC be the number of points in the comparison class. NR = NC for this study, but do not have to be equal. The ROC curve is generated by first calculating P t,ref for each EEG data point X t in both the reference class and the comparison class. Then, the P t,ref values are sorted in decreasing order. The ROC curve creation begins at the lower left hand corner of a blank curve plot. Each point with P t,ref 0.5 (most likely that the EEG point is from the reference class) results in the creation of an upward line segment of length one unit. Each point with P t,ref < 0.5 (most likely that the EEG point is from the comparison class) in the creation of a line segment of length one unit to the right. The AUC metric is the ratio of the area under the generated ROC curve divided by the area under a perfect ROC curve (which climbs from (0,0) to (0, NR), then moves laterally from (0, NR) to (NC, NR) and is equal to one in this case). 123

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An AUC=0.5 (or ROC=0.5) is equivalent negligible dynamical feature space similarity between the reference class and comparison class. AUC=1.0 (or ROC=0) refers to the maximum measurable dynamical feature space similarity between the reference class and comparison class. Experimental Setup The following procedure was applied to each stimulation epoch (an epoch defined as a VNS on cycle and one off cycle) for each patient using SVMs and then repeated for LR. The EEG segment occurring 8 seconds (two window lengths) prior to stimulation start is selected as the reference class. The reference class was represented as an mn array of STLmax values where n is the number of channels and m is one less than the total number of stimulations occurring during the EEG recording. Setting m as one less than the total number of detected stimulations ensures that only complete VNS epochs are included in the analysis (as the last stimulation intersected with the end of the recording for all six patients). For each patient, the reference class utilized STLmax estimates from all n=25 channels from the time period of 8 seconds (two full window lengths) prior to stimulation start, for all m stimulations. The comparison class was initially established as an mn array of STLmax values occurring at the start of the stimulation for all m stimulations included for each patient. The SVM and LR classifiers are trained and tested for separation of the reference and comparison class combination. Once the accuracies are obtained, the reference class is advanced 4 seconds (one full window length) and the process is repeated throughout the epoch with the last comparison class occurring 200 seconds after stimulation start. The end point corresponds to the end of the 3 minute interstimulation cycle, which is the final endpoint which Results Figures 4-10, 4-11, 4-12, and 4-13 as well as table 4-4 demonstrate a similar performance between the LR and SVM results. Using both methods, the same two patients which produced 124

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the greatest STLmax feature separation between non-stimulation and stimulation epochs (patients A and D) also possessed the greatest stimulation frequency, 30 Hz, whereas the patient with the lowest separation (patient B) also possessed the lowest stimulation frequency, 20 Hz. In addition, patient D produced the second greatest separation while possessing highest stimulation frequency of 30 Hz. On the other hand, Patient F also had the greatest stimulation frequency of 30 Hz yet only achieved an intermediate separation value compared to the other patients (though patient F is seizure-free whereas patients A, B, and D are not). The final noteworthy observation the width was the lowest (250 microseconds) and Patient B who demonstrated the least separation. There was no apparent trend regarding the degree of separation using either LR or SVM and output current. One interesting connection with the clinical status was that the patients whom experienced the greatest amount of separation (patients A and D) were also taking more types of AED medications (patients A and D each were on four medications, patient B was on three medications, all other patients were only taking two medications). Another interesting connection to the clinical status is that the patient with the largest number of monthly seizures (patient B) also demonstrated the least amount of STLmax feature separation between non-stimulation and stimulation. Discussion The LR and SVM classification results suggest that EEG dynamical pattern changes (in terms of the STLmax measure) between stimulation and non-stimulation may be related to the stimulation frequency parameter. Lomarev et al. reported that a 20 Hz stimulation frequency produced significant blood flow increase over 5 Hz in numerous brain regions such as the orbitofrontal cortex, hypothalamus, and thalamus in VNS patients (2002). These regions may 125

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brain regions may be responsible for observed covariation of STLmax dispersion with stimulation frequency. At a first glance it seems counterintuitive that the output current did not appear to demonstrate a similar LR or SVM classification accuracy trend as pulse width and stimulation frequency, as a study demonstrated that higher stimulation parameter settings (such as frequency, output current, and pulse width) are associated with greater seizure reduction than lower settings (Ben-Menachem et al., 1994). However, the output current increase mentioned in (Ben-Menachem et al., 1994) was accompanied by increases in frequency and pulse width and thus the observed therapeutic effect in that study can not be attributed to changes in an individual parameter. Furthermore, the values of the other two parameters mentioned in the study by Ben-Menachem et al. (frequency and pulse width) did show indications of a connection with EEG dynamical changes, which is encouraging. Patient Bs large amount of seizures accompanying the lowest LR and SVM separation is an interesting observation. It is difficult to draw preliminary conclusions about clinical connections to the brain dynamical behavior as Patient B's stimulator was set at the lowest pulse width and the lowest stimulation frequency of all six patients. However, a potential connection between this patient's clinical behavior and the observed EEG patterns can be viewed from an interesting perspective first described in seizure prediction research studies. Considering the electroencephalographic and clinical effects observed during seizures, it is possible that the VNS therapeutic effect is enacted by artificially replicating the theorized therapeutic seizure mechanism first suggested by Iasemidis et al. (2004). By adopting this perspective, patient B's seizures could be seen as the result of the VNS failing to replicate the resetting function of a real seizure. Thus, the brain is then permitted to 126

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seize in order to reset itself. This observation is congruent with the notion that patient B has the lowest STLmax feature separation for both LR and SVM between the VNS on (which could be considered a VNS artificial seizure) and VNS off class (which from an artificial seizure perspective could be viewed as a post-ictal period for the artificial seizure). It is worth mentioning that all six patients are considered as responders to VNS therapy by a definition of experiencing at least a 50% seizure frequency reduction following one year of VNS therapy (Morell et al., 2006). The observation that patients A and D were taking the most types of AEDs and demonstrated the highest STLmax feature separation between non-stimulation and stimulation is reasonable. Again, from the view of a seizures resetting mechanism described in the previous paragraph, the two additional AEDs could possibly be enhancing effectiveness of the VNS resetting phenomenon as characterized by increased STLmax separation between VNS on and VNS off. This study was submitted to Computing and Optimization in Medicine and Life Sciences Vol. 3, under the title "A Data Mining Approach to the Investigation of EEG Biomarker Existence for Vagus Nerve Stimulation Therapy Patients", with authors Nikita Boyko, Michael Bewernitz, Vitaliy Yatsenko, Panos Pardalos, Georges Ghacibeh, Basim Uthman (Boyko et al., 2008). Conclusions The interesting results of these studies may be indicative of EEG dynamical effects of VNS and suggest the LR, SVM and biclustering may serve as useful data classification tools for use in an online real-time seizure control application. Biologically, these results may be related to the trait pointed in a study by Olejniczak et al. which discovered a short-term suppression of epileptiform sharp waves following VNS from a hippocampal depth-electrode (2001). While the 127

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scalp electrodes used to collect the EEG data for this chapter cannot achieve the fidelity of hippocampal depth electrodes, it is possible that the scalp EEG data mining analysis results may reflect the same therapeutic effect as observed in the hippocampus by Olejniczak et al. (2001). The biological significance of the potential covariation of the EEG patterns with the pulse width and stimulation frequency parameters may be related to studies which demonstrated cerebral blood flow patterns corresponding to the pulse width (Mu et al., 2004) and stimulation frequency (Lomarev et al., 2002) parameters in VNS patients. Additional patients are needed to validate such claims against possible type 1 error. However, additional patients would also provide the opportunity to potentially uncover any VNS-induced EEG dynamical changes which may have been missed in this small sample (thus reducing the chance of type 2 error). A difficulty for this type of clinical research is recruiting patients with similar clinical situations (e.g. similar stimulation parameter configurations) in order to strengthen any observed connections between EEG behavior and stimulation parameters. For example, if numerous patients with similar stimulation parameters could be recruited, the patients may be taking different medications in different doses, etc. While it may be tempting to consider altering drug paradigms to mitigate inter-subject variability, practical and ethical concerns must be kept in mind at all times when attempting to alter patient treatment regimes for research purposes. In addition, the impact of epileptic seizures on these EEG features and classification techniques is important for generating a robust stimulation-response model. Thus, as the clinical circumstances such seizure occurrence can affect observed EEG dynamical patterns, it is worth mentioning that each patient's last seizure time prior to this studys EEG recording session is unknown. The time at which the last seizure occurred may be important factor for the patients 128

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which are not seizure free (patients A, B, C, and D) as there exists a period of reduced seizure susceptibility for a period of time following a generalized tonic-clonic seizure. Thus, patients A, C, and D could have experienced generalized tonic clonic seizures prior to the study recording session and thus been influenced by this period of reduced seizure susceptibility. Such an scenario could have contributed to the lack of seizures occurring during the recording session and also influenced seizure dynamics. In addition, if patient B had not experience a generalized tonic-clonic seizure prior to the study recording session then this patient's large number of seizures may have been partially induced due to the lack of said seizure protection phenomena following a seizure. Despite exclusion of stimulation epochs containing seizure activity from analysis, patient Bs seizures during the recording session still may have altered the observed EEG patterns. The rationale for such as claim is the observation of dynamical EEG shifts (in terms of the STLmax measure) identified from minutes to hours prior to epileptic seizures (Iasemidis et al., 1988; Iasemidis, 1991; Iasemidis et al., 1994, 1996, 1997). Thus, conclusions about patient B must be carefully considered as the seizures themselves could affect the observed EEG classification results. There is also a possibility of error in the monthly seizure rate as described by the patients. A 2007 study by Hoppe et al. demonstrated documentation inaccuracies in patient seizure counts (Hoppe et al., 2007). Thus, caution must be exercised in any epilepsy study which incorporates seizure information that was documented by patients. Thus, in an ideal study, additional consideration should focus on recruiting a group of patients with similar epilepsy cases (e.g. similar focus locations). By studying multiple patient groups each with similar variants of epilepsy, experimental findings are strengthened and the findings may help tailor resulting VNS therapy devices. 129

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In order further the understanding of EEG effects accompanying VNS it is important to track EEG feature patterns in patients before, immediately after, and for at least six months after implantation. A longitudinal study starting before VNS implantation and ending 6-12 months after implantation would provide insight into the evolution of EEG dynamical patterns before and after VNS parameter adjustment. In addition, such an analysis would help determine the presence of EEG characteristics present prior to VNS implantation for each individual patient. Thus, such a study design would add strength to post-implantation EEG patterns which are not observed prior to VNS implantation. In the case that pre-VNS data is not available for a particular patient of interest, patients whom are receiving VNS for depression treatment may serve as useful control subjects. Such patients could help determine how brain dynamics in VNS patients are influenced by epilepsy and seizures. The potential knowledge gained from these suggested studies could lead us one step closer to the creation of an EEG marker for optimal VNS parameters. In addition, as the relationship of EEG patterns stimulation parameters and clinical outcome in VNS patients is not clearly defined, then it is possible that the EEG measure parameters or perhaps the measures used in data classifiers are suboptimal. Thus, additional EEG features should be utilized for possible improvements in EEG dynamical comparisons. Complexity measures entropy measures have demonstrated success as data mining features for extracting brain dynamical information and classifying neural states (Chaovalitwongse et al., 2006). 130

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Figure 4-1. Rationale for studying EEG patterns which may be associated with the effect of VNS on the brain. Ultimate goal Experimental objective Clinical Literature Review / Future Ex p eriments Stimulation parameters Clinical effect EEG measures 131

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Sz free 1-5 sz/month 5-10 sz/month >10 sz/month OC = 1.25 mA PW = 250 SF = 25 Hz On = 30 sec Off = 5 min OC = 0.75 mA PW = 250 SF = 20 Hz On = 30 sec Off = 5 min OC = 1.0 mA PW = 250 SF = 20 Hz On = 30 sec Off = 5 min OC = 1.25 mA PW = 250 SF = 20 Hz On = 30 sec Off = 5 min OC = 1.25 mA PW = 500 SF = 20 Hz On = 30 sec Off = 5 min OC = 1.25 mA PW = 750 SF = 20 Hz On = 30 sec Off = 5 min OC = 1.25 mA PW = 250 SF = 30 Hz On = 30 sec Off = 5 min Figure 4-2. Conceptual EEG dynamics model in three-dimensional feature space for testing stimulation parameter configurations in newly-implanted VNS patients. Adjusting the stimulation parameters results in an altered dynamical state of the brain denoted by the coordinates in three-dimensional feature space. The models colored regions relate the EEG dynamical state to its predicted clinical outcome. 132

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Table 4-1. VNS stimulation parameters Patient A B C D E F Output Current (mA) 1.75 1.5 2.5 2 1.25 0.75 Stimulation Frequency (Hz) 30 20 25 30 20 30 Pulse Width (s) 500 250 500 500 500 750 On Time (seconds) 30 30 30 30 30 30 Off Time (minutes) 5 5 5 3 5 3 Magnet Output Current (mA) 2 1.75 2.75 2 1.5 0.75 Magnet On Time (seconds) 60 60 60 30 60 60 Magnet Pulse width (s) 500 500 500 500 500 750 Figure 4-3. EEG electrode placement. Electrodes were positioned according to the 10-20 electrode placement system which assigns locations proportionally spaced locations (e.g. 10%-20%) with respect to the size of the patients head. 133

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Figure 4-4. STLmax class designation for biclustering analysis. 134

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A B Figure 4-5. Biclustering heatmap of STLmax from A) patient A and B) patient B. 135

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Table 4-2. Patient information for epilepsy patients with the VNS implant. Patient A B C D E F Age 38 53 54 29 54 54 Right frontal Right temporal Focus Left frontal Right frontal Right temporal Left frontal unknown Left temporal Mean seizures per month 3 30 2 3 0 0 # of seizures during recording 0 14 0 0 0 0 Seizure Type C. Partial with infrequent secondary gen. C. Partial with infrequent secondary gen. C. Partial with infrequent secondary gen. C. Partial with infrequent secondary gen. C. Partial with infrequent secondary gen. C. Partial with infrequent secondary gen. Duration of VNS therapy (years) > 1 year > 1 year > 1 year > 1 year > 1 year > 1 year Gab Lev Gab Carb Chlor Preg Lam Phen Top Lam Gab Lev Lev Top Lev Medications* Preg *Gab = Gabapentin, Lam = Lamotrigine, Lev = Levetiracetam, Preg = Pregabalin, Phen = Phenobarbital, Top = Topiramate, Carb = Carbamazepine, Chlor = Chlorazepate Table 4-3. SVM separation accuracy and seizure information. Patient Mean SVM separation Average monthly seizure rate Seizures during recording A .9284 3 0 B .7788 30 14 C .8359 2 0 D .9807 3 0 E .9454 0 0 F .8982 0 0 *Average monthly seizure rate of zero indicates seizure freedom. 136

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Figure 4-6. Mean SVM separation accuracy value across the stimulations for each individual intra-stimulation window. Figure 4-7. VNS output current and the corresponding mean SVM separation accuracy over 24 hours. 137

