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Implementation and Analysis of Dynamic Causal Modeling for EEG/MEG Data

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Implementation and Analysis of Dynamic Causal Modeling for EEG/MEG Data
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  ImplementationandAnalysisofDynamicCausal ModelingforEEG/MEGData    Diplomarbeit vorgelegtvon  ChristianHimpe  Betreuer:Prof.Dr.MarioOhlberger  InstitutfürNumerischeundAngewandteMathematik Münster,Februar2011   Contents   1Introduction5  1.1Motivation....................................5 1.2OverviewandGoal...............................5  2InverseModelingforNeuronalActivity7  2.1Concept.....................................7 2.1.1PriorProbabilityDistribution.....................7 2.2TheInverseModel...............................7 2.2.1TheDynamicSubmodel........................8 2.2.2TheForwardSubmodel........................18 2.2.3TheCombinedModel.........................22 2.3ParameterEstimationandEM-Algorithm..................24 2.3.1MeanandCovarianceEstimation...................25 2.3.2TheEM-Algorithm...........................29 2.3.3PosteriorProbabilities.........................35  3Implementation37  3.1Paradigms....................................37 3.1.1Parallelization..............................37 3.1.2Modularization.............................37 3.1.3TheLayout...............................37 3.2DescriptionofImplementedClasses......................38 3.2.1SpecicationandDataImportClass.................38 3.2.2DataFeedProviderClass.......................39 3.2.3DriftGeneratorClass.........................39 3.2.4CombinedSystemClass........................39 3.2.5ModularizedDynamicSystemClasses................39 3.2.6ModularizedForwardSystemClasses.................40 3.2.7SolverClass...............................40 3.2.8OutputClass..............................41 3.2.9BayesClass...............................41  4NumericalExperimentsandValidationwithRealandArticialEEGData43  4.1PreliminaryRemark..............................43 4.2ArticialEEGData..............................43 4.2.12-RegionTests.............................43 4.2.23-RegionTests.............................46 3   4.2.3Conclusion...............................51 4.3RealEEGData.................................51 4.3.1Hypothesis...............................52 4.3.2DataPreprocessing...........................52 4.4PerformanceAnalysis..............................57 4.5Outlook.....................................59  5Appendix60  5.1ProgramUsage.................................60 5.2Dependencies..................................60 5.3ProgramandSourceCodeLicense......................60 5.4Abbreviations..................................61 5.5SymbolIndex..................................61 Bibliography.....................................62 4   1Introduction    1.1Motivation  Analyzingconnectivityofbrainregionsthroughdatareectingneuronalactivityisan inverseproblemthatcanbeapproachedwithatwocomponentmodel,whoseparameter distributionisestimatedwithBayesianinference,basedupon[22],utilizinganExpec- tationMaximization(EM)algorithmtoestimatetheparameterdistributionunderthe givendata.DynamicCausalModeling(DCM)isaprocedurethatallowstomakethese deductionsabouttheinteractionbetweenneuronalpopulationsasfoundinthebrain,by testinghypothesisonthecouplingbeweentheseregionsofthebrain.Givenanexperi- mentthatencouragestheactivityofthebrainregionsinquestion,DCMestimatesthe parametersoftheinversemodelthatsimulatestheneuronalactivityandthuscanverify orfalsifythishypothesis.DynamicCausalModelingcameintobeingin2003througharesearchpaperbyKarl Friston(see[17]).ThiswasanextensionofformerresearchintheanalysisoffMRItime series.Before,inaseriesofarticlesfrom2000to2001(see[14],[16],[15],[13]),theanalysis ofasinglebrainregionwiththehemodynamicBalloonmodelbythemeansofparameter estimationwasestablished.DynamicCausalModelingcombinedthissingleregionmodel withamultiregionmodelthatnegotiatesthecouplingbetweentheconsideredregions, whilethehemodynamic(singleregion)modelthenconvertstheoutputofthemulti regionmodeltoameasuredresponse.In2006theconceptofDynamicCausalModeling wasextendedfromfMRItoEEG/MEGwithanewmathematicalmodel(see[6]).This modelwasinitiallydevelopedbyJansen([28]).In2003and2005([8],[5])thisJansen modelwasrenedfromasingleregionmodeltoamultiregionmodelbyOliverDavid andKarlFriston,andwasnamedtheneuralmassmodel,whichwasthenextendedwith variousimprovements(forexamplesee[47],[31]). 1.2OverviewandGoal  ThegoalofthisworkistosummarizetheinversemodelsofDCMfortwomethodsofdata acquisition(fMRIandEEG/MEG)andoutlinethecompositionoftheemployedEM- algorithmfortheparameterdistributionestimationprocedure,aswellasimprovingthis algorithmintermsofperformance.Furthermore,thisworkisaccompaniedbyamodular implementationofthepresentedmethods,thatistestedwithsyntheticandreal-lifedata (providedbytheWWUInstituteofPhysiologyIinMünster)andbenchmarkedagainst theoriginalEM-algorithm.5 
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