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Human Motor Control through Electrocorticographic Brain Machine Interfaces

Permanent Link: http://ufdc.ufl.edu/UFE0022530/00001

Material Information

Title: Human Motor Control through Electrocorticographic Brain Machine Interfaces
Physical Description: 1 online resource (156 p.)
Language: english
Creator: Gunduz, Aysegul
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: neuroprosthesis
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Brain machine interfaces (BMIs) aim to provide new rehabilitation options and channels of interaction to patients who have lost their ability to move their limbs due to disease or injury to the central or peripheral nervous system. Brain activity produces a variety of electrical signals that can be measured through diverse recording technologies and are potential candidates for BMI inputs. Electrocorticogram recordings (ECoG) provide an intermediate level of abstraction between invasive microarray recordings that penetrate the tissue and noninvasive scalp recordings (EEG). In order to map ECoG activity to motor behavior, extraction of the appropriate spatiotemporal and spectral control features is critical. Though they provide higher amplitude, less noisy and broader band signals compared to EEG recordings, extraction of signatures of motor events in spontaneous ECoG activity still entails challenges and remains unexplored. Herein, clinical behavioral paradigms are developed to record and analyze very broadband ECoG from two epileptic patients participating in reaching, pointing and cursor tracking tasks. Although historically frequencies above the high gamma band have been discarded as background activity, we study all frequencies up to the Nyquist frequency (of 6.1kHz) by dividing the broadband into logarithmically equal bands, yielding passbands of equal center frequency to bandwidth ratio. The role of the spectral resolution, in which the broadband is partitioned, in the reconstruction of the patients' hand trajectories is studied through crosscorrelations, event related synchronizations, directional tuning, and source separation methodologies. Mapping of neural modulations to goal-oriented motor behavior is achieved via the traditionally used linear adaptive filters and as a novelty through nonlinear echo state networks with upto 85% correlation between actual and reconstructed hand trajectories. Regularization methodologies for online feature selection and subspace projection through semiblind source separation algorithms are implemented for further reduction of the vast feature space. Removal of interictal spiking activity present across the sensorimotor cortex of the patients, which supresses the motor control features, is studied through source separation. The reconstructed hand trajectories are analyzed through spatial and spectral sensitivity. Presence of motor features up to 6kHz is shown as a novel contribution in the field of ECoG BMIs.
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.
Statement of Responsibility: by Aysegul Gunduz.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Principe, Jose C.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022530:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022530/00001

Material Information

Title: Human Motor Control through Electrocorticographic Brain Machine Interfaces
Physical Description: 1 online resource (156 p.)
Language: english
Creator: Gunduz, Aysegul
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: neuroprosthesis
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Brain machine interfaces (BMIs) aim to provide new rehabilitation options and channels of interaction to patients who have lost their ability to move their limbs due to disease or injury to the central or peripheral nervous system. Brain activity produces a variety of electrical signals that can be measured through diverse recording technologies and are potential candidates for BMI inputs. Electrocorticogram recordings (ECoG) provide an intermediate level of abstraction between invasive microarray recordings that penetrate the tissue and noninvasive scalp recordings (EEG). In order to map ECoG activity to motor behavior, extraction of the appropriate spatiotemporal and spectral control features is critical. Though they provide higher amplitude, less noisy and broader band signals compared to EEG recordings, extraction of signatures of motor events in spontaneous ECoG activity still entails challenges and remains unexplored. Herein, clinical behavioral paradigms are developed to record and analyze very broadband ECoG from two epileptic patients participating in reaching, pointing and cursor tracking tasks. Although historically frequencies above the high gamma band have been discarded as background activity, we study all frequencies up to the Nyquist frequency (of 6.1kHz) by dividing the broadband into logarithmically equal bands, yielding passbands of equal center frequency to bandwidth ratio. The role of the spectral resolution, in which the broadband is partitioned, in the reconstruction of the patients' hand trajectories is studied through crosscorrelations, event related synchronizations, directional tuning, and source separation methodologies. Mapping of neural modulations to goal-oriented motor behavior is achieved via the traditionally used linear adaptive filters and as a novelty through nonlinear echo state networks with upto 85% correlation between actual and reconstructed hand trajectories. Regularization methodologies for online feature selection and subspace projection through semiblind source separation algorithms are implemented for further reduction of the vast feature space. Removal of interictal spiking activity present across the sensorimotor cortex of the patients, which supresses the motor control features, is studied through source separation. The reconstructed hand trajectories are analyzed through spatial and spectral sensitivity. Presence of motor features up to 6kHz is shown as a novel contribution in the field of ECoG BMIs.
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.
Statement of Responsibility: by Aysegul Gunduz.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Principe, Jose C.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022530:00001


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HUMANMOTORCONTROLTHROUGHELECTROCORTICOGRAPHICBRAIN MACHINEINTERFACES By AYSEGULGUNDUZ ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2008 1

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c r 2008AysegulGunduz 2

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Tomyparentsfortheirloveandsupport 3

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ACKNOWLEDGMENTS Thisdissertationhasbeentwentyoneyearsinthemaking.Ir emembertherst daymyfatherdroppedmeoatschool.Theyearwas1987andIha vebeeninschool eversincethatSeptembermorning.Forthepasttwentyoneye ars,therefore,Ihavebeen gatheringtheknowledgeandskillsthathaveenabledmetowr itethisdissertation.Ihave metmanymanypeoplealongthewaywhomIamindebtedto,yetIw illonlyhavethe chancetothankahandful. IwouldliketostartbythankingmyundergraduateadvisorDr .AydanErkmenfor persuadingmetoearnmydoctorate'sdegree.Withoutherenc ouragementandcontagious idealism,thisdissertationwouldnothavehappened.Iwoul dalsoliketothankmy master'sadvisorDr.HamidKrimforgivingmetheopportunit ytopursuemygraduate studiesintheUnitedStates. IthasbeenanhonorformetoworkwithDr.JoseC.Principe,wh oforthepast fouryearshasguidedmewithuncannywisdom,endlesspatien ceandwittyhumor.He alwaysremindedmethatknowledgeisnotastaticentitythat youputintoboxesinyour brainandclosethelidonceyouaredoneusingit,ratherknow ledgeisdynamic.Ihope thedaywillcomewhenIwillbe\thinkingliketheelectrical engineer"heaspiresmeto be.IwouldliketothankDr.JustinC.Sanchezforhispractic alityandencouragement alongtheway,andforalwayspointingoutthefullhalfofthe glasswhenIcouldnot seeanythingbuttheemptyhalf.IamthankfultoDr.PaulR.Ca rneyforprovidingthe patientsforourexperiments.Iwouldliketothankmycommit teemembersDr.JohnG. HarrisandDr.JianboGaofortheirtimeandinput. IhavemademanycolleaguesattheComputationalNeuroengin eeringLaboratory (CNEL),someofwhomIalsohavetheprivilegeofcallingmycl osestfriends.Dr.Yiwen Wanghasbeenanirreplaceablepartofmylifeforthelastfou ryears.Neitherofuscould havemadeitwithoutthecalmingpresenceoftheother.Iwoul dliketoacknowledgeJack DiGiovanna,Dr.AntonioR.C.Paiva,andShalomDarmanjianw hohavebeentherewith 4

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mefromthestart,throughtheseveralupsandmanydownsofth isdegree.Iwouldliketo thankDr.NadiaMammoneandMarianaAlmeidaformakingthise xperienceanenjoyable one.IamgratefultoDr.MustafaCanOzturkforhiscollabora tiononESNs.Aspecial \meow"goesouttoIlParkforhelpingoutwiththeformatofth isdissertation.Iwould liketothankallCNELerswhomIcouldnotlistherefortheirh elpandsupport. IamindebtedtoShannonChillingworth,JanetHolman,Marcu sMooreandJulie Veal,thepeoplebehindthecurtain,whohavemagicallymade lifearoundthedepartment andatCNELsoeortlesslyeasy. IwouldliketothankmysisterZeynepforbeingsuchaninspir ationtome.Havingto quithercareerasadancerafter14yearsofballetandmodern danceeducationduetoa kneeinjury,sheshowedallofusthatwithenoughheartandde terminationyoucanrestart andthriveinlife,nomatterwhatitthrowsatyou.Iwouldlik etosendmydeepestthanks tomyparentsFahriyeandDr.SukruGunduzwhohavemadeprovi dinguswiththebest educationpossible,theforemostpriorityintheirlives.T heirlove,supportandprideinme havebeenthefuelthatkeptmegoingalltheseyears. Asanalnote,IwouldliketothankmyhusbandRizwanforsitt ingbehindthatdoor whichIhappenedtoaccidentallyknockonsomesixyearsago. Therestisachapteronits own ::: 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 15 CHAPTER 1INTRODUCTION .................................. 17 1.1LevelsofAbstractionsinBMITechnologies .................. 17 1.2CurrentECoG-BasedBMIs .......................... 21 1.3Motivation .................................... 25 1.4ChallengeswithECoGBMIs .......................... 27 1.5Outline ...................................... 28 2PATIENTSANDBEHAVIORALEXPERIMENTDESIGN ........... 30 2.1Patients ..................................... 31 2.2BehavioralTasks ................................ 34 2.3SignalAcquisition ................................ 35 3ANALYSISOFMOVEMENTRELATEDFEATURESINECOG ........ 40 3.1FunctionalSpectralAnalysis .......................... 40 3.2DirectionalTuningofECoGFeatures ..................... 48 3.3AnalysisofMotorRelatedPotentialsUsingSourceSepar ationMethods .. 53 3.3.1DenoisingSourceSeparation ...................... 54 3.3.2AnalysisofMovementRelatedECoGPotentialsviaDSS ...... 56 4LINEARMAPPINGOFECOGMOTORFEATURESTOBEHAVIOR .... 73 4.1WienerFilter .................................. 75 4.2NormalizedLeastMeanSquares ........................ 81 4.3WeightDecay .................................. 83 4.4GammaFilter .................................. 85 4.5ComparisonofLinearFilters .......................... 88 5REGULARIZATIONTHROUGHFEATURESELECTIONANDSUBSPACE PROJECTION .................................... 102 5.1LeastAngleRegressionforOnlineFeatureSelection ............. 102 5.1.1ThresholdSelectionThroughSurrogateData ............. 105 5.2MappingofDSSComponentstoBehavior .................. 107 6

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5.3InterictalSpikeRemovalThroughDSS .................... 113 6NONLINEARMAPPINGOFECOGMOTORFEATURESTOBEHAVIOR 121 6.1EchoStateNetworks:AnIntroduction .................... 122 6.2EchoStateNetworksforECoGBMIs .................... 125 7CONCLUSIONS ................................... 135 7.1Discussion .................................... 135 7.2SummaryofContributions ........................... 138 7.3FutureDirections ................................ 138 APPENDIX:REALTIMECLOSEDLOOPSYSTEMIMPLEMENTATION ..... 141 REFERENCES ....................................... 148 BIOGRAPHICALSKETCH ................................ 156 7

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LISTOFTABLES Table page 2-1Motorresponsetoelectricalstimulationofsubduralgr ids ............. 32 3-1ECoGspectralfrequencybands ........................... 43 3-2Cosine-tunedECoGfeaturesforPatient1 ..................... 51 3-3Cosine-tunedECoGfeaturesforPatient2 ..................... 52 4-1WienerlterperformanceresultsforPatient1 ................... 77 4-2WienerlterperformanceresultsforPatient2 ................... 77 4-3TheeectofthehighestspectralbandontheWienerlter performance .... 79 4-4NLMSperformanceresultsforPatient1 ...................... 82 4-5NLMSperformanceresultsforPatient2 ...................... 82 4-6WeightdecayperformanceresultsforPatient1 .................. 85 4-7WeightdecayperformanceresultsforPatient2 .................. 86 4-8GammalterperformanceresultsforPatient1 .................. 88 4-9GammalterperformanceresultsforPatient2 .................. 88 4-10FilterperformancecomparisonsforPatient1 .................... 89 4-11FilterperformancecomparisonsforPatient2 .................... 89 5-1LARperformanceresultsforPatient1 ....................... 108 5-2LARperformanceresultsforPatient2 ....................... 108 5-3WienerlterperformanceresultswithDSScomponentsfo rPatient1 ...... 108 5-4WienerlterperformanceresultswithDSScomponentsfo rPatient2 ...... 108 5-5Wienerlterresultsbeforeandafterinterictalspiker emoval ........... 119 6-1ESNperformanceresultsforPatient1 ....................... 126 6-2ESNperformanceresultsforPatient2 ....................... 126 6-3Performancecomparisonoflinearandnon-linearlters forPatient1with n =4 spectralbands ..................................... 130 8

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LISTOFFIGURES Figure page 1-1BlockdiagramofaBMIsystem.[Reprintedwithpermissio nfromE.C.Leuthardt etal.,2006.Theemergingworldofmotorneuroprosthetics: Aneurosurgical perspective.Neurosurgery(vol.95,pg.3,Figure1).] ............... 18 1-2Schematicoflevelsofbrainsignalabstractionwithcor respondingregionallocalizations anddomains.[ReprintedwithpermissionfromE.C.Leuthard tetal.,2006.The emergingworldofmotorneuroprosthetics:Aneurosurgical perspective.Neurosurgery (vol.95,pg.3,Figure2).] .............................. 19 1-3Theprotectivelayersofthemeninges:dura,arachnoida ndpiamatter. ..... 21 2-1Schematicoftheend-to-endBMIsystem ...................... 30 2-2Invivoplacementoftheelectrodegridina3x3cm 2 areaofcortexandtherelative electrode,gyri,sulci,andvasculaturerelationships. ................ 32 2-3Gridlocalization.A)Electrodeplacementandnumberin gforPatient1(left) andPatient2(right)asindicatedbythesurgeon.B)Anatomi callocalizationof gridelectrodesforPatient1andC)Patient2viaT1MRimagin g. ........ 37 2-4Behavioraltrajectoriesona20x30cmscreen .................... 38 2-5ExperimentalsessionperformedbyPatient1.Thesessio nstartswiththecenter-out taskfollowedbythetrajectoryselectiontask,repeatedov erin5trials. ..... 38 2-6Powerspectraldensityestimatesofthehorizontalandv erticalhandtrajectories duringtheexperimentalsessionperformedbyPatient1. ............. 39 3-1Synchronizedbehaviortrajectories(middle)andbroad bandECoGrecordings fromchannels8(top)and30(bottom)forA)Patient1andB)Pa tient2. .... 41 3-2A-B):Toprow:PowerdensityspectraofECoGrecordingsf romPatient1computed over5secsforchannels8and30duringmotortask.Bottomrow :PSDsofthe samechannelswhilethepatientisnotinvolvedinexperimen talparadigm(waiting formovementonset).C-D)SameplotsforPatient2. ............... 44 3-3Synchronizedbehaviortrajectoriesintwodimensions( top)andpowerofpassband ECoGrecordingsfrom32channelsfromPatient1.Topthreeba ndshowvisual event-relatedsynchronization.Thepatientstoppedthebe havioratthesecond halfofthelasttask. ................................. 45 3-4Left:Cross-correlationbetweenverticalhandtraject oriesandchannelspectral poweracrossforA) n =32,C) n =16,E) n =8bandsforPatient1.Right: Cross-correlationbetweenhorizontalhandtrajectoriesa ndchannelspectralpower acrossforB) n =32,D) n =16,F) n =8bandsforPatient1. .......... 60 9

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3-5Left:Cross-correlationbetweenverticalhandtraject oriesandchannelspectral poweracrossforA) n =32,C) n =16,E) n =8bandsforPatient2.Right: Cross-correlationbetweenhorizontalhandtrajectoriesa ndchannelspectralpower acrossforB) n =32,D) n =16,F) n =8bandsforPatient2. .......... 61 3-6TuningcurvesofA)channel16andB)channel31lteredbe tween15-18Hzfor Patient1.TuningcurvesofC)channel15lteredbetween178 -219HzandD) channel2lteredbetween408-501HzforPatient2. ................ 62 3-7Top:Thedistributionofthepreferredanglesofthefeat ureswith R 2 > 0 : 60for Patient1.Bottom:Thedistributionofthepreferredangles ofthecosine-tuned featureslistedinTable3-2. ............................. 63 3-8Top:Thedistributionofthepreferredanglesofthefeat ureswith R 2 > 0 : 60for Patient2.Bottom:Thedistributionofthepreferredangles ofthecosine-tuned featureslistedinTable3-3. ............................. 63 3-9Tuningcurveofchannel14lteredbetween4879-6110Hzs howsmultimodal tuning/preferenceforPatient1. ........................... 64 3-10A)ModulationindicesforPatient1areaveragedoverth espectralbandsand superimposedonthe6x6electrodegrid.B)Modulationindic esforPatient1 areaveragedoverthespatialchannelsandplottedversusth ecentralfrequency ofthespectralbands. ................................. 64 3-11A)ModulationindicesforPatient2areaveragedoverth espectralbandsand superimposedonthe4x8electrodegrid.B)Modulationindic esforPatient2 areaveragedoverthespatialchannelsandplottedversusth ecentralfrequency ofthespectralbands. ................................. 65 3-12BlockdiagramoftheiterativeDSSalgorithm. ................... 65 3-13Thedenoisingfunctionforwhichthesourcesmovementr elatedsourcesshallbe extracted. ....................................... 66 3-14Themagnitudeofcorrelationcoecientsbetweentheor deredcomponentsand thehandtrajectoriesforPatient1. ......................... 66 3-15Top:FirstDSScomponentsuperimposedontheverticalh andtrajectory.Bottom: ThirdDSScomponentsuperimposedonthehorizontalhandtra jectory.Allcomponents andtrajectoriesarenormalizedbytheirstandarddeviatio ns. ........... 67 3-16A)Mixingcoecientsoftherstcomponentareaveraged overthespectralbands andsuperimposedontheelectrodegrid.B)Mixingcoecient softherstcomponent areaveragedoverthespatialchannelsandplottedversusth ecentralfrequency ofthespectralbands.C)Mixingcoecientsofthethirdcomp onentaveraged overthespectralbands.D)Mixingcoecientsofthethirdco mponentaveraged overthespatialchannels. ............................... 68 10

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3-17Componentsextractedfromsurrogatedatasuperimpose dontheverticalhand trajectory(leftcolumn)andhorizontalhandtrajectory(r ightcolumnshownin asegmentof60secs). ................................. 69 3-18Themagnitudeofcorrelationcoecientsbetweentheor deredcomponentsand thehandtrajectoriesforPatient2. ......................... 70 3-19Top:FirstDSScomponentsuperimposedontheverticalh andtrajectory.Bottom: 18 th DSScomponentsuperimposedonthehorizontalhandtrajecto ry.Allcomponents andtrajectoriesarenormalizedbytheirstandarddeviatio ns. ........... 71 3-20A)Mixingcoecientsoftherstcomponentareaveraged overthespectralbands andsuperimposedontheelectrodegrid.B)Mixingcoecient softherstcomponent areaveragedoverthespatialchannelsandplottedversusth ecentralfrequency ofthespectralbands.C)Mixingcoecientsofthe18 th componentaveraged overthespectralbands.D)Mixingcoecientsofthe18 th componentaveraged overthespatialchannels. ............................... 72 4-1Linearltertopologyofasingleinput-singleoutputsy stem.) ........... 74 4-2PerformancemeasuresacrossspectralbandsofPatient1 asafunctionofWiener lterorder, L through(A):meancorrelationcoecients,(B):normalized mean squarederrors. .................................... 80 4-3SpatialandspectralsensitivitiesofPatient1with L =8orderWienerlters. A)Spatialsensitivityof32channelsacross n =32passbands,B)Spectralsensitivities of n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie sfor n =16 passbands.E-F)Sensitivitiesfor n =8passbands. ................. 91 4-4SpatialandspectralsensitivitiesofPatient2with L =8orderWienerlters. A)Spatialsensitivityof32channelsacross n =32passbands,B)Spectralsensitivities of n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie sfor n =16 passbands.E-F)Sensitivitiesfor n =8passbands. ................. 92 4-5NormalizedweightdistributionsofltersforPatient1 beforeandafterweight decaywithvarying valuesforA) n =32,B) n =16,C) n =8bands. ..... 93 4-6NormalizedweightdistributionsofltersforPatient2 beforeandafterweight decaywithvarying valuesforA) n =32,B) n =16,C) n =8bands. ..... 94 4-7Feedforwardltertopology. ............................. 95 4-8Theleakyintegrator. ................................. 95 4-9WienerreconstructedtrajectoriesforPatient1withA) n =32,B) n =16,C) n =8bands. ..................................... 96 4-10WienerwindowedCCvaluesforPatient1withA) n =32,B) n =16,C) n =8 bands. ......................................... 97 11

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4-11WienerwindowedMSEvaluesforPatient1withA) n =32,B) n =16,C) n =8bands. ..................................... 98 4-12WienerreconstructedtrajectoriesforPatient2withA ) n =32,B) n =16,C) n =8bands. ..................................... 99 4-13WienerwindowedCCvaluesforPatient2withA) n =32,B) n =16,C) n =8 bands. ......................................... 100 4-14WienerwindowedMSEvaluesforPatient2withA) n =32,B) n =16,C) n =8bands. ..................................... 101 5-1SchematicshowingtheNLMSandLARcoecientsintheonli nefeatureselection algorithm. ....................................... 105 5-2A:LARtrajectoryreconstructionsfromtheoriginaldat aofPatient1with n = 8spectralbands,B)LARtrajectoryreconstructionsfromth esurrogatedata. Thethresholdswereselectedtominimizethenumberofselec tedfeaturesfrom thesurrogatedata. .................................. 109 5-3A)TheselectedfeaturesofPatient1ateverytimeinstan ceforthereconstruction ofthehorizontaltrajectory,B)Theselectedfeaturesfort hereconstructionof theverticaltrajectory.Notethatthemagnitudesofthewei ghts, w LAR ,forthe correspondingselectedfeaturesarenotrerectedinthisbi narygure. ...... 109 5-4A)ThespatialsensitivityoftheLARcoecientsofPatie nt1averagedover timeandspectralbandssuperimposedontheelectrodegrid, B)Thespectral sensitivityoftheLARcoecientsaveragedovertimeandspa tialgridisplotted againstthecenterfrequenciesof n =8bands. ................... 110 5-5A:LARtrajectoryreconstructionsfromtheoriginaldat aofPatient2with n = 8spectralbands,B)LARtrajectoryreconstructionsfromth esurrogatedata. Thethresholdswereselectedtominimizethenumberofselec tedfeaturesfrom thesurrogatedata. .................................. 110 5-6A)TheselectedfeaturesofPatient2ateverytimeinstan ceforthereconstruction ofthehorizontaltrajectory,B)Theselectedfeaturesfort hereconstructionof theverticaltrajectory.Notethatthemagnitudesofthewei ghts, w LAR ,forthe correspondingselectedfeaturesarenotrerectedinthisbi narygure. ...... 111 5-7A)ThespatialsensitivityoftheLARcoecientsofPatie nt2averagedover timeandspectralbandssuperimposedontheelectrodegrid, B)Thespectral sensitivityoftheLARcoecientsaveragedovertimeandspa tialgridisplotted againstthecenterfrequenciesof n =8bands. ................... 111 5-8A)ReconstructedtrajectoriesforPatient1fromthers tandthirdDSScomponents, B)Windowedmagnitudeofcorrelationcoecients,C)Window edmean-squared errors. ......................................... 112 12

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5-9A)ReconstructedtrajectoriesforPatient2fromthers tand18 th DSScomponents, B)Windowedmagnitudeofcorrelationcoecients,C)Window edmean-squared errors. ......................................... 113 5-10A)RecordingsfromPatient1demonstratingepileptici nterictalspikes.B)Recordings fromPatient2demonstratingepilepticartifacts. .................. 115 5-11A)HistogramofthestandarddeviationsoftheECoGchan nelsfromPatient1. B)Thestandarddeviationsarespatiallysuperimposedonth eelectrodegrid. .. 116 5-12Interictalspikesextractedviathresholdlocalizati onanddenoisingaveraging. .. 117 5-13Mixingmatricesoftheextractedinterictalcomponent sspatiallysuperimposed overthesubduralelectrodes. ............................. 118 5-14Spectralpowersofsomechannelsinthepassband2623-6 100Hzbefore(left) andafter(right)interictalspikeremovalsuperimposedon theverticaltrajectory (showninred). .................................... 119 6-1BlockdiagramofanEchoStateNetwork ...................... 123 6-2Sensitivityattime t forChannel1ofPatient1with n =32bandsasafunction of. .......................................... 125 6-3ESNreconstructedtrajectoriesforPatient1withA) n =32,B) n =16,C) n =8bandswith N =500states. .......................... 127 6-4ESNwindowedCCvaluesforPatient1withA) n =32,B) n =16,C) n =8 bands. ......................................... 128 6-5ESNwindowedMSEvaluesforPatient1withA) n =32,B) n =16,C) n =8 bands. ......................................... 129 6-6ESNreconstructedtrajectoriesforPatient2withA) n =32,B) n =16,C) n =8bandswith N =1000states. ......................... 130 6-7ESNwindowedCCvaluesforPatient2withA) n =32,B) n =16,C) n =8 bands. ......................................... 131 6-8ESNwindowedMSEvaluesforPatient2withA) n =32,B) n =16,C) n =8 bands. ......................................... 132 6-9SpatialandspectralsensitivitiesofESNswith N =500statesforPatient1.A) Spatialsensitivityof32channelsacross n =32passbands,B)Spectralsensitivities of n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie sfor n =16 passbands.E-F)Sensitivitiesfor n =8passbands. ................. 133 13

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6-10SpatialandspectralsensitivitiesofESNswith N =1000statesforPatient 2.A)Spatialsensitivityof32channelsacross n =32passbands,B)Spectral sensitivitiesof n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie s for n =16passbands.E-F)Sensitivitiesfor n =8passbands. ........... 134 A-1Circuitcomponentsthatallowrecordingfrom32channel sofECoGdatapassed throughapre-amplier.Therawdatasampledat12207Hzisal sostoredin datatanks. ...................................... 142 A-2Therawchannelsarelteredinfourspectralbands. ................ 144 A-3Thecountersetsthe\EndofBlock"raghightoindicate10 0msecsofnon-overlapping timewindows. ..................................... 145 A-4Constantintegrationofpower.Whenanendofblockisrea ched,thepowerin thepreviousblockissubtractedfromthecurrentpower. ............. 145 A-5StoringandsendingthepassbandpowerstoMATLABthroug hthevariable\Power". 146 A-6Therealandmodeloutputcursorpositionsarereceivedf romMATLABtobe storedinadatatank. ................................ 147 A-7VericationblockthatallowsMATLABtocheckwhetherth epowerattheend ofeachblockisreceived. ............................... 147 14

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy HUMANMOTORCONTROLTHROUGHELECTROCORTICOGRAPHICBRAIN MACHINEINTERFACES By AysegulGunduz August2008 Chair:JoseC.PrincipeMajor:ElectricalandComputerEngineering Brainmachineinterfaces(BMIs)aimtoprovidenewrehabili tationoptionsand channelsofinteractiontopatientswhohavelosttheirabil itytomovetheirlimbsdueto diseaseorinjurytothecentralorperipheralnervoussyste m.Brainactivityproducesa varietyofelectricalsignalsthatcanbemeasuredthroughd iverserecordingtechnologies andarepotentialcandidatesforBMIinputs.Electrocortic ogramrecordings(ECoG) provideanintermediatelevelofabstractionbetweeninvas ivemicroarrayrecordingsthat penetratethetissueandnoninvasivescalprecordings(EEG ).InordertomapECoG activitytomotorbehavior,extractionoftheappropriates patiotemporalandspectral controlfeaturesiscritical.Thoughtheyprovidehigheram plitude,lessnoisyandbroader bandsignalscomparedtoEEGrecordings,extractionofsign aturesofmotoreventsin spontaneousECoGactivitystillentailschallengesandrem ainsunexplored.Herein,clinical behavioralparadigmsaredevelopedtorecordandanalyzeve rybroadbandECoGfromtwo epilepticpatientsparticipatinginreaching,pointingan dcursortrackingtasks.Although historicallyfrequenciesabovethehighgammabandhavebee ndiscardedasbackground activity,westudyallfrequenciesuptotheNyquistfrequen cy(of6.1kHz)bydividing thebroadbandintologarithmicallyequalbands,yieldingp assbandsofequalcenter frequencytobandwidthratio.Theroleofthespectralresol ution,inwhichthebroadband ispartitioned,inthereconstructionofthepatients'hand trajectoriesisstudiedthrough crosscorrelations,eventrelatedsynchronizations,dire ctionaltuning,andsourceseparation 15

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methodologies.Mappingofneuralmodulationstogoal-orie ntedmotorbehaviorisachieved viathetraditionallyusedlinearadaptiveltersandasano veltythroughnonlinearecho statenetworkswithupto85%correlation.Regularizationm ethodologiesforonlinefeature selectionandsubspaceprojectionthroughsemiblindsourc eseparationalgorithmsare implementedforfurtherreductionofthevastfeaturespace .Removalofinterictalspiking activitypresentacrossthesensorimotorcortexofthepati ents,whichsupressesthemotor controlfeatures,isstudiedthroughsourceseparation.Th ereconstructedhandtrajectories areanalyzedthroughspatialandspectralsensitivity.Pre senceofmotorfeaturesupto 6kHzisshownasanovelcontributionintheeldofECoGBMIs. 16

