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Comparison of algorithms for epileptic seizure detection

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Title:
Comparison of algorithms for epileptic seizure detection
Creator:
Ramachandran, Ganesan
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[Gainesville, Fla.]
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University of Florida
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English

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Datasets ( jstor )
Detection ( jstor )
Electrodes ( jstor )
Electroencephalography ( jstor )
Entropy ( jstor )
Epilepsy ( jstor )
False alarms ( jstor )
Seizures ( jstor )
Signals ( jstor )
Statistical discrepancies ( jstor )
DETECTION, EEG, EPILEPSY, EXPONENTS, LYAPUNOV, SEIZURE, STLMAX
Dissertations, Academic -- Electrical and Computer Engineering -- UF ( lcsh )
Electrical and Computer Engineering thesis, M.S ( lcsh )
Electroencephalography -- Data processing ( lcsh )
Epilepsy -- Diagnosis ( lcsh )
Signal processing -- Digital techniques -- Data processing ( lcsh )
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government publication (state, provincial, terriorial, dependent) ( marcgt )
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Abstract:
ABSTRACT: The purpose of this thesis was to devise on-line, automated algorithms to detect epileptic seizures, so that continuous monitoring of epileptic patients becomes feasible. This work was motivated by recent advances made by the Bioengineering Research Partnership at the University of Florida who proposed and developed the short-term largest Lyapunov exponent (STLmax) of electroencephalography (EEG) data as a good candidate for seizure prediction and detection. The STLmax shows three properties pertaining to the transition from normal to epileptic state. They are as follows: --A change in the mean value during the seizure, which can be detected using a simple threshold --A quick rise in the mean value immediately after the drop which, combined with the drop, can be detected using a variance measuring mechanism like entropy --Interlocking among channels that can be detected using a distance measure like Diks distance. Hence three methods are compared, each exploiting a different property. The methods are explained in increasing order of complexity. The trade-offs involved and the options available are described so that the user of this algorithm can customize it for the application intended. Also the bottlenecks encountered are explained so that further advancements can be made.
Thesis:
Thesis (M.S.)--University of Florida, 2002.
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Includes bibliographical references.
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Mode of access: World Wide Web.
General Note:
Title from title page of source document.
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Includes vita.
Statement of Responsibility:
by Ganesan Ramachandran.

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University of Florida
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Copyright Ramachandran, Ganesan. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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12/1/2003
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029835236 ( ALEPH )
53465516 ( OCLC )

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COMPARISON OF ALGORITHMS FOR EPILEPTIC SEIZURE DETECTION By GANESAN RAMACHANDRAN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2002

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Copyright 2002 by Ganesan Ramachandran

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This work is dedicated to millions of people with epilepsy

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ACKNOWLEDGMENTS First and foremost I extend my sincere gratitude to my advisor Dr. Jose C. Principe without whom this work would not have been possible. I would like to thank Dr. Chris J. Sackellares for serving on my thesis committee and for helping me understand the neurological concepts and requirements. I would also like to thank Dr. John G. Harris for serving on my thesis committee. I extend my sincere thanks to Dr. Paul R. Carney and Dr. Deng S. Shiau for assisting me in understanding the epilepsy data and the medical concepts involved. I would like to thank Dr. Deniz Erdogmus, Dr. Young Yoon and Mr. Yadunandana N. Rao for their timely technical advice. I wish to express my special thanks to my family and relatives. I am grateful to my parents for their support and their faith in me. Finally, I would like to thank all my colleagues and friends for their assistance. iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT.......................................................................................................................xi CHAPTER 1 INTRODUCTION......................................................................................................1 Epileptic Seizures: Some Facts..................................................................................1 Motivation and Purpose.............................................................................................2 Brief Review of Existing Methods............................................................................2 Manual EEG Monitoring..................................................................................2 Classical Signal Processing Methods................................................................3 Artificial Neural Networks (ANNs)..................................................................4 Wavelets and Other Signal Decomposition Methods.......................................4 Nonlinear Dynamic Methods............................................................................4 Problems Associated with the Comparison of Existing Methods.....................5 Outline........................................................................................................................6 2 NONLINEAR DYNAMIC PREPROCESSING........................................................7 STLmax: Brief Introduction......................................................................................7 Properties of STLmax................................................................................................9 Data Set....................................................................................................................10 3 DETECTION METHODS........................................................................................15 Brief Introduction to Event Detection and Hypothesis Testing...............................15 Event Detection...............................................................................................15 Hypothesis Testing..........................................................................................15 Bayes criterion........................................................................................15 Neyman-Pearson criterion......................................................................16 Receiver Operating Characteristic (ROC)..............................................17 Detection Methods...................................................................................................17 Method 1: Subset of STLmax and Threshold.................................................17 Method 2: STLmax and Entropy....................................................................22 v

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Brief introduction to entropy..................................................................22 Brief introduction to variance.................................................................23 Estimation of parameters........................................................................24 Experiment..............................................................................................29 Method 3: Entrainment in STLmax and Seizure Detection............................34 Brief introduction: Diks test and Diks distance......................................34 Estimation of parameters........................................................................37 Experiment..............................................................................................42 4 RESULTS AND CONCLUSION.............................................................................46 Results and Discussion............................................................................................46 Definitions and Trade-offs..............................................................................46 Alarm Clustering.............................................................................................47 Results on the Training Set.............................................................................48 Results on the Test Set....................................................................................52 Case studies: Best Performance on the Test Set.............................................56 Case 1: Quick Detector: STLmax...........................................................56 Case 2: Slow Detector: Variance with L=60..........................................57 Case 3: Slow Detector: Variance with L=1............................................58 Conclusion and Directions for Future Work............................................................59 LIST OF REFERENCES...................................................................................................61 BIOGRAPHICAL SKETCH.............................................................................................64 vi

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LIST OF TABLES Table page 2-1 Patient details...............................................................................................................14 2-2 Distribution of data among training and testing sets...................................................14 3-1 Cost of decision...........................................................................................................16 4-1 Table of mnemonics....................................................................................................49 4-2 Best detection rates on test set for false alarm rate < 1/h (ordered by result).............59 4-3 Best detection rates on test set for false alarm rate < 1/h (ordered by method)..........60 vii

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LIST OF FIGURES Figure page 2-1 The STLmax value during a seizure............................................................................9 2-2 Placement of electrodes used to record the ECoG in the 6 patients............................11 2-3 Example EEG and STLmax signatures for partial secondarily generalized Seizure..12 2-4 Example EEG and STLmax signatures for complex partial seizure...........................12 2-5 Example EEG and STLmax signatures for subclinical seizure...................................13 2-6 Example EEG and STLmax signatures for simple partial seizure..............................13 3-1 Multi-channel STLmax data during a seizure.............................................................18 3-2 Minimum among STLmax channels...........................................................................19 3-3 Average among STLmax channels..............................................................................19 3-4 Maximum among STLmax channels...........................................................................20 3-5 Variance among STLmax channels.............................................................................20 3-6 STLmax channels shown independently.....................................................................21 3-7 Searching for optimal ...............................................................................................24 3-8 Searching for optimal ..............................................................................................25 3-9 Histogram of STLmax data.........................................................................................26 3-10 Entropy as a function of L.........................................................................................27 3-11 Entropy as a function of 0 ........................................................................................27 3-12 Variance as a function of L........................................................................................28 3-13 STLmax values during a seizure...............................................................................29 3-14 Entropy of STLmax channels during a seizure.........................................................30 viii

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3-15 Variance of STLmax channels during a seizure........................................................30 3-16 Spatial minima for entropy and variance of STLmax channels during a seizure......31 3-17 Spatial average for entropy and variance of STLmax channels during a seizure......32 3-18 Spatial maxima for entropy and variance of STLmax channels during a seizure.....32 3-19 Spatial variance among entropy and variance of STLmax channels during a seizure........................................................................................................................33 3-20 Variance and Entropy of STLmax channels shown independently...........................33 3-21 STLmax data during a seizure...................................................................................37 3-22 Autocorrelation of STLmax data during a seizure....................................................38 3-23 Values of r 1 for = 2 to 10........................................................................................39 3-24 Zoomed version of values of r 1 for = 2 to 10..........................................................40 3-25 Values of r 2 for = 2 to 10........................................................................................40 3-26 STLmax values during a seizure...............................................................................42 3-27 Diks distances during a seizure.................................................................................42 3-28 Minimum among pair-wise Diks distance between STLmax channels during a seizure........................................................................................................................43 3-29 Average among pair-wise Diks distance between STLmax channels during a seizure........................................................................................................................44 3-30 Maximum among pair-wise Diks distance between STLmax channels during a seizure........................................................................................................................44 3-31 Variance among pair-wise Diks distance between STLmax channels during a seizure........................................................................................................................45 3-32 Diks distance between STLmax channels shown independently..............................45 4-1 Figure showing the delay between the instant of the actual event to the instant of the alarm....................................................................................................................46 4-2 Subset of STLmax.......................................................................................................47 4-3 ROC for a maximum allowable delay of 1 minute on the training set........................49 4-4 ROC for a maximum allowable delay of 5 minutes on the training set......................49 ix

