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Techniques for Analysis of Neural Activity

Permanent Link: http://ufdc.ufl.edu/UFE0022636/00001

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Title: Techniques for Analysis of Neural Activity Spontaneous and Evoked
Physical Description: 1 online resource (120 p.)
Language: english
Creator: Bollimunta, Anil
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: alpha, bayesian, causality, cortex, current, electrodes, field, granger, inferiortemporal, laminar, multi, oscillation, quadrupole, rhythm, sink, source, spike, striate, thalamus, variability
Biomedical Engineering -- Dissertations, Academic -- UF
Genre: Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Oscillatory activity is the hallmark of electrical activity recorded from the cerebral cortex. Unraveling the mechanisms of cortical oscillations is relevant for understanding the role they play during normal cognitive process as well as during various pathological states like epilepsy, Parkinson's disease, schizophrenia etc. Traditionally the mechanisms of neuronal oscillations have been studied in-vitro in slices. The experimental and analysis techniques employed include extracellular field potential recordings with multi-electrode arrays or laminar electrodes, current source density analysis, phase analysis, trisection, neurochemical manipulation etc. Although the wealth of data generated by these in-vitro studies has been highly informative, to what degree these findings generalize to intact behaving brain are not clear. With the advent of sophisticated experimental techniques it is now possible to record neural activity from multiple sites in the intact cortex simultaneously. This, however, presents new challenges for the analysis techniques, for example, the lesion method of trisection, while instrumental in identifying the laminar generator of oscillatory activity in slice preparations, is difficult to apply in behaving animals. This dissertation presents a comprehensive framework for inferring the mechanisms of oscillations in cortical networks in-vivo. Specifically, Granger causality analysis, as a principled approach for inferring causal influence among time series, is used in lieu of the trisection method in in-vitro studies. Traditional analysis techniques like current source density analysis are complimented with Granger causality analysis to infer the mechanisms of 'alpha rhythm' in the cortex and the thalamocortical system. How ongoing oscillation affects stimulus processing is of much interest to neuroscientists. For example, how the phase and amplitude of the alpha oscillation prior to the stimulus presentation affects the latency and intensity of action potential firing in neurons can aid in our understanding of the role of oscillatory activity in information processing. This would require estimation of the parameters of evoked response on a trial by trial basis. This dissertation develops, using the Bayesian inference framework, a comprehensive framework for estimating the parameters of evoked response in single or multi-unit recordings on a trial by trial basis.
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 Anil Bollimunta.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Ding, Mingzhou.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-02-28

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022636:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022636/00001

Material Information

Title: Techniques for Analysis of Neural Activity Spontaneous and Evoked
Physical Description: 1 online resource (120 p.)
Language: english
Creator: Bollimunta, Anil
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: alpha, bayesian, causality, cortex, current, electrodes, field, granger, inferiortemporal, laminar, multi, oscillation, quadrupole, rhythm, sink, source, spike, striate, thalamus, variability
Biomedical Engineering -- Dissertations, Academic -- UF
Genre: Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Oscillatory activity is the hallmark of electrical activity recorded from the cerebral cortex. Unraveling the mechanisms of cortical oscillations is relevant for understanding the role they play during normal cognitive process as well as during various pathological states like epilepsy, Parkinson's disease, schizophrenia etc. Traditionally the mechanisms of neuronal oscillations have been studied in-vitro in slices. The experimental and analysis techniques employed include extracellular field potential recordings with multi-electrode arrays or laminar electrodes, current source density analysis, phase analysis, trisection, neurochemical manipulation etc. Although the wealth of data generated by these in-vitro studies has been highly informative, to what degree these findings generalize to intact behaving brain are not clear. With the advent of sophisticated experimental techniques it is now possible to record neural activity from multiple sites in the intact cortex simultaneously. This, however, presents new challenges for the analysis techniques, for example, the lesion method of trisection, while instrumental in identifying the laminar generator of oscillatory activity in slice preparations, is difficult to apply in behaving animals. This dissertation presents a comprehensive framework for inferring the mechanisms of oscillations in cortical networks in-vivo. Specifically, Granger causality analysis, as a principled approach for inferring causal influence among time series, is used in lieu of the trisection method in in-vitro studies. Traditional analysis techniques like current source density analysis are complimented with Granger causality analysis to infer the mechanisms of 'alpha rhythm' in the cortex and the thalamocortical system. How ongoing oscillation affects stimulus processing is of much interest to neuroscientists. For example, how the phase and amplitude of the alpha oscillation prior to the stimulus presentation affects the latency and intensity of action potential firing in neurons can aid in our understanding of the role of oscillatory activity in information processing. This would require estimation of the parameters of evoked response on a trial by trial basis. This dissertation develops, using the Bayesian inference framework, a comprehensive framework for estimating the parameters of evoked response in single or multi-unit recordings on a trial by trial basis.
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 Anil Bollimunta.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Ding, Mingzhou.
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: UFE0022636:00001


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Myheartiestthankstomyadvisor,Dr.MingzhouDing,forhisconstantguidanceovertheyears.Ithankhimforgivingmegreatfreedomtopursuemyresearchinterests,forhisinnitepatiencetowardsmywhimsandfancies,andforhisconstructivecriticism.ThankstoourcollaboratorsDr.KevinKnuth,andDr.CharlesSchroederforsharingwiththedatausedinthepresentwork,andforthevaluablediscussions.IthankYonghongandMukeshfortheirhelpwiththecomputationinthepresentwork.ThankstoPete,ShabeerandChadforallthegoodtimes.And,aspecialthankstoSheriforbeingthebestthingtohappentomeinGainesville. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 ABSTRACT ........................................ 10 CHAPTER 1INTRODUCTION .................................. 12 2INFERRINGTHEGENERATORSOFCORTICALOSCILLATIONS ..... 16 2.1FieldPotentialsandCurrentSourceDensityMethod ............ 16 2.2CurrentSourceDensityAnalysisofEvokedPotentialsinStriateCortex .. 20 2.3CurrentSourceDensityAnalysisofOngoingActivity:PhaseRealignedAveragingTechnique .............................. 21 3ALPHARHYTHM .................................. 26 3.1Introducton ................................... 26 3.2Experiment ................................... 27 3.2.1Paradigm ................................. 27 3.2.2Recordings ................................ 28 3.3AnalysisProtocol ................................ 29 3.3.1CurrentSourceDensityAnalysisofAlphaRhythm .......... 29 3.3.2CSDandMUACoherence ....................... 30 3.4LaminarDistributionofAlphaGeneratorsinV4 ............... 30 3.5LaminarDistributionofAlphaGeneratorsinV2 ............... 32 3.6LaminarDistributionofAlphaGeneratorsinIT ............... 33 4INTERACTIONBETWEENGENERATORS ................... 39 4.1MultivariateSpectralAnalysis ......................... 40 4.1.1BivariateTimeSeriesandPairwiseGrangerCausality ........ 40 4.1.1.1Timedomainformulation .................. 40 4.1.1.2Frequencydomainformulation ................ 42 4.1.2TrivariateTimeSeriesandConditionalGrangerCausality ...... 46 4.1.2.1Timedomainformulation .................. 46 4.1.2.2Frequencydomainformulation ................ 48 4.2EstimationofAutoregressiveModels ..................... 51 4.3AssessmentofStatisticalSignicance ..................... 54 4.4InteractionofAlphaCurrentGeneratorsinV4,V2andIT ......... 54 4.5Unipolar,BipolarandSingleTrialCSD ................... 58 5

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............ 59 4.7Discussion .................................... 59 4.7.1NeuronalMechanismsoftheAlphaRhythminV2,V4andIT ... 60 4.7.2CorticalHeterogeneityandAlphaRhythm .............. 62 4.7.3AlphaRhythmandBehavior ...................... 63 5ALPHARHYTHMINTHESTRIATECORTEXANDTHALAMOCORTICALINTERACTIONS ................................... 72 5.1Introduction ................................... 72 5.2LaminarDistributionofAlphaCurrentGeneratorsinV1 .......... 73 5.3InteractionBetweenAlphaCurrentGeneratorsinV1andThalamocorticalInteractions ................................... 75 5.4Discussion .................................... 77 6SINGLE-TRIALESTIMATIONOFEVOKEDSPIKETRAINS ......... 90 6.1Introduction ................................... 90 6.2ModelsofSingleTrialSpikeTrains ...................... 92 6.3BayesianEstimationFramework ........................ 93 6.4AlgorithmImplementation ........................... 98 6.5ApplicationstoSimulatedandNeuralSpikeTrainData ........... 99 6.5.1ApplicationtoSimulatedData ..................... 99 6.5.2ApplicationtoNeuralSpikeTrainData ................ 100 6.6DiscussionandSummary ............................ 102 7CONCLUSIONS ................................... 108 REFERENCES ....................................... 110 BIOGRAPHICALSKETCH ................................ 120 6

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Table page 4-1CoherenceandGrangercausalityanalysisinareaV4. ............... 64 4-2GrangercausalitybetweengranularandinfragranularlayersinareaV4. ..... 64 4-3VisualareaV2:Grangercausalityanalysis ..................... 64 4-4PeakGrangercausalityandcoherencevaluesinareaV2. ............. 65 4-5GrangercausalityanalysisinIT. .......................... 65 4-6Correlationbetweenalphapowerandreactiontime. ................ 65 5-1Grangercausalityresultsbetweenlayers4Cand5/6ofthestriatecortex. .... 78 5-2Interactionbetweenlayers3Band5/6ofthestriatecortex. ............ 78 5-3VisualareaV1:Grangercausalityresultsbetweenlayers1/2and5/6. ..... 78 7

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Figure page 2-1Relationamongelds,currentsandunitactivities ................. 23 2-2Currentssinksandsourcesintheextracellularspaceofapyramidalneuron ... 23 2-3Currentsourcedensityanalysisofevokedpotentialsinstriatecortex ...... 24 2-4Laminarrecordingofongoingoscillation ...................... 24 2-5Illustrationofphaserealignedaveraging ...................... 25 2-6Experimentalexampleofphaserealignedaveragingtechnique .......... 25 3-1LaminaralphacurrentgeneratorsinV4 ...................... 35 3-2LaminaralphacurrentgeneratorsinV2 ...................... 36 3-3LaminaralphacurrentgeneratorsinIT ....................... 37 3-4AreaV4:Alphacurrentgeneratorsindierentpenetrations ........... 37 3-5AreaV2:Alphacurrentgeneratorsindierentpenetrations ........... 38 3-6AreaIT:Alphacurrentgeneratorsindierentpenetrations ............ 38 4-1Schematicofcausalinuences ............................ 65 4-2PerformanceoftheMVARmodelestimation ................... 66 4-3Spectrumofresidualprocess ............................. 66 4-4GrangercausalityanalysisbasedonsingletrialCSDdata ............. 67 4-5GrangercausalityanalysisbasedonunipolarLFPandMUAdata ........ 68 4-6GrangercausalityanalysisinareaV4 ........................ 69 4-7GrangercausalityanalysisinareaV2 ........................ 70 4-8GrangercausalityanalysisinareaIT ........................ 71 4-9Correlationbetweenalphaamplitudeandreactiontime .............. 71 5-1IllustrationofanatomicalconnectivitybetweenthalamusandV1 ........ 79 5-2Ongoingtoevoked:currentsourcedensity ..................... 80 5-3Ongoingtoevoked:singletriallaminareldpotentialrecordinginV1 ...... 81 5-4AlphapowerdistributionandCSD-MUAcoherence ................ 82 8

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............. 82 5-6Attentionalmodulationofalphaamplitude ..................... 83 5-7AttentionalmodulationofCSDamplitudeacrossdierentlayersinV1 ..... 83 5-8AttentionalmodulationofCSD-MUAcoherenceinV1 .............. 83 5-9Interactionbetweenlayer5/6andotherlayers ................... 84 5-10Interactionbetweenlayer4Candotherlayers ................... 85 5-11CoherencespectrumbetweenLGNandV1 ..................... 86 5-12AttentionalmodulationofGrangercausalitybetweeninfragranularandothergenerators ....................................... 87 5-13Attentionalmodulationofinteractionbetweengranularandothergenerators .. 88 5-14Attentionalmodulationofthalamocorticalcoherence ............... 89 6-1Illustrationoftrialtotrialvariability ........................ 105 6-2Performanceofthealgorithmonsimulateddata .................. 106 6-3Singletrialestimationalgorithmappliedtorealdata ............... 107 9

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Oscillatoryactivityisthehallmarkofelectricalactivityrecordedfromthecerebralcortex.Unravelingthemechanismsofcorticaloscillationsisrelevantforunderstandingtheroletheyplayduringnormalcognitiveprocessaswellasduringvariouspathologicalstateslikeepilepsy,parkinson'sdisease,schizophreniaetc.Traditionallythemechanismsofneuronaloscillationshavebeenstudiedin-vitroinslices.Theexperimentalandanalysistechniquesemployedincludeextracellulareldpotentialrecordingswithmulti-electrodearraysorlaminarelectrodes,currentsourcedensityanalysis,phaseanalysis,trisection,neurochemicalmanipulationetc.Althoughthewealthofdatageneratedbythesein-vitrostudieshasbeenhighlyinformative,towhatdegreethesendingsgeneralizetointactbehavingbrainarenotclear.Withtheadventofsophisticatedexperimentaltechniquesitisnowpossibletorecordneuralactivityfrommultiplesitesintheintactcortexsimultaneously.This,however,presentsnewchallengesfortheanalysistechniques,fore.g.,thelesionmethodoftrisection,whileinstrumentalinidentifyingthelaminargeneratorofoscillatoryactivityinslicepreparations,isdiculttoapplyinbehavinganimals.Thisdissertationpresentsacomprehensiveframeworkforinferringthemechanismsofoscillationsincorticalnetworksin-vivo.Specically,Grangercausalityanalysis,asaprincipledapproachforinferringcausalinuenceamongtimeseries,isusedinlieuofthetrisectionmethodinin-vitrostudies.Traditionalanalysistechniqueslikecurrentsource 10

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Howongoingoscillationaectsstimulusprocessingisofmuchinteresttoneuroscientists.Forexample,howthephaseandamplitudeofthealphaoscillationpriortothestimuluspresentationaectsthelatencyandintensityofactionpotentialringinneuronscanaidinourunderstandingoftheroleofoscillatoryactivityininformationprocessing.Thiswouldrequireestimationoftheparametersofevokedresponseonatrialbytrialbasis.Thisdissertationdevelops,usingtheBayesianinferenceframework,acomprehensiveframeworkforestimatingtheparametersofevokedresponseinsingleormulti-unitrecordingsonatrialbytrialbasis. 11

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Oscillatoryactivityisthehallmarkofelectricalactivityrecordedfromthecerebralcortex.Basedonthefrequencyofsignalrhythmicity,theyareclassiedas:delta(1-3Hz),theta(3-8Hz),alpha(8-14Hz),beta(14-30Hz)andgamma(30-90Hz).Unravelingthemechanismsofcorticaloscillationsisrelevantforunderstandingtheroletheyplayduringnormalcognitiveprocess( Ward 2003 )aswellasduringvariouspathologicalstateslikeepilepsy( Castro-Alamancos&Tawara-Hirata 2007 ),parkinson'sdisease( Farmer 2002 ),schizophrenia( Spenceretal. 2003 ; Schnitzler&Gross 2005 ; Uhlhaas&Singer 2006 )etc.Althoughsomeoscillatoryphenomenathathavebeenextensivelystudied,forexamplesleepspindles,arethoughttooriginatefromthethalamus( Steriadeetal. 1990 ),thegenesisofavarietyofoscillationsisthoughttobeintheneocortex( LopesdaSilva 1991 ; Connors&Amitai 1997 ; Gray&McCormick 1996 ).Anumberofmechanismshavebeenidentiedthatcontributetothegenerationofneuraloscillations.Atthesinglecelllevelspeciccombinationsofionicconductancescanleadtorhythmicdischarge( Steriadeetal. 1990 ; Silvaetal. 1991 )throughburstring.Thisrhythmicityisthenampliedbyensemblesofneuronswithsimilarphysiologicalproperties.Oscillationcanalsooccurasanemergentphenomenoninaninterconnectednetworkofneurons( Ritz&Sejnowski 1997 ).Inthiscase,nosingleneuroniscapableofdischargingrhythmicallyinisolation,butanetworkofneuronswithreciprocalsynapticactivationsarethesourceoftheoscillatoryactivity. Traditionallythemechanismsofcorticaloscillationshavebeenstudiedinvitroinslices( Silvaetal. 1991 ; Flint&Connors 1996 ).Theexperimentaltechniquesemployedincludeextracellulareldpotentialrecordingswithmulti-electrodearraysorlaminarelectrodes,intracellularunitrecording,trisection,neurochemicalmanipulationetc.Itisthoughtthattheslicepreparationskeeptheintra-corticalcircuits,orthecolumnarorganizationbetweenthesixlayersofthecortex,relativelyintactforgeneratingoscillatory 12