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CHAPTER1 INTRODUCTION Theneuromuscularchannelsthroughwhichthebraincontrol sitsexternalenvironment canbedisruptedbymanydierentdiseasessuchasamyotroph iclateralsclerosis(ALS), brainstemstroke,brainorspinalcordinjury,musculardys trophies,multiplesclerosis, orbyamputationandlossoflimbs[ 100 ].Itisestimatedthatnearlytwomillionpeople suerfromlossofvoluntarymusclecontrolintheUnitedSta tesandmuchmorearound theworld[ 9 21 64 65 100 ].Brainmachineinterfaces(BMIs)aimtodecodetheintent tocontroltheexternalworldfrombrainactivityandtransl ateitintonewcommunication channelsofinteractionforlocked-inpatients[ 49 ].Othertermsusedinengineeringand neuroscienceliteratureforBMIsaredirectbraininterfac es,motorneuroprosthesis, andbraincomputerinterfaces(BCIs)whenexperimentsareb asedonsolecomputer interaction.AblockdiagramofahighlevelBMIisdepictedi nFigure 1-1 (reprintedfrom [ 52 ]).ThemaincomponentsofaBMIaredataacquisitionsystems ,featureextraction mechanisms,mappingofthesefeaturesintocommandsforthe outputsystemsthrough models,andnallytheoutputsystemswhichallowthepatien tstocontrolexternal devices.Inthisstudy,wedesignandanalyzeeachoftheseco mponentsthatbuildupa humanmotorcontrolBMI. 1.1LevelsofAbstractionsinBMITechnologies AsobservedinFigure 1-1 ,brainactivityproducesavarietyofelectricalsignalsth at canbemeasuredthroughdiverserecordingtechnologiesand arepotentialcandidates forBMIinputs.Actionpotentials,orneuralspikes,canber ecordedfromindividual neuronsviamicroelectrodearraysthatpenetratethebrain tissue.Withthesame electrodescoherentdendriticactivityfromsmallcellens emblescalledlocaleld potentialscanbegathered.Electricalcurrentsproducedb ysynchronyovercortical areasontheorderof1-1.5centimetersquarescanbemeasure dwithgridelectrodes placedontheduramatter(epidural)oronthecortex(subdur al);and3-6centimeter 17

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Figure1-1.BlockdiagramofaBMIsystem.[Reprintedwithpe rmissionfromE.C. Leuthardtetal.,2006.Theemergingworldofmotorneuropro sthetics:A neurosurgicalperspective.Neurosurgery(vol.95,pg.3,F igure1).] squareswithscalpelectrodes.Thesemacroscopicsignalsa recalledelectrocorticographs (ECoG)andelectroencephalographs(EEG),respectively.F igure 1-2 showsthespatial coverage/resolutionandlevelofinvasivenessofthesesig nalsusedinBMIoperation (reprintedfrom[ 52 ]). Duetotheinvasivenatureoftheirrecordingprocedureandp roximitytoneural source,microarrayrecordingsofactionpotentialshaveth ehighestspatialresolution, highestfrequencyrangeandhighestsignal-tonoiseratios .Themechanismofaction potentialgenerationwasdescribedinthegroundbreakingw orkofHodgkinandHuxley [ 34 ]andtodayiswellunderstood.Firingratesofsingleneuron swithin50to100 msectimewindowsinthemotorcortexwereshowntobenelytu nedwithdirectional movementofprimatehands[ 28 ]andthecumulativesumsofdirectionalvectorsweighted 18

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Figure1-2.Schematicoflevelsofbrainsignalabstraction withcorrespondingregional localizationsanddomains.[Reprintedwithpermissionfro mE.C.Leuthardt etal.,2006.Theemergingworldofmotorneuroprosthetics: Aneurosurgical perspective.Neurosurgery(vol.95,pg.3,Figure2).] bytunedneuronrings,knownaspopulationvectors,wereus edtopredictthedirection intent.Intheliteraturespike-ratebasedBMItechnologie sdevelopedonprimateshave beenreportedtosuccessfullyreconstructhandtrajectori es.Sometypicalresultshave shownreconstructionsaccountingtoover60%ofthevarianc einactualhandmovements [ 84 91 ]andcorrelationratesabove70%[ 95 ].Overall,neuralringratesalthough providinglowtemporalresolutionhaverepeatedlyprovedt obesuccessfulfeaturesfor encodingmotormechanisms.However,thesameinvasivenatu rethatbringsaboutall thepositiveaspectsofmicroarrayrecordingsalsoprohibi tstheirimplantationonhuman patients.Biocompatibilityissuescausedeteriorationof therecordedsignalsthroughtime duetoinrammationsonthebraintissueandencapsulationof theelectrodetips.Therisks involvedintheimplantationoftheseelectrodesinahumanb raincanonlybejustied whenbiocompatiblemicroarrayswithlonglifespanshavebe enwarranted[ 52 ]. Duetothelargeregionalcoverage,distancetothecortical sourcesandinhomogeneous conductivityofdura,skull,andscalp[ 66 ],theunderlyingmechanismsgeneratingEEG arenotentirelyunderstood.Theproductionofpotentialsi sduetothesuperpositionof manyalignedandsynchronousdipolesources[ 66 ].Alargeareaofthecortexneedstobe 19

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synchronouslyactivetobevisibleonthescalp[ 63 ].Thecoactivationofsourcesisrelated toneuralsynchronyandisusedtodescribetheamplitudemod ulationsinextracellular recordingsthatoccurduringstatechanges[ 71 ].InEEGrecordings,thesesynchronizations tendtooccurinthelowfrequencies( < 50-60Hz)[ 63 ]andhighfrequenciesareattenuated (duetolackofsynchronyandmediumresistivity).Moreover ,muscleandeyemovement artifactsandconductionoverlargedistancesdecreasethe SNRinEEGrecordings. However,thenon-invasivenatureofthescalpelectrodesma kesthemthemostappealing signalacquisitiontechniqueforhumanBMIs.Pfurtschelle retal.[ 70 ]haveobservedmu (8-12Hz)andbeta(12-25Hz)rhythmdesynchronizationswit hmotionexecutionand motionimagery,alsoknownaseventrelateddesynchronizat ion(ERD).Wolpawetal. [ 57 58 81 100 ]haveshownpatientswereabletocontroltheirmuandbetaER Dsfor closed-loop2-dimensionalcursorcontrolwithtrainingpe riodsthatspan2-3weeks. ECoGisanintermediatesignalingmodalitybetweeninvasiv emicro-electrodesand non-invasiveEEG.Figure 1-3 showsthemeninges,themembranousprotectivelayers, surroundingthebrain.Meningesliesbeneaththescalpands kullandconsistsofthree layers:dura,arachnoidandpiamatter.ForECoGrecordings ,electrodearraysare implantedinthesubduralspacebetweentheduraandarachno idmatter,whichentails craniotomyandincisionsintheduramatter.Inseveralstud ies,long-termsubdural implantsshowedminimaltissuereactionwhilecontinuingt oprovidehighSNRrecordings [ 6 55 56 89 101 ]. ThecollectedsignalinECoGhasnerspatialresolution(Fi gure 1-2 ),i.e.itisthe cumulativesumofdendriticactivityandactionpotentials acrossasmallerensemble andhasamplitudesontheorderof5-10timesofthatEEG[ 52 97 ].Nunez'stheoretical dipolestudiesleadtoacorticalpotential-to-scalppoten tialratioofalso5-10whenthe assumeddipoleareaofcorrelatedsourcesisabout5-10cm 2 [ 66 ](thelowertheareaof correlateddipoles,thehighertheratio).Thisincreasein signalamplitudeimprovesSNR intherecordings.Inadditiontothis,ECoGdoesnotsuerfr omEEGartifactssuch 20

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Figure1-3.Theprotectivelayersofthemeninges:dura,ara chnoidandpiamatter. aseyemovementormuscleinterferences[ 52 ].ThelogpowerofbothECoGandEEG signalsdropacrossfrequencywiththeempirical1 =f b b 2 1formula[ 23 ].However, inEEGtheattenuationofhighfrequenciesbetweenthescalp andthecorticalsources isduetoacombinedeectofspatiallteringbytheheadvolu meconductorandthe tendencyforhighertemporallterstooccurwithhigherspa tialfrequencies[ 66 ].The humanbrain-to-skullconductivityratioisreportedtobe2 5 7bymeansofcortical potentialimagingtechnology[ 45 ].TheattenuationofECoGpotentialswithfrequency, ontheotherhand,isonlyduetothecapacitive-resistivepr opertiesofthecorticaltissue. Hence,thefrequencybandwidthofECoGissignicantlyhigh erthanthatofEEG.Infact gamma(60-100Hz)andhighgamma(100-300Hz)bandshavebeen employedincurrent ECoG-basedBMIsasdiscussednext. 1.2CurrentECoG-BasedBMIs Implantationofsubduralelectrodesareclinicallyrestri ctedtodiagnosticsof pre-surgicalepilepticpatients.Therefore,theECoG-bas edBMIstudiesreviewed hereinhaveallbeenperformedbyparticipatingepilepsypa tients,whorequireinvasive monitoringofcorticalactivityforlocalizationofseizur eonset[ 52 87 ].Thoughepileptogenic focusmonitoringhasbeenperformedonpatientsfordecades ,onlyinthelastdecadehave 21

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neurophysiologicalandBMIstudiesbeenperformedinparal leltomonitoringonthese patients[ 63 ].ThemodulationofECoGactivitywithmotorbehaviorhasbe enextensively analyzedthroughtwomajormethodologies: eventrelatedpotentials and eventrelated spectralchanges Levineetal.[ 35 54 ]makeuseoftemplatesextractedfromeventrelatedpotenti als (ERPs)whichareaveragesofbrainactivityalignedtotheon setofrepetitivemotortasks (suchasngerextensions,wristrotations,etc.).Intheco ntextofBMIs,ERPsaremore specicallyreferredtoasmotor-evokedpotentials(mEPs) [ 94 ].Averagingtheneural activityacrossrepetitionsofthesamemotortaskincrease sthesignal-to-noiseratioand providesatrendofresponseoftheunderlyingneuralensemb letothatparticulartask. ChannelswhoseERPsyieldadistinctive\averageERPtempla te"areselectedandthe restisignored.TheaverageERPtemplatesspanned3seconds beforeandaftermotion onset.Onlinecross-correlationsbetweenthesetemplates andthecontinuousECoG testpatternrecordedwhilethepatientisperformingthesa memotortaskiscomputed. Normalizedcross-correlationsthatwerehigherthananexp erimentallydetectedthreshold weremarkedasdetectedmotorexecution.Cuesfortargetons etswereusedasreferences toreducethefalsealarmrates.Thedierencebetweendetec tionratesandfalsealarm rateswereabove50%for12ofthe15patients[ 35 ].Thesestudieshavebeenconductedas abasisforreal-timedirectbraininterfaces[ 54 ]. Eventrelatedspectralchangesaremovementrelatedincrea seordecreaseinpower ofcertainbrainrhythms. Eventrelateddesynchronization (ERD)inthealpha(8-13Hz, alsocalledthemurhythm)andbeta(15-30Hz)rhythmswerer stdiscoveredinEEG recordings[ 57 58 81 100 ]andarealsoobservedinECoG[ 11 71 ].Moreover,induced gamma(40-80Hz)andhighgammaactivities(80-200Hz),whic hcannotbeobservedin EEGduetolimitedspectralbandwidth,werereportedas eventrelatedsynchronization (ERS)withECoGrecordings[ 1 2 12 71 ].Thespatialcoverageareaofsynchronization inthefastrhythmswerefoundtobemorelocalizedcomparedt othedesynchronizationof 22

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theslowrhythms 1 .Inarecentlargestudyconsistentpowerincreaseinthehig hgamma band(76-100Hz)anddecreaseinpowerinlow-frequencyband (8-32Hz)withrepetitive motortasks(involvingthehandandtongue)wherereportedi nrelevantelectrodes (Brodmannarea4)of22patients[ 62 ]. Mehringetal.[ 60 ]incorporatedlowfrequencyERDinhumanECoGfordirection al classicationina4-target(spreadevenlyonacircularper imeterintwo-dimensions) center-outtask[ 28 ].Low-frequencyfeatureswereextractedfromtheECoGreco rdingsby smoothing55msecsofnon-overlappingdatabySavitsky-Gol ayltersduringmovement starttoendandconcatenatingthesevectorsforeachchanne l.Theextractedfeatures fromhalfofthetrialstoeachofthe4directionswereusedto trainapenalizedlinear discriminantclassier.Thisfeatureextractionparadigm wasinitiallyappliedtoLFPs frommonkeymotorcorticeswithdiscriminationpowersinth erangeof[0.4,0.5](with amedianof0.49),abovethechancelevelof0.25.However,wi thhumanECoGdata discriminationpowerswerereportedtobeinthelowerrange sof[0.30,0.4](withamedian of0.34).Inaddition,whenanalyzingmEPstheridge(P1)-ra vine(N1)-ridge(P2)-ravine(N2) patterncommonlyseeninLFPmEPs[ 76 ]wasnotobservedinhumanECoG.Mehringet al.attributethedierenceinresultstodistanceofelectr odesites,dierenceinspecies, dierenceintaskexecutionanddurationofexecution[ 60 ].Thesamefeatureextraction methodologyandpenalizedlineardiscriminantanalysiswa sappliedtoclassifyingipsi-and contralateralindexngermovementsanddiscriminationpo werof100%wasattainedon anelectrodefromtheprimarymotorcortex[ 4 ] Leuthardtetal.[ 50 51 63 ]appliedERD/ERStoECoGspectraforclosed-loop controlofaone-dimensionalcursorwithmotorandspeechim agery.Powerspectra computedatrestandduringmotorimagery(from0to200Hz)we recompared.The 1 Thisisduetothefactthatforfastrhythms,onlysmallgroup sofneuronscanfollow thebeatperfectlyduetolimitationsofaxonconductancean dsynapticdelays[ 8 ]. 23

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channelsandfrequencybinswithmostsignicanttask-rela tedchangeswereidentiedas featurestocontrolthecursor(atmost2channelsand3frequ encybinswereselected). Theparticipantswereinstructedtousemotorimagerytomov ethecursorup.Thecursor automaticallymoveddownatrest.Thegoalwastohittwotarg ets,atthetopandbottom ofthescreen(correspondingtoa50%chancelevel).Patient sshowed74-100%accuracy inshorttrainingperiodsof3-24minutes[ 50 ].Inaddition,open-looptwo-dimensional cursorcontrolwasimplementedbylinearlyERSinthegammaa ndhighgammabands collectedfrom3-4sitestothecursorpostions.Ina4-targe ttaskthemodeloutputyielded correlationcoecientsof[0.45-0.54]inthehorizontalax isand[0.45,0.49]inthevertical axis.Ina8-targettaskthecorrelationcoecientsbetween thecursorandmodeloutput werereportedas[0.50,0.59]and[0.06,0.10]inthehorizon talandverticalaxes,respectively. Williamsetal.[ 20 97 ]implementedone-dimensionalclosed-loopcontrolwith auditoryimagery(aswellasmotorimagery)withpatientswh osesubduralelectrodeswere implantedovertheirsensorimotorcortexbyemployingthes amemethodology(mu-beta ERD,andhigh-gammaERS).Duringthescreeningperiod,3-6c hannelsand2frequency binswereselectedascontrolfeaturesforauditory/motori mageryacross4patients.The patientswereinstructedtocontrolacursormovingfromthe lefttorighttohitoneof2 to8targetsontherighthandsideofthescreen.Throughself -modulationoftheirrhythms patientsachieved70%andaboveaccuracyofhittingthecorr ecttargetwithtraining periodsof45minutesover2-7days. Decodingtwo-dimensionalhandtrajectoriesusingECoGhas onlybeenrecently exploredbySchalketal.[ 82 ]andPistohletal.[ 73 ].Intheformer,vesubjectstracked acursormovinginacircleat0.16Hzviaajoystick.Thespect ralamplitudesofseven bands(8-12Hz,18-24Hz,35-42Hz,42-70Hz,70-100Hz,100-1 40Hz,140-190Hz)were computedin333msecwindowswith50%overlap.Throughvisua linspectionchannelsin whichthemodulationoftherawECoGsignalswerecorrelated withkinematicparameters wereobserved.Schalketal.coinedtheseamplitudemodulat edlocations localmotor 24

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potential andaddedthe333msecrunningaverageoftherawsignalstoth efeaturevector, yieldingatotalof8featuresper64channels.Thisfeaturev ectorwasusedtolinearly predictthekinematicparametersimmediatelyfollowingth e333msecwindow(nofurther tapdelayswereused).Thehighdimensionalityofthefeatur evectorwasreducedthrough acorrelation-basedfeatureselector[ 99 ]whichidentieschannelsthathavehighmutual informationwiththekinematics,whileeliminatingchanne lsthathavehighcross-channel correlations.Thecorrelationcoecientsbetweenthekine maticsandthemodeloutputs forinvecross-validationfoldswerebetween[0.50,0.81] (withamedianof0.71)and [0.18,0.80](withamedianofmedian0.51)forthesubjectwi thhighestperformance. Sensitivityanalysisshowedthatlocalmotorpotentialshi ghlycontributedtothetrajectory reconstructionacrossallsubjects,whereasthesensitive bandsdieredacrosskinematics (horizontalvs.vertical).Thesensitiveareaswerefoundt obethemotorandpre-motor cortices(Brodmannareas4and6).Theyreportedthatemploy ingacommonaverage referencelterimprovedperformancebyremovinglowspati alfrequencies. Pistohletal.[ 73 ]designedatargetselectiontaskinwhichvesubjectsguid eda cursorontooneofninetargetsalignedona3x3grid.Thegoal wastoreconstructthe cursortrajectoryratherthanclassifytargets.TheECoGsi gnalswerelowpassltered with0.75secwindowsofSavitsky-Golaylters(whichprese rvetheextremawhile smoothening).Thesmoothenedsignalsfromallchannelsfor medthemeasurementvector attime t andsixkinematicsattime t (horizontalandverticalpositions,velocitiesand acceleration)formedthestatevectortobeusedinaKalman lter[ 40 ].Theoptimalvalue for wasndfoundtobe125msec.Acrossalltrialscorrelationco ecientsof0.40 0.1 wereattainedwithtwopatientsthathadcoverageoverthemo torarea.Anabundanceof interictalactivitywasobservedforoneofpatientswithlo werperformanceresults. 1.3Motivation InECoGneuroprosthesisdesignmanyquestionsstillremain unanswered.Therst questionthatcomestomindis:\Atwhatspectralcoverage(b andwidth)shouldthe 25

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signalsberecorded?".UntilrecentlyECoGdatahasbeenrec ordedatthelowsampling frequenciescommonlyusedforrecordingofclinicalEEGand frequencybandsabovethe gammabandhadmainlybeendiscardedasbackgroundactivity ornoise[ 24 { 26 ].With therevelationofmovementrelatedsynchronizationinhigh gammaactivities(80-200Hz) [ 12 ],moreandmoreECoGstudiesbegantoanalyzefasteractivit ies(frequenciesupto 300Hz)[ 1 2 12 62 71 ].Recentworkhasbeenpublishedontheultrafastfrequenci es andfull-bandEEG,claimingthatthetherangeofEEGismuchb roaderthanithasbeen assumed(upto1500Hz)[ 3 67 ].Thesendingsmotivateustorecordbroadbandsignalsto studythepossibilitiesofcapturingneuralensembleactiv itieswithECoGsynchronizingat evenhigherfrequenciesthancurrentlyincorporatedinBMI technologies. Therhythmicityofmacroscopicsignalsprovidesameansofq uantitativelydescribing therecordings,asthefrequencyoftherhythmsthatarecorr elatedtoactions,eventsor stimulicanbemeasured.ThroughoutthehistoryofEEGtechn ology,EEGfrequencies havebeenconvenientlyclassiedintobands[ 10 ].Inthecontextofmotorsystemanalysis, bandshavebeenidentiedbymeansofcomparingspectralden sitiesduringmovement executionofshorttaskswithareststate.However,duringc ontinuousmovement execution,empiricalextractionofbandsisnotfeasible.A notherimportantquestion inECoGBMIdesignthereforeis:\Atwhatspectralresolutio nshouldECoGfeaturesbe extractedandmappedtobehavior?". Thenextquestionweseektoaddressis:\Atwhattemporaldep thsshouldtheECoG spectralfeaturesbefedtoltermodels?".IninvasiveBMIl iterature,thereareextensive studiesonthecorrelationbetweentimelagsandhandmoveme nts[ 95 ].Neuralactivityone secondpriorthecurrenthandmovementarecommonlyusedast hedefactoltermemory depth.NosuchstudiesarepresentinthecurrentECoGBMIlit erature.Asmentionedin theprevioussection,Schalketal.[ 82 ]employECoGfeaturesextractedfromawindowof 333msecbeforethemovementexecution.Pistohletal.[ 73 ]useECoGmeasurements125 26

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msecpriorthekinematics.Wesystematicallystudyoptimal ltermemorydepthsinlinear models. OncetheECoGfeaturesareanalyzed,anotherquestionarise s.Mostsimplyput, BMIsinquiretondafunctionalrelationshipbetweenneura lactivityandmotor behavior.Sincethehumanbrainisanonlineardynamicalsys tem,\canthisfunctional relationshipbewellapproximatedthroughlineartranslat ions,orshouldnonlinearmodels beemployed?". Finally,weask:\Canthespatial,temporalandspectralfea turesthatcontributethe mosttothereconstructionofmotorbehaviorbeselectedthr oughsophisticatedmethods?". Inthisstudy,weaddresseachofthesequestions. 1.4ChallengeswithECoGBMIs Implantationofsubduralelectrodesinhumanpatientsareo nlyperformedwhen theseizureorigincannotbelocalizedbyEEGorwhentheepil eptogenicareaisnear eloquentbrainareasandfurtherdelineationisrequired[ 48 ].Permissionforimplantation ofsubduralelectrodesforBMIexperimentalpurposesisver yunlikelytobegranteddue tothecomplicationsinvolved.Hence,ECoGBMIstudiesarel imitedtoanalyzingneural activitygeneratedformotorcontrolinepilepsypatients. Althoughafterimplantation patientswhoseepileptogenicfocusisremotefromthemotor arearesumenormalmotor activies,itishardtostatethattheconditionwillnotaec ttheBMIstudieswith 100%certainty.Interictalspikingactivity,observedasn on-stationaryhighamplitude discharges,canbepresentintheglobalsensorimotorsyste mcouldpotentiallycorrupt themotorcontrolfeatures[ 30 ].Furthermore,patientsparticipatinginthestudies aresubjecttomedicationstotreatepilepsy.Thesemedicat ionscansuppressneural activityandreducepatientinvolvementinmotortasks.Mor eover,theclinicalrecording environmentissubjecttovariousnoisesourcesandequipme ntthatcaninterferewith ECoGmonitoring,andpost-surgerychangesinthecorticale nvironmentmayleadto degradationofrecording.Anotherissueisthatasthemainf ocuswiththesepatientsis 27

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epilepsymonitoringtheBMIstudiesneedtobeconductedins hortexperimentaldurations andthenumberofsessionsarelimitedduetotheshortmonito ringtimes(Patients undergosurgerywithin1-2weeks).Shortdatacollectionsc ausedicultiesinmodeling throughsupervisedlearningsinceenoughdataneedstobeal locatedfortrainingand testing[ 32 ]. Otherchallengesariseinprocessingoftherecordedoronli neECoGsignals.The numberofneuronsinthespatialcoverageofsubduralelectr odesareintherangeoftensof thousandsofsources.IninvasiveBMIsystemsthehighresol utionactivityofoneneuron canbeisolatedanditscorrelationortuningtothemotorbeh aviorcanbeeasilyanalyzed. Withsubduralelectrodesthechallengeistoisolateoutofm illionsofsourcestheones thataremodulatedwithbehavior.AsweshallseeinChapter3 itishardtoyieldne directionaltuningsfromECoGelectrodes.Otherchallenge sincludethenonstationarity oftherecordingswhenthesamemotortaskhasbeenperformed duetothefunctional variabilityofthehumanmotor,premotor,parietal,andsom atosensorycortices.Again, thisboilsdowntothenecessityofisolatingsourcesmodula tedtothemotortaskfromthe highlyvariablebackgroundactivity. 1.5Outline Motivatedbytheneed,applications,andchallengesinvolv edinbuildinghumanmotor prosthesis,weexploremodalitiestobuildBMIsystemsfore xecutionofcontinuousmotor actionswithdirectinputsfromhumanECoGdata.Inspiredby ring-ratebasedinvasive BMIsandmotor-inducedrhythmicsynchronizations/desync hronizationsinEEGbased BCIs,westudytheamplitudeandfrequencymodulationsofth esubduralrecordings overthesensorimotorcortex.Weundertakethechallengeof exploringtheessential temporal,spatial,andspectralcharacteristicsofbroadb andECoGpotentialsinvolved intheexecutionofcontinuousmulti-dimensionalmotoract ionswhichareyettobefully understoodorutilized.Exploratorytoolsfortheextracti onofvaluablefeaturesincludein depthspectralanalysis,directionaltuningandsemiblind sourceseparationmethods. 28

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Next,weaddressthechallengesinvolvedinadaptivelymapp ingtheECoGactivity intomotorbehaviorinopen-loopexperiments,suchashighv ariabilityinrecordeddata, noiseremovalandregularizationofmulti-dimensionaldat a.Modeloutputsofhand trajectoriesbasedonECoGfeaturesarestudiedintermsofs patio-spectralsensitivities. Wefurtheraspiretodesignclosed-loopexperimentsinwhic hnotonlythemodelsadaptto thepatients'ECoGactivity,butpatientsalsotraintoadap ttoregulatetheinputtothe models. Theorganizationofthisdissertationisasfollows:Theexp erimentalBMIsetup,the recordingmethods,thepatientsandthebehavioraltasksar epresentedinchapter2.The exploratoryanalysisoftheECoGfeaturesinthecontextofm otorexecutionisdescribed inChapter3.Next,thelinearmodelsinvolvedinmappingthe extractedfeaturesinto themotorbehaviorareexplainedinChapter4.Chapter5expl oreschannelselectionand projectionbasedregularizations,followedbynonlinearm odelingintheChapter6.Finally, concludingremarksandpossiblefuturedirectionsareprov idedinChapter7.Interested readerscanndtheimplementationofclosed-loopdatacoll ectionsystemsandbehavioral experimentsintheAppendix. 29

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CHAPTER2 PATIENTSANDBEHAVIORALEXPERIMENTDESIGN Themulti-componentBMIsystemwassetupattheNeuroprosth eticsResearchGroup Laboratory,UniversityofFlorida.Intheexperimentalpar adigm,subduralelectrode recordingswerecollectedfrompatientswhiletheyweretra cingacursoronacomputer screenwithapre-denedpath.Theschematicofthedesigned systemispresentedin Figure 2 .Fromtheimplantedelectrodes,neuralactivityacrosscha nnelsareamplied, digitizedandfedintoabankofdigitalsignalprocessorsth roughopticalcables.The digitizedsignalsarestoredinacomputerwhichalsoprovid estheexperimentaltaskand visualfeedbacktothepatientthroughascreen.Inthischap terwedescribeindetailthe signalacquisitiontechniquesandhardwarecomponentsoft hesystem,thepatientsandthe behavioralparadigmsthatwereperformed. n r r n r r r r r n r r r n r r r # r Figure2-1.Schematicoftheend-to-endBMIsystem 30

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2.1Patients Thepatientsvolunteeringinourstudiesweresubjecttoext raoperativesubdural gridevaluationatShandsHospitalattheUniversityofFlor idaaspartoftreatmentof intractablecomplexpartialepilepsy.Bothpatientsweref emaleright-handedteenagers (Patient1:14yearsold,Patient2:15yearsold).Priortosu bduralelectrodeimplantation surgery,theywentthroughscreeningwhichinvolvedEEGsca lpandregularneuropsychological testing,andmagneticresonanceimaging(MRI).Thesetests establishedtheabsenceof motororsensorydecits.This,howeverdoesnotguaranteet hatthedisordermaynot aectthefunctionofthemotorcortexforBMIstudies[ 79 ].Thefeaturesandmodels designedinthesestudies,andthereportedresults,maynot necessarilyapplytoa normallyfunctioningbrain. Thesurgicalimplantationoftheelectrodegridswasperfor medaccordingto establishedprotocols[ 47 ].Thegridsconsistedofplatinum-iridiumelectrodes,4mm in diameterspacedat1cmcenter-to-centerdistances,whichw ereembeddedin1.5mm thicksilasticsheet,leaving2.3mmoftheelectrodediamet erexposed.Figure 2.1 depicts a3x3cm 2 surfaceofgridssuperimposedonthecorticalsurfacewhich allowsarelative comparisonoftheelectrodesizeandspacingswiththesulci ,gyri,andvasculatureon thecortex[ 79 ].Thepositionoftheelectrodeswereselectedstrictlyfor epileptogenic focusandnotbiasedbyourexperiments.Theelectrodenumbe ringandapproximate positionsasindicatedbythesurgeonatthetimeofsurgerya representedinFigure 2.1 A. Notethatforbothpatientsthegridsareimplantedonthelef ttemporallobe(allowing themtousetheirrighthandsforthebehavioraltasks).Pati ent1wasimplantedwitha 6x6gridarray,Patient2witha4x8arraypositionedasrequi redfortheirepileptogenic localizationtreatment.Electricalstimulationofthesub duralgrids[ 93 ]yieldedthe locationoftheprimarymotorcortexbythepatients'motorr esponse.Thestimulation paradigmconsistedof50Hzbiphasicwaveswithpulsedurati on0.3msec,lasting2-5sec withaninitialintensityof2mA,increasedatincrementsof 1-2mA[ 79 ].Motorresponses 31