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4-5 ROC for a maximum allowable delay of 10 minutes on the training set....................50 4-6 ROCs of voting schemes for a maximum allowable delay of 1 minute on the training set.................................................................................................................50 4-7 ROCs of voting schemes for a maximum allowable delay of 5 minutes on the training set.................................................................................................................51 4-8 ROCs of voting schemes for a maximum allowable delay of 10 minutes on the training set.................................................................................................................51 4-9 ROC for a maximum allowable delay of 1 minute on the test set...............................52 4-10 ROC for a maximum allowable delay of 5 minutes on the test set...........................53 4-11 ROC for a maximum allowable delay of 10 minutes on the test set.........................53 4-12 ROCs of voting schemes for a maximum allowable delay of 1 minute on the test set..............................................................................................................................54 4-13 ROCs of voting schemes for a maximum allowable delay of 5 minutes on the test set..............................................................................................................................54 4-14 ROCs of voting schemes for a maximum allowable delay of 10 minutes on the test set........................................................................................................................55 4-15 ROCs of different seizure types using minimum STLmax with maximum delay = 1 minute.....................................................................................................................56 4-16 ROCs of different seizure types using spatial variance of time variance of STLmax channels with maximum delay = 10 minutes.............................................57 4-17 ROCs of different seizure types using spatial variance of time variance of STLmax channels with maximum delay = 10 minutes.............................................58 x

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science COMPARISON OF ALGORITHMS FOR EPILEPTIC SEIZURE DETECTION By Ganesan Ramachandran December 2002 Chair: Jose C. Principe Department: Electrical and Computer Engineering The purpose of this thesis was to devise on-line, automated algorithms to detect epileptic seizures, so that continuous monitoring of epileptic patients becomes feasible. This work was motivated by recent advances made by the Bioengineering Research Partnership at the University of Florida who proposed and developed the short-term largest Lyapunov exponent (STLmax) of electroencephalography (EEG) data as a good candidate for seizure prediction and detection. The STLmax shows three properties pertaining to the transition from normal to epileptic state. They are as follows: A change in the mean value during the seizure, which can be detected using a simple threshold. A quick rise in the mean value immediately after the drop which, combined with the drop, can be detected using a variance measuring mechanism like entropy Interlocking among channels that can be detected using a distance measure like Diks distance. Hence three methods are compared, each exploiting a different property. The methods are explained in increasing order of complexity. xi

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The trade-offs involved and the options available are described so that the user of this algorithm can customize it for the application intended. Also the bottlenecks encountered are explained so that further advancements can be made. xii

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CHAPTER 1 INTRODUCTION Epileptic Seizures: Some Facts Merriam Webster’s Dictionary defines epilepsy as “any of various disorders marked by disturbed electrical rhythms of the central nervous system and typically manifested by convulsive attacks usually with clouding of consciousness.” A seizure is a sudden, involuntary change in behavior, muscle control, consciousness, and/or sensation. A seizure is often accompanied by an abnormal electrical discharge in the brain. Symptoms of a seizure can range from sudden, violent shaking and total loss of consciousness to muscle twitching or slight shaking of a limb. Staring into space, altered vision, and difficult speech are some of the other behaviors that a person may exhibit while having a seizure. Approximately 10% of the U.S. population will experience a single seizure in their lifetime (Source: The Epilepsy Foundation). Epilepsy is not a disease but a term used to indicate recurrent seizures. The detrimental effects of epileptic seizures vary from momentary lapse of muscle control to death. According to the World Health Organization, epilepsy affects approximately 4 million people in North America and Europe. Worldwide, 40 million people are believed to have epilepsy. Though the mechanism of production and progression of epileptic seizures are not completely understood, recent research (Sackellares et al. 2000) postulated that it is a procedure in which the brain goes from a chaotic state to a more ordered state. The seizure may serve the purpose of breaking the order and enabling the brain to go back to normalcy. 1

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2 Motivation and Purpose The purpose of this work is to come up with a seizure detection algorithm that is Online, Completely automated (once the parameters are fixed), Patient independent. Some of the uses of such an algorithm are To avoid the need of a certified electroencephalographer during the EEG recording. This is helpful in case of continuous monitoring over days To evaluate a seizure warning algorithm To serve as a stopping criterion in case of automated anti-epileptic drug delivery To serve as a screening method to detect epilepsy. This work was motivated by recent advances made by the Bioengineering Research Partnership (BRP) at the University of Florida in developing an automated seizure warning device. Research done by the group so far has shown that the short-term largest Lyapunov exponent (STLmax) is a good candidate for seizure prediction and detection. The STLmax shows three properties pertaining to the change from normal to epileptic state. Hence three methods are compared each exploiting a different property. Brief Review of Existing Methods Manual EEG Monitoring Until recently, epilepsy was diagnosed by recording EEG from the patient’s scalp (drawn on sheets of paper). Later, the electroencephalographer goes through tons of paper identifying seizure patterns. To go through even an hour of recording, the electroencephalographer may have to spend 2 to 3 hours looking for patterns. Even now, the gold standard for registering seizures is through visual inspection by the

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3 electroencephalographer during the recording. The electroencephalographer monitors the patient visually and with the EEG recordings. One of the main objectives of this work is to avoid the need for his/her presence so that continuous monitoring for days becomes easier. Results obtained in this work are validated against the work of a board-certified electroencephalographer. Classical Signal Processing Methods Over many years, attempts have been made to automate the seizure-detection process using classical signal processing methods. Both time and frequency domain methods have been applied to scalp and depth EEG data. The time domain techniques include the following: Instantaneous power/energy of EEG (Litt et al. 1999) Median filtering (Echauz et al. 1999) Template matching (Qu and Gotman 1997) Matched filtering (Saltzberg et al. 1971) Correlation Average wave amplitude and duration (Qu and Gotman 1997) And some of the frequency domain techniques include the following: Power spectral density ( Roessgen et al. 1998) Dominant frequency Some groups have tried combining both time and frequency domain techniques with varying degrees of success (Jerger et al. 2001). Classical signal processing methods are much simpler and offer real-time detection with relative ease over other methods like nonlinear dynamic methods or artificial neural networks (ANNs). However, constrained

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4 by the assumptions of linearity and stationarity, most methods often characterize the chaoticity present in the EEG as random noise. Artificial Neural Networks (ANNs) Of late, seizure detection using ANN is becoming increasingly popular (Pradhan et al. 1996, Webber et al. 1996, Weng and Khorasani 1996). Most recent publications involve ANNs using some of the time and frequency domain methods to extract features to train the network. But any method that uses ANN is faced with the following set of problems: Since the a-priori probability of nonseizure activity is much higher than the seizure, adequate training in seizure patterns is difficult to accomplish. Duration and pattern of each seizure may be different. Also, the transition from inter-ictal to ictal and reverse may not be abrupt. Therefore, the definition of a desired response is difficult to standardize. Wavelets and Other Signal Decomposition Methods Inspired by the time-frequency changes during seizures, signal decomposition has been one of the popular methods for seizure detection. The work by Gotman et al. (1976) paved the way for decomposing EEG into half waves. His method compares relative amplitude in the decomposed half waves during spikes and short waves (SSW), to that during background. Further attempts by Gabor et al. (1996) and Osorio et al. (1998) using Daubechies wavelet have claimed significant results. Gabor et al. (1996) uses wavelets to extract features for feeding a neural network for seizure detection. Osorio et al. (1998) uses wavelets as a preprocessing step and uses median filtering for detection. Nonlinear Dynamic Methods The popularization of chaos theory created a lot of interest in applying it for quantification, prediction and control of biological events including epilepsy (Schiff et al. 1994). Most of the methods use correlation integral/dimension (Lerner 1996) or