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Steriade 2004 ),theimpactofwhichonthelaminarorganizationofcorticaloscillationsremainsunclear. Withtheadventofsophisticatedexperimentaltechniquesitisnowpossibletorecordneuralactivityfrommultiplesitesintheintactcortexsimultaneously.Simultaneousrecordingsoflocaleldpotentials(LFP)andmulti-unitactivity(MUA)withlaminarmultielectrodeshavebeenextensivelyusedtounderstandtheintra-corticalowofinformationuponstimuluspresentation,aswellastoshedlightontheintra-corticalgeneratorsofeventrelatedpotentials(ERP)recordedonthescalp( Mitzdorf 1985 ; Schroederetal. 1995 ).Inthesestudiescurrentsourcedensity(CSD)analysishasbeentheworkhorseinlocalizingtheledpotentialrecordingtotheactivityofdiscreteneuronalgroupsandinstudyingtheowofinformationincorticalcircuitsuponstimuluspresentation. However,someoftheexperimentalandanalysistechniquesmentionedabovearenotreadilyapplicableforstudyingthemechanismsofoscillationsincorticalnetworksin-vivo.First,CSDofongoingneuralactivityismorediculttoascertain.SingletrialCSDestimatestendtobenoisy( Shahetal. 2004 ; Lakatosetal. 2005 2007 ),andasthereis 13

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Dingetal. 2006 ; LeVanQuyen&Bragin 2007 ),canbeusedinlieuofthetrisectionmethodinin-vitrostudies.Thepresentworkpresentsacomprehensiveframeworkforinferringthemechanismsofoscillationsincorticalnetworksin-vivo.Chapter2beginswithabasicoverviewoftherelationshipbetweeneldpotentialsandcurrentsourcedensity.WeillustratetheCSDmethodbyapplyingittounderstandstimulusevokedinformationprocessinginthestriatecortexofthemacaquemonkey.WethenillustratehowtheCSDanalysiscanbeperformedontheongoingoscillationsbyintroducingthe'PhaseRealignedAveragedTechnique'.Inchapter3weinferthecorticalgeneratorsofthe'alpharhythm'intheextra-striateareasV2,V4andITbyapplyingthePRATtechnique.Chapter4beginswithareviewoftheessentialmathematicalelementsofGrangercausalitywithspecialemphasisonitsspectraldecomposition,anddiscussespracticalissuesconcerninghowtoestimatesuchmeasuresfromtimeseriesdata.Wethenstudytheinteractionbetweendierentgeneratorsofthe'alpharhythm'(identiedinChapter3)intheextrastriateareasV2,V4andIT.Inchapter5westudythelaminarorganizationofthe'alpharhythm'inthestriatecortex(V1),andthethalamo-corticalinteractionsunderdierentattentionalstates. Howongoingoscillationaectsstimulusprocessingisofmuchinteresttoneuroscientists.Forexample,howthephaseandamplitudeofthealphaoscillationpriortothestimuluspresentationaectsthelatencyandintensityofactionpotentialringinneuronscanaidinourunderstandingoftheroleofoscillatoryactivityininformationprocessing.Thiswouldrequireestimationoftheparametersofevokedresponseonatrialbytrialbasis. 14

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Brody 1999b ; Truccoloetal. 2002 ).Forexample,areductioninPSTHamplitude,asonevariesanexperimentalparameter,mayhavetwocontributingfactors.First,theevokedresponseissmalleroneachindividualtrial.Second,theevokedresponseremainsthesamebutthelatencyjitteronatrial-by-trialbasisisincreased.ThesetwosituationsmayentaildierentphysiologicalinterpretationsofthereducedPSTH.Inchapter6,usingtheBayesianinferenceframework,wedevelopacomprehensiveframeworkforestimatingtheparametersofevokedresponseinsingleormulti-unitrecordingsonatrialbytrialbasis.Chapter7presentstheconclusionsofthepresentworkandsuggestsfuturedirections. 15

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Intracellularrecordingsareidealforstudyingtheelectrophysiologicalpropertiesofneurons.However,tostudytheroletheyplayinthegenerationofoscillationsincorticalnetworksinin-vivorequirestheabilitytosimultaneouslyrecordactivityoftheaerentdriversandtheirtargetneurons.Simultaneousintracellularrecordingsfromanatomicallyconnectedneuronsarediculttoperformin-vivo.Localeldpotentials(LFPs),togetherwithpopulationspikesindexedbymulti-activity(MUA),providecomplementarymeasuresofmassactionneuraldynamicsatboththeinputandoutputlevel( Mitzdorf 1985 ; Einevolletal. 2007 ).Inthelightofthelaminarorganizationofthecortexintocorticalcolumns,simultaneousrecordingsofLFPsandMUAwithlaminarmulti-electrodesprovideviablesignalsforinferringthecorticalcircuitryinvolvedinoscillations.However,LFPswhicharemeasuredagainstadistantreferenceareanindirectmeasureoftheactivityoftheunderlyingneurons(seeFig. 2-1 ).SubjectingtheLFPstocurrentsourcedensity(CSD)analysishasbeenthestandardanalysistechnique( Nicholson 1973 ; Mitzdorf 1985 ; Schroederetal. 1995 )forinterpretingtheunderlyingneuralactivity.TheessentialfeaturesoftheCSDmethod,aswellasthebasicargumentsforinterpretingitsresults,arereviewedinSect. 2.1 .Section 2.2 illustratestheCSDmethodinanalysisofevokedpotentialsinstriatecortex.InSect. 2.3 weillustratehowCSDmethodcanbeappliedtospontaneousactivity. 16

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2-2 illustratesthedistributionofcurrentowresultingfromexcitatory(EPSP)orinhibitory(IPSP)postsynapticactionsonatypicalcorticalpyramidalcell.AnIPSPatthesomacausesanetowofpositiveionsoutofthecellFig. 2-2 Aresultinginanactivesourceintheextracellularmedium.Thisactivesourcenearthesomaiscompensatedbyowofpositiveionsintothecellatdistanceawayfromthesomathroughthedendrites,resultinginapassivesink.Similarly,anEPSPonthedendriteresultsinanactivesinkatthedendritesandapassivesourcenearthesomaFig. 2-2 B.Thesesinksandsourcesintheextracellularmediumresultinpotentialgradientswhichcanberecordedbyanextracellularelectrode.Atthemacroscopiclevelsynchronousactivityamonganensembleofneuronswithsimilarphysiologicalpropertiescausenetowofcurrentsintotheextracellularmediumresultinginaeldpotentialdistribution.Thelowfrequencyband(0.1-500Hz)oftheextracellularlyrecordedpotentialsareknownasthelocaleldpotentialsandarethoughttopredominantlystemfromthedendriticprocessingofthesynapticinputs( Mitzdorf 1985 ; Einevolletal. 2007 ).Whereas,thehighfrequencyband(500-2000Hz),knownasthemulti-unitactivity,isconsideredtoreecttheringactivityoftheneuronalpopulation.Hence,LFPs,togetherwithpopulationspikes(MUA),providecomplementarymeasuresofensembleneuraldynamicsatboththeinputandoutputlevel. InferenceofthesinkandsourcedistributionsfromtheeldpotentialsrequirestheapplicationoftheCSDanalysis.TherelationbetweenCSDandLFPsisanalogoustodiscretelocalizedchargesversustheirdissipated,superimposedpotentialeldsinelectrostatics.Thesinksandsources,incontrastwiththeeldpotentials,arespatiallylocalizedphenomena.Therefore,theCSDmethodleadstoafarhigherspatialresolutionoftheunderlyingneuralactivity. CSD(I)atthemacroscopiclevelisthevolumeaverageoftheindividualmicroscopicmembranecurrents.Theprincipleofthecontinuityofthecurrentimpliesthatthevolumeaverageofthemembranecurrentdensity(Jm)isequivalenttothedivergenceofthe 17

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Undertheassumptionofapurelyohmicconductivemedium whereEistheelectriceldintheextracellularspaceandistheconductivitytensor.Theaboveequationincorporatesthequasi-staticapproximationtotheMaxwell'sequations.Thisapproximationisvalidaswithintherangeoffrequenciesofphysiologicalinterest(0-lkHz),thecontributionofcapacitive,inductive,magneticeectscanbeneglected( Mitzdorf 1985 ).SubstitutingEbythegradientofthescalarpotential()wegetalinearrelationbetweenthecurrentdensityandthegradientoftheeldpotentialintheextracellularspace EliminatingJfromEqs. 2{1 and 2{3 ,wegetthePoissonequationforthecontinuoussourcedistribution ThisrelationappliestotheimplementationoftheCSDanalysiswithinavolumeoftissuewithathree-dimensionalelectrodearray.CSDanalysisonLFPsrecodedwithalaminarorone-dimensionalelectrodearraycanbederivedfromEq. 2{4 ifwefurtherassumethatconductivityinthesampleddirectionisapproximatelyisotropic,theprincipalaxisofcurrentowisparalleltothesamplingaxisandthereisnocurrentownormaltothesamplingaxis.Theseassumptionsappeartobereasonableforforthecortexconsideringitslaminarorganizationandtheelongatednatureofthedendritesoftheprincipalorpyramidalcells.Equation 2{4 isreducedto @z2=I:(2{5) 18

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Experimentally,thespatiotemporallocaleldpotentialsdenotedbyaregenerallyrecordedusingalineararrayelectrodewithmultipleequallyspacedrecordingcontactssamplingactivityfromallsixlayersofthecortex.ThesecondspatialderivativeinEq. 2{5 canbeestimatedbythefollowing3-pointnite-dierenceapproximation @z2(z+h)2(z)+(zh) (h)2:(2{6) wherehisthedistancebetweenadjacentrecordingsites.ThisisthesimplestformoftheCSDmethodandcanbeunderstoodintuitively.Sincetheamountofcurrentowisdirectlyproportionaltothegradientofeldpotential,changesinthepotentialgradientintheextracellularspace,whichisapurelypassivemedium,reectscurrentsthatenterorleavethecellmembrane. Inthephysiologicalsituationsencounteredinthecortex,twotypesofgeneratorsmayoccurinprinciple.First,pyramidalneurons,becauseoftheirprominentapicaldendrites(seeFig. 2-2 ),giverisetosink/sourcedipolesthatgenerateapotentialeldthatispositiveintheregionofthesourceandnegativeintheregionofthesink.Theeldpotentialdecays,withlimitvalues=1=z2,awayfromtheCSDdistributionandiscalledfareld.Second,Incontrasttopyramidalneurons,stellatecellshaveasphericaldendriticconguration,andgiverisetoasource/sink/sourcedistribution.Theeldpotential,calledclosedeld,doesnotshowapolarityreversal,hasmaximumamplitudeatthelocationofthecentralpartoftheCSDanddecaysfasterawayfromtheCSDdistribution( Mitzdorf 1985 ; Tenkeetal. 1993 ). Figure 2-2 illustratestheambiguityininferringtheneuronalactivitiesfromtheCSDdistribution.SynapticinputsthatgiverisetoIPSPnearthesomaorEPSPattheapicaldendritescanresultinsimilarCSDdistribution.Thissituationcanbedisambiguatedwithadditionalinformation,likeforexamplesingleormulti-unitrecordings.SinceIPSPsresult 19

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Mehtaetal. 2000a ).Figure 2-3 Bshowsthelaminarproleofvisualeventrelatedpotentialsrecordedwithalaminarmulti-electrode(Fig. 2-3 A)with14equallyspacedcontacts.Thevisualstimuliwere10sashesgeneratedbyaphotostimulator(seeSect. 3.2 foradetaileddescriptionoftheexperiment).Exceptforapolarityreversalataroundelectrodecontact9,thepeaksintheERPsarewidelydissipatedoverthedepth.IncontrasttheCSDprole(Fig. 2-3 C)iswellstructuredandrevealsdiscreteevents.Withthewealthofknowledgeabouttheanatomyandthephysiologyofthestriatecortex,itispossibletoidentifytheoriginsofsinksandsourcesintheCSDdistribution.Thegranularlayersinthestriatecortexarethemainrecipientofthevisualinformation,reachingtheretina,relayedthroughthelateralgeniculatenucleus(LGN).Thecurrentsinks(red)inthegranularlayers(arrowinFig. 2-3 C)aretheresultoftheexcitatorysynapticinputfromthegeniculateaerentsonthestellatecellsintheselayers.TheconcomitantincreaseintheMUAactivity(arrowinFig. 2-3 D)supportsthisimpression.Moreover,thethecurrentsinksinthegranularlayersandtheincreaseinMUAactivitycorrespondtothenegativepeaksintheERPs,conrmingthattheunderlyingneuronalensembleisdepolarized.Thesinksinthegranularlayersarefollowedbysources(blue)andaconcomitantdecreaseinMUAactivity,reecting'afterhyperpolarization'( Schroederetal. 1995 ).Theinformationreachingthegranularlayersisrelayedtothesupragranularlayersthroughintracorticalsynapses.Itcanbeseenthatthesinkinthesupragranularlayersfollowsthesinksgranularlayers.TheearlysourceintheinfragranularlayermightreectfeedforwardinhibitionfromLGN. 20

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Tenkeetal. 1993 ).Thishypothesisisyettobeconrmedexperimentally. TheabovedescriptionofanexperimentalapplicationillustratestheusefulnessoftheCSDmethodininferringthecorticalcircuitsinvolvedinthegenerationofevokedeldpotentials.ThenextsectionshowshowtheCSDmethodcanbeappliedtoinferthegeneratorsofongoingoscillatoryactivity. Shahetal. 2004 ; Lakatosetal. 2005 2007 ),andasthereisnostimulus-relatedtrigger,eldpotential(FP)averagingrequiresanalternateprocedureforthealignmentoftrials.Thephaserealignedaveragingtechnique(PRAT),developedhere,issuchaprocedure.Figure 2-4 showsaonesecondalphaoscillationepochrecordedwithalaminarelectrodeinvisualarea,V4.Sinceitisreasonabletoassumethatdierentcyclesoftheongoingoscillationaretheresultofthesameunderlyingneuralactivities,thegoalofinferringthegeneratorsoftheoscillatoryactivitycanbereducedtoidentifyingthegeneratorsunderlyingatypicalalphaepoch.A'typical'alphaepochcanbeestimatedbyepochingthecontiguoussegmentoftheongoingoscillationintosmallepoch,containingtwoorlesscycles,andusingthephaseasthetriggertorealigndierentepochs.Figure 2{4 Bshowsdierentalphaepochs,fromelectrodecontact12,withrandomphaseoverlaidoneachother.Figure 2-5 Ashowsthesameepochsafterrealigningwithrespecttothephaseofthedominantalphafrequency.Therealignedepochscanthenbeaveragedtogeta'typical'alphaepochs(overlaidinFig. 2-5 A).Torealignthedatafromalltheelectrodecontactsandtocalculatetheaveragecurrentsourcedensitythefollowingprocedurewasemployed.(1)Thepowerspectrumofeachrecordingcontactforagivenelectrodewasestimatedandthecontactshowingthehighestpowerspectraldensityatthealpha 21

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Csicsvarietal. ( 2003 )forasimilarmethodusingband-passltereddata.Foreaseofreferenceinthesequel,theaboveprocedurewillbecalledthephaserealignedaveragingtechnique(PRAT),andtheresultingaveragedLFPandCSDarereferredtoasPRAT-LFPandPRAT-CSD,respectively. Figure 2-6 showstheapplicationofthePRATprocedureontheongoingalphaoscillationinareaV4.ThePRAT-LFPandPRAT-CSDareanalogoustotheevokedERPandCSD,respectively.IncontrasttothewidelydissipatednatureofPRAT-LFP,PRAT-CSDdistributionshowsdiscretelocalizedevents.Asdiscussedabove,concomitantlyrecordedMUAactivitycanfurtheraidintheinterpretationofthePRAT-CSDdistribution.Inthecontextofstudyingevokedpotentials,asourceorsinkisconsideredactiveifsimultaneouslyrecordedMUAisdepressedorenhanced,indexingnetlocalhyperpolarizationordepolarization,respectively.Forongoingoscillatoryactivity,themembraneundergoesrhythmictransitionbetweenhyperpolarizationanddepolarization.Inparticular,duringthedepolarizingphaseoftheoscillation,thepacemakercellsreburstsofactionpotentials,which,viasynaptictransmission,entrainneuralactivityinotherlaminaeandcorticalareas.Forthepresentwork,signicantphasecoherencebetweenCSDandMUAisusedtoindicatethatacurrentgeneratorisaccompaniedbyrhythmicringandthushasthepotentialofbeingapacemaker.Inaddition,thephasespectrumbetweenCSDandMUAattheoscillationfrequencycanbeusedtohelpassessifduringanalphaepoch,asink(orsource),correspondswithincrease(ordecrease)inMUA. 22