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fromthestimulation,usingthenumberingconventioninFig ure 2.1 AareprovidedinTable 2-1 $ %& & & () && + ,./ + 0 12 + 1 Figure2-2.Invivoplacementoftheelectrodegridina3x3cm 2 areaofcortexandthe relativeelectrode,gyri,sulci,andvasculaturerelation ships. Table2-1.Motorresponsetoelectricalstimulationofsubd uralgrids Patient1Patient2 RightHand22,28RightHand2,3RightWrist23,24,30RightArm14,15RightForearm22,30RightBicep29RightSensoryArm27 Thelocationoftheelectrodegridswerealsoevaluatedafte rsurgeryusingMRI undertheguidanceofaboardcertiedradiologist.InFigur es 2.1 C-D,thepost-operative T1weightedimagesareshownforeachofthepatientsinthiss tudy.Themethodof deningtheanatomicallocationofthegridconsistedofrs tidentifyingthepost-central gyrusworkingfromthemidlineandthenfollowingittothece ntralsulcus.Withthese landmarks,thegridelectrodeswereidentiedandlabeledi ntheimagesandmarkerswere applied.Therelativepositionsoftheelectrodeswithresp ecttothecentralsulcusand surroundinggyriallowedassociationoftheelectrodeswit heitherpremotor(PM),primary motor(M1),somatosensory(S),andposteriorparietal(PP) cortices.Multipleimages wererequiredtocompletelylocalizethegridwithrespectt othecentralsulcusasshown 32

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bythepartiallabelingofthegridineachimageduetothecli nicalimagingprotocolthat determinesslicethicknessandimagingorientation[ 79 ].Othermethodsoflocalization includemappingsoftheMRIslicesintotheTalairachspace[ 90 ]. Thepatientsinvolvedwerefullyrecoveredfromthegridele ctrodeimplantation surgerywithin48hourspost-surgeryandwerefullyalertan dattentiveatthetimeof testing.Duringtheirepilepsyworkup,thepatientswereta peredfromtheirpresurgical anticonvulsantmedications(topirimate,oxcarbazepine) tofacilitateseizureevaluation. Whenthebehavioraltaskswereperformed,thepatientswere seizurefreeforatleast6 hourspriortotesting[ 79 ]. Forthedurationoftheexperimentstheclinicalmonitoring systemswerereplacedby therecordingparadigmpresentedinFigure 2.1 ,whichwasapprovedbytheUniversityof FloridaInstitutionalReviewBoards 1 .Aboardcertiedneurologist(Dr.PaulCarney, M.D.)andthetechniciansofShandsHospitalEpilepsyMonit oringUnitwerepresentto monitorthepatientduringthestudyincompliancewiththe\ standardofcare"ofepilepsy practice.Duringthetimeofthestudy,theclinicalepileps ymonitoringteamhadfull accesstotheECoGmonitoringsysteminconjunctionwithvid eosurveillancetoensure completepatientsafety[ 79 ]. Theelectrodescoveredmainlytheprimarymotor(M1)andpre motor(PM)cortices withsomeonthesomatosensory(S1)andposteriorparietal( PP)cortices.Theprimary motorcorticalneuronsmediatetheplanningandinitiation ofcomplexsequencesof voluntarymovements[ 75 ].Asdiscussedearlier,movementcanbeelicitedbyverylow intensitystimulationintheprimarymotorcortex.Neurons inthepremotorcortexhave responsesthatarelinkedintimetotheoccurrenceofmoveme ntsasintheprimary motorarea[ 75 ].However,insteadofdirectlycommandingtheinitiationo famovement, PMneuronsencodethe\intentiontoperformamovement"orra therthe\selection 1 http://irb.ur.edu/ 33

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ofmovementsbasedonexternalevents"[ 75 ].InconditionalmotortasksPMneurons ofmonkeyshavebeenreportedtoreattheappearanceoftheg ocue,wellbeforethe executionofthetask[ 75 ].Theposteriorparietalcortex,ontheotherhandisregard edas asensorimotorinterfaceforplanningandcontrolofvisual lyguidedmovement,whereby theeye-centeredframeofreferenceismappedtoarepresent ationofmotorerrorina hand-centeredframeofreference[ 7 ]. 2.2BehavioralTasks IntheexperimentalparadigmsinourBMIsystem,thepatient swerecuedtofollow withtheirrightindexngerapredenedcursortrajectoryp resentedonanLCDscreen withanactiveareaof(20x30cm).Figure 2.1 showssnapshotsofthescreenasobserved bythepatientduringexperimentation.Thehorizontal(x)a ndvertical(y)coordinatesof thetrajectoryduringanentiresessionareprovidedinFigu re 2.2 .Thetrajectoryconsisted oftwo(repetitious)components:acommonlyusedcenterout cursorcontroltask[ 28 ]and atargetselection[ 14 ]task.Thecenterouttaskconsistedofsmoothlyvaryingtra jectories thatformedapatternextendingfromthecentertopredened locations(invisibletothe patent)attheedgesoftheworkarea.Forthetargetselectio ntask,color-codedtargetsare arrangedinasequenceatthetopofthescreenandthepatient wasrequiredtomoveto eachofthem.Thisbehaviormimicsacomputeruser'smovemen ttoselectanicononthe screen.Inasinglesession,thepatientswererequiredtore peattheentiretasksixtimes. Thesametrajectorywasrepeatedforeachtrial.Forthepati entspresentedhere,Patient 1wasabletocompletethetasksataspeedthatwas15%fasterP atient2.Allbehavioral taskswereacquiredconcurrentlywiththerecordingofneur onalmodulationsfromthe implantedECoGgrids[ 79 ]originallysampledat381.5Hzandfurtherdownsampledto 10Hz.Thespectralcharacteristicsofthetrajectorieswil llaterbeexploitedduringthe extractionofrelevantmotorfeatures(seeChapter3).Figu re 2.2 showsthepowerspectral densitiesofthehorizontalandverticaltrajectoriescomp utedovertheentirerecording 34

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sessionforPatient1(4mins).Thedominantfrequenciesare ofveryslownature,below 1.5Hz. Themotortaskshereinfocusonarmreachingandpointing.Fo rparalyzedpatients, reachingandpointingoerstwocriticalfunctions:reachi ngenablesonetoextendinto theexternalenvironmentandexpandtherangesofgoalsavai lable,whilepointingenables onetocommunicatewhichgoalisofinterest[ 85 ].Thesebehaviorsemphasizetheneural decisionmechanismsformotorexplorationandthevisualfe edbackoftheperformed actions.Thesevisuomotortasksrequiremotorcommandstha torientapatient'sarmand locomotiontowardavisualinputwhichisalsoknownassenso rimotorapproachmapping [ 98 ]. 2.3SignalAcquisition Multichannelsubduralpotentialswerecollectedsynchron ouslywhilethepatients wereengagedinthebehavioraltask.Forourexperiments,we weremotivatedtosetup aseparaterecordingsystem(asshownintoFigure 2 )duetothelimitedfrequency resolutionofthesystemavailableintheclinicforepileps ymonitoring.Wepreviuosly discussedthetheoryimplyingobservablepotentialsupto1 0kHzinECoG[ 66 ],whereas mostclinicalsystemsdonothavethecapabilityofrecordin gaboveasamplingfrequency of1kHz.Withthedesignedsystem,wewereabletosampletheE CoGsignalsat12,207 Hz[ 79 ]. AcustomcablewasdesignedtointerfacetheclinicalAd-Tec h(Racine,Wisconsin) electrodeswiththebiopotentialampliers,whoselengthw askepttoaminimumto minimizenoisecontaminationencounteredintheclinicale nvironment.TheTucker-Davis Techologies(TDT;Alachua,Florida)[ 92 ]MedusaPreAmpsperformanalog-to-digital conversionandsendtheampliedneuronalactivityoptical lytoaveprocessorTDT Pentusarecordingsysteminwhichthedataislteredandtim esynchronizedwiththe behavioraltrajectories.Thesamplingratewaschosenasha lfthenativeDSPclock, 24414.1Hz.Thepotentialsfromthesampledcorticalareasw eredigitizedwith16bits 35

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ofresolutionandbandpasslteredfrom1to6kHz.Thedesign edsystemiscapableof recordingfrom32electrodessimultaneously 2 [ 79 ]. Adesktopcomputer(DellXPS,Pentium4,3GHz,2GBRAM,1TBHa rddisk,RAID 5conguration)runningMatlabv7wasgeneratingthedesire dbehavioraltrajectoriesand communicatingwiththebankofDSPsthroughActiveXcommand s.Thedatawasthen sentviaabi-directionalgigabitPCIinterfacebetweenthe recordingcomputerwhichwas storingdataandgeneratingthedesiredbehaviorwhilecomm unicatingwiththeDSPs. Finally,thedesiredtrajectoriesweresenttoasecondcomp utermonitorplacedinfront ofthepatient.Thepatientwasthencuedtofollowthecursor trajectorywiththeirindex nger.Behavioraltrajectoryrecordingswerealsostoredw ithasharedtimeclockand sampledat381.5HzonthePentusasystem. Closed-loopexperimentswithnewbehavioralparadigmsare implementedandare describedintheAppendix.Theseexperimentshavenotbeenc onductedatthetimeof publication. 2 Activityfromelectrodes33-36oftheimplanted6x6gridsof Patient1werenot recorded. 36

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34 3 5 5 6 3 7 78 9 6 A : ; < => ?@A =B CD E F B G < H IJK LM N L O IP LM B C Figure2-3.Gridlocalization.A)Electrodeplacementandn umberingforPatient1(left) andPatient2(right)asindicatedbythesurgeon.B)Anatomi callocalization ofgridelectrodesforPatient1andC)Patient2viaT1MRimag ing. 37

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-15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 Center-Out Trajectory Tracking -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 Target Selection Figure2-4.Behavioraltrajectoriesona20x30cmscreen 0 50 100 150 200 250 -10 -5 0 5 10 X-axis 0 50 100 150 200 250 -15 -10 -5 0 5 10 Time (sec)Y-axis Center-out task Targetselection Figure2-5.ExperimentalsessionperformedbyPatient1.Th esessionstartswiththe center-outtaskfollowedbythetrajectoryselectiontask, repeatedoverin5 trials. 38

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0 1 2 3 4 5 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 Frequency (Hz) Power Spectral Density Estimate Horizontal Vertical Figure2-6.Powerspectraldensityestimatesofthehorizon talandverticalhand trajectoriesduringtheexperimentalsessionperformedby Patient1. 39

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CHAPTER3 ANALYSISOFMOVEMENTRELATEDFEATURESINECOG Extractionofthefeaturesfromneuralactivitythatregula tethemotorintentand executionistheforemostcrucialelementinmodelingbehav ior.ThefeaturesofECoGthat aretunedwithmotorbehaviorarenotasdirectorwellunders toodasspikecountingin invasiveBMIs.Extractingmotorbehaviorfeaturesfromthe ECoGdataischallengingdue tothemanysignalsourcesinvolvedwhichmodulateindiere ntamplitudeandfrequency ranges,thevariabilityinECoGactivityduringexecutiono fthesamemotortasksand hightemporalresolutionthatincreasesthenumberoffreep arametersextensivelyin modelsemployingtapdelaylines. Inthischapter,westartwithexploratoryanalysisoftheEC oGrecordingstostudy thetemporal,spatialandspectralmovement-relatedmodul ations.First,wepresentan event-relatedspectralanalysisinwhichrestandbehavior alstatesarecompared.This isfollowedbyspectraldecompositionofthebroadbandreco rdingsintonon-overlapping bandsuniformlyspacedinthelogwarpedfrequencydomainas meansofextracting movementrelatedrhythms.Wethenexplorethedirectionalc orrelationor\tuning"ofthe spatio-spectralfeaturestothehandmovementdirectionth roughtuningcurveanalyses. Finally,weexploitthespectralcharacteristicsofthehan dtrajectoriesinordertoextract theneuralrhythmsmodulatingthemotortaskthrough denoisingsourceseparation ,a recentlyintroduceddecompositionframeworkwhichextrac tshiddenstructuresofinterest withindatabylteringthesourceestimatesbasedonaccumu latedknowledge,presumed signalcharacteristics,orexperimentalsetups[ 80 ]. 3.1FunctionalSpectralAnalysis Therhythmicityofmacroscopicsignalsprovidesameansofq uantitativelydescribing therecordings,asthefrequencyoftherhythmsthatarecorr elatedtoactions,eventsor stimulicanbemeasured.ThroughoutthehistoryofEEGtechn ology,EEGfrequencies havebeenconvenientlyclassiedintobands[ 10 ].InChapter1,studieswithEEG 40

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -1 0 1 x 10 -4 Voltage (V) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -1 0 1 x 10 -4 Time (sec)Voltage (V) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -20 -10 0 10 Displacement Horizontal Vertical A 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -20 -10 0 10 Displacement (cm) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -5 0 5 x 10 -4 Voltage (V) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -10 -5 0 5 x 10 -4 Time (sec)Voltage (V) Horizontal Vertical B Figure3-1.Synchronizedbehaviortrajectories(middle)a ndbroadbandECoGrecordings fromchannels8(top)and30(bottom)forA)Patient1andB)Pa tient2. revealingevent-relateddesynchronizationswithslowpot entials( < 50Hz),inparticular withmuandbetarhythms,werediscussedwithmotortasks.Ag aininChapter1,it wasmentionedhowthebroadbandnatureofECoGallowedforus eofhigherfrequency bands,gammaandfastgammawhichshowedsynchronizationwi thavarietyofvisual, auditory,motorandimagerytasks.Hence,westartanalysin gthespectralpropertiesof ourrecordings. Throughthedataacquisitionsystemtherawsignalsarereco rdedatasamplingrate of f s =12207Hz.ECoGspectralrangesbeyondthehighgammafreque ncieshavenever beenstudiedorincorporatedinneuroprosthesisapplicati ons.Inouranalysisweoptto studythethewholebroadbandspectralrangeuptotheNyquis tfrequency.Exemplary 41

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recordingsfromtheneuroprostheticexperimentalparadig marepresentedinFigures 3-1 A-BforPatients1and2,respectively.Time-synchronizedb ehavioralrecordingsand ECoGfromtwochannels,onefromthepre-motorarea(top)and theotherfromthe primarymotorarea(bottom)areplottedoveraveseconddur ation.Voltagesinthe rangeof 100 Vareobserved.Combinationsoflow-amplitudefastoscilla tionswere mixedwithlargeamplitudeslowandsharpwaves.Themiddles ubplotcontainsasegment ofthetargetselectiontrajectoryin(x,y)coordinateswhe rethecenterofthescreenis locatedat(0,0)andtheexcursionsrangefrom 15cmindisplacement. Thepowerspectraldensities(PSD)softhesechannels(inth e5secwindowsshown) forPatient1areprovidedinthetoprowofFigures 3-2 A-Bfromwhichwediscern the1 =f trend.PSDsof5secsofrecordingsfromthesamechannelsrig htbefore themovementonsetareprovidedinFigures 3-2 A-B.ComparingtherespectivePSDs weobserveevent-relatedsynchronizations(increaseinsp ectralpower)inspectral rangesof145-215Hz,512-572Hz,850-940Hz,1121-1240Hz,a nd5925-6110Hz.This givesusareferenceastowhichbandsmayshowmodulationsco rrelatingtothehand trajectory.ThePSDsarecalculatedthesamewayforPatient 2andpresentedin Figures 3-2 C-D.ComparingthebeforeandaftermovementonsetPSDsforc hannel8, weobserveaslightevent-relateddesynchronizationinthe slowfrequenciesandaslight event-relatedsynchronizationinthespectralrangeof243 0-2520Hz.Aslightevent-related synchronizationinthesamerangeispresentinchannel30as well. Inordertoperformasystematicanalysis,wedecomposetheb roadbandspectrum intonon-overlappingintervalsofequalbandwidthinthelo garithmicfrequencydomain throughabankof constant-Qlters .Theparameter Q isdenedastheratioofthecenter frequencytothebandwidthofthebandpasslter.ConstantQ lterstherebyrefertoa familyofltersforwhichtheringingoftheimpulserespons esareapproximatelyconstant. Thisisimportantbecausewearegoingtouseseveralbandpas sltersinthisworkand extractfeaturesfromtheiroutput.Hence,forlowercenter frequenciesthespectralband 42

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Table3-1.ECoGspectralfrequencybands Spectralbandswith n =32 n =16 n =8 8-10Hz8-12Hz8-18Hz10-12Hz12-15Hz12-18Hz15-18Hz18-23Hz18-28Hz18-42Hz23-28Hz28-34Hz28-42Hz34-42Hz42-52Hz42-63Hz42-96Hz52-63Hz63-88Hz63-106Hz88-96Hz96-118Hz96-145Hz96-219Hz118-145Hz145-178Hz145-219Hz178-219Hz219-270Hz219-331Hz219-501Hz270-331Hz331-408Hz331-501Hz408-501Hz501-616Hz501-758Hz501-1147Hz616-758Hz758-932Hz758-1147Hz932-1147Hz1147-1410Hz1147-1734Hz1147-2623Hz1410-1734Hz1734-2133Hz1734-2623Hz2133-2623Hz2623-3226Hz2623-3967Hz2623-6110Hz3226-3967Hz3967-4879Hz3967-6110Hz4879-6110Hz 43

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10 2 10 3 10 -12 10 -10 10 -8 10 -6 Before Movement OnsetChannel 8 10 2 10 3 10 -12 10 -10 10 -8 10 -6 Frequency (Hz)Motor Task A 10 2 10 3 10 -12 10 -10 10 -8 Before Movement OnsetChannel 30 10 2 10 3 10 -12 10 -10 10 -8 Frequency (Hz)Motor Task B 10 1 10 2 10 3 10 -12 10 -10 10 -8 10 -6 Channel 8Rest 10 1 10 2 10 3 10 -12 10 -10 10 -8 10 -6 Frequency (Hz)Motor Task C 10 1 10 2 10 3 10 -10 10 -5 Channel 30Rest 10 1 10 2 10 3 10 -10 10 -5 Frequency (Hz)Motor Task D Figure3-2.A-B):Toprow:PowerdensityspectraofECoGreco rdingsfromPatient1 computedover5secsforchannels8and30duringmotortask.B ottomrow: PSDsofthesamechannelswhilethepatientisnotinvolvedin experimental paradigm(waitingformovementonset).C-D)SameplotsforP atient2. isnarrow,whereasthepassbandaroundhighcenterfrequenc iesarewider.Theoptimal numberofltersintheconstantQ lterbankisgoingtobeexploredthroughmodeling. Weinitiallystartedwithalargenumberofltersandtheban dswillbefurthermerged orsplitasnecessarythroughouttheanalysis.Thespectral rangefrom8Hz 1 to6.1kHz 1 Slowrhythmshavebeenwellstudiedintheliteratureandthe slowestbandthathas beenfoundcorrelatedwithcontralateralmotoractsisthem urhythmwhichcorresponds to8-12Hz[ 72 ].Slowerrhythmssuchasthedeltaandthetawavesarerelate dtosleep cyclesandthehippocampus,respectively[ 8 ]. 44

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0 50 100 150 200 250 -20 0 20 Displacement (cm) 0 50 100 150 200 250 0.5 1 1.5 2 x 10 -12 Power4.8-6.1 kHz 0 50 100 150 200 250 0 1 2 x 10 -12 Power932-1147 Hz 0 50 100 150 200 250 0 1 2 x 10 -11 Power145-178 Hz 0 50 100 150 200 250 0 2 4 x 10 -10 96-118 HzPower 0 50 100 150 200 250 0 5 x 10 -10 Power63-88 Hz 0 50 100 150 200 250 0 1 2 x 10 -9 23-28 Hz Time (sec)Power Figure3-3.Synchronizedbehaviortrajectoriesintwodime nsions(top)andpowerof passbandECoGrecordingsfrom32channelsfromPatient1.To pthreeband showvisualevent-relatedsynchronization.Thepatientst oppedthebehavior atthesecondhalfofthelasttask. isuniformlydividedinto n =32segments.Thiscorrespondstoacentralfrequencyto bandwidthratioisof Q = f c =B =4 : 85.ThespectralbandsarelistedinTable 3-1 .The verynarrowbandwidthallocatedtoslowpotentialssuggest thatforthe Q -lterdesignthe numberofltersneednotbeincreasedfrom n =32.Hence,wesetthehighestspectral resolutioninouranalysisto n =32bands.Wemergetwoconsecutivepassbandstoattain n =16bandsandfurthermerginginthesamefashionyields n =8bands.InTable 3-1 we seethatfor n =8theslowerbandscorrespondtotherangesofthewell-know nmu,beta, gammaandhighgammarhythms.Thus,thisisselectedasthelo westspectralresolution. Foreachofthefrequencybands,wedesignedlinear-phaseFI Rltersandcompensatedfor thegroup-delay. ThemodulationoftheECoGcomponentsrelatedtomovementca nbecapturedby thepowerofbandpasslteredECoGsignalswhichiscomputed innon-overlapping100 45

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msectimebinsasfollows: x kj ( t n )= Z t n +1 t n V 2 j;k ( t ) dt (3{1) where V j;k isthelteredECoGamplitudesignalinfrequencyband k onchannel j and t n +1 = t n +100 msec .Throughvisualinspectionweobserveevent-relatedsynch ronization inthreespectralbands(outofthe n =32)withpassbandsof161 : 5Hz 16 : 5Hz, 1040Hz 107 : 5Hz,and5 : 5kHz 0 : 6kHz(whichwererevealedinFigure 3-2 ).Theincrease ofpowerinthesethreebandssynchronizedwiththehandtraj ectoryisgiveninFigure 3-3 alongwiththreeotherexemplarybandswheresignicantERS isnotobserved.Wenote thatthepatientstoppedthebehaviorinthelasthalfofthel asttrial,whichexplainsthe decreaseinpowerbeforethelasttrajectoryiscompleted.I nFigure 3-3 wealsoobserve thatthecross-channelcorrelationinthemodulatedbandsi sratherhigh.InChapter4,we shallseethatinfacttheconditionnumbersofthecorrelati onmatricesamongstchannels inthesebandsareveryhigh. Wequantifythecorrelationbetweenthehandtrajectoriesa ndthespectralfeatures foreachbandateachchannelforPatient1inFigure 3-4 .Theleftcolumnofgures arethecross-correlationsfortheverticalhandtrajector y,whiletherightcolumnisfor thehorizontal.Thethreerowsofgurecorrespondto n = f 32 ; 16 ; 8 g spectralbands. Ineachguretheverticalaxisrepresentsthelogarithmicf requencyscalebetween 8-6110Hzdividedinto n bands.Withineachbandthecross-correlationsbetween thetrajectoriesandthebandpasslteredsignalsfrom32ch annelsarepresented (Hencethereare32 n rowsineachgure).Thechannelsinthesamespectral bandsyieldsimilarlevelsofcorrelationwithbehaviorand henceweseetheblockof similarcolorsineachbandinFigure 3-4 .Thehorizontalaxesrepresentsthetime lagsinseconds.Foreachcross-correlationblock,thehigh estcross-correlationisfound atthezerothlag.Westartbyexaminingthecross-correlati onsfortheverticalhand trajectory,i.e.theleftcolumninFigure 3-4 .With n =32weseethreebands: f 4897 6110Hz ; 932 1147Hz ; 145 178Hz g thatarehighlycorrelatedwiththe 46

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behavior.Theresolutionfortheband145-178Hzislostwhen thebandsaremerged, butotherbandsthatshowedhintsofcorrelationprevailed. With n = f 16 ; 8 g the highlycorrelatedbandsare f 3967 6110Hz ; 1147 1734Hz ; 758 1147Hz g and f 2623 6110Hz ; 1147 2623Hz g ,respectively.Anotherimportantobservationwemake isrelatedtothememorydepth/causalrelationshipbetween thespectralpowersandthe motorbehavior.Thecross-correlationsarehighupto1-1.5 secsoftimelag.Thismemory depthwillserveasagoodreferencewhenwearebuildingmode lsinvolvingtap-delay-lines. Notethataround2secsoftimelagthereisahighnegativecor relation.Thisisdueto thecyclicnatureofthehandtrajectory.Ifwereferbacktot hevertical(green)hand trajectoryin 3-1 ,weseethatthetimedierencebetweenamaximumandaminimu mis about2secs. Now,westudythecorrelationsforPatient1withthehorizon talaxis,i.e.theright columnofFigure 3-4 .Thehighlycorrelatedbandsaresimilar,butwithanegativ e correlationinthehighestband.Thehighestcorrelationwi ththisbandalsoisnotat thezerothlagbutratheraround1.5secoftimelag.Thehighc orrelationsintheother bandsalsofallmuchfaster(before1sec).Thenegativehigh correlationsalsoappear muchfaster(around1.5sec).Thiscanbeduetothefastercom ponentsinthehorizontal handtrajectory(comparedtothevertical).Overallthemag nitudesofcross-correlation, ascanbeobservedthroughthecolorbars,aremuchlowercomp aredtotheverticalhand trajectory. ThesameplotsforPatient2areprovidedinFigure 3-5 .Onceagainthechannelsin thesamespectralbandsyieldsimilarlevelsofcorrelation withbehaviorandthehighest cross-correlationsineachbandarefoundatthezerothlag. Againwestartbyexamining thecross-correlationsfortheverticalhandtrajectory,i .e.theleftcolumninFigure 3-5 With n =32weseethatthebands2133-2623Hzand758-932Hzarecorre latedwiththe behavior.Moreover,thereisaslightnegativecorrelation intheslowerbands.Thesetwo resultsareinaccordwiththeERSandERDobservationsofFig ures 3-2 C-D.Justlike 47

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withPatient1,thecross-correlationsarehighupto1-1.5s ecsoftimelagandarecyclic around2secs.WhenwestudythecorrelationsforPatient2wi ththehorizontalaxis,i.e. therightcolumnofFigure 3-5 ,weagaininferthatthehighlycorrelatedbandsaresimilar butwithanegativecorrelation.Also,thereisslightposit ivecorrelationintheslowbands. Overall,aswasthecasewithPatient1,themagnitudesofcro ss-correlationaremuchlower comparedtotheverticalhandtrajectory. Tosummarize,fromthisanalysisweobserved: ::: whichspectralbandsarecorrelatedwithbehavior. ::: thatthecross-channelcorrelationwithinabandisquitehi gh. ::: thatmergingthebandscanbeadvantageousforthehigherfre quencybands, whereasresolutionmaybelostfortheslowerbands. ::: aroundwhatmemorydepthsweshouldbuildourtrajectorymap pinglters. ::: thatthecross-correlationsarecyclicduetothenatureoft hebehavior. ::: thatthecorrelatedchannelsandmemorydepthsforthetwotr ajectorydimensions arenotnecessarilythesame. ::: thatthecorrelatedbandsarenotnecessarilythesameforth etwopatients. ::: thatforbothsubjects,therecordingsyieldhighercorrela tionwiththevertical handtrajectorycomparedtothehorizontal. 3.2DirectionalTuningofECoGFeatures Inneuroscienceliterature,asinglemotorneuron'sphysio logicresponsetoa behavioraltaskhasbeendescribedusingdirectionaltunin gcurves.Asoriginally derivedfromacenter-outtaskbyGeorgopoulus[ 28 ],thetuningcurverelatesthemeanof movement-relatedcellactivitytomovementdirection.The preferreddirectionofaneuron, measuredindegrees,isthedirectionwhichyieldsthemaxim alringresponseovermany trials.Weighingthepreferreddirectionswiththeneurala ctivitiesinthepopulationgives aresultantdirectionvectorcalledthe\populationvector "whichhasbeenshowntobe correlatedwiththeactualmovementdirection[ 28 ]. 48

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TheinterpretationofdirectionaltuningofECoGfeaturesi spotentiallyverydierent thanthisclassicalviewasECoGismeasuringanaggregateof neuronalpotentials. Thegoalisnottoinfertheangleofdirectionthroughpopula tionvectors,butrather toanalyzethecorrelationsbetweenspectralpowersanddir ectionalanglestoidentify features(frequencybandsandmotorareas)thatcanultimat elycontributetoBMI models.Wekeeptheterminologyof\tuningcurves"asithasb eenusedinmesoscopicand macroscopicliterature,butwewouldliketoemphasizethat thisisjustanothercorrelation studyandthatECoGelectrodescannotbe\assigned"adirect ionalangleastheycollect activityfromacorticalareaof1-15.cm 2 Inthemesoscopicandmacroscopicliteraturewendthefoll owingtuningstudies. Rickertetal.[ 76 ]computedtuningofLFPamplitudesatthewellknownP1,N1,P 2,N2 signaturesofthemovement-relatedpotentialsandreporte dthatthepercentageoftuned LFPswashigherforthecombinedgammaandhighgammaband(63 -200Hz)comparedto thebetaband(16-42Hz).ThemaximumpercentageoftunedLFP sforthegammaband was32%attainedatN1(35msecaftermovementoset).Heldma netal.[ 33 ]studiedthe tuningofthechangeofLFPspectralamplitudeduringmoveme nt(comparedtobaseline) forthebeta,gammaandhighgammabands.15%ofthehighgamma LFPswereposition tunedwithanincrementalchangeinspectralamplitudewher eas10%ofthebetaLFPs weretunedwithdecreasedspectralamplitudes.Schalketal .[ 82 ]showedthattuned electrodeswerelocalizedinsmallareasacrossdierentpa rtsofthemotorcortexand demostratedhighspatialcorrelationsoftheseareasacros sfrequencybands. Herein,weanalyzethecorrelationoftheECoGpowertotheha ndmovement directioninthe n =32frequencybands.Thespaceofhandmovementdirectionra nging from0 o to360 o wasdividedinto8binswith45 o ofresolution.Cosinetuningofthepower acrosstheangleofdirectionasadaptedfromGeorgopoulus[ 28 ]isformulatedasfollows. Let i = i 45 o for i =0 ; 1 ;:::; 7andlet P i denotetheaveragedpowerduring movementexecutionintherespectiveangles.Thenpowermay beapproximatedasa 49