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5 Lyapunov exponents (Sackellares et al. 2000). Results obtained so far further study in the field. However, some difficulties are associated with using nonlinear dynamics on a signal like EEG/ECoG. One of the most important problems is that these techniques need a large amount of stationary data for a good parameter estimation, which we do not have in the case of EEG, which is known to be nonstationary. Also, the computational complexity involved in these methods proves to be a bottleneck for real-time implementations. Problems Associated with the Comparison of Existing Methods Though a number of research groups (Litt. et al. 1999, Qu and Gotman 1997, Webber et al. 1996, Sackellares et al. 2000) have been presenting automated algorithms for seizure detection, many of them suffer from at least one of the following drawbacks: Failure to mention the distribution of data between training and test sets Failure to describe the trade-off among computational complexity, false alarm rate, % of hits and the time delay involved (i.e., the time the algorithm takes after the seizure onset before declaring it as a seizure) Failure to mention why it works (or otherwise), so that further advancements can be made using the algorithm Patient specific Seizure type specific A direct comparison of results is not made due to the following reasons: Results on continuous data set can be much different from results on selected data segments. For example, one can always find pieces of data that give excellent results, whereas only a good algorithm can work on a continuous data set. Hence, in this work, an effort is made to maximize continuity in the data recordings used. The identification and classification of seizures are highly subjective to electroencephalographers. Also, no two electroencephalographers may agree with the point of onset of the same seizure.

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6 An algorithm that gives 1 false alarm per hour on a patient who has 4 seizures per hour might be better than another algorithm that produces 0.5 false alarms per hour on a patient who seizes only once a day. The definition of a hit and false alarm might be different among algorithms. Depending on the application, a quick but poor detector might be preferable over a better detector that takes longer to detect or vice versa. In some applications (say in a portable device), a simple, poor algorithm is preferable over a complex but better algorithm. Outline This thesis is organized as follows. Chapter 2 gives a brief theoretical introduction to Lyapunov Exponents and about the properties of STLmax that can be used for seizure detection. It also explains the data set on which the experiments are conducted. Chapter 3 discusses about the three methods experimented. Chapter 4 compares the results and concludes.

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CHAPTER 2 NONLINEAR DYNAMIC PREPROCESSING This chapter gives a brief introduction to Lyapunov exponents and the properties of STLmax data. It also gives the details about the data set used in this work. STLmax: Brief Introduction Lyapunov exponents (Lyapunov, 1893, Bylov et al. 1966) characterize the divergence in nearby trajectories over time in an attractor (Oseledec, 1968). For example, in , we can see that the maximum Lyapunov exponent has a value of 1.2 bits/s during the seizure. This means that if we make a mistake in locating a point in a trajectory by a margin of 1 in a million which corresponds to approximately 20 bits (1,000,000 ~ 2 20 ) then we can predict the trajectory of the point for only the next 20/1.2 ~ 16.67 seconds (Wolf et al. 1985). Figure 2-1 Since the EEG/ECoG signal is non-stationary, the Lyapunov exponents can only be computed using a time-segment of the data (Wolf et al. 1985). Though there is a spectrum of m Lyapunov exponents, m being the embedding dimension of the data, we are interested only in the largest among them. The short-term largest Lyapunov Exponent termed as STLmax has been proposed by the BRP group at the University of Florida for epileptic seizure detection & prediction (Iasemidis et al. 1990), as it characterizes the predictability/chaoticity of the data. Since, in this thesis, the transition from normal to epileptic state has been interpreted as the transition from chaotic to a more ordered state, STLmax becomes a natural choice. 7

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8 If we denote by L the estimate of the short-term largest Lyapunov exponent STLmax (Wolf et al. 1985, Iasemidis & Sackellares 1991) then L = )0()(21,,log1jijiaXtXNiatN )()()0(,jijitXtXX )()()(,ttXttXtXjiji where t i =t 0 +(i-1)t , t j =t 0 +(j-1)t, with i [1,N a ] and j [1,N] t is the evolution time for Xi,j . If the evolution time t is given in seconds, then L is in bit/sec t 0 is the initial time point of the fiducial trajectory X(t i ) is a vector of the fiducial trajectory t (X(t 0 )) where t = t 0 +(i-1)t, X(t 0 ) = [x(t 0 ),,x(t 0 +(p-1)] T , and X(t j ) is a properly chosen vector X(t i ) in the phase space X i,j (0) = X(t i )-X(t j ) is a perturbation of the fiducial orbit at t i and X i,j (t) = X(t i +t)-X(t j +t) is the evolution of X i,j (0) after time t N a is the necessary number of iterations for the convergence of the L estimate for a data segment of N points (absolute time duration T) If t is the sampling period of the time domain data, T = (N-1) t = N a t(p-1) The phase space reconstruction is done with an embedding dimension p of 7 and delay of 7 samples. The values of t and T are fixed at 20 points & 10.24 seconds respectively (Iasemidis and Sackellares 1991). STLmax values are calculated for each channel independently with a non-overlapping window of 2048 ECoG samples, which makes the time scale of each STLmax point as 10.24 seconds. Since seizures typically last from 45 seconds to 2 minutes, we can expect to see seizure activity only for 5 to 10 samples of STLmax data.

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9 Properties of STLmax The STLmax data show 3 patterns pertaining to epileptic seizures. They are as follows: 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 8 9 10 minutesSTLmax in bits/second STLmaxchannel1STLmaxchannel2STLmaxchannel3STLmaxchannel4seizure point Figure 2-1 The STLmax value during a seizure. A drop in the mean value. This can be interpreted as the state of brain, when measured by the STLmax, becoming more ordered (Iasemidis and Sackellares 1991). This can be used to detect seizures by a simple threshold mechanism. A quick rise immediately following the seizure. The mean value of the STLmax in the immediate post-ictal state is higher than that during the pre-ictal state. This can be interpreted as the seizure serving as a resetting mechanism for the brain. (Iasemidis and Sackellares 1991, Iasemidis and Sackellares 1996). This, in signal processing terms, denotes an increase in the dynamic range/variance that can be used for detection. Interlocking between different channels before a seizure (Iasemidis and Sackellares 1996). This, in signal processing terms, means that the distance (say, Euclidean or Diks) between different channels may be reducing when the ictal event is pending.

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10 Figure 2-1 shows an example seizure. However it should be noted that the STLmax does not always show such obvious characteristics for all seizures. One of the reasons is that the parameters involved in the estimation of STLmax are tuned to better represent the ictal state than the inter-ictal state. But the optimal parameter setting for different type of seizures may be different. The current set of parameters work very well for complex partial seizures evolving into secondarily generalized seizures. Hence we can expect a degradation of quality for other types of seizures. Data Set The experiments are conducted on a set of 6 patients with temporal lobe epilepsy (TLE). All the patients are immune to drugs and are candidates for brain surgery. The ECoG (ElectroCorticoGram) data is recorded from depth electrodes as shown in Figure 2-2. Each circle represents a single electrode contact. The location of depth electrodes and subdural electrodes is depicted schematically. A R and A L represent subdural electrode strips placed under the right and left orbitofrontal cortex. B R and B L are subdural strips that are placed under the inferior temporal cortex. C R and C L are mulitcontact depth electrodes inserted stereotactically in the right and left hippocampi respectively. The ECoG data from the electrodes was first digitized with a sampling frequency of 200 Hz with 10 bits of precision. It is then band pass filtered at 0.1-70 Hz and recorded into VHS tapes along with the monitoring video recording. Even in the case of implanted electrodes, data corruption can occur. For example, if the wire connecting the electrode to the recording device is loose or broken, we lose the data. The corrupted portions of the data are removed instead of being replaced with zeros. It is because zeros misrepresent the data. Of course concatenating the data also misrepresents the data as the adjoining

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11 segments may be in totally different states, though it makes the data seem continuous. For all the patients almost the entire data set is continuous. Effort is made to minimize the number of breaks in the data except when it is inevitable. Over 1000 hours of data are analyzed in this work. Figure 2-2 Placement of electrodes used to record the ECoG in the 6 patients considered in this work. The data set contains four different types of seizures (Dreifuss 1981). They are: PSG: Complex Partial evolving to Secondarily Generalized (Figure 2-3) CP: Complex Partial (Figure 2-4) SC: Sub Clinical (Figure 2-5) SP: Simple Partial (Figure 2-6)

