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In Silico Model of In Vitro Dissociated Cortical Networks on Planar Microelectrode Arrays

Permanent Link: http://ufdc.ufl.edu/UFE0021735/00001

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Title: In Silico Model of In Vitro Dissociated Cortical Networks on Planar Microelectrode Arrays
Physical Description: 1 online resource (136 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

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Subjects / Keywords: 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: The advent of in vitro neural cultures on planar micro-electrode arrays (MEAs) has created the ability to chronically study the computational and dynamic properties of a reduced two-dimensional neuronal network of approximately 25 to 50 thousand neurons. However, even in these reduced networks the complexity is such that experimentation alone is often inadequate to explain network phenomena at cellular levels. A complimentary approach is to create realistic in silico models of these networks that simulate the individual neuronal and network properties of in vitro networks. Since these models allow the detailed analysis from individual cells to network interactions, they can often provide additional insight into the interaction of populations of neurons at a level that is impossible to accomplish using standard in vitro techniques. The primary focus of this dissertation is to describe a model of these 2D networks that incorporates generalizations and simplifications of properties of living neural tissue and the MEA technology that measures activity in vitro. This model incorporates multiple neuronal cell types, structural connectivity among those cells, and properties of individual cells including synaptic depression, facilitation, and plasticity. In addition, an important aspect of neural systems is their ability to self-regulate the dynamics of their activity. Unlike previous models of these networks, this property and a dynamic amplitude dependent plasticity rule has been included in the model which solves some of the issues with previous models. The result is a model that produces spontaneous and evoked burst patterns at time scales similar to that of in vitro cultures. Development of the self-regulating model has led to a better understanding of synaptic changes underlying network phenomena. The experimental validation of the model described in the following chapters provides insight into the network changes documented from other experimental protocols. Specifically, the separability of stimulation (and simulated stimulation) using differing MEA channels is shown. In addition, the location of plastic changes are traced when using tetanizing stimulation. In summary, a self-regulating model able to reproduce many emergent properties of in vitro networks was developed, validated, and used to explain the response to several common stimulation protocols. The model provides an excellent foundation to manipulate and study the network dynamics of plasticity; interpretation of the model output leads to detailed hypothesis and predictions that can be tested within the model and verified against in vitro experiments.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Demarse, Thomas.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2008-11-30

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Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021735:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021735/00001

Material Information

Title: In Silico Model of In Vitro Dissociated Cortical Networks on Planar Microelectrode Arrays
Physical Description: 1 online resource (136 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: 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: The advent of in vitro neural cultures on planar micro-electrode arrays (MEAs) has created the ability to chronically study the computational and dynamic properties of a reduced two-dimensional neuronal network of approximately 25 to 50 thousand neurons. However, even in these reduced networks the complexity is such that experimentation alone is often inadequate to explain network phenomena at cellular levels. A complimentary approach is to create realistic in silico models of these networks that simulate the individual neuronal and network properties of in vitro networks. Since these models allow the detailed analysis from individual cells to network interactions, they can often provide additional insight into the interaction of populations of neurons at a level that is impossible to accomplish using standard in vitro techniques. The primary focus of this dissertation is to describe a model of these 2D networks that incorporates generalizations and simplifications of properties of living neural tissue and the MEA technology that measures activity in vitro. This model incorporates multiple neuronal cell types, structural connectivity among those cells, and properties of individual cells including synaptic depression, facilitation, and plasticity. In addition, an important aspect of neural systems is their ability to self-regulate the dynamics of their activity. Unlike previous models of these networks, this property and a dynamic amplitude dependent plasticity rule has been included in the model which solves some of the issues with previous models. The result is a model that produces spontaneous and evoked burst patterns at time scales similar to that of in vitro cultures. Development of the self-regulating model has led to a better understanding of synaptic changes underlying network phenomena. The experimental validation of the model described in the following chapters provides insight into the network changes documented from other experimental protocols. Specifically, the separability of stimulation (and simulated stimulation) using differing MEA channels is shown. In addition, the location of plastic changes are traced when using tetanizing stimulation. In summary, a self-regulating model able to reproduce many emergent properties of in vitro networks was developed, validated, and used to explain the response to several common stimulation protocols. The model provides an excellent foundation to manipulate and study the network dynamics of plasticity; interpretation of the model output leads to detailed hypothesis and predictions that can be tested within the model and verified against in vitro experiments.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Demarse, Thomas.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2008-11-30

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0021735:00001


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INSILICOMODELOFINVITRODISSOCIATEDCORTICALNETWORKSONPLANARMICROELECTRODEARRAYSByKARLPAULDOCKENDORFADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2008 1

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c2008KarlPaulDockendorf 2

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ForMarissa,theloveofmylife 3

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ACKNOWLEDGMENTSIwouldliketothankmyfamilyandfriendsfortheirloveandencouragement.Iwouldalsoliketothankmyadvisor,Dr.ThomasDeMarse,forhisguidanceandsupport.Thisdissertationwouldnothavebeenpossiblewithouthim.IwouldalsoliketothankmylabmatesforprovidingapositiveandfriendlyworkingenvironmentandtheUniversityofFloridaAlumniAssociationforfunding.Finally,IwouldespeciallyliketothankMarissaFallonwhoprovidedthelove,support,andmotivationnecessarytopersevere. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 NOMENCLATURE .................................... 11 ABSTRACT ........................................ 13 CHAPTER 1INTRODUCTION .................................. 15 2BACKGROUND ................................... 18 2.1Fundamentals .................................. 19 2.1.1DevelopmentandMorphologyofNeuralActivityInVitro ...... 20 2.1.2ActionPotentialsandIonchannels .................. 21 2.1.3ConnectivityInVivoandInVitro ................... 24 2.2EmergentProperties .............................. 25 2.2.1InVitroActivity ............................ 25 2.2.2ExperimentalEvidence ......................... 27 2.3Modeling ..................................... 29 2.3.1OriginofInVitroActivity ....................... 29 2.3.2ModelsofIndividualNeurons ..................... 31 2.3.3ModelsofSynapses ........................... 32 2.3.4CumulativeModelsofInVitroNetworks ............... 33 3AMPLITUDEDEPENDENTSYNAPTICPLASTICITY ............. 36 3.1Background ................................... 36 3.2Results ...................................... 37 3.2.1FixedPointAnalysis .......................... 41 3.2.2WeightDistributions .......................... 43 3.2.3SynapticModicationbyCorrelatedInput .............. 45 3.3Conclusions ................................... 46 4SELF-REGULATINGINSILICOMODELOFINVITRONEURONALNETWORKS ..................................... 48 4.1Introduction ................................... 48 4.2AModelofInVitroNetworks ......................... 50 4.2.1ModelingtheSpatialPositionofEachNeurononanMEA ..... 50 4.2.2IndividualNeurons ........................... 52 4.2.3TheRoleofEndogenouslySpikingNeurons .............. 54 5

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4.2.4SynapticConnectivity:ModelingtheStructuralInformationofInVitroNetworks ............................. 55 4.2.5SynapticActivationandConductionDelays ............. 56 4.2.6SynapticPlasticity ........................... 57 4.3Results ...................................... 58 4.3.1ComparisonofGeneralSpontaneousActivityintheModelVersusInVitro ................................. 59 4.3.2ComparisonofEvokedActivity .................... 64 4.3.3AnalysisofModelParameters ..................... 64 4.4Discussion .................................... 69 4.4.1TheASTDPVersusSTDPArgument ................. 70 4.4.2SelfRegulation ............................. 71 4.4.3ParameterEects ............................ 71 4.4.4FutureWork ............................... 72 4.4.5Summary ................................. 72 5SEPARABILITYANDREPEATABILITYOFELECTRICALSTIMULATION 73 5.1Introduction ................................... 73 5.2Methods ..................................... 75 5.2.1CellCulture ............................... 75 5.2.2Acquisition ................................ 75 5.2.3DataandStimulusProtocols ...................... 75 5.2.4ClassicationMethods ......................... 77 5.2.4.1SmoothedPSTH ....................... 78 5.2.4.2NormalizationofPSTHforclassication .......... 79 5.2.4.3L2distance .......................... 79 5.3Results ...................................... 80 5.3.1InputReconstructionPerformance ................... 80 5.3.2SurrogateData ............................. 81 5.3.3TrainingSetSize ............................ 83 5.3.4TrainingSetSamplingandNonstationarity .............. 84 5.3.5SeparabilityofStimulationsInSilico ................. 86 5.4Conclusions ................................... 87 5.4.1SeparabilityandReliabilityofElectricalStimulation ......... 89 5.4.2ComputationalPerspective ....................... 90 5.4.3FutureWork ............................... 91 6SIMULATEDINVITROPLASTICITY ...................... 92 6.1Introduction ................................... 92 6.2Simulations ................................... 93 6.2.1RapidMultichannelStimulus ...................... 93 6.2.2TetanicStimulus ............................ 94 6.2.3PairedRare-FrequentStimulus ..................... 94 6.3Results ...................................... 96 6

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6.3.1SpontaneousPlasticity ......................... 96 6.3.2ProbePlasticity ............................. 96 6.3.3RapidMultichannelStimulationPlasticity .............. 98 6.3.4TetanicPlasticity ............................ 103 6.3.5PairedRare-FrequentStimulationAdaptation ............ 108 6.4Discussion .................................... 110 6.4.1UtilityoftheModel ........................... 112 6.4.2PlasticityDuetoStimulation ...................... 112 6.4.3FutureWork ............................... 113 7CONCLUSIONS ................................... 115 7.1CriticalAssessment ............................... 115 7.2FutureWork ................................... 117 7.3SignicanceandContribution ......................... 118 APPENDIX AEFFICIENTIMPLEMENTATIONOFNETWORKSIMULATION ....... 120 BSIMULATINGELECTRICALSTIMULATION .................. 122 REFERENCES ....................................... 124 BIOGRAPHICALSKETCH ................................ 136 7