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sinusoidalfunctionofdirectionalangle: P = b 0 + b 1 sin( )+ b 2 cos( )= b 0 + c 1 cos( 0 ) wherethebiasandcoecientsofthesinusoidsarecomputeda s: b 0 =1 = 8 7 X i =0 P i (3{2) b 1 =1 = 4 7 X i =0 P i sin( i )(3{3) b 2 =1 = 4 7 X i =0 P i cos( i )(3{4) c 1 = q b 21 + b 22 (3{5) 0 =tan 1 b 1 b 2 (3{6) Here 0 isthepreferredangleoftheelectrodeand c 1 rerectstheincreaseinECoG powerat 0 [ 28 ].Theratioof c 1 over b 0 yieldsthe indexofmodulation I : I = c 1 b 0 (3{7) whichrerectstheincreaseinpowerovertheoverallmeanwhe nmovementisexecutedin thedirectionofthepreferredangle.Thismetricallowsfor acomparisonacrosschannels. The coecientofdetermination R 2 ,yieldsatnessmeasureforcosinetuning: R 2 = 4 c 21 P i ( P i b 0 ) 2 (3{8) Cosinetuningisconsideredsignicantfor R 2 > 0 : 70[ 28 ]andfeatureswith R 2 > 0 : 60 canberegardedastuned.Finally,plottingtheaveragedpow erasafunctionofdirectional anglesyieldsthetuningcurve. Asnotedearlier,thecoecientofdetermination, R 2 ,ismeasureofhowwellthe featureistunedtoacosinefunction.Itthereforeattribut eslowvaluestofeatures withmultimodalpreference(suchasthetuningcurveshowni nFigure 3-9 ).Hence, 50

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Table3-2.Cosine-tunedECoGfeaturesforPatient1 FrequencybandChannelnumberPreferredangle 0 R 2 I (%) 8-10Hz1433 o 0.758 10-12Hz29224 o 0.7214 15-18Hz1110 o 0.7111 15-18Hz1318 o 0.7310 15-18Hz16170 o 0.9910 15-18Hz3112 o 0.8730 18-23Hz13335 o 0.968 18-23Hz1512 o 0.8215 18-23Hz3115 o 0.8215 23-28Hz920 o 0.8810 23-28Hz14217 o 0.7215 23-28Hz260 o 0.7111 28-34Hz16171 o 0.7710 34-42Hz27343 o 0.7410 34-42Hz3125 o 0.7211 52-63Hz2381 o 0.7210 63-78Hz3256 o 0.7830 270-331Hz2610 o 0.7833 501-616Hz53 o 0.704 758-932Hz1186 o 0.793 1147-1410Hz29190 o 0.746 1410-1734Hz28200 o 0.784 1734-2133Hz2180 o 0.714 1734-2133Hz25179 o 0.714 1734-2133Hz28167 o 0.843 3226-3967Hz25164 o 0.775 theindexofmodulation, I ,isabettersuitedmeasuretocompareamongstchannelsand frequencybands.Figures 3-10 and 3-11 demonstratethemodulationindicesaveraged acrossfrequencybandstoemphasizethetuningofthespatia lchannels(left)andthe modulationindicesaveragedspatiallytoemphasizethespe ctralbands(right).ForPatient 1,Figure 3-10 Ashowsthattuningiswidelyspreadacrosschannelswithfew localized highmodulationindices.Theselocalizationscorrespondt oelectrodesoverthepre-motor (PMd)andprimarymotor(M1)cortices.TwooftheseM1electr odeshadshownmotor responsetoelectricalstimulation(aslistedinTable 2-1 ).Thespectralbandswithhigh modulationindicesasshowninFigure 3-10 Bareinaccordwiththosebandsdetectedin 51

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Table3-3.Cosine-tunedECoGfeaturesforPatient2 FrequencybandChannelnumberPreferredangle 0 R 2 I (%) 8-10Hz1831 o 0.8036 10-12Hz1845 o 0.8464 15-18Hz2237 o 0.7862 18-23Hz1947 o 0.7642 18-23Hz2154 o 0.8769 28-34Hz10173 o 0.8015 34-42Hz544 o 0.8323 42-52Hz2246 o 0.768 52-63Hz2241 o 0.767 78-96Hz12358 o 0.7912 118-145Hz561 o 0.726 178-219Hz15195 o 0.9711 178-219Hz29223 o 0.796 219-270Hz1158 o 0.823 219-270Hz14158 o 0.873 270-331Hz21209 o 0.755 331-408Hz2922 o 0.804 408-501Hz2349 o 0.932 616-758Hz21221 o 0.881 758-932Hz829 o 0.732 932-1147Hz17156 o 0.731 1410-1734Hz320 o 0.731 2133-2623Hz5244 o 0.793 2133-2623Hz6230 o 0.844 2133-2623Hz8265 o 0.843 2133-2623Hz9260 o 0.773 2133-2623Hz12235 o 0.833 2133-2623Hz13256 o 0.874 2133-2623Hz14241 o 0.874 2133-2623Hz24285 o 0.822 2133-2623Hz26259 o 0.804 2623-3226Hz12181 o 0.781 52

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Figure 3-4 .ThespreadofthemodulationindexissimilarforPatient2( Figure 3-11 A) withfewlocalizedhighmodulationindicesoverthepre-mot or(PMd)andprimarymotor (M1)cortices.OneoftheM1electrodeshadshownrightarmre sponsetoelectrical stimulation(refertoTable 2-1 ).Thespectralbandswithhighmodulationindicesas showninFigure 3-10 BareinaccordwiththosebandsdetectedinFigure 3-5 witha distinctiveincreaseinmeanpoweracrosstheslowbands. Overall,theECoGpowerinthe n =32passbandswiththissubjecthasshown evidenceof\tuning"todirectionalangles,notintheclass icalsensebutthrougha resultantpreferreddirectionfromacollectiveactivityo fneurons.Thepercentageof cosine-tunedfeaturesislowduetothelackofspatialresol ution.Still,themodulation indicesacrossspatialgridwereabletoidentifyM1channel swithforearm,wristandbicep responsestostimulation.Moreover,themodulationindice sacrossspectracapturedthe samespectralbandsrevealedintheprevioussection. 3.3AnalysisofMotorRelatedPotentialsUsingSourceSepar ationMethods Asmentionedmanytimesearlier,ECoGpotentialsarethecum ulativesumof dendriticactivityandpostsynapticpotentialsfrommanys ynchronizedsources.Within thesesynchronizedsources,ourgoalistoextracttheonest hatmodulatethemotor behaviorexecutedbythesubjects.Forthispurpose,linear instantaneoussource separationmethodologiescanbeappliedtothedataforexpl oratoryanalysisofthe extractedcomponentsandtheirpossiblecausalrelationsh iptothemotorbehavior.Any sourceseparationalgorithmbasedonthelinearinstantane ousmixingassumptionof hiddensourcesisformulatedas: X = AS + ; ^ S = WX ; (3{9) wheretheobservationmatrix, X ,consistsof M measurementsrecordedoverthe observationtime t =1 ;:::;T .Thesemeasurementsareassumedtobelinearcombinations of N sources,denotedbythesourcematrix S ,collectedunderGaussiannoise, .Ifthe 53

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measurementsarecollectedthroughspatialsensors,themi xingmatrix A yieldsthespatial patternsofthesources[ 80 ].Thedemixingmatrix W yieldsthesourceestimates. Principalcomponentanalysis (PCA)isoneofthemostcommonlyemployed techniquesinexploratorydataanalysisusedforreducingt hedimensionalityofthe data.Therstprincipalcomponentaccountsforasmuchofth evariabilityinthedata aspossible,andeachsucceedingcomponentaccountsforasm uchoftheremaining variabilityaspossible.PCAusestheeigenvectorsoftheco variancematrixanditonly ndstheorthogonalaxesofthedataundertheGaussianassum ption.Fornon-Gaussian data,PCAsimplyde-correlatesthesources[ 86 ]. Independentcomponentanalysis (ICA), ontheotherhand,isacomputationalmethodforseparatinga multivariatesignalinto additivesubcomponentsassumingstatisticalindependenc eofthenon-Gaussiansource signals[ 36 ].Bothtechniquesare blindsourceseparation methodsastheyminimally -ifever-exploitpriorknowledgeonthedata,thedesiredch aracteristics,orsource generation.Still,PCAandICAmaybevaluabletoolsyieldin gphysicallymeaningful datarepresentations,dependingonhowtheunderlyingassu mptionsaresuitableforthe data.InneuralengineeringapplicationsPCAiscommonlyus edinspikesorting[ 53 ]and dataregularization[ 41 ],whereasICAhasprovedtobeausefultoolinisolatingEOG, ECGandotherartifactsinEEG[ 44 68 ]. 3.3.1DenoisingSourceSeparation Inthepreviouschapter,weobservedtheslowtemporalbehav iorofthehand trajectories(withthemostprominentoscillationsbelow1 .5Hz).Henceinthesource separation,weareseekingneuralrhythmicsourceswhichex hibitslowcarrieramplitude modulationsinthisfrequencyrange.Weincorporatethisde siredcharacteristictothe sourceextractionviaanewlyintroducedmethodologycalle d denoisingsourceseparation (DSS)[ 80 ].Unlikeblindsourceseparationmethodologies,DSSexplo itsknowledgeabout thesourcesandthephysicalsystemtoextractdesiredstruc tureswithinthedata(e.g. non-Gaussianity,spectralcontent,generalshapepattern setc.),unlikethemostwidely 54

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usedICAalgorithms.Thismethodseemsparticularlyapprop riateforourproblembecause inBMIsweknowthetimescale/spectralcomponentoftheECoG componentthatweare interestedin,whichisgivenbythemovement.Afunctionalm appingthataccentuates thedesiredcharacteristicsandsuppressesunwantedbackg roundiscalledthe\denoising" stageofthealgorithm.IntheDSSframework,sourcesareext ractedonecomponentata time, s i ,allowingdierent denoisingfunctions tobeemployedfortheextractionofvarious desiredstructures.Ifseveralcomponentsareextractedfo rthesamedenoisingfunctions, thecomponentsarerankedaccordingtotheprominenceofthe desiredfeatures. TheDSSalgorithmconsistsoffoursuccessivesteps[ 37 ]: 1.Centeringandwhiteningthedatathrougheigenvaluedeco mposition. Y = D 1 = 2 VX (3{10) where D isthediagonalmatrixofeigenvaluesofthecovariancematr ixof X ,andthe matrix V ismadeupofthecorrespondingeigenvectors.Thewhitening transform makesthecovariancestructureofthedatauniform(i.e. YY T = I )andany orthogonalprojectioninthewhitenedspaceyieldsuncorre latedcomponents[ 37 ]. Thereby,theadvantageofwhiteningisthatanorthogonalde mixingmatrix, W woulddecomposethewhiteneddata, Y ,intouncorrelatedsources, ^ S 2.Sourceestimationbydemixingthedata: s i = w Ti X ; (3{11) where w i isacolumnofthedemixingmatrix.Thislinearprojectionof whiteneddata alsoyieldssourceswithunitcovariance. 3.Denoisingthesourceestimates: ^ s i = f ( s i )(3{12) f ( )isthedenoisingfunctionwhichischosentomaximizethede siredpropertieson thesourceestimate.Denoisingfunctionscanbelinearorno nlineartoutilizetheprior informationonthedata. 4.Reestimationandorthogonalizationofthedemixingmatr ix: w i = X ^ s Ti (3{13) 55

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Thereestimateddemixingvectorisorthogonalizedtothepr eviouslyfoundcolumns of W throughGram-Schmidtorthogonalization[ 36 ]inordertoyielduncorrelated sourceestimatesinthenextiteration. Steps2-4areiteratedforeachsourceestimateuntiltheang lebetweentheprevious andcurrentdemixingestimatesislessthanapresetthresho ld, orwhenthemaximum numberofiterationsisreached.Thewholeprocessisrepeat edforasmanycomponents anddenoisingfunctionsasnecessarylimitedonlybythenum berofobservedvariables. ThealgorithmissummarizedinFigure 3-12 3.3.2AnalysisofMovementRelatedECoGPotentialsviaDSS Denoisingsourceseparationisappliedtothepowersignatu resfromeachspectral bandacrossallchannelsintheelectrodegrid.Asmentioned earlier,theslownatureofthe desiredsignal( < 1.5Hz)suggeststhataslowlyvaryingmodulationintheECoG rhythms shouldbesought.Thuswechoosetoperformdenoisingbasedo nfrequencycontent.The denoisingfunctionemployedinthisanalysisisalow-pass lterwithacutofrequency at1Hz(seeFigure 3-13 ).Thestoppingcriteriafortheiterativealgorithmisathr eshold =0 : 01 o betweenthetwoconsecutivedemixingvectorsorreachingap resetmaximum numberofiterations, m =200. Thecorrelationcoecientsbetweentheextracted1024comp onentsfrom32channels across32spectralbandsareplottedinFigure 3-14 forPatient1.Therstextracted component,whichshowsthemostprominentdesiredcharacte risticsandthehighest correlationwiththeverticaltrajectory,andthethirdcom ponentwhichshowsthehighest correlationwiththehorizontaltrajectoryarearesuperim posedontherelativehand trajectoriesinFigure 3-15 (Boththecomponentsandthetrajectoriesarenormalizedby theirstandarddeviations).Thehighercorrelationoftheh orizontaltrajectorywiththe thirdcomponent(ratherthantherst)makessenseduetothe factthatthespectralrange ofthecomponentsincreasewiththeirextractionorderandt hehorizontaltrajectoryhas higherspectralcomponentsthantheverticaltrajectory.O verall,signicantcorrelations ( r > 0.15)arenotobservedbeyondthefthcomponent. 56

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Asasidenote,wewouldliketopointputthatthehigherpower inthersttrial observedinthetopplotofFigure 3-15 isalsoobservedinFigure 3-3 .Thisobservation maybeexplainedby habituation ,whichistheattenuationofmovement-relatedpotentials duringprolongedperformanceofasequenceofidenticalmov ements[ 27 ].Itisattributed toexecutingthetasksinanautomaticfashionwithdecrease dintentionalinvolvement andincreasedfatigue[ 17 ].Whenanovelstimulusormovementarises,increasedatten tion booststheevent-relatedpotentials.However,provinghab ituationisbeyondthescopeof theworkandFigure 3-15 servestoshowthenon-stationarityinthespectralpowers. Nextweanalyzethemixingcoecientscorrespondingtothe rstandthird DSScomponentsspatiallyandspectrally.Weaveragethemix ingcoecientsacross spectralbandstoattainFigures 3-16 A-CandacrosstheelectrodegridtoattainFigures 3-16 B-D.Figure 3-16 Ashowsthecontributingchannelstotherstcomponentwhic his awidespreadarea.Thisplotoverlapsinagooddegreewithth espatialdistributionof modulationindexpresentedintheprevioussection(Figure 3-10 ).Thechannelswithlittle ornocontributionaredominatedwithinterictalspikesasw eshallseeinChapter5(A DSS-basedinterictalspikeremovalalgorithmwillbeprese ntedinChapter5).Thespectral bandscontributingtotherstcomponentcanbeseeninFigur e 3-16 B.Theseareintotal agreementwiththehighlycorrelatedbandsseenintheprevi oustwosections(correlation andtuninganalyses). Figure 3-16 Cshowsthecontributingchannelstothethirdcomponentwhi chhasa morelocalizedstructure.ThisplotalmostcomplementsFig ure 3-16 A(withtheabsence ofchannelswithinterictalartifactsinbothgures).Thes pectralbandscontributingto thethirdcomponentcanbeseeninFigure 3-16 B.Againquitetheoppositeofthelocalized bandsoftherstcomponent,therearemorespectralbandsco ntributingtothethird component.Still,thesebandshavepreviouslyrevealedsom ecorrelationwiththemotor taskinFigure 3-4 57

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Theamplitudesofthemixingcoecientsoftherstcomponen tarelargerthan thoseofthesuccessiveonesduetothelowpassdenoisingfun ction.Oncetherstsource componentsareextractedandremovedfromtheinputchannel s,theresultantsignalis strippedfromtheslowmodulations(thedesiredcharacteri stics).Hencethefollowing componentswillhavepowerinhigherendsofthespectrum.Du etothe1 =f powerrule, thecoecientscorrespondingtothesubsequentcomponents aremuchsmaller.Themixing coecientsforthethirdcomponentaresmallerasseeninFig ure 3-16 .Thedierent regionallocalizationsismostlikelyduetotheremovaloft herstandsecondcomponents whichcoverawideareaofthepre-motorandprimarymotorare as,leavingasmallareaof theprimarymotorcortexforthethirdcomponent. Now,itispossiblethatthecorrelationsbetweenthecompon entsandthetrajectories areduetothesinusoid-likenatureofthedesiredtrajector y,i.e.,theresultsmaybe overts.Characterizationofoverttedresultsispossibl ethroughsurrogatedatasetswhich havethesameFourieramplitudesasthedatabuthaverandomp hases[ 83 ].Thekeypoint inthissurrogategenerationmethodisthatthesquaredampl itudeoftheFouriertransform isaperiodogramestimatoroftheconventionalpowerspectr aldensity[ 88 ].Hence,the surrogatesmimictheautocorrelationfunctionoftheorigi naltimeseries,butanyother structureislost.Figure 3-17 depictstherstDSScomponentsextractedbycreatingone surrogateforeachchanneloftherawrecordingsandlterin gtheminthesamespectral bands.Theseparticularbandswereselectedastheyhadshow nhighcorrelationwiththe verticalhandposition.TheDSSdecompositionwasmadedire ctlyonthe32channelsof eachband.Thecorrelationcoecientsbetweenthevertical trajectorieshavesignicantly reduced( << 0 : 15)whichweakensthepossibilityofoverttedresultswith theoriginal recordings. Thecorrelationcoecientsbetweentheextracted1024comp onentsfrom32channels across32spectralbandsforPatient2areplottedinFigure 3-18 .Thecorrelationswith orderedcomponentsdonotdecayasfastasinthecasewithPat ient1.Moreover,themost 58

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signicantcorrelationwiththehorizontalaxisisobserve dtobewiththe18 th component. Therstextractedcomponent,whichshowsthemostprominen tdesiredcharacteristics andthehighestcorrelationwiththeverticaltrajectory,a ndthe18 th componentare superimposedontherelativehandtrajectoriesinFigure 3-19 (Boththecomponents andthetrajectoriesarenormalizedbytheirstandarddevia tions).Overall,signicant correlations( r > 0.15)arenotobservedbeyondthersttwentycomponents. Nextweanalyzethemixingcoecientscorrespondingtothes etwoDSScomponents spatiallyandspectrally.Weaveragethemixingcoecients acrossspectralbandstoattain Figures 3-20 A-CandacrosstheelectrodegridtoattainFigures 3-20 B-D.Figure 3-20 A showsthecontributingchannelstotherstcomponentwhich coverstwooftheresponsive electrodestoelectricalstimulationandoverlapstoadegr eewiththespatialdistribution ofmodulationindexpresentedintheprevioussection(Figu re 3-11 ).Thespectralbands contributingtotherstcomponentcanbeseeninFigure 3-20 B.Theseareintotal agreementwiththehighlycorrelatedbandsseenintheprevi ouscorrelationsections. Figure 3-20 Cshowsthecontributingchannelstothe18 th componentwhichhasa morewidespreradstructure.Thespectralbandscontributi ngtothethirdcomponentcan beseeninFigure 3-20 B.Justtheoppositeofthelocalizedbandsoftherstcompon ent, therearelessspectralbandscontributingtothethiscompo nent.Thesebandsarein accordwiththebandsthathadhighmodulationindices. Tosumup,wewereabletoprojectthe32 n dimensionalinputspaceinto componentsthatarecorrelatedwiththehandtrajectories. Moreso,thesecomponents wereselectedinawaythatisinagreementwiththeprevioust hreestudies(ERS,spectral correlationanalysisanddirectionaltuning).Weshalluti lizeDSSmethodologyagainin Chapter5whereweshallbuildmodelswiththeextractedcomp onentsasameansof regularizationandforapreprocessingstageforintericta lspikeremoval[ 30 ]. 59

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Time Lag (sec)Channels clustured in 32 Spectral Bands (log(Hz))Cross-correlations Between ECoG Activity and Vertical Hand Position 0.5 1 1.5 2 2.5 3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 8 Hz 6110 Hz A Cross-correlations Between ECoG Activity and Horizontal Hand Position Time Lag (sec)Channels clustured in 32 Spectral Bands (log(Hz)) .5 1 1.5 2 2.5 3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 8 Hz 6110 Hz B Cross-correlations Between ECoG Activity and Vertical Hand Position Time Lag (sec)Channels clustured in 16 Spectral Bands (log(Hz)) 0.5 1 1.5 2 2.5 3 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 8 Hz 6110 Hz C Cross-correlations Between ECoG Activity and Horizontal Hand PositionChannels clustured in 16 Spectral Bands (log(Hz))Time Lag (sec) 5 10 15 20 25 30 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 8 Hz 6110 Hz D Time Lags (sec)Channels clustered in 8 Spectral Bands (log(Hz))Cross-Correlations Between ECoG Activity and Vertical Hand Position 0.5 1 1.5 2 2.5 3 -0.2 -0.1 0 0.1 0.2 0.3 8 Hz 6110 Hz E Channels Clustered in 8 Spectral Bands (log(Hz))Time Lags (sec) Cross-Correlations Between ECoG Activity and Horizontal Hand Position 0.5 1 1.5 2 2.5 3 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 8 Hz 6110 Hz F Figure3-4.Left:Cross-correlationbetweenverticalhand trajectoriesandchannelspectral poweracrossforA) n =32,C) n =16,E) n =8bandsforPatient1.Right: Cross-correlationbetweenhorizontalhandtrajectoriesa ndchannelspectral poweracrossforB) n =32,D) n =16,F) n =8bandsforPatient1. 60

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Time Lag (sec)Channels Clustered in 32 Spectral Bands (log(Hz))Crosscorrelations Between ECoG Activity and Vertical Hand Position 0.5 1 1.5 2 2.5 3 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 1 Hz 6100 Hz A Time Lag (sec)Channels Clustered in 32 Spectral Bands (log(Hz))Crosscorrelations Between ECoG Activity and Horizontal Hand Position 0.5 1 1.5 2 2.5 3 -0.05 0 0.05 0.1 0.15 8 Hz 6110 Hz B Time Lag (sec)Channels Clustered in 16 Spectral Bands (log(Hz))Crosscorrelations Between ECoG Activity and Vertical Hand Position 0.5 1 1.5 2 2.5 3 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 8 Hz 6110 Hz C Time Lag (sec)Channels Clustered in 16 Spectral Bands (log(Hz))Crosscorrelations Between ECoG Activity and Horizontal Hand Position 0.5 1 1.5 2 2.5 3 -0.1 -0.05 0 0.05 0.1 8 Hz 6110 Hz D Time Lag (sec)Channels Clustered in 8 Spectral Bands (log(Hz))Crosscorrelations Between ECoG Activity and Vertical Hand Position 0.5 1 1.5 2 2.5 3 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 8 Hz 6110 Hz E Time Lag (sec)Channels Clustered in 8 Spectral Bands (log(Hz))Crosscorrelations Between ECoG Activity and Horizontal Hand Position 0.5 1 1.5 2 2.5 3 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 8 Hz 6110 Hz F Figure3-5.Left:Cross-correlationbetweenverticalhand trajectoriesandchannelspectral poweracrossforA) n =32,C) n =16,E) n =8bandsforPatient2.Right: Cross-correlationbetweenhorizontalhandtrajectoriesa ndchannelspectral poweracrossforB) n =32,D) n =16,F) n =8bandsforPatient2. 61

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0 45 90 135 180 225 270 315 360 0.68 0.7 0.72 0.74 0.76 0.78 0.8 0.82 Directional angle ( o )Mean PowerR 2 =0.99, I=10% A 0 45 90 135 180 225 270 315 360 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Directional angle ( o )Mean PowerR 2 =0.87, I=30% B 0 45 90 135 180 225 270 315 360 1.15 1.2 1.25 1.3 1.35 1.4 Directional angle ( o )Mean PowerR 2 =0.97 C 0 45 90 135 180 225 270 315 360 2.74 2.76 2.78 2.8 2.82 2.84 Directional angle ( o )Mean PowerR 2 =0.93 D Figure3-6.TuningcurvesofA)channel16andB)channel31l teredbetween15-18Hz forPatient1.TuningcurvesofC)channel15lteredbetween 178-219Hzand D)channel2lteredbetween408-501HzforPatient2. 62

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0 45 90 135 180 225 270 315 360 0 0.2 0.4 Distribution of Preferred Directions of Tuned Channels (R 2 >0.60) 0 45 90 135 180 225 270 315 360 0 0.2 0.4 Directional angle ( o ) Distribution of Preferred Directions of Cosine Tuned Channels (R 2 >0.70) Figure3-7.Top:Thedistributionofthepreferredanglesof thefeatureswith R 2 > 0 : 60for Patient1.Bottom:Thedistributionofthepreferredangles ofthecosine-tuned featureslistedinTable 3-2 0 45 90 135 180 225 270 315 360 0 0.2 0.4 Distribution of Prefered Direction of Tuned Channels (R 2 >0.6) 0 45 90 135 180 225 270 315 360 0 0.2 0.4 Distribution of Prefered Direction of Cosine Tuned Channels (R 2 >0.7) Directional Angle Figure3-8.Top:Thedistributionofthepreferredanglesof thefeatureswith R 2 > 0 : 60for Patient2.Bottom:Thedistributionofthepreferredangles ofthecosine-tuned featureslistedinTable 3-3 63

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0 45 90 135 180 225 270 315 360 2.4 2.6 2.8 3 3.2 3.4 3.6 Directional angle ( o )Mean PowerR 2 =0.50, I=14% Figure3-9.Tuningcurveofchannel14lteredbetween48796110Hzshowsmultimodal tuning/preferenceforPatient1. TemporalAnteriorModulation Index of Channels (%) 1 2 3 4 5 6 1 2 3 4 5 6 0 1.1 2.2 3.3 4.4 5.5 6.6 7.7 8.8 9.9 11 A 10 1 10 2 10 3 2 4 6 8 10 12 14 16 18 Frequency (Hz)Modulation Index, I (%) B Figure3-10.A)ModulationindicesforPatient1areaverage doverthespectralbandsand superimposedonthe6x6electrodegrid.B)Modulationindic esforPatient 1areaveragedoverthespatialchannelsandplottedversust hecentral frequencyofthespectralbands. 64

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TemporalAnteriorModulation Index of Channels (%) 1 2 3 4 5 6 7 8 4 3 2 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A 10 1 10 2 10 3 0 5 10 15 20 25 30 35 40 Frequency (Hz)Modulation Index (%) B Figure3-11.A)ModulationindicesforPatient2areaverage doverthespectralbandsand superimposedonthe4x8electrodegrid.B)Modulationindic esforPatient 2areaveragedoverthespatialchannelsandplottedversust hecentral frequencyofthespectralbands. QRS TUV S V W X YZ[ \ U ] ^ T S_ ` T S Y V a UV Y S ^ S V W b cd e a U _S f S V W g UU ^ T S_ ` T S Y V X Q h i j k l m n bc X e Figure3-12.BlockdiagramoftheiterativeDSSalgorithm. 65

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -160 -140 -120 -100 -80 -60 -40 -20 0 20 Frequency (Hz)Magnitude (dB) Figure3-13.Thedenoisingfunctionforwhichthesourcesmo vementrelatedsourcesshall beextracted. 10 0 10 1 10 2 10 3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Ordered DSS ComponentsCorrelation Coefficients Horizontal Vertical Figure3-14.Themagnitudeofcorrelationcoecientsbetwe entheorderedcomponents andthehandtrajectoriesforPatient1. 66

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50 100 150 200 250 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Component#1, CC Y =0.35 50 100 150 200 250 -2 -1 0 1 2 3 Component#3, CC X =0.41 Time (sec) DSS Component # 1 Vertical Hand Trajectory DSS Component # 3 Horizontal Hand Trajectory Figure3-15.Top:FirstDSScomponentsuperimposedontheve rticalhandtrajectory. Bottom:ThirdDSScomponentsuperimposedonthehorizontal hand trajectory.Allcomponentsandtrajectoriesarenormalize dbytheirstandard deviations. 67

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TemporalAnteriorSpatial Mixing Coefficients of First DSS Component 1 2 3 4 5 6 1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 A 10 1 10 2 10 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Frequency (Hz)Spectral Mixing Coefficients of First DSS Component B TemporalAnteriorSpatial Mixing Coefficients of Third DSS Component 1 2 3 4 5 6 1 2 3 4 5 6 0 0.05 0.1 0.15 0.2 0.25 0.3 C 10 1 10 2 10 3 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Spectral Mixing Coefficients of Third DSS ComponentFrequency (Hz) D Figure3-16.A)Mixingcoecientsoftherstcomponentarea veragedoverthespectral bandsandsuperimposedontheelectrodegrid.B)Mixingcoe cientsofthe rstcomponentareaveragedoverthespatialchannelsandpl ottedversusthe centralfrequencyofthespectralbands.C)Mixingcoecien tsofthethird componentaveragedoverthespectralbands.D)Mixingcoec ientsofthe thirdcomponentaveragedoverthespatialchannels. 68