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Straightarrowsdenotecausalrelationships.Squarearrowsdenoteinferentialtechniquesneededtounderstandthecausalrelations CurrentssinksandsourcesintheextracellularspaceofapyramidalneuronproducedbyEPSPandIPSP 23

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A)LaminarelectrodeB)EvokedpotentialsC)CurrentsourcedensityD)Multiunitactivity EpochofongoingalphaoscillationrecordedwithalaminarelectrodeinareaV4. 24

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A)Phaserealignedalphaepochs.Averagealphaepochisoverlaid(red).B)Alphaepochsbeforephaserealignment CurrentsourcedensityofongoingactivityderivedbyphaserealigningthealphaepochsinareaV4.Phaserealignedandaveragedeldpotentialsareoverlaid 25

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Shaw 2003 ; Niedermeyer 2005 ).Nearly80yearsafteritsdiscovery( Berger 1929 ),itsgenesis,cellularmechanisms,andfunctionsremainunclear.Typically,thealpharhythmislargestinmagnitudewiththeeyesclosedandattenuatesoneyeopeningandduringtasksrequiringvisualattention( Steriadeetal. 1990 ).Thishasledtothenotionthatthepresenceofthealpharhythmsigniesanidlingstateofthebrain,orperhapsevenamechanismofactiveinputsuppression( Wordenetal. 2000 ).Morerecentevidencehasbeguntomodifythisnotionbyshowingthatthemagnitudeofthealpharhythmcanalsoincreaseinavarietyofexperimentalparadigmsincludingworkingmemoryandmentalimagery,knownasrejectiontasks,whereattentionisrequiredtobedirectedinternally( Ray&Cole 1985 ; Cooperetal. 2003 ; Shaw 2003 ; Palva&Palva 2007 ). Theinitialhypothesisregardingthegenesisofthecorticalalpharhythmemphasizedthepacemakingroleofthethalamus( Andersen&Andersson 1968 ).Thetestingofthishypothesisinathalamicanimalswasinconclusive,withreportsofbothadecrease( Ohmotoetal. 1978 ; Lukashevich&Sazonova 1996 ),andnoeectonthecorticaleldpotentials( Toumskoy&Maiorchik 1969 ; Yazawaetal. 2001 ).Aseriesofin-vivostudiesindogs( LopesdaSilvaetal. 1973a b ; LopesdaSilva&vanLeeuwen 1977 ; LopesdaSilvaetal. 1980 )suggestedthatthealpharhythmcouldbeofacorticaloriginwithlargelayer5pyramidalneuronsactingaspacemakers( Steriadeetal. 1990 ; LopesdaSilva 1991 ). Steriadeetal. 1990 ; Silvaetal. 1991 ).Thehypothesisregardingthepace-makingroleoflayer5pyramidalcellshasbeentested 26

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Silvaetal. 1991 ; Flint&Connors 1996 ).Moreover,layer5pyramidalneuronshavebeenimplicatedinthemechanismoftheaugmentingresponse( Castro-Alamancos&Connors 1996a c b ),aresonance-likephenomenonobservedonrepetitivestimulationat10Hz.ThesendingshavemotivatedrecentcomputationalmodelsoflowfrequencyEEGrhythmstoincorporateanalphapacemakerattheleveloflamina5( Jonesetal. 2000 ; Karamehetal. 2006 ).Oscillationsinthe10Hzband,whichdonotshowtheclassicalphareactivity,canalsoberecordedfromvisualcorticalareasotherthantheparieto-occipitalcomplex,raisingtheinterestingpossibilitythatthealphaoscillationmightbeorganizeddierentlyindierentareasofthecortex.Usingslicepreparationsfromtheentorhinalcortex, Lukatch&MacIver ( 1997 )showedthat,inthetemporallobe,itisthesupragranularlayersthatplayedtheroleofanalphafrequencypacemaker. Whileinvitropreparationshaveprovenaninvaluabletoolforunderstandingthephysiologyofcorticaloscillations,recentwritingshavecautionedabouttheapplicabilityofthendingsmadeinthesepreparationstotheintactbrain( Steriade 2004 ).Oneofthegoalsofthepresentworkistostudythelaminarorganizationofthe"spontaneous"alpharhythmindierentareasofthevisualcortexinthealertmonkeys.Forthispurpose,weusedpreviouslyrecorded( Mehtaetal. 2000a )laminarprolesofeldpotentialsandmultiunitactivity(MUA)wererecordedfromLGN,V1,V2,V4andinferotemporalcortex(IT)usinglineararraymultielectrodesthatsampledfromalllayerssimultaneously.Belowwedescribetheexperimentalparadigm,recordingsandtheanalysisprotocol.Sections 3.4 3.5 3.6 and 4.4 describethetheresultsfortheextrastriateareasV2,V3andIT.TheresultsforstriateandLGNarepresentedinchapter5. 3.2.1Paradigm 27

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Mehtaetal. 2000a ).Therearetwoconditions.InCondition1,themonkeywaspresentedwithamixedstreamofauditoryandvisualstimuli.Thevisualstimuliwere10sashesgeneratedbyaGrassPS22PhotoStimulator.Ineachsensorymodality,astandardstimulusoccurred86%ofthetimeandanoddballstimulus14%ofthetime.Selectiveattentionwasmanipulatedbyinstructingthemonkeytoresponsetotheoddballstimulusintheattendedmodalityonly.Taskdicultywasbalancedbetweenthemodalities.InCondition2,themonkeyperformedtheoddballdetectiontaskintheauditorydomainintheabsenceofvisualstimulation.Inthistask,100msdurationpuretoneswerepresentedat1.5Hz,withthestreamof"standard"stimulirandomlyinterruptedbytonesthatdieredinfrequency(deviants).Themonkeywasrequiredtorespondtothedeviantsfollowingtheonsetofanoddballstimulus.Aliquidrewardwasgiventocorrectresponses. 3-1 Aforaschematic).Theinter-contactspacingwas150minV1,150minV2and200minV4andIT.Multiplepenetrationsweremadeineachofthethreevisualcorticalareas.Datawerecollectedduringperiodsofadequatetaskperformance(i.e.,>80%targetdetection).Thepenetrationsduringwhichthelaminarelectrodereliablysampledactivityfromalllayerswereselectedforanalysis.Thiswasjudgedbycomparingthepatternofevokedpotentialswithpreviouslypublishedresults( Mehtaetal. 2000a b ).Thedatasetanalyzedhereconsistsof2penetrationsinV1,2penetrationsinV2,2penetrationsinV4,and3penetrationsinITforsubjectB,and2penetrationsinV1,2penetrationsinV2,2penetrationsinV4,and1penetrationinITforsubjectV.InadditiononepenetrationinLGNforsubjectBwasrecordedsimultaneouslywithaV1penetrations. 28

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Schroederetal. 1995 )fromwhichthealphacurrentgeneratorswereidentied. 29

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3-1 Bdepictsa200msepochofLFPdatafromV4inwhich2fullcyclesofarhythmicoscillationat10Hzareapparent.Notethateachundergoespolarityinversioninthemiddlecorticallayersandtheiramplitudesappearlargestintheinfragranular(IG)layers.Spectralpowerat10HzcomputedoverallepochsofLFPdataconrmedthisimpression;asshowninFig. 3-1 D,alphapowerintheIGlayersisconsistentlyhigherthaninthegranular(G)andsupragranular(SG)layersforallfourpenetrationsinbothmonkeys.Togeneratethe10Hzcurrentsourcedensity(CSD)prole,weappliedthePRATmethodbyselectingthecontactwiththehighestspectralpowerasthephaseindexcontact(contact12forFig. 3-1 ).TheresultingPRAT-LFPandthePRAT-CSDprolederivedfromitaresuperimposedinFig. 3-1 C,onthetimescaleofonecycleofthe10Hzoscillation.OverlainontheseprolesareMUAsignalsfromasubsetoftherecordingcontacts.Currentsources(blue)andsinks(red)underlyingthegenerationoftheoscillatoryalphaeldactivityarereadilyidentiedinG,IGaswellasSGlayerswherethecurrentsinks(red)correspondtonegativePRAT-LFPs.Thesecharacteristics 30

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3-1 Cwerefoundtobeconsistentacrossallfourpenetrationsinbothmonkeys(Fig. 3-4 ).Asnotedby Csicsvarietal. ( 2003 ),thechoiceofthephaseindexcontactbiasestheCSDtowardsdetectingneuralactivityclosetothatelectrodecontact.Wefoundthatusingadierentcontact,forexamplechannel6intheabovedataset,resultedinastrengtheningofalphacurrentsinGandSGlayersandaweakeningintheIGlayers,butdidnotchangetheoverallCSDprole. TheincreasesinMUAaccompanyingthemiddleandlowerlayersinksinthelatterhalfoftheepochdisplayedinFig. 3-1 Csuggestthatthesesinksreectnetdepolarizationofthelocalneurons,andconcomitantMUAdecreasessuggestthatthereverseistruefortheco-locatedcurrentsources(blue)intheinitialpartoftheepoch.Theearlyandlatepartsoftheepochthusappeartorepresentthelowandhighexcitabilityphasesofthelocalalphaoscillation.Toassessmorequantitativelytheextenttowhichtheringprobabilityofthelocalneuronsaroundagivencurrentgeneratorisphase-lockedtothealphacurrentoscillation,weestimatedthecoherencebetweenCSDandMUAforeachalphacurrentgenerator.Thecoherencespectrahaveclearpeaksataround10HzintheIGandGlayersasshowninFig. 3-1 E.Thepeakcoherenceis0.18(p<0:01)inIGlayers,and0.16(p<0:01)inGlayer,suggestingthattheseareactivecurrentgeneratorswheretheneuronalringisphase-lockedtotheoscillatorycurrent.Incontrast,theCSD-MUAcoherencefortheSGlayerdidnotshowanalphapeak(Fig. 3-1 E)andthecoherencevalueat10Hzwasnotsignicant(0.002,p=0:23).NotethattheSGcurrentgeneratorisoutofphasewiththatinGandIGlayers.AplausibleexplanationforthelackofsignicantCSD-MUAcoherenceintheSGlayersisdampeningduetoinhibition( Schroederetal. 1995 ). TheCSD-MUArelationshipcanbefurtherquantiedbycomputingtheirrelativephaseat10Hztohelpdeterminewhetherincreaseinringinalocalgroupofneuronsaroundagivencurrentgeneratorcorrespondstoasink,andthus,reectsnetlocalneuronaldepolarization.Thephasespectrum(notshown)wasfoundtobecontinuousin 31

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TheCSD-MUAcoherencecharacteristicswereconsistentacrossthreepenetrationsfromtwomonkeys.ThefourthpenetrationshowedlittlephasicvariationinMUAuponvisualstimuluspresentation,andwasexcludedfromtheCSD-MUAcoherenceanalysis.Thus,theconsistentbiasingoftheCSD-MUAcoherencetowardstheGandtheIGlayers(Fig. 3-1 E),togetherwiththelaminardistributionofalphapowerinFig. 3-1 D,stronglysuggestthattheneuralensemblesintheGandIGlayersarepotentialalphapacemakers.ThemorepreciserelationshipbetweenthesepotentialpacemakersisexaminedbyaGrangercausalityanalysisbelow.Aunidirectionalcausalinuenceat10Hzfromonepotentialpacemakertoanotherwouldestablishtheformerthetruealphapacemaker. 3-2 A;herecontact12wasusedasthephaseindexcontact.Temporalalternationsofcurrentsources(blue)andsinks(red)occurringatthealphafrequencycanbeseeninIG,GaswellasSGlayers.TheselaminarcharacteristicswerepresentinallfourV2penetrations(Fig. 3-5 ).Inaddition,thesimilaritybetweenthePRAT-CSDproleinV2andthatinV4isreadilyidentiable.Thedistributionofthe10HzpoweracrossdierentlayersexhibitsincreasedvariabilityascomparedtoV4,thoughtheIGlayersstillhavethehighestpowerinthreeoutoffourpenetrations(Fig. 3-2 B).ForonepenetrationthehighestalphapoweroccursintheSGlayers. TheCSD-MUAcoherencespectrainV2showninFig. 3-2 CarealsosimilartothoseinV4(Fig. 3-2 E).Thebiasisagaintowardthelowercorticallayers.Thepeakcoherence(9Hz)inIGand(8Hz)Glayersarefoundtobe0.096(p<0:01)and0.082(p<0:01), 32

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3-2 B.BasedontherelationshipofMUAchangeswiththelocalcurrentsinkandsourcedistributions,theearlyandlateportionsoftheepochrepresentthelowandhighexcitabilityphasesofthelocalalphaoscillation,respectively.TheCSD-MUAcoherencecharacteristicsareconsistentintwopenetrationsinonemonkey.ThetwopenetrationsintheothermonkeydidnotshowclearevokedMUAonthepresentationofavisualstimulusandwerenotincludedintheCSD-MUAcoherenceanalysis. 3-3 AshowsThePRAT-LFPandPRAT-CSDprolesfromarepresentativepenetrationwherethephaseindexcontactwascontact6.AcomparisonwithFig. 3-1 andFig. 3-2 revealedanumberofqualitativedierences.First,thealphacurrentgeneratorintheSGlayers(aroundcontacts5,6and7)isstrongandhasanunderlyingsource/sink/sourceconguration.Second,supercialtotheSGlayergenerator,arelativelystrongalphacurrentgeneratorisseenaroundcontact3.Third,thealphacurrentgeneratorintheIGlayers(aroundcontact10)isweak.Fourth,noalphacurrentisseeninthegranularlayer.Theselaminarcharacteristicsaregenerallyconsistentacrossallfourpenetrationsinbothmonkeys(Fig. 3-6 ).ThestrengthoftheIGlayergeneratorisveryweakexceptforonepenetration.AlsoincontrasttoV2andV4,the10HzLFPpowerinITisgenerallyhigherintheSGlayersthanintheIGandGlayers(Fig. 3-3 B).Likealphapower,CSD-MUAcoherenceshowsasupragranularbias(Fig. 33

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C).Thepeak(10Hz)coherencevaluesatcontacts5,6and7arefoundtobe0.16(p<0:01),0.16(p<0:01)and0.12(p<0:01),respectively.TheCSD-MUAcoherenceattheweakcurrentgeneratorintheIGlayersisnotsignicantatp=0:05level(Fig. 3-3 C).TheCSD-MUAcoherenceatthegeneratoraroundcontact3isweak(0.06,10Hz)butsignicant(p<0:01).TheseCSD-MUAcoherenceresultsareconsistentintwopenetrationswherequalityMUAdatawererecorded.TheMUAsfromtheremainingtwopenetrationsdidnotshowclearphasicchangeuponvisualstimuluspresentationandwerethusexcludedfromCSD-MUAcoherenceanalysis. Thesource/sink/sourcecongurationforthealphacurrentgeneratorintheSGlayersmostlikelyreectssynapticactivityofthesupercialpyramidalneuronensemble.Thesizeofthebasaldendriticarborofthesupercialpyramidalneuronshasbeenshowntoincreasealongtheoccipito-temporalhierarchyofthemacaquemonkeywiththearbordiameterreachingdimensionsofaround400m( Elstonetal. 1999 )inIT.Additionally,thesinksatcontact5and7inFig. 3-3 AcorrespondtothelargestnegativedeectionsinthePRAT-LFPs(overlaidonPRAT-CSDinFig. 3-3 A).ThemeanphasedierencesinalpharangebetweenCSDandMUAatcontacts3,5,6and7werefoundtobe15:4o2:3o;166:8o3:4o;38:7o4:4oand174:8o3:72o(n=2penetrations;CSDleading),respectively.Theseresults,alongwithconcomitantMUA(Fig. 3-3 A),suggestthattheobservedCSDpatternislikelytheresultofbasaldendriticexcitationwhereincreasedringcoincidedwithsinksatthebasaldendrites.ThustheearlypartoftheepochdisplayedinFig. 3-3 Arepresentsthelowexcitabilityphaseofthelocalalphaoscillation,whilethelaterepochofoppositesignactivityrepresentsitshighexcitabilityphase. 34

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ResultsforV4.A)Schematicofthemulti-electrodewith14equallyspaced(200m)contacts.B)Ashortsegment(100ms)ofFPs.C)PRAT-CSDdisplayedasacolorcodedplot,whichisthesecondspatialderivativeofphaserealignedandaveragedPRAT-FPs(smoothtraces,blue).TheYaxisiselectrodecontactsfrom2to13.Thecontactsusedforbipolarderivationsareshowntotheleft.AsingleepochofMUAfromthreecontactsissuperimposed(black).D)Laminardistributionofthepeak(10Hz)LFPpoweracrossallpenetrationsinbothmonkeys.E)CSD-MUAcoherencespectraforthepenetrationshowninC. 35