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12 0 1 2 3 4 5 6 7 8 9 10 -6000 -4000 -2000 0 2000 4000 minutesEEG in microvolt 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 STLmax in bits/sminutes Figure 2-3 Example EEG and STLmax signatures for partial secondarily generalized Seizure 0 2 4 6 8 10 0 5 10 minutesSTLmax in bits/s 0 2 4 6 8 10 -5000 0 5000 EEG in microvoltminutes Figure 2-4 Example EEG and STLmax signatures for complex partial seizure

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13 0 2 4 6 8 10 2 4 6 8 10 minutesSTLmax in bits/s 0 2 4 6 8 10 -5000 0 5000 minutesEEG in microvolt Figure 2-5 Example EEG and STLmax signatures for subclinical seizure 0 2 4 6 8 10 0 5 10 STLmax in bits/sminutes 0 2 4 6 8 10 -5000 0 5000 10000 minutesEEG in microvolt Figure 2-6 Example EEG and STLmax signatures for simple partial seizure

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14 From Figures 2-3 to 2-6, we can see that there are commonalities (drop in STLmax) and differences for each type of seizure. Hence we can expect that the level of difficulty in detecting a seizure will vary depending on the type of the seizure. Table 2-1Table 2-1 Patient details summarizes the details for each of the six patients. The unusually high number of breaks in patient 4 is due to intermittent data corruption at the end of recording. Length of STLmax data # of seizures Type Patient # Patient ID Sex Age # of channels Samples Hours # of breaks CP PSG SC SP Total 1 P063 F 41 30 74471 ~211 2 19 3 1 0 23 2 P117 M 29 28 51231 ~146 0 8 0 10 1 19 3 P161 F 38 32 7929 ~22 0 8 0 0 0 8 4 P062 M 60 28 100940 ~287 154 0 7 0 0 7 5 P028 F 45 26 30480 ~87 4 3 0 6 0 9 6 P097 M 19 28 112785 ~321 6 2 8 7 0 17 Total 377836 ~1075 166+5 40 18 24 1 83 The data from patient 1 was used as the training set and data from patients 2-6 was used as the test set. Table 2-2 describes distribution of the data set among training and test sets Table 2-2 Distribution of data among training and testing sets Training set Test set # of samples % of data set # of samples % of data set Data length 74471 19.7 303365 80.29 # of seizures 23 27.7 60 72.3

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CHAPTER 3 DETECTION METHODS Brief Introduction to Event Detection and Hypothesis Testing Event Detection Event detection can be defined as detection of an event of interest buried under noise (Van Trees 2001). It differs from event classification because in classification, we know what we are looking for and what all the other alternatives are. For example, if we need a device that looks into a coin and tells whether it is showing “Heads” or “Tails” irrespective of the orientation of the coin, then we are posed with a classification problem. But if we need a device that tells whether or not there is a coin present in the view, then it is a detection problem. Some examples of detection problem include: searching for a submarine with passive sonar identifying/listening to a voice in a cocktail party searching for forest fire in satellite images Hypothesis Testing Bayes criterion A Bayes test (Bayes, 1763) is based on two assumptions. They are: The source outputs are governed by probability assignments, which are denoted by P 0 and P 1 respectively, and called a-priori probabilities. A cost is assigned to each possible course of action. The problem of characterizing EEG/STLmax as background and seizure can be formulated as a binary hypothesis testing. If we denote the hypothesis H 1 for a seizure 15

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16 activity, then we can denote the absence of it by hypothesis H 0 . Let P 0 and P 1 denote the a-priori probabilities of H 0 and H 1 respectively. Table 3-1 Cost of decision Table 3-1 Actual event H 0 H 1 Detected event Cost Probability of occurrence Cost Probability of occurrence H 0 C 00 P 00 C 01 P 01 H 1 C 10 P 10 C 11 P 11 shows the cost associated with each type of decision. C 01 denotes the cost of missing a seizure and C 10 denotes that of a false alarm. The total cost of this decision mechanism is given as: C= C 00 P 00 P 0 + C 01 P 01 P 1 + C 10 P 10 P 0 + C 11 P 11 P 1 If we assume that there is no cost for making correct decisions, then C 00 and C 11 will be zero. If the a-priori probabilities of H 0 and H 1 and costs of missing a seizure and raising a false alarm are known, minimizing the value of C is straightforward. But when they are unknown, as in this case, a method known as Neyman-Pearson criterion (Neyman and Pearson 1933) can be used to implement the decision. Neyman-Pearson criterion In many practical applications, the costs of decisions and/or the a-priori probabilities are not known. For example, in our application, the cost of missing a seizure depends on whether it is being used in an automated drug delivery or just to operate a recording device to record seizures. Assuming that there is no cost associated with correct decisions, we will have C 00 and C 11 to be zero. Under such circumstances, the user can determine a false alarm probability P 10 he/she can afford and try to find a detector that

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17 gives the best detection probability 1-P 01 . According to Neyman-Pearson criterion, one can still make optimal decisions by working only with the probabilities of detection and the false alarms (Helstrom 1968). To apply this criterion when the decision is based on the outcome of a single measurement of some quantity r (we will see in chapter 4 that this quantity is a threshold to declare seizures), the results of the detection scheme are presented in the form of a monotonically increasing function, plotting the false alarm probability against the probability of detection. The user selects simply the operating point on this curve, which provides the best probability of detection for a given (user selected) false alarm rate. Receiver Operating Characteristic (ROC) This term is borrowed from the field of radar communications. For example, in detecting an enemy missile it represents the trade-off between missing an incoming missile and raising a false alarm. We can use the same analogy to represent missing a seizure and raising a false alarm. Since in our application (continuous EEG monitoring), the rate at which false alarms occur is more relevant than its probability, the results are shown as the trade-off between the average number of false alarms per hour to the number of seizures detected. Detection Methods Method 1: Subset of STLmax and Threshold Since we have multiple channels of STLmax data, there are number of possible combinations. For example, the detection mechanism can operate on a subset of the data, or it can be done in each of the channels independently with a voting scheme. Figure 3-1 shows the collective behavior of different STLmax channels during a seizure.

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18 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 8 9 10 minutesSTLmax in bits/second Figure 3-1 Multi-channel STLmax data during a seizure From Figure 3-1, we can see that for this seizure almost all the channels converge and have a low value during a seizure. This can be interpreted as a drop in the minimum STLmax among the channels (Figure 3-2) a drop in the average STLmax among the channels (Figure 3-3) a drop in the maximum STLmax among the channels (Figure 3-4) a drop in the variance among the channels (Figure 3-5)

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19 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 minutesSTLmax in bits/sinstantaneous spatial minimum Figure 3-2 Minimum among STLmax channels 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 8 Average STLmaxminutesSTLmax in bits/second Figure 3-3 Average among STLmax channels

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20 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 8 9 10 Maximum STLmaxSTLmax in bits/secondminutes Figure 3-4 Maximum among STLmax channels 7970 7975 7980 7985 7990 7995 8000 8005 0 0.5 1 1.5 2 2.5 minutesSTLmax in bits/sinstantaneous spatial variance Figure 3-5 Variance among STLmax channels

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21 7970 7975 7980 7985 7990 7995 8000 8005 0 5 10 7970 7975 7980 7985 7990 7995 8000 8005 0 5 10 7970 7975 7980 7985 7990 7995 8000 8005 0 5 10 7970 7975 7980 7985 7990 7995 8000 8005 0 5 10 Figure 3-6 STLmax channels shown independently Figure 3-6 shows that the detection mechanism can also operate on the individual channels independently and a voting can decide on the final outcome. Our hypothesis is that, for a seizure to happen, there might be a critical mass of brain areas, which have to display a drop in STLmax.