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0 10 20 30 40 50 60 -5 0 5 4.88-6kHz 0 10 20 30 40 50 60 -5 0 5 930-1150Hz 0 10 20 30 40 50 60 -5 0 5 145-180HzTime (sec) Figure3-17.Componentsextractedfromsurrogatedatasupe rimposedonthevertical handtrajectory(leftcolumn)andhorizontalhandtrajecto ry(rightcolumn showninasegmentof60secs). 69

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10 0 10 1 10 2 10 3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Ordered DSS ComponentsCorrelation Coefficients Horizontal Vertical Figure3-18.Themagnitudeofcorrelationcoecientsbetwe entheorderedcomponents andthehandtrajectoriesforPatient2. 70

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0 20 40 60 80 100 120 140 160 -4 -3 -2 -1 0 1 2 3 Component # 1, CC X = 0.35 DSS Component # 1 Vertical Trajectory 0 20 40 60 80 100 120 140 160 -4 -3 -2 -1 0 1 2 3 Time (sec) Component # 18, CC X = 0.28 DSS Component # 18 Horizontal Trajectory Figure3-19.Top:FirstDSScomponentsuperimposedontheve rticalhandtrajectory. Bottom:18 th DSScomponentsuperimposedonthehorizontalhand trajectory.Allcomponentsandtrajectoriesarenormalize dbytheirstandard deviations. 71

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TemporalAnteriorSpatial Mixing Coefficients of First DSS Component 1 2 3 4 5 6 7 8 4 3 2 1 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 A 10 1 10 2 10 3 Frequency (Hz)Spectral Mixing Coefficients of First DSS Component B TemporalAnteriorSpatial Mixing Coefficients of 18 th DSS Component 1 2 3 4 5 6 7 8 4 3 2 1 0.3 0.4 0.5 0.6 0.7 0.8 C 10 1 10 2 10 3 Spectral Mixing Coefficients of 18 th DSS ComponentFrequency (Hz) D Figure3-20.A)Mixingcoecientsoftherstcomponentarea veragedoverthespectral bandsandsuperimposedontheelectrodegrid.B)Mixingcoe cientsofthe rstcomponentareaveragedoverthespatialchannelsandpl ottedversusthe centralfrequencyofthespectralbands.C)Mixingcoecien tsofthe18 th componentaveragedoverthespectralbands.D)Mixingcoec ientsofthe 18 th componentaveragedoverthespatialchannels. 72

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CHAPTER4 LINEARMAPPINGOFECOGMOTORFEATURESTOBEHAVIOR InBMIsystems,neuralactivityhastobetranslatedintocom mandsthatwillallow theusertocontroltheoutputchannelsofthesystem(whethe ritbeacomputercursor, oraprostheticlimb).Thedesignedmodelshavetolearnthee xecutionofbehavior asperformedbythepatientandtopredictthecontinuumofth ebehaviorfromnovel ECoGactivity.ThefunctionalrelationshipbetweentheECo Gactivityandthedesigned behavioraltaskisnon-stationaryinnatureastherecorded activityisquitevariable fordierenttrialsofthesametask.Asidesfromrepeatabil ity,giventhemultiple-input multiple-output(MIMO)architectureoftheBMIsystem,the modelswillsuerfrom largenumberoffreeparametersduetohightrainingcomplex itiesandoverttingwith insucientlengthsofrecordingsallocatedfortraining. Inthischapter,wedesignlinearmodelstomapthespectralp owerfeaturesextracted fromECoGrecordingstothepositionofthecursoronthescre enwhichthepatientsare tracingwiththeirrightindexngers.TheECoGfeaturestha tarepresentedasinputsto themodelarelabeledas x kj ( t ),where j =1,2, ::: ,32indicatestheelectrodenumberasgiven inFigure2-2,and k donatesthebandpassfrequenciesofthelteredsignal.The desired signals,donatedby d X ( t )and d Y ( t ),arethehorizontal(x-axis)andvertical(y-axis) positionofthecursor(andthusthepositionoftherightind exngerofthepatient)onthe 20x30cmdisplaywiththeoriginofthecoordinatesystematt hecenterofgravityofthe screen.Finally,themodeloutputsare y X ( t )and y Y ( t ). Patient1performedvetrialsofcenter-outtaskfollowedb ytargetselection(as showninFig2-5)in3.87minutes.Thepatientstoppedthetas kmidwayinthelasttrial andthispartofthedatawasdiscarded.2.33minutesoftheda tawhichcorrespondsto therstthreetrialsisusedfortrainingandtheremainingo neandahalftrialisusedfor testingthemodels.Patient2performedfourtrialsin4.65m inutesofwhichtherst3.5 minuteswereusedinmodeltraining. 73

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opq rs tu v q vw opq opq x yz {| v} ~ z {| €z {|  z {| x Figure4-1.Linearltertopologyofasingleinput-singleo utputsystem.) Theperformanceofthemodelsarequantiedineachdimensio n(horizontaland vertical)bythefollowingtwomeasures:1.Correlationcoecient(CC)orPearson's r indicatesthedegreeoflineardependence betweenthereconstructedandtheactualhandtrajectories ,andiscomputedby: CC = cov( d;y ) d y (4{1) Thecorrelationcoecientissimplythecovariancebetween theoriginaland reconstructedtrajectories, d and y ,normalizedbytheirstandarddeviations.Thisis themostcommonlyusedmeasureinECoGBMIliterature[ 4 50 73 82 ].Although thismeasurererectsthetrackingcapabilityofthemodel,i tdoesnotmeasurethe biasintheestimation. 2.Normalizedmeansquarederror(MSE)isthesumofsquaredd ierencebetweenthe reconstructedandactualtrajectoriesoverthevarianceof theactualtrajectory: MSE = P e 2 ( t ) P d 2 ( t ) (4{2) MSEcomplementsthecorrelationcoecientandisthecostfu nctionofthelinear modelsusedthroughoutthischapter. Bothoftheabovemeasuresarecomputedovernon-overlappin gwindowsof5secsand themeanandstandarddeviationsofthesemeasuresonthetes tsetarereportedasthe performancestatistics. Withadaptivelinearltersthehand/cursorpositionatany giventimeismodeled throughafunctionoftheshort-termhistoryoftheECoGsign al.Suchadynamicalmodel 74

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requiresasystemwithsucientmemoryforaproperfunction almappingfromtheneural modulationstothemotoroutput.Withtheadditionoftapdel aylines(TDL)ateach channel,thenumberoflterparameters,i.e.thesizeofthe weightmatrix,becomesthe productofthenumberofchannels, M =32,thenumberofoutputdimensions, C =2,and thememorydepthoftheTDL, L ,whichshallbedeterminedempirically.Werstfeed thefeaturesextractedfromeachofthebandpassltersinto themodelsseparately.The TDLoutputsaretranslatedintothecursorcoordinatesyste mbymeansoftheweight matrix, w ,andlinearcombiners.Thisoperationismathematicallyde scribedinEqn.4-1 andshownschematicallyinFigure 4-1 y c ( t )= n X k =1 L 1 X i =0 M X j =1 x kj ( t i ) w kc ( i;j )+ b kc (4{3) where c denotesoneofthetwooutputdimensions(horizontal,X-orv ertical,Y-), w kc ( i;j ) isthe( i;j ) th entryoftheweightmatrixmappingactivityinthe k th bandtothe c th dimensionand b kc istheestimationbiasofthemodelwhichcanbedroppedfromt he modeliftheinputsanddesiredsignalarecenteredaroundth eirmean[ 42 ].Forthe remainderofthechapter,themeanvaluesoftheECoGfeature sandmotoractivitywillbe subtractedtoattainzeromeansignalsandtodiscardmodelb ias. 4.1WienerFilter Asdenedearlier,themean-squarevalueoftheestimatione rror(MSE)ofalinear adaptivemodelisgivenby: J = E e 2 ( t ) = E ( d ( t ) y ( t )) 2 (4{4) andisalsoregardedasthecostfunction.TheWiener-Hopfeq uation[ 32 ]yieldtheoptimal weightsthatminimizestheMSE: w c =( R ) 1 P c (4{5) 75

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where R istheautocorrelationmatrixofallECoGactivity,compose dof LxL correlation matricesbetweeneachfeature(channelpowerinacertainba nd)withtheautocorrelation matricesoftheindividualfeaturesalignedatthediagonal inblocks. R ,therefore,isofsize ( L M n )x( L M n )andisnotnecessarilysymmetric. P c isthecross-correlationmatrix betweentheinputfeaturesandthedesiredtrajectoryinthe c th dimension.Itisofsize ( L M n )x( C ).Forconvenience,wedroptheindex c standingforoutputdimensions. Foritsinversetoexist, R hastobeanonsingularmatrix.Withinadequatedata lengthsornoisydata R canbeestimatedpoorlyandbeclosetosingular.Thiseects the estimateoftheweightmatrix.Especiallywhentheinputcha nnelsarehighlycorrelated, theweightmatrixcanhaveanarticiallylargevariance.Ah ighconditionnumber indicatesanearlysingularmatrix. Ridgeregression isaregularizationmethodwhichaims tomaketheWienersolutionmore\well-conditioned"throug hminimizingtheMSEwith theconstraintthat k w k .Theoptimalweightmatrixthenhastheform: w =( R + I ) 1 P (4{6) where( R + I ) 1 isnowanonsingularmatrix.Throughthesingularvaluedeco mposition ofthe N M inputmatrix, X = U V T ,ageometricinterpretationofridgeregressioncan bemadeforthemodeloutput: y = X XX T 1 X T d = U 2 + I 1 U T d (4{7) = M X i =1 u i 2i 2i + u Ti d where u i aretheprincipalcomponentsof X and 2i isthevarianceofthedatainthat direction.Fromabove,weseethatridgeregressionshrinks theprincipalcomponentsof thedata.Moreover,principalcomponentsalongthedirecti onwhichtheinputhaslower varianceareshrunkmore.Ridgeregressionisthereforeals ocalleda shrinkage method. 76

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Table4-1.WienerlterperformanceresultsforPatient1 nL Cond#RegularizedCC X CC Y MSE X MSE Y Cond# 3283.30e121030 : 49 0 : 150 : 86 0 : 110 : 94 0 : 640 : 36 0 : 18 1681.09e121290 : 47 0 : 160 : 84 0 : 170 : 96 0 : 600 : 37 0 : 22 146.16e12850 : 55 0 : 210 : 87 0 : 170 : 83 0 : 500 : 34 0 : 20 888.65e111400 : 49 0 : 190 : 85 0 : 160 : 96 0 : 650 : 38 0 : 25 141.53e13910 : 52 0 : 250 : 87 0 : 180 : 84 0 : 580 : 36 0 : 23 203.46e12670 : 48 0 : 290 : 85 0 : 210 : 80 0 : 530 : 34 0 : 30 252.30e12550 : 59 0 : 250 : 84 0 : 220 : 79 0 : 500 : 32 0 : 29 Table4-2.WienerlterperformanceresultsforPatient2 nL Cond#RegularizedCC X CC Y MSE X MSE Y cond# 3281.26e13330 : 40 0 : 210 : 65 0 : 211 : 09 1 : 120 : 67 0 : 27 1685.48e12360 : 40 0 : 200 : 67 0 : 241 : 08 1 : 110 : 61 0 : 25 144.53e12250 : 47 0 : 220 : 78 0 : 151 : 08 0 : 990 : 64 0 : 26 881.33e11480 : 34 0 : 220 : 58 0 : 301 : 09 1 : 180 : 68 0 : 26 141.53e13910 : 38 0 : 200 : 66 0 : 281 : 07 1 : 020 : 68 0 : 26 201.39e12290 : 36 0 : 220 : 73 0 : 231 : 03 0 : 950 : 66 0 : 25 252.05e12250 : 37 0 : 210 : 71 0 : 280 : 98 1 : 010 : 65 0 : 22 Theregularizationparameter canbefoundthroughcross-validation.Practically, however,itisselectedbyadesirablevaluefortheinputsig nal-to-noiseratioSNR)and usingthefollowingestimationfortheratio: SNR tr [ R ] (4{8) WesetthedesiredSNRto30dBandempiricallycomputethetra ceofthecovariance matrixanddetermine [ 41 ].Theconditionnumbersbeforeandafterregularizationof ltersforvaryingnumberofspectralbands,lterordersar eprovidedinTables 4-1 and 4-2 forPatients1and2,respectively. TheonlyparameterinWienerlterdesignisthelterorder, L .IninvasiveBMI literature,thereareextensivestudiesonthecorrelation betweentimelagsandhand movements[ 95 ].Neuralactivityonesecondbeforethecurrenthandmoveme ntare commonlyusedastheltermemorydepth.Nosuchstudiesarep resentintheECoGBMI 77

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literature.Schalketal.[ 82 ]employspectralamplitudesofsevenbandsandtherunning averageofECoGactivityinawindowofonly333msecbeforeth emovementexecution astheinputstoalinearlter.Pistohletal.[ 73 ]usemeasurements125msecpriorthe kinematicsinKalmanlters.Herein,wedeterminetheoptim allterorderempirically basedonthecross-correlationresultsattainedintheprev iouschapter.Wehadobserved thatmemorydepthsbeyond1-1.5secsmaynotbenecessary. Whenallthechannelslteredineachspectralrangeareprov idedasinputsto theWienerlter,theinversionoftheautocorrelationmatr ixbecomescomputationally intensiveandlimitsthelterorderforwhich R canbecomputedbeforememory bandwidths(ofthecomputer)arebreached.For n =32spectralbands,thelter orderislimitedto L =8,correspondingtoamemorydepthof800msecs.For n =16 and n =8themaximumfeasiblelterordersare L =14and L =25,respectively.The performanceresultsoftheltersforoptimallterordersa reprovidedinTables 4-1 and 4-2 forPatients1and2,respectively.Thesignicanceofimpro vementoftheperformance oftheltersfrom n =32and L =8weretestedviapairwise t -tests,whichstatistically testthehypothesisthatcomparedperformanceresultscome fromdistributionswithequal means.Ifaperformancemeasurehasameansignicantlylarg erthantheother,thisis detectedthroughrightorleft-sidedtests. Asthenumberoffrequencybandsisdecreased,welosespectr alresolution.However, thislossisnoteectivelyrerectedineitherofTables 4-1 and 4-2 .For L =8, t -tests didnotdetectasignicantchangeinperformancebetween n = f 32 ; 16 ; 8 g .For n =16, t -testsbetween L =8and L =14didnotrevealsignicantimprovedperformance. Theperformancereducesforhigherlterorders( L =20,25)of n =8sincethestandard deviationoftheresultsincreased.Still,signicantchan geinperformancewasnotdetected amongstthedierentlterordersfor n =8with t -tests.Hence,alterorder L =8(or memorydepthof800msec)maybesucient. 78

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Table4-3.TheeectofthehighestspectralbandontheWiene rlterperformance InputbandsL CC X CC Y MSE X MSE Y All32bands80 : 48 0 : 150 : 86 0 : 110 : 94 0 : 640 : 36 0 : 18 Onlythehighestband80 : 40 0 : 260 : 83 0 : 131 : 02 0 : 410 : 41 0 : 18 First31bands80 : 34 0 : 250 : 81 0 : 141 : 07 0 : 680 : 50 0 : 22 Inordertobreakfreefromthelimitationofmemorybandwidt handtoexplorehigher lterorders,wefeedthe n =32spectralbandsofPatient1,oneatatimetoWiener lters.Figure 4-2 presentsthemeanCCandMSEvaluesforthetwodimensionsacr oss frequenciesandforlterordersfrom L = f 5 ; 10 ; 15 ; 20 ; 25 ; 30 g ,whichdemonstratesthat MSEvaluesdonotsignicantlyvaryfrom L =5to L =30.Thesameclaimcanbemade fortheCCvaluesforspectralbandsthatyieldhighcorrelat ion.Hence,alterorderof L =8mayverywellbeacceptablefor n =32bands.Moreover,weshouldconsiderthe physiologicalbasisbehindthelters.Employingmemoryde pthsmorethan1.5-2seconds isphysiologicallyexcessiveasreactiontimesofmotorsys temsaremuchlower[ 61 ],[ 15 ]. AlsowithPatient1,wehaveseenthatthehighestspectralba ndisveryhighly correlatedwiththeverticaltrajectory.Individually,th isbandaloneyieldsverticalCC valuesthatarestatisticallyequivalenttotheCCperforma ncewhenallfeaturesfrom allbandsareused.Moreover,theverticalCCvaluesarestat isticallyequivalentwhen thepassbandpowersofthisbandissubtractedfromtheinput set.Intermsofvertical MSE,however,utilizingthepowersinallspectralbandsyie ldsthebestperformanceas comparedtoutilizingthehighestbandaloneandwiththeinp utsetstrippedfromthe highestband.Theseresultsaresummarizedin 4-3 Onanothernote,Figure 4-2 suggeststhespectralbandsthatyieldthebest performancemeasuresaretheoneswhoserstDSScomponents showedhighestcorrelation withthehandtrajectoriesandshowedhightuningcharacter istics. Sanchezetal.[ 77 ]haveproposedasensitivitymeasurefortheinputchannels basedontheWienersolution.Itisaquantitativewayofrank ingtheimportanceofthe electrodesthataremodulatedtobehaviorandcontributeto thereconstructionofthe 79

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5 10 15 20 25 30 0.2 0.3 0.4 0.5 0.6 Band #Mean Wiener CC X L = 5 L = 10 L = 15 L = 20 L = 25 L = 30 5 10 15 20 25 30 0.2 0.4 0.6 0.8 Band #Mean Wiener CC Y A 5 10 15 20 25 30 0.8 0.9 1 1.1 Band #Mean Wiener MSE X L = 5 L = 10 L = 15 L = 20 L = 25 L = 30 5 10 15 20 25 30 0.4 0.6 0.8 1 1.2 Band #Mean Wiener MSE Y B Figure4-2.PerformancemeasuresacrossspectralbandsofP atient1asafunction ofWienerlterorder, L through(A):meancorrelationcoecients,(B): normalizedmeansquarederrors. modeloutputtrajectories.Inthelinearmodel,theoutputs aredirectlyrelatedtothe inputtapsthroughtheweightfunction.Thus,acrossnormal izedinputs,thosewiththe weightvectorsofgreatestmagnitudewouldcontributesign icantlytothemodeloutput. Hencesensitivityismathematicallydenesas: S j = 1 2 L X c = X;Y L 1 X i =0 j w c ( i;j ) j (4{9) Wefurtheraveragethesensitivitiesacrossfrequencyband stoattainspatialsensitivity andacrosselectrodegridstoattainspectralsensitivity. Thesemeasuresarepresentedin Figure 4-3 forPatient1.Thespatialsensitivityofthe n =32bandsiswidespreadwith highlocalizationsinthePMdandM1areas.ThreeoftheM1ele ctrodesforwhichhand, wrist,forearmandbicepresponsestoelectricalstimulati onwereobservedarerevealed tohavehighsensitivities.Moreover,thesensitivespectr albandscorrespondbothto thefeaturesidentiedinDSS(refertoFigure 3-16 )andthebandsforwhichtuningwas observed(refertoFigure 3-10 ).InFigures 4-3 D-Fcorrespondingto n =16and n =8 bands,itisobservedthatthesensitivitiesofsomeofthepa ssbandsarelost.However,this iscompensatedbyputtingmoreemphasisontheimportantspa tio-spectralfeaturesthat 80

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werepreserved.Thiscanexplainthenarrowerspatialsensi tivitylocalizationsinFigures 4-3 C-E. Wefurtheraveragethesensitivitiesacrossfrequencyband stoattainspatialsensitivity andacrosselectrodegridstoattainspectralsensitivity. Thesemeasuresarepresentedin Figure 4-3 forPatient1.Thespatialsensitivityofthe n =32bandsiswidespreadwith highlocalizationsinthePMdandM1areas.ThreeoftheM1ele ctrodesforwhichhand, wrist,forearmandbicepresponsestoelectricalstimulati onwereobservedarerevealed tohavehighsensitivities.Moreover,thesensitivespectr albandscorrespondbothto thefeaturesidentiedinDSS(refertoFigure 3-16 )andthebandsforwhichtuningwas observed(refertoFigure 3-10 ).InFigures 4-3 D-Fcorrespondingto n =16and n =8 bands,itisobservedthatthesensitivitiesofsomeofthepa ssbandsarelost.However,this iscompensatedbyputtingmoreemphasisontheimportantspa tio-spectralfeaturesthat werepreserved.Thiscanexplainthenarrowerspatialsensi tivitylocalizationsinFigures 4-3 C-E. 4.2NormalizedLeastMeanSquares TheWienersolutionprovidestheoptimalsolutionforstati onarysystems,however, thebrainisanonstationarydynamicsystemthatgeneratesd ierentneuralresponsesto thesamestimulus. Normalizedleastmeansquares isanonlinegradientdescentalgorithm whichminimizesinstantaneoussquarederrorataratenorma lizedbythepowerinthe inputtapvectorinordertocontendwithnonstationarity[ 32 ].Theweightupdatesare formalizedas: w ( n +1)= w ( n ) P x r J ( n )(4{10) = w ( n ) P Mj =1 k x j k 2 + r @ k e ( n ) k 2 @ w (4{11) = w ( n )+ P Mj =1 k x j k 2 + r e ( n ) x 81

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Table4-4.NLMSperformanceresultsforPatient1 nL CC X CC Y MSE X MSE Y 3280 : 48 0 : 150 : 85 0 : 120 : 94 0 : 630 : 36 0 : 19 140 : 47 0 : 210 : 87 0 : 140 : 84 0 : 540 : 34 0 : 17 1680 : 45 0 : 190 : 83 0 : 160 : 98 0 : 600 : 37 0 : 22 140 : 54 0 : 220 : 87 0 : 160 : 85 0 : 510 : 33 0 : 20 250 : 64 0 : 190 : 81 0 : 430 : 81 0 : 430 : 34 0 : 24 880 : 47 0 : 200 : 83 0 : 170 : 97 0 : 650 : 37 0 : 27 140 : 52 0 : 250 : 86 0 : 180 : 86 0 : 590 : 35 0 : 26 250 : 58 0 : 220 : 84 0 : 230 : 80 0 : 490 : 31 0 : 31 Table4-5.NLMSperformanceresultsforPatient2 nL CC X CC Y MSE X MSE Y 3280 : 46 0 : 220 : 67 0 : 221 : 07 1 : 070 : 61 0 : 27 140 : 52 0 : 200 : 77 0 : 161 : 07 0 : 940 : 63 0 : 30 1680 : 46 0 : 180 : 66 0 : 231 : 07 1 : 060 : 57 0 : 24 140 : 51 0 : 220 : 77 0 : 161 : 07 0 : 920 : 58 0 : 26 250 : 55 0 : 280 : 75 0 : 221 : 00 0 : 950 : 58 0 : 25 880 : 56 0 : 240 : 62 0 : 291 : 07 0 : 990 : 59 0 : 22 140 : 60 0 : 240 : 70 0 : 250 : 99 0 : 930 : 63 0 : 23 250 : 52 0 : 220 : 71 0 : 240 : 99 0 : 970 : 57 0 : 26 where x j ( n )=[ x j ( n ) x j ( n 1) x j ( n L +1)]istheinputtapvectoratchannel j and is thelearningrateorstepsizewhichadjuststhespeedofconv ergenceofthealgorithm. r is asmallconstantwhichpreventsdivergenceincaseofverysm allinputsignals.Duetoits computationalsimplicityandlessmemorydemand,wecanimp lementNLMSwithhigher orders, L> 8,for n =32.Apartfromthelterweights,theonlyparameterinvolv edin thelterdesignisthelearningrate, Tables 4-4 and 4-5 presenttheperformancemetricsacrossvaryingparameters for Patients1and2,respectively.Acrossallrowsthereisnota signicantimprovementof performancethatwascapturedby t -tests. 82

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4.3WeightDecay AdaptiveregularizationcanbeincorporatedintotheNLMSa lgorithmthrough rewritingtheinstantaneouscostfunctionas: ( n )= k e ( n ) k 2 + k w ( n ) k 2 (4{12) = J ( n )+ ( n ) Thegradientdescentupdateequationfortheweightsthenbe comes: w ( n +1)= w ( n ) P x r ( n ) r ( n )= w ( n ) P x r J ( n ) w ( n )(4{13) Duetothethirdtermintheaboveequationthisregularizati onmethodiscalled weightdecay Larsenetal.[ 46 ]suggestedthattheregularizationparameter canbeadaptively estimatedbyminimizingthegeneralizationerrorina K -foldcross-validationscheme.The maintrainingset, T ,isdividedinto K equalnonoverlappingsegments.Ateachstage onesegmentisleftoutasthevalidationset, k ,while w k isoptimizedon T k withan xed (0).Thegeneralizationerrorforthetrainedweightsisgiv enbytheaverageofthe cross-validationerrors: & =1 =K K X k =1 J k (4{14) andtheregularizationparameterisoptimizedthroughgrad ientdescent: ( t )= ( t 1) # @& @ (4{15) Thederivativeofthecross-validationerrorwithrespectt otheregularization parameterisderivedin[ 46 ]as: @J k @ = @ @ w k H 1 k @J k @ w k (4{16) = w Tk [ ( t ) I + R k ] 1 E f e k x k g 83

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wherethesubscript k referstothe k th cross-validationsetfortheerror,inputsand autocorrelationfunction. H k = @ 2 @ w @ w T istheHessianofthecostfunction.Theoverall regularizationparameterupdateequationisasfollows: ( t +1)= ( t )+ #=K K X k =1 w Tk [ ( t ) I + R k ] 1 E f e k x k g (4{17) Once converges,theregularizedNLMSsystemweightsaretrained accordingto thegradientdescentupdateequation.Justlikeinridgereg ressionweightdecayreduces thevarianceoftheweightsandincreasesthenumberofweigh tswhosemagnitudesare signicantlyclosetozero.Thisreducestheeectivenumbe rofparametersofthemodel. Unfortunately,thecomputationoftheHessianmatrixentai lslargematrixinversions andwerunintomemorybandwidthissues.Thus,wendtheopti malweightdecay parameterempirically.Theoptimal wouldlowertheweightvariancebutwouldprevent thereconstructiontrajectoryfromshrinkage.Foreach valueweplotthehistogramof theoriginalweightsandtheshrunkweights.Wepickthe valuethatisyieldssignicant weightshrinkage,butdoesnotsignicantlyincreasetheMS Evalues.Wepickthelter parametersthatprovidedthebestNLMSresults.Theweightd ecayresultsascomparedto theNLMSresultsareprovidedinTables 4-6 and 4-7 forPatients1and2,respectively.The normalizeddistributionofweightsbeforeandafterweight decayforvarious valuesare presentedinFigures 4-5 and 4-6 .LetusexamineFigure 4-5 (Patient1)rst.For n =32, theoptimalvalueof is10 6forwhichthenumberofweightsclosetozeroincreasedby 10%.For n =16,theoptimal =5 10 6 forwhichtheMSEdidnotincreasesignicantly andtheweightsclosetozeroincreasedby20%.For n =8,wechoose opt =10 5 ,sincean increaseinMSEisnotobserved,whereas40%moreweightsshr unk.FromFigure 4-6 and Table 4-7 ,weobservethatforPatient2, =10 7wastoosmalltomakeanimpactonthe weights.Forall n = f 32 ; 16 ; 8 g theoptimalvalueof is10 6forwhichtheverticalMSE didnotincreasesignicantlyandtheweightsclosetozeroi ncreasedby20-30%. 84

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Table4-6.WeightdecayperformanceresultsforPatient1 nL CC X CC Y MSE X MSE Y 321400 : 47 0 : 210 : 87 0 : 140 : 84 0 : 540 : 34 0 : 17 10 7 0 : 46 0 : 190 : 87 0 : 140 : 84 0 : 550 : 35 0 : 16 10 6 0 : 45 0 : 190 : 87 0 : 140 : 85 0 : 560 : 36 0 : 15 5 10 6 0 : 42 0 : 210 : 87 0 : 150 : 88 0 : 610 : 42 0 : 15 10 5 0 : 40 0 : 230 : 86 0 : 170 : 92 0 : 660 : 50 0 : 16 10 4 0 : 39 0 : 240 : 79 0 : 211 : 01 0 : 800 : 82 0 : 17 162500 : 64 0 : 190 : 81 0 : 430 : 81 0 : 430 : 34 0 : 24 10 7 0 : 59 0 : 190 : 81 0 : 270 : 84 0 : 520 : 33 0 : 25 10 6 0 : 60 0 : 190 : 80 0 : 280 : 84 0 : 520 : 33 0 : 25 5 10 6 0 : 63 0 : 210 : 80 0 : 290 : 87 0 : 590 : 36 0 : 23 10 5 0 : 63 0 : 220 : 79 0 : 290 : 89 0 : 650 : 41 0 : 21 10 4 0 : 61 0 : 260 : 78 0 : 280 : 98 0 : 860 : 77 0 : 14 81400 : 52 0 : 250 : 86 0 : 180 : 89 0 : 630 : 35 0 : 26 10 7 0 : 47 0 : 270 : 85 0 : 190 : 89 0 : 630 : 34 0 : 27 10 6 0 : 46 0 : 280 : 85 0 : 200 : 88 0 : 630 : 34 0 : 26 5 10 6 0 : 45 0 : 250 : 86 0 : 200 : 88 0 : 640 : 36 0 : 24 10 5 0 : 44 0 : 230 : 87 0 : 210 : 90 0 : 640 : 39 0 : 22 10 4 0 : 40 0 : 220 : 84 0 : 210 : 99 0 : 780 : 67 0 : 16 Acrossbothtables, t -testsonceagainfailtoyieldasetofparametersthatsigni cantly performbetter. 4.4GammaFilter Thelinearltersstudiedthusfarwereniteimpulserespon se(FIR)lters.Innite impulseresponse(IIR)ltersaremoreadvantageousinsyst emswheredeepmemoryis requiredforadequateadaptation,oncestabilityisensure dduringadaptation.Memory depthisassociatedwiththelengthoftheimpulseresponse, andforFIRsystemsmemory depthandlterorderarecoupled[ 74 ],whereasIIRlters,forthesamememorydepth, requirelowerlterorders. Thegammalter[ 74 ]isafeedforwardIIRlterwitharestrictedfeedbackarchi tecture. ThegeneralizedfeedforwardmodelisgiveninFigure 4-7 .Thesystemequationsareas 85