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LISTOFTABLES Table page 4-1Neuronparameters .................................. 54 4-2Synapseparameters .................................. 58 4-3Self-regulatingmodelburststatistics ........................ 63 5-1Averagedclassierperformance ........................... 80 6-1ExperimentalSynapticChanges ........................... 102 8

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LISTOFFIGURES Figure page 2-1Culturedcorticalnetworksandmicroelectrodearrays ............... 19 2-2Classicmyelinatedneuronstructure ......................... 22 2-3Classicactivitypatternofmatureculture ...................... 26 3-1Amplitudeandspiketimingdependentplasticitycurve .............. 38 3-2Stablevalueofsynapticweightforxedpre-postspiketimings .......... 39 3-3Amplitudedependentplasticity ........................... 40 3-4FrequencydependentnatureoftheASTDPrule .................. 41 3-5Convergenceinthedistributionof200weightsusingASTDP ........... 42 3-6ComparisonofASTDPandSTDPweightdistributions .............. 44 3-7Histogramofsynapticweightswithmultiplicativenoise .............. 44 3-8Stabilizedvaluesofsynapticweightsfrompre-andpostsynapticconductancebasedinput ...................................... 45 4-1Ellipticaldropletcross-section ............................ 51 4-2Simulatedandrealneuronpositionsandconnections ............... 53 4-3Variabilityinsimulatednetworkactivity ...................... 60 4-4Spontaneousmodelactivity ............................. 61 4-5Inter-spikeintervaldistribution ........................... 62 4-6Histogramofringratesinsimulateddish0002 .................. 63 4-7Burstlengthdependence ............................... 64 4-8Elicitedmodelactivity ................................ 65 4-9Unimodalsynapticweightdistribution ....................... 66 4-10Neuroninputduringbursting ............................ 67 4-11Inputscalecompensation .............................. 68 4-12Inputscalespatialdistribution ........................... 69 4-13Examplesynapticweighttraces ........................... 70 5-1Stimuluspatterns ................................... 76 9

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5-2Stimulusblanking ................................... 76 5-3Representativeexampleofmulti-channel,smoothedPSTHs ............ 78 5-4Classicationperformancebasedonvaryingthepost-stimuluswindow ...... 82 5-5Trainsetsizeinuencedperformance ........................ 83 5-6Averageperformanceofclassierswithvariedstimulationandwindowsize ... 85 5-7Rapidstimulationnonstationarity .......................... 86 5-8Modelrapidmultichannelstimulusresponse .................... 88 6-1Variationinspontaneousnetworkactivitypriortosimulatedexperiments .... 95 6-2Spontaneousuctuationsinsynapticweightsthroughoutthesimulatednetwork 97 6-3Histogramsofplasticsynapticweightsduringspontaneousactivity ....... 98 6-4Burstcontrolusingrapidmultichannelstimulation ................ 99 6-5Stabilityoflargeandsmallsynapticweightsandtheeectofstimulation .... 100 6-6Eectofhighfrequencystimulationonconnectivity ................ 101 6-7Eectofhighfrequencystimulationonplasticsynapticweights ......... 102 6-8EectoftetanicstimulationonthenetworksimulationasdeterminedbyprobesofsimulatedMEAchannels ............................. 104 6-9Eectoftetanicstimulationonsynapticweightsinnetworksimulation ..... 105 6-10Reproducibilityoftheeectsoftetanicstimulation ................ 106 6-11Modulationofstimulusresponsebyprioractivity ................. 107 6-12Inuenceofshort-termdynamicsonburstresponse ................ 108 6-13Eectofpairedrare-frequentstimulationonresponse ............... 109 6-14Eectofpairedrare-frequentstimulationonplasticsynapticweights ...... 110 6-15Localizedsynapticandscalingchanges ....................... 111 A-1Divisionpointfornetworkmodelsimulation .................... 121 A-2Pseudocodeofmodelrunloop ............................ 121 10

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NOMENCLATURE Denotesameanvalue Denotesastandarddeviation P Denotesthesummationofaseriesofterms Denotesatimeconstant AMPA -amino-3-hydroxy-5-methyl-4-isoxazolepropionicacid AP Actionpotential ASTDP Amplitudeandspiketimingdependentplasticity BCM Bienenstock-Cooper-Munroatypeofsynapticplasticitymodel Ca+2 Calciumion Cl)]TJET1 0 0 1 144 468.967 cm0 g 0 G1 0 0 1 -144 -468.967 cmBT/F15 11.955 Tf 149.853 468.967 Td[(Chloride EPSC Excitatorypost-synapticcurrent EPSP Excitatorypost-synapticpotential GABA -aminobutyricacid HH Hodgkin-Huxleyaneuronmodeltype Hz Hertz IPSC Inhibitorypost-synapticcurrent IPSP Inhibitorypost-synapticpotential K+ Potassiumion LIF Leakyintegrate-and-reaneuronmodeltype LTD Long-termdepression LTP Long-termpotentiation MEA Micro-ormulti-electrodearray ms Millisecond mV Millivolt Na+ Sodiumion NMDA N-methyl-D-asparticacid 11

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nS Nanosiemen pA Picoampere PSP Post-synapticpotential STD Short-termdepression STDP Spike-timingdependentplasticity STP Short-termpotentiation 12

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyINSILICOMODELOFINVITRODISSOCIATEDCORTICALNETWORKSONPLANARMICROELECTRODEARRAYSByKarlPaulDockendorfMay2008Chair:ThomasB.DeMarseMajor:BiomedicalEngineeringTheadventofinvitroneuralculturesonplanarmicro-electrodearraysMEAshascreatedtheabilitytochronicallystudythecomputationalanddynamicpropertiesofareducedtwo-dimensionalneuronalnetworkofapproximately25to50thousandneurons.However,eveninthesereducednetworksthecomplexityissuchthatexperimentationaloneisofteninadequatetoexplainnetworkphenomenaatcellularlevels.Acomplimentaryapproachistocreaterealisticinsilicomodelsofthesenetworksthatsimulatetheindividualneuronalandnetworkpropertiesofinvitronetworks.Sincethesemodelsallowthedetailedanalysisfromindividualcellstonetworkinteractions,theycanoftenprovideadditionalinsightintotheinteractionofpopulationsofneuronsatalevelthatisimpossibletoaccomplishusingstandardinvitrotechniques.Theprimaryfocusofthisdissertationistodescribeamodelofthese2DnetworksthatincorporatesgeneralizationsandsimplicationsofpropertiesoflivingneuraltissueandtheMEAtechnologythatmeasuresactivityinvitro.Thismodelincorporatesmultipleneuronalcelltypes,structuralconnectivityamongthosecells,andpropertiesofindividualcellsincludingsynapticdepression,facilitation,andplasticity.Inaddition,animportantaspectofneuralsystemsistheirabilitytoself-regulatethedynamicsoftheiractivity.Unlikepreviousmodelsofthesenetworks,thispropertyandadynamicamplitudedependentplasticityrulehasbeenincludedinthemodelwhichsolvessomeoftheissueswithpreviousmodels.Theresultisamodelthatproducesspontaneousand 13

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evokedburstpatternsattimescalessimilartothatofinvitrocultures.Developmentoftheself-regulatingmodelhasledtoabetterunderstandingofsynapticchangesunderlyingnetworkphenomena.Theexperimentalvalidationofthemodeldescribedinthefollowingchaptersprovidesinsightintothenetworkchangesdocumentedfromotherexperimentalprotocols.Specically,theseparabilityofstimulationandsimulatedstimulationusingdieringMEAchannelsisshown.Inaddition,thelocationofplasticchangesaretracedwhenusingtetanizingstimulation.Insummary,aself-regulatingmodelabletoreproducemanyemergentpropertiesofinvitronetworkswasdeveloped,validated,andusedtoexplaintheresponsetoseveralcommonstimulationprotocols.Themodelprovidesanexcellentfoundationtomanipulateandstudythenetworkdynamicsofplasticity;interpretationofthemodeloutputleadstodetailedhypothesisandpredictionsthatcanbetestedwithinthemodelandveriedagainstinvitroexperiments. 14

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CHAPTER1INTRODUCTIONCulturednetworksofprimaryneuronsfromthebraindevelopingexvivohavebeenusedtostudypropertiesofneuronsfordecades.Typicalinvestigationshavefocusedondatacollectedfromafewneuronsusingglassmicro-pipetterecordingse.g.,patchclamp,loosepatch,wholecellrecordings.Whilethisrecordingtechnologyhasledtodetailedinformationaboutthepropertiesofindividualneuronsitisnowclearthatthecomputationalpropertiesoftheseneuronsareembeddedwithintheinteractionsamongmanythousandsofneuronsi.e.,aneuralpopulation.Hence,theabilitytosimultaneouslymeasuretheactivityfromhundredsofneurons,providedbymultichannelmicroelectrodearraysisanimportantsteptoincreaseourunderstandingofhowindividualneuronsinteracttoproducethesecomputationalproperties.Unfortunatelyevenwithadvancedrecordingcapabilitiesprovidedbythesearraysmuchofthepropertiesofbothneuronsandnetworksisunknown.Theabilitytomeasurethatdetailedinformationwouldenhanceourunderstandingofthefunctionalpropertiesofthesenetworks.Computersimulatedmodelsofthesenetworks,insilicomodels,couldprovidethatdetailedinformation.Modelsoflivingneuronalnetworksenableanalysisrequiringthiscomprehensivecollectionofdata.However,manymodelslacktheabilitytoreproducesimilaractivityanddistributionsofmodelvariables.Thefollowingdissertationovercomestheshortcomingsofothermodelsbytheadditionofseveralnewfeatures.Specically,thisworkhasleadtoaninnovativemodelabletodemonstrateexperimentallyinducedchangesandregulateitsownactivity.Incorporatedinthisnetworkmodelisanewmodeloflong-termsynapticchanges,anewmethodforsimulatingtheneuralinterfaceMEAsintothosenetworks,anewmethodforspatialdistributionandconnectivity,andanewdistributionofsynapticparameters.ThisdissertationbeginswithadiscussionoftheknownpropertiesoftheindividualneuronsandnetworkphenomenonthathavebeenrecordedwithMEA 15