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22 Method 2: STLmax and Entropy Brief introduction to entropy We know that Renyi’s entropy of order is denoted as (Renyi 1960), 1,0)(ln11)(dxxfxH where, is the p.d.f. of the continuous random variable x. f for the case of quadratic entropy (=2), we get dxxfxH)(ln)(22 We can compute this entropy non-parametrically using Parzen window method (Parzen 1962) with a Gaussian kernel. The multidimensional Gaussian kernel is denoted as ))()(21exp()2(1)(12/12/TkxxxG where is the covariance matrix. Using this method, the p.d.f. of the data can be estimated as (Principe et al. 2000), NiiXxxGNxf12),(1)( Simplifying, we get NiNjjixxGNxH11222)2,(1ln)( and the information potential NiNjjixxGNxV1122)2,(1)(

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23 In our case, since we are computing temporal entropy for each channel of STLmax data individually, our data is one-dimensional. Using recursive estimates, we get nLnininnxxGLVV111)()1( We can also vary the kernel size adaptively according to the data using the recursive sample variance estimator (x) n+1 =(1-) (x) n +x n 2 = 1 , where is a normalizing constant. Brief introduction to variance We know that the variance of a random variable x is given by, ]])[[(22xExE where E is the expectation operator. If the distribution of x is unknown, then we can estimate the variance from its samples. The most common unbiased estimator for variance is given by: 2112)1(11LjiLiixLxL , i=1 L If x is a non-stationary time signal, we can estimate the variance using a recursive estimator as follows: 211221)1(11)1(LjiLiinnxLxL , L1

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24 where is a forgetting factor and L is the number of samples in the window corresponding to the region of stationarity. The instantaneous recursive estimator for variance corresponding to L=1 is given by, 2221))(1(nnnnx , L=1 where, nnnx)1(1 is the recursive estimate for mean of x. Estimation of parameters Estimation of The value of is chosen such that the recursive estimates for average and 1 show a significant change during seizure (7987 th minute), while being as smooth as possible during non-seizure state. 7980 8000 8020 8040 0 5 10 lambda=0.01 7980 8000 8020 8040 0 5 10 lambda=0.02 7980 8000 8020 8040 0 5 10 lambda=0.05 7980 8000 8020 8040 0 5 10 lambda=0.1 7980 8000 8020 8040 0 5 10 lambda=0.2 7980 8000 8020 8040 0 5 10 lambda=0.5 Figure 3-7 Searching for optimal

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25 From Figure 3-7, we can see that the values of <0.02 prove to be too less, as the variance becomes too smooth to track changes in the signal. However, on the other side, values equal to and above 0.1 prove to be too high as they make the variance too sensitive to abrupt changes in the input signal. Performing a finer search in the range of 0.03 to 0.1 (corresponding to a memory range of 10-30 samples for the gamma integrator), we can see from Figure 3-8 that values in the range from 1/15 to 1/25 do not affect the final result much. Therefore, we can choose =1/15 as a compromise. 7960 7980 8000 8020 8040 0 2 4 6 8 10 1/lambda=10 7960 7980 8000 8020 8040 0 2 4 6 8 10 1/lambda=15 7960 7980 8000 8020 8040 0 2 4 6 8 10 1/lambda=20 7960 7980 8000 8020 8040 0 2 4 6 8 10 1/lambda=25 Figure 3-8 Searching for optimal

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26 Estimation of 1 & L Figure 3-9 shows the histogram of 30 channel STLmax data from patient #1. From this we can see that it is approximately Gaussian with mean around 4 and standard deviation around 2. Note that the Gaussian shape comes from the fact that the data is non-stationary and a long data record is used to compute the histogram. Therefore, by the central limit theorem, the histogram approaches Gaussian shape. We know that the value of roughly corresponds to the standard deviation of the input data. Hence we can guess that it should be around 2. Since the value of 1 varies in the range of 0.5-3.5, we can expect the value of 0 to be around 2. -2 0 2 4 6 8 10 12 14 16 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 Figure 3-9 Histogram of STLmax data

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27 7970 7980 7990 8000 8010 8020 1.5 2 2.5 T=2 7970 7980 7990 8000 8010 8020 1 1.5 2 T=10 7970 7980 7990 8000 8010 8020 1 1.5 2 T=30 7970 7980 7990 8000 8010 8020 1 1.5 2 T=60 7970 7980 7990 8000 8010 8020 1 1.5 2 T=90 7970 7980 7990 8000 8010 8020 1 1.5 2 T=180 Figure 3-10 Entropy as a function of L Figure 3-10 shows the entropy as a function of L with 0 =2 and =1/15. Here, we can see that values of L from 30 and above prove to be good. Therefore a value of L=60 (corresponding to 10 minutes of STLmax data) is chosen. We can confirm the choice of 0 by experimenting the values of 0 with=1/15 and L=60. 7960 7980 8000 8020 8040 8060 1 1.5 2 2.5 sigma=0.5 7960 7980 8000 8020 8040 8060 1.2 1.4 1.6 1.8 2 sigma=1 7960 7980 8000 8020 8040 8060 1.2 1.4 1.6 1.8 2 sigma=2 7960 7980 8000 8020 8040 8060 1.4 1.6 1.8 2 2.2 sigma=5 7960 7980 8000 8020 8040 8060 1.8 2 2.2 2.4 2.6 sigma=10 7960 7980 8000 8020 8040 8060 2 2.2 2.4 2.6 2.8 sigma=20 Figure 3-11 Entropy as a function of 0

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28 We can see that justifies the choice of 0 =2. Therefore the experiments are conducted using parameters 0 =2, =1/15 and L=60 for entropy. We can see from that increasing the value of L makes the variance estimate smoother. But it also delays the response of the system significantly due to the averaging. For comparison purposes, the same L (60) and values found for entropy are used to estimate the variance. Figure 3-11 Figure 3-12 Figure 3-12 Variance as a function of L 7970 7975 7980 7985 7990 7995 8000 8005 0 1 2 3 variance of STLmaxL=60 (10 minutes)minutes 7970 7975 7980 7985 7990 7995 8000 8005 0 1 2 3 variance of STLmaxL=1

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29 Experiment 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 8 9 10 minutesSTLmax in bits/second STLmaxchannel1STLmaxchannel2STLmaxchannel3STLmaxchannel4seizure point Figure 3-13 STLmax values during a seizure We can see in Figure 3-13 that there is a shift in the mean during a seizure (at 133.15 hours). We would like to have a signal that varies little during the background state and shows a nice change when the signal goes into epileptic state. One such measure is entropy. We can use entropy in two different ways, As a criterion to choose a subset of STLmax values. Our hypothesis is that a subset of electrodes (say 5) that have the least variability during background state, and show the shift in mean during the seizure should be able to detect seizures better than the average of all electrodes. So we choose 5 electrodes that have the least entropy at the point of interest during background state and average the STLmax values of those 5 electrodes. Unfortunately, our results do not support our hypothesis and hence will not be reported here.

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30 As a time-series to detect the seizures. Our hypothesis is that a measure of variability can capture the large variations in amplitude in the vicinity of a seizure (i.e., the drop during the transition from pre-ictal to ictal and the quick rise during the transition from ictal to post-ictal). We can use a simpler measure like variance also to perform the same function. The following figures support this argument by showing a marked increase in the entropy and variance during a seizure. The delay between the seizure onset and the peak of the entropy (or variance) is due to the memory involved in the calculation of entropy. 7970 7975 7980 7985 7990 7995 8000 8005 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 minutesentropy of STLmax Figure 3-14 Entropy of STLmax channels during a seizure 7970 7975 7980 7985 7990 7995 8000 8005 0 0.5 1 1.5 2 2.5 3 3.5 minutesvariance Figure 3-15 Variance of STLmax channels during a seizure

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31 From Figure 3-14 and Figure 3-15, we can see that almost all the channels converge for entropy and diverge for variance and have a high value during a seizure. This can be interpreted as An increase in the instantaneous minimum among the channels (Figure 3-16) An increase in the instantaneous average among the channels (Figure 3-17) An increase in the instantaneous maximum among the channels (Figure 3-18) A decrease/increase in the instantaneous variance among the channels (). This on entropy does not show any particular characteristics during a seizure. The results in both the training and test sets also indicate that this is a poor choice. However, this measure on variance shows a considerable increase during seizures that can be used for detection Figure 3-19 An increase in variability shown by a critical mass of brain areas () Figure 3-20 7970 7975 7980 7985 7990 7995 8000 8005 0 1 2 varianceminutes 7970 7975 7980 7985 7990 7995 8000 8005 2 2.5 3 3.5 entropyinstantaneous spatial minimum Figure 3-16 Spatial minima for entropy and variance of STLmax channels during a seizure

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32 7970 7975 7980 7985 7990 7995 8000 8005 2 2.5 3 3.5 entropyinstantaneous spatial average 7970 7975 7980 7985 7990 7995 8000 8005 0 1 2 3 varianceminutes Figure 3-17 Spatial average for entropy and variance of STLmax channels during a seizure 7970 7975 7980 7985 7990 7995 8000 8005 0 2 4 varianceminutes 7970 7975 7980 7985 7990 7995 8000 8005 2.5 3 3.5 entropyinstantaneous spatial maximum Figure 3-18 Spatial maxima for entropy and variance of STLmax channels during a seizure

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33 7970 7975 7980 7985 7990 7995 8000 8005 0 0.01 0.02 0.03 0.04 entropyinstantaneous spatial variance 7970 7975 7980 7985 7990 7995 8000 8005 0 0.1 0.2 0.3 0.4 minutesvariance Figure 3-19 Spatial variance among entropy and variance of STLmax channels during a seizure 7970 7975 7980 7985 7990 7995 8000 8005 2 3 4 multiple electrodes showing seizure patterns entropy 7970 7975 7980 7985 7990 7995 8000 8005 2 3 4 entropy 7970 7975 7980 7985 7990 7995 8000 8005 0 2 4 variance 7970 7975 7980 7985 7990 7995 8000 8005 0 2 4 minutes variance Figure 3-20 Variance and Entropy of STLmax channels shown independently From Figure 3-14 to Figure 3-20, we can see that both variance and entropy behave similarly.