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Table4-7.WeightdecayperformanceresultsforPatient2 nL CC X CC Y MSE X MSE Y 321400 : 52 0 : 220 : 77 0 : 161 : 07 0 : 940 : 63 0 : 30 10 7 0 : 53 0 : 220 : 77 0 : 161 : 07 0 : 940 : 64 0 : 29 10 6 0 : 53 0 : 220 : 77 0 : 161 : 05 0 : 950 : 66 0 : 29 5 10 6 0 : 56 0 : 230 : 78 0 : 161 : 03 0 : 970 : 76 0 : 29 10 5 0 : 60 0 : 250 : 77 0 : 161 : 03 0 : 980 : 83 0 : 29 10 4 0 : 64 0 : 210 : 74 0 : 211 : 04 1 : 021 : 00 0 : 30 161400 : 51 0 : 220 : 77 0 : 161 : 07 0 : 920 : 58 0 : 26 10 7 0 : 51 0 : 220 : 77 0 : 161 : 07 0 : 920 : 58 0 : 26 10 6 0 : 53 0 : 220 : 77 0 : 171 : 05 0 : 930 : 60 0 : 26 5 10 6 0 : 58 0 : 230 : 77 0 : 191 : 01 0 : 950 : 67 0 : 26 10 5 0 : 60 0 : 250 : 77 0 : 211 : 01 0 : 960 : 74 0 : 27 10 4 0 : 68 0 : 210 : 75 0 : 231 : 04 1 : 010 : 97 0 : 29 82500 : 52 0 : 220 : 71 0 : 240 : 99 0 : 970 : 57 0 : 26 10 7 0 : 52 0 : 220 : 71 0 : 240 : 99 0 : 970 : 57 0 : 26 10 6 0 : 53 0 : 220 : 71 0 : 230 : 98 0 : 980 : 59 0 : 26 5 10 6 0 : 60 0 : 190 : 71 0 : 230 : 98 1 : 000 : 66 0 : 25 10 5 0 : 62 0 : 210 : 71 0 : 240 : 98 1 : 010 : 73 0 : 24 10 4 0 : 64 0 : 230 : 70 0 : 241 : 01 1 : 060 : 95 0 : 23 follows: Y ( z )= K X k =0 w k X k ( z )(4{18) X k ( z )= G ( z ) X k 1 ( z ) ;k =1 ; 2 ;:::;K X 0 ( z )= X ( z ) ;k =1 ; 2 ;:::;K whichyieldthefollowingsystemtransferfunction: H ( z )= Y ( z ) X ( z ) = K X k =0 w k ( G ( z )) k (4{19) Clearly,thestabilityofthesystemdependsonthestabilit yof G ( z ).Thetransferfunction utilizedingammafunctionsistheleakyintegratordepicte dinFigure 4-8 andhasthe followingclosedform: G ( z )= z (1 ) (4{20) 86

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where(1 )isthegaininthefeedbackloop.Thesystemisstablewhenth epolelies insidetheunitcircle,i.e.for0 << 2.For =1thesystemreducestoatapdelay line.For < 1additionalmemorydepthissuppliedforlowfrequencycomp onentsatthe expenseofthehighfrequencycomponents.Thiswouldbedesi rableinourlterdesignas thehandtrajectoriesoscillateatlowfrequencies.Themem orydepthofagammalteris D K = K .Thesignicanceofthisresultisthatforaxedlterorder thememorydepth canbeadjustedbyvarying (i.e.memorydepthandlterorderaredecoupled). Thetimedomainsystemequationsforthegammaltersareexp ressedas: x k ( n )=(1 ) x k ( n 1)+ x k 1 ( n 1) ;k =1 ; 2 ;:::;K y ( n )= K X k =1 w k x k ( n )= wX r ( n )(4{21) x 0 ( n )= x ( n ) where X r ( n )=[ x 0 ( n ) x 1 ( n ) x K ( n )] T .Theanalytical(Wiener)solutionfortheweights forxed aregivenrespectivelyby: w = E X r ( n ) X r ( n ) T 1 E X r ( n ) d ( n ) T (4{22) Thesystemcanalsobeadaptedtoobtaintheoptimal parameter,yetweoptto empiricallysearchforthebestcombinationof and L byiterationfor = f 0 : 1 ; 0 : 2 ;:::; 0 : 9 g Theanalyticalsolutionentailsthesamecomputationalreq uirementsastheWiener solutionandhencesuersthesamecomputationalmemorylim itations.However,dueto theuncoupledltermemorydepthandorders,an L =8orderltercanhavememory depthsfrom890msecsto8secs.Theattainedperformancemea suresforthebest and L combinationsaresummarizedinTables 4-8 and 4-9 for L = f 3 ; 5 ; 8 g .Noneoftheresults presentedintherowsweresignicantlybetterthanwith n =32and L =8accordingto t -testsforeitherpatient.Infact,theperformanceworsene dforPatient2for n =3. 87

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Table4-8.GammalterperformanceresultsforPatient1 nL Memorydepth(secs)CC X CC Y MSE X MSE Y 3280.32.670 : 33 0 : 290 : 81 0 : 220 : 82 0 : 460 : 31 0 : 16 50.31.670 : 33 0 : 270 : 80 0 : 220 : 87 0 : 520 : 33 0 : 15 30.13.000 : 37 0 : 230 : 82 0 : 210 : 87 0 : 540 : 33 0 : 15 1680.42.000 : 37 0 : 310 : 81 0 : 230 : 82 0 : 380 : 34 0 : 18 50.41.250 : 37 0 : 270 : 81 0 : 220 : 90 0 : 490 : 35 0 : 17 30.13.000 : 38 0 : 250 : 81 0 : 230 : 88 0 : 460 : 33 0 : 16 880.51.600 : 37 0 : 220 : 80 0 : 270 : 84 0 : 470 : 35 0 : 23 50.31.670 : 36 0 : 230 : 80 0 : 260 : 86 0 : 480 : 34 0 : 22 30.13.000 : 36 0 : 250 : 81 0 : 270 : 88 0 : 510 : 30 0 : 17 Table4-9.GammalterperformanceresultsforPatient2 nL Memorydepth(secs)CC X CC Y MSE X MSE Y 3280.24.000 : 54 0 : 310 : 76 0 : 251 : 15 1 : 270 : 59 0 : 22 50.15.000 : 48 0 : 270 : 70 0 : 251 : 12 1 : 260 : 61 0 : 22 30.50.600 : 33 0 : 240 : 56 0 : 221 : 08 1 : 240 : 64 0 : 30 1680.18.000 : 44 0 : 220 : 74 0 : 261 : 01 1 : 180 : 56 0 : 28 50.15.000 : 37 0 : 230 : 73 0 : 261 : 03 1 : 220 : 56 0 : 23 30.40.750 : 34 0 : 230 : 56 0 : 241 : 08 1 : 240 : 59 0 : 29 880.24.000 : 59 0 : 270 : 72 0 : 260 : 95 1 : 160 : 55 0 : 24 50.15.000 : 50 0 : 250 : 71 0 : 250 : 96 1 : 160 : 56 0 : 24 30.13.000 : 41 0 : 230 : 59 0 : 241 : 01 1 : 230 : 68 0 : 26 4.5ComparisonofLinearFilters Inordertocomparethefourtypesoflinearltersandthethr eechoicesofnumberof spectralbands,foreachlterwechoosetheperformanceres ultswiththebestmeanvalue andloweststandarddeviationintheperformancemetricsas t -testsdidnotrevealthebest parametersandpresenttheminTables 4-10 and 4-11 .Moreover, t -testarenotableto revealthebestperforminglterasthestandarddeviations oftheresultsareveryhigh. Hence,aWienerlteroforder L =8in n =8spectralbandswouldbethesimplestlinear lterdesignapplicabletothisdataset.Theoutputtraject oriesoftheWienerltersin Tables 4-10 and 4-11 areplottedinFigures 4-9 and 4-12 ,forPatients1and2,respectively. ThewindowedCCvaluesandMSEvaluesareprovidedinFigures 4-10 and 4-11 for Patient1andinFigures 4-13 and 4-14 forPatient2. 88

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Table4-10.FilterperformancecomparisonsforPatient1 n Filter L #ofparam.CC X CC Y MSE X MSE Y 32Wiener881920 : 49 0 : 150 : 86 0 : 110 : 94 0 : 640 : 36 0 : 18 NLMS1414336(+1)0 : 55 0 : 210 : 87 0 : 170 : 83 0 : 500 : 34 0 : 20 WeightDecay1414336(+3)0 : 45 0 : 190 : 87 0 : 140 : 85 0 : 560 : 36 0 : 15 Gamma88192(+1)0 : 33 0 : 290 : 81 0 : 220 : 82 0 : 460 : 31 0 : 16 16Wiener1471680 : 55 0 : 210 : 87 0 : 170 : 83 0 : 500 : 34 0 : 20 NLMS2512800(+1)0 : 64 0 : 190 : 82 0 : 250 : 81 0 : 430 : 34 0 : 24 WeightDecay2512800(+3)0 : 63 0 : 210 : 80 0 : 290 : 87 0 : 590 : 36 0 : 23 Gamma84096(+1)0 : 37 0 : 310 : 81 0 : 230 : 82 0 : 380 : 34 0 : 18 8Wiener1435840 : 52 0 : 250 : 87 0 : 180 : 84 0 : 580 : 36 0 : 23 NLMS143584(+1)0 : 52 0 : 250 : 86 0 : 180 : 86 0 : 590 : 35 0 : 26 WeightDecay143584(+3)0 : 44 0 : 230 : 87 0 : 210 : 90 0 : 640 : 39 0 : 22 Gamma82048(+1)0 : 37 0 : 220 : 80 0 : 270 : 84 0 : 470 : 35 0 : 23 Table4-11.FilterperformancecomparisonsforPatient2 n Filter L #ofparam.CC X CC Y MSE X MSE Y 32Wiener881920 : 40 0 : 210 : 65 0 : 211 : 09 1 : 120 : 67 0 : 27 NLMS1414336(+1)0 : 52 0 : 200 : 77 0 : 161 : 07 0 : 940 : 63 0 : 30 WeightDecay1414336(+3)0 : 53 0 : 210 : 77 0 : 161 : 05 0 : 950 : 66 0 : 29 Gamma88192(+1)0 : 54 0 : 310 : 76 0 : 251 : 15 1 : 270 : 59 0 : 22 16Wiener1471680 : 47 0 : 220 : 78 0 : 151 : 08 0 : 990 : 64 0 : 26 NLMS147168(+1)0 : 51 0 : 220 : 77 0 : 161 : 07 0 : 920 : 58 0 : 26 WeightDecay147168(+3)0 : 58 0 : 230 : 77 0 : 191 : 01 0 : 950 : 67 0 : 26 Gamma84096(+1)0 : 54 0 : 310 : 76 0 : 251 : 15 1 : 270 : 59 0 : 22 8Wiener2564000 : 37 0 : 210 : 71 0 : 280 : 98 1 : 010 : 65 0 : 22 NLMS256400(+1)0 : 52 0 : 220 : 71 0 : 240 : 99 0 : 930 : 63 0 : 23 WeightDecay256400(+3)0 : 53 0 : 220 : 71 0 : 230 : 98 0 : 980 : 59 0 : 26 Gamma82048(+1)0 : 59 0 : 270 : 72 0 : 260 : 95 1 : 160 : 55 0 : 24 Theoverallcorrelationcoecientsareacceptableforthei nterfaceswearetrying tobuild.However,thenormalizedMSEvaluesarequitehigh. Therecouldbeseveral possiblereasonsforthis.First,theltersarenotabletos witchoasthepatientsare waitinginbetweentasks.InFigure 4-11 weobservethatthehighestMSEsoccurduring thesetaskswitchingperiods.Inadditiontothis,wehadobs ervedthatthepowerover timeandacrosstrialsdecrease.Sowearetrainingthelter sonhigherpowerinputsand testingthemonalowerpowerinput.Thiscanbeseeninthesec ondtargetselection 89

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taskofthetestset.Hence,leave-one-outtypeoftraining/ testingschemesmayyield betterMSEresults.Inaddition,anybiasintheoutputwould bererectedintheMSE calculations. Wecannotskiptomentiontheperformancedierencebetween theverticaland horizontalaxesofthetrajectory.Inthepreviouschapterw ehadseenthatthehorizontal axiswaslesscorrelatedwiththeECoGactivityforbothpati ents.Thismayberelatedto thelowdeviationofactivityfromtheorigininthehorizont aldirection.Especiallyinthe targetselectiontask,thespanoftheverticalaxisismuchh igher.Also,theorientation ofthecomputerscreencouldbeafactor.Thesetofmusclesin volvedinmovingone's handupanddownisquitedierentthanthoseinvolvedinmovi ngleftandright.Hence, thecoverageoftheelectrodesoverthemusclesrelatedtoth eformermaybebetterthan thelatter.Still,asweobservedthesameperformancedier enceacrossdimensionsin bothpatients,therstreasoning(lowdeviationofactivit yinthehorizontalaxis)ismore sound. Ontheotherhand,theperformancedierencebetweenthepat ientsismorelikely tobeduetothecoverageoftheelectrodes.AslistedinTable 2-1 ,Patient1responded tomoreelectrodeswithmoremusclessetsinvolvingtherigh tarmwhenelectrically stimulated,comparedtoPatient2.Also,asweshallseeinth enextchapter,theinterictal activityinPatient1isquasiperiodicandmorelocalizedwh ichmaybeovercomethrough linearlters,whereastheinterictalactivityofPatient2 isburstyandspreadacrossthe wholeelectrodegrid,aectingthemodelingperformance. 90

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TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A 10 1 10 2 10 3 0 Spectral SensitivityFrequency (Hz) B TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 C 10 1 10 2 10 3 10 -2 Spectral SensitivityFrequency (Hz) D TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 E 10 1 10 2 10 3 Spectral SensitivityFrequency (Hz) F Figure4-3.SpatialandspectralsensitivitiesofPatient1 with L =8orderWienerlters. A)Spatialsensitivityof32channelsacross n =32passbands,B)Spectral sensitivitiesof n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie s for n =16passbands.E-F)Sensitivitiesfor n =8passbands. 91

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TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 7 8 4 3 2 1 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 A 10 1 10 2 10 3 Spectral SensitivityFrequency (Hz) B TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 7 8 4 3 2 1 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 C 10 1 10 2 10 3 Spectral SensitivityFrequency (Hz) D TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 7 8 4 3 2 1 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 E 10 1 10 2 10 3 Spectral SensitivityFrequency (Hz) F Figure4-4.SpatialandspectralsensitivitiesofPatient2 with L =8orderWienerlters. A)Spatialsensitivityof32channelsacross n =32passbands,B)Spectral sensitivitiesof n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie s for n =16passbands.E-F)Sensitivitiesfor n =8passbands. 92

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0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Magnitude of Weights Normalized Distribution of Weights d =0 d =10 -7 d =10 -6 d =5x10 -6 d =10 -5 d =10 -4 A 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Magnitude of Weights Normalized Distribution of Weights d =0 d =10 -7 d =10 -6 d =5x10 -6 d =10 -5 d =10 -4 B 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Magnitude of Weights Normalized Distribution of Weights d =0 d =10 -7 d =10 -6 d =5x10 -6 d =10 -5 d =10 -4 C Figure4-5.NormalizedweightdistributionsofltersforP atient1beforeandafterweight decaywithvarying valuesforA) n =32,B) n =16,C) n =8bands. 93

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0.005 0.01 0.015 0.02 0.025 0.03 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Magnitude of Weights Normalized Distribution of Weights d =0 d =10 -7 d =10 -6 d =5x10 -6 d =10 -5 d =10 -4 A 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Magnitude of Weights Normalized Distribution of Weights d =0 d =10 -7 d =10 -6 d =5x10 -6 d =10 -5 d =10 -4 B 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Magnitude of Weights Normalized Distribution of Weights d =0 d =10 -7 d =10 -6 d =5x10 -6 d =10 -5 d =10 -4 C Figure4-6.NormalizedweightdistributionsofltersforP atient2beforeandafterweight decaywithvarying valuesforA) n =32,B) n =16,C) n =8bands. 94

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‚ƒ „… †‡ ˆ‰ Š‹ ŠŒ ‚ƒ „… ‚ƒ „…  Ž ‘ Š’ “ ”  ‘ • ‘ –  ‘  Figure4-7.Feedforwardltertopology. —™ š › œ  › œ  Figure4-8.Theleakyintegrator. 95

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10 20 30 40 50 -10 -5 0 5 10 X posWiener Testing Time (sec) 10 20 30 40 50 -10 -5 0 5 10 Y posTime (sec) A 10 20 30 40 50 -10 -5 0 5 10 X posWiener Testing Time (sec) 10 20 30 40 50 -10 -5 0 5 10 Y posTime (sec) B 10 20 30 40 50 -10 -5 0 5 10 X posWiener Testing Time (sec) 10 20 30 40 50 -10 -5 0 5 10 15 Y posTime (sec) C Figure4-9.WienerreconstructedtrajectoriesforPatient 1withA) n =32,B) n =16,C) n =8bands. 96

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10 20 30 40 50 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 CC YTime (sec) A 10 20 30 40 50 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 CC YTime (sec) B 10 20 30 40 50 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 CC YTime (sec) C Figure4-10.WienerwindowedCCvaluesforPatient1withA) n =32,B) n =16,C) n = 8bands. 97

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10 20 30 40 50 0.5 1 1.5 2 MSE XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 1 MSE YTime (sec) A 10 20 30 40 50 0.5 1 1.5 MSE XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 MSE YTime (sec) B 10 20 30 40 50 0.5 1 1.5 MSE XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 1 MSE YTime (sec) C Figure4-11.WienerwindowedMSEvaluesforPatient1withA) n =32,B) n =16,C) n =8bands. 98

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20 40 60 80 100 -10 -5 0 5 10 X posWiener Testing Time (sec) 20 40 60 80 100 -10 -5 0 5 10 Y posTime (sec) A 20 40 60 80 100 -10 -5 0 5 10 X posWiener Testing Time (sec) 20 40 60 80 100 -10 -5 0 5 10 Y posTime (sec) B 20 40 60 80 100 -10 -5 0 5 10 X posWiener Testing Time (sec) 20 40 60 80 100 -10 -5 0 5 10 Y posTime (sec) C Figure4-12.WienerreconstructedtrajectoriesforPatien t2withA) n =32,B) n =16,C) n =8bands. 99

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20 40 60 80 100 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 20 40 60 80 100 0.2 0.4 0.6 0.8 CC YTime (sec) A 20 40 60 80 100 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 20 40 60 80 100 0.2 0.4 0.6 0.8 CC YTime (sec) B 20 40 60 80 100 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 20 40 60 80 100 0.2 0.4 0.6 0.8 CC YTime (sec) C Figure4-13.WienerwindowedCCvaluesforPatient2withA) n =32,B) n =16,C) n = 8bands. 100

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20 40 60 80 100 1 2 MSE XWiener Testing Time (sec) 20 40 60 80 100 0.2 0.4 0.6 0.8 1 1.2 1.4 MSE YTime (sec) A 20 40 60 80 100 1 MSE XWiener Testing Time (sec) 20 40 60 80 100 0.2 0.4 0.6 0.8 1 1.2 1.4 MSE YTime (sec) B 20 40 60 80 100 1 2 MSE XWiener Testing Time (sec) 20 40 60 80 100 0.2 0.4 0.6 0.8 1 1.2 MSE YTime (sec) C Figure4-14.WienerwindowedMSEvaluesforPatient2withA) n =32,B) n =16,C) n =8bands. 101

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CHAPTER5 REGULARIZATIONTHROUGHFEATURESELECTIONANDSUBSPACE PROJECTION Inthepreviouschapter,regularizationwasappliedthroug hridgeregressionand weightdecaytoreducethevarianceinthelinearweightsand throughtheleakyintegrator todecreasethenumberoftapsinthegammalter.Inthischap terthelinearmodels areregularizedthroughdecreasingthenumberofinputs/fe aturesthatarefedtothe lters.Forthispurposeonehastoidentifythefeaturestha taremostimportanttothe reconstructionofthedesiredtrajectories.Thiscanofcou rsebeaccomplishedthrough selectingthemostsensitivechannelsasrevealedbythesen sitivityanalysespresentedin thepreviouschapter.However,thetwoapproachespresente dheredirectlyextractthe featureswithouthavingtodesignlterswiththewholefeat urespace.Therstalgorithm, leastangleregression ,isabletoselectthefeaturesthataremostcorrelatedwith the desiredateachtimestamp,makingupforanynonstationarit iesintheneuralactivity. Thesecondmethodutilizestheprojectionofthedataontoit sDSScomponents.The selectedsubspaceallowsforareductionoftheparametersi nthemodels.Analsection inthischapteraddressestheissueofinterictalspikeremo valasameanstoimprovelter performance.ThispreprocessingstagealsoreliesonDSSme thodologies. 5.1LeastAngleRegressionforOnlineFeatureSelection IntroducedbyEfronetal.[ 18 ] leastangleregression (LAR)isanonlinevariable selectionalgorithmwhichimplementsshrinkageatlowcomp utationalcomplexities.The algorithmcomputesthecorrelationbetweentheinputchann elsandthedesiredsignalsand modelstheoutputasaweightedsumofonlythehighlycorrela tedchannelsforthewhole lengthofthedatasets.Theiterativeselectionprocedures tartsobyrankingthechannels accordingtothemagnitudeoftheircorrelationswiththede sired, ~ d ,andselectingthetwo channelswiththehighestcorrelations, ~x C 1 ~x C 2 ,whicharestoredinaset A .Theoutputis modeledas ~y (1)= r 1 ~x C 1 (1),where r 1 isselectedsuchthattheresidual, ~r (1)= ~ d (1) ~y (1), isequallycorrelatedwith ~x C 1 and ~x C 2 ,i.e. ~r bisectstheanglebetweenthetwochannels. 102

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Atthenextiteration, ~y (2)= ~y (1)+ r 2 ~r (1)where r 2 isselectedsuchthat ~r (2)isthe equiangularvectorbetween(i.e.equallycorrelatedwith) ~x C 1 ~x C 2 ~x C 3 .Thealgorithm stopswhentheL1-normof r reachesapresetthresholdvalue. Beforeweexplainthemathematicalprocedureofthealgorit hmletusdene somevariables.Assumingatthe m th iterationthecross-correlationvectorbetween theresidualandtheinputvariablesis c ,theindicesofinputsthathavethehighest correlationsarestoredintheset A = f k : j c k j = c max g where c max =max k fj c k jg ,for k =1 ; 2 ;:::;M .Let 1 A beavectorofonesoflengthequalingthesizeof A .Letusdene u A =[ s k u k ] k 2 A ,where s k =sign( c k ).Then R A = u A u TA isasubmatrixoftheinput autocorrelationmatrix.Thealgorithmwantstomoveinthed irectionoftheequiangular vectorbetweentheelementsof u A ,whichcanbefoundby: v A = u A A R 1 A 1 A (5{1) A = 1 A R 1 A 1 A 1 = 2 a = u T v A istheinnerproductbetweenallinputsandtheequiangularv ector.Finally,the stepsizetotakeontheequiangularvectorisgivenby: r =min k 2 A C + c max c k A a k ; c max + c k A + a k (5{2) where\min + "indicatesthattheminimumistakenoverinputswhichyield positivevalues. Withthesedenitionsthealgorithmcanbestructuredasfol lows: 1.Initialize w LAR =0, c = u T d 2.Themodeloutputisgivenby y = w T LAR u 3.Compute c max andstorethehighestcorrelatedinputindicesin A andform u A 1 A 4.Computetheequiangularvector v A ,andthestepsize r ,fromEqns. 5.Themodeloutputisupdated y = y + r v A whichyieldsthefollowingweightupdates fortheindicesin A : w A LAR = w A LAR + s A A R 1 A 1 A (5{3) 103

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6.Computethecross-correlationbetweentheinputsandthe residual: c = u T d y = c r a (5{4) 7.Iteratethrough(3)-(6)while j w LAR j < InMIMOsystems,theinputvariablesintotheLARalgorithma retheweightedtap delaylinesofeachchannel(refertoFigure 5-1 ): u k ( n )= w k x k ( n ) ;k =1 ; 2 ;:::;M (5{5) x k ( n )=[ x k ( n ) x k ( n 1) :::x k ( n L +1)] T FortheproposedLARalgorithm,thesystemweightswouldbet rainedtoyieldchannel modeloutputs u k =[ u k (1) u k (2) u k ( N )] T andthechanneloutputswithhighest correlationswiththedesiredwouldbeselected.Thisproce durehoweverassumesthat thesystemisstationaryandthatonlythechannelsthatprov idetheoverallhighest correlationsshouldbeselected.Asdiscussedearlier,the brainisnotastationarysystem. Moreover,withthedirectionaltuninganalysis,westudied howthepoweronchannels modulatewiththedirectionofthehandmovement.Thus,anal gorithmthatselectsinput variableslocallyintimewouldbemoresuitable.Suchamodi edLARalgorithmwas developedbyKimetal.[ 43 ].Thealgorithmreliesonrecursivelycomputingtheinput autocorrelationandcross-correlationvectorbetweenthe inputsanddesired: c ( n +1)= c ( n )+ d ( n +1) T u ( n +1)(5{6) R ( n +1)= R ( n )+ u ( n +1) u ( n +1) T where istheforgettingfactor.Thisalgorithmbringsaboutaseto fLARweightsfor eachtimesampleofthedatasets.Hence,ateachtimeinstanc eweknowwhichchannelor combinationofchannelscontributetothemodeloutputthem ost.Forchannelselection inreal-time,theLARweightscanbetrainedsimultaneously asthemodelweightsare 104

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Ÿ  ¡ Ÿ  ¡ ¢£ ¤ ¦ § £ ¤ ¦ ¨ £ Ÿ  ¡ Ÿ  ¡ ¢ ¤ ¦ § ¤ ¦ ¨ ¤ ¦ ¨ Figure5-1.SchematicshowingtheNLMSandLARcoecientsin theonlinefeature selectionalgorithm. adaptedviaNLMS.Thenewsystemweightupdateequationbeco mes: w ( n +1)= w ( n )+ w LAR ( n ) x ( n ) e ( n )(5{7) TherearetwoissueswiththeapplicationofLARtotheECoGre cordings.First,the equiangularvectorexistbetweenlinearlyindependentvec torswhichisnotthecaseforthe ECoGchannels.However,thisiscompensatedforbyselectin glowthresholds.Secondand moreimportantly,thehandtrajectoriesareusedtocalcula tetheLARcoecientsateach timestamp.Hence,LARcannotbeutilizedasasupervisedmod el,ratheritislimitedto beusedasananalysistoolwherewecantrytounderstandwhyt hechosenchannelsand spectralbandswhereimportantfortrajectoryreconstruct ionatthatparticularpointin time.5.1.1ThresholdSelectionThroughSurrogateData Theselectionoftheoptimalthreshold, ,fortheLARalgorithmistrickyasthe LARalgorithmcan\track"thedesiredsignal(ratherthann dafunctionalmapping) forsuboptimalthresholdvalues.Forthispurposeweengage surrogatedataasacontrol 105

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setgeneratedthesamewayasdescribedinChapter3.Theopti mal shouldselecta convincingsetoffeaturesfromtheoriginalinputsthatcan reconstructthetrajectory, whereasitshouldselectminimalfeaturesfromthesurrogat eset(whenbothdatasets arefedintotheLARalgorithmseparately).Thesurrogateda tadoesnothaveacausal relationshipwiththetrajectories(asitisalmostashued versionoftheoriginaldata), thusiftheLARalgorithmyieldsgoodtrajectoryreconstruc tionwewillconcludethatthe thresholdneedstobelowered.Kimetal.[ 43 ]proposedthattheLARfeatureselection algorithmshouldstartonlyifthecorrelationbetweenthed esiredandthereconstructed trajectorythroughNLMSaloneisgreaterthanasecondthres hold, NLMS .BothLAR thresholdsshallbedeterminedempirically.Thecorrelati onbetweenthedesiredand NLMSoutputiscomputedthrough: C NLMS ( n )= C NLMS ( n )+ P Mm =1 u m ( n +1) d ( n +1) p P u ( n +1) P d ( n +1) (5{8) ThepowerestimatesoftheNLMSoutputanddesiredarecomput edby: P u ( n +1)= P u ( n )+ u 2 ( n +1)(5{9) P d ( n +1)= P d ( n )+ d 2 ( n +1)(5{10) TheNLMSweightsaretrainedfor100samplesbeforetheLARal gorithmstarts. TheNLMSlearningratesfortheonlineLARalgorithmareseth ighenoughsothat evenwithoutthesubsetselectiongoodperformancecanbeat tainedfortheoriginalset. ButtheyarenottoohighsuchthattheLARalgorithmwillnoth avetocompensate foroscillatinglearningcurves.TheNLMSdesignparameter sare n =8, L =8,and =0 : 1.TheLARdesignparametersare =0 : 80, =0 : 25, X NLMS =0 : 40,and Y NLMS =0 : 60.Thethresholdforthehorizontalaxisthresholdislower astheNLMS performanceinthataxisisnotashighastheverticalaxisfo reitherpatient.TheLAR performanceresultsaresummarizedinTables 5-1 and 5-2 .Fortheselectedthresholdand forPatient1ontheaverage0.20%and0.51%oftheinputfeatu reswerechosenateach 106