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technology.Amodelofthesenetworksisthendescribedoutliningthemajorfeaturesofthismodel.Themodelisthenanalyzedandcomparedwithknownfeaturesofthesenetworksandvalidatedagainstexperimentalndings.Chapter 2 providesthereaderwithabriefsurveyoftheeldofdissociatedculturedprimaryneuronsfromratcortexonMEAs.Itdetailsseveralimportantaspectsofthesenetworksandcitesreferencesforfurtherreading.Additionally,thechapterdetailsrelatedmodelsofneuralnetworkswithwhichourmodel,developedlater,maybecompared.InChapter 3 ,webeginthedevelopmentofourmodelbydevelopingandimplementinganewamplitudedependentsynapticplasticityrule.Theruleisdevelopedtoproducesynapticweightdistributionsthatmirrorthosefoundinvitro.Acommoncriticismandshortcomingofothermodelsinthiseldaretherelackofplausibleweightdistributions.Thenewlong-termplasticitymodelistestedusingsimulatedactivitytodemonstrateitsabilitytoreectnegativeandpositivecorrelationsembeddedinneuralsignals.AmodelofinvitrodissociatedneuronalnetworksisformedinChapter 4 .Thenetworkmodelincorporatesacommonlyusedneuronmodelandshort-termplasticitymodel,andthenewlydevelopedlong-termplasticityrulefromChapter 3 withselfregulationandisbuiltonnoveldistributionsforspacingandconnectivitywithinthesenetworks.Thismodelissimulatedandseveralobservationsaremadeandcomparedwithculturednetworks.Additionally,thechapterlistsequationsdescribingthedynamicsoftheneuronsandsynapsesandfollowswithadiscussionofthespatialdistributionofneuronsandthedistributionsusedtodetermineinterconnectivity.Chapter 5 detailstheresultsofmultichannelrapidandslowstimulationoftheneuralnetworkinvitro.Theintentofthischapteristodeterminetheuniquenessofextracellularstimulationthroughdierentpointsinthenetwork.Wethenshowthatwhilestimulationresponsesaredierentiable,theydochangeovertime.Chapter 6 istheculminationoftheresearchwithsimulatedexperimentationonthemodeldevelopedChapter 4 .Theconsequencesofstimulationareshownwithrespectto 16

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activityandchangesinsynapticweights.Conclusionsarethendrawnaboutthestateofculturesintheseexperimentalsetups.ThisdissertationincludesAppendices A and B describingthemethodsfollowedinimplementationofthesimulatorwithrespecttoneuronandsynapsecalculationsandhowelectricalstimulationactivatescomponentsofthesimulator.Theseareimportantdetailswhenunderstandingstimulationexperimentsinthemodel. 17

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CHAPTER2BACKGROUNDThecomplexityofinvivoneuralsystemshasbeenamajorhurdletounderstandingtheirfunctionthatscientistshavetriedtoovercomeformanydecades[ 1 ].Onecommonstrategytoovercomethisproblemistocreateasimpliedinvitroanaloguecomposedofculturedneuronsthataremoreaccessablethantheirinvivocounterparts.AlthoughInvitroculturesaresimpliedtheyrepresentabetterstartingpointforunderstandingemergentnetworkpropertiesofneuronalnetworkscomparedtotacklinganentireintactcortex.However,evensmallinvitronetworksofculturedneuraltissue25,000-50,000cellsarestillquitecomplex,withtheabilitytoexhibitlargerepertoiresofringpatterns[ 2 { 4 ].Understandingnetworkdynamicseveninthesesimpliednetworksisthekey,however,toelucidatingtheadaptiveandmemorypropertiesofneuralnetworks[ 5 ].Towardthisend,arraysofmicro-electrodesofMEAshavebeendevelopedthatcanmeasuretheactivityfromasmallpopulationofneuronsinthesenetworksbothinvitroandinvivo.TheseMEAsactasaninterfaceintotheneuralpopulationandareusedtomeasureandinteractwiththespatialandtemporalrelationshipsofneuralactivitytounderstandtheirfunction.Infact,applyingtheseinterfacesinvitrohasprovidedacriticalsteptostudyingandunderstandingthebasicprinciplesoftheirnetworkoperation.Studiesusingthesenetworksarenowadvancingonthegoalofcreatingnovelhybridcomputingarchitecturesandadvancedunsupervisedlearningalgorithms.Acommontechniquetoachievethisgoalhasbeentocreateinsilicomodelsoflivingneuronalnetworkstostudytheircomputationalpropertiesandtranslatethosepropertiesintonovelcomputingmethods.Thischapterbeginsbydescribingthefundamentalsofneuralcellcultureonplanarmicro-electrodearraysfollowedbyabriefdescriptionoftheknownpropertiesoftheneuronsandthenetworksinwhichtheyareembedded.Theremainderofthechapterwilldiscussthepreliminarymodelingworkofthesedissociatedculturesthathasbeenconductedinthiseld. 18

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2.1Fundamentals a bFigure2-1.CulturedcorticalnetworksandmicroelectrodearraysMEAs.aMicroelectrodearraywith60electrodes.bMagniedviewofneuronsculturedonanMEA.AlsoshownaretheextracellularrecordingelectrodeslocatedinthecenteroftheMEA.Typically,non-activeneuronshaveamembranepotentialofapproximately)]TJ/F15 11.955 Tf 9.299 0 Td[(65mV,whichcanbechangedthroughelectricalorchemicalstimulation.Whenthemembranepotentialisraisedpasttheneuron'svoltagethresholdforthecascadeofionchannelopening,theneurondepolarizesandthemembranepotentialmaypeaknear+30mVbeforereturningtotheresting,non-active,membranepotential.Theselargechangesinvoltageareknownasactionpotentialsandreferredtomoreinformallyasthering"oftheneuron.TheactionpotentialsofnearbyneuronscanbedetectedextracellularlythroughtheelectrodesembeddedintheMEA. Theinvitroneuronalnetworksusedinthisresearchareculturedfromdisassociatedembryonicday18ratcortexaccordingto[ 6 ].Briey,embryonicday18Sprague/DawleyorFischer344ratcortexBrainBitsaredissociatedwithWorthingtonPapainDissociationSystem.About20,000-50,000cellsareplatedoneachmicroelectrodearrayMEA,seeFigure 2-1 ,whicharepre-coatedby100L0.1%polyethyleneiminePEI,Sigmaand10LlamininSigma.TheMEAsarecoveredwithFEPasemi-permiablemembranelids[ 6 ],whichreducestheculturemedia'sevaporationwhileallowinggasexchange.Theculturedcellsarekeptinthe35.5C,5%CO2formorethan1month.Halfoftheculturemedia,whichconsistedofDulbeccosmodiedEaglesmediumDMEMGibcocontaining10%inactivatedequineserumHyClone,isreplacedbiweekly.LamininandPEItreatmentscreateamorefavorableenvironmentforthegrowthofneurons.Laminin 19

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anextracellularmatrixproteinisboundbyextracellularintegrinbindingreceptorsespecially61intheneuralcellmemrbrane;thisproteinbindingincreasesurvivabilityandneuriteoutgrowth[ 7 ].PEIchangesthesurfacechemistryoftheculturedishmakingithydrophilic,andthus,favorableforneuronsurfaceadherence.Cellsareplatedoneachplanarmicro-electrodearrayMEA,seeFigure 2-1 fordetails,whicharemultichannelrecordingandstimulationelectricalgridsembeddedinacoatedglassdish.Amajorityofthecellsplatedareneuraltissuewithaminorbutsignicantportionofglialandsupportcells.Invivohistologyshowsthat80%oftheneuraltissuecellsareexcitatoryneuronsthatcausehypo-polarizationofpost-synapticmembranesand20%areinhibitorythatcausehyper-polarization.Survivabilityofthesecellthroughdisassociationistypically90%[ 8 ].Invitrostaining[ 8 9 ]yieldsresultsthatshowtherelativeportionofinhibitorytoexcitatoryneuronsissimilartothoseinvivo.2.1.1DevelopmentandMorphologyofNeuralActivityinDissociatedCul-turesofPrimaryCorticalNeuronsPrimarycorticalneuronsthatareextractedfromembryonicratcorticesrapidlybegintoextendaxonstotheirneighborswithinafewhours.Synapsesformbetweencellsandasaresulttheneuronsproduceuncorrelatedringwithintherstfewdays.Astheneuronsdevelop,changesinactivitycloselyfollowtheincreaseinthenumberandtypeofsynapsesduringtherst30days[ 10 { 13 ].Withinoneweek,theybegintoreinsmallclustersofactionpotentialswhicharesuperimposedonspontaneousvoltageuctuations[ 14 ].Overthefollowingweeks,complexburstsofactivityemergeasthenetworkconnectivity,numberofsynapses,andmorphologye.g.,excitatoryvs.inhibitorymatures.Burstingin-vitrocloselyresemblestheactivityofdevelopingbrainsinanimals[ 15 ].Aftertwoweeks,theseburstsgraduallybecomemorepronouncedandseizure-like,enteringaphasewhereburstswillsometimeslastforseveralseconds[ 3 4 16 ].Duringthethirdandfourthweeksinvitrothelengthoftheburstsbegintoshortentodurationsof100to200mswithinterburstintervalsrangingfrom1to15seconds.This 20