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Figure 4-8. VNS pulse width and the corresponding mean SVM separation accuracy over 24 hours. Figure 4-9. VNS signal frequency and the corresponding mean SVM separation accuracy over 24 hours. 138

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Figure 4-10. SVM Separation accuracy throughout the VNS epoch, averaged across all epochs. Stimulation begins at t=0 seconds. Figure 4-11. Overall mean SVM separation averaged across intra-epoch time points and all epochs. 139

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Figure 4-12. LR separation quality throughout the VNS epoch, averaged across all epochs. Stimulation begins at t=0 seconds. Figure 4-13. Overall mean LR AUC averaged across intra-epoch time points and all epochs. 140

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Table 4-4. Mean SVM and LR separation accuracy and patient seizure information. Patient Overall mean SVM separation Overall mean LR separation Seizures per month Seizures during recording A 0.8082 0.9701 3 0 B 0.4746 0.5104 30 14 C 0.6171 0.7571 2 0 D 0.7536 0.9658 3 0 E 0.7210 0.8878 0 0 F 0.6885 0.8319 0 0 141

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CHAPTER 5 ANALYSIS OF INTERSTIMULATION BRAIN DYNAMICS IN VAGUS NERVE STIMULATION THERAPY The Identification of a marker of desired VNS operation would greatly expedite the VNS parameter adjustment process in newly-implanted patients. This study faces two significant challenges: 1) the underlying therapeutic mechanism of VNS is still poorly understood, and 2) despite some interesting results reported in innovative research studies, the electroencephalographic effects of vagus nerve stimulation are not clearly defined. From the perspective of dynamical disorder (see chapter 2), there is reason to believe any such potential stimulation-induced EEG effects are likely to be elucidated from dynamical EEG analysis (Uthman et al., 2007). Further Characterizations/Investigations of EEG-Effects in VNS Therapy Preliminary data mining results described in chapter four present interesting EEG dynamical phenomena with biological interpretations that are consistent with the theory about the physiological resetting role of a seizure. Of additional interest is the behavior of the brain between VNS stimulations. Viewing inter-stimulation brain behavior provides a means to determine how the brain recovers after VNS therapy (or artificial seizures). In addition, this analysis duration also provides information about the brain while is not being actively influenced by a therapeutic action (e.g. VNS or the therapeutic effect of a seizure). Thus, as non-ictal EEG can help provide information about the seizure imminent state, so to may the inter-stimulation EEG intervals provide information additional information about the brains response to VNS which may not be available while the VNS is active. This chapter focuses on characterizing the temporal dynamical behavior of the EEG signals during the periods when the VNS is inactive. 142

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Building on the successes of the data mining approaches in chapter four, this chapter aims to further characterize EEG patterns which may be related to VNS. The brains behavior will be characterized during all periods of respite from VNS. Dynamical EEG Measures as Markers for Neurological Diseases and Disorders The success of EEG markers for the treatment of neurological disorders is the primary motivation for this study. Such signature observations of pathological activity have greatly boosted diagnosis, treatment, and therapeutic evaluation of a range of neurological disorders (Krystal et al., 1996, 1997, 2000; Asyali et al., 2007; Ding et al., 2007; Quintana et al., 2007) including epilepsy (Iasemidis et al., 1996; Pardalos et. al, 2003, 2004; Chaovalitwongse et al., 2005, 2006; Ding et al., 2007; Schevon et al., 2007). Additional details can be found in chapters 2 and 3. Despite reported interest in the application of such a technique to the EEG signals for improving VNS epilepsy therapy (Uthman et al., 2007), studies have been published which do not support the presence of VNS-induced EEG effects (Hammond et al., 1992; Salinsky et al., 1993; Koo, 2001; Rizzo et al., 2004; Marrosu et al., 2005). Though long-term VNS-induced EEG changes on epileptic interictal spikes (Koo, 2001) epileptiform sharp waves in the hippocampus (Olejniczak et al., 2001), interictal epileptiform discharges (Janszky et al., 2005; Santiago-Rodriguez and Alonso-Vanegas, 2006), gamma activity and desynchronization (Marrosu et al., 2005), and spectral content of sleep (Rizzo et al., 2004) have been reported, the time frame for observing such an effect renders it less useful the current task of expediting VNS parameter calibration in newly-implanted patients. Physiological behavior such as alterations in the interitical spiking rate is congruent with the characteristics dynamical diseases and disorders. The class of disorders termed dynamic disorders demonstrates complex behavior patterns which evolve over time. Specifically, these 143

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disorders have been broadly described as undergoing a temporal disruption in the underlying physiological control mechanisms which results in a period of abnormal dynamical behavior (Mackey and Glass, 1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003; Colijn and Mackey, 2005). Thus, studying epilepsy therapy from the vantage point of a dynamical disorder is a rational approach. Koos observation of the VNS effect on interictal spiking rate (2001) demonstrates that relatively short-term EEG effects (such as interictal spikes) are the manifestation of long-term modulatory VNS effects (e.g. after several months). Thus, this observation raises the possibility of less obvious short-term manifestations of VNS modulatory effects existing in the EEG. Such EEG effects may be detectable using EEG measures that have demonstrated successful neural state characterization such as preictal transitions in seizure prediction studies (Casdagli et al., 1996; Chaovalitwongse et al., 2005; Iasemidis and Sackellares, 1991; Iasemidis et al., 1993; Iasemidis et al., 2003, 2004; Le Van Quyen et al., 2001; Lehnertz, 1999; Lehnertz and Elger, 1995; Osorio et al., 2001). The purpose of identifying dynamic disorders is that successful treatment may result from manipulation of some physiologic control parameter into a range associated with healthy dynamics of the observed variables (Milton, 2000). One example of this is a seizure control strategy where thehealthy range of STLmax t-index values (associated with seizure transition) in maintained by therapeutic intervention (Iasemidis et al., 2003; Good et al., 2004, 2005). An analogous scenario may apply to VNS parameter adjustment in newly-implanted patients where the VNS parameters may be adjusted in order to elucidate a brain dynamical response or state that has been previously established as indicative of desired or even optimal seizure protection. 144

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Thus, the achieved neural state as described by dynamical EEG responses associated with different stimulation parameters over time may serve as marker for VNS treatment and facilitate rapid determination of optimal VNS parameters. An example of this concept is illustrated for a brain dynamics model involving three dynamical measures in chapter 4, figure 4-2. Realistically, mapping the clinical outcome to subregions of a multidimensional feature space will likely be very complex and require numerous additional features for adequate characterization. While determining the proper features to best represent the brain behavior and its relationship to stimulation parameters in VNS is a daunting task, this study aims to provide an in-depth evaluation of a number of EEG measures which have demonstrated sensitivity to neural state changes in other studies. For these reasons, the current study aims to identify electroencephalographic markers which are sensitive to the stimulation parameter configuration in patients with the VNS implant. If such electroencephalographic markers are identified, and if the electrographic markers are found to correlate with clinical efficacy then these findings could be applied to determine optimal VNS stimulation parameters on a patient-by-patient basis. Data Description This study utilized EEG data from six patients undergoing VNS therapy for epilepsy. Extensive patient information can be found in chapter four. The recordings were acquired under GCRC protocol # 614 / IRB protocol #617-2004, "Neurophysiologic Measures of Vagus Nerve Stimulation" GCRC in Shands Hospital at The University of Florida. EEG data was acquired from channels Fp1, Fp2, F3, F4, C3, C4, P3, P4, O1, O2, F7, F8, T3, T4, T5, T6, A1, A2, Fz, Cz, Pz, Leye, Reye, Lmn, and Rmn using CPz (located between Cz and Pz) as a reference. The data were acquired at 512 Hz sampling rate using 16-bit precision from an amplifier with 0.16 Hz high pass filter and 105 Hz low pass hardwired filters. The mandibular notch channel near the 145

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location where the jaw and skull contact one another provides information about the nearby temporal lobe. See figure 5-1 for electrode locations. The ECG electrode was placed near the pulse generator to introduce the VNS waveform in the ECG channel when the stimulator is active. Thus, the VNS signature waveform was introduced into the ECG (see figure 4-4) to provide an effective means to identify stimulation times by modifying a channel that is not used in the quantitative analysis. A summary of patient clinical information can be found in tables 4-1 and 4-2. Ideally, the baseline recording from each involved patient should be compared to their own EEG after implantation in order to strengthen claims that observed EEG patterns are the result of VNS and thus were not present prior to implantation. However, baseline EEG data was not available for this set of patients. As no baseline data was available for the VNS study, an interictal EEG recording from a temporal lobe epilepsy patient of ~24 hours in duration provided courtesy of the Freiburg Center for Data Analysis and Modeling at the Albert-Ludwigs Universitt Freiburg (University of Freiburg), Freiburg, Germany (Winterhalder et al., 2006) was utilized as a control dataset. The interictal EEG data came from patient p012 and was acquired at 512 Hz. The data were acquired from three focal channels (TBa4, TBb6, HR7) and three non-focal channels (TLb2, TLb3, TLc2). The patient has a right hippocampal seizure focus which gives rise to simple partial, complex partial, and generalized tonic-clonic seizures. The control dataset was utilized with artificial stimulation times based on both a 5 minute interstimulation interval and a 3 minute interstimulation interval. The Surrogate Analysis Method The surrogate data analysis method is a statistical approach for identifying nonlinearity in a time series. The best expression of the surrogate data method is from a statistical hypothesis 146

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testing framework (Theiler et al., 1992). This formulation requires a null hypothesis to test against and some test statistic. The null hypothesis is a possible description of system output which is tested to determine how well it models the observed data. The test statistic is a quantity calculated from the sample data to determine whether or not to reject the null hypothesis. Surrogate data analysis typically defines the null hypothesis such that the time series data are described by a specific process belonging to a broader class of processes (Schreiber and Schmitz, 2000). A common null hypothesis asserts that the time series data are generated by a general Gaussian linear stochastic process (Theiler et al, 1992). However, different realizations that fit within this broad category can result in surrogates with different power spectra and distributions. This scenario and may cause the test statistic may mistake such variations for deviations from the null hypothesis and falsely reject the null hypothesis (Schreiber and Schmitz, 2002). The can be approach using pivotal statistics or using constrained realizations (Theiler and Prichard, 1996). Pivotal statistics are measure created such that do not depend on mean or standard deviation under the null hypothesis. The constrained realization method enforces a requirement that all surrogates display the same power spectrum and distribution of values as the original data (Theiler and Prichard, 1996; Schreiber and Schmitz, 2000). Under the constrained realization approach the randomization method covers the pivotal requirement and thus opens up the possibility to use numerous non-pivotal test statistics for testing the null hypothesis. While the surrogate method is useful for suggesting the presence of nonlinear signal components, this technique cannot be used to characterize the specific type of observed nonlinear behavior. For example, while it is valid to utilize a Lyapunov exponent to test the null hypothesis, surrogate analysis cannot indicate that an observed nonlinear signal is the result of low-dimensional chaos (Pritchard et al., 1995; Palus, 1997; Schreiber and Schmitz, 2000). 147

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Surrogate data sets were generated using the algorithm proposed by Schreiber and Schmitz to produce same power spectrum and amplitude distribution as the original dataset (1996). The algorithm runs as follows. Let represent an EEG signal of length n. Store sorted list of the raw EEG values, ns sortns, and the absolute value of the amplitudes of the discrete Fourier transform (equation 3-11) of which is denoted as ns kS First the original data are randomly shuffled ns 0ns Each iteration consists of two actions. At iteration step i, the signal from the previous iteration 1ins is brought to the desired power spectrum by computing the Fourier transform and replacing the amplitudes 1ikS with those of the original signal kS and performing the inverse Fourier transform. The original complex Fourier phase values of the signal from the previous iteration 1ins remain unchanged when reconstructing the signal ins having the desired power spectrum. While this step enforces the correct power spectrum, it usually disrupts the signal amplitude distribution. Thus, the second step in an iteration is to rank order the resulting time series ins and replace the ranked indices with the ranked amplitudes from the original signal sortns, Performing the rank ordering will thus alter the power spectrum calculate in step i+1, thus requiring the entire procedure to repeat. After each iteration, the deviation from the original power spectrum is checked and the process repeats until a given accuracy is achieved. The Role of Surrogate Data Analysis in EEG studies Nonlinear measures such as complexity, chaoticity, and information-based measures can be useful in the analysis of the output of complex systems such as the brain (Lehnertz and Elger, 1995; Pincus, 1995; Lehnertz, 1999; Le Van Quyen et al., 2001; Osorio et al., 2001; Iasemidis et al., 2003, 2004). However, analysis of less complex systems may not require the application of 148

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nonlinear methods as they may provide the same (or perhaps less) information about the system at hand while often resulting in increased computational cost. Thus, an original application of surrogate analysis was to provide partial justification for the use of nonlinear analysis methods in EEG studies. Surrogate data analysis has provided support for the presence of nonlinear components of EEG signal in various types of epilepsy (Casdagli et al., 1995; 1996, 1997; Lopes Da Silva et al., 1999; Jung et al., 2003; Liu et al., 2007). Additionally, observations have been made regarding the different neural states in epilepsy such as interictal, preictal, ictal, and postictal the corresponding occurrence of significant nonlinearity (Pijn et al., 1997; Jung et al., 2003) as well as a measure of the amount of nonlinearity (e.g. the magnitude of the p-value when comparing original to surrogate data) ( Liu et al., 2007). In addition, surrogate data analysis has demonstrated changes in nonlinear signal component expression following various brain stimuli such as transcranial magnetic stimulation (Jing and Takigawa, 2002), drug treatment (Ferenets et al., 2006) compared to baseline EEG. As any similar studies regarding VNS was could not be located, such an analysis may provide a means for quantifying EEG effects related to VNS parameters and perhaps clinical outcome. In addition the following analysis may provide an improved understanding of the brains EEG response to VNS and potentially provide insight into how it delivers its therapy. Nonlinearity Analysis of Interstimulation EEG The following study is motivated by a desire to characterize the interstimulation EEG dynamics in VNS patients and identify potential covariation with stimulation parameters using surrogate EEG analysis. The underlying hypothesis (stated as null) which motivates this study is EEG dynamics during the interstimulation period are unrelated to the stimulation parameters in VNS patients. The interstimulation period is targeted in order to track the brains post 149

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stimulation response which may contain useful EEG dynamical information relating to the stimulation parameter configuration. Under this experimental setup, it is logical to compare to the results to a control patient which utilizes artificial stimulation times. Resulting EEG dynamical differences between the VNS patient interstimulation epochs and the control patient artificial interstimulation epochs could provide convincing support for the existence of VNS-induced EEG effects which may be related to the VNS parameters. Choosing a Test Statistic By utilizing the constrained realization approach to surrogate data analysis, the options for a test statistic become more plentiful as the requirement for a pivotal test statistic is now relinquished (Theiler and Prichard, 1996). Based on the successful application of entropy measures in EEG nonlinearity test studies (Thomasson et al., 2000; Burioka et al., 2003,2005; Ferenets et al., 2006), as well as the general success in classifying neural states from EEG (Bruhn, 2000; Bruhn, 2001; Bruhn, 2003; Absolo, 2005; Ferenets et al., 2006), the approximate entropy (ApEnt) measure will serve as the test statistic. The ApEnt measure was calculated within non-overlapping windows of size 2048 points (4 seconds). A window of this size falls within a reasonable range utilized for computing ApEnt in terms of clinical and theoretical relevance (Pincus, 1995). The noise threshold r=0.2*std was selected as a result of studies which successfully correlated the ApEnt EEG measure to clinical drug anesthesiology levels (Bruhn, 2000; Bruhn, 2001; Bruhn, 2003; Ferenets et al., 2006), as well as a study which used ApEnt to characterize background EEG in patients with Alzheimers Disease (Absolo, 2005). The phase space mapping process utilized an embedding dimension of 7 is used based on previous EEG complexity studies quantifying neural state transitions in patients with mesial temporal lobe epilepsy (Iasemidis et al. 1988; Iasemidis et al., 1990; 150