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timestamp,whereasthesamevaluesforthesurrogatedataar e0.05%and0.11%.For Patient2,ontheaverage0.25%and0.65%featuresareselect edwiththeoriginaldata, whereasthesevaluesdroppedto0.11%and0.31%withthesurr ogatedata.Theoriginal dataperformswell(comparedtotheltersinthepreviousch apter)duetothefactthat theLARalgorithmallowsfor\switchingo"duringthetrans itionperiodsbetweentwo tasks.TheCCvalueswiththesurrogatedataarenotprovided inthetableasforlong rangesoftimestheoutputequalszero.Theoutputguresare plottedforbothdatasetsin Figures 5-2 and 5-5 .TheMSEvaluesaredrasticallylowfortheoriginaldataset ,whereas forthesurrogatedatanofeatureswereselectedformostoft hedurationofthedataset. Theselectedfeaturesfortheoriginaldatasetforbothdime sionsofthetrajectoryaregiven inFigures 5-3 and 5-6 .Notethatontheaveragethereisaconsistencyintheselect ed spectralbandsacrossthedurationofthedataset.Although thelowerbandsseemtobe selectedfrequently,theseplotsdonotrerectthemagnitud eoftheLARcoecients. ThesensitivityoftheLARalgorithmisattainedbyaveragin gacrossthetrajectory dimensionsandacrosstime.Forspatialsensitivity,anave rageisalsotakenacrossthe bandsandforspectralsensitivityanaverageistakenacros stheelectrodegrid,bothof whicharepresentedinFigures 5-4 and 5-7 forPatient1and2,respectively.Wecompare theseplotswiththeWienersensitivityplotsofFigures 4-3 E-Fand 4-4 E-F.Boththe spectralandspatialsensitivitiesaremorelocalizedforL ARasexpected.Still,themost importantspectralbandsarecapturedwithLAR.Mainlyelec trodesfromthepremotor areaareselected.Thismightbeduetothehighcorrelationa mongstchannelsandthefact thatintheenumerationofthechannels,thepre-motorchann elscomerst.Overall,this algorithmgivesusanideaabouttheredundanciesinthefeat uresetandthenonstationary inthedata. 5.2MappingofDSSComponentstoBehavior InChapter3westudiedthedenoisingsourceseparationofth e32spectralbands across32channelsasananalysistooltoextractthebandsan dchannelsthatwere 107

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Table5-1.LARperformanceresultsforPatient1 No.ofselectedchannelsMSE DatasetXYXY Original0.521.300 : 38 0 : 420 : 26 0 : 15 Surrogate0.130.270 : 85 0 : 850 : 89 0 : 26 Table5-2.LARperformanceresultsforPatient2 No.ofselectedchannelsMSE DatasetXYXY Original0.651.670 : 30 0 : 470 : 25 0 : 18 Surrogate0.270.800 : 88 0 : 940 : 77 0 : 31 Table5-3.WienerlterperformanceresultswithDSScompon entsforPatient1 Components L No.ofparametersCC X CC Y MSE X MSE Y 1:1024881920 : 27 0 : 160 : 56 0 : 211 : 00 0 : 800 : 88 0 : 24 1:58400 : 48 0 : 310 : 83 0 : 150 : 90 0 : 690 : 34 0 : 24 15750 : 45 0 : 260 : 85 0 : 140 : 91 0 : 630 : 31 0 : 18 251250 : 47 0 : 270 : 83 0 : 200 : 81 0 : 540 : 30 0 : 17 1,38160 : 45 0 : 310 : 81 0 : 140 : 85 0 : 590 : 44 0 : 33 15300 : 39 0 : 280 : 83 0 : 150 : 84 0 : 520 : 41 0 : 29 25500 : 46 0 : 260 : 84 0 : 190 : 75 0 : 450 : 36 0 : 26 Table5-4.WienerlterperformanceresultswithDSScompon entsforPatient2 Components L No.ofparametersCC X CC Y MSE X MSE Y 1:2081600 : 53 0 : 310 : 63 0 : 251 : 33 1 : 260 : 73 0 : 36 153000 : 63 0 : 260 : 57 0 : 281 : 30 1 : 070 : 80 0 : 37 255000 : 55 0 : 500 : 50 0 : 271 : 31 1 : 070 : 89 0 : 46 1,188160 : 45 0 : 290 : 54 0 : 311 : 02 1 : 110 : 87 0 : 37 15300 : 39 0 : 280 : 61 0 : 280 : 99 1 : 000 : 87 0 : 33 25500 : 46 0 : 270 : 57 0 : 300 : 96 1 : 000 : 85 0 : 36 108

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20 40 60 80 100 120 -10 -5 0 5 10 LAR with original dataX pos 20 40 60 80 100 120 -10 -5 0 5 10 Time (sec)Y pos A 20 40 60 80 100 120 -10 -5 0 5 10 LAR with surrogate dataX pos 20 40 60 80 100 120 -10 -5 0 5 10 Time (sec)Y pos B Figure5-2.A:LARtrajectoryreconstructionsfromtheorig inaldataofPatient1with n =8spectralbands,B)LARtrajectoryreconstructionsfromt hesurrogate data.Thethresholdswereselectedtominimizethenumberof selectedfeatures fromthesurrogatedata. Time (sec)Spectral bands, n=8Selected features across time 20 40 60 80 100 110 120 8 Hz 6110 Hz A Spectral bands, n=8Time (sec) Selected features across time 20 40 60 80 100 110 120 8 Hz 6100 Hz B Figure5-3.A)TheselectedfeaturesofPatient1ateverytim einstanceforthe reconstructionofthehorizontaltrajectory,B)Theselect edfeaturesforthe reconstructionoftheverticaltrajectory.Notethatthema gnitudesofthe weights, w LAR ,forthecorrespondingselectedfeaturesarenotrerectedi nthis binarygure. correlatedwithbehavior.ReferringbacktoFigure 3-14 ,weseethattherstve DSScomponentsshowedsignicantcorrelation.Moreover,t hecontributions(mixing coecients)ofeachnewextractedcomponentdecreasesatar ateof1 =f .Hence,we shallutilizetheprojectionontothesourcespaceofthers tsignicantcomponents asameanstoreducetheparametersintheWienerlterdesign .Butrstweemploy 109

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TemporalAnterior 1 2 3 4 5 6 1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 A 10 1 10 2 10 3 Spectral SensitivityFrequency (Hz) B Figure5-4.A)ThespatialsensitivityoftheLARcoecients ofPatient1averagedover timeandspectralbandssuperimposedontheelectrodegrid, B)Thespectral sensitivityoftheLARcoecientsaveragedovertimeandspa tialgridis plottedagainstthecenterfrequenciesof n =8bands. 20 40 60 80 100 120 -10 -5 0 5 10 LAR with original dataX pos 20 40 60 80 100 120 -10 -5 0 5 10 Time (sec)Y pos A 20 40 60 80 100 120 -10 -5 0 5 10 LAR with surrogate dataX pos 20 40 60 80 100 120 -10 -5 0 5 10 Time (sec)Y pos B Figure5-5.A:LARtrajectoryreconstructionsfromtheorig inaldataofPatient2with n =8spectralbands,B)LARtrajectoryreconstructionsfromt hesurrogate data.Thethresholdswereselectedtominimizethenumberof selectedfeatures fromthesurrogatedata. all1024componentsfromPatient1asthelterinput.Thelt erperformanceresults areprovidedinTable 5-3 .Theperformanceisquitelowwithallcomponents.Thisis becausethecomponentsareallsphered(withunityvariance )andalthoughthelast componentscontributeverylittletothemotorfeatures,th eyareatthesamescaleas therstcomponents.Theresultsfortheprojectionofonlyt herstvecomponents 110

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Time (sec)Spectral bands, n=8Selected features across time 20 40 60 80 100 120 140 8 Hz 6110 Hz A Spectral bands, n=8Selected features across time Time (sec) 20 40 60 80 100 120 140 8 Hz 6110 Hz B Figure5-6.A)TheselectedfeaturesofPatient2ateverytim einstanceforthe reconstructionofthehorizontaltrajectory,B)Theselect edfeaturesforthe reconstructionoftheverticaltrajectory.Notethatthema gnitudesofthe weights, w LAR ,forthecorrespondingselectedfeaturesarenotrerectedi nthis binarygure. TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 7 8 4 3 2 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 A 10 1 10 2 10 3 Spectral SensitivityFrequency (Hz) B Figure5-7.A)ThespatialsensitivityoftheLARcoecients ofPatient2averagedover timeandspectralbandssuperimposedontheelectrodegrid, B)Thespectral sensitivityoftheLARcoecientsaveragedovertimeandspa tialgridis plottedagainstthecenterfrequenciesof n =8bands. forPatient1,asprovidedinTable 5-3 ,arenotsignicantlybetterthantheWiener lterresultspresentedinthepreviouschapter.However,w henonlytherstandthird components,whichcorrespondtothecomponentsmostcorrel atedwiththeverticaland horizontaltrajectoriesrespectively,areutilizedtheho rizontalMSEhasdecreasedata15% 111

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10 20 30 40 50 -10 -5 0 5 10 X posWiener Testing Time (sec) 10 20 30 40 50 -10 0 10 Y posTime (sec) A 10 20 30 40 50 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 CC YTime (sec) B 10 20 30 40 50 0.5 1 1.5 MSE XWiener Testing Time (sec) 10 20 30 40 50 0.2 0.4 0.6 0.8 1 MSE YTime (sec) C Figure5-8.A)ReconstructedtrajectoriesforPatient1fro mtherstandthirdDSS components,B)Windowedmagnitudeofcorrelationcoecien ts,C)Windowed mean-squarederrors. signicancelevelfor L =25asveriedthrough t -tests.ThelteroutputsalongwithCC andMSEdistributionsacrosstimearepresentedinFigure 5-8 ForPatient2,weutilizetheprojectionontothesourcespac eofthersttwenty componentsasameanstoreducetheparametersintheWiener lterdesignsincethe decayofthecorrelationcoecientswereslower.Theresult sfortheprojectionofonly thesecomponentsareprovidedinTable 5-4 ,andarenotsignicantlybetterthanthe Wienerlterresultspresentedinthepreviouschapter.Inf act,theMSEvaluesfor theverticaltrajectoriesseemhigher.Thismaybeduetothe high-amplitudespiky artifactsinthecomponentswhichincreasetheoverallMSEs .Evenwhenonlytherst 112

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20 40 60 80 100 -10 0 10 20 X posWiener Testing Time (sec) 20 40 60 80 100 -10 0 10 20 Y posTime (sec) A 20 40 60 80 100 0.2 0.4 0.6 0.8 CC XWiener Testing Time (sec) 20 40 60 80 100 0.2 0.4 0.6 0.8 CC YTime (sec) B 20 40 60 80 100 1 2 MSE XWiener Testing Time (sec) 20 40 60 80 100 0.5 1 1.5 MSE YTime (sec) C Figure5-9.A)ReconstructedtrajectoriesforPatient2fro mtherstand18 th DSS components,B)Windowedmagnitudeofcorrelationcoecien ts,C)Windowed mean-squarederrors. andeighteenthcomponentsarefedtothelter(whichcorres pondtothecomponentsmost correlatedwiththeverticalandhorizontaltrajectoriesr espectively),thereisnosignicant improvement.ThelteroutputsalongwithCCandMSEdistrib utionsacrosstimeare presentedinFigure 5-9 5.3InterictalSpikeRemovalThroughDSS Oneissuewehavenotaddressedthusfaristhenecessityofpr eprocessingstagesfor artifactremovalbeforethefeatureextractionandmodelin gstages.Sinceimplantationof subduralelectrodesinhumanpatientsislimitedtopatient sseekingepilepsysurgery,one mustconsiderforBMIsthattheabnormalactivityofepilept ictissuecouldinruencemotor 113

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decoding.IntheBMIliterature,theseizureonsetzoneofth esubjectsparticipatingin BMIstudiesareremotefromtheprimarymotorcortex(whichi salsothecasewithour patients),however,interictalspikingactivitycanbepre sentintheglobalsensorimotor system.Thepresenceofinterictalspikesisobservedasnon -stationaryhighamplitude dischargesandcouldpotentiallycorrupttheamplitudemod ulatedmotorfeatures. Tocontendwiththisproblem,independentcomponentanalys is(ICA)[ 36 ]hasbeen proposedtolocalizeandseparateinterictalsourcesfromb ackgroundEEG[ 44 ]andMEG [ 68 ].However,duetoitsdesirableproperties(asdescribedin Chapter3),weexplore andisolateECoGinterictalspikingactivityviaDSSandstu dythemotorfeaturesinthe \corrected"channelsaftertheremovaloftheepileptogeni csources. Figures 5-10 A-Bshowchannels(correspondingtothesametimewindowasF igures 3-1 A-B)thataredominatedbyhighamplitudedischarges.These epileptiformactivities arecommonlyobservedinfocalepilepsiesbetweenseizures andarecalled interictal spikingactivity [ 13 ].Interictaldischargesareduetodynamicchangesinexcit ationand synchronizationwithinarestrictedaggregateofepilepti cneuronsandareexpressedby high-amplitude,fasttransients,commonlyfollowedbyasl owwavethatlastsseveral hundredsofmilliseconds[ 13 ].Thewidespectrumofinterictaldischargesincludesspik es, sharpwavesandspike-and-wavecomplexes[ 5 ].Interictalspikingactivitycanbepresentin theglobalsensorimotorsystemwithoutassociatedrecogni zableclinicalmanifestations[ 19 ]. Therefore,isolationofECoGinterictalspikesisanimport antpreprocessingchallengefor BMImodelinginthepresentconditionsofusingepilepticpa tients. Examiningthedata,weobservethatforPatient1theinteric talspikesareof quasiperiodicnature(recallFigure 5-10 ).Weshallexploitthisquasiperiodicnatureof theobservedinterictalspikesbyaveragingacrosstherepe titiousperiodsinorderto increaseSNRonthesourceestimateoftheinterictalactivi ty[ 30 ].Channelsthatare heavilycontaminatedbyinterictalactivityhavehighstan darddeviationsandhencewere detectedthroughsortingstandarddeviationsofthechanne ls.Figure 5-11 Ashowsthe 114

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0 1 2 3 4 5 -2 0 2 x 10 -4 Ch # 21 0 1 2 3 4 5 -2 0 2 x 10 -4 Ch # 26 0 1 2 3 4 5 -4 -2 0 2 x 10 -4 Time (sec)Ch # 29 A 0 10 20 30 40 50 60 -6 -4 -2 0 2 4 6 x 10 -4 Ch # 6 0 10 20 30 40 50 60 -4 -2 0 2 4 6 x 10 -4 Ch # 19 0 10 20 30 40 50 60 -4 -2 0 2 4 6 x 10 -4 Ch # 25Time (sec) Figure5-10.A)RecordingsfromPatient1demonstratingepi lepticinterictalspikes.B) RecordingsfromPatient2demonstratingepilepticartifac ts. 115

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1 2 3 4 5 6 7 x 10 -5 0 1 2 3 4 5 6 Standard Deviations A TemporalAnterior 0 1 2 3 4 5 6 x 10 -5 B Figure5-11.A)HistogramofthestandarddeviationsoftheE CoGchannelsfromPatient 1.B)Thestandarddeviationsarespatiallysuperimposedon theelectrode grid. histogramofthestandarddeviationsofthechannelsandFig ure 5-11 Bshowsthespatial distributionofthestandarddeviations.Thehistogramsho wsthatthevechannelswith higheststandarddeviationsstandoutfromtherestofthech annelswhichisconformedby visualinspection. Thespikesinthesechannelsarelocalizedthroughthreshol dingtheECoGmagnitudes bythreetimesthestandarddeviationsofthechannels.Inte rspikeintervals(ISI)are denedasthetimebetweenthepeaksoftwoconsecutivespike s.Eachpeak-to-peak periodisdilatedtothemedianofinterspikeintervalsonth echannel,andspiketriggered averagingisperformedonthesourceestimates.Thedenoise dsourceestimateisfound byreplacingtheaveragedinterspikeperiods(oflengthequ altomedianISI)intotheir originalperiods.Thisaveragingprocessisthe\denoising function"appliedtothesource estimates.Thisdenoisingprocessincreasestheintericta lactivity-to-backgroundactivity ratio.Thealgorithmstopswhentheanglebetweentheconsec utivedemixingvectorsis lessthan =0 : 1 o orwhenthemaximumnumberofiterations, m =200isreached. Figure 5-12 depictstheextractedquasiperiodicinterictalsourceson adatasetof1 minute(aspreprocessingthewholedatasetsampledat12,20 7Hzistoocomputationally demanding).Thecorrespondingmixingvectorsofthesesour cesarespatiallysuperimposed 116

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0 2 4 6 8 -2 0 2 4 Comp #1 0 2 4 6 8 -4 -2 0 2 Comp #2 0 2 4 6 8 -5 0 5 Comp #3 0 2 4 6 8 -2 0 2 4 6 Comp #4 0 2 4 6 8 -2 0 2 4 6 Comp #5Time (sec) Figure5-12.Interictalspikesextractedviathresholdloc alizationanddenoisingaveraging. ontheelectrodegridinFigure 5-13 .Notethatfortheextractionofeachsource,weusea dierentdenoisingfunctionbasedonthethresholdingonap articularchannel.Therefore, thecomponentnumbersinFigure 5-13 donotrerectanysortofordering(asrespectto thevarianceofthedesiredproperties).Theactivitiesare observedtobehighlylocalized. Thecorrectedchannelswereattainedbyremovingtheinteri ctalcomponentsweightedby theirmixingcoecients: X cor = X 5 X i =1 a Ti s i (5{11) Figure 5-14 showsthepowerofcorrectedchannelsbandpasslteredbetw een 2623-6100Hz.Thisbandwasfoundtobehighlycorrelatedwit htheverticalaxiswhich issuperimposedontheoriginalandcorrectedpowerplots.O nthersttopchannels wecanobservethatinterictalspikeremovalhasincreasedt hecorrelationbetweenthe channelpowersandverticaltrajectory,whereasononechan nel(bottomrow)themotor modulationisremoved. 117

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TemporalAnteriorComponent #1 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 TemporalAnteriorComponent #2 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 TemporalAnteriorComponent #3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 TemporalAnteriorComponent #4 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 TemporalAnteriorComponent #5 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Figure5-13.Mixingmatricesoftheextractedinterictalco mponentsspatially superimposedoverthesubduralelectrodes. Theperformanceresultswiththeoriginalchannelsandthed enoisedchannelstoa Wienerlteroforder L =8and n =8spectralbandsfortheshorteneddatasetof1min issummarizedinTable1.Overall,withall32channelsin8sp ectralbands,theresults afterinterictalspikeremovalwerebetter(higherCC,lowe rMSE),yetwasnotsignicant enoughtopassthe t -tests.Wethenrepeatedtheexperimentswithonlythechann elsthat 118

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10 20 30 40 50 60 Channel #28 10 20 30 40 50 60 Channel #29 10 20 30 40 50 60 Channel #32 10 20 30 40 50 60 Channel #26 10 20 30 40 50 60 Channel #28 10 20 30 40 50 60 Channel #29 10 20 30 40 50 60 Channel #32 10 20 30 40 50 60 Channel #26 Time (sec) Figure5-14.Spectralpowersofsomechannelsinthepassban d2623-6100Hzbefore (left)andafter(right)interictalspikeremovalsuperimp osedonthevertical trajectory(showninred). Table5-5.Wienerlterresultsbeforeandafterinterictal spikeremoval DatasetChannels CC X CC Y MSE X MSE Y OriginalAll0 : 21 0 : 150 : 78 0 : 191 : 00 0 : 610 : 37 0 : 22 320 : 40 0 : 300 : 60 0 : 281 : 09 0 : 720 : 61 0 : 32 260 : 38 0 : 330 : 77 0 : 191 : 12 0 : 710 : 37 0 : 28 CorrectedAll0 : 34 0 : 220 : 79 0 : 200 : 90 0 : 510 : 33 0 : 24 320 : 29 0 : 330 : 81 0 : 161 : 09 0 : 690 : 45 0 : 44 260 : 44 0 : 200 : 42 0 : 281 : 22 0 : 750 : 76 0 : 16 weredominatedbyinterictalspikes.Whenonlychannel#32b andpasslteredin8bands isfedtotheWienerlter,theverticalCCandMSEshowimprov ementatasignicance levelof15%.Ontheotherhand,whenonlychannel#26,whichw asthechannelthat becamelesscorrelatedwiththeverticaltrajectoryinFigu re 5-14 ,theCCandMSE performancesdecreaseatasignicancelevelof10%. Tosumup,wepresentedaninterictalspikeremovalmethodol ogybasedondenoising sourceseparation.Unlikeotherblindsourceseparationte chniques(suchasICA),we didnothavetoperformthesimultaneousextractionofall32 components(whichis computationallyextensive)andthenstudywhichcomponent sconsistedofinterictal activity.Instead,weexploitedtheobservedquasiperiodi cnatureoftheinterictal spikes.Channelswithhighamplitudedischargesweredetec tedbysimplethresholding mechanismsandtheselocalizationswereusedfortheextrac tionofthecomponents 119

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(denoisingfunctions)whichreducedcomputationalcosts. Thespatiallyweighted componentsweresubtractedfromtheECoGmeasurementsandn otonlywerethe highlydominatedchannelswerecorrectedbutalsothelowam plitudepropagationof theinterictalactivitytotheneighboringchannelswerere moved.Furtherexperiments includingthewholedatasetandmorespectralresolution( n =32)wouldprovidemore conclusionsastowhetherthispreprocessingstageimprove sperformanceingeneralor suppressesmotorfeaturesinsomespatialneighborhoods. Weshouldpointoutthatthisquasiperiodicityisspecicto Patient1andthatthis propertyisnotaglobalpropertyofECoGinterictalspikes. Infact,thesamemethodology cannotbeappliedtoPatient2,inwhichtheartifactsareran dom,bursty,andnot localized. 120

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CHAPTER6 NONLINEARMAPPINGOFECOGMOTORFEATURESTOBEHAVIOR Inthepreviouschaptersweanalyzedthelinearrelationshi pbetweenthespectral powerinECoGrecordingsandthetrajectoriesandbuiltmode lsthatlinearlytranslated theneuralactivity.Althoughlinearltershavewellestab lished,low-complexitytraining methodologies,thereconstructedtrajectoriesmaybesubo ptimalsincetheoutputis limitedtomappingsintheinputspace.Theintrinsicneurop hysiologicalmappingof amplitudemodulatedcontrolfeaturestomotorbehaviormay requirenonlinearmappings. Inneuralnetworksliterature,themostcommonneuralarchi tecturefordynamical modelingisthetimedelayneuralnetwork(TDNN)whichrepla cesthelinearcombiner oftheWienerlterwithastaticmulti-layerperceptron(ML P)[ 31 ].Thetapdelay line,constructsasucientlylargestatespacefromtheinp uttimeserieswheretimeis implicit.Theparameters(weights)oftheMLPareadaptedth roughthebackpropagation algorithm.TDNNshavebeenusedinBMIexperimentsandoera nonlinearmapping throughhiddenprocessingelements;howeverthenumberofp arametersofthemodel scaleswiththeembeddingofthehighdimensionalinput,jus tlikeinthelineartapdelay linearchitectures,andthuscreatingproblemswithmodelg eneralization[ 42 ].Forreal-time clinicalapplications,modelsofloworderthatareeasytot rainandrequirelowmemory aredesirable. Toovercometheproblemofmodelorder,recurrentneuralnet works(RNNs)have beenimplementedinBMIsastheytakeadvantageofworkingwi ththecurrentdata samplesonlyandmovethememorystructuretothehidden,rec urrentlayerinsteadof thedelayedembeddingofTDNN[ 78 ].Thememoryisprovidedbythefeedbackcreated bytherecurrentconnectionsbetweentheneurons.Oneofthe mainpracticalproblems withRNNsisthedicultytoadaptthesystemweights.Variou salgorithms,suchas backpropagationthroughtimeandreal-timerecurrentlear ning[ 96 ],havebeenproposedto trainRNNs;however,thesealgorithmssuerfromcomputati onalcomplexity,resultingin 121

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slowtraining,complexperformancesurfaces,thepossibil ityofinstability,andthedecayof gradientsthroughthetopologyandtime[ 31 ]. Echostatenetworks (ESNs)arerecurrentnetworkparadigmswhichaddressthe dicultieswithRNNtraining[ 69 ].Inthischapter,westudymappingsfromspectral ECoGfeaturestohandmovementsusingechostatenetworksan dleakyechostate networks. 6.1EchoStateNetworks:AnIntroduction IntroducedbyJaeger,echostatenetworks(ESNs)[ 38 ]areRNNswithsimplied andecientlearningstages.ESNspossessa\large"recurre nttopologyofnonlinear processingelements(PEs)whichconstitutesa\reservoiro frichdynamics"[ 39 ]and containinformationaboutthehistoryofinputand/oroutpu tpatternswhenproperly dimensioned.TheoutputsoftheseinternalPEs(theechosta tes)arefedtoamemoryless butadaptivereadoutnetworkwhichisgenerallylinearandr eadsthereservoirand producesthenetworkoutput.TheinterestingpropertyofES Nisthatonlythememoryless readoutistrainedwithleastsquares,whereastherecurren ttopology W hasxed connectionweights.ThisreducesthecomplexityofRNNtrai ningtosimplelinear regressionwhilepreservingtherecurrenttopology.Moreo ver,byintegratingleakyneurons intheESNstructure,thememorydepthofthesystemisincrea sedwithoutincreasing lterorders. Figure 6-1 depictsanESNwith M inputchannels, N internalPEsand C=2 output units.Thevalueoftheinputunitattime n is u ( n )=[ u 1 ;u 2 ( n ) ;:::;u M ( n )],ofinternal PEsare x ( n )=[ x 1 ;x 2 ( n ) ;:::;x N ( n )],ofoutputunitsare y ( n )=[ y 1 ;y 2 ( n ) ;:::;y L ( n )]. Theconnectionweightsaregiveninan N x M weightmatrix W in =( w in ij )forconnections betweentheinputandthestates,inan N x N matrix W =( w ij )forconnectionsbetween thePEs,inan L x N matrix W out =( w out ij )forconnectionsfromPEstotheoutputunits, inan N x L matrix W back =( w back ij )fortheconnectionsthatprojectbackfromtheoutput totheinternalPEs,inan L x M matrix W inout forconnectionsfrominputunitstooutput 122

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Figure6-1.BlockdiagramofanEchoStateNetwork units,andinan L x L matrix W outout forconnectionsbetweenoutputunits[ 38 ].Usually, theactivationoftheinternalPEsisupdatedaccordingto: x ( n )= f ( W in u ( n )+ Wx ( n 1)+ W back y ( n 1))(6{1) where f =( f 1 ;f 2 ;:::;f N )aretheinternalunit'sactivationfunctions. Alternatively,eachPEcanbeimplementedwithaleakyinteg ratorneuronwith leakageparameter ,decayrate andthefollowingupdateequation: x ( n )=(1 ) x ( n )+ f ( W in u ( n )+ Wx ( n 1)+ W back y ( n 1))(6{2) Theleakyneuronimplementationutilizesthegammadelayop eratorinthe recurrenciesandisparticularlyusefulwhenlargermemory depthsarerequired.We usetheleakyneuronimplementationsincetheECoGsignalsc hangerapidlywhereasthe desiredhandpositionisatamuchslowerrate.All f i 'sarechosentobehyperbolictangent 123

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functions, tanh ( : ).Theoutputfromthereadoutnetworkiscomputedaccording to: y ( n )= f out ( W out x ( n )+ W inout u ( n )+ W outout y ( n 1))(6{3) where f out =( f out 1 ;f out 2 ;:::;f out N )aretheoutputunit'snonlinearfunctions.Generally, thereadoutislinear(i.e. f out isidentity).Foralinearreadout,theoptimaloutputweigh t matrix, W out cancomputedusingtheWienersolution. AbasicnecessarypropertyforESNreservoiristhe inputforgettingproperty which statesthatfortheESNlearningprincipletowork,thereser voirmustasymptotically forgetinputhistory.Ithasbeenshownin[ 38 ]thattheinputforgettingpropertyis equivalentto stateforgetting ,thatis,thereservoirmustforgetitsinitialstateafter sucientlylongtime.The echostatecondition canbelinkedtothespectralradiuswhich isthelargestamongtheabsolutevaluesoftheeigenvalueso fthereservoir'sweightmatrix, denotedby jj W jj .Thisspectralradiushastobelessthanunity, jj W jj < 1.Infact, thisconditionstatesthatthedynamicsoftheESNisuniquel ycontrolledbytheinput andtheeectofinitialstatesvanishes.Fortheleakyneuro ncase,itisrequiredthat jj W +(1 ) W jj belessthanunity,[ 39 ]. Inordertoassessthecontributionsofthechannelsandspec tralbands,westudythe rateofchangesinthemodeloutputsasthemodulationofchan nelsvariesovertime.Due tothehiddenlayer,weapplythechainruletoformthisrelat ionship: @ y ( n ) @ u ( n ) = @ y ( n ) @ x ( n ) @ x ( n ) @ u ( n ) = W Tout D n W in (6{4) @ y ( n ) @ u ( n 1) = W Tout D n W T D n 1 W in (6{5) @ y ( n ) @ u ( n n ) = W Tout D n n Y i =1 W T D n i W in (6{6) where D n = diag [ f 0 ( z 1 ( n )) f 0 ( z 2 ( n )) f 0 ( z N ( n ))]and z ( n )= W in u ( n )+ Wx ( n 1). Thisyieldsaninstantaneoussensitivityoftheoutputtoon eoftheinputs.The temporaldecayofinputsisplottedinFigure 6-2 .Experimentally,wedeterminethe 124

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0 0.5 1 1.5 2 2.5 3 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 D (sec) Temporal Sensitivity Vertical sensitivity Horizontal sensitivity Figure6-2.Sensitivityattime t forChannel1ofPatient1with n =32bandsasa functionof. sensitivitydepthtobearound2secs.Henceateachtimestam pthetemporalsensitivity oftheoutputtoaninputiscomputedastheaveragesoftheins tantaneoussensitivities over30samples(10additionalsamplesguaranteedecayedse nsitivities).Wefurther averageacrosspassbandsandchannelstoattainthespatiotemporalandspectro-temporal sensitivitiesoftherecurrentnetwork. 6.2EchoStateNetworksforECoGBMIs FortheapplicationofESNstoourBMIproblem,werstinitia lizetheinputmatrix W in withuniformlydistributedrandomnumbersscaledbetween[ -c/2,c/2].Theboundary valueswerechosensuchthatforthelargestspectralradius r =0 : 9,thestatesarenot overlysaturated.Thereservoirmatrix W isformedofelementsthattakeonthevalues f 0 ; 1 ; 1 g withprobabilities p; (1 p ) = 2 ; (1 p ) = 2respectively,where p ,represents thesparsenessofthereservoirmatrix. W isfurthernormalizedbyitsthemaximum eigenvalueandscaledbythedesiredspectralradius.Forth eexperimentsherein,we set p =0 : 95.Thenonlinearityinthereservoirischosentobethehype rbolictangent function, f ( x )= tanh ( x ).Theparametersthatarevariedarethenumberofechostate s, 125

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Table6-1.ESNperformanceresultsforPatient1 nN k W k c CC X CC Y MSE X MSE Y 325000.40.90.010 : 33 0 : 250 : 85 0 : 170 : 98 0 : 540 : 27 0 : 16 25000.30.90.010 : 43 0 : 300 : 85 0 : 130 : 92 0 : 570 : 57 0 : 29 165000.30.90.010 : 54 0 : 280 : 82 0 : 210 : 90 0 : 430 : 43 0 : 36 25000.30.90.010 : 53 0 : 220 : 83 0 : 190 : 84 0 : 390 : 28 0 : 18 85000.20.90.10 : 39 0 : 260 : 85 0 : 180 : 95 0 : 550 : 30 0 : 16 10000.80.90.010 : 39 0 : 290 : 85 0 : 140 : 99 0 : 590 : 31 0 : 16 Table6-2.ESNperformanceresultsforPatient2 nN k W k c CC X CC Y MSE X MSE Y 322500.20.90.010 : 41 0 : 280 : 74 0 : 221 : 19 1 : 360 : 48 0 : 27 10000.20.90.010 : 41 0 : 250 : 71 0 : 211 : 20 1 : 300 : 48 0 : 26 1610000.10.90.10 : 44 0 : 280 : 75 0 : 261 : 22 1 : 370 : 43 0 : 24 20000.10.90.010 : 56 0 : 240 : 81 0 : 241 : 12 1 : 420 : 46 0 : 18 85000.10.90.10 : 61 0 : 280 : 76 0 : 271 : 16 1 : 400 : 35 0 : 23 10000.10.90.10 : 55 0 : 280 : 76 0 : 280 : 99 1 : 170 : 38 0 : 22 N = f 250 ; 500 ; 1000 ; 2000 ; 2500 g ,thereservoirspectralradius, r = f 0 : 5 ; 0 : 7 ; 0 : 9 g andthe leakageparameter =[0 : 1:0 : 1:1](where =1correspondstotheregular/non-leaky ESN).TheESNsaretrainedonthesametrainingsetsasthelin earlters.Theinitial1 secofthestatematrixisdiscardedastransientactivitybe foreattainingtheleastsquare solutionfortheoutputweights, W out .Duetotherandominitializationsoftheinputand reservoirmatrices,fteenMonteCarlosimulationswereru nforeachsetofparameters. Performanceresultsfromselectedsimulationsforbothpat ientsarepresentedinTables 6-1 and 6-2 ,respectively. Overall,theleakyESNwhichaddsmemorydepthstothemodely ieldedbetter performancethantheregularESNarchitecture.Thespectra lradiusof0.9which providesthehighestvarianceinthestates,alsoprovidedb etterperformanceacrossall parametersandbothpatients.Asinthecaseofothermodels, theverticaltrajectory reconstructionperformanceisfarbetterthatthehorizont alcase.Exemplarytrajectories ofthereconstructedtrajectories,thewindowedCCandMSEv aluesaredepictedin Figures 6-3 6-4 6-5 forPatient1andinFigures 6-3 6-7 6-8 forPatient2. 126

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0 10 20 30 40 50 60 ESN X Output 0 10 20 30 40 50 60 ESN Y Output Time (sec) A 0 10 20 30 40 50 60 -15 -10 -5 0 5 10 15 ESN X Output 0 10 20 30 40 50 60 -20 -10 0 10 20 ESN Y OutputTime (sec) B 0 10 20 30 40 50 60 -15 -10 -5 0 5 10 15 ESN X Output 0 10 20 30 40 50 60 -20 -10 0 10 20 ESN Y Output C Figure6-3.ESNreconstructedtrajectoriesforPatient1wi thA) n =32,B) n =16,C) n =8bandswith N =500states. Wefurtheraveragethetemporalsensitivitiesacrossdimen sions,frequencybandsto attainspatialsensitivityandacrosselectrodegridstoat tainspectralsensitivity.These measuresarepresentedinFigures 6-9 and 6-10 .ForPatient1,thespatialsensitivityof the n =32bandsiswidespreadwithhighlocalizationsinthePMdan dM1areas.Just likeintheWienerltercase,thewithlowernumberofbands, wehavenarrowerspatial sensitivities.Moreover,thespatialsensitivitiesofthe ESNsandWienerlteroverlap.In thecaseofspectralsensitivities,ESNsandtheWienerlte rsidentifythesamespectral rangesasthemostsensitive.Similarobservationscanbema dewithPatient2.Spatial sensitivityiswidespreadinthecase n =32withhighpositiveandnegativesensitivities 127

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0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN CC X 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN CC YTime (sec) A 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN CC X 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN CC YTime (sec) B 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN CC X 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN CC Y C Figure6-4.ESNwindowedCCvaluesforPatient1withA) n =32,B) n =16,C) n =8 bands. overlappingwiththoseoftheWienerlter.Areaswithhighs patialsensitivitiesbecome narrowerwith n =16 ; 8bands.Finally,thesamesensitivespectralrangesastheW iener lterarecaptured. ForPatient1,thenonlinearrecurrentarchitecturehasnot providedastatistically signicanceoverthelinearmethods.However,inaprevious studyinwhichwehad coarselydividedthebroadbandspectrumintofourbandsbet ween:1-30Hz,30-100Hz, 100-300Hzand300Hz-6.1kHz,theESNswereabletoidentifyt hesensitiveportionsof thehighfrequencybandandyieldedstatisticallysignica ntreconstructionperformance (refertoTable 6-3 ).Inotherwords,ESNswereabletoprunethefeaturesthatco ntributed 128

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0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN MSE X 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN MSE YTime (sec) A 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN MSE X 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN MSE YTime (sec) B 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN MSE X 0 10 20 30 40 50 60 0 0.2 0.4 0.6 0.8 1 ESN MSE YTime (sec) C Figure6-5.ESNwindowedMSEvaluesforPatient1withA) n =32,B) n =16,C) n =8 bands. tothereconstructionofthetrajectoriesinacoarsespectr alresolutionmuchbetterthan thelinearlters.Astheperformanceofthelinearmodelsan dESNsarestatistically equivalentforboththemaximalresolutionof n =32andminimalresolutionof n =8 inourcurrentstudy,weconcludethatthehigherbandsdonot requirefurthersplitting. Theequivalenceofperformanceinthecurrentstudycanbeat tributedtothenespectral resolutionofthecurrentfeaturesets. 129

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0 20 40 60 80 100 -15 -10 -5 0 5 10 15 ESN X Output 0 20 40 60 80 100 -20 -10 0 10 20 ESN Y OutputTime (sec) A 0 20 40 60 80 100 -15 -10 -5 0 5 10 15 ESN X Output 0 20 40 60 80 100 -20 -10 0 10 20 ESN Y OutputTime (sec) B 0 20 40 60 80 100 -15 -10 -5 0 5 10 15 ESN X Output 0 20 40 60 80 100 -20 -10 0 10 20 ESN Y OutputTime (sec) C Figure6-6.ESNreconstructedtrajectoriesforPatient2wi thA) n =32,B) n =16,C) n =8bandswith N =1000states. Table6-3.Performancecomparisonoflinearandnon-linear ltersforPatient1with n =4 spectralbands FrequencyBandsWienerFilterESNLeakyESN CC X CC Y CC X CC Y CC X CC Y 300-6kHz0 : 39 0 : 260 : 48 0 : 270 : 50 0 : 270 : 61 0 : 290 : 49 0 : 260 : 63 0 : 28 100-300Hz0 : 34 0 : 210 : 35 0 : 250 : 33 0 : 220 : 50 0 : 270 : 36 0 : 260 : 52 0 : 27 60-100Hz0 : 35 0 : 240 : 41 0 : 220 : 37 0 : 250 : 39 0 : 230 : 43 0 : 250 : 45 0 : 26 1-60Hz0 : 33 0 : 160 : 41 0 : 250 : 39 0 : 260 : 43 0 : 260 : 41 0 : 250 : 44 0 : 26 Ontheotherhand,forPatient2, t -testsrevealanimprovementintheMSEvaluesofthe verticalreconstructionoverthelinearltersatasignic ancelevelof0.05,forallthree choicesofnumberofspectralbands. 130

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0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN CC X 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN CC YTime (sec) A 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN CC X 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN CC YTime (sec) B 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN CC X 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN CC YTime (sec) C Figure6-7.ESNwindowedCCvaluesforPatient2withA) n =32,B) n =16,C) n =8 bands. 131

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0 20 40 60 80 100 0 0.5 1 1.5 ESN MSE X 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN MSE YTime (sec) A 0 20 40 60 80 100 0 0.5 1 1.5 2 ESN MSE X 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN MSE YTime (sec) B 0 20 40 60 80 100 0 0.5 1 1.5 2 ESN MSE X 0 20 40 60 80 100 0 0.2 0.4 0.6 0.8 1 ESN MSE YTime (sec) C Figure6-8.ESNwindowedMSEvaluesforPatient2withA) n =32,B) n =16,C) n =8 bands. 132

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TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 A 10 1 10 2 10 3 Frequency (Hz)Spectral Sensitivity B TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 C 10 1 10 2 10 3 Frequency (Hz)Spectral Sensitivity D TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 1 2 3 4 5 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 E 10 1 10 2 10 3 Frequency (Hz)Spectral Sensitivity F Figure6-9.SpatialandspectralsensitivitiesofESNswith N =500statesforPatient1. A)Spatialsensitivityof32channelsacross n =32passbands,B)Spectral sensitivitiesof n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie s for n =16passbands.E-F)Sensitivitiesfor n =8passbands. 133

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TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 7 8 4 3 2 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 A 10 1 10 2 10 3 Frequency (Hz)Spectral Sensitivity B TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 7 8 4 3 2 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 C 10 1 10 2 10 3 Frequency (Hz)Spectral Sensitivity D TemporalAnteriorSpatial Sensitivity 1 2 3 4 5 6 7 8 4 3 2 1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 E 10 1 10 2 10 3 Frequency (Hz)Spectral Sensitivity F Figure6-10.SpatialandspectralsensitivitiesofESNswit h N =1000statesforPatient 2.A)Spatialsensitivityof32channelsacross n =32passbands,B)Spectral sensitivitiesof n =32passbandsacrosstheelectrodegrid.C-D)Sensitivitie s for n =16passbands.E-F)Sensitivitiesfor n =8passbands. 134

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CHAPTER7 CONCLUSIONS 7.1Discussion InspiredbythepromisingperformancesofinvasiveandEEGbasedBMIs,we conductedaexploratoryyetsystematicanalysisofECoGsig naturesformotorcontrol. Thedatasetsusedinthisdissertationwerecollectedfrome pilepticpatientsinuncontrolled clinicalconditions,yetstillenabledthereconstruction oftrajectoriesofreachingand pointingtaskswithcorrelationsupto85%.Insteadofdisca rdinghighfrequencyactivity, weutilizedthewholespectrumoftherecordedsignalsandex ploredthecrosscorrelation betweenthebandpassedltersandthehandtrajectorystart ingwithhighspectral resolution,mergingthebandsuptothepointwherewell-kno wnneuralrhythmswere capturedinthelowerendofthespectrum.Wehaveshownthati nfactsomeofthemost sensitivebandswereinhigherendofthespectrum,thoughth especicbandsdiered acrosspatients.Thisisevidencethatselectingahandfulo fpre-denedbandsmayaect thegeneralizationcapacityofthemodels.Eventhoughthey werefedthroughwitha vastamountoffeatures,thedesignedlinearandnonlinear lterswereabletocapture thefeaturesthathadproventobehighlycorrelatedwithbeh aviorthroughtheearlier analyses(crosscorrelation,tuningandDSS).Duetothedyn amic,nonstationarynatureof neuralmodulations,theseresultsareinfactencouragingb ecauseinaclosed-loopsystem participitantsmaybeabletomodulateabandeasierthanoth ersandhavingtheluxuryof feedingeverybandwouldproveuseful. Wereconstructedtrajectoriesfromfeaturesatthreedier entlevelsofspectral resolution.Astherewerenosignicantdierenceinperfor mance,wecanconcludethat thelowestresolutionlevelatwhichthewell-knownneuroph ysiologicalrhythmsare maintained( n =8)istheoptimalresolutionasitminimizesthenumberofpa rameters involvedinthemodels. 135

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Comparingthelinearltersamongstthemselves,onewouldh aveexpectedthat NLMS,whichmakesupfornonstationarityinthedata,wouldi mprovetheperformance oftheWienerlter.Thesamecanbesaidforweightdecayorth egammalterwhich signicantlyreducethenumberofparametersinthemodels. Thereasonforthestatistical equivalenceismostlikelythelargeamountofvariationint heresults,whichinturn isduetothepoorperformancein-betweentrials(whenthecu rsorwasathalt)and duringashorttransitionperiodatthebeginningofdieren ttasks.Hadwedissectedthe trajectoriesintotransitionperiods,targetreachingand center-outtasks,andcomputed theresultsseparately,theremighthavebeenmoreconsiste ncyinperformancewithinthe groups. Inourstudies,thenonlinearmodelsdidnotsignicantlyim provetheperformance forPatient1.Reasonsforthismightincludethelimited,cy clicandsimplenatureof thetrajectories,orthefactthatndingamappingfromtheh ighdimensionalinput spacetothetwo-dimensionalhandtrajectoryispossible.C onsideringthelinearanalysis resultswithcrosscorrelation,directionaltuningandDSS ,andcomparingthesimilarities betweenthespectralandspatialsensitivitiesofthelinea randnonlinearmodels,this resultisnotstartling.ForPatient2,ontheotherhand,the MSEvaluesofthevertical trajectoryimprovedatasignicancelevelof5%.Thisresul tmaybearerectionofthe interictalactivityinPatient2.Recallthattheintericta lactivityinPatient1consisted ofquasi-periodicspikes.Thelinearltersmayhavebeenab letocompensateforsuch artifacts.Ontheothertheinterictalartifactsobservedw ithPatient2wherespontaneous burstyactivities.Thenonlinearltersmayhavebeenablet omitigatetheeectsofthis sortofartifacts. Withlittleimprovementontheperformance,weasksourselv eswhetherthisisthe bestperformanceanymodelormethodcanachieve.Oneparame terwehavenotstudied inthisdissertationisthewindowsizeoftheintegrationin tervalonwhichwecomputethe powersinthepassbands.Itisxedat100msecs,yieldingasa mplingfrequencyof10Hz 136

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forustodesignthemodelsaround.Asmallerwindowsizewoul dincreasethetemporal resolution,however,itwouldalsoincreasethelterorder sforthesamememorydepth (insecs).Smallerwindowswouldofcoursebenecessaryifth emotortaskhadhigher frequencycontent.Ontheotherhand,largerwindowsizeswo uldyieldmuchsmoother inputstotheltersanddecreasethenumberofparameters,b utmightnotbeableto yieldgoodmodelgeneralizationduetothelossoftemporalr esolution.Onceagain,the maximumintegrationwindowwoulddependonthefrequencyco ntentofthedesired signals.Anotherpossiblereasonistheshortdurationofth edatasets.Wecanonlytrain ourmodelsforthreerepetitionoftrials.Withlongerdatas etsbettergeneralizationmaybe achieved. Inbothpatientsweconsistentlyachievedbetterreconstru ctionwiththeverticalhand trajectory.Asthesetofmusclesinvolvedinhorizontalmov ementdiersfromtheones duringverticalmovement,thecoverageoftheelectrodesmi ghtbethecauseoftheresults. However,asthisisobeservedinbothpatients,thereasonin gofthelowerperformance inthehorizontalaxisismorelikelytobebecausetheexperi mentsweredesignedto spantheverticalaxismorethanthehorizontalandthatthec ursorismostofthetime aroundtheoriginofthehorizontalaxis.Hence,iftheexper imentswererepeatedthe coordinatesystemrotated90 o ,weanticipatetohavehigherCCandlowerMSEvaluesfor thehorizontalaxisaswell.Inthefutureweshallmakesurei nexperimentaldesignsthat bothaxesarespannedequallyinawiderange. ThereasonforthebetterperformanceofPatient1overPatie nt2,ontheotherhand, canbeattributedtothecoverageofthemotorarea.Aswepoin tedoutinChapter2 (recallTable2-1),Patient1respondedtoelectricalstimu lationofsevensubduralgrid electrodeswithvedierentmotorresponses,whereasPati ent2onlyrespondedwithtwo motorresponsesoverfourelectrodes.Sincetheelectrodel ocalizationswereselectedbased onclinicalneedsforthetreatmentofpatients,theywereno tplacedtocovertheprimary motororpremotorareasinordertomaximizetheperformance oftheBMImodels. 137

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Overall,thelocalizationofthegridplaysahugeroleinthe reconstructedtrajectoriesas itistheonlymeansforustoextractmotorsignatures.Moreo ver,theinterictalactivity wasuniquetoeachpatient.Whileitwasquasiperiodicinnat urefortherstPatient allowingforthemodelstocompensateforit,itwasmorerand omandburstyforthe secondPatient. 7.2SummaryofContributions Belowisabriefsummaryofthecontributionsthisdisserati onhasbroughttotheeld ofhumanelectrocorticographicneuroprosthesis: Weshowedthatmotorcontrolsignaturesarepresentinhuman ECoGatfrequencies upto6.11kHzwhichhavebeendiscardedasnoiseinotherprev iousstudies.These frequencieshaveproventocontributetothereconstructio nofhandtrajectoriesmore thantheslowrhythmsthathavebeenemployedthusfar. WeexamineddierentspectralresolutionsatwhichECoGfea turesshouldbe extractedandmappedtobehaviorandproposedthattheoptim alresolutionwasthe onethatminimizedthelterorderswhilemaintainingphysi ologicallyknownslow rhythms. WestudiedthetemporaldepthsatwhichtheECoGspectralfea turesshouldbefedto ltermodelsthroughcrosscorrelationanalysisanddirect experimentation. Weappliednonlinearmodelswhichhadneverbeenemployedin ECoGBMIsand foundthatthesamesensitivespatialandspectralfeatures werecapturedaswasin thelinearmodels.TheMSEperformanceofPatient2wasimpro vedwiththevertical handtrajectory. WewereabletoutilizeLARandDSStoselectspatial,tempora landspectralfeatures thatcontributethemosttothereconstructionofmotorbeha vior.However,westill proposethatfeedingthelterswithallfeaturescanbebene cialinclosed-loop systemsduetothenonstationaryandplasticnatureofthebr ain. 7.3FutureDirections \ Theproblemwithyoungpeopleisthattheythinktheyhaveall thetimeintheworld. -Dr.JoseC.Principe Althoughareal-timeclosed-loopsystemwasimplemented(r efertotheAppendix), wehavenothadthechancetoconductexperimentswithpatien ts.Patientfeedbackisa crucialcomponentofaBMIsystemthatallowsnotonlyforthe trainingofthemodels, 138

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butalsoallowsthepatientstolearnhowtocontrolthemodul ationsoftheirneural activitytomaximizesystemperformance.Italsocompensat esfornonstationaritiesthat arelikelytooccurinbetweensessionsand/ortrials.Wewou ldliketotestourmodelsin real-timewithpatientfeedbackandstudythelearningtren dsofpatientsandwhatcanbe donetodecreasethetrainingtimeofpatients. WestartedoutwiththepremisethatstudyingECoGmovementr elatedpotentials wasanintermediatestepforustounderstandneuroprosthes issystemsbasedon non-invasiveEEGrecordingswhichhavelessspectralresol utionandhighersingal-to-noise ratios.Withtheexperiencewehavegained,theanalysistoo lswehaveexhausted,andthe modelswehaveimplemented,webelievethatwearereadyfort hischallenge.Although thefeatureextractionwillprovetobeamuchbiggerchallen gecomparedtoECoG,the clinicalfreedom,coverageofallcorticalareas,andtheun restrictedaccesstovolunteers willsurelyallowsustoexperimentwithmanybehavioraltas ks,variouscorticalareasand acrossmorethanahandfulofparticipants. Finally,insteadofhavingsupervisedtrainingsessionsfo rthemodelsfollowedby trainingsessionsforthepatients,itismoredesirablefor themodelsandparticipants to co-adaptively learnhowtoincreasetheperformanceofthesystem.Recents uccess instudieswithratsthatlearnhowtocontrolaroboticarmco -adaptivelywitharobot controller(computer)through reinforcementlearning [ 16 ]isveryinspiring.Through interactionswiththeirenvironments(e.g.rat'sinteract ionwiththerobotarmthrough modulatingitsneuralactivityandtherobotcontroller'si nteractionwiththeratandrobot armthroughrobotmovementcommands),theybothlearnhowto maximizetherewards theycanattaininatrialsession(e.g.drinkingwaterrewar dfortherat)[ 16 ].Although implementedinapurelyinvasiveparadigm,inwhichmicroar rayelectrodesareimplanted inspecicregionsoftheprimarymotorcortexwhichhasbeen showntobepredictiveof limbmotionandtoyieldmodulationsenablingneuroprosthe siscontrolwithoutphysical 139

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movements[ 16 ],similarlearningalgorithmscanbeadaptedforECoGandev entuallyEEG neuroprosthesis. 140

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APPENDIX:REALTIMECLOSEDLOOPSYSTEMIMPLEMENTATION TDTsReal-TimeProcessorVisualDesignStudio[ 92 ]isarexibleenvironmentthat allowstocreateDSPprogramsthatcanbeusedinreal-timeap plications.Customcode developedusingTDT'sActiveXcontrolscanloadandruncirc uits,updatevariableswithin processingchains,orreaddatafrombuersinreal-timeina nyprogrammingenvironment thatsupportsActiveXcontrols,includingMATLAB[ 92 ]. Wedesignedaclosed-loopsystemwhichincorporatesthedat acollectedinreal-time fromTDTcircuitsintoMATLABthroughwhichthemodelingsch emescoveredin Chapters4and6ofthisdissertationwereimplemented.Them otortaskparadigm,i.e.the cursorthatistracedbythepatientsisalsoimplementedthr oughaMATLABinterface. WhentheMATLABprogramcallstheTDTcircuitthroughActive Xcontrols,ahardware reset(labeledas\@Reset"inthecircuitdiagrams)clearst hebuersandinitializes counterstozero.Thedatafrom32ECoGchannelsisfedtothep ipebusafterpassing throughpre-ampliers,andisrecordedatasamplingrateof 12207Hz(seeFigure A-1 ). InFigure A-2 therawchannelsarelteredinfourspectralbandswhosepas sbands weredeterminedearlier.Thenumberofspectralbandscanbe easilyincreasedto n = 8 ; 16 ; 32.ThebandpasslteredsignalsaresenttoasecondDSPtosh aretheloadofthe mainDSP.AtthesecondDSP,thebandpasssignalsarestoredi nadatatank.Atthe mainDSP,thepowersofbandpasssignalsarecomputedinnonoverlappingblocksof100 msec.Inordertokeeptrackoftimewindowsof100msecs(or12 20samples),ablocksize counter,showninFigure A-3 ,isimplemented.Thecounterisresetedatthehardware resetwhenthecircuitiscalledbyMATLABandonlystartscou ntingwhentheEnable ragcontrolledbyaMATLABvariable,\startCounting",equa lsone.Whenthecounter outputbecomes1220,asveriedbyacomparator,the\EndofB lock"raggoeshigh.The counter,havingreached1220,rollsbackto0. Figure A-4 showstheblockdiagramofthepowerintegratorsforonespec tralband (thesameblockisrepeatedfortheotherthreebandsintheor iginalcircuit).Inthetop 141

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FigureA-1.Circuitcomponentsthatallowrecordingfrom32 channelsofECoGdata passedthroughapre-amplier.Therawdatasampledat12207 Hzisalso storedindatatanks. row,thebandpasslteredsignalismultipliedbyitselfate achtimesampleandaddedto thepowersoftheprevioustimesamplesstoredin\SUM1".Whe n\EndofBlock"=0,the variable\SUBTRACT1"=0also.So\SUM1"storesallthepassb andpowerin100msecs. Whentheendofblock(100msec)isreached,\SUBTRACT1"=-\S UM1"(seebottom row),whichisaddedbackto\SUM1"inthetoprow.Hence,thep oweroftheprevious blockissubtractedoncewhilethepowerinthenewblockisco ntinuouslyadded.Thisway thepowerineachnon-overlapping100msecblockisstoredin \SUM1",butweutilizethe variable\SUBTRACT1"insteadbyscalingitby-1inFigure A-5 Now,wehavetosendthecomputedpassbandpowerstoMATLAB.T hisisagain achievedthroughActiveXcontrolsandaMATLABvariablecal led\Power".Asthecircuit isrunningat12207Hz,wesampleandholdthecomputedpowers andonlysenditto 142

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MATLABwhenanendofblockisreachedthroughaserialstorag ebuer.Thecomputed powersarealsostoredinadatatank(Figure A-5 ). AsthemodeloutputsarecomputedviaMATLAB,asecondcursor isdisplayedin theMATLABinterface.Finally,tosynchronouslystoretheE CoGdataandthecursor positions,therealandreconstructedcursorpositionsare senttothecircuittobestoredin adatatank.ThisstageisdemonstratedinFigure A-6 Asaprecaution,asecondcounter,showninFigure A-7 ,countshowmanytimesthe \EndofBlock"raghasgonehigh.ThisnumberissenttoMATLAB throughthevariable \Cntr".MATLABalsocountsthenumberoftimesithasreceive danewpowervalues. Thisisdonetoverifythatthepowerattheendofeachblockha sbeensenttoMATLAB. Ifatone100msectimestamp,thepowerisnotsenttoMATLAB,d uetothedisparity betweenthetwocounters,MATLABwaitsuntilitreceivesthe powervalue.Duringthis waitperiod,themodeloutputcursorlagsbehind.Thisonlyh appensifthecomputer processoriskeptbusythroughotherprograms.Whenonlythe implementedsystem (MATLABandTDTcircuit)isrunning,thedataiscorrectlyse nttoandfromMATLAB withnotimedelayordataloss. 143

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FigureA-2.Therawchannelsarelteredinfourspectralban ds. 144

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FigureA-3.Thecountersetsthe\EndofBlock"raghightoind icate100msecsof non-overlappingtimewindows. FigureA-4.Constantintegrationofpower.Whenanendofblo ckisreached,thepowerin thepreviousblockissubtractedfromthecurrentpower. 145

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FigureA-5.StoringandsendingthepassbandpowerstoMATLA Bthroughthevariable \Power". 146

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FigureA-6.Therealandmodeloutputcursorpositionsarere ceivedfromMATLABtobe storedinadatatank. FigureA-7.VericationblockthatallowsMATLABtocheckwh etherthepoweratthe endofeachblockisreceived. 147

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BIOGRAPHICALSKETCH AysegulGunduzwasborninAnkara,Turkey.ShereceivedherB .S.degreewith honorsinelectricalandelectronicsengineeringwithacon centrationontelecommunications fromMiddleEastTechnicalUniversity,Turkeyin2001.From 2001to2004,sheworked asaresearchassistantatNorthCarolinaStateUniversity, DepartmentofElectricaland ComputerEngineering,whereshespecializedinimageproce ssing.ShereceivedherM.S. degreein2003throughherthesisentitled\Compressionand TransmissionofDriver's LicenseImagesoverVeryNarrowbandWirelessChannels,"in whichshewroteprotocols fortheNorthCarolinaCriminalJusticeInformationNetwor k(CJIN).In2004,shejoined theDepartmentofElectricalandComputerEngineeringatth eUniversityofFlorida topursueherPh.D.undertheguidanceofDr.JoseC.Principe intheComputational NeuroengineeringLaboratory(CNEL).Herresearchisinthe developmentofbrain machineinterfacesbasedonhumanelectrocorticograms.He rstudieshavebeenfundedby theNationalScienceFoundation,DefenseAdvancedResearc hProjectsAgency(DARPA) andtheChildren'sMiracleNetwork. 156