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phenomenaofspontaneousburstsisobservedinmanyculturednetworksofdierentcelltypes,regardlessoftheoriginalsourceoftheneuronsthemselves[ 17 ]includingcellsfromthespinalcord[ 18 ],retina[ 19 20 ],andhippocampus[ 21 ].After30daysinculture,thenetworkbecomesadevelopmentallystable2-dimensionalnetworkproducingactivitypatternssimilartothatproducedthroughoutitsremaininglifetime[ 6 22 ].Atthispointthecompositioni.e.,celltype,receptors,etc.ofthesenetworksresemblesthatoftheirinvivocousins[ 8 9 14 23 24 ].Connectivitybetweenneuronsinthesenetworksdonotappeartobemediatedthroughgapjunctions[ 14 ].Attheendofthisdevelopmentalperiodithasbeenestimatedthateachneuronismono-synapticallyconnectedtoapproximately10-30%ofitsneighbors[ 2 14 ].Onceformed,thisconnectivityappearstoberelativelystable.Theconnectionsformedinthesecultureshavebeendescribedasrandom[ 2 ];however,selectivityofconnectionhasbeennotedalthoughnopatternedstructurehasbeenfoundlikethatofanintactcortex.Thus,thesenetworksthatcansometimescontainover105neuronsand108connectionsseemtobeoperatingonthesamefundamentalprinciplesandexhibitcomplexbehavior,butlackdenedstructuralorganization.2.1.2ActionPotentialsandIonchannelsThestructuralanatomyofneuronsvarywidelyinorganisms,eveninonesubclassofneurons[ 25 ].However,mostneuronshaveacommontheme:inputandoutput.Neuronsreceiveinputfromandsendoutputtoconnectionswithotherneuronscalledsynapses.Inputsaretypicallyreceivedthroughhighlyarborizeddendrites,soma,andaxonhiloc,seeFigure 2-2 .Outputsaretypicallytransmitteddowntheaxontotheterminalswheretheneuronisconnectedtootherneurons.Thearborizationofthedendritesandaxonandthelocationofthecellbodycanvarygreatlybetweenneurontypes.Dendritesprovidepassiveoractiveconductionofinputtowardtheaxonandback-propagationofactionpotentialsawayfromtheaxon.Thecellbodycontainsthegeneticinformationinthecellandprovidesamajorityofthemetabolismandprotein 21

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Figure2-2.Classicmyelinatedneuronstructure.Labelsindicatedthecellbodyknownalsoasthesoma,dendrites,andaxonlabeledattheaxonhilocandcontinuestotheterminals.Otherneuronsconnecttothedendritesandcellbodyafewalsocanconnectattheaxonhiloc[ 25 ],wheretheyreleasechemicalmessengersthataectthepostsynapticmembranevoltage.Theaxonhilocisthelowestthresholdportionofthecellmembranefortheinitiationofanactionpotential.Theactionpotentialthenpropagatestowardtheaxonterminalsandback-propagatesthroughthedendrites.Atthesynapsesintheaxonterminalstheneuronreleasesneurotransmittersontothepost-synapticneurons. formationandpackaging.Axonsprovideshortandlongdistanceconnectionstootherneurons.SomeaxonsarewrappedbyaninsulativemyelinsheathfromaSchwanncellallowingforfastsaltitoryconductionoftheactionpotentialsAPs.Corticalneuronsexhibitmanypropertiesthatinclude,butarenotlimitedto:inputscaling[ 26 { 30 ],dynamicvoltagethreshold[ 27 28 31 { 35 ],short-termsynapticdepressionandfacilitationalsoknownasfrequency-dependentsynapses[ 25 26 36 { 40 ],long-termsynapticdepressionandfacilitation[ 36 41 { 47 ],sodium-channelinactivation[ 28 { 30 48 { 50 ],calciumtransients[ 47 51 { 53 ],afterhyperpolarization[ 31 32 ],axoncabledelay[ 2 4 54 { 56 ],GABAreversalpotentialdevelopment[ 53 57 { 59 ],synapticvesiclereleasefailure[ 60 { 62 ],receptordesensitizationandsensitization[ 39 40 ],multipleneurotransmitterexpressionwithvaryingdynamicsie,AMPA,NMDA,GABAA,GABAB,andothers[ 63 { 65 ],back-propagationofactionpotentials[ 34 66 { 69 ],and 22

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membranevoltagedependentvesiclerelease[ 70 ].Allthesepropertiesinteracttogeneraterichspatiotemporalactivitypatternsinvivoandinvitro.Theinput-scaling,dynamicvoltagethreshold,sodiumchannelinactivation,afterhyperpolarization,andGABAreversalpotentialdevelopmentarepropertiesaectingneuronmembranesthataremodulatedinresponsetoaerentandeerentactivity.Whiletheseneuralpropertieshavedierenttimescalesandmethodofaction,ingeneraltheyactasnegativefeedbacktomodulatehighlevelsofeerentactivity.Similarly,short-termsynapticpotentiationanddepression,calciumtransients,andreceptordesensitizationandsensitizationarepropertieslocaltosynapsesthataecttheecacyofsynapticcouplingofpre-synapticandpost-synapticneuronsknowninmodelingassynapticweighttransiently.Thesepropertiesactonfasttimescalesforenhancementorweakeningofresponsetosynapticactivity.Thechangestheyinduceoftendecayfadewithtimeconstantslessthanonesecond.However,long-termsynapticpotentiationanddepressionisthoughttorelyonthecoincidenceofactionpotentialstriggeringpre-synapticvesiclereleaseandtheback-propagationofactionpotentialsfromthepost-synapticneurontothesynapse.Thelong-termchangesarebelievedtobestablelonger30minutes[ 71 ].Eachoftheseattributesofneuronsarecomplexbythemselves;tounderstandthewholepicture,onemustrealizethatneuronsareselectiveinformingconnectionswithotherneuronsandatwhatspatialpointtheyconnect.Thesepin-pointconnectionsinteractwitheachothertoactivatenearbyvoltagesensitivereceptorsorpreventthepropagationofbuiltupvoltageinadendriticarborbyexcitationorinhibition,respectively.Thelatterofthesetwoabilitiesisknownasshuntingandenablesaneurontoinhibitthepostsynapticneurontoselectivelylisten"toinputandpreventback-propogationofanactionpotentialtothatdendriticarbor.Back-propogationofAPsiscrucialtoplasticchangesthatoccuratsynapsesasthatistheirmeansofndingout"abouttheactionpotentialtheneuronred,enablingchangesbasedonpre-andpostsynapticactivitydiscussedlater.ThispropagationofAPsortho23

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andantidromicallyhasothereectsalso.TheAPs"reset"theneuron'smembraneandasaconsequencearefractoryperiodensues.Inaddition,thepropagatingAPcaninactiviteionchannelsreducingtheneuron'sabilitytoinitiateanotherAP.Consequently,thestateofthenetworkisaresultofspecictimingsandlocationsofactivityandconnectivity.2.1.3ConnectivityInVivoandInVitroOvertherstmonthinvitro,theneuronsreconnectforminganetworkreachingamature"stateafter30days.Duringthisperiod,neuronsextendprojectionsneuritesthatconnecttootherneuronsandformsynapses.Theextensionofneuritesislargelydeterminedbyinterneuronchemicalmessagingandhormonespresentinvivo.Evidencealsoexistthatthesignalsconductedbythewould-bepre-andpostsynapticneuronsaectsthepropabilityofconnection[ 72 ].Synapticbuttonsprovideasmallcleftbetweentheaxonterminalanddendriticspine,inwhichspacechemicalcommunicationisusedbetweenneurons.Dependingonthetypeofneuronaxonscanextendlongdistancestoformconnectionswithotherneurons.Thesesynapsestypicallytransmitinformationfromthepresynaptictothepostsynapticneuronthroughchemicalmessengers,calledneurotransmitters,whenactionpotentialsaretriggered[ 65 70 ].Thesynapsesinducepostsynapticcurrentsthatareintegrated,withinputfrommanyothersynapses,bythepostsynapticneuron.Dierentneurotransmittersareexpressedbydierentneurontypes.Mostcommonly,excitatoryneuronsreleaseglutamateactivatingaglutamatereceptor,suchasAMPA,NMDA,ormetabotropicglutamatemGlureceptors.InhibitoryneuronsreleaseGABAactivatingaGABAreceptor,suchasGABAA,GABAB,orGABACreceptors.Eachreceptorforthevariousneurotransmittershavevaryingpropertiesincludingkineticloading-time,unloading-time,numberofbindingsites,andvoltagesensitivity.Inaddition,thereceptorsdistributeddierentlywithrespecttolocationontheneuron.Inhibitorysynapsesaretypicallyproximaltothedendritictrunks,cellbody,andaxonhiloc.Excitatorysynapsearefoundalloverthedendritictreandinthesameplacesasinhibitorysynapses;however,AMPA 24