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Iasemidis et al., 1999). The time delay embedding process utilized a delay =7 corresponding to14 ms (Iasemidis et al., 1990; Zaveri et al., 1993; Iasemidis et al., 1996). Experimental Design The amount of surrogates were selected based on a model proposed by Schreiber and Schmitz which considers a residual probability of a false rejection by random chance with a corresponding significance level of 1001 % (2000) The proposal suggests creating an amount of surrogates M=2*K/ -1 such that the probability that the data will reject the null hypothesis by chance is for a two-tailed test (Schreiber and Schmitz, 2000). Due to the intensive computational complexity of this procedure, this preliminary analysis utilizes K=1 and =0.1 for the purposes of selecting the amount of surrogate data copies. Thus, this study uses 19 surrogates. EEG surrogates were calculated in non-overlapping windows of length 2048 points (4 seconds). This window size is considered to be within a reasonable range for surrogate data generation (Schreiber and Schmitz, 1996). This is also used as the window length utilized in the calculation of the ApEnt measure used as the test statistic. The mean value of each ApEnt point across all 19 surrogates is computed to the surrogate datasets to a single time series which is then compared to the original signal (Casdagli et al., 1996; 1997; Liu et al., 2007). For patients with a 5 minute interstimulation time a window of 73 points represented the interstimulation period. For patients with a 5 minute interstimulation time a window of 73 points represented the interstimulation period. For patients with a 3-minute interstimulation time, a 43 point window represented the interstimulation time. Statistical testing was performed using a two-tailed paired-t test. For 95% certainty and 72 degrees of freedom and 42 degrees of freedom the critical t-values are t= 1.993 and t=2.018, respectively. 151

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This preliminary study assesses the dynamical structure of EEG signals during VNS interstimulation periods. The dynamical structure is evaluated by testing each interstimulation epoch against a null hypothesis of a Gaussian linear process using surrogate datasets for all epochs for all six patients. The hypothesis, stated as null is: H0: EEG dynamics during an interstimulation epoch are described by a Gaussian linear stochastic process. Results For each patient and for each channel, the hypothesis was tested using approximate entropy of the EEG of VNS deactivation epoch (see figure 5-3 through 5-12 and tables 5-1 through 5-3). Patients A and B showed a notable increase in the amount of interstimulation epochs demonstrating a nonlinear signature occurring across most channels occurring between 11 pm until 7 am. The control patient showed a decrease in a nonlinear fingerprint occurrence in non-focal channels during the same time of day. The fraction of epochs across the entire recording and all channels which displayed a nonlinear signature (could reject H0 at the given significance) displayed a potential negative correlation with the pulse width parameter for all six patients. In addition, patient F showed nonlinear signatures in fewer epochs than any other patient (35.1% of all epochs could reject H0 at the given significance), followed by patient E (39.0%). Both of these patients are seizure free. Patient Bs EEG showed the most nonlinear fingerprints having 52.3% of the epochs rejecting H0 at the given significance level. While patient F showed the most nonlinearity, patient F had the greatest stimulation frequency (30 Hz) and the greatest pulse width (750 s). Patient B had the lowest stimulation frequency (20 Hz) and the shortest pulse width (250 s). The fraction of epochs which displayed nonlinear signatures for the 152

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control patient with 5-minute and 3-minute interstimulation times were 42.5% and 37.2%, respectively. In general, the lower the monthly seizure rate, the less nonlinear signatures were observed. According figure 5-3, patient F (seizure-free) produced a smaller fraction of nonlinear interstimulation epochs than the 3-minute control whereas patient D (~3 seizures per month) produced a larger fraction of nonlinear epochs than the 3-minute control. A similar trend was observed in the patients with the 5-minute interstimulation time. Patients C and E (seizure free and ~ seizures per month, respectively) generated a smaller fraction of nonlinear epochs than the 5-minute control whereas patients A and B (~3 seizures per month and ~30 seizures per month, respectively) displayed a larger fraction of nonlinear epochs than the 5-minute control. Patients A, B, D, and F showed noticeably higher expressions of nonlinearity in channels located near foci than non-focal channels. The control patient demonstrated a high density of nonlinear behavior in non-focal channels during waking hours which is diminished around 11 pm 7 am, except for the TLc2 channel which shows a greater fraction of epochs demonstrating nonlinear signatures than other channels. Discussion In regards to the connection of EEG patterns stimulation parameters, the most obvious observation was the potential relationship between the fraction of epochs which displayed nonlinearity and the pulse width parameter. In addition, Patient F produced the smallest fraction of epochs presenting a nonlinear signature (35.1% of epochs could reject H0 at the given significance level) and patient had the highest stimulation frequency (30 Hz) and the highest pulse width (750 s) of all six VNS patients. Patient Bs EEG presented the greatest fraction of epochs presenting a nonlinear fingerprint (52.3% of epochs could reject H0) whereas the patient 153

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had the lowest stimulation frequency (20 Hz) and the lowest pulse width (250 s) of all six VNS patients. The underlying biology driving this EEG behavior could be related to a study which demonstrated an acute suppression of epileptiform activity in the hippocampus during VNS (Olejniczak et al., 2001). Perhaps enhanced suppression of epileptiform activity is responsible for the diminished nonlinearity in patients with fewer seizures. Also, a study has demonstrated that the 250 s pulse width parameter results in blood flow mitigation to significantly more brain regions (e.g. hippocampus, sup. temp. lobe) than a 500 s pulse width in VNS patients (Mu et al., 2004). Perhaps pulse width related blood-flow reductions reported by Mu et al. are responsible for any such changes in epileptiform activity suppression which may have been detected by the surrogate data analysis. In addition, patients E and F demonstrated the lowest fraction of epochs presenting a nonlinear signature (39% and 35.1%) and also happen to be the only two patients which are seizure-free. This may be aligned with the clinical observation that the absence of bilateral interictal epileptiform discharges was the only EEG predictor of seizure freedom (Janszky et al., 2005). Future studies should include characterizing the profile of interictal epileptiform discharges for relationship to linear and nonlinear measures. In patients A and B there was a notable increase in the amount of interstimulation epochs demonstrating a nonlinear signature occurring across most channels at times around 11 pm until 7 am. The increase in the occurrence of nonlinear signature may have been partially resulted from the patient being drowsy or asleep. A surrogate analysis study by Shen et al. demonstrated a considerable number of EEG segments displaying a nonlinear signature during stage 2 sleep and may be the result of K-complexes (Shen et al., 2003). 154

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The control patient demonstrated a high density of nonlinear behavior in non-focal channels during waking hours which is diminished around 11 pm 7 am, except for the TLc2 channel which shows a greater fraction of epochs demonstrating nonlinear signatures than other channels. Patients A, B, D, and F showed a greater fraction of epochs presenting nonlinear signatures in channels located near foci than non-focal channels. This observation is aligned with the literature where focal electrodes demonstrated higher nonlinearity than non-focal electrodes (Casdagli et al., 1995, 1996, 1997). While the control patient provides information from a patient with a similar epileptic condition and recorded at the same frequency as the VNS patients, the depth electrode recordings from the control patient provide limits to what can be suggested to conclusions about VNS-induced scalp-EEG patterns. The ideal control would be use baseline from each patient using an identical electrode setup. The fraction of epochs rejected the null hypothesis is a necessary condition for nonlinear dynamical, however, these results are not sufficient to suggest a particular type of nonlinearity (e.g. surrogate analysis cannot prove the existence of low-dimensional chaos). Changing parameters (e.g. the dimensionality or noise threshold) for ApEnt may improve sensitivity to potential VNS-induced EEG effects and thus provide the possibility to relate said effects to stimulation parameters and ultimately to the clinical outcome. The results, combined with studies documenting the ability of various nonlinear measures to quantify neural states motivates the usage of nonlinear as well as linear measures to examine EEG dynamical behavior which could be associated with VNS stimulation. 155

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Temporal Evolution of Interstimulation EEG Dynamics The results of the previous experiment characterized the presence of nonlinear EEG signal components throughout each of the interstimulation epochs for each of the six patients undergoing VNS therapy for epilepsy. However, as surrogate analysis does not provide characterization of nonlinear signal components, it is possible that the properties of the detected nonlinear components may distinguish the control patient from the VNS patient. Thus, additional characterization signal dynamics would enhance the findings from the surrogate analysis. This experimental perspective aims to analyze the observed nonlinear signal components and further characterize how brain dynamical patterns behave during the period between stimulations. This study is motivated by an underlying hypothesis (stated as null) H0: Interstimulation EEG dynamics are time invariant in patients undergoing VNS therapy for epilepsy. While VNS is believed to induce its therapeutic effect via long-term modulation (Koo, 2001), this long-term effect may manifest as changes in short-term temporal dynamical behavior compared to baseline which would be consistent with the traits of a dynamical disorder such as epilepsy (Mackey and Glass, 1977; Mackey and an der Heiden, 1982; Milton and Mackey, 1989; Belair et al., 1995; Milton and Black, 1995; Milton, 2000; Lopes Da Silva et al., 2003). Thus, it is possible that the brain dynamics during the interstimulation epochs in VNS patients will be distinguishable from a control patient, which would provide support for the use of EEG dynamical analysis for the study of VNS effects. Furthermore, EEG dynamical behavior during the interstimulation period may be related to stimulation parameters. Data Description Six patients undergoing VNS therapy for intractable epilepsy were analyzed in this study. The continuous scalp-EEG recordings are approximately 24 hours in duration and were obtained 156

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at the Shands Hospital GCRC protocol # 614, IRB protocol #617-2004, Neurophysiologic Measures of Vagus Nerve Stimulation at the University of Florida, Gainesville. Available clinical information for the six patients is summarized in tables 4-1 and 4-2. The electrode positions are described in figure 5-1. VNS activation times were obtained from the ECG channel, which was recorded from an electrode placed in close proximity to the VNS pulse generator. The ECG channel was otherwise excluded from this study. EEG Dynamical Measures Quantitative EEG analysis is a broad field incorporating numerous methods for quantifying various properties of EEG signals (see chapter 3). In order to improve the characterization of the dynamical evolution, this study utilized multiple EEG measures. Each of the EEG analysis techniques first applies a phase space transformation after which the relevant information is extracted. The phase space mapping procedure of Takens (1981) was applied using an embedding dimension of 7 is used based on previous studies in which the epileptic attractor was characterized from EEG recordings of patients with mesial temporal lobe epilepsy (Iasemidis et al. 1988; Iasemidis et al., 1990; Iasemidis et al., 1999). For an embedding dimension of 7, a time delay of =7 samples corresponding to14 ms is applied. This time delay value has demonstrated success in characterizing the rhythm of a typical seizure in temporal lobe epilepsy (Iasemidis et al., 1990; Zaveri et al., 1993; Iasemidis et al., 1996;). Approximate entropy This ApEnt measure (see equations 3-16 to 3-19) has been utilized to study EEG patterns in Alzheimers disease patients (Absolo, 2005), as a surrogate marker for anesthesia depth (Bruhn 2000, Bruhn 2001, Bruhn 2003), detecting epileptic seizures (Absolo 2007; Srinivasan, 2007), and as a test statistic for characterizing EEG nonlinearity (Thomasson et al., 2000; 157

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Burioka et al., 2003,2005; Ferenets et al., 2006). Thus, it may be useful for characterizing brain dynamics during interstimulation intervals. The noise threshold was set at 20% of the signals standard deviation r=0.2*std was applied based on studies which successfully correlated ApEnt with drug anesthesia levels (Bruhn, 2000; Bruhn, 2001; Bruhn, 2003; Ferenets et al., 2006) and a study characterizing background EEG in patients with Alzheimers Disease (Absolo, 2005). The 2048 point (4 second) window selected for this study is within a range that has been described as being clinically and theoretically appropriate (Pincus, 1995). Correlation sum For a collection of points in some vector space, the correlation sum is the fraction of all possible vector pairs which are closer than a given distance r for a particular norm distance norm (see equation 3-2). The correlation sum is estimated after mapping the EEG into phase space. The correlation sum is often used to estimate the correlation dimension (equation 3-27) which has been extensively utilized in physiological data (Kantz and Schreiber, 1995) such as neural state classification studies using EEG (Tirsch et al., 2000, 2004), as well as seizure prediction (Elger et al., 1998; Martinerie et al., 1998). However, since use of an absolute radius can result in a heavy EEG amplitude sensitivity (Osorio et al., 2001), this study utilizes a relative radius measure (with respect to the diameter of the dataset in phase space) for brain dynamics characterization (Casdagli et al., 1996, 1997, Merkwirth et al., 2002). Correlation sum was estimated using the TSTOOL package (Merkwirth, 2002) for Matlab. Theiler recommends application of an exclusionary window to a range of points surrounding each reference point in order to avoid embedding vectors on the same trajectory (Theiler et al., 1986). Based on the results of similar studies, a 250 ms (128-point) exclusion 158

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window around reference points and a search radius r=0.2 (10% of attractor diameter) were implemented (Casdagli et al., 1996, 1997). Mean angular frequency in phase space A modification to the Lyapunov exponent measures, the mean angular frequency in phase space measure ( ) quantifies the angular frequency of the phase space evolution of two nearest neighbor points relative to a reference point (Iasemidis et al., 2001, 2002, 2003). Conceptually, this measures the average rate of change of a system state. The measure is related to the Lyapunov exponent, which measures the local stability of a system. A study quantifying neural states in epilepsy found that preictal, ictal, and postictal states corresponded with medium, high, and lower values of respectively (Iasemidis et al., 2002, 2003). In addition, the dynamic entrainment / disentrainment and seizure resetting phenomena observed before and after epileptic seizures using the STLmax measure has also been described with (Iasemidis et al., 2003). Thus, the sensitivity of to changes in neural state makes it a candidate for quantifying any EEG dynamics changes which may be associated with VNS. The window length selected for this study, 2048 points, is the same window length as was used in Iasemidis et al. (2001, 2002, 2003). Short-term maximum Lyapunov exponent The STLmax measure has been shown to be useful for providing dynamical information about the neural state of the epileptic brain. Studies performed on EEG from human patients (Iasemidis and Sackellares, 1990; Iasemidis and Shiau et al., 1999; Iasemidis et al., 2001; Iasemidis and Pardalos et al. 2003; Iasemidis and Shiau et al., 2003) and animal models of epilepsy (Nair et al., 2004, 2005, 2006; Talathi et al., 2008) imply that the evolution of the brain to a state of greater spatio-temporal order correlates with spontaneous seizures. This 159

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phenomenon is presented as a temporally progressive increase in the similarity among so-called critical channels measured by STLmax calculated from multichannel EEG recordings. Thus, sensitivity of STLmax to neural state changes in epilepsy indicated by the above studies makes the measure a reasonable candidate for identification and characterization of potential VNS-induced EEG effects. The window duration for calculating STLmax needs to be short to provide temporally local information about the brains dynamics yet contain enough points for the algorithm to converge (additional information about this can be found in chapter 3). The 2048 point (4 second) window size chosen for this study is suggested to provide a sufficiently stable STLmax estimate in previous neural state classification studies in epilepsy (Iasemidis and Sackellares, 1999). Also, use of the shortest window length possible for STLmax estimation can help provide a stationary segment for estimating local dynamical information. As such, while maintaining a window length of the recommended number of data points for algorithmic convergence, the 512 Hz sampling frequency provides improved time resolution over previous studies (which utilized a 200 Hz frequency). The evolution time parameter was set to T = 41 msec (21 samples) based on successful neural state classification studies that utilized them (Iasemidis and Sackallares, 1999). Experimental Design This preliminary investigation into the temporal evolution of the EEG between stimulations will start searching for coarse dynamics transitions between the first and second halves of each epoch where the VNS is deactivated. The rationale for this class designation is to assess the existence of any short-term transitions, to characterize the temporal evolution where it exists, compare with a similar experimental setup in a control patient and determine any correlation to clinical parameters. The underlying hypothesis (stated as null) which motivates 160

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this study is EEG dynamics during the interstimulation period are unrelated to the stimulation parameters in VNS patients. Figure 5-13 shows an illustration indicating how the measures were grouped to examine the temporal evolution of these dynamical measures during VNS-OFF. As shown in figure 5-13, EEG measures corresponding to the first half of an epoch are compared to EEG measures corresponding to the second half of an epoch for each channel, for all channels (except ECG). Using 4 second windows to calculate the various EEG measures, the The preliminary hypotheses (stated as null) are formulated for the purpose of characterizing the EEG behavior associated with stimulation in the VNS patients: H1: The EEG dynamics as quantified by approximate entropy are time invariant while VNS is deactivated. H2: The EEG dynamics as quantified by correlation sum are time invariant while VNS is deactivated. H3: The EEG dynamics as quantified by mean angular frequency in phase space are time invariant while VNS is deactivated. H4: The EEG dynamics as quantified by short-term maximum Lyapunov exponent are time invariant while VNS is deactivated. These hypotheses aim to answer the question of how the dynamical brain behavior as described by these four nonlinear EEG measures evolves over time between stimulations. Such an analysis may identify EEG patterns which are sensitive to particular stimulation parameter configurations as well as the candidate measures for detecting such patterns. The control patient underwent two similar tests; one which utilized stimulation times with a 3 minute off duration, and a second test which utilized stimulation times with a 5 minute off duration. The hypotheses were tested with a two-tailed unpooled two-sample t-test with =0.05 using the Matlab Statistics Toolbox. The tests were performed assuming unequal variances and utilized Satterthwaite's approximation for the effective degrees of freedom. For a measure window size of 2048 points (4 seconds), the first and second halves of the interstimulation epoch 161

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each contain 36 values of each measure for patients A,B,C,E (whom have a 5 minute interstimulation duration) and 21 values of each measure for patients D and F (whom have a 3 minute interstimulation duration). The same statistical testing method was used to test the control patient. The control patient was tested with artificial stimulation times using 3-minute and 5-minute interstimulation duration. Results As figures 5-22 and 5-24 show, for all patients the ApEnt and measures resulted in a larger fraction of epochs rejecting H1 and H3 (respectively) than the control patient for the majority of the 25 EEG channels. When using the correlation sum measure, the majority of electrodes had a greater fraction of epochs reject H2 for patient A than the control patient. However, the correlation sum did not show any such trend for any other patients. For all four measures, patient C rejected the four hypotheses in 2-3 times more interstimulation epochs than the control patient. For all four measures, patient F produced the fewest amount of interstimulation epochs that rejected the null hypothesis than any other patient. Numerous observations can be made regarding focal and non-focal electrode behavior according to tables 5-3, 5-5, 5-7, 5-9. In terms of the ApEnt measure, the focuses of patients A,B,C, and F produced significant dynamical complexity fluctuations during more interstimulation epochs than their corresponding non-focal areas, and greater than the control focus. This phenomenon could be related to studies where electrodes in the vicinity of an epileptogenic focus displayed more prominent nonlinear behavior (Casdagli et al., 1995, 1996, 1997). The correlation sum measure suggested that the focus and non-focus of patient A demonstrated significant time varying dynamics in more interstimulation epochs than the control. For all six patients, the showed significant temporal dynamics variation in more epochs than 162

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the corresponding control patient. With regards to the spatial comparison of focal and non-focal electrodes, the STLmax measure did not show any obvious trends. The main finding in regards to the dynamical behavior throughout the day (see figures 5-14 through 5-21) is the overall trend of diminished dynamical variance between approximately 11 pm and 7 am for all four measures in patients A (~epoch 130) and C (~epoch 140). Patient Bs seizures were accompanied by significant temporal fluctuation in the dynamical measure before and after seizures. As stimulation epochs which overlapped with seizures were excluded from the study, these dynamical alterations occurred within about 10 minutes of the seizure. Discussion This study aimed to characterize the interstimulation EEG periods using a range of dynamical EEG measures which have demonstrated sensitivity to neural state changes such as those observed in epilepsy. Patient C had highest output current (2.5 mA) as well as the greatest amount of epochs (45.6%, 36.8%, 36.1%, and 21.8%) showing time varying dynamics of all the patients as measured by the ApEnt correlation sum, and STLmax measures, respectively (see figures 5-26 through 5-29). Patient A showed similar ApEnt and behavior (35.7% and 31.0% of interstimulation epochs demonstrated significant temporal variance for both measures, whereas control values were 21.8%, 10.5%, respectively) compared to patient C and had the second highest output current (1.75 mA). Patient F showed an opposite trend having the lowest output current (0.75 mA) where ApEnt, and STLmax produced the smallest fraction epochs rejecting H1, H3, and H4 (23.8%, 20.2% and 14.3% whereas control values produced 16.9%, 7.9%, and 19.4%, respectively). The ApEnt measure quantifies the regularity in a time series (Pincus, 1995; Absolo et al., 2007), the measure provides an estimate of the stability of the 163

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reconstructed attractor in phase space (Iasemidis et al., 2002, 2003), and STLmax provides a measure of chaoticity of a signal (Iasemidis et al., 1991). Thus, the similar behavior of these three measures implies the EEG could be undergoing fewer changes in the regularity, stability and observed chaoticity in patient F than patients A and C. Overall, the ApEnt and measures demonstrated the greatest deviation from the control patient, the broadest range of the fraction of epochs showing time varying dynamics, and a potential covariation with output current. For these reasons, the ApEnt and measures may potentially find use as EEG biomarkers for VNS. Biologically, these results may be related to the findings of studies which identified a current threshold for suppression of chemically induced seizure models. For example, seizures induced in a low Ca2+ model could be suppressed with currents greater than 1A (Warren and Durand, 1998). In addition, seizures induced in a high K+ model could be suppressed with currents greater than 4A (Nakagawa and Durand, 1991). Yet patient F has been seizure free for at least one year at the time of recording, while patients A and C have mean seizure rates of 3 and 2 seizures per month (respectively). In general, higher values of VNS parameters are associated with improved seizure protection (Ben-Menachem et al., 1994). So while at first it may seem counterintuitive that the patient with the lowest output current (patient F) is seizure free, keep in mind that the aforementioned study is referring to collective impact of output current, pulse width, and stimulation frequency. So even though patient Fs output current (0.75 mA) is less than patient As (1.75 mA) and patient Cs (2.5 mA), patient F has higher pulse width (750 s) than patients A and C (both 500 s). In addition, patients A and F have the greatest stimulation frequency of all the patients in the study (30 Hz) whereas patient C has a 25 Hz stimulation frequency. 164

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In addition, patient F has a shorter interstimulation interval (3 minutes) compared to patients A and C (both 5 minutes). It is tempting to attribute patient Fs seizure freedom to this patient having a greater amount of stimulation cycles over time, however patient E is also seizure free and has a 5 minute interval. It is interesting that all four measures behaved in a similar manner for patient F whom had the lowest output current and was seizure free. Perhaps when the output current raises above a particular threshold value the neuronal activity is affected in such a manner that it becomes more erratic and thus results in more rapid dynamical transitions. The minimum current threshold for suppression of epileptiform activity in seizure observed by Nakagawa and Durand (1991) as well as Warren and Durand (1998) may be responsible for this. This could explain why patients A, B, C, D and E whom had greater output currents than patient F produced results less consistent with the other dynamical measures than for patient F. Regarding the relationship to the time of day to EEG dynamical effects, the most obvious trend was the period corresponding to 11 pm and about 7 am (see figures 5-14 and 5-16). The reduced dynamical temporal variance for all four measures in A (~epoch 130) and C (~140) during this period compared to other times of day is likely related to the fact that the patients are drowsy or asleep. A recent study by Rizzo et al. (2004) demonstrated that an overall increase in EEG total power both in sleep and wakefulness after long-term VNS treatment compared to pre-treatment EEG, so it is plausible that the dynamical measures during sleep were influenced by the VNS. However, EEG sleep studies have demonstrated a decrease in the mean and standard deviation of the ApEnt measure (Acharya et al., 2005; He et al., 2005) during sleep compared to wakefulness, which is aligned with the observation of diminished variation of the ApEnt measure during times when the patient is presumed to be asleep. In addition, a study by Acharya et al. 165

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showed an increase in mean and a decrease in standard deviation for most sleep stages (2005). Thus, the observation of STLmax behavior during sleep is aligned with the literature. Therefore, while VNS has been shown to affect the sleep EEG signal (Rizzo et al., 2004), the behavior of the nonlinear measures during a period when the patient is drowsy or asleep is consistent with sleep patterns in people without VNS implants. Conclusions The results from the surrogate EEG analysis show a potential between the fraction of epochs which displayed nonlinearity and the pulse width parameter. In addition, Patient F produced the smallest fraction of epochs presenting a nonlinear signature (35.1% of epochs could reject H0 at the given significance level) and patient had the highest stimulation frequency (30 Hz) as well as highest pulse width (750 s) of all six VNS patients. Patient Bs EEG presented the greatest fraction of epochs presenting a nonlinear fingerprint (52.3% of epochs could reject H0) whereas the patients stimulator was programmed with the lowest stimulation frequency (20 Hz) and the lowest pulse width (250 s) of all six VNS patients. In addition, patient B demonstrated the greatest amount of monthly seizures. It is possible that neuronal modulation may be sensitive to the duration of the individual pulses in a manner which may manifest as increased linearity of neuronal output. For example, Mu et al. (2004) demonstrated that 250 s showed blood flow reduction to significantly more brain regions than 500 s. However, such an observation requires additional patients for verification. Also, patients E and F demonstrated the lowest fraction of epochs presenting a nonlinear signature (39% and 35.1%) and are also the only two patients which are seizure-free. This observation may be aligned with the clinical observation that the absence of bilateral interictal epileptiform discharges was the only EEG predictor of seizure freedom (Janszky et al., 2005). While interictal epileptiform discharge detection was not included in this study, future studies should include the spatio-temporal 166

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distribution of interictal epileptiform discharges in the characterization process. Comparison with linear and nonlinear EEG measures may provide additional information relevant to the connection between stimulation parameters and EEG patterns. The results from the temporal analysis of interstimulation dynamics demonstrate a potential manifestation of the VNS long-term modulation effect in terms of the interstimulation dynamics behavior. In particular, the ApEnt and measures displayed a potential covariation the output current parameter, demonstrated the greatest deviation from the control patient, the broadest range of the fraction of epochs showing time varying dynamics. For these reasons, the ApEnt,and measures could serve as EEG biomarkers for VNS. In light of this result, its possible that when the current reaches a threshold level the neuronal activity intensifies such that the summed output (the EEG) behaves more erratically (in terms of more rapidly fluctuating dynamical measures such as ApEnt and ,). This phenomena could be related to the observation of minimum stimulation current thresholds were needed to suppress epileptiform activity in low Ca 2+ (Warren and Durand, 1998) and high K + (Nakagawa and Durand, 1991) seizure models. Overall, the two interstimulation analysis experiments (analysis of nonlinearity and analysis of temporal variation) showed potential connections EEG covariation with the pulse width, output current, and signal frequency parameters. Such effects may be useful as an EEG biomarker of optimal VNS settings. Additional studies should be performed on a larger sample of patients in order to validate these claims. In addition, baseline EEG recordings obtained prior to VNS implantation are crucial for determining which EEG effects in the VNS patient could be associated with VNS and which effects appeared to be present in the EEG prior to VNS implantation. 167

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The EEG measures were likely suboptimal as they were selected based on similar studies. Though it is difficult to select the proper parameters in measures used in an expeditionary study such as this one, a good place to start may be to calibrate the measures such that they are able to capture and unfold an epileptic attractor in phase space. From this perspective, future VNS studies which utilize phase space embedding transformations should utilize a patients own seizures to determine the dimension and delay for embedding signals. In addition, study of the VNS in this setup is limited by the fact that the stimulator is programmed for chronic regular stimulation. Thus, though these studies aim to characterize the short-term EEG effects after stimulation, the short-term affect is produced by the cumulative effect of a large number of stimulations. Thus, an interesting study to help truly elucidate the effects of an individual stimulation or a group of stimulations would be to record prestimulation baseline for a group of patients, perform a single VNS stimulation, and perform an additional EEG recording while keeping output current at zero milliamps to examine any post-stimulation effects. Such an analysis may be one of the best ways to provide the most objective insight into the EEG effects of VNS without concern of any long-term modulatory effects. In addition, tracking the progression of such measures over time (e.g. 3 months, 6 months, 12 months after implantation) and comparing with the patients own baseline EEG recording are a desirable approach to examining EEG dynamics in patients with VNS. The seizures that patient B underwent during the recording session could likely have had a far reaching impact on the observed dynamics patterns, as EEG dynamical transitions have been documented as occurring several minutes to several hours prior to seizures (Iasemidis et al., 2004). One potential improvement to this study is to record multiple days of recordings in order to compare a sufficient amount of interictal data, which has been defined as being at least 168

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8 hours away from a seizure (Pardalos et al., 2003; Hively et al., 2005; Chaovalitwongse et al., 2006). This would eliminate pre-seizure dynamical transitions as an additional variable to influence results. If this were not possible, one other possibility would be to examine only the EEG data that occurs at least 8 hours away from any detected seizure in a patient. One challenging aspect this approach is that the amount of EEG that would be allowed in the study would be diminished significantly (e.g. two-thirds of a single day would be excluded due to a single seizure), and with only a handful of seizures at the wrong time would render this approach infeasible. Though sleep staging was not included in this research protocol obtaining the precise sleep times with manual and/or computer automated sleep staging for each patient should be included in future work. This would help to further examine the observation that the four EEG measures underwent less variation over time during the periods between about 11 pm and about 8 am. The preliminary study of temporal evolution of dynamics used a two tailed test to determine the means are different or not. A future study should look at the direction of the two way test to determine if regularity, stability, or chaoticity are increasing or decreasing throughout the duration of the interstimulation interval. Such information may provide additional insight into the dynamical behavior and the stimulation parameters (e.g. a trend of decreasing or increasing the dynamical measures may be related to the stimulation parameters, the clinical status of the patient, or even the time of day). Ultimately this study may lead to a method of surgical VNS testing, e.g. surgically exposing the left vagus nerve so a diagnostic vagus nerve stimulation device could be temporarily attached to the patient, stimulations could be applied in the operating room and the 169

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EEG signal can be analyzed. If this setup were to prove successful, it may provide a method to prescreen patients for responsiveness to VNS therapy prior to undergoing the implantation process. An article related to these studies was published under the title Optimization of epilepsy treatment with vagus nerve stimulation with authors Basim Uthman, Michael Bewernitz, Chang-Chia Liu, and Georges Ghacibeh (Uthman et al., 2007). 170

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Figure 5-1. Map of EEG electrode location for the VNS patients. The electrodes were positioned according to the 10-20 electrode placement system which assigns locations proportionally spaced locations (e.g. 10%-20%) with respect to the size of the patients head. A B Figure 5-2. Electrode positions for the control patient from A) an inferior and right view and B) axial slice view of the brain. Red circles indicate focal electrodes (TBa4, TBb6, HR7), blue circles indicate non-focal electrodes (TLb2, TLb3, TLc2). Images provided for this publication courtesy of the Freiburg Center for Data Analysis and Modeling at the Albert-Ludwigs Universitt Freiburg (University of Freiburg), Freiburg, Germany. 171

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01002003004005006007008000.30.350.40.450.50.55Fraction of interstimulation epochs displaying a nonlinear signature (rejecting H0 at 95% significance)Pulse width (s) Patients 5 min off Patients 3 min off Control 5 min off Control 3 min off F E A D, C B Figure 5-3. Comparison of pulse width parameter to the fraction of epochs displaying a nonlinear signature in the six patients treated with VNS. The fraction of epochs displaying a nonlinear signature in control patient using the 3-minute and 5-minute off pseudo stimulation times are represented by the column of six triangles (3 minute off times) and six squares (5 minute off times). Figure 5-4. Patient A surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 172

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Figure 5-5. Patient B surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. The red lines indicate seizures. Figure 5-6. Patient C surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 173

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Figure 5-7. Patient D surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. Figure 5-8. Patient E surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. Figure 5-9. Patient F surrogate data analysis results over 24 hours during the interstimulation epoch. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 174

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fp1-CPzfp2-CPzf3-CPzf4-CPzc3-CPzc4-CPzp3-CPzp4-CPzo1-CPzo2-CPzf7-CPzf8-CPzt3-CPzt4-CPzt5-CPzt6-CPza1-CPza2-CPzfz-CPzcz-CPzpz-CPzleye-CPzreye-CPzlmn-CPzrmn-CPz A B C D E F Figure 5-10. The fraction of all interstimulation epochs per channel which rejected the null hypothesis H0 using ApEnt for A) patient A, B) patient B, C) patient C, D) patient D, E) patient E, F) patient F. 175

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Table 5-1. Surrogate analysis results summary for all six patients with the VNS implant. % of epochs where the ApEnt measure rejected H0 channel A B C D E F fp1-CPz 58.27% 42.37% 42.15% 29.31% 38.89% 36.27% fp2-CPz 61.42% 38.56% 40.61% 32.76% 36.90% 31.62% f3-CPz 56.30% 62.71% 57.85% 64.53% 30.95% 31.13% f4-CPz 44.49% 60.17% 49.04% 42.12% 36.11% 35.05% c3-CPz 27.56% 31.36% 52.11% 30.05% 37.70% 34.80% c4-CPz 29.92% 77.54% 50.57% 38.18% 49.21% 27.45% p3-CPz 38.98% 24.58% 48.66% 31.53% 32.94% 19.61% p4-CPz 28.35% 50.00% 41.76% 39.66% 34.92% 22.55% o1-CPz 27.17% 39.41% 47.89% 42.86% 36.11% 33.33% o2-CPz 28.74% 36.02% 51.34% 55.17% 44.05% 33.82% f7-CPz 57.09% 85.17% 35.25% 36.45% 27.38% 39.95% f8-CPz 66.14% 78.39% 35.25% 33.50% 37.70% 41.67% t3-CPz 46.46% 48.31% 32.95% 39.16% 39.29% 55.64% t4-CPz 42.13% 78.81% 44.83% 43.10% 42.06% 54.66% t5-CPz 24.02% 48.73% 36.78% 38.42% 31.35% 48.77% t6-CPz 24.80% 46.19% 45.98% 50.25% 33.33% 35.05% a1-CPz 53.54% 56.78% 37.16% 34.24% 42.86% 32.60% a2-CPz 44.49% 47.88% 51.34% 35.22% 40.87% 32.60% fz-CPz 71.65% 30.08% 36.78% 44.33% 40.48% 27.94% cz-CPz 60.63% 51.69% 27.59% 34.98% 47.62% 26.72% pz-CPz 61.81% 47.88% 21.46% 41.63% 56.35% 22.30% leye-CPz 51.97% 43.64% 33.33% 41.38% 42.06% 47.79% reye-CPz 53.54% 61.44% 30.65% 61.08% 44.84% 34.31% lmn-CPz 56.30% 59.75% 25.29% 30.79% 30.16% 42.16% rmn-CPz 43.70% 61.02% 23.37% 27.83% 39.68% 30.15% # epochs 254 236 261 406 252 408 denotes focal EEG channel 176

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Figure 5-11. Control patient (with 5-minute artificial stimulation times) surrogate data analysis results over 24 hours for all artificial interstimulation epochs. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. Figure 5-12. Control patient (with 3-minute artificial stimulation times) surrogate data analysis results over 24 hours for all artificial interstimulation epochs. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. Table 5-2. Control patient surrogate analysis results summary. % of epochs where the ApEnt measure rejected H0 channel Control 5 minute 'off' time Control 3 minute 'off' time TBA4 22.65% 19.41% TBB6 29.27% 22.85% HR7 27.18% 26.54% TLB2 43.21% 40.05% TLB3 51.57% 44.72% TLC2 81.53% 70.02% # epochs 261 406 denotes focal EEG channel 177

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1 Figure 5-13. Experimental setup for characterizing the temporal evolution EEG dynamics during interstimulation intervals in patients undergoing VNS therapy for epilepsy. The double head arrows indicate a statistical comparison is made between the EEG feature segments represented by the shaded rectangles. VNS on/off Epoch 2 Epoch n EEG feature for channel 1 EEG feature for channel 2 EEG feature for channel 26 First half of an interstimulation p erio d Second half of an interstimulation period For the purposes of this study, a full stimulation epoch consists of 30 seconds of stimulation and either a 3 or 5 minute off p eriod. 178

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A B C D Figure 5-14. Patient A temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 179

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A B C D Figure 5-15. Patient B temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. The red lines indicate seizures. 180

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A B C D Figure 5-16. Patient C temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 181

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A B C D Figure 5-17. Patient D temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 182

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A B C D Figure 5-18. Patient E temporal evolution of dynamics analysis results over 24 hours for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 183

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A B C D Figure 5-19. Patient F temporal evolution of dynamics analysis results for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 184

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A B C D Figure 5-20. Control patient (with 5-minute artificial stimulation times) temporal evolution of dynamics analysis results for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 185

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A B C D Figure 5-21. Control patient (with 3-minute artificial stimulation times) temporal evolution of dynamics analysis results for A) ApEnt, B) correlation sum, C) and D) STLmax. Yellow indicates that particular interstimulation epoch (abscissa) for the channel of interest (ordinate) rejected the null hypothesis. 186

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Table 5-3. Approximate entropy analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt measure. % of epochs rejecting H1 channel Patient A Patient B Patient C Patient D Patient E Patient F fp1-CPz 40.94% 31.78% 47.13% 18.23% 34.92% 24.75% fp2-CPz 40.94% 43.64% 43.30% 20.20% 32.94% 24.26% f3-CPz 44.09% 49.58% 52.11% 21.67% 31.75% 25.00% f4-CPz 40.55% 41.53% 49.43% 24.14% 30.95% 29.90% c3-CPz 42.13% 38.14% 42.53% 20.44% 28.57% 23.53% c4-CPz 29.53% 33.47% 50.57% 24.14% 29.37% 26.72% p3-CPz 27.17% 35.59% 47.89% 22.41% 24.60% 19.36% p4-CPz 26.38% 25.42% 50.57% 22.41% 26.59% 20.59% o1-CPz 38.98% 41.53% 47.51% 24.14% 24.21% 22.55% o2-CPz 38.58% 37.29% 49.81% 22.91% 30.16% 22.79% f7-CPz 36.22% 54.24% 50.96% 27.34% 38.49% 24.51% f8-CPz 38.98% 54.24% 47.89% 25.37% 37.70% 28.43% t3-CPz 42.91% 50.85% 43.30% 29.80% 34.92% 30.39% t4-CPz 33.46% 43.22% 40.23% 23.65% 37.70% 30.88% t5-CPz 33.86% 52.54% 39.08% 20.94% 32.14% 30.15% t6-CPz 37.80% 41.10% 41.38% 25.86% 35.32% 28.43% a1-CPz 40.55% 50.42% 34.10% 31.53% 35.71% 24.75% a2-CPz 35.43% 50.00% 41.00% 28.08% 36.11% 23.28% fz-CPz 37.40% 34.32% 46.74% 19.21% 28.97% 21.08% cz-CPz 29.92% 23.31% 48.28% 17.49% 25.40% 18.87% pz-CPz 20.47% 26.69% 36.78% 21.67% 18.65% 17.65% leye-CPz 37.40% 29.24% 50.19% 24.38% 34.92% 17.40% reye-CPz 32.68% 37.71% 50.96% 24.88% 35.71% 18.87% lmn-CPz 37.80% 46.61% 44.83% 24.38% 40.48% 19.85% rmn-CPz 29.92% 47.88% 44.06% 21.43% 36.90% 21.81% # epochs 254 236 261 406 252 408 denotes focal EEG channel 187

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fp1-CPzfp2-CPzf3-CPzf4-CPzc3-CPzc4-CPzp3-CPzp4-CPzo1-CPzo2-CPzf7-CPzf8-CPzt3-CPzt4-CPzt5-CPzt6-CPza1-CPza2-CPzfz-CPzcz-CPzpz-CPzleye-CPzreye-CPzlmn-CPzrmn-CPz A B C D E F Figure 5-22. Approximate entropy analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt measure. Table 5-4. Approximate entropy analysis results for the control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H1 using the ApEnt measure. % of epochs rejecting H1 channel Control 5 minute 'off' time Control 3 minute 'off' time TBA4 22.65% 18.18% TBB6 25.44% 17.94% HR7 23.34% 15.23% TLB2 20.91% 17.69% TLB3 23.69% 19.66% TLC2 14.63% 13.02% TBA4 261 406 denotes focal EEG channel 188

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Table 5-5. Correlation sum analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H2 using the correlation sum measure. % of epochs rejecting H2 channel Patient A Patient B Patient C Patient D Patient E Patient F fp1-CPz 25.98% 18.64% 34.10% 12.07% 20.24% 10.54% fp2-CPz 26.38% 16.10% 29.12% 12.81% 19.84% 8.82% f3-CPz 19.29% 12.71% 24.90% 9.85% 18.65% 11.52% f4-CPz 18.11% 10.17% 26.05% 12.81% 18.25% 11.52% c3-CPz 19.29% 13.98% 21.84% 10.59% 17.86% 10.54% c4-CPz 15.75% 15.25% 19.92% 12.07% 18.25% 9.31% p3-CPz 13.39% 11.86% 14.94% 11.58% 15.48% 9.80% p4-CPz 12.99% 8.47% 13.79% 12.32% 15.87% 9.31% o1-CPz 15.35% 8.90% 13.03% 11.82% 13.49% 10.29% o2-CPz 17.32% 8.47% 13.79% 14.29% 11.90% 13.73% f7-CPz 16.93% 9.75% 31.80% 11.82% 21.43% 10.54% f8-CPz 16.14% 9.32% 29.50% 12.32% 18.65% 10.29% t3-CPz 22.44% 10.59% 22.22% 11.08% 18.65% 12.25% t4-CPz 16.54% 6.78% 21.07% 13.30% 21.83% 11.52% t5-CPz 15.35% 10.17% 13.41% 9.85% 12.30% 9.31% t6-CPz 11.81% 9.32% 17.24% 12.07% 21.83% 8.33% a1-CPz 11.81% 13.56% 23.37% 11.08% 21.03% 10.29% a2-CPz 16.54% 13.56% 22.22% 15.27% 18.25% 11.03% fz-CPz 22.05% 12.71% 25.67% 11.33% 17.46% 12.01% cz-CPz 17.32% 8.05% 11.11% 9.61% 18.65% 12.25% pz-CPz 14.57% 7.63% 9.96% 11.33% 15.08% 6.13% leye-CPz 14.96% 13.56% 27.97% 10.10% 17.06% 10.05% reye-CPz 16.54% 12.71% 32.57% 13.55% 17.06% 8.33% lmn-CPz 13.78% 7.20% 21.84% 9.36% 17.46% 11.03% rmn-CPz 12.60% 8.47% 24.90% 11.58% 16.27% 9.56% # epochs 254 236 261 406 252 408 denotes focal EEG channel 189

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fp1-CPzfp2-CPzf3-CPzf4-CPzc3-CPzc4-CPzp3-CPzp4-CPzo1-CPzo2-CPzf7-CPzf8-CPzt3-CPzt4-CPzt5-CPzt6-CPza1-CPza2-CPzfz-CPzcz-CPzpz-CPzleye-CPzreye-CPzlmn-CPzrmn-CPz A B C D E F Figure 5-23. Correlation sum analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H2 using the correlation sum measure. Table 5-6. Correlation sum analysis results for the control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H2 using the correlation sum measure. % of epochs rejecting H2 channel Control 5 minute 'off' time Control 3 minute 'off' time TBA4 11.50% 8.60% TBB6 10.80% 8.85% HR7 8.71% 8.11% TLB2 9.76% 7.13% TLB3 8.71% 8.35% TLC2 5.57% 7.37% # epochs 261 406 denotes focal EEG channel 190

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Table 5-7. Mean angular frequency in phase space analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H3 using the measure. % of epochs rejecting H3 channel Patient A Patient B Patient C Patient D Patient E Patient F fp1-CPz 38.19% 30.51% 37.93% 23.89% 39.68% 20.10% fp2-CPz 35.83% 22.46% 38.70% 22.66% 32.94% 24.02% f3-CPz 29.53% 26.27% 41.00% 24.88% 34.92% 19.36% f4-CPz 27.95% 27.12% 41.76% 23.65% 33.73% 21.32% c3-CPz 30.31% 26.27% 38.70% 22.17% 36.51% 18.38% c4-CPz 34.25% 35.17% 31.80% 26.11% 41.67% 19.61% p3-CPz 31.89% 27.54% 35.25% 27.83% 33.33% 17.89% p4-CPz 26.38% 22.88% 32.95% 22.91% 33.73% 18.14% o1-CPz 29.53% 23.73% 39.46% 25.62% 28.97% 19.12% o2-CPz 29.92% 20.34% 34.87% 26.85% 33.33% 21.81% f7-CPz 34.25% 25.00% 43.68% 24.38% 33.73% 19.12% f8-CPz 31.10% 23.73% 39.46% 27.34% 35.32% 20.10% t3-CPz 39.37% 24.58% 41.00% 23.40% 38.10% 19.85% t4-CPz 29.92% 22.46% 31.42% 27.59% 34.13% 21.08% t5-CPz 28.74% 25.00% 31.42% 26.35% 26.59% 21.08% t6-CPz 25.59% 21.61% 31.42% 22.41% 37.30% 20.098% a1-CPz 24.80% 19.92% 31.03% 26.60% 31.35% 18.87% a2-CPz 27.56% 22.03% 31.80% 30.30% 32.54% 18.38% fz-CPz 27.95% 36.02% 39.46% 23.40% 34.52% 20.83% cz-CPz 29.53% 23.73% 40.61% 20.94% 30.16% 21.57% pz-CPz 31.10% 24.58% 34.48% 25.37% 29.37% 19.61% leye-CPz 37.80% 29.66% 42.53% 26.60% 34.92% 20.83% reye-CPz 32.68% 28.81% 37.93% 26.85% 31.35% 21.57% lmn-CPz 32.68% 23.31% 34.10% 19.70% 34.92% 18.38% rmn-CPz 29.13% 22.88% 37.93% 25.12% 30.16% 23.77% # epochs 254 236 261 406 252 408 denotes focal EEG channel 191

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fp1-CPzfp2-CPzf3-CPzf4-CPzc3-CPzc4-CPzp3-CPzp4-CPzo1-CPzo2-CPzf7-CPzf8-CPzt3-CPzt4-CPzt5-CPzt6-CPza1-CPza2-CPzfz-CPzcz-CPzpz-CPzleye-CPzreye-CPzlmn-CPzrmn-CPz A B C D E F Figure 5-24. Mean angular frequency in phase space analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H3 using the measure. 192

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Table 5-8. Mean angular frequency in phase space analysis results for control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H3 using the measure. % of epochs rejecting H3 channel Control 5 minute 'off' time Control 3 minute 'off' time TBA4 12.20% 7.13% TBB6 13.59% 8.60% HR7 9.41% 8.85% TLB2 8.01% 7.13% TLB3 8.36% 6.88% TLC2 11.50% 9.09% # epochs 261 406 denotes focal EEG channel 193

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Table 5-9. Short-term maximum Lyapunov exponent analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H4 using the STLmax measure. % of epochs rejecting H4 channel Patient A Patient B Patient C Patient D Patient E Patient F fp1-CPz 29.13% 30.08% 40.23% 18.23% 31.35% 17.65% fp2-CPz 28.35% 32.20% 33.72% 16.50% 29.37% 17.89% f3-CPz 29.13% 27.54% 35.25% 17.49% 28.97% 15.93% f4-CPz 24.41% 15.25% 37.55% 15.52% 22.22% 19.12% c3-CPz 24.80% 15.25% 44.06% 14.78% 26.98% 18.63% c4-CPz 21.26% 14.41% 39.85% 16.75% 23.81% 12.50% p3-CPz 19.69% 16.10% 35.63% 16.26% 19.84% 10.54% p4-CPz 17.72% 15.25% 37.55% 16.01% 19.84% 11.27% o1-CPz 23.23% 19.07% 35.25% 15.52% 21.43% 13.48% o2-CPz 20.47% 16.95% 31.80% 17.00% 25.40% 11.76% f7-CPz 24.41% 22.88% 42.53% 17.73% 28.17% 13.97% f8-CPz 26.77% 30.51% 37.16% 17.00% 19.84% 15.69% t3-CPz 40.94% 27.12% 43.68% 24.88% 26.98% 14.95% t4-CPz 29.53% 15.25% 40.61% 20.94% 27.78% 21.57% t5-CPz 25.20% 19.92% 32.95% 17.49% 23.41% 20.34% t6-CPz 17.32% 15.68% 38.70% 16.26% 22.62% 15.93% a1-CPz 24.41% 31.78% 32.95% 24.88% 30.16% 13.24% a2-CPz 30.71% 28.81% 38.31% 21.18% 17.06% 12.25% fz-CPz 24.41% 19.07% 25.29% 18.97% 26.19% 10.54% cz-CPz 15.75% 15.25% 26.44% 11.82% 21.83% 10.78% pz-CPz 21.65% 15.25% 25.67% 14.04% 25.79% 11.52% leye-CPz 26.38% 23.73% 44.83% 14.29% 25.40% 15.20% reye-CPz 23.23% 19.07% 38.31% 18.97% 19.05% 12.50% lmn-CPz 16.93% 17.80% 34.87% 12.81% 19.84% 12.01% rmn-CPz 20.08% 20.76% 30.27% 14.04% 15.87% 9.56% # epochs 254 236 261 406 252 408 denotes focal EEG channel 194

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fp1-CPzfp2-CPzf3-CPzf4-CPzc3-CPzc4-CPzp3-CPzp4-CPzo1-CPzo2-CPzf7-CPzf8-CPzt3-CPzt4-CPzt5-CPzt6-CPza1-CPza2-CPzfz-CPzcz-CPzpz-CPzleye-CPzreye-CPzlmn-CPzrmn-CPz A B C D E F Figure 5-25. Short-term maximum Lyapunov exponent analysis results for VNS patients. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H4 using the STLmax measure. 195

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Table 5-10. Short-term maximum Lyapunov exponent analysis results for the control patient. Results are expressed as the fraction of epochs in each channel which rejected hypothesis H4 using the STLmax measure. % of epochs rejecting H4 channel Control 5 minute 'off' time Control 3 minute 'off' time TBA4 26.13% 20.88% TBB6 32.06% 26.78% HR7 27.87% 22.11% TLB2 21.60% 14.25% TLB3 19.86% 16.95% TLC2 15.68% 15.72% # epochs 261 406 denotes focal EEG channel 0.511.522.5300.10.20.30.40.5Fraction of epochs showing significant temporal variationOutput current (mA) Patients 5 min off Patients 3 min off Control 5 min off Control 3 min off C D A B F E Figure 5-26. ApEnt results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. 196

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00.511.522.5300.050.10.150.20.25Fraction of epochs showing significant temporal variationOutput Current (mA) Patients 5 min off Patients 3 min off Control 5 min off Control 3 min off C D A B E F Figure 5-27. Correlation sum results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. 0.511.522.5300.10.20.30.40.5Fraction of epochs showing significant temporal variationOutput current (mA) Patients 5 min off Patients 3 min off Control 5 min off Control 3 min off C D A F B E Figure 5-28. results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. 197

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0.511.522.530.10.20.30.40.5Fraction of epochs showing significant temporal variationOutput current (mA) Patients 5 min off Patients 3 min off Control 5 min off Control 3 min off C D A E B F Figure 5-29. STLmax results and the corresponding output current setting. Results are expressed as the fraction of interstimulation epochs showing significant temporal variation. 198

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CHAPTER 6 A NOVEL GENERALIZED ABSENCE SEIZURE DETECTION ALGORITHM Absence epilepsy makes up about 8% of child epilepsy cases with peak occurrence between 6-7 years of age (Berkovic, 1996). Absence seizures are clinically characterized by brief, transient loss of awareness, responsiveness, and memory. These paraxoysmal discharges have a sudden onset, are often less than 5 seconds in duration, cease abruptly without postictal effects and can occur multiple times per day. Absence seizures are generalized with regular and symmetrical 2.5-3.5 Hz SWDs (Panayiotopoulos et al., 1994). Figure 6-1 shows an example of an electrographic absence seizure. The antiepileptic drugs valproic acid and ethosuximide are the most commonly-used drugs for treating absence epilepsy. For additional information on absence epilepsy, see chapter 2. Seizure detection is an important procedure for the treatment of epilepsy. In particular, there are areas wherein seizure detection can benefit epilepsy treatment; rapid seizure annotation and online real-time EEG analysis. Seizure detection algorithms can greatly improve the rate at which physicians analyze EEG recordings by providing a tool to help point out EEG waveforms which are likely to be epileptiform discharges. Such an algorithm can improve the efficiency of health care for epilepsy treatment. The other popular application of seizure detection algorithms is for online real-time analysis. Such analysis is useful in the research field for enhancing the understanding of how EEG activity correlates to the clinical status of the patient or for cognitive testing in animal models of epilepsy. For some epilepsy variants, such as mesial temporal lobe epilepsy, seizure detection may provide a basis for an implantable seizure control device (e.g. utilizing a drug pump and/or neural stimulation apparatus). For generalized absence epilepsy, it is possible that 199

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someday an online real-time absence seizure detection algorithm may be integrated with scalp-EEG recordings as part of medical checkups in patients with generalized absence epilepsy. In addition to seizure detection, such an algorithm can be extended to perform seizure stratification and provide a histogram of seizure count versus seizure duration. The ability to automatically stratify seizures may provide additional useful information for evaluating therapeutic effect (e.g. compare the seizure stratification histogram profile before and after therapeutic intervention). For these reasons, the purpose of this study is examine a novel method for expediting detection and stratification of SWDs such as those found in generalized absence epilepsy. Methods Previous automated SWD detection algorithms typically relied on thresholding methods and performed well in animal seizure models (Westerhuis et al. 1996; Fanselow et al., 2000; Van Hese et al., 2003). Energy Method for SWD Detection One method calculates the signal energy (Van Hese et al., 2003) and establishes a threshold energy level which designates spike and wave activity or non-spike and wave activity. In each window, the signal energy is calculated as 1021LnSknxkE (6-1) where a detection is signified if the calculated energy exceeds a chosen threshold value for four consecutive windows. 200

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Fanselow Method for SWD Detection The Fanselow method (Fanselow et al., 2000) establishes a voltage threshold which allows classification of SWDs. The method is based on the maximum absolute value of the EEG amplitude within a window SknxkALn1max1,...,0 (6-2) A threshold is set for each subject. If three consecutive windows are above the threshold, a SWD detection is made. Westerhuis Method for SWD Detection The Westerhuis method (Westerhuis et al., 1996) estimates the first derivative of the EEG signal which is referred to as the steepness of signal. The maximum value of this steepness in consecutive, non-overlapping windows is evaluated as SkndkDLn1max1,...,0 (6-3) where nxnxnd1 (6-4) A positive detection is made if D exceeds a certain threshold value in four consecutive windows. The threshold is automatically determined on the basis of the EEG during wakefulness. This method showed strong performance in Genetic Absence Epilepsy Rats from Strasbourg (GAERS). This study aims to address improvements in the following areas; minimize detection lag (which is critical for online utilization of such a seizure detection device), decreasing window size (to help increase detection time resolution), increasing robustness to noise, and simplified detection calibration. For these reasons, supervised machine learning algorithms were utilized 201

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with the intention of providing a robust seizure detector. The two features selected for this algorithm are Teager-Kaiser energy and dynamic time warping distance. Dynamic Time Warping Dynamic time warping (DTW) is one of the most well-studied temporal pattern similarity measures (Rabiner et al., 1978). This method utilizes a dynamic programming approach to align a test time series to a template time series and provides an alignment distortion measure to ascertain pattern similarity. For two time series X and Y of equal length nYX pattern similarity is established by aligning time series X with time series Y using the minimum computed alignment distortion. The distortion path is obtained by warping time for each signal such that the minimum alignment distance between the two signals is achieved. This study applies the DTW measure to two EEG signals of equal length though the signals do not need to be the same length. YXDalign, DTW has been used extensively in biological applications such as ECG analysis (Jen and Hwang, 2007; Kotas, 2008), EEG spiking pattern recognition (Chi et al., 2007), analysis of event-related potentials (Casarotto et al., 2005), fingerprint recognition (Kovacs-Vajna, 2000), and medical imaging reconstruction (Okumura et al., 2007). The DTW measure has demonstrated utility as a kernel function for support vector machine based seizure prediction algorithms in temporal lobe epilepsy (Chaovalitwongse and Pardalos, 2008). The minimum DTW distance can be obtained using the following dynamic programming technique. First, an n x n alignment array is generated where each element of the array represents a distance metric for all combinations of points between the two signals. In this array the (i,j)th element is the distance between points x i and y j Euclidean distance 2,jijiyxyxd is 202

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typically used as the distance measure. A warp path KwwW,...,1 is then constructed where K is the length of the warp path for which YXKYX,max Element k of the warping path represents Element k of the warp path represents a matching point of the two time series, where corresponds to index i of time series X and index j of time series Y. A warping path must begin at the first sample of both time series, jiwK, ji, 1,11 w and must finish at the last sample of both time series, nnwK, An additional constraint requires the warping path indices i and j to increase monotonically. That is, jiwk, and '',jiwk where and The optimal warp path possesses the minimum warping cost defined as 1'iii 1'jjj KkjkikalignwwdKYXD1,,,1min, (6-5) This problem can be approached from a dynamic programming perspective where the path is advanced by one unit on the i axis, one unit on the j axis, or both. Thus, this approach only requires evaluation of cumulative distance found in adjacent elements, 1,1,11,min,,jiDjiDjiDxxdjiDji (6-6) Teager-Kaiser Energy In 1990, Kaiser first derived Teagers nonlinear energy algorithm in discrete time domain to calculate the energy of a sound (Kaiser, 1990). The Teager-Kaiser energy (TKE) operator has demonstrated sensitive to both amplitude and frequency changes in time series signals. This measure has demonstrated utility feature for the detection of seizures and high frequency 203

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epileptiform activity (Zaveri et. al., 1993; Smart et. al., 2005; Gardner et. al., 2006). This study utilizes the mean value of the TKE operator across a window, (6-7) 122111NkkXkXkXNXTKE where N is the length of the window of interest. Empirical Study In order to investigate the possibility of seizure detection and stratification, two experiments are presented, each classifying a different subset of the seizure: Separate the beginning of each seizure from randomly-selected non-seizure segments Separate the end of each seizure from randomly-selected non-seizure segments. Separating the beginning of the seizure from non-seizure segments (experiment one) tests the seizure detection abilities of the detector whereas distinguishing the end of a seizure from non-seizure segments (experiment two) is a critical task in seizure stratification. These two experiments provide an initial framework for testing the SVM classifiers ability to stratify generalized SWDs. This empirical study is motivated by an underlying hypothesis that SVMs are capable of distinguishing neural states (seizure and non-seizure) in a newly-diagnosed patient with typical absence seizures. The signal features consist of the DTW distances between a template SWD signal the test window to be classified, both of which are 0.3 seconds in duration. This section describes the EEG data acquisition, data sampling and feature extraction, SVM training and testing, and results. EEG Data Acquisition Approximately 24 hours of scalp EEG data were acquired from a SleepMed DigiTrace ambulatory EEG recording device. The data were acquired at 200 Hz with an input range of 0.6 204

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mV with built-in filter of 0.5-70 Hz. A bipolar, longitudinal, chain electrode recording montage was employed to provide 16 EEG channels (Fp1-F3, F3-C3, C3-P3, P3-O1, Fp2-F4, F4-C4, C4-P4, P4-O2, Fp1-F7, F7-T3, T3-T5, T5-O1, Fp2-F8, F8-T4, T4-T6, T6-O2) as well as two auxiliary channels which were not utilized. This EEG study utilized the F3-C3 and F4-C4 channels because provide high-quality representations of the SWDs yet are located reasonably far away from facial muscles. The patient underwent 93 seizures during the ~24 hour continuous EEG recording. Seizure times were verified by a board-certified clinical electroencephalographer. Data Sampling and Feature Extraction Each data sample consists of extracted features from an EEG window one second in duration. Within the one-second data sample window, a sub-window of 0.3 seconds in duration is advanced with 50% overlap from the start of the data sample window to the end of the data sample window (providing 5 sub-windows and thus 5 features per data sample window per EEG channel). Thus for channels F3-C3 and F4-C4 there are ten features representing each data sample window. For each sub-window within the data sample, the DTW similarity feature is obtained via comparison with an archetypical SWD template. Figures 6-2 and 6-3 illustrate the DTW distance metric in this application. The study uses 93 SWD templates (one selected from each seizure) which are centered on the spike and 0.3 seconds in duration. SWD templates are reassigned randomly such that no seizure uses its own template for feature extraction. The seizure class consists of data sample windows from all 93 seizures. The non-seizure class consists of a total of 93 non-seizure data sample windows randomly selected from ~24 hour continuous EEG recording with the following constraints: 205

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Must be at least 60 seconds away from any seizure onset or offset Must be at least 0.1 seconds away from another non-seizure sample The training dataset consists of the 93 seizure and 93 non-seizure data sample windows. SVM Training and Testing The soft-margin SVM classifier with a RBF kernel is applied to this problem based on success in other neural state classification problems (Kaper et. al., 2004; Acir and Gzelis, 2005; Bewernitz et. al., 2006; Lehmann et. al., 2007; Seref et al., 2006). A range of SVM parameters which demonstrated satisfactory results in similar EEG classification studies were applied to this study. Thus, each SVM cycle was performed for all nine combinations of cost=10,100,1000 (Kaper et al., 2004; Acir and Gzelis, 2005) and the RBF parameter sigma=20,40,60 (Kaper et. al., 2004; Lehmann et al., 2007). SVM training is performed using a 10-fold cross validation scheme. This scheme employs a resampling technique in which the seizure and non-seizure classes are first randomly shuffled. Next, 10 % (~9 samples) of the shuffled seizure class and 10% (~9 samples) of the shuffled non-seizure class are extracted (individually for each class) and combined to form the test set. In general, SVM training is optimal for training datasets with equal numbers of data points from each class. Otherwise, the classifier can be biased towards the class which had more training points. The remaining 90% of each class is used to train the SVM classifier which is then tested on the extracted testing dataset. Upon testing the SVM, the test dataset is replaced in the shuffled training data and the succeeding 10% block of each shuffled class is extracted to form the next test set. This validation scheme repeats until the last 10% block of each shuffled class is extracted and tested. This study repeats the sampling, feature extraction, resampling, training and testing cycle 1000 times. 206

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Detector Performance Evaluation The detection sensitivity and specificity are used to evaluate the performance of the SVM seizure detector. This involves categorizing the classification results into one of four possible outcomes: True positives (TPs) refer to the correct classification of seizure segment True negatives (TNs) refer to the correct classification of a non-seizure segment False positives (FPs) refer to the incorrect classification of a non-seizure segment as a seizure False negatives (FNs) refer to the incorrect classification of seizure segment as a non-seizure The four possible detection outcomes may be illustrated in the context of figure 6-4. A classification result is considered a TP if a seizure EEG sample is classified as a seizure sample. A classification result is considered a TN if a non-seizure EEG sample is classified as a non-seizure sample. A classification result is considered a FP if a non-seizure EEG sample is classified as a seizure sample. Finally, a classification result is considered a FN if a seizure EEG sample is classified as a non-seizure sample. The sensitivity and specificity measures often used for evaluating detector performance can be derived from these four outcome quantities. Sensitivity is the fraction of positive samples that are classified as positive: FNTPTPySensitivit (6-8) where positive refers to the seizure class. Specificity refers to the fraction of negative samples that are classified as negative: FPTNTNySpecificit (6-9) 207

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where negative refers to the non-seizure class. Results The mean value of sensitivity and specificity are reported for 100 SVM detection trials, where each trial underwent 10-fold cross validation for one of the nine combinations of SVM parameters. The results for experiment one, seizure detection of the first second of each seizure are shown in table 6-1. Results from experiment two, seizure stratification experiment performing detection on the last second of each seizure are summarized in table 6-2. Discussion As is shown in table 6-1 and figures 6-5, 6-6, 6-7, the SVM classifiers overall best performance is experiment ones application where the SVM is function as a seizure-onset detector (classifying the first second of each seizure). This result makes sense in comparison with experiment two where the last second of the seizure is classified as a first step towards a seizure stratification application (figures 6-8, 6-9, 6-10). The beginnings of the seizures appear more visually similar to one another than the ends of the seizures. Even still, the performance of the classifier in the experiment two setup demonstrated high sensitivity and specificity for numerous parameter combinations. The observation that classification is less affected by SVM parameters in experiment one compared to experiment two is a reasonable phenomena. Due to stronger electroencephalographic similarity among various seizures at onset compared to offset, then the beginning of the seizures may be more regular in feature space than the seizure offset. Thus, the alterations in SVM parameters do not seem to have as large of an effect on the results of experiment one as with experiment two. In particular, the classifier varied more with changes in cost for experiment two than experiment one, which could be due to a loss of generality resulting from over fitting the more variant seizure offset period. 208

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These results show promise for the SVM application to seizure detection and stratification. Such a tool may provide benefit to clinicians and researchers by providing a means to rapidly annotate as well as provide a clinically interesting measure of drug effect on a histogram of seizure durations. Thus, this line of work may lead to a greater understanding of the therapeutic effects of AEDs. Future studies will provide a more comprehensive evaluation of features. While the DTW measure performed well, other similarity measures (such as similarity index) may be worth implementing. In addition, adding more EEG channels may improve classification performance though channel addition imposes a computational burden increase. These results should be validated in additional patients. Finally, an important future step is to implement this algorithm in a pseudo-online fashion to assess the robustness to noise. While SVMs provide exceptional generalization abilities, a sliding window classifier will provide an interesting assessment of how the classifier copes with the challenges of real-time EEG acquisition. An expansive review article regarding support vector machines in neuroscience applications was accepted for publication under the title support vector machines in neuroscience with authors Onur Seref, O. Erhun Kundakcioglu, and Michael Bewernitz (Seref et al., 2007). 209

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Figure 6-1. Approximately 6 seconds of scalp-EEG demonstrating the 2.5-3.5 Hz spike-wave discharge that defines an electrographic absence seizure (data provided courtesy of Dr. Gregory Holmes). 210

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Figure 6-2. DTW comparison of two different SWD segments. The top signal is a 300 ms SWD segment. Bottom signal is a 300 ms segment of a different SWD. The DTW distance is about 2.4 x 10 7 211

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Figure 6-3. DTW comparison of a SWD segment with a random interictal segment. Top signal is a 300 ms EEG segment of a SWD. Bottom signal is 300 ms of interictal EEG. The DTW distance is about 5.1 x 10 7 Reality Seizure Non-seizure Seizure True Positive False Positive Non-seizure False Negative True Negative Prediction Figure 6-4. Seizure classification evaluation framework. 212

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Table 6-1. Classification performance using the first second of each seizure. Sigma Cost Sensitivity Specificity Mean 20 10 97.11% 96.94% 97.02% 20 100 96.45% 96.46% 96.45% 20 1000 96.37% 96.43% 96.40% 40 10 97.18% 97.04% 97.11% 40 100 96.56% 96.49% 96.53% 40 1000 96.19% 96.37% 96.28% 80 10 97.10% 97.04% 97.07% 80 100 96.82% 96.62% 96.72% 80 1000 96.04% 96.31% 96.18% Table 6-1. Classification performance using the last second of each seizure. Sigma Cost Sensitivity Specificity Mean 20 10 94.85% 93.46% 94.16% 20 100 91.98% 93.10% 92.54% 20 1000 90.25% 92.07% 91.16% 40 10 95.04% 93.34% 94.19% 40 100 93.03% 93.27% 93.15% 40 1000 89.91% 92.13% 91.02% 80 10 94.93% 93.29% 94.11% 80 100 93.86% 93.29% 93.58% 80 1000 90.74% 92.63% 91.69% 213

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Sz NSzSz NSzSigma = 20Cost = 100Sz NSzSigma = 20Cost = 10Sigma = 20Cost = 10000.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%Percent of classification type Sz Detection NSz Detection Figure 6-5. Seizure detection performance for RBF parameter sigma=20 using the first second of each seizure. Sigma = 40Cost = 1000Sigma = 40Cost = 10Sz NSzSigma = 40Cost = 100Sz NSzSz NSz0.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%Percent of classification type Sz Detection NSz Detection Figure 6-6. Seizure detection performance for RBF parameter sigma=40 using the first second of each seizure. 214

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Sz NSzSz NSzSigma = 80Cost = 100Sz NSzSigma = 80Cost = 10Sigma = 80Cost = 10000.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%Percent of classification type Sz Detection NSz Detection Figure 6-7. Seizure detection performance for RBF parameter sigma=80 using the first second of each seizure. Sz NSzSz NSzSigma = 20Cost = 100Sz NSzSigma = 20Cost = 10Sigma = 20Cost = 10000.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%Percent of classification type Sz Detection NSz Detection Figure 6-8. Seizure detection performance for RBF parameter sigma=20 using the last second of each seizure. 215

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Sz NSzSz NSzSigma = 40Cost = 100Sz NSzSigma = 40Cost = 10Sigma = 40Cost = 10000.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%Percent of classification type Sz Detection NSz Detection Figure 6-9. Seizure detection performance for RBF parameter sigma=40 using the last second of each seizure. Sigma = 40Cost = 1000Sigma = 40Cost = 10Sz NSzSigma = 40Cost = 100Sz NSzSz NSz0.00%10.00%20.00%30.00%40.00%50.00%60.00%70.00%80.00%90.00%100.00%Percent of classification type Sz Detection NSz Detection Figure 6-10. Seizure detection performance for RBF parameter sigma=80 using the last second of each seizure. 216

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CHAPTER 7 DISCUSSION AND CONCLUDING REMARKS Epilepsy is a disorder of the brain which is characterized by intermittent synchronized discharges of large populations of neurons. This disorder can greatly impact a patients life in numerous ways including financial, social, professional, and psychiatric effects. While AED therapy may help keep seizures at bay in some patients others are not so fortunate. In the last few decades, savvy researchers have taken advantage of the rapid progression of computer technology, biomaterials, signal analysis advances and medical knowledge advancement to extract relevant EEG features in order to enhance epilepsy treatment. Computational neuroscience is an exciting frontier which is providing numerous options for addressing neurological disorders which may have been inconceivable decades ago. The ability to map the brains states in terms of the status of a dynamic neurologic disorder will likely be a highly sought-after research goal for years to come. This dissertation has helped provide preliminary data mining and dynamical EEG analyses to help uncover patterns which may be related to stimulation parameters and ultimately improve our understanding of the mechanisms that produce the VNS therapeutic effect. In addition, a study outlining a novel generalized spike wave detection algorithm was outlined here as well. These projects aim towards creation of bedside and/or implantable real-time seizure control devices. Towards Real-Time EEG Analysis Tools for the Bedside and Implantation The exciting progress made in the characterization of sophisticated disease and disorders modeling schemes is part of the driving force this research. The characteristics of the class of disorders known as dynamic disorders provide an interesting framework to approach the problem of improving existing and creating new therapeutic approaches. This perspective treats such disorders as deviations from a range of healthy dynamics in the underlying physiologic control 217

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systems. Such a perspective implies therapeutic approaches which involve a fusion of medicine, biology, and engineering. Numerous researchers are investigating the possibility of applying a systems control approach to the epileptic brain in order to reduce the burden of epileptic seizures. Some of the studies presented in this dissertation are geared towards such an approach and aim to improve the VNS therapy modality. Patients with newly-implanted VNS systems undergo a period often lasting several months of sub-optimal therapy. During this period, patients may need to undergo numerous visits to the doctors office in order to fine-tune the stimulation parameters for clinical efficacy and tolerance. Such a process results in increased medical treatment costs and all the while the patients may be at a higher risk to seizures due to sub-optimal stimulation parameters. One of the goals of the work presented it to examine the possibility of an EEG marker of optimal VNS therapeutic efficacy to help expedite the process of tuning parameters in newly-implanted patients. The main focus of the research on the VNS data is to characterize EEG characteristics in numerous VNS patients in order to assess any relationships to stimulation parameters. If such a relationship can be established and if the effects could then be geared towards a final outcome, then such EEG characteristics may find use in a bedside device for rapid VNS calibration or even in an implantable control system for optimal VNS therapy. The studies presented in chapter four represent data mining approaches to characterizing such EEG effects. Data Mining Approaches to Characterizing EEG Patterns Data mining tools have demonstrated an extensive capacity to discover patterns in biological datasets including EEG signals. Data mining is the process of applying algorithms to extract patterns in large datasets. While the human eye is often the best pattern detector of all, data mining algorithms can work on exceedingly large datasets and examine complex multidimensional datasets. One of the most attractive features of data mining tools are their 218

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ability to perform clustering data subsets according to inherent similarities or in a supervised manner. For the purpose of characterizing EEG patterns in patients undergoing VNS therapy for epilepsy, data mining methods provide a useful tool for elucidating preliminary patterns which incorporate an expansive representation of features from all channels. The biclustering experiment provided a characterization of the EEG patterns which may be related to VNS therapy. The observations were based on patterns of the STLmax measure, which assumes a chaotic framework and provides a measure of the sensitivity of the signal to initial conditions. Though the brains behavior may not always be consistent with a low-dimensional chaos model, the chaoticity measure has provided an ability to classify neural states in epilepsy (e.g. interictal or far from a seizure, preictal or seizure imminent, ictal or during a seizure, and postictal or the period of altered consciousness following a seizure). Thus, the measure was selected as a candidate for detecting EEG patterns which may be related to VNS therapy. The study demonstrated separability between the VNS on and off states for which all of patient As electrodes contributed to and only a few frontal and temporal electrodes in patient B contributed to. The biological relevance of these results may be related to study which discovered that VNS-induced acute suppression of epileptiform activity in a hippocampal depth electrode (Olejniczak et al., 2001). Though the study by Olejniczak et al. utilized depth electrodes, it is possible that scalp EEG recordings may display some manifestation of such an EEG effect observed at a hippocampal depth electrode. From this perspective, perhaps the STLmax behavioral differences between patients A and B are associated with enhanced suppression of epileptiform activity in patient A compared to patient B. An interesting future application of biclustering would be to examine the EEG effects during non-stimulation in an unsupervised manner. Such an experiment would provide a highly objective method to determine spatio219

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temporal patterns of EEG features. Based on the results of chapter 5, future experiments should include both linear and nonlinear features to help ensure proper characterization of the wide range of EEG dynamical behavior patterns observed during these studies. This work was published in the paper Biclustering EEG data from epileptic patients treated with vagus nerve stimulation, authored by Stanislav Busygin, Nikita Boyko, Panos Pardalos, Michael Bewernitz, and Georges Ghacibeh (Busygin, 2007). The next experiment examined the patterns of the raw EEG behavior in feature space using support vector machines. The accuracy at which the SVMs could separate the raw EEG between two adjacent EEG segments, a reference segment during stimulation and successive non-overlapping windows was interpreted as a robust measure of EEG similarity (or dissimilarity) and compared with stimulation parameters. The study determined observed a potential covariation between the EEG and the pulse width and stimulation frequency parameters. A study by Mu et al. showed that a 250 s VNS pulse width caused reduced blood flow in significantly more brain regions (e.g. hippocampus, sup. temp. lobe) than 500 s (2004). Perhaps these regions may be responsible for covariation of EEG feature space dispersion with pulse width parameter. Furthermore, a recent study demonstrated that a 20 Hz stimulation frequency produced significant cerebral blood flow increases (e.g. in the orbitofrontal cortex, hypothalamus, and thalamus) compared to 5 Hz in VNS patients (Lomarev et al., 2002). It is possible that the altered blood flow in these regions may be responsible for the observed covariation of EEG feature space dispersion with stimulation frequency. In addition, patients where seizure free and patients which experienced a small number of seizures per month resulted in greater separation accuracy between the reference class and all subsequent comparison classes in a VNS epoch. The patient with the most seizures per month 220

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resulted in the poorest separation between the reference class and all adjacent classes. This phenomenon could be the multichannel analog of the dynamic resetting effect between two EEG channels postulated by Iasemidis et al. which states that a seizure resets the brain from an unfavorable state to a more favorable state (Sackellares and Iasemidis, 1997; Iasemidis et al., 2004). Thus, the results were interpreted as electroencephalographic evidence that the VNS mimics the therapeutic resetting effect of a seizure. Future studies involving SVM would apply the algorithm in an unsupervised manner to help provide unbiased information about patterns in the data. Also, modification of the support vector machine algorithm, such as adaptive feature scaling (Grandvalet et. al., 2003) can help provide insight into the relevance of each input feature for SVM classification. This study is published in an article titled Quantification of the Impact of Vagus Nerve Stimulation Parameters on electroencephalographic Measures with authors Michael Bewernitz, Georges Ghacibeh, Onur Seref, Panos Pardalos, Chang-Chia Liu, Basim Uthman (Bewernitz, 2007). The final study utilized SVMs and LR to analyze the time-varying feature space separation of the STLmax dynamical measure in patients undergoing VNS therapy. With an eye towards the VNS replicating the resetting effect of a seizure, this study aimed to characterize potential relationships between the EEG and stimulation parameters using an experimental setup similar to Iasemidis et al. (2004). Thus, a reference class was selected at 8 seconds prior to the stimulation onset and was comprised of the STLmax value of all channels for all stimulations combined. Similarly, each succeeding non-overlapping window for all channels for all epochs was compared with the reference class. The study demonstrated that the observed pattern changes may be related to the stimulation frequency parameter. Lomarev et al. demonstrated that a 20 Hz stimulation frequency produced significant cerebral blood flow increases (e.g. in the 221

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orbitofrontal cortex, hypothalamus, and thalamus) compared with the 5 Hz stimulation frequency in VNS patients (Lomarev et al., 2002). The brain regions which showed a pulse-width dependent blood flow in the study by Lomarev et al. may be the source of the observed covariation of EEG feature space dispersion with stimulation frequency. Also, it was speculated that the poor STLmax separation between VNS on (which may be considered as a VNS artificial seizure) and VNS off in patient B combined with patient Bs high seizure frequency (compared with the other patients) is aligned with the dynamic seizure resetting effect described by Iasemidis et al. (2004). In addition, this experiment demonstrated the concept previously observed by Bewernitz et al. (2007) except while using the STLmax measure. Thus, the connection between the observed effect and the observations of Iasemidis et al (2004) are stronger. This study was submitted to Computing and Optimization in Medicine and Life Sciences Vol. 3, under the title "A Data Mining Approach to the Investigation of EEG Biomarker Existence for Vagus Nerve Stimulation Therapy Patients", with authors Nikita Boyko, Michael Bewernitz, Vitaliy Yatsenko, Panos Pardalos, Georges Ghacibeh, Basim Uthman (Boyko et al., 2008). In regards to the biological impact, these results may be related to the phenomenon discovered in a study by Olejniczak et al. where a short-term suppression of epileptiform sharp waves was observed following VNS from a hippocampal depth-electrode (2001). While the scalp electrodes used to collect the data in these analyses cannot achieve the recording quality of hippocampal depth electrodes, it is possible that the scalp EEG data mining analysis results may reflect the same therapeutic effect as observed in the hippocampus by Olejniczak et al. (2001). Analysis of Interstimulation Dynamics The studies described in chapter 5 focus analysis on the EEG dynamics occurring during interstimulation epochs. While the comparisons of stimulation to non-stimulation epochs 222

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provided interesting results with clinical significance, the advantage of this experimental setup is that the possibility of direct neural modulation is eliminated. Thus, the results are more likely to be due to an after-effect of stimulation rather than due to immediate neuronal modulation. The first experiment performed an extensive nonlinearity characterization using surrogate EEG analysis. Each epoch was compared to 19 surrogate datasets using the ApEnt measure. The most obvious connection of the EEG with the stimulation parameters was a covariation with the pulse width. In addition, the two seizure-free patients (E and F) produced the lowest fraction of epochs which displayed a nonlinear fingerprint (e.g. rejected the null hypothesis at the given significance level). These results may be related to a study by Olejniczak et al. which reported an acute VNS-induced suppression of epileptiform activity in the hippocampus (2001). Though the effect was observed from a hippocampal depth electrode in the study by Olejniczak et al., it is possible that some manifestation of the effect is present in the scalp-EEG signal analyzed in the present study. The VNS-enhanced suppression of epileptiform activity reported in the literature may be responsible for the diminished nonlinearity in patients with fewer seizures. The cause of any epileptiform activity suppression may be related to a pulse-width dependency of blood flow to various brain regions (e.g. hippocampus and superior temporal lobe) reported by Mu et al., 2001. The observation that the seizure-free patients expressed the least amount of nonlinearity may be congruent with the findings of Janszky et al. where the absence of bilateral interictal epileptiform discharges was the only EEG predictor of seizure freedom (2005). Thus, future studies should include epileptiform discharges in order to help further characterize the EEG effect associated with VNS. Shen et al. demonstrated that K-complex expression patterns can affect nonlinearity in surrogate analysis of sleep EEG (2003). The observed nonlinearity increases in patients A and B 223

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during late night (~11pm until ~7am) may be the result of altered k-complex expression during sleep (though other patients did not show this trend). The VNS is known to cause an increase in the overall EEG power during sleep (Rizzo et al., 2004). The nature of surrogate data analysis is to provide a yes/no answer to the question of nonlinearity, but does not provide information on what type of nonlinearity is observed. All in all, these results suggest that nonlinear measures may someday demonstrate sensitivity to the outcome of VNS effect. In addition, this study motivates the usage of linear and nonlinear measures in conjunction with one another as well as specific waveforms such as epileptiform discharges in order to characterize the complex signal patterns present in EEG. The second study in chapter five aimed to characterize any time dependence of the EEG dynamics during the interstimulation epochs. This preliminary study was executed by performing a statistical comparison of the first half of each interstimulation epoch to the second half. The study utilized four measures which have demonstrated success in classifying neural state changes in epilepsy; ApEnt, correlation sum, and STLmax. The study showed that the patient with the greatest amount of interstimulation epochs demonstrating significant time variation (for Apent, correlation sum, and ) also had the highest output current (2.5 mA for patient C). Patient A showed a similar trend and had the second highest output current (1.75 mA). Patient F showed an opposing trend with 0.75 mA output current and the smallest fraction of interstimulation epochs showing time variation. The ApEnt and measures demonstrated a noticeably larger deviation from the control in all six patients than the other two measures, as well as sensitivity to the output current. These two observations suggest that the ApEnt and measures may be good candidates for EEG biomarkers in VNS patients. Biologically, these results may be related two studies which demonstrated an electrical current threshold for 224

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epileptiform activity suppression when stimulating the hippocampus in a low Ca2+ seizure model (Warren and Durand, 1998) and a high K+ seizure model (Nakagawa and Durand, 1991). A paper related to these interstimulation dynamics studies was published under the title Optimization of epilepsy treatment with vagus nerve stimulation with authors Basim Uthman, Michael Bewernitz, Chang-Chia Liu, and Georges Ghacibeh (Uthman et al., 2007). Remarks on VNS Results The variation in observed sensitivity in these measures to the various VNS parameters suggest that different EEG measures are better suited for providing different information about the EEG signal than other measures. Intuitively, it seems logical that a complex system such as the epileptic brain may require several EEG measures for adequate characterization for therapeutic intervention purposes. This observation is underscored in light of the intermittent expression of nonlinear signatures in various interstimulation epochs. Future studies should address the characterization task using a blend of linear and nonlinear measures. In addition, future studies require additional patients to validate the interpretation of these results. Baseline EEG recordings would provide additional support for the existence of EEG-induced VNS effects by providing an opportunity to demonstrate the absence of such patterns prior to implantation. After acquisition of the necessary baseline data, an interesting study would be to examine the changes induced by the first stimulation. Thus, after the first stimulation, a subsequent VNS deactivation and EEG acquisition may be applied. This would provide a highly objective experimental setup possible for identifying short-term VNS effects. Subsequent follow-up recording sessions may provide additional characterization of the summed modulatory effect of chronic VNS. The time of the last seizure should be obtained from the patient for all such studies. The reason for this is that the patient undergoes a brief period of increased seizure protection after 225

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some seizures (e.g. generalized tonic-clonic seizures). Thus, if the patient is under the influence of this particular neural state, then that would provide a reduced chance of seizure which is not consistent with the patients standard behavior. This information would be helpful for interpreting results. In addition, caution must be exercised when interpreting the results of patients whom undergo seizures. As dynamical transitions can occur several minutes to several hours prior to a seizure, many researchers operationally define the interictal period as being a minimum of 8 hours away from a seizure (Pardalos et al., 2003; Hively et al., 2005; Chaovalitwongse et al., 2006). Thus, the occurrence of a handful of seizures may produce an unknown amount of influence on EEG dynamics. For this reason, future studies may withhold analysis of EEG signals occurring within 8 hours of a seizure. Seizure Detection and Stratification The final project of this dissertation applied SVM classification in a preliminary experiment geared towards a seizure detection and stratification system in patients with generalized absence epilepsy. The seizure detection system utilized DTW distance with a reference vector centered on a spike as the extracted feature. As spike and wave discharges in absence epilepsy are generalized and often have a highly characteristic pattern. The first experiment in this study performed SVM training and testing for the detection of the first second of the seizure versus randomly selected non-seizure EEG which was located at least one minute away from a seizure and at least 0.1 second away from another non-seizure segment. Though both experiments present high sensitivity and specificity, the SVM classifier performed better at classifying the first second of the seizure than final second o the seizure. This is likely due to stronger electroencephalographic similarity among the different seizures at onset compared to offset. Alteration of the RBF kernel bandwidth did not appear to appear the results much. Variation of the cost parameter produced a greater effect on accuracy in experiment two than 226

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experiment one. This is likely due to a loss of generality resulting from rigid over fit models which may occur when the cost is sufficiently high. Such an algorithm may benefit clinicians and researchers by providing a means to rapidly annotate EEG signals as well as a means to provide a clinically interesting measure of therapeutic efficacy (e.g. distribution of seizure durations may vary before and after drug therapy, and thus a measure of this distribution may find clinically relevant information which a raw seizure count would miss). A future direction of this project is to implement the classifier in a real-time situation to test how the algorithm deals with the challenges presented in real-time EEG analysis. This study was submitted to a 2008 volume of the Optimization and Its Applications book series under the title A Novel Algorithm for the Detection and Stratification of Generalized Absence Seizures with authors Michael Bewernitz, Onur Seref, Basim Uthman, and Panos M. Pardalos. In relation to this work, a review article regarding support vector machines in neuroscience applications was accepted for publication under the title support vector machines in neuroscience with authors Onur Seref, O. Erhun Kundakcioglu, and Michael Bewernitz (Seref et al., 2007). Final Remarks The collection of studies presented address preliminary challenges involved with development of online real-time EEG analysis systems for bedside and/or implantable therapy or diagnosis enhancement tools. The choice of EEG source and extracted features for such a tool is one of the greatest challenges presented to researchers in this field. Brain activity can be measured on numerous scales from individual neurons up to macroscopic field potentials representing large regions of the cerebral cortex. In addition, ensuring high-fidelity recordings is an additional challenge requiring careful consideration for preprocessing tasks such as artifact 227

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rejection and filtering. In addition to the complex nature of EEG analysis, the EEG data source itself is limited in what it can tell a person about the brain. As technology improves and electronic components become smaller, faster, and more efficient, future implantable therapeutic control prostheses may also implement chemical sensors for quantifying neurotransmitter concentrations, for example. Inclusion of additional information related to brain function could greatly enhance the characterization of brains behavior and potentially augment the performance of implantable therapeutic control devices. 228

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BIOGRAPHICAL SKETCH Michael Andrew Bewernitz was born and raised in the state of Michigan in the United States of America. Michael received his Bachelor of Science degree in chemical engineering with a biochemical engineering option from Michigan State University in 2002. He enrolled the Ph.D. program of the J. Crayton Pruitt Family Department of Biomedical Engineering in 2003 under the guidance of Dr. J. Chris Sackellares in the Brain Dynamics Lab. After three productive years, Michael joined Dr. Panos Pardalos in the Center for Applied Optimization in the summer of 2006. In summer of 2007, Michael earned his Master of Engineering degree from the J. Crayton Pruitt Family Department of Biomedical Engineering. He went on to complete his Doctor of Philosophy in spring of 2008. Michael has written and presented three conference talks, produced four journal publications, one book chapter, participated in the creation of a patent, helped create four IRB medical research protocols on which he served as a sub-investigator, participated in the creation of a bioengineering research fellowship grant, as well as an NIH R21 grant. He has worked as a visiting researcher at the Allegheny-Singer Research Institute in Pittsburgh, PA under the guidance of Dr. Kevin Kelly for two months during the summer of 2005. Michaels research interests include data mining biomedical time-series datasets and neural state classification using electroencephalographic recordings obtained from patients or animal models of neurological disorders.


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