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ResultsforV2.A)PRAT-CSDdisplayedasacolorcodedplot,whichisthesecondspatialderivativeofphaserealignedandaveragedPRAT-FPs(smoothtraces,blue).TheYaxisiselectrodecontactsfrom2to13.Thecontactsusedforbipolarderivationsareshowntotheleft.AsingleepochofMUAfromthreecontactsissuperimposed(black).B)Laminardistributionofthepeak(10Hz)LFPpoweracrossallpenetrationsinbothmonkeys.C)CSD-MUAcoherencespectraforthepenetrationshowninC. 36

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ResultsforIT.A)PRAT-CSDdisplayedasacolorcodedplot,whichisthesecondspatialderivativeofphaserealignedandaveragedPRAT-FPs(smoothtraces,blue).TheYaxisiselectrodecontactsfrom2to13.Thecontactsusedforbipolarderivationsareshowntotheleft.AsingleepochofMUAfromthreecontactsissuperimposed(black).B)Laminardistributionofthepeak(10Hz)LFPpoweracrossallpenetrationsinbothmonkeys.C)CSD-MUAcoherencespectraforthepenetrationshowninC. AlphacurrentgeneratorsindierentpenetrationsinareaV4.PRAT FPareoverlaid 37

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AlphacurrentgeneratorsindierentpenetrationsinareaV2.PRAT FPareoverlaid AlphacurrentgeneratorsindierentpenetrationsinareaIT.PRAT FPareoverlaid 38

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Theaboveanalysisislargelydescriptive,andonlypartiallyaddressedtherelationshipamongdierentlaminarcurrentgenerators.Inparticular,boththegranularandinfragranularlayersremainviablecandidatesforalphapacemakinginV2andV4.ToexplorethisissuefurtherwecarriedoutaGrangercausalityanalysis.Fortwosimultaneouslymeasuredtimeseries,oneseriescanbecalledcausaltotheotherifwecanbetterpredictthesecondseriesbyincorporatingpastknowledgeoftherstone Weiner ( 1956 ).Thisconceptwaslateradoptedandformalizedby Granger ( 1969 )inthecontextoflinearregressionmodelsofstochasticprocesses.Specically,ifthevarianceofthepredictionerrorforthesecondtimeseriesatthepresenttimeisreducedbyincludingpastmeasurementsfromthersttimeseriesinthelinearregressionmodel,thenthersttimeseriescanbesaidtohaveacausal(directionalordriving)inuenceonthesecondtimeseries.Reversingtherolesofthetwotimeseries,onerepeatstheprocesstoaddressthequestionofcausalinuenceintheoppositedirection.Fromthisdenitionitisclearthattheowoftimeplaysanessentialroleinallowinginferencestobemadeaboutdirectionalcausalinuencesfromtimeseriesdata.Alternatively,improvementinpredictioncanalsobeviewedfromtheperspectiveofcomparingrelativeestimatesofconditionalprobability.Recentworkhasmodeledtherelationbetweenmultiplepointprocessesalongthisview(Okatanetal.,2005;Truccoloetal.,2005).Inouranalysis,thebipolarLFPdataconstitutethetimeseries,andGrangercausalinuenceisequatedwiththedirectionofsynaptictransmissionbetweenneuronalensembles.Physiologically,rhythmicsynapticactivity(LFP)inaneuronalensemblegivesrisetoperiodicburstsofactionpotentialring(MUA),which,throughsynaptictransmission,drivestherhythmicsynapticactivityinthetargetneuronalensemble.Thus,evaluationofthecausalrelationbetweentwobipolarLFPtimeseriesformsthebasisforidentifyingthelayercontainingthepacemakingcellsinacolumn.Inthisstudy,Grangercausalityanalysis,asaprincipled 39

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Freiwaldetal. 1999 ; Bernasconietal. 2000 ; Liangetal. 2000 ; Baccala&Sameshima 2001 ; Brovellietal. 2004 ; Hesseetal. 2003 ; Dingetal. 2006 ),isusedinlieuofthetrisectionmethodinin-vitrostudiestoidentifythelaminarpacemakersofthealpharhythm.BelowwereviewtheessentialmathematicalelementsofGrangercausalitywithspecialemphasisonitsspectraldecomposition.Wethendiscusspracticalissuesconcerninghowtoestimatesuchmeasuresfromtimeseriesdata.InSect. 4.4 weapplythetechniquetostudytheinteractionbetweenthealphacurrentgeneratorsidentiedinthepreviouschapter. Geweke 1982 1984 ; Dingetal. 2006 ). 40

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wherethenoisetermsareuncorrelatedovertimeandthecovariancematrixisgivenby =0B@22221CA(4{5) Theentriesaredenedas2=var(2t);2=var(2t);2=cov(2t;2t).IfXtandYtareindependent,thenfb2jgandfc2jgareuniformlyzero,2=0,1=2and1=2.ThisobservationmotivatesthedenitionoftotalinterdependencebetweenXtandYtas wherej:jdenotesthedeterminantoftheenclosedmatrix.Accordingtothisdenition,FX;Y=0whenthetwotimeseriesareindependent,andFX;Y>0whentheyarenot. ConsiderEqs. 4{1 and 4{3 .Thevalueof1measurestheaccuracyoftheautoregressivepredictionofXtbasedonitspreviousvalues,whereasthevalueof2representstheaccuracyofpredictingthepresentvalueofXtbasedonthepreviousvaluesofbothXtandYt.Accordingto Weiner ( 1956 )and Granger ( 1969 ),if2islessthan1,thenYtissaidtohaveacausalinuenceonXt.Thiscausalinuencecanbequantiedby NotethatFX!Y=0whenthereisnocausalinuencefromYtoXandFX!Y>0whenthereis.Similarly,onecandenecausalinuencefromXtoYas 41

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When2iszero,FX:Yisalsozero.When2isnotzero,FX:Y>0. Theabovedenitionsimplythat ThetotalinterdependencebetweentwotimeseriesXtandYtcanbedecomposedintothreecomponents:twodirectionalcausalinuencesduetotheirinteractionpatterns,andtheinstantaneouscausalityduetofactorspossiblyexogenoustothe(X;Y)system(e.g.acommondrivinginput). 4{3 and 4{4 intermsofthelagoperator wherea2(0)=1,b2(0)=0,c2(0)=0andd2(0)=1.FouriertransformingbothsidesofEq. 4{11 leadsto wherethecomponentsofthecoecientmatrixA(!)aregivenby

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4{12 intothetransferfunctionformatweobtain wherethetransferfunctionisH(!)=A1(!)whosecomponentsare Afterproperensembleaveragingwegetthespectralmatrix wheredenotescomplexconjugateandmatrixtranspose. Thespectralmatrixcontainscrossspectraandautospectra.IfXtandYtareindependent,thenthecrossspectraarezeroandjS(!)jequalstheproductoftwoautospectra.ThisobservationmotivatesthespectraldomainrepresentationoftotalinterdependencebetweenXtandYtas wherejS(!)j=Sxx(!)Syy(!)Sxy(!)Syx(!)andSyx(!)=Sxy(!).Thisdecompositionofinterdependenceisrelatedtocoherencebythefollowingrelation: wherecoherenceisdenedas

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Considerthecasewhen2=0.InthiscasethereisnoinstantaneouscausalityandtheinterdependencebetweenXtandYtisentirelytheresultoftheinteractionsthroughtheregressiontermsontherighthandsidesofEqs. 4{3 and 4{4 .Thespectrumhastwoterms.Therstterm,theintrinsicpart,involvesonlythevarianceof2t,whichisthenoisetermthatdrivestheXttimeseries.Thesecondterm,thecausalpart,involvesonlythevarianceof2t,whichisthenoisetermthatdrivesYt. If2isnotzeroitisdiculttoattributethepoweroftheXtseriestodierentsources.Wenowconsideratransformation,callednormalization,introducedby Geweke ( 1982 )thatremovesthecrosstermandmakestheidenticationofanintrinsicpowertermandacausalpowertermpossible.Left-multiplying onbothsidesofEq. 4{12 ,weobtain wherec3(!)=c2(!)2 4{20 istheinverseofthenewcoecientmatrix~A(!): ~H(!)=0B@~Hxx(!)~Hxy(!)~Hyx(!)~Hyy(!)1CA=1 det~A0B@d3(!)b2(!)c3(!)a2(!)1CA:(4{21) 44

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~Hxx(!)=Hxx(!)+2 ItiseasytoseethatExand~Eyareuncorrelated,thatis,cov(Ex;~Ey)=0.ThevarianceofthenoisetermforthenormalizedYtequationis~2=222 4{20 ,similarly,thespectrumofXtisfoundtobe: ThersttermisinterpretedastheintrinsicpowerandthesecondtermasthecausalpowerofXtduetoYt.ThisrelationshowsthatportionofthetotalpowerofXtatfrequency!thatiscontributedbyYt.BasedonthisinterpretationwedenethecausalinuencefromYttoXtatfrequency!as ~Hxx(!)2~Hxx(!):(4{24) Notethatthisdenitionofcausalinuenceisexpressedintermsoftheintrinsicpowerratherthanthecausalpower.Itisexpressedinthiswaysothatthecausalinuenceiszerowhenthecausalpoweriszero(i.e.,theintrinsicpowerequalsthetotalpower),andincreasesasthecausalpowerincreases(i.e.,theintrinsicpowerdecreases). Bytakingthetransformationmatrixas0B@12 ^Hyy(!)2^Hyy(!);(4{25) where^Hyy(!)=Hyy(!)+2 45

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weachieveaspectraldomainexpressionforthetotalinterdependencethatisanalogoustoEq. 4{10 inthetimedomain,namely: Notethat,undergeneralconditions,thesespectralmeasuresrelatetothetimedomainmeasuresas: 2RfX;Y(!)d!;FX!Y=1 2RfX!Y(!)d!;FY!X=1 2RfY!X(!)d!;FY:X=1 2RfX:Y(!)d!: 4-1 ,apairwiseanalysiswillgivethesamepatternsofinteractonlikethatinFig. 4-1 B.Todisambiguatethesesituationsrequiresadditionalmeasures.ConditionalGrangercausalityanalysishastheabilitytoresolvewhethertheinteractionbetweentwotimeseriesisdirectorismediatedbyanotherrecordedtimeseriesandwhetherthecausalinuenceissimplyduetodierentialtimedelaysintheirrespectivedrivinginputs. 46

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4-1 B)orismediatedentirelybyZt(Fig. 4-1 A)wecarryoutthefollowingprocedure.First,letthejointautoregressiverepresentationofXtandZtbe wherethecovariancematrixofthenoisetermsis 3=0B@33331CA(4{30) NextweconsiderthejointautoregressiverepresentationofallthreeprocessesXt,YtandZt wherethecovariancematrixofthenoisetermsis 4=0BBBB@xxxyxzyxyyyzzxzyzz1CCCCA Theintuitivemeaningofthisdenitionisquiteclear.WhenthecausalinuencefromYttoXtisentirelymediatedbyZt(Fig. 4-1 A),fb4jgisuniformlyzero,andxx=3.Thus,wehaveFY!XjZ=0,meaningthatnofurtherimprovementinthepredictionofXt

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4-1 B),theinclusionofpastmeasurementsofYtinadditiontothatofXtandZtresultsinbetterpredictionsofXt,leadingtoxx<3,andFY!XjZ>0. 4{29 and 4{29 thenormalizedequationsare whereD11(0)=1,D22(0)=1,D12(0)=0,cov(xt;zt)=0,andD22(0)isgenerallynotzero.wenotethatvar(xt)=3andthisbecomesusefulinwhatfollows. ForEqs. 4{32 4{33 and 4{33 thenormalizationprocessinvolvesleft-multiplyingbothsidesbythematrix

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Toproceedfurtherweneedthefollowingimportantrelation( Geweke 1984 ) anditsfrequencydomaincounterpart: ToobtainfYZ!X(!),weneedtodecomposethespectrumofX.TheFouriertransformofEqs. 4{35 and 4{36 gives: and 49

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4{38 canbeequatedwiththatfromEq. 4{39 ,wecombineEq. 4{38 andEq. 4{39 toyield, ThersttermcanbethoughtofastheintrinsicpowerandtheremainingtwotermsasthecombinedcausalinuencesfromYandZ.Thisinterpretationleadsimmediatelytothedenition jQxx(!)^xxQxx(!)j(4{41) WenotethatSxxisactuallythevarianceof3taspointedoutearlier.OnthebasisoftherelationinEq. 4{37 ,thenalexpressionforGrangercausalityfromYttoXtconditionalonZtis ItcanbeshownthatfY!XjZ(!)relatestothetimedomainmeasureFY!XjZ(!)via 2ZfY!XjZ(!)d!;(4{43) undergeneralconditions. TheabovederivationismadepossiblebythekeyassumptionthatX(!)andZ(!)inEq. 4{38 andinEq. 4{39 areidentical.Thiscertainlyholdstrueonpurelytheoretical 50

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Chenetal. 2006 ).ThesubsequentcalculationsofconditionalGrangercausalityarebasedonthispartitionmatrixprocedure. Dingetal. 2000 ).Thisconsiderationismotivatedbythegoalofapplyingautoregressivemodelinginneuroscience.Itistypicalinbehavioralandcognitiveneuroscienceexperimentsforthesameeventtoberepeatedonmanysuccessivetrials.Underappropriateconditions,timeseriesdatarecordedfromtheserepeatedtrialsmaybeviewedasrealizationsofacommonunderlyingstochasticprocess. LetXt=[X1t;X2t;:::;Xpt]Tbeapdimensionalrandomprocess.HereTdenotesmatrixtransposition.Inmultivariateneuraldata,prepresentsthetotalnumberofrecordingchannels.AssumethattheprocessXtisstationaryandcanbedescribedbythefollowingmthorderautoregressiveequation whereA(i)areppcoecientmatricesandEt=[E1t;E2t;:::;Ept]Tisazeromeanuncorrelatednoisevectorwithcovariancematrix. ToestimateA(i)and,wemultiplyEq. 4{44 fromtherightbyXTtk,wherek=1;2;;m.Takingexpectations,weobtaintheYule-Walkerequations 51

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ForasinglerealizationoftheXprocess,fxigNi=1,wecomputethecovariancematrixinEq. 4{45 accordingto ~R(n)=1 Ifmultiplerealizationsofthesameprocessareavailable,thenwecomputetheabovequantityforeachrealization,andaverageacrossalltherealizationstoobtainthenalestimateofthecovariancematrix.(NotethatforasingleshorttrialofdataoneusesthedivisorNforevaluatingcovariancetoreduceinconsistency.Duetotheavailabilityofmultipletrialsinneuralapplications,wehaveusedthedivisor(Nn)intheabovedenitionEq. 4{46 toachieveanunbiasedestimate.)Itisquiteclearthat,forasinglerealization,ifNissmall,onewillnotgetgoodestimatesofR(n)andhencewillnotbeabletoobtainagoodmodel.Thisproblemcanbeovercomeifalargenumberofrealizationsofthesameprocessisavailable.Inthiscasethelengthofeachrealizationcanbeasshortasthemodelordermplus1. Equations 4{44 containatotalofmp2unknownmodelcoecients.InEq. 4{45 thereisexactlythesamenumberofsimultaneouslinearequations.Onecansimplysolvetheseequationstoobtainthemodelcoecients.AnalternativeapproachistousetheLevinson,Wiggins,Robinson(LWR)algorithm,whichisamorerobustsolutionprocedurebasedontheideasofmaximumentropy.Thisalgorithmwasimplementedintheanalysisofneuraldatadescribedbelow.ThenoisecovariancematrixmaybeobtainedaspartoftheLWRalgorithm.Otherwiseonemayobtainthrough =R(0)+mXi=1A(i)R(i):(4{47) HerewenotethatRT(k)=R(k). 52

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Akaike 1974 )denedas Ntotal(4{48) whereNtotalisthetotalnumberofdatapointsfromallthetrials.Plottedasafunctionofmthepropermodelordercorrespondtotheminimumofthisfunction.ItisoftenthecasethatforneurobiologicaldataNtotalisverylarge.Consequently,forareasonablerangeofm,theAICfunctiondoesnotachieveaminimum.AnalternativecriterionistheBayesianInformationCriterion(BIC),whichisdenedas Thiscriterioncancompensateforthelargenumberofdatapointsandmayperformbetterinneuralapplications.Analstep,necessaryfordeterminingwhethertheautoregressivetimeseriesmodelissuitedforagivendataset,istocheckwhethertheresidualnoiseiswhite.Heretheresidualnoiseisobtainedbycomputingthedierencebetweenthemodelspredictedvaluesandtheactuallymeasuredvalues. Onceanautoregressivemodelisadequatelyestimated,itbecomesthebasisforbothtimedomainandspectraldomaincausalityanalysis.Specically,inthespectraldomainEq. 4{44 canbewrittenas where isthetransferfunctionwithA(0)beingtheidentitymatrix.FromEq. 4{50 ,afterproperensembleaveraging,weobtainthespectralmatrix 53