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34 Method 3: Entrainment in STLmax and Seizure Detection Brief introduction: Diks test and Diks distance In simple words, Diks test (Diks et al. 1996) measures the Euclidean distance between two multidimensional probability distributions constructed from the delay vectors normalized by its variance. Consider the case of N 1 vectors { iX }i ( 11N X =[x(n), x(n-), x(n-2),,x(n-(m-1)]), with probability distribution iX ), and N 2 vectors {Y i }i, with probability distribution 21N Y). Realizations of these vectors are denoted by their lowercase analogs. The smoothed versions of the multidimensional distributions i k ') are constructed as k '( r ) = d s k '( s )( r , s ) for k {1,2}, where ( r ,) is the Gaussian kernel defined as, s ( r , s ) = ( 2 d ) -m e | r s |/(2d) 2 2 , where d>0 functions as bandwidth to the system. An unbiased estimator )('1r of ' r ) is )('1r = ),(1111iNixrN since the expected value of ( r , s ) is, d iX iX )( r , iX ) = ' r ) We know that the square of the Euclidean distance between the distributions can be given as, Q= (2d ) m d r [' r )-' r )] 2

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35 More details about the properties of the measure can be obtained from Diks et al. (1996). It is claimed that the above distance becomes zero if and only if the two distributions are identical. By determining whether a consistent estimator of Q is significantly above zero we can test the null hypothesis against all alternatives . To find an unbiased estimate for Q it is convenient to rewrite the equation for Q as Q Q = Q 11 +Q 22 -2Q 12 where, Q kl = (2d ) m d r ' k r )' l r ) By defining, h ( s ,t )=e | s -t |/(4d), 2 2 we get the estimate as Q = 11211NjiN h(,) + iX jX 21221NjiN h(Y i ,Y j ) 2111212NjNiNN h(, iX jY ) the variance V c (Q) of Q under the null hypothesis and conditionally on the set of N 1 +N 2 observed vectors is a function of N 1 , N 2 and the set of N 1 +N 2 vectors. If N= N 1 +N 2 and iz =. Nifor NyNifor xNii11.......1......................1 then the variance under the null hypothesis conditionally on Niiz1} is, V c () = Q 212211221)3)(1()1()2()1(2ijNjiNNNNNNNN

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36 in which, jiijggHij where, ),(21),(1jiNjijizzhNzzhHij and ijijjiHNg21 the quantity S is defined by, )(QVQSc is a random variable with zero mean and unit standard deviation under the null hypothesis. Diks test requires that the value of S to be computed for several possible combinations of N 1 and N 2 using Monte Carlo simulations. A decision is made about whether the two given probability distributions are close to each other or not by observing the number of times S takes a value less than 3. In this work, since Monte Carlo simulations are not viable for a practical real-time seizure detector, the value of Q and its variance are calculated only once using the class labels. Also, the result obtained using this method is used as another signal instead of declaring whether the signals are close to each other or not. Hence we call it as Diks distance rather than Diks test.

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37 Estimation of parameters Estimation of embedding parameters Using the same argument as the one used in the estimation of STLmax (Iasemidis and Sackellares 1991), the product (m-1) should be equal to the first minimum of the autocorrelation function. Therefore, first the autocorrelation of a 12 minute data-segment containing a seizure in the training set (seizure #1) is found. The data-segment used for computing the autocorrelation is given in and its autocorrelation is given in Figure 3-21 Figure 3-21 STLmax data during a seizure Figure 3-22 0 2 4 6 8 10 12 1 2 3 4 5 6 7 8 9 10 minutesSTLmax in bits/second

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38 -80 -60 -40 -20 0 20 40 60 80 0 500 1000 1500 2000 2500 lagautocorrelation Figure 3-22 Autocorrelation of STLmax data during a seizure We can find the first minimum of the autocorrelation using the zero crossing of its first difference which, in this case, is found to be at lag=34. Therefore, we can predict that the product (m-1) will be around 34. Next, the embedding dimension m is found using false nearest neighbors method (Kennel, Brown and Abarbanel 1992) on the same data segment. The values of are iterated from 2 to 10. We know that the Euclidian distance between X i and its neighbor X j is 1022)]()([),(mkjidknxknxrnR . Also, we know that the two criteria for declaring a neighbor as a false neighbor are: 11),()()(todjiRrnRknxknxr

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39 112)(toAdARnRr where, 212])([1NnAxnxNR NnnxNx1)(1 The values R to1 and A to1 are found as follows: 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 tour1max. and min. values of r1 for tou=2 to 10 Figure 3-23 Values of r 1 for = 2 to 10. From Figure 3-23, we can see that the values of r 1 range from 0 to 60. However, for some values of , the maximum value r 1 crosses is less than 10. Therefore, the value of R to1 must be less than 10.

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40 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 tour1max.(<10) and min. values of r1 for tou=2 to 10 Figure 3-24 Zoomed version of values of r 1 for = 2 to 10. 2 3 4 5 6 7 8 9 10 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 tour2max. and min. values of r2 for tou=2 to 10 Figure 3-25 Values of r 2 for = 2 to 10.

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41 Taking a closer look, we can see from Figure 3-24 that the maximum R to1 can take is less than 7. Therefore, R to1 =2 is chosen to be a good compromise. From Figure 3-25, we can see that the range of r 2 is from 1 to 3 for varying values of and m. Therefore, the value of A to1 must be less than 3 and greater than 1. Using the same argument as R to1 , a value of A to1 = 2 gives a good compromise. Finally, the pairs of m and that approximate the product (m-1) of 34 are searched for. It is found that the pairs (m,) = (5,9), (6,7), (7,6), (8,5) all serve the purpose. Since the pairs (6,7) and (8,5) give a product closer to 34 than the other two, they get the first preference. Since (6,7) uses lesser embedding dimension compared to the other choice, it is preferred as it reduces computational complexity in the algorithms being used. The phase space reconstruction is done using = 7 and m = 6 and signal segments of 60 samples (corresponding to 10 minutes duration). Equal lengths of data are used to find the pair-wise Diks distance. N 1 and N 2 hence become 25 (60-(6-1)*7). Estimation of Kernel Bandwidth d The value of d corresponds to the standard deviation of the data. Using the results from the estimation of 0 in the calculation of entropy and Figure 3-9, we can guess that the approximate range of d would be 2. The values of d are iterated from 0.0001 to 100 and the range 0.1 to 5 is found to give similar results. Therefore, to make calculations easier, the value is chosen to be equal to 1.

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42 Experiment 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 8 9 10 minutesSTLmax in bits/second STLmaxchannel1STLmaxchannel2STLmaxchannel3STLmaxchannel4seizure point Figure 3-26 STLmax values during a seizure From Figure 3-26, we can see that the STLmax values get more and more entrained (Iasemidis and Sackellares 1991) as it approaches the seizure. This entrainment can be captured by a pair-wise distance measure. Since the STLmax data is nonlinear and non-stationary, Diks test can be used to measure the closeness between different channels. 7970 7980 7990 8000 8010 8020 8030 -15 -10 -5 0 5 10 15 20 25 30 35 minutesDiks distances Figure 3-27 Diks distances during a seizure

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43 From Figure 3-27, we can see that almost all the channels converge and have a low value during a seizure. This can be interpreted as a decrease in the minimum among channels () Figure 3-28 Figure 3-28 Minimum among pair-wise Diks distance between STLmax channels during a seizure a decrease in the average among channels (Figure 3-29) a decrease in the maximum among channels () Figure 3-30 a decrease in the dynamic range (or variance) among the channels() Figure 3-31 a minimum number of channels showing a decrease in value corresponding to a critical mass of entrained electrodes during a seizure. This can be captured using a voting scheme among channels () Figure 3-32 7970 7975 7980 7985 7990 7995 8000 8005 -15 -14 -13 -12 -11 -10 -9 -8 minutesDiks distanceinstantaneous spatial minimum

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44 7970 7975 7980 7985 7990 7995 8000 8005 -10 -5 0 5 10 minutesDiks distanceinstantaneous spatial average Figure 3-29 Average among pair-wise Diks distance between STLmax channels during a seizure 7970 7975 7980 7985 7990 7995 8000 8005 0 5 10 15 20 25 30 minutesDiks distanceinstantaneous spatial maximum Figure 3-30 Maximum among pair-wise Diks distance between STLmax channels during a seizure

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45 7970 7975 7980 7985 7990 7995 8000 8005 0 50 100 150 200 minutesDiks distanceinstantaneous spatial variance Figure 3-31 Variance among pair-wise Diks distance between STLmax channels during a seizure 7970 7975 7980 7985 7990 7995 8000 8005 -10 0 10 20 30 multiple electrodes showing seizure patterns 7970 7975 7980 7985 7990 7995 8000 8005 -10 0 10 20 30 7970 7975 7980 7985 7990 7995 8000 8005 -10 0 10 20 30 minutes Figure 3-32 Diks distance between STLmax channels shown independently

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CHAPTER 4 RESULTS AND CONCLUSION Results and Discussion Definitions and Trade-offs In this chapter, first the results on the training set are discussed. In order to compare different methods, the following criteria are used: percentage of seizures detected, number of false alarms per hour, maximum amount of delay between the seizure onset and the instant the algorithm declares it as a seizure. For example, in , if the alarm begins at the instant at which the signal reaches its minimum (at 7994 th minute), then we can see that there is approximately a 7 minutes delay involved in the procedure. Figure 4-1 Figure 4-1 Figure showing the delay between the instant of the actual event to the instant of the alarm resolution of the algorithm. 7970 7975 7980 7985 7990 7995 8000 8005 0 5 10 15 20 25 30 minutesinstantaneous maximum among Diks distances 46

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47 The following definitions are used to determine the above criteria: Hit: The alarm turns ON within the maximum allowed delay from the seizure onset. False alarm: Any alarm that does not belong to the above category. Alarm Clustering 7970 7975 7980 7985 7990 7995 8000 8005 1 2 3 4 5 6 7 minutesSTLmax in bits/second Figure 4-2 Subset of STLmax. From Figure 4-2, we can see that this particular threshold produces two alarms for the same seizure. This situation occurs due to our definition of a hit and a false alarm. We can avoid such situation and reduce the number of false alarms drastically by clustering such alarms. In the data set under study, the shortest interval between successive seizures is just above 18 minutes. Therefore all alarms that occur within a span of 18 minutes can

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48 be clustered into one without having to fear about one alarm representing more than a seizure. This corresponds to the resolution of the algorithm i.e., the minimum amount of time the algorithm requires between seizures to identify them separately. In this work, a conservative estimate of 15 minutes is used. Also if an alarm lasts for more than 15 minutes, it is reset after 15 minutes and counted as more than one alarm. However, it is noted that only 2 out of the 83 seizures has a neighbor that is closer than 30 minutes. Therefore, a more lenient algorithm can choose a resolution of 25 minutes thereby reducing the false alarm rate by as much as 40%. Results on the Training Set Experiments are conducted for delays of 1 to 15 minutes with the constraint that the false alarm rate should be less than or equal to 1 per hour. Since the accuracy of each method depends on the time for their parameters to stabilize, as seen in , the following section discusses the ROCs for delay values of 1, 5 and 10 minutes. Since the voting scheme has one more criterion to trade off (i.e., the number of votes necessary), it is shown separately. Figure 4-1 Figures 7.2 to 7.4 show the ROCs for all the experiments except the voting schemes. Figures 7.5 to 7.7 show the ROCs of STLmax, Diks distance, entropy and variance for delays of 1, 5 and 10 minutes respectively. The figures shown in this section are not the complete ROCs. Only the best results for each of the signals (STLmax, Diks distance, entropy and variance) for each false alarm rate are shown to improve visibility of the plots. To make the comparison easier, the axes are set to show detection rates from 50% to 100% and the false alarm rates from 0.1/h to 1/h. Table 4-1 describes the mnemonics used in the plot.

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49 Table 4-1 Table of mnemonics Subset Signal Minimum Average Maximum Variance STLmax minlmax meanlmax maxlmax lmaxvar Diks mindiks meandiks maxdiks diksvar Entropy minent meanent maxent entvar Variance minvar meanvar maxvar varvar 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 55 60 65 70 75 80 85 90 95 100 Comparison of ROCs with alarm duration=15 min., and max.delay=1# of false alarms / hour% of hits minlmaxmeanlmaxmaxlmaxlmaxvarmindiksmeandiksmaxdiksdiksvarminentmeanentmaxententvarminvarmeanvarmaxvarvarvar Figure 4-3 ROC for a maximum allowable delay of 1 minute on the training set. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 50 60 70 80 90 100 Comparison of ROCs with alarm duration=15 min., and max.delay=5# of false alarms / hour% of hits minlmaxmeanlmaxmaxlmaxlmaxvarmindiksmeandiksmaxdiksdiksvarminentmeanentmaxententvarminvarmeanvarmaxvarvarvar Figure 4-4 ROC for a maximum allowable delay of 5 minutes on the training set.

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50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 50 60 70 80 90 100 Comparison of ROCs with alarm duration=15 min., and max.delay=10# of false alarms / hour% of hits minlmaxmeanlmaxmaxlmaxlmaxvarmindiksmeandiksmaxdiksdiksvarminentmeanentmaxententvarminvarmeanvarmaxvarvarvar Figure 4-5 ROC for a maximum allowable delay of 10 minutes on the training set. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 60 70 80 90 100 Comparison of ROCs with max.delay=1min. on training set# of false alarms / hou r % of hits STLmaxDiksentropyvariance Figure 4-6 ROCs of voting schemes for a maximum allowable delay of 1 minute on the training set.

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51 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 60 70 80 90 100 Comparison of ROCs with max.delay=5min. on training set# of false alarms / hour% of hits STLmaxDiksentropyvariance Figure 4-7 ROCs of voting schemes for a maximum allowable delay of 5 minutes on the training set. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 60 70 80 90 100 Comparison of ROCs with max.delay=10min. on training set# of false alarms / hou r % of hits STLmaxDiksentropyvariance Figure 4-8 ROCs of voting schemes for a maximum allowable delay of 10 minutes on the training set. From Figures 4-3 to 4-8, we can see that using STLmax directly for detection outperforms all other methods when we have a restriction on the maximum delay. It is mainly due to the inherent delay present in the computation of Diks distance, variance

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52 and entropy. Therefore, if the application requires a quick detector at the expense of performance, the recommended solution would be a subset of STLmax. Also, we can see that STLmax outperforms any other method for high detection rates. This is expected as the training set consists maximally of complex partial seizures, which show visible characteristic patterns in STLmax during seizures. However, if the false alarm requirements are stringent (say less than 0.2/h), then Diks distance, entropy or variance can be used. Results on the Test Set 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 55 60 65 70 75 80 85 90 95 100 Comparison of ROCs with alarm duration=15 min., and max.delay=1# of false alarms / hour% of hits minlmaxmeanlmaxmaxlmaxlmaxvarmindiksmeandiksmaxdiksdiksvarminentmeanentmaxententvarminvarmeanvarmaxvarvarvar Figure 4-9 ROC for a maximum allowable delay of 1 minute on the test set.

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53 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 50 55 60 65 70 75 80 85 90 95 100 Comparison of ROCs with alarm duration=15 min., and max.delay=5# of false alarms / hour% of hits minlmaxmeanlmaxmaxlmaxlmaxvarmindiksmeandiksmaxdiksdiksvarminentmeanentmaxententvarminvarmeanvarmaxvarvarvar Figure 4-10 ROC for a maximum allowable delay of 5 minutes on the test set. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 50 55 60 65 70 75 80 85 90 95 100 Comparison of ROCs with alarm duration=15 min., and max.delay=10# of false alarms / hour% of hits minlmaxmeanlmaxmaxlmaxlmaxvarmindiksmeandiksmaxdiksdiksvarminentmeanentmaxententvarminvarmeanvarmaxvarvarvar Figure 4-11 ROC for a maximum allowable delay of 10 minutes on the test set.

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54 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 60 70 80 90 100 Comparison of ROCs with max.delay=1min. on test set# of false alarms / hou r % of hits STLmaxDiksentropyvariance Figure 4-12 ROCs of voting schemes for a maximum allowable delay of 1 minute on the test set 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 60 70 80 90 100 Comparison of ROCs with max.delay=5min. on test set# of false alarms / hou r % of hits STLmaxDiksentropyvariance Figure 4-13 ROCs of voting schemes for a maximum allowable delay of 5 minutes on the test set

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55 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 60 70 80 90 100 Comparison of ROCs with max.delay=10min. on test set# of false alarms / hour% of hits STLmaxDiksentropyvariance Figure 4-14 ROCs of voting schemes for a maximum allowable delay of 10 minutes on the test set From Figures 4-9 to 4-11, we can see that STLmax works better for quick detectors. Otherwise, variance and entropy outperform other methods in most of the cases. From Figures 4-12 to 4-14, we can see that the voting schemes perform a little poorer than their counterparts (around 2-5% lesser detection rate for the same false alarm rate). The main reason is that though there might be a critical mass mechanism operating during seizures, the amount of brain involved may be different from seizure to seizure. Also, different types of seizures may require different number of votes for detection. Therefore, voting schemes may be effective only when the patient is known to have a particular type of seizure.

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56 Case studies: Best Performance on the Test Set Case 1: Quick Detector: STLmax From Figures 4.9 to 4.14, we can see that the subsets of STLmax (average & minimum) perform better than others for quick detectors (delay less than a minute). Therefore, it is studied (spatial minimum) in detail with the following parameters/constraints: Maximum delay allowed = 1 minute Maximum false alarm rate =1/h 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 10 20 30 40 50 60 70 80 90 100 # of false alarms / hour% of hitsROC for different seizure types using min STLmax with max. delay = 1 min. SCSPPSGCPtotal Figure 4-15 ROCs of different seizure types using minimum STLmax with maximum delay = 1 minute. From Figure 4-15, we can see that for this method, complex partials with or without evolving to secondarily generalized ones are more detectable than sub-clinical and simple partial seizures.

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57 Case 2: Slow Detector: Variance with L=60 From Figures 4.9 to 4.14, we can see that the subsets of variance (spatial variance among channels) perform better than others for slow detectors (delay less than 10 minutes). Therefore, we study in detail the following parameters/constraints: Maximum delay allowed = 10 minutes Maximum false alarm rate =1/h 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 55 60 65 70 75 80 85 90 95 100 # of false alarms/ hour% of hitsROC for different seizure types using variance of STLmax with max. delay=10 min SCSPPSGCPtotal Figure 4-16 ROCs of different seizure types using spatial variance of time variance of STLmax channels with maximum delay = 10 minutes. From Figure 4-16, we can see that the method performs well regardless of the seizure type. However, even in this case, we can see that clinical seizures are more detectable compared to sub clinical seizures (5-10% higher detection rates for the same false alarm rate).

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58 Case 3: Slow Detector: Variance with L=1 We observed that even for the case of L=1, the subsets of variance (spatial variance among channels) perform better than others for slow detectors (delay less than 10 minutes). Therefore, here we study in detail the following parameters/constraints: Maximum delay allowed = 10 minutes Maximum false alarm rate =1/h 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 50 55 60 65 70 75 80 85 90 95 100 # of false alarms / hour% of hits SCSPPSGCPtotal Figure 4-17 ROCs of different seizure types using spatial variance of time variance of STLmax channels with maximum delay = 10 minutes. From Figure 4-17, we can see that the method performs well regardless of the seizure type. However, even in this case, we can see that clinical seizures are more detectable compared to sub clinical seizures (2-5% higher detection rates for same false alarm rates). Also, we can observe that L=1 case performs a little better than L=60 case (~5% higher detection rates for same false alarm rates).

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59 Conclusion and Directions for Future Work In this work, three different methods were studied in their increasing order of complexity. The results are summarized in Table 4-2. Table 4-2 Best detection rates on test set for false alarm rate < 1/h (ordered by result) Delay 1 5 10 Min. STLmax (62%) Var. Variance (95%) Var. Variance (97%) Min. Diks (56%) Max. Entropy (88%) Max. Entropy (93%) Ave. STLmax (55%) Ave. Variance (83%) Ave. Variance (92%) Ave. Entropy (50%) Max. Variance (80%) Max. Variance (88%) Max. STLmax (48%) Min. Diks (80%) Ave. Entropy (83%) Max. Entropy (45%) Ave. Entropy (80%) Min. Diks (80%) Var. STLmax (43%) Min. STLmax (71%) Max. Diks (77%) Var. Variance (43%) Max. Diks (70%) Var. Diks (75%) Ave. Diks (40%) Min. Variance (70%) Min. STLmax (73%) Ave. Variance (40%) Min. Entropy (70%) Var. Entropy (71%) Max. Variance (38%) Var. Diks (68%) Min. Variance (70%) Var. Entropy (38%) Ave. Diks (65%) Min. Entropy (65%) Min. Entropy (38%) Ave. STLmax (63%) Ave. Diks (65%) Max. Diks (37%) Var. Entropy (58%) Ave. STLmax (63%) Var. Diks (37%) Max. STLmax (50%) Max. STLmax (50%) Min. Variance (30%) Var. STLmax (43%) Var. STLmax (43%) For quick detection, STLmax performed better than the others. This is expected due to the inherent delay in the computation of variance, entropy and Diks distance. Also, subsets STLmax performed better than others in the case of complex partial seizures and secondarily generalized seizures. Variance and Entropy gave a good generalization for all types of seizures under study. Due to the simplicity of the computation, variance is ideally suited for real time implementation. One of the reasons for the poor performance of Diks distance may be due to the number of parameters involved in the computation. The parameters found using the training set may not be the optimal for the test set. Also, the use of Diks distance is based on the assumption of entrainment between electrodes. This assumption may not be true for all types of seizures.

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60 Table 4-3 Best detection rates on test set for false alarm rate < 1/h (ordered by method) Delay (minutes) Signal Subset 1 5 10 Spatial minimum 62% 71% 73% Spatial average 55% 63% 63% Spatial maximum 48% 50% 50% STLmax Spatial variance 43% 43% 43% Spatial minimum 56% 80% 80% Spatial average 40% 65% 65% Spatial maximum 37% 70% 77% Diks distance Spatial variance 37% 68% 75% Spatial minimum 38% 70% 65% Spatial average 50% 80% 83% Spatial maximum 45% 88% 93% Entropy Spatial variance 38% 58% 71% Spatial minimum 30% 70% 70% Spatial average 40% 83% 92% Spatial maximum 38% 80% 88% Variance Spatial variance 43% 95% 97% We do not claim our methods to be superior or inferior to other methods due to the reasons mentioned in Chapter 2. But we provide the reader with options that can be customized to suit his/her needs. Seizure detection using the variance of STLmax (subset: spatial variance) is recommended for seizure predictor. The same method is also recommended for any application that has a mechanism of calculating STLmax efficiently and that does not require a quick detector. Further improvements may be possible when the parameters in the calculation of STLmax can be adapted over time.

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BIOGRAPHICAL SKETCH Ganesan Ramachandran was born in Madurai, India, on February 10 th , 1978. Ganesan was awarded a Bachelor of Engineering degree in Electronics and Communication Engineering in 1999 from Regional Engineering College, Tiruchirappalli, India. After finishing his undergraduate degree, Ganesan worked as a VLSI and Embedded Systems Engineer at WIPRO Technologies Ltd., Bangalore, India from 1999 to 2000. In fall 2000, Ganesan enrolled at the University of Florida to start his graduate study in Electrical and Computer Engineering. In spring 2001, under Dr. Jose Principe’s supervision, Ganesan joined the Bioengineering Research Partnership as a research assistant, where he found his interest in combining traditional signal processing methods with nonlinear dynamic methods for epilepsy research. 64