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toNMDAreceptorcountsarehigherclosertothepointofactionpotentialinitiationandloweratthedistalportionsofthedendrites.Theseconnectionsarenotxedonceformed.Indeed,neuronalnetworksinvivohavebeenshowntocontinuouslyundergosynapticpruningandformationinvivo[ 72 ];however,generalpathwaysaremaintained.Invivo,manyfeedbackandfeedforwardpathwayshavebeenidentied.Thesepathwayshavealsobeenassociatedwitheachofthelayersofthecortexorotherstructures[ 73 ].Whilestrongchemotacticinuencesorganizethelayersoftheneocortex,evidencealsoexiststhattheorganizationofneuralstructureishighlydeterminedbyinputsinvivo[ 74 ].Inspiteofthis,invitronetworksdevelopandconnectinwhathasbeenreferredtoasrandomly."Theconnectivityinvitrobetweenneuronshasbeennotedat10-30%withapproximately40%ofpairsbeingconnectedatleastmonosynaptically[ 14 ].Connectionsaremostlylocalwithfewlongdistancebothinvivoandinvitro.Networkinputfromsensorysystems,forexample,areabsentinvitroandthisfactormaypotentiallyinuencethedevelopmentofthetheseculturedcells.2.2EmergentPropertiesRegardlessofthenuancesofneuronsandsynapses,theultimategoalinthisworkistogenerateanetworklevelmodelofinvitroproperties.Mostimportantaretheemergentpropertiesthatleadtocomputationandlearning.Invivocorticesareabletolearnassociations,performreasoning,andpredictoutcomesofevents;althoughtheseareloftygoals,theybeginwithlowerlevelinvestigationofnetworkpropertiesandactivity.Thesimulatednetworksthatcanaccomplishthisareapplicableeverywhere.2.2.1InVitroActivityGenerally,theculturesexhibitspontaneousactivityofindividualunitssingleneuronsbytheendoftherstweekandbegintohavetemporalclusteringofactionpotentials.Throughtheremainderofdevelopment,increasingnumbersofunitsareactiveintheseclustersofactionpotentials;thisisalsoaccompaniedbytighterclustering, 25

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Figure2-3.Classicactivitypatternofmatureolderthan30daysinvitroculture.Eachpointindicatesthedetectionofanactionpotential.PlottingtimeversuschanneloftheMEAisreferredtoasarasterplot.Exampleburstsoccurapproximatelyat17sec,21sec,etc.Burstsaretypicallycharacterizedbycross-channelsynchronizedoccurrenceofhighringratesorsignicantincreasesinringrates.Asexample,theSIMMUXburstdetectionalgorithmisbasedondeningaburstlet"asasequenceof4ormoreofactionpotentialsonasinglechannelwithaninter-spikeintervalISIlessthanthanone-fourththeinverseaveragespikedetectionrateforthatchannel.Aburstthenisthesynchronousoccurrenceofburstletsonmultiplechannels[ 75 ].Burstscanbelessthan100millisecondstogreaterthan10seconds.Typically,however,matureburstsareafewhundredmilliseconds[ 76 ].Multiplesub-burstscanoccurinasingleburst.Theoriginofburstinginvitroisthoughttooccurfromafewendogenouslyactiveneuronsandinherentnetwork-basedrhythmgenerationproperties[ 50 77 { 79 ]. increasesinsynchronyacrosschannels,andincreasesintheirregularityofthetimingoftheclusters[ 2 4 76 ].Ithasbeenshownthatendogenouslyactiveneurons[ 50 80 ]generatespontaneousactivityintheculturethatleadstotheaperiodicsynchronizedringofmanyoftheneuronsintheculture.Thesesynchronizedclustersofeventsarereferredtoasbursts,"seeFigure 2-3 .Theburstingpatternschangedramaticallyoverthecourseofthedevelopmentalperiod[ 4 23 79 ],changingfromsmallirregularburststolargermoreperiodicburststhentoirregularlysizedandtimedbursts. 26

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Asmentionedabove,populationburstingismarkedbynetwork-widesynchronizationofactivity.Afterbursts,thenetworkentersarefractoryperiodofquiescence,inwhichactionpotentialsaretypicallynotdetected.Beforebursts,sparseactivityisoftendetectedonseveralchannels.Thissparseactivityhasbeenimplicatedasendogenouslyactiveneuronsorneuronsactivatedbythem.Typically,severalhundredmillisecondstosecondsofendogenousactivityisrecordedbeforeaburstisinitiated.Endogenouslyactiveneuronsregulateactivityandrespondtoexcitationandinhibition[ 80 81 ].Similarburstsofactivityareseeninvivoduringdevelopment.Inaddition,thisactivityhasbeenrelatedtospindlesandepilepticseizures[ 82 83 ].Epilepsyisoftenassociatedwithdeaerentationofneuronsincriticalcorticalcircuitry[ 84 ],oftenleadingexperimentertoviewtheanaloglackofinputinvitroasthecauseofburstingactivity.Ifthisisinfacttrue,electricalstimulationhasthepotentialtocontrolburstsinvitrobydesynchronizingrefractoryperiodsofthecomponentsinthenetwork.2.2.2ExperimentalEvidenceMEAshavebeenutilizedwithneuralculturestoprovideasimplemultichannelextra-cellularrecordingandstimulationgrid.Sincetheirinception,experimentershaveemployedthemtofacilitateunderstandingthebehaviorofnetworksgrownonthesecultureplatforms.Whiledatahavebeencollectedonspontaneousactivity[ 3 4 ]andexplanationsastoitsoriginshavedeveloped[ 23 50 78 85 86 ],manystimulation-basedexperimentsdonotconclusivelyprovethemechanismunderlyingthechanges.Forexample,Jimboet.al.[ 87 ]showedlong-termpathwayspecicchangesoverhoursthroughtetanicstimulation;however,therewasnoabilitytocontrolpathwaypotentiationordepression.TheyprobedrecordedtheresultfromasinglestimulationtheresponseofdetectedneuronstostimulationofeachMEAchannel;thenrapidstimulation0Hzofachannelwasrepeatedlyperformed.Theresponsewasagainprobedhourslater.Theresultshowedsignicantchangesintheresponseofmanyneuronstotheprobingofeachchannel.Incontrast,Eytanet.al.[ 88 ]demonstratedatemporarychangeinthenetwork's 27

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responsetostimulusonaselectedchannel.Moreover,theywereabletoelicitchangesinaspecieddirectionpotentiationordepressionbyusinglowfrequencyofhighfrequencystimulationprotocols;however,theeectfadedafterseveralminuteselapsedwithoutthestimulationprotocol.AnothernotableexperimentisthatofWagenaaret.al.[ 83 ].Theyattemptedburstcontrolwiththeuseofcyclicrepetitionof2-25randomizedchannelsatratesupto50stimulationspersecond.Throughthistechnique,theyweresuccessfulinachievingburstsuppressionwithhighstimulationrates;however,burstingactivityreturnedaftertheprotocolwasdiscontinued.Usingamodelthatreplicatesthesebehaviors,andothersobservedinvitro,willhelptoanswerquestionsthatwouldotherwiseremainunanswered.Otherexperimentalworkrevealssomeself-regulatorypropertiesoftheneuronalnetworks.BiandPoo[ 42 ]performedxedpre-andpostsynapticinductionofactionpotentials.TheresultoftheAPpairingspositivelyornegativelyaectedsynapticecacydependentonwhetherthepairwaspresynapticthenpostsynapticpre-postorpostsynapticthenpresynapticpost-pre,respectively.Inaddition,experimentalevidenceimpliedanamplitudedependencytherebyshowingameansofstabilizingsynapticecacychangesseeChapter 3 .Turriaganoet.al.exploredahigherlevelphenomenainthesenetworksbyblockingexcitationorinhibitionoverlongtimeperiods[ 28 89 ].Theyfoundthatafterremovingtheblockade,activitywasincreasedwhenblockadedecreasesactivity.Similarly,activitywasdecreasedwhenblockaderaisedactivity.Theseregulatorymechanismsgraduallychangedoverhours.Lathemet.al.[ 77 ]exploredtheuseofchemicalstoalteractivityinvitro.Byintroducingnaturallyoccurringinvivohormones,theywereabletopreventburstingandgenerateasynchronousactivity.Theseexperimentsshowthemanywaysinwhichneuralnetworksadapttotheirenvironmentalstimulusorlackthereof. 28

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2.3ModelingUnderstandingandcontrollingtheoriginandpropagationofneuralcultureactivityiscrucialtothedevelopmentofmanyneuro-technologies.Tothisend,manypropertiesofthesenetworkshavebeenexamined[ 4 50 76 90 ],yetcorrelatingchangesatthesynapselevelinneuronalnetworkstonetworkactivityisnearlyimpossibleinvitrobecauseofthenumerousrecordingsitesthatwouldberequired.However,replicatingnetworkactivityinamodelmayallowtheobservationofotherwiseunseensynapticchanges.Largenetworkmodelsarepossiblenowthatcomputationalpowerhasincreasedandsimplieddynamicsofneuronshavebeendescribed[ 91 ].Manysimpliedrulesforsynapticchangeshavealsobeenproposed[ 42 45 ].Whilethesesimplicationsareanexcellentsourcesforcomprehendingthebehaviorofneuronsandsynapsesattheunitlevel,itisdiculttopredictwhatwillhappenwhenprojectingtheserulestotheinvitrocaseofapproximately105neuronsand108synapses.Presumably,thedynamicsofthenetworkareinheritedfromtheinteractionofitsconstituents.Thus,thedynamicpropertiesoftheneuronsandtheirconnectionsdescribethepropertiesofthenetworkeventhoughtheythemselvesmaynotbeabletoexhibittheemergentpropertiesofthenetwork.Moreover,itisdiculttoascertainthefeaturesrelevanttocreatetheemergentproperties.Notonlybecausesomemechanismsarenotwelldocumented,butalsotherearealargenumberofdocumentedmechanisms,eachinvolvingmanycomplexchemicalinteractionkinetics.Simplicationoftherelevantmechanismsisnecessaryforinclusioninlargenetworkmodels.Furthermore,everymodeldrawscriticsduetolackofstrictbiologicanalogiesorsimpliedvariability.2.3.1OriginofInVitroActivityBurstingisoneofthemostpredominatpatternsofactivityobservedwithinculturednetworks.Theoriginofburstinginvitroarisesfromtherecurrentactivationofthenetworkthatissupportedbytheextensiveconnectivityenablingthemtoperpetuatethisactivity.Howevertheexactmechanismsthatproduceburstingarestillamatterof 29