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Brovellietal. 2004 )tobuildabaselinenull-hypothesisdistributionfromwhichstatisticalsignicancecanbederived.Considertwochannelsofrecordingswithmanyrepeatedtrials(onetrialbeinga200msepochforthiswork).Wecanreasonablyassumethatthedatafromdierenttrialsareapproximatelyindependentofoneanother.Randomlypairingdataforchannel1withdataforchannel2fromadierenttrialleadstothecreationofasyntheticensembleoftrialsforwhichthereisnointerdependencebetweenthetwochannelsbasedonconstruction.Thetemporalstructurewithinachannelispreserved.Performingsuchrandompairingwithmanydierentpermutationswillresultinadistributionofcoherenceorcausalityspectracorrespondingtothenullhypothesisofnostatisticalinterdependence.Thecalculatedvalueforagivenstatisticfromtheactualdataiscomparedwiththisbaselinenullhypothesisdistributionfortheassessmentofsignicancelevels.Bootstrapresamplingtechniques( Efron 1982 )wereusedtoestimatecondenceintervals. 3-1 thethreebipolarsignalsare:SG=LFP(contact6)-LFP(contact4),G=LFP(contact9)-LFP(contact7),andIG=LFP(contact12)-LFP(contact10).FortheV2penetrationinFig. 3-2 wehaveSG 54

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3-3 ,thetwobipolarderivationsare:SG=LFP(contact7)-LFP(contact4)andIG=LFP(contact12)-LFP(contact10).Thebipolartreatmentremovestheeectoffareldsandthecommonreferenceandyieldslocaleldpotentials(LFP)whichwereanalyzedbybivariate(V2,V4andIT)andconditionalGrangercausalitymeasures(V2andV4).BasedontheAkaikeInformationCriterion(AIC)amodelorderof10(50ms)waschosenasatradeobetweensucientspectralresolutionandover-parameterization. Fig. 4-2 showstheperformanceoftheMVARestimationon5secondsofcontiguousbipolarLFPdatafromtheIGlayer.MVARmodelbasedprediction(bluecurveinFig. 4-2 )closelyfollowsthebipolarLFPdata(redcurve).Thedierencebetweenthepredictionanddatai.e.theresidualprocessisoverlaid(greencurve).Anadequateparametricmodeltofthedatameansthattheresidualnoiseprocessmustbetemporallyuncorrelated(white).Fig. 4-3 showstheFourierbasedpowerspectrumofthedata,MVARmodelpredictionandtheresidualprocessshowninFig. 4-2 .Thepowerspectrumoftheresidualprocess(greencurveinFig. 4-3 )doesnothaveanyprominentpeaksuggestingthattheprocessiswhite.InadditiontheDurbin-Watsontestwasusedtocheckthegoodnessoft.Thewhitenessoftheresidualswasconrmedatthep=0.05signicancelevel. InV4,forIGandGlayers,theLFPpowerspectraexhibitclearpeaksaround10Hz(Fig. 4-6 A).Thecoherencespectrumhasapronouncedpeakat9Hz,wherethepeakvalueis0.55(p<0:001),asshowninFig. 4-6 B.Thissuggeststhatthealphacurrentsintheselayersarehighlysynchronized.TheGrangercausalityspectrumofIG!Gshow(Fig. 4-6 D)astrongpeakat9Hzwithapeakvalue1.18(p<0:001),whereasthecausalityintheotherdirection(G!IG)isnotsignicant(Fig. 4-6 C),indicatingthatneuralactivityintheGlayerisstronglydrivenbythatintheIGlayers.ThestrongIG!Glayercausalinuenceisfoundforallfourpenetrationsinbothmonkeys(seeTable 4-1 ),whereasGlayershowaweakbutsignicantcausalinuenceontheIG 55

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4-1 ).ToexaminetheinuenceoftheSGlayersontheinteractionbetweentheGandIGlayersweincludethebipolarsignalfromtheSGlayerandperformedconditionalGrangercausalityanalysis.TheGrangercausalityfromIGtoGlayerafterconditioningoutSGlayeractivityisnearlyidenticaltothebivariatecase(Fig. 4-6 D)exceptforasmalldecreaseinpeakvalue.TotestwhetherthesmalldecreaseissignicantwecomparedthemeansofthebootstrapresampleddistributionsofthepeakGrangercausalityvaluesfromthespectrumofthebivariateandconditionalcausalityanalysisbyStudent'st-test.ForthepenetrationshowninFig. 3-1 ,thesmalldecreaseinpeakvalue(1.18to1.04)issignicant(p<0:05),butforallotherpenetrations,thedecreaseisfoundtobenotsignicantatp=0:05signicancelevel,suggestingthattheSGlayershasnoinuenceontheinteractionbetweentheIGandGlayers.ThisisanexpectedresultastheCSD-MUAcoherenceanalysishasalreadydemonstratedthattheSGalphacurrentgeneratorisnotstronglyactiveinthesensethatitisnotaccompaniedbyrhythmicring. TheinteractionbetweentheIGandSGlayerswasstudiedbyrstperformingabivariateanalysis.Figures 4-6 Eand 4-6 Fshowthepowerandcoherencespectra,respectively.ThepowerofthebipolarLFPsignalfortheSGlayerhasaclearpeakat8Hz.Thecoherencespectrumalsopeaksat8Hzwithapeakvalueof0.15(p<0:001),indicatingasignicant(butweak)synchronybetweenthelocalalphacurrentsinthesetwolayers.GrangercausalityagainrevealsIGasthedriveroftheSGcurrentwiththepeakvalueof0.36(p<0:001)at8Hz(Fig. 4-6 H).Thecausalinuenceintheoppositedirection(SG!IG)isnotsignicant(Fig. 4-6 G).SignicantIG!SGisfoundinallfourpenetrationsinbothmonkeys(Table 4-2 ).TheSG!IGinuenceisweakbutsignicant(0.03,p<0:01)inonepenetrationandnotsignicantintheotherthree.Finally,theroleoftheGlayerontheinteractionbetweenIGandSGalphaactivitieswasstudiedbyperformingconditionalcausalityanalysis.AfterconditioningouttheinuenceoftheGlayer,thepeak(10Hz)GrangercausalityoftheIGdrivingtheSGlayeris 56

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4-6 H).ThissignicantreductionisfoundinallfourpenetrationsandsuggeststhatpartofIGinuenceonSGlayerscouldbemediatedbytheGlayer. InV2,thecircuitorganizationunderlyingthealpharhythmwasfoundtobenearlyidenticaltothatofV4.ForthedatashowninFig. 3-2 ,thepowerandcoherencebetweenthebipolarLFPsignalsinIGandGlayersareshowninFigs. 4-7 Aand 4-7 B,respectively.Bothpowerandcoherencespectrahavepeaksinthealpharangewithapeakcoherenceof0.42(p<0:001)at10Hz.ThebivariateGrangercausalityspectrumrevealsthat(Figs. 4-7 CandD)theIGlayersexertasignicantcausalinuenceontheGlayerwithapeakvalueof0.46(p<0:001)at9Hz,andthecausalinuenceintheoppositedirectionisnotsignicant.TheIGlayersarefoundtobedrivingtheGlayeracrossallfourpenetrationsinbothmonkeys(Table 4-3 ).IntwopenetrationsGlayerhasaweakbutsignicant(0:03;p<0:01;0:05;p<0:01)causalinuenceontheIGlayers.TheG!IGinuenceisnotsignicantintheothertwo.ConditioningouttheSGlayeractivityresultsinasmallbutsignicantdecreaseinIG!Gcausalinuence(Fig. 4-7 DandTable 4-3 )intwopenetrations(p<0:01;p<0:01). IGandSGlayersarecoherent(0.11at10Hz,Fig. 4-7 F)withIGdrivingSGwithapeakGrangercausalityvalue0.12(p<0:001)at10Hz(Figs. 4-7 G,H).WhenactivityoftheGlayerisconditionedoutthestrengthofthedrivingfromIGtoSGdecreasessignicantly(t=11.36,p<<0:001)from0.12to0.03(Fig. 4-7 H)andthereductionisfoundtobesignicantacrossthreepenetrations(Table2).LikeinV4,theIGlayercurrentisfoundtobeconsistentlydrivingtheotherlayersinthealphafrequencyrangeacrossallfourpenetrationsinbothmonkeys(Table 4-4 ). InIT,thepreviousanalysis(Fig. 3-3 )revealedaprominent,activealphacurrentgeneratorintheSGlayersandaweak,passiveoneintheIGlayer.TheirinteractionisstudiedbysubjectingthetwobipolarLFPsignalstoabivariateMVARmodel.Thepowerspectrashowapeakaround11Hz(Fig. 4-8 A)andthecoherencespectrumhasapeakat 57

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4-8 B).TheGrangercausalityanalysisindicatesthattheSGlayeralphacurrentexertsasignicantcausalinuenceontheIGcurrentaround10Hzwherethespectralpeakvalueis0.29(p<0:001)(Fig. 4-8 C).Thecausalinuenceintheoppositedirectionisnotsignicant(Fig. 4-8 D).IncontrasttoV4andV2,theSGlayersinITarefoundtobeconsistentlydrivingtheIGlayersinthealphafrequencyrangeinallfourpenetrationsforbothmonkeys(Table 4-5 ),andtheIG!SGdrivingisveryweek. Lakatosetal. ( 2005 2007 ); Shahetal. ( 2004 ),andexcessivenoisecanleadtospuriouscausalityresults( Nalatoreetal. 2007 ).However,Grangercausalityanalysisresults,fortheV4penetrationinFig. 3-1 ,basedonsingletrialCSDdataarenearlyidenticaltothoseusingbipolarLFPdata(Fig. 4-4 ).CSDpowerspectrumatIG,GandSGlayershaveaclearpeakat10Hz(Fig. 4-4 A,E).Coherencespectrumshows(Fig. 4-4 B,F)thatthetransmembranecurrentsatGandSGlayersarecoherentwithIGlayer.GrangercausalityanalysisrevealedIGlayerdrivingbothGandSGlayers(Fig. 4-4 D,H),whereastheoppositedirections(G!IG,SG!IG)arenotsignicantatp=0.05(Fig. 4-4 C,G).ConditionalGrangercausalityanalysisrevealedthatSGlayeractivityhasnoinuenceontheinteractionbetweenIGandGlayergenerators(Fig. 4-4 D),whereasIG!SGispartlymediatedbytheGlayer. GrangercausalityanalysisusingeitherbipolarLFPorsingletrialCSD,asanindexforlocalneuronalactivityaroundagenerator,revealedidenticallaminarorganizationofthealpharhythminthecortex.Thisobservationwasfairlyconsistentacrossdierentpenetrationsforallareas. Figure 4-5 illustratestheadvantageofusingbipolarLFPorsingletrialCSD,asanindexoflocalneuronalactivity,overunipolarLFPorMUAactivityforstudyingtheinteractionbetweendierentgeneratorsoftheoscillation.MVARspectralanalysis 58

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3-1 A,showsveryhighcoherenceoverabroadfrequencyrange(Fig. 4-5 B).ThisisexpectedasunipolarLFPsaresubjecttovolumeconduction.Grangercausalityanalysisshowsbi-directionalcausalinuencebetweenIGandGlayers(Fig. 4-5 C,D),unlikeunidirectionaldrivingfromIGtoGlayerseenwithbipolarLFPandsingletrialCSDbasedanalysis.Fig. 4-4 EshowsthepowerspectrumofthemeancenteredMUAactivityatthecurrentgeneratorsatGandIGlayers.AlthoughMUAisanindexofspikingactivityofalocalgroupofneurons,thepowerspectrumdoesnotshowapeakinthealphafrequencyrange.Thesameistrueforcoherence(Fig. 4-5 F)andGrangercausalityanalysis,whichisfoundtobebidirectional(Fig. 4-5 G,H). 3-1 3-2 ,and 3-3 areshownasscatterplotsinFig. 4-9 A, 4-9 B,and 4-9 C,respectively.InFig. 4-9 A(V4),theSpearmanrankcorrelationwasr=-0.69(p<0:01).Similarly,inFig. 4-9 B(V2),theSpearmanrankcorrelationwasr=-0.56(p<0:01).SuchsignicantnegativecorrelationswerefoundinallfourV2penetrations(Table 4-6 )andthreeV4penetrations(Table 4-6 ).IntheremainingV4penetrationthecorrelationwasnegativebutdidnotreachsignicance(r=0:16;p=0:09).IncontrasttoV4andV2,alphapowerinITshowedapositivecorrelationwithauditoryRT(Fig 4-9 C.)inthreepenetrations.Intheremainingpenetrationthecorrelationwasalsopositivebutnotsignicant(r=0:18;p=0:1). Flint&Connors ( 1996 )and Silvaetal. ( 1991 )foundthatlayer5pyramidalcellsinsensorycorticesredrhythmicallyatratesappropriatefordrivingthegenerationofalphabandLFPrhythms,while Lukatch&MacIver ( 1997 )concludedthatintheentorhinalcortex,alpharhythms 59

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Schroederetal. 1995 ),arisingfromlocalinhibitorymechanismsorfrominhibitoryinputtothesupercialpyramidalcellsfromlayer5interneurons( Dantzker&Callaway 2000 ; Baccietal. 2005 ; Watts&Thomson 2005 ),asspeciedinarecentmodelofalpharhythm( Karamehetal. 2006 ). BivariateGrangercausalityanalysisindicatedthatinV2andV4,theIGlayerwasconsistentlydrivingtheGaswellastheSGlayers,suggestingthatthetruealphapacemakerwascontainedintheIGlayers.WetestedfurtherwhetherthecausalinuencefromIGtoSGlayers,revealedbybivariateGrangercausalityanalysis,couldbemediatedbytheGlayer.Asanalternativetopartialcoherenceanalysis( LopesdaSilvaetal. 1980 ; Kocsisetal. 1999 ),conditionalGrangercausalityteststhedirectionalinuencesbetweentwosignalsaftertheinuencefromathirdsignalisstatisticallyconditionedout( Geweke 1984 ; Chenetal. 2006 ; Dingetal. 2006 ).Here,conditioningouttheactivityoftheGlayerrevealedasignicantdecreaseofinuencefromtheIGtoSGlayers.However,theconditionalcausalinuenceremainedstatisticallysignicant,suggestingthatthecausalinuencefromtheIGtoSGlayershasbothadirectcomponentandacomponentmediatedbytheGlayer. 60

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Lund 2002 ; Douglas&Martin 2004 )columnprovidesthebasisforunderstandingthendings.Forexcitatoryneurons,axonsfromgranularlayercellssynapseonthepyramidalcellsinthesupragranularlayers(2/3)whichinturnsendaxonsthatsynapseoninfragranularpyramidalneurons.Infragranularpyramidalneuronscompletethecircuitbysendingaxonsintothegranularlayer.Morerecentworkhasemphasizedtheroleofinhibitoryneuronsinthegenesisofneuraloscillations( Buzsaki 2006 ).ThepertinentprojectioninthisregardistheinputofIGlayerpyramidalcellstotheinterneuronpopulationswhichinhibitneuralactivityinSGlayers.Consistentwiththeanatomicalpathways,allpairwisecoherences,IG-G,IG-SG,G-SG,arehighinthealphaband,indicatingsynchronizedinter-laminaroscillations.Ourresultsgeneralizetheinvitrondings( Silvaetal. 1991 ; Flint&Connors 1996 )totheintactbraininawakeandbehavingmonkeysinthatinV2andV4,thealpharhythmhasalocalcorticalgenerator( Steriadeetal. 1990 )withacolumnarpacemakerattheleveloflayer5. ThelaminarorganizationofalpharhythminITdieredfromthatinV2andV4.CSDanalysisrevealedaprominentalphacurrentgeneratorintheSGlayerandaweakoneintheIGlayer,butnoneintheGlayer.GiventhatbasalSGdendriticarborsareenlarged(upto400m)inIT( Elstonetal. 1999 ),theSGcurrentgeneratormostlikelyreectstheactivityofsupercialpyramidalneurons.ThelaminarLFPpowerdistributionhadamaximumoverthecurrentgenerator(Fig.3B),consistentwiththisassertion.CSD-MUAcoherencewassignicantintheSGlayers.FortheIGlayergeneratorCSD-MUAcoherencewasnotsignicant.TheoscillatorycurrentsinSGandIGlayerswerehighlysynchronous,exhibitingsignicantcoherencearound10Hz.GrangercausalityanalysesindicatedthatneuralactivityintheSGlayersconsistentlydrivesthatintheIGlayers.Itisnoteworthythattheentorhinalcortexinvitrostudyby Lukatch&MacIver ( 1997 )suggestedthattheSGlayersmightcontainthepacemakerofalpharange 61

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Elstonetal. 1999 ; Elston 2003 )andothers( Benavides-Piccioneetal. 2002 ; DeFelipeetal. 2002 )haveshownthatthemorphologyandspinedensityoftheprincipalorpyramidalcellsdieracrosscorticalareas.Specically,alongtheventralstreamofthevisualcortexthereisaprogressiveincreaseincellsize,diameterofthedendriticarbor,branchingpattern,andspinedensityoflayer3pyramidalneurons,leadingtotheirabilitytosampleinputsfromincreasinglylargenumberofsources.Althoughlayer5pyramidalneuronsshowasimilarincrease( Elston&Rosa 2000 ),thesamplingabilityofthelayer3pyramidalcellsinhigherorderareas(e.g.IT)isfurtherenhancedbyasimilarincreaseinthesizeoftheintrinsic'axonalpatches'madebyneighboringlayer3pyramidalneurons( Lundetal. 1993 ; Fujita 2002 ).Theenhancedsamplingabilityofsupercialpyramidalcells(especiallylayer3)inITleadstolargerreceptiveeldandincreasedspontaneousactivityrelativetodeeperlayers(Fig.3B).Inlowerorderareas,thepyramidalneuronsinlayer5havemoreextensivehorizontalconnectivityandstrongerintegrativeproperties( Telfeian&Connors 2003 ),supportingtheobservedhigherspontaneousactivityindeeplayersinV4andV2(Fig.1DandFig.2B).Ourresultsfurtherdemonstratethatlayerswithhigherspontaneousactivitiesalsocontainthepacemakersofthealpharhythm. Dierencesinpyramidalneuronmorphologyacrossareasarecomplimentedbydierencesindistributionandaxonalprojectionsofinhibitoryneurons( Kritzeretal. 1992 ; Defelipeetal. 1999 ),andinextrinsicconnectionstothecorticalcolumns( Rockland 2002 ).Overall,itseemsclearthattheintrinsiccircuitryofthecorticalcolumnsvariesacrossareas( Lundetal. 1981 ; Elston 2002 ),challengingtheviewthat 62

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Mountcastle 1978 ; Douglasetal. 1989 ).Specicaspectsofintrinsiccircuitrymightbeimportantforgeneratingfunctionalspecicitywithinacorticalarea.Forexample,atthetopofthehierarchyoftheventralvisualstream,theITareamightbecriticalforthedisseminationoftop-downattentionalandcontextual( Gilbert&Sigman 2007 )signalstothelowerordervisualandsubcorticalareas.ThiscouldbeaccomplishedbytheSG!IGdrivinginuencereportedhereinconjunctionwiththefeedbackprojectionsarisingfromtheIGpyramidalneurons. 4-9 Aand 4-9 B),isconsistentwiththeintermodalattentionexperimentbyFoxeetal.(1998)andtheclassicalreactivityofthealpharhythm( Shaw 2003 ).However,thealphaactivityinIT,hasanentirelydierentlaminarorganizationthanV2andV4,andapositivecorrelationwithauditoryRT(Fig. 4-9 C).Thefactthatthebehavioralcorrelatesofalpharhythmsappeardierentforthelower-andhigher-ordervisualcorticesisconsistentwiththeideathattheseareasaredierentiallyinvolvedininternally-versusexternally-directedprocessingstates,asdenedby( Ray&Cole 1985 ; Shaw 2003 ).Critically,thelaminarorganizationofthealpharhythmindierentcorticesmaybelinkedtothefunctionstheysupport. 63

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CoherenceandGrangercausalityanalysisinareaV4. PenetrationIG$GIG!GG!IG(IG!G)=SG Peakfrequencyinbrackets.NS:notsignicant. Table4-2. GrangercausalitybetweengranularandinfragranularlayersinareaV4. PenetrationIG$SGIG!SGSG!IG(IG!SG)=G Peakfrequencyinbrackets.NS:notsignicant. Table4-3. VisualareaV2:Grangercausalityanalysis PenetrationIG$GIG!GG!IG(IG!G)=SG Peakfrequencyinbrackets.NS:notsignicant. 64

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PeakGrangercausalityandcoherencevaluesinareaV2. PenetrationIG$SGIG!SGSG!IG(IG!SG)=G Peakfrequencyinbrackets.NS:notsignicant. Table4-5. GrangercausalityanalysisinIT. PenetrationIG$SGIG!SGSG!IG Peakfrequencyinbrackets.NS:notsignicant. Table4-6. Correlationbetweenalphapowerandreactiontime. PenetrationV2V4IT 10:560:430:3820:450:160:1830:380:690:7240:120:290:39 Twodistinctpatternsofconnectivityamongthreetimeseries.Apairwisecausalityanalysiscannotdistinguishthesetwopatterns. 65

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Overlaidare5secondsofbipolarLFPdata(red)fromtheinfragranularlayer,MVARmodelbasedprediction(blue),andresidual(green). FourierbasedpowerspectrumofthebipolarLFPdata,MVARmodelbasedpredictionandresidualprocessshowninFig. 4-2 66

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GrangercausalityanalysisbasedonsingletrialCSDdata.A)PowerspectraofCSDsignalsatgranular(G)andinfragranular(IG)layers.B)CoherencespectrumbetweenthetwoCSDsignalsin(a).C)andD)GrangercausalityspectrabetweenGandIG.E)PowerspectraoftheCSDsignalsatsupragranular(SG)andIGlayers.F)CoherencespectrumbetweentheCSDsignals.G)andH)GrangercausalityspectrabetweenSGandIG. 67

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GrangercausalityanalysisbasedonunipolarLFPandMUAdata.A)PowerspectraofunipolarLFPsignalsatgranular(G)andinfragranular(IG)layers.B)Coherencespectrumbetweenthetwounipolarsignalsin(a).C)andD)GrangercausalityspectrabetweenGandIG.E)PowerspectraoftheMUAsignalsatsupragranular(SG)andIGlayers.F)CoherencespectrumbetweentheMUAsignals.G)andH)GrangercausalityspectrabetweenSGandIG. 68

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GrangercausalityanalysisinareaV4.A)PowerspectraofbipolarLFPsignalsatgranular(G)andinfragranular(IG)layers.B)CoherencespectrumbetweenthetwobipolarsignalsinA.C)andD)GrangercausalityspectrabetweenGandIG.Herex!ydenotesxdrivingyand(x!y)=zdenotesxdrivingyafterconditioningoutz.E)PowerspectraofthebipolarLFPsignalsatsupragranular(SG)andIGlayers.F)Coherencespectrumbetweenthetwobipolarsignals.G)andH)GrangercausalityspectrabetweenSGandIG. 69

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GrangercausalityanalysisinareaV2.A)PowerspectraofbipolarLFPsignalsatgranular(G)andinfragranular(IG)layers.B)CoherencespectrumbetweenthetwobipolarsignalsinA.C)andD)GrangercausalityspectrabetweenGandIG.Herex!ydenotesxdrivingyand(x!y)=zdenotesxdrivingyafterconditioningoutz.E)PowerspectraofthebipolarLFPsignalsatsupragranular(SG)andIGlayers.F)CoherencespectrumbetweenthetwobipolarsignalsinE.G)andH)GrangercausalityspectrabetweenSGandIG. 70

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GrangercausalityanalysisinareaIT.A)PowerspectraofbipolarLFPsignalsatgranular(G)andinfragranular(IG)layers.B)CoherencespectrumbetweenthetwobipolarsignalsinA.C)andD)GrangercausalityspectrabetweenGandIG.Herex!ydenotesxdrivingyand(x!y)=zdenotesxdrivingyafterconditioningoutz.E)PowerspectraofthebipolarLFPsignalsatsupragranular(SG)andIGlayers.F)CoherencespectrumbetweenthetwobipolarsignalsinE.G)andH)GrangercausalityspectrabetweenSGandIG. ScatterplotsshowingstrongcorrelationofalphapowerwithreactiontimeinvisualareasV2(A),V4(B)andIT(C).Insets:Spearmanrankcorrelationcoecient.Linearleast-squaresbesttstothedataaresuperimposed. 71

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Jones 2001 ).Collateralsoftheseaerentsalsomakeweakprojectionstolayer6(Fig. 5-1 ).Incontrasttothecorecells,matrixcellssenddiuseprojectionstolayer1and2ofthestriatecortex.Feedbackfromthestriatecortextothe(core)relaycellsoriginatefromlayer6ofthesamecorticalcolumntowhichtheysendaerentinput.Thistopographicrelationshipbetweentherelaycellsandinfragranularlayersofthestriatecortexisthoughttobeinstrumentalinestablishingcoherentoscillationsbetweenthethalamusandthecortex( Jones 2002 ).Theaforementioneddiuseprojectionsofthematrixcellsandthefeedbackfromlayer5neurons(Fig. 5-1 ),inthestriatecortex,tothematrixcellsinthepulvinarnucleusandLGNarethoughttobeinvolvedinsustaininglargescalesynchronybetweenthethalamusandcortex. Anumberofinvivostudieshavereportedsynchronousalphaoscillationsbetweenthethalamusandthecortex( LopesdaSilvaetal. 1973a ; Rougeul-Buser&Buser 1997 ).Althoughcorticalslicestudies( Silvaetal. 1991 )haveimplicatedlayer5pyramidalneuronsasthepacemakersofalpharhythmsinthecortex(seeSect. 3.1 ),recentstudiesusingslicepreparationsofLGNhaveidentiedasubsetofcorecellsthathavetheabilitytointrinsicallyoscillateinthealphafrequencyrange,throughhightthreshold(HT)bursting( Hughesetal. 2004 ).Thisisconsideredtobeapotentialmechanismbywhichthethalamuscanpromotealphaoscillationsinthecortex( Hughes&Crunelli 2005 ; Lorinczetal. 2008 ). 72

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3.2 ).Incondition1,bothauditoryandvisualstimuliwerepresentedwhilethesubjectpayedattentiontothevisualstimuli.Incondition2,thesubjectpayedattentiontotheauditorystimuliandnovisualstimuluswaspresented.Attentionalmodulationofthelaminarorganizationofthealpharhythmandthalamocorticalinteractionswerestudiedbyanalyzingtheongoingdataduringthetwoconditions.Theongoingdataduringcondition1consistedof200msepochsofprestimactivitypriortothepresentationofthevisualstimulus. Figure 5-2 Ashowsthelaminarorganizationofthealphacurrentgenerators,whilethesubjectwaspayingattentiontotheauditorystimuli,inarepresentativepenetrationinV1.AlphacurrentgeneratorscanbeseenintheIG,GandtheSGlayers.Specically,astronggeneratorcanbeattheborderbetweenlayers5and6.Thisgeneratorisoutofphasewiththegeneratoratlayer4C.ThisrelationshipissimilartothatseeninCSDdistributionevokedbyvisualstimulation(Fig. 5-2 B),suggestingthatthegeneratorsatlayers5/6and4CcouldbetheresultofdrivinginputfromLGN.However,thereareessentialdierences.First,therelationofthesegeneratorswiththeeldpotentialsisdierentfromongoingtoevoked.whiletheERPsshowpolarityreversalatlayer4CintheevokedCSD(Fig. 73

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B),nosuchpolarityreversalisseeninPRAT-LFP(Fig. 5-2 A).Thisdierenceisalsotrueforsingletrialongoingandevokedpotentials(Fig. 5-3 ).Second,likeinV2andV4,theinfragranularlayershavesignicantlyhigheralphapowerthantheotherlayers(Fig. 5-4 A).Thesedierencessuggestthatthealphacurrentgeneratoratlayer5/6hasanintracorticalcomponentratherthanbeingtheresultofthalamicinputtotheselayers. ThePRAT-CSDdistributionwasconsistentacrossallpenetrationsinbothmonkeys(Fig. 5-5 ).Otherthanlayer5/6and4C,alphacurrentgeneratorscanalsobeseenatlayer1/2andattheborderbetween4Aand3B(seeFig. 5-5 ).Thesegeneratorsareinphasewiththeoneinlayer5/6.TheCSD-MUAcoherencespectrum,forthepenetrationshowninFig. 5-2 A,wasfoundtobesignicantinthealphafrequencyrangeatallthecurrentgenerators(Fig. 5-4 B),suggestingthattheseareactivecurrentgeneratorsandareviablecandidatesforpacemaking.TheCSD-MUAphasespectrum(Fig. 5-4 C)isoutofphasewiththeMUAactivityatallelectrodecontacts,implyingthatincreaseinMUAcorrespondswithsinksandhencedepolarizationofthelocalneuronalensemble. Figure 5-6 showstheattentionalmodulationofalphaamplitudeacrossthelaminae.Itcanbeseenthatswitchingattentionfromtheauditorytothevisualmodality,broughtasignicantdropinalphaamplitudeacrossalllayers.Thisdropisespeciallypronouncedinthegranularandtheinfragraularlayers.PRAT-CSDdistributiondidnotshowaqualitativedierencebetweenthetwoattentionalconditions.Alphacurrentgeneratorscouldbeseeninlayers5/6,4C,3Band1/2,likeinFig. 5-2 A.AscanbeinferredfromFig. 5-6 theamplitudeoftheCSDshowedmodulationwithattention.Figure 5-7 showsthemodulationduetoattentiononsingletrialCSDamplitudeacrossdierentlaminae.ItcanbeseenthatCSDamplitudeshowedgreatestdropinthegranularandtheinfragranularlayers.CSD-MUAatdierentgeneratorsforthepenetrationshowninFig. 5-2 Aalsoshowedadecreasewithattention(Fig. 5-8 ). 74

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4.5 )tostudytheinteractionbetweendierentgenerators.Figure 5-9 showsthecoherenceandtheGrangercausalityspectrafortheinteractionbetweenthegeneratorinlayer5/6withthosein4C,3Band1/2.ThesingletrialCSDpowerspectraatgenerators5/6and4Cexhibitedclearpeaksat10Hz(Fig. 5-9 A).Thecoherencespectrumhasapronouncedpeakat10Hz,wherethepeakvalueis0.62(p<0:001),asshowninFig. 5-9 B.Thissuggeststhatthealphacurrentsintheselayersarehighlysynchronized.TheGrangercausalityspectrumof5=6!4Cshow(Fig. 5-9 D)astrongpeakat10Hzwithapeakvalue0.33(p<0:001).Thecausalityintheotherdirection4C!5=6wasalsosignicant(Fig. 5-9 C)withapeakvalue0.13(p<0:001)at11Hz,suggestingthatalphacurrentgeneratorsinlayers4Cand5/6haveabidirectionalrelationship.Thisresultwasconsistentacrossallpenetrations(Table 5-1 )Moreover,conditioningoutactivityoflayer3Bdidnotaect4C!5=6andresultedinasmallbutsignicantdrop(0.33to0.28,p<0:01).However,inallotherpenetrationsconditioningoutlayer3BdidnotresultinasignicantchangeintheGrangercausalityvalues(Table 5-1 ),suggestingthat3Bhasnoinuenceonthebidirectionalrelationshipbetween4Cand5/6.Incontrasttothebidirectionalrelationshipbetween4Cand5/6,layer5/6wasfoundtobeconsistentlydrivingboth3Band1/2layergenerators(Fig. 5-9 G,H,K,LandTables 5-2 5-3 ).Conditioningoutlayer4Cactivityresultinsignicantdropin5=6!3Baswellas5=6!1=2(Tables 5-2 5-3 ).Thisisanexpectedresultas4Cand5/6haveabidirectionalrelationship.Layer4Cwasalsofoundtobeconsistentlydrivingboth3Band1/2(Fig. 5-10 ).Andconditioningout5/6resultedinasignicantdropintheGrangercausality 75

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5-10 D,H).Theseresultsindicatethatlayer4Cand5/6togetherplaytheroleofthealphaoscillationpacemakerinthestriatecortex. TostudytheinuenceoftheLGNonthealphacurrentgeneratorsindierentlayersofV1weanalyzedlaminardatarecordedsimultaneouslywithaV1penetration.ThelaminarelectrodeusedtorecordLGNactivitywasofthesamekindasusedinthecortex.Thepatternofevokedpotentials(notshown)elicitedbyvisualstimulationindicatedthattheelectrodesampledactivityfromtheparvocellularlayers.WesubjectedtheLFPrecordingfromLGNandbipolarderivationsfromV1tomultivariatespectralanalysis.FortheV1penetrationinFig. 5-2 Athethreebipolarsignalsare:SG=LFP(contact4)-LFP(contact1),G=LFP(contact8)-LFP(contact5),andIG=LFP(contact13)-LFP(contact10).Figure 5-11 showsthecoherencespectrabetweeneachoftheLFPcontactsinLGNandbipolarderivationsinV1.ItcanbeseenthateachoftheLGNcontactshassignicant(p<0:01)coherencewiththesupragranularactivityinV1,inthealphafrequencyrange.Thecoherenceatthegranularandtheinfragranularlayerswasfoundtobenotsignicant.AlthoughweseeasignicantcoherencebetweenLGNandV1,Grangercausalityspectradidnotshowanysignicantdrivingineitherdirection. Tostudytheaectsofattentionontheintracorticalcircuitsinvolvedinthegenerationofalpharhythm,wecomparedthecoherenceandGrangercausalityspectraduringtheattendvisualconditiontothatoftheattendauditoryconditiondescribedabove.DuringattentiontothevisualmodalitythecoherenceandGrangercausalityspectra,showninFig. 5-9 and 5-10 showedsignicantdrops(Fig. 5-12 and 5-13 ).However,attentiondidnothaveanyqualitativechangeonthepatternofinteractionsbetweendierentalphacurrentgeneratorsinV1,i.e.,layer5/6and4Cstillshowedabidirectionalrelationship(Figs. 5-12 B, 5-13 B),andwerefoundtobedrivingthegeneratorsin3Band1/2layers.AttentiontothevisualmodalityalsoresultedinadropintheamplitudeofthecoherencespectrumbetweenLGNandthesupragranularlayersofV1(Fig. 5-14 ). 76

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5-2 A)suggeststhatthealpharhythminthestriatecortexistheresultoftheinterplaybetweentheactivityoftheselayers.Thereciprocalanatomicalprojections( Callaway 1998 )betweenlayer4Cand5/6couldbethebasisforthisinterplay.Sincelayer4CisthemainrecipientoftheaerentinputfromtheLGN,itiseasytothinkofthisintracorticalinterplayastheonebetweenthalmocorticalandintracorticalmechanisms.Signicantcoherence(Fig. 5-14 )betweenLGNandthesupragranularlayersofthestriatecorteximplicatethediuseprojectionsfromthematrixcells( Jones 2002 )insustainingthalamocorticalsynchrony.However,thelackofcoherenceandGrangercausalitydrivingbetweenLGNandthegranularlayersdoesnotnecessarilyimplythatLGNhasnoinuenceonthegranularlayersasthepresentrecordingsareveryunlikelytobetopographic. Thesignicantdecreaseinalphaamplitude(Fig. 5-6 )tovisualattentionisconsistentwiththetraditionalunderstandingofthealpharhythm( Niedermeyer 1997 ).Moreover,thebiggestdecreaseinsingletrialCSDamplitude(Fig. 5-7 )isseeninlayers4Cand5/6supportingthehypothesisthatalpharhythmistheresultoftheinterplaybetweentheactivitiesattheselayers.ThesignicantdecreaseinLFPandsingletrialCSDamplitudeattheselayersisaccompaniedbyasimilardropincoherenceandGrangercausalityspectrum(Fig. 5-12 A).However,theinteractionpatternbetweendierentalphacurrentwasqualitativelysimilarbetweenthetwoattentionalconditions. 77

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Grangercausalityresultsbetweenlayers4Cand5/6ofthestriatecortex. Penetration5=6$4C5=6!4C4C!5=6(5=6!4C)=3B Peakfrequencyinbrackets.NS:notsignicant. Table5-2. Interactionbetweenlayers3Band5/6ofthestriatecortex. Penetration5=6$3B5=6!3B3B!5=6(5=6!3B)=4C Peakfrequencyinbrackets.NS:notsignicant. Table5-3. VisualareaV1:Grangercausalityresultsbetweenlayers1/2and5/6. Penetration5=6$1=25=6!1=21=2!5=6(5=6!1=2)=4C Peakfrequencyinbrackets.NS:notsignicant. 78

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IllustrationofanatomicalconnectivitybetweenthalamusandV1 79

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Ongoingtoevoked:currentsourcedensity.A)PRAT-CSDshowedasacolorcodedplot.PRAT-LFPareoverlaid.B)EvokedCSDforthesamepenetration.ERPsareoverlaid. 80

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Laminarrecordingofacontiguousepochofongoingandevokedactivity 81

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AlphapowerdistributionandCSD-MUAcoherence.A)Laminardistributionofthepeak(10Hz)LFPpoweracrossallpenetrationsinbothmonkeys.B)CSD-MUAcoherencespectraforthepenetrationshowning. 5-2 AC)PhasespectrumofCSD-MUAcoherence.ColorcodeissameasinB PRAT-CSDandPRAT-LFPindierentpenetrations. 82

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Attentionalmodulationofalphaamplitudeinlaminareldpotentialsacrossdierentpenetrations AttentionalmodulationofCSDamplitudeacrossdierentlayersinV1 AttentionalmodulationofCSD-MUAcoherenceforthepenetrationshowninFig. 5-3 83

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SingletrialCSDbasedGrangercausalityanalysisforthepenetrationshowninFig. 5-3 .A,EandIshowthepowerspectrumofthesingletrialCSDatlayers5/6,4C,3Band1/2.B,FandJshowcoherencespectrum.C,D,G,H,KandLshowGrangercausalityspectrum.Herex!ydenotesxdrivingyand(x!y)=zdenotesxdrivingyafterconditioningoutz. 84

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SingletrialCSDbasedGrangercausalityanalysisforthepenetrationshowninFig. 5-3 .OtherconventionsarethesameasinFig. 5-9 85

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CoherencespectrumbetweenLGNandV1 86

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AttentionalmodulationofinteractionbetweeninfragranularandothergeneratorsforthepenetrationshowninFig. 5-3 87

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AttentionalmodulationofinteractionbetweengranularandothergeneratorsforthepenetrationshowninFig. 5-3 88

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Attentionalmodulationofthalamocorticalcoherence 89

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Tolhurstetal. 1983 ; Vogelsetal. 1989 ; Guretal. 1997 ; Shadlen&Newsome 1998 ; Leeetal. 1998 ; Truccoloetal. 2002 ).Oneformofthevariabilityistheresponselatencyjitter,i.e.,theonsetofresponsetorepeatedpresentationsofthesamestimuluscanvaryfromtrialtotrial( Richmond&Optican 1987 ; Munoz&Wurtz 1993 ; Hapleaetal. 1994 ; Seidemannetal. 1996 ; Gawneetal. 1996 ; Raigueletal. 1999 ).Anotherformofvariabilityisthevariableshapeoftheneuralactivation(e.g.trial-to-trialvariationinactivationamplitude)followingastimulus( Bach&Kruger 1986 ; Vogelsetal. 1989 ; Arielietal. 1996 ).Measuresthatarebasedonaveragingacrosstrials,suchastheperi-stimulushistogram(PSTH)andcross-correlogram,canbeadverselyaectedbysuchtrial-to-trialvariability.Forexample,areductioninPSTHamplitude,asonevariesanexperimentalparameter,mayhavetwocontributingfactors.First,theevokedresponseissmalleroneachindividualtrial.Second,theevokedresponseremainsthesamebutthelatencyjitteronatrial-by-trialbasisisincreased.ThesetwosituationsmayentaildierentphysiologicalinterpretationsofthereducedPSTH.Ifaresearcherisinterestedinthetimewhenthemaximumringoccurs( Kassetal. 2003 ),thenthePSTHpeaktimemaynotbeagoodestimate,sincetheactualmaximumringtimevariesfromtrialtotrial.Inaddition,correlatedvariationsbetweendierentneuronsineitheramplitude(excitability)andlatencyoverrepeatedstimuluspresentationscanresultinpeaksinthecross-correlogram( Brody 1999b ).Suchpeaks,withoutanunderstandingoftheirorigin,maythenbemisconstruedasevidenceforspike-spikesynchronybetweendierentneurons.Ontheotherhand,singletrialparameterssuchasamplitudescalingfactorsandlatencyshiftsarethemselvesinterestingphysiologicalvariables,providinginformationforunderstandingmechanismsof 90

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DiCarlo&Maunsell 2005 ; Nawrotetal. 2003 )toinvestigatewhethertheringactivityofaneuronencodesmotorpreparationormotorexecution.2.Howongoingoscillationaectsstimulusprocessingisofmuchinteresttoneuroscientists.Forexample,howthephaseandamplitudeofthealphaoscillationpriortothestimuluspresentationaectsthelatencyandintensityofactionpotentialringinneuronscanaidinourunderstandingoftheroleofoscillatoryactivityininformationprocessing. Biophysically,trial-to-trialvariabilityinringisthoughttobe( Arielietal. 1996 )theresultofrandomuctuationsintherestingpotentialofacell.Suchuctuationsinrestingpotentialsmightbeinducedbyvariationsintheongoingactivityinthenetworkinwhichtheneuronsareembedded.Itthusappearsthatvariabilityinneuronalringisquiteinevitableandthisproblemhasbeguntodrawresearchattention.However,themajorityofthepreviouslypublishedmethodsforestimatingsingle-trialparametersinneuronalspiketrainshavefocusedoneithertheamplitudevariabilityorthelatencyvariability.( Brody 1999a )proposedamethodforestimatingtheamplitudescalingfactorswhichreliesonanestimateofthebackgroundringratefromaveragingthepre-stimulusactivities.Althoughthealgorithmissuccessful,itrequiresthattherebenolatencyvariabilityinresponses. Nawrotetal. ( 2003 )developedanalgorithmforestimatingthetrial-by-trialdierencesinthetemporallatencyofthespikeresponses.Thespiketrainsarerstconvolvedwithakerneltogetadynamicrateproleforeachtrial.Relativelatenciescorrespondingtoanoptimalalignmentoftrialsarethenestimatedbymaximizingthetotalpairwisecorrelationsofthecontinuousrateproles. Baker&Gerstein ( 2001 )proposedaBayesianmethodforestimatinglatencyvariationsona 91

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Hereweproposeacomprehensiveframeworkthatcanserveasatheoreticalguidelineformodelingandestimatingparametersofsingle-trialspiketrainsrecordedinthesensoryormotorevokedresponseparadigms.Ourmethodcloselyfollowsthatdescribedby Truccoloetal. ( 2003 )andby Knuthetal. ( 2006 )forestimationofsingle-trialmulticomponentevent-relatedpotentials(ERPs).Theringrateoveratrialismodeledbyafamilyofrateproleswithatrial-invariantwaveformbuttrial-dependentamplitudescalingfactorsandlatencyshifts.WeformulateourestimationprobleminaBayesianframeworksothatfuturemodicationscanbeeasilymadetoincorporatenewlyacquiredpriorinformation.Here,byassigninguniformpriorsforthemodelparameters,ourapproachisequivalenttoamaximumlikelihoodsolution.Viaaniterativexed-pointalgorithm,thevaluesofthesingle-trialamplitudeandlatencyparametersareobtainedasvaluesthatmaximizetheposteriorprobability(MaximumaPosteriori,orMAP,solution).Wedemonstratetheeectivenessofthealgorithmonsyntheticdata,aswellasdataobtainedfromintracranialrecordingsinthemacaqueperformingasensorimotortask. Brody 1999b ; Nawrotetal. 2003 ).Ageneralmodelcapturingboththeseaspectsofvariabilitycanbewrittenas 92

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Azouz&Gray 1999 ; Kisley&Gerstein 1999 ; Bach&Kruger 1986 ; Arielietal. 1996 ).Withthehelpofthisassumptionourmodelreducesto whereg(t)includesboththespontaneousandevokedactivity. Sivia&Skilling 2006 ).Earlierworkshavedescribedsimilarsingle-trialestimationtechniques( Truccoloetal. 2003 ; Knuthetal. 2006 ),whicharecloselyrelatedinformtosourceseparationproblemsinneuroscience( Knuth 1999 2005 ; Rowe 2002 ).AccordingtoBayestheorem,theposteriorprobabilityofmodelparametersMgivendataDandpriorinformationIcanbewrittenas Forthespiketrainmodeldenedintheprevioussection,theposteriorprobabilitybecomes 93

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Nowforasingletrialwiththesequenceofspiketimest1;t2;::::;tnintheinterval(0;T),thelikelihoodisgivenby( Jaynes 1990 ; Gregory 2005 ; Kassetal. 2003 2005 ) ThislikelihoodfunctionfollowsnaturallyifweassumethatthespiketrainsaregeneratedbyaninhomogeneousPoissonprocess.FromaBayesianperspective,thederivationoftheabovelikelihoodusesprobabilitytheoryaslogic( Jaynes 1990 ; Gregory 2005 ).Thelatterconsiderationcanbeinvokedwhentheresearcherisfacedwithanitesetoftrialsandisuncertainaboutthefrequencydistributionoveralargesetofidenticallyrepeatabletrials.Foranensembleofrecordedtrials,sincetheprobabilityweassignfortheoccurrenceofaspikeinatrialisnotinuencedbyourknowledgeoftheoccurrenceornonoccurrenceofspikesinanyothertrial,wecanwritethelikelihoodofthedataastheproductoftheindividuallikelihoods,i.e., Intheabsenceofdetailedknowledgeabouttheparametersg;farg;frgwetaketheirpriordistributiontobeuniform,withappropriatecutosreectingphysiologicallyreasonablerangesofvalues, 94

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Takingthelogarithmoftheposterioryields ln(P)/ln[RYr=1exp(ZT0r(t)dt)nrYi=1r(tir)](6{9) Lettingtheright-handsidebedenotedbyQwethenhave Thereareseveralmethodsbywhichonecanevaluatetheposteriorprobability.Theserangeincomplexityfromthemoststraightforwardmaximumaposteriori(MAP)solutiontothemoresophisticatedclassofMarkovchainMonteCarlo(MCMC)methods.TheMAPsolutionseekstoidentifythesetofparametervaluesthatmaximizestheposteriorprobability.Inthissense,itreturnsthemostprobablesolution.TheMCMCmethodsareaclassofmethodsthatsampletheposteriorprobabilityandprovideinformationaboutitsgeneralshapeandextentoftenviatherstandsecondmoments(meanandcovariance).Inthepast,MCMCmethodswerecomputationallyintensivewhenappliedtoproblemswithalargenumberofmodelparameters,aswehavehere.SincecomputershaveincreasedinspeedandMCMCcomputationaltechnologieshaveadvanced,wearecurrentlylookingintoapplyingsomeofthesenewtechniques.However,inthepresentworkwepresentafastandpracticalalgorithmthatreturnstheMAPsolutionbywayofaniterativexedpointtechnique. Oursignalmodelisrathercomplexasitconsistsoftherateprole,thesingle-trialamplitudescalingfactorsandthesingle-triallatencyshifts.Sincetherateprolecanaccommodateanoverallamplitudescaleandalatencyshift,ourmodelisinherentlydegenerate.Tosolvethisproblem,wesimplyconstraintheaverageamplitudescaletobe 95

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TheMAPsolutioncanbefoundbycalculatingthepartialderivativesofthelogarithmoftheposteriorprobabilitywithrespecttoeachofthemodelparametersandsettingthepartialderivativestozero.Thisleadstoapracticalandstraightforwardestimationalgorithm.Toproceedfurtherwemakeapracticalassumption.Wedividethethetimeintervaloftheexperiment(0;T)intosmallintervalsofsize'b'andassumethatthereisnosignicantchangeintherateofringwithineachinterval.Letthebinsbedenedbytheintervals(tj;tj+1);j=1;:::;K1;t1=0;tK=T.Thenbytheabovepiecewiseconstantassumption Thistransformstheproblemintooneofspikecountswhichiswidelyusedinpractice.ThenQbecomes whereyr;jisthespikecountinthejthbinoftherthtrial.Notethattheintegralhasbeenapproximatedbyasummationinthersttermontheright-handside.UsingEq.( 6{2 )weobtain TherstpartialderivativeofQwithrespecttog(t)foraspecictimepointtis @g(t)=RXr=1(bar)+RXr=1(yr;j+int[r=b]1 whereint[r=b]denotestheintegerpartoftheenclosedvariable.Setting@Q @g(t)=0gives 96

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Similarly,weobtaintheestimateoftheamplitudescalingfactorarbysetting@Q @ar=0,namely, @ar=bKXj=1g(tjr)+KXj=1(yr;j1 whichcanbesolvedtoyield Notethatthenumeratoristhetotalnumberofspikesinthetrial. Forthelatencyshiftparameters,setting@Q @r=0leadstothefollowingequation whereg0(tjr)isthetimederivativeofg(tjr).Thesolutionforrismoredicultsincerappearsintheargumentoftheratefunction.Again,intuitioncanbegainedbydirectlyexaminingtheconditionsforthemaximizationofthelogarithmoftheposterior.Asrisvaried,onlythesecondterminEq.( 6{12 )isrelevantforthemaximizationoftheposterior.Thersttermisrelatedtotheareaundertheratefunctionwhichisindependentofr.ThesecondterminEq.( 6{12 )isnothingbutthecross-correlationbetweenthespikecountandtherateprole,consideringthatlogarithmisamonotonicfunction.Thusweestimaterby ItisinterestingtonotethatthelatencyestimationprocedurehereissimilartoWoody'smatchedlteralgorithmforlatencyestimationofevent-relatedpotentials( Woody 1967 ). 97

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(0)Atm=0,theinitialvaluefortheamplitudescalingfactorsandthelatencyshiftsaresettoa0r=1,0r=08r.ThePSTHistakenastheinitialestimationforg0(t).Afterthisinitialization,eachiterationconsistsofthefollowingfoursteps. (1)Foralltrials,estimatethesingletriallatencyshiftsaccordingto (2)Estimatetherateproleaccordingto (3)Foralltrialsestimatetheamplitudescalingfactorsaccordingto (4)Incrementtheiterationindex:m=m+1;repeat(1)through(3)forMiterations. Theiterationprocedureisstoppedoncethetheestimatesfromsuccessiveiterationsdonotimprovebymorethan1%. 98

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6.5.1ApplicationtoSimulatedData NotethattheGaussianfunctioniscenteredat500msoverthetriallengthwhichwassetto1000ms.Thelatencyshiftsforeachtrialweresampledfromauniformdistributionintheinterval(200ms;200ms).Theamplitudescalingfactorsweresampledfromauniformdistributionintheinterval(5;15).Themeanamplitudescalingfactoristhus10whichwillbeusedbelowtocalculatethetheoreticalmeanratefunction.Figure 6-1 Ashowsarasterplotof20trialsoutatotalof50generated,withparametersB=1Hzand=80ms.ToobtainthePSTH,anappropriatebinwidthneedstobechosen.BinwidthsthataretoolargecanresultinpoorresolutionoflatenciesandbinwidthsthataretoosmallcanresultinanoisyestimateofPSTHwhenrelativelyfewspikesarepresentinatrial.Wechooseanoptimalbinwidthof10msaftersomepreliminaryanalysis.Figure 6-2 BshowsthePSTHforthedatainFig. 6-1 A.Thetheoreticalratefunctionisplottedasasmoothcurve.(Wenotethat,intheabsenceoflatencyvariability,thetheoreticalmeanringratefunctionis10timesthefunctioninEq.( 6{23 ).)Aswecansee,duetotrial-to-triallatencyvariability,thePSTHinthiscaseisapoorestimateofthetheoreticalratefunction.Inparticular,theestimatedmeanpeakringrateis30%smallerthantheactualmeanpeakringrate. Nextweappliedthealgorithmdescribedintheprevioussectiontothesyntheticdata.Theinitialvaluesofthesingle-triallatencyshiftswereinitializedto0mswhiletheinitial 99

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6-1 Bwasusedastheinitialestimateoftheratefunction.Single-triallatencyshiftsandamplitudescalingfactorswereobtainedafterthealgorithmwasappliedtothedatasetfor5iterations.Figure1CshowstherasterplotafterrealigningthetrialsaccordingtotheestimatedlatenciesbyEq.( 6{19 ).Figure 6-1 DgivesthePSTHforthedatainFig. 6-1 C.ThenewPSTHismuchsharperthantheinitialestimationandcloselyfollowsthetheoreticalrateproleusedtogeneratethesyntheticdataset. Theperformanceofthealgorithmwasevaluatedbycomparingtheestimatedlatencyshiftsandamplitudescalingfactorstotheiroriginalcounterparts.Figures 6-2 Aand 6-2 BshowtheplotsoftheestimatedlatencyshiftsandtheamplitudescalingfactorswiththeiractualvaluesforthedatasetshowninFigure1A.Theaccuracyoftheestimateswasevaluatedbycalculatingthecorrelationcoecientwiththeiractualvalues(seeFigs. 6-2 C-F). Theperformanceofthealgorithmwasalsoevaluatedforvariousvaluesoftheparameters,denotedsd(standarddeviation),andB.ThereliabilityoftheestimatesofthelatencyshiftsdeterioratedasweincreasedorB(Figs. 6-2 Cand 6-2 E),butthealgorithmcontinuedgivingreliableestimatesfortheamplitudescalingfactorsovertheparameterrangeexamined,asshowninFigs. 6-2 Dand 6-2 F. Gardner 2004 ).Inthisdataset,collectedby Gardneretal. ( 1999 ),single-unitrecordingsweremadefromthepostcentralgyrushandareainrhesusmonkeystrainedinaprehensiontask.Theanimalsweretrainedtograsp,lift,hold,andlowerobjectsofspecicshapeatspeciedlocationsintheworkspace.Uponcuetheanimalsapproachedandgraspedtherewardedobject,andthenliftedandheldtheobjectbrieybeforerelaxing.Figure 6-3 Ashowstherasterplotof26trialsofaneuron 100

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Gardneretal. 1999 )identiedas`tunedtoactivateoncontact.'Heretimezeroindicatesthegraspcompletiontime.Onaverage,contactoccurredaround-152ms. Gardneretal. ( 1999 )foundthatthecontacttunedneuronswerethemostfrequentlyobservedtype.Theseneuronswerefoundtoactivateatcontact,ringatsignicantlyhigherratesduringthepositioningofthehandupontheobjectandgraspformationcomparedtotheapproachorsubsequentgraspstages.Anintervalof1000mswhichincludedtheapproach,contactandgraspstagesofthebehavioraltaskwaschosenforanalysis.Thisintervalisshorterthantheavailabledatalength,allowingustoavoidanyendeectsresultingfromtheshiftingoftrialsforlatencycorrection.Thedatawerebinnedintointervalsofsize50ms,andthePSTHwasthencomputedandshowninFig. 6-3 B.Wecouldnotchooseasmallerbinsizebecausethenumberofspikesineachtrialissmall. Thesingle-triallatencyshiftandamplitudescalingfactorwereestimatedbytheiterativealgorithmpresentedabove.Theiterationswerestoppedoncetheestimatesfromsuccessiveiterationsdidnotimprovebymorethan1%.Inourinvestigationsonbothsyntheticandexperimentaldatatheestimatesquicklyconvergedinapproximately5iterations.Figure 6-3 Cshowstherasterplotofthespiketrainsaftershiftingfortheestimatedlatencies,andthecorrespondingPSTHisgiveninFig. 6-3 D.(WenotethattimezeroinFigs. 6-3 Cand 6-3 Disusedfordisplaypurposesandisnolongeranindicationofthegraspcompletiontimeaswehaveshiftedeachtrialaccordingtoitslatencyestimation.)Asexpected,theratefunctioninFigure3Dissharperandsignicantlyhigher,whichissimilartothatseeninoursimulationstudyinFig. 6-1 .Thisisanindicationthatthereistrial-to-triallatencyvariabilityintheoriginaldataandouralgorithmcorrectlycapturesthelatencyoneachindividualtrial. Figures 6-3 Eand 6-3 Fdisplaythehistogramsofestimatedsingle-triallatencyshiftsandamplitudescalingfactors,respectively.Thesehistogramsgivetherangeofvariabilityofthesingle-trialamplitudeandlatencyoftheratefunction.Forexample,thesingle-trialamplitudeoftheratefunctionvariesasmuch50%.Thelatencyvariability 101

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Gardneretal. 1999 ).Thissuggeststhat,althoughtheneuronisidentiedastunedtoactivateoncontact,itsringrateproleexhibitsvariabilityfromtrialtotrialwithrespecttothecontacttime,afactcapturedbyourspiketrainmodel,Eq. 6{2 .Furtherphysiologicalmeaningsofthesesingletrialparameterscanbeexaminedifvariousbehavioralvariablesareavailableforacorrelationalanalysis( Truccoloetal. 2003 ). Gerstein&Kiang 1960 ; Richmond&Optican 1987 ; Kassetal. 2003 ; Lee&Mumford 2003 ).Typically,thetemporalproleofringrate,thePSTH,iscomputedbyaveragingacrosstrials.Thetrial-to-trialvariabilityinneuronalspiketrainscanadverselyaectthisaverage.Single-trialanalysis,suchastheonepresentedhere,mayprovideawaytohelpmitigatesuchadverseeects.Methodsforestimatingsingle-trialparametersofneuronalspiketrainshaveappearedinthepast.Ourtechniquediersfromthepreviousmethodsinanumberofsignicantways.BakerandGerstein'smethod(2001)isbasedontheexplicitassumptionthattheinterspikeintervalsaregammadistributed.ThegammaparameterisestimatedbytheinterspikeintervaldistributioninsteadoftreatingitasaparameterintheBayesianinferenceframework.AresearcherseldomhastheknowledgethatthespiketrainsrecordedoveranitenumberoftrialsaregammaorPoissondistributed.Ourmethoddoesnotmakesuchspecicassumptions.Furthermore,theyassumedthattheringratefollowsasteplikeresponseprole.Thisisnotveryrealisticforactualneuronalresponses.Brody'smethod(1999)wasformulatedonintuitivegrounds.Itreliesonan 102

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6{2 )rendersthisstepunnecessary.ThepartofBrody'salgorithmforestimatingtheamplitudescalingfactorsduringthepost-stimulusperiodissimilartoours.Nawrotetal.'smethod(2003)estimatesthetrial-by-trialdierencesinthetemporallatencyofthespiketrainresponses.Thespiketrainsarerstconvolvedwithakerneltogetadynamicrateproleforeachtrial.Relativelatenciescorrespondingtoanoptimalalignmentoftrialsarethenestimatedbymaximizingthetotalpairwisecorrelationsofthecontinuousrateproles.Ouralgorithmsuggestsanimprovementintheprocedureproposedby Nawrotetal. ( 2003 ).Insteadofcalculatingpairwisecorrelationsbetweenthesingletrialrateproles,weformulatedamatched-lterprocedure,similartothatproposedby Woody ( 1967 )forEEGs,whicharisesnaturallyastheMAPsolutioninourframework. Insummary,themaincontributionofthisworkistopresent,fromaBayesianperspective,auniedframeworkfortheestimationofsingle-trialspike-trainparameters.Analysisoftheposteriorprobabilitydistributionhasresultedinasimpleve-stepalgorithmfortheMAPsolutionandhencefortheparameterstobeestimated.Theeectivenessofouralgorithmwasrsttestedonsyntheticdataandthenonexperimentalsingle-unitspike-trainrecordingsfromthesensorimotorcortexofbehavingmonkeys.Theresultisamoreaccurateestimationoftheneuronalringrateaswellasthesingle-trialamplitudesandlatencies.Inaddition,asshowninFig. 6-3 ,theseparametersprovideinformationaboutthesingle-trialbehavioroftheneuron. Itisworthnotingthatourmodelassumesatrial-invariantprolefortherateofringwithlatencyandamplitude(excitability)variability.Theseformsofvariabilitiesarethemostfrequentlyencounteredinneurophysiologyandtheyhavebeenextensivelyreported( Bach&Kruger 1986 ; Vogelsetal. 1989 ; Richmond&Optican 1987 ; Munoz&Wurtz 1993 ; Gawneetal. 1996 ; Arielietal. 1996 ; Seidemannetal. 1996 ; Raiguel 103

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, 1999 ).Considerationofadditionalsingle-trialeects,aspointedoutby Ventura ( 2004 ),isatopicofinterest.Analternativemodelfortherateprolecouldbebasedonparameterizedpolynomialsorsplines( Venturaetal. 2002 ).Priorinformationoftheshapeoftheprolecouldthenbespeciedintheformofconstrainingtheparameterstoparticularvalueranges.TheBayesianframeworkcouldbeusedtoestimatethesenewparametersofinterest.However,addingalargenumberofparametersislikelytocausethexed-pointalgorithmtogetstuckinlocalsolutions.InthiscaseonewillberequiredtotakeanMCMCsamplingapproach.Wefoundtheseapproachestobecomputationallyintensiveforthenumberofparametersinourmodel.However,computerspeedshavechangeddramaticallyinthelasttwoyears.Inaddition,newMCMCalgorithmshavebeenintroduced,suchasNestedSampling( Sivia&Skilling 2006 )thataremuchmoreecient. 104

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RasterplotandPSTH.A)Rasterplotof20trialsoutofatotalof50generated.B)Comparisonofthetheoreticalmeanratefunction(smoothline)usedtosimulatethespiketrainswiththePSTHobtainedfromthedatain(A).C)Rasterplotofthesame20trialsin(A)afteradjustingforsingle-triallatencyshifts.D)TheratefunctionestimatedbythePSTHafteradjustingforsingle-trialparametersandthetheoreticalmeanratefunction. 105

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Performanceofthealgorithmonsimulateddata.A)Plotofestimatedlatencyversusactuallatency.B)Plotofestimatedamplitudescalingfactors(ampsf)versusactualampsf.(C),(D),(E),(F)Performanceofthealgorithm,measuredbythecorrelationcoecientsbetweentheactualandestimatedparameters,aswechangedtheparameters,denotedassd(standarddeviation),andBinEq. 6{23 usedtoconstructthesyntheticdata. 106

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Performanceonrealdata.A)Rasterplotof26trialsforaneuronin Gardneretal. ( 1999 ).Time0indicatesthetimeofgraspcompletion.B)TheratefunctionestimatebythePSTHforthedatainFigure3A.C)Rasterplotofthesame26trialsin(A)afteradjustingforsingle-triallatencyshifts.D)TheratefunctionestimatebythePSTHforthelatencycorrecteddata.E)Histogramofsingle-triallatencies.F)Histogramofsingle-trialamplitudescalingfactors. 107

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Thedissertationpresentedacomprehensiveframeworkforthecharacterizationofcorticaloscillatorynetworks.Anovelprocedure,PRAT,wasdevelopedtoinferthegeneratorsofoscillatoryactivityrecordedwithlaminarmulti-electrodes.TherelationbetweenCSDandconcomitantlyrecordedMUAactivitywasused,togetherwitheldpotentials,toinfertheunderlyingneuronalactivities.Grangercausalityanalysis,asaprincipledapproachforinferringcausalinuenceamongneuraltimeseries( Freiwaldetal. 1999 ; Bernasconietal. 2000 ; Liangetal. 2000 ; Baccala&Sameshima 2001 ; Brovellietal. 2004 ; Hesseetal. 2003 ; Dingetal. 2006 ),wasusedinlieuofthetrisectionmethodinin-vitrostudiestostudytheinteractionsbetweendierentgeneratorsinferredbythePRATmethod.Theframeworkwasappliedtounderstandthemechanismsofthecorticalalpharhythmindierentareasofthevisualcortex(V1,V2,V4andIT).Theresultsindicatecontrastingmechanismsofthealpharhythmindierentareasofthevisualcortex.WhileinV1,alphaoscillationseemedtobeaninterplaybetweenthegranularandtheinfragranularlayers,resultsinV2andV4indicatethatalphaoscillationintheseareasisgeneratedbylayer5pyramidalneurons.Incontrasttotheoccipitalareas,alphaoscillationinareaITwasfoundtooriginatefromthesupragranularpyramidalneurons.ThendingsinareaITarearguablythebiggestdiscoveryofthepresentworkandhasimplicationsfortheinterpretationofscalpEEGrecordings.Sourcelocalizationstudiesinhumans( Hari&Salmelin 1997 ; LopesdaSilva 2004 ; Feigeetal. 2005 )havefoundthatthealpharhythmismaximalalongthemidlineovertheposterior-occipitalareas.Ifalphacurrentgeneratorsinhumanlateraloccipitalcomplex(LOC),consideredtheanalogueofthemacaqueIT,haveasimilarsupragranularsource/sink/sourceconguration,thequadrupolesformedbytheradiallyorganizeddendriteswouldgiverisetoaclosedelddecayingfasterthanatypicaldipoleconguration( Mitzdorf 1985 ; LopesdaSilva&Rotterdam 2005 ).Asaresult,neuralensemblesinLOCandsurroundingareasmight 108

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LopesdaSilvaetal. 1980 ).Itisalsoconsistentwiththendingthatphase-resetofthealphaoscillationappearstocontributetotheP1/N1complexoftheERPrecordedovertheposteriormidline,butnottothatrecordedovermorelateralscalpregions.Andinthelightofreportsthatsupragranularpyramidalneuronsinhigherorderareas,fore.g.prefrontal,haveanevenbiggerbasaldendriticarborthaninIT( Elston 2003 ),quadrupolesourcesmightbemorewidespreadthaninitiallythought. 109

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AnilBollimuntawasbornin1979,inHyderabad,India.Theyoungestoftwochildren,hegrewupmostlyinHyderabad,graduatingfromAtomicEnergyCentralSchoolin1997.HeearnedhisB.Tech.inmechanicalengineeringfromtheIndianInstituteofTechnology(IIT)atMadrasin2002.UpongraduatinginJuly2002withhisB.Tech.inmechanicalengineering,AnilewtotheUnitedStatesandenteredthegraduateprogramattheCenterforComplexSystemsandBrainSciencesatFloridaAtlanticUniversity(FAU)inBocaRaton.In2004,AnilmovedtoUniversityofFloridaatGainesvilletopursueaPh.D.degreeinbiomedicalengineering.AftergraduationAnilintendstotakeupapostdoctoralpositiontopursuehisresearchinterestsinbrainsciences. 120