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debate.Thepropertiesofthesenetworksthatproduceburstingcanbedividedintothemechanismsthatinitateaburst,andthosethatterminateaburstonceithasbegun.First,burstingisnotduetoadiusechemicalprocessesinthemediathatsomehowsynchronizesthenetwork.Maedaet.al.[ 76 ]hasshownthatphysicalsectioningthenetworkintoquadrantsusingalaserresultsinquadrantsthatgraduallydesynchronizeovertime.Tabaket.al.01[ 92 ]hasshowninatheoreticalstudythattheterminationoftheburstisadeterministicprocessthatmustberelatedtoasomesortoflongduration>100msrefractoryperiodthatsuppressesactivitybutdecaysoverintervalsinwhichactivityisabsent.Insupportofthisnotion,thedurationofabursthasbeenshowntobepositivelycorrelatedwiththeprecedingIBIreectingthedecayofthisinhibitoryprocess[ 93 94 ].Oneearlycandidateforthisrefractoryprocesswastheroleofintra-cellularcalciumandslowinactivationofsodiumcurrentsoscillationsthatcoincidewiththeringratewithinandbetweenbursts[ 52 95 ].Duringtherepeatedringofaneuronwithinaburst,theintracellularcalciumlevelsincreaseandgraduallyaccumulatereducingtheabilityoftheneurontore.However,Darbonet.al.[ 96 ]hasshownthatcalciumalonecannotbethesoledeterminateofburstinitiationortermination.Ifelevatedcalciumlevelswereresponsibleforburstterminationthenyouwouldexpectthepeakcalciumleveltobecorrelatedwiththeendoftheburst.However,actualmeasurementsofthepeakofcalciumconcentrationoccurwellbeforetheterminationoftheburst.Second,theonsetofeachburstisnotpreciselytimedwiththerecoveryofcalciumasadeterministicprocessmightsuggest.Finally,Darbonetalhypothesizedthatifincreasesincalciumconcentrationwereresponsibleforbursttermination,thenarticiallyincreasingcalcuimduringtheonsetofaburstshouldpresumablyshortenthedurationofthatburstanditdidnot.Itappearsthatamechanismsuchasshort-termdepressionandrecoveryofsynapticecacy[ 39 78 ]mayplayakeyroleinbursttermination.Accordingtothisidea,therepeatedringofaneuronduringaburstgraduallyincreasesshort-termdepressionofthatneuron'ssynapses 30

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leadingtotheeventualfailureofsynaptictransmission.Asaresultburstingcannolongerpropagatethroughoutthenetworkandtheburstterminates[ 80 ].Thesesynapsesrecoverovertimeandeventuallysetthestageforanotherbursttooccur.Theinitiationofaburstappearstobeastochasticprocessthatisprimarilyproducedbyendogenouslyactiveneuronsthatareactivebetweenbursts[ 77 ].Forexample,Lathamet.al.000hasshownthatthenumberofthesecelltypesmeasuredinvitroisdirectlycorrelatedwiththeamountofburstingthatoccurs.Thesecellsmayalsoconstitutesocalled"triggernetworks"embeddedwithintheoverallnetworkwhosesynapticstrengthisstrongenoughtotriggeraburst.Theconceptbehindthisideaisthatparticularneuronsorsetofneuronsthatarestronglyconnectedandretogethersuchastheendogenouslyactiveneurons,cancauseasequenceofAPsthatcancascadethroughoutthenetwork.Inagreementwiththis,itwasshownthatburststendtostartinahandfulofsimilarwaysineachculture[ 79 ].Thiscombinationofproperties,synapticdepressionforbursttermination,andendogenouslyactiveneuronsamong"triggernetworks"aretwoimportantfeaturesthatshouldbeincludedinanymodelofthesenetworks.2.3.2ModelsofIndividualNeuronsManyneuronmodelsexistthatencompassvaryingdegreesofbiologicalrealismandcomputationalsimplicity.Someoftheubiquitousmodelsaretheleakyintegrate-and-reLIF[ 97 98 ],Hodgkin-HuxleyHH[ 99 ],Morris-LecarML[ 100 ],Fitzhugh-Namigo[ 101 ],andIzhikevichmodels[ 54 91 ].Foramorecomprehensivecomparison,see[ 91 ].TheHodgkin-Huxleymodelwasdevelopedtomodelionchannelgatinginagiantsquidaxon[REFS]andisoneofthemostelborateandwidelyusedmodelsofanindividualneuron,ionchannels,andsynapses.Themodelparametershavesincebeenextendedtodescribeotherneurontypesdependingonspecickineticsbutstillrequiressignicantamountsofcomputationtimecomparedwithothermodels.Theleakyintegrate-and-remodelisverysimpleandubiquitousinmodelingdespiteitslackofbiologicalattributesandinabilitytorereboundspikesorburstsunderconstantinput.ALIFneuron 31

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consistsofasinglevariablethatintegratesinputsandresanactionpotentialwhenapredeterminedthresholdisreached.Thevariableresetsandthenbeginstointegratenewinputs.Additionally,aleakinesstermisincorporatedthatdischargestheintegrationvariableovertime,whichaddsminimalbiologicalsimilarity.TheIzhikevichmodelusesareducedformoftheHHneuronmodelasitsbasis.Theseneuronsconsistoftwovariableswithanon-linearreset.Onevariabledenotesmembranevoltageintegratingsynapticcurrentsandenablingadynamicthreshold,whilethesecondvariableencompassesthedominantpersistentcurrentsofthecellbeingmodeled.ThisvariablereductionenablestheIzhikevichmodeltomaintianmanybiologicalpropertieswhilesignicantlyreducingcomputationtime.Onecomponentofthebiologythatisoftenoverlookedwhiledevelopingnetworkmodelsiscabledelayofaxons.Cabledelayreferstotheconductiontimeforanactionpotentialtopropagatefromtheinitiationpointtotheaxonterminalwhereitcommunicatestopostsynaptictargets.TheraceconditionsthatdevelopbecauseofthishaveasignicantimpactonpathwaysastimingsareimplicatedinalteringsynapticecacydiscussedlaterinthisChapter.Anothercomponentofneuralmodelsinvitroisspontaneousactivity.Twopredominatethemesexist:randomringofanyneuronorsuprathresholdnoiseinjectedintoaselectnumberofneurons.Giventheendogenousneuron'squiescenceafterburstsneithermodelisaccurate.2.3.3ModelsofSynapsesWhilesynapticactivationisgenerallyunderstood,synapticplasticityisasubjectofwidedebate.Still,synapticactivationisgenerallymodeledinoneoftwoways:ascurrentinducingsynapsesorthroughbindingandunbindingreceptorkineticsthatalterpostsynapticconductance.Thelatteristhemorebiologicallyrelevantofthetwo.Severalformsofsynapticplasticityhavebeenidentiedoverawiderangeoftime-scales.Frequency-dependentsynapsescanalterecacyrapidlybasedonringrateresultinginchangesinpostsynapticconductancesbetweeneachpresynapticaction 32

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potential.Frequency-dependentsynapsescanexhibitshort-termdepressionSTDand/orshort-termpotentiationSTP.Typicallytheyreturnnearsomebaselinevalueinmillisecondstoseconds.Synapticdepressionandpotentiationalsooccurinlongerlastingformcalledlong-termdepressionLTDandlong-termpotentiationLTPthatcanbestablefromminutestohours.Long-termsynapticchangeswereillustratedbyMarkramet.al.[ 102 ]andBiandPoo[ 42 ].Theynotedbothdependencyonfrequencyandtimingofpre-andpost-synapticAPsforchangesinsynapticecacy.SincethenLTPandLTDhavebeenfoundtobemodulatedbyanumberoffactors[ 45 47 89 102 ]andexpressedasaresultofseveraldierentchangesatthesynapses.Specically,AMPAreceptortrackingtothesynapticmembranecanbeincreasedbyalackofpostsynapticactivity,andvesiclereleaseprobabilityincreasesattheaxonterminalswithrepeatedpresynapticactivity.Regardless,synapseshavethepotentialtobehighlyplasticandassuchareoftensingledoutasthelocationforlearning.2.3.4CumulativeModelsofInVitroNetworksModelingcanaccelerateunderstandingofinvitronetworksbyexploringthenetworkinwaysthatwouldotherwisebenearlyimpossible.Equippedwithmodelexplanations,newprotocolsmayberapidlydevelopedforinducingshort-andlong-termmodication.Modelscansimulateexperimentsmorerapidlythanexperimentscanbeperformedoninvitrocultures.Inaddition,themodelprovidesthemeanstoperformmultipleexperimentsontheexactsameculture"bystartingthemodelintheexactsameconnectivityandinitialconditions.Developingandevaluatingamodelwillilluminatetheeectindividualunitshaveonthenetwork.Inaddition,usingamodelthatregulatesitsownactivityiscriticaltounderstandingtheculture'sselfregulation.Asimpliedyethighlyaccuratemodelwouldprovetobeaboontoresearchintheeldofinvitroneuronalnetworks.Severalcurrentmodelsexistthatincorporatevariouspropertiespreviouslymentioned.AmodeldevelopedinPotter'sgroup[ 103 ]bringstogetherlong-termplasticityruleswithfrequency-dependentsynapsesandattemptstomimicneuronsonanMEA.Their 33

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modelisabletoachievespontaneousandevokedpopulationbursts.Inaddition,atetanusfollowedbybackgroundstimulationtotheirmodelisabletoproducestableweightchangesasmeasuredbyacenterofgravityfunction.AnothermodeldesignedinBen-Jacob'sgroup[ 104 ],whichalsousesfrequency-dependentsynapses,emphasizestheimportanceofinhomogeneitytoproducepopulationburstswithinter-spikeintervalssimilartoinvitrocultures.LyttonandSejnowskistudiedtheeectsofsynchronizationbyinhibitoryneuronsusingbothasimpliedandcomplexmodelofindividualneurons[ 105 ].Theydemonstratedhowinhibitorypost-synapticpotentialscanmodulateanincreaseordecreaseinthetargetneuron'sringratedependingonthestateofthetargetneuron.Lathamet.al.proposedamodelthatsupportsthehypothesisthatthefractionofendogenouslyactivecellsisakeycomponenttotheburstingbehaviorofneuronalcultures[ 50 77 ].Izhikevichet.al.proposesaneuralnetworkmodelinspiredbytheanatomyofthecerebralcortex"thattheyusetoanalyzeprecisetimingofself-organizedneuronalgroupstheyrefertoaspolychronousgroups[ 54 106 ].Theyareabletocharacterizethesegroupsthatpresentthemselvesasmillisecondtime-lockedpreciseringpatterns.Manyotherkindsofneuralmodelsexistincludingthosedesignedtomimicotherportionsofthenervoussystemasidefromcortex.Forexample,Buteraet.al.haveamodelofrespiratoryrhythmgenerators,whichalsoexhibitpopulationbursting[ 48 107 108 ].TheirmodelsrelyonslowNa+andK+membranecurrentstoproducebursting.YetanothermodelofneuraltissuecomesfromTabaket.al.whomhaveamodelofdevelopingchickspinalcordcultures[ 78 ].Theyclaimthatinahomogenousmodelofexcitatoryneurons,burstingismodulatedbyfastsynapticdepressionmimicsinvitrodatamorecloselythandoesburstingmodulatedbyareductioninneuralexcitability.Moreinformationonneuralculturemodelingcanbefoundin2reviewsbyDarbonandStreit[ 80 109 ].Thisdissertationseekstodetermineandutilizetheimportantpropertiesofneuronsandsynapsestoimplementemergentnetworkdynamicsinsimulation.Thisresearch 34

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canbeappliedtodevelopingself-regulatingandlearningnetworkstocontrolarticialembodimentslikethosepresentedin[ 103 110 ].Inaddition,themodelcanbeusedtoexplorethecomputationalpropertiesofthesenetworksandtoinvestigateneuronalgroupformation[ 60 106 111 ]andratecoding,eventuallyleadingtoabetterunderstandingofinteractionswithcorticalnetworks,whichwillenablebetterencodinganddecodingschemesforbrainmachineinterfaces.Chapter 3 and 4 describethedetailsofourmodelbeginningwithanimportantandnovelfeaturesofthismodel,thatis,amplitudedependentplasticity. 35

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CHAPTER3AMPLITUDEDEPENDENTSYNAPTICPLASTICITYSynapsesareoftenindicatedasthelocationforlog-termchangesassociatedwithlearning;assuch,itiscriticaltodevelopamodelofsynapticdynamicsthatincorporatestheiradaptationbasedonpre-andpostsynapticsignaling.Long-termsynapticplasticityrulesexistinabroadvarietyfromsimpletocomplex,incorporatingmanyphysiologicalphenomena.Throughthischapter,asimplerulecapableofmimickinginvitrodistributionsofsynapticweightsispresentedandexplored.3.1BackgroundOften,long-termsynapticchangesaremodeledusingaderivationofspike-timingdependentplasticitySTDPinlargenetworkmodelssimulatinginvitroneuronaldynamics.STDPisanintuitivemethodforneuronalsynapsestoemphasizecausalHebbianstylerelationshipsimplicatedasamethodforlearning[ 112 ].ThetemporaldependanceofsynapticecacywasreportedbyMarkramet.al.[ 102 ]andBiandPoo[ 42 ]throughinvitroexperiments.TheSTDPlearningruleisasubstantialsimplicationofbiologicalfactorsthatarestillnotwellunderstood.ForareviewofSTDP,seeDanandPoo[ 113 ].Innetworkmodels,computationalsimplicityisoftenimportantbecauseofthenumerouscomponentsthatmustbecalculatedateachtimestep.Admittedly,theprevalentuseoftypicalSTDPisunlikelyduetotheaccuracyofthemodel[ 45 ];indeed,itscomputationalsimplicitymakesitattractiveforlargenetworkmodels.Generally,STDPrulesgenerateabimodaldistributionofsynapticweightsbecausethereisnostableequilibriumstate[ 112 ].Asaresult,thesynapticweightsareforcedtowardthehighestorlowestvalues,whicharearticiallyconstrained.However,physiologicaldataindicatethatpeakexcitatorypost-synapticpotentialsEPSPsaretypicallyunimodallong-taileddistributions[ 114 ]. 36

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Articialconstraintsandbiashavebeenaddedtoothermodelsinanattempttobalancethedistributionofweights.Songet.al.[ 112 ]wereabletogenerateunimodalsynapticweightdistributionsusingbiasandrestrictedoperationalrange.OtherformsofSTDP,withadditionalspikeinteractionrules,alsogeneratedistributionswithlessgroupingneartheminumumandmaximumvalues.Indeed,CateauandFukai[ 115 ]showedmostnon-weightdependentSTDPwindowingfunctionsgenerateextremevaluesofsynapticweights.Recently,Bienstock-Cooper-MunroBCMruleshavegainedattention[ 116 ],however,manyofthoserulesalsosuerfrombimodaldistributions.OurapproachattemptstobuilduponSTDP[ 42 102 ]withasimplebutpowerfulmodicationofSTDPcalledamplitudeandspike-timingdependentplasticityASTDP.InthispaperwedescribethealgorithmandanalyzethepropertiesofASTDP.TheresultsshowthatASTDPweightsareindependentofpre-andpostsynapticringratesbutnottheirtimings;however,therateofchangeistightlycoupledtoringrate.Multiplicativenoise,usedin[ 117 ],dominatestheweightdistributionofASTDP.Inaddition,weshowthatpartiallycorrelatedpre-andpostsynapticconductancesproducediscerniblechangesinsynapticweights.3.2ResultsBiandPoo[ 42 ]showthattheamplitudedependencyofsynapticchangesisnon-linearandinverselyrelatedtotheinitialweight;thisrelationshipgeneratesstrongpotentiationforweaksynapsesandweakpotentiationforstrongsynapses.Inotherwords,strongsynapsesarebiasedfordepressionandweaksynapsesandbiasedforpotentiation.ThemodelofsynapticchangesproposedhereextendsthenotionofSTDPtoincludeadependencyontheinitialweightofthesynapse,seeFigure 3-3 .Thisdependencywasshowntoexistforpotentiationandnotfordepressionbasedonpercentchangeoftheweight.Assumingthereissomeweightdependencyfunctionfwforpotentiation,wechoosefwtohaveboundingvaluesforw=0andw=1andapproximatetheresultsobtainedbyBiandPoofor[0.08,0.8]nS.Thus,thegeneralformoftheequationsusedfor 37

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Figure3-1.Amplitudeandspiketimingdependentplasticitycurve.Forexcitatorysynapses,theamountofchangeisdependentoninitialweight.IncontrasttotheclassicSTDPcurve,theASTDPcurveillustratesweightdependentchangesinpotentiationwithlargechangesforsmallweightsandsmallerchangesforlargeweights.Graphamplituderepresentsvaluesforasinglepre-postorpost-prespikepairing.Theupperandlowersurfacesrepresenttheregionsforpotentiationanddepression,respectively. calculatingamplitudedependentsynapticchangesareshownbelowwherewrepresentsthesynapticweightinnanosiemens.PresynapticActionPotentials:w=)]TJ/F22 11.955 Tf 9.298 0 Td[(wDincXne)]TJ/F24 5.978 Tf 5.756 0 Td[(tpostn DPostsynapticActionPotentials:w=wPincfwXne)]TJ/F24 5.978 Tf 5.756 0 Td[(tpren Pfw=e)]TJ/F23 7.97 Tf 6.586 0 Td[(w 38

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aControlSimulation bSimulationwithSpikeJitter cHighFrequencySimulationFigure3-2.Stablevalueofsynapticweightforxedpre-postspiketimingssimulationresults.StablevalueofsynapticweightinnSforxedpre-postspiketimingsa,candxedpre-postspiketimingswithspikejitterGaussian=0msand=2msb.Synapticweightsinaatfrequencieslowerthan10Hzandsmalldelaysms
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Figure3-3.Amplitudedependentplasticity.ApplyingtheruleinFigure 3-1 forapotentiationprotocolblueanddepressionprotocolred.ThiscurvemimicsthetgeneratedbyBiandPoo[ 42 ];however,giventheparameterspresentedinthischapter,theprotocolconsistedof240spikepairs,asopposedtothe60usedbyBiandPoo.LargerPincandDincvalueswouldlowerthenumberofrequiredpairstoachievethiscurve. DincandPincareconstantsthateectrateofdepressionandpotentiation,respectively.isaconstantthatdeterminestheemphasisofweightfeedback.Itshouldbenotedthat=0fw=1isamultiplicativeSTDPupdaterule[ 118 ].PincandDincproportioncanbeusedtomodulatethedistributionofsimulatedsynapsesbuttheirscaleaectstherateofchangeinthesynapticweights.DandParethetimeconstantsforthedepressionandpotentiationwindows,respectively.EstimatedvaluesoftheparametersusedareDinc=:001,Pinc=:004,=3:2nS)]TJ/F21 7.97 Tf 6.587 0 Td[(1,D=35ms,andP=20ms.NoticethelargedependencyoftheweightupdatecurveoninitialweightandtheasymmetryofthetimewindowsfordepressionandpotentiationthatcanbeobservedinFigure 3-1 .Matlabcomputationofsynapticweightshowsa25%increaseincomputationtimerequiredtocalculatefwascomparedwithanSTDPrule.However,theadditional 40

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Figure3-4.FrequencydependentnatureoftheASTDPrule.UncorrelatedhomogeneousPoissonspiketrainsweregeneratedtosimulateonlythefrequencydependentnatureoftheASTDPrulebaseduponpre-andpostsynapticactivity.MonteCarlosimulationswereperformedwithvetrialsperdatapoint.Frequenciesshownrangefrom2to40Hz.Colorintensityindicatesaveragetimeinsecondsforsettlementfromtheinitialweightof0:1nS.Foruncorrelatedspiketrains,synapticweightssettledtothesamevalue:26nSafterasucienttimeperiod. computationtimeisnegatedifsaturativecalculationsanecessityforSTDPareremovedfortheweightvalueinASTDP.3.2.1FixedPointAnalysisWiththenegativefeedbackofsynapticweighttoplasticity,uncorrelatedpre-andpostsynapticinputwilldrivesynapticweightstowardastablevalue.Usingrepeatedpre-andpostsynapticpatternsofactionpotentials,thisstablepointisshowninFigure 3-2a asfunctionofspiketimings.Theeectsofinputcorrelationinrealisticsignalsareaddressedinafollowingsubsection.Reinforcementofsynapticweights,byrepetitionofpre-andpostsynaptictimings,arerequiredtomaintainpotentiatedordepressedsynapsesbetweencoupledneuronswhenthoseneuronsactivateatalternatetimingsduetonetworkactivity.TheprocessofsynapticchangeunderASTDPisabalancebetweencorrelated 41

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Figure3-5.Convergenceinthedistributionof200weightsusingASTDP.SynapsesweresimulatedusingarticialhomogeneousPoissonspiketrainspre-andpostsynapticallywithmeanringratesselectedfromatruncatedGaussiandistribution=20Hz,=4Hz,andmin=4Hz.Postsynapticspikesarecomposedof5%ofpresynapticspikesosetbyauniquedelaypersynapseGaussian=synapsedelayand=3msandjitterperspikeGaussian=0msand=2ms.Synapticweighttracesarecoloredfromblacktolightgreycorrespondingtoinitialsynapticweight.Inthisgure,theconvergenceofweightsareinuencedbytheirringrateanddistancefromthesettlingpoint.Thesettlingpointisprimarilytunedbythebalanceofthetimingofpostsynapticspikesthatarepresentinthepresynapticspiketrainandtheuncorrelatedactivity.Thiscanbeseeninthespreadthenalweightsirrespectiveofinitialweight. 42

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positiveandnegativelagsinpre-andpostsynapticactivityanduncorrelatedactivityi.e.noisethatdrivestheweighttowardastablepoint.Furthermore,synapticunreliabilityincreasesnoisestabilizingtheweightfurtherasdemonstratedin[ 119 ];however,thisphenomenaisnotaddressedhere.Todeterminethefrequencydependencyofthexedpointandrateofconvergence,uncorrelatedhomogeneousPoissonspiketrainsweresimulatedpre-andpostsynaptically.Thexedpointwasapproximately0.26nSandindependentofpre-andpostsynapticringratesforuncorrelatedspiking.However,thesettlingtimevariedoverordersofmagnitudeseeFigure 3-4 fortheringratesof2to40Hz.Theconvergenceofsimulateduniformlydistributedsynapticweightswithavarityofpre-andpostsynapticactivityisshowninFigure 3-5 .Therateofconvergenceisdeterminedbypre-andpostsynapticringrates,thenumberofsimulatedpresynapticinducedpostsynapticactionpotentialsdatanotshown,anddistancefrominitialweighttothexedpoint.3.2.2WeightDistributionsThedistributionsofweightscreatedbytheASTDPandSTDPruleweresimulatedtoshowthebimodalandunimodalnatureofSTDPandASTDP,respectively.Torecreatenetwork-likeinputs,PoissonspiketrainsweregeneratedwithvaryingfrequenciesanddelaysseeFigure 3-6 .Asexpected,theSTDPrulepromotesthedevelopmentofabimodalweightdistributionandtheamplitudedependentversionpromotestheconvergenceofweightstoaunimodaldistribution.Multiplicative,weightscaled,synapticmodicationnoiseinducedlargechangesinthedistributionofsynapticweightsseeFigure 3-7 .Usingthisnoiseintroducedin[ 117 ],thevarianceoftheweightdistributionisgreaterthanASTDPwithoutnoiseandtheskewispositiveineachsimulationthatwasperformedregardlessoftheshapeofthedistributionwhennoweightdependentsynapticmodicationnoiseispresent.The 43

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Figure3-6.ComparisonofASTDPandSTDPweightdistributions.Upper:Histogramshowingtheunimodaldistributionof1000weightsusingASTDP.Lower:Histogramshowingthebimodaldistributionof1000weightsusingSTDPmax=1;min=0:1.SynapsesweresimulatedusingarticialhomogeneousPoissonspiketrainspre-andpostsynapticallywithmeanringratesselectedfromaGaussiandistribution=20Hz,=4Hz,andmin=4Hz.PostsynapticspikesarecomposedofarandompercentageofpresynapticspikesGaussian=8%,=3%,andmin=3%osetbyauniquedelaypersynapseGaussian=synapsedelayand=3msandjitterperspikeGaussian=0msand=2ms. Figure3-7.Histogramofsynapticweightswithmultiplicativenoise.WhiletheASTDPtypicallygeneratesunimodaldistributions,addingzeromeangaussiannoise=0:015scaledbytheamplitudeofsynapticweightcausestheweightdistributionmeantoshiftnegatively,variancetoincrease,andtheskewtobecomepositivesimilartothatshownby[ 117 ].Otherwise,parameterswereidenticaltotothoseinFigure 3-6 44

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a b cFigure3-8.Stabilizedvaluesofsynapticweightsfrompre-andpostsynapticconductancebasedinput.Simulationresultsoftheapproximatestablevalueofsynapticweightinnanosiemensfrompre-andpostsynapticconductancebasedinputderivedfrom[ 120 ]forpyramidalcells.Plotsshowaveragedsynapticweightforvaryinginputcorrelationandcorrelationlag.aSharedAMPAinput.bSharedGABAAinput.cSharedAMPAandGABAAinput.Initially,allweightswere0:2nS.Synapticconductanceisaddedtotheexcitatorypostsynapticconductanceaftereachpresynapticactionpotentialanddecayswithatimeconstantof3ms.Thedelayfrompresynapticactionpotentionaltosynapticactivationis2:0ms.Simulationslasted10minuteswithpre-andpostsynapticringratesapproximately15Hz.Datawereaveragedoverthenal10secondspertrialandthreetrialsperdatapoint.Also,notethedieringscalesofthecolorbarsdemonstratingthesuperiorityofinhibitorycontroloversynapticweight.WhenbothInhibitoryandexcitatoryconductancesaresimilarpre-andpostsynaptically,theminimumandmaximumweightvaluesareatshortertimelagsthanifonlyexcitatoryorinhibitoryconductancesarecorrelated. dierenceisduetothelargeamplitudeofnoisebasedchanges=0:015relativetotheamplitudeoftimingbasedchangesPincandDinc.3.2.3SynapticModicationbyCorrelatedInputToshowtheeectsofinputcorrelation,apre-andpostsynapticneuronaresimulatedusingIzhikevich'smodelofregularspikingRScorticalneurons[ 32 ]coupledviaasingle 45

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conductancebasedsynapsegovernedbytheASTDPequations.ThreeAMPAandGABAAconductancetimeseriesaregeneratedaspresynapticinput,postsynapticneuroninput,andcommoninputtobothneuronsusingOrnstein-Uhlenbeckrandomwalkprocesses[ 120 ].AsshowninFigure 3-8 ,theaverageresultingweightindicatesthestrongdependenceoftheeectofcorrelatedinput.Duringsimulation,thefractionofsimilarpre-andpostsynapticGABAAconductanceproducedlargerchangesinsynapticweightthanthefractionofAMPAinput.LargesynapticconductancesareproducedwithcommonAMPAandGABAAinputtopre-andpostsynapticneurons.ThephenomenaoflargeGABAAeectscouldbearesultofslowertimeconstantsassociatedwithGABAAconductancesalongwithlargeramplitudes.Interestingly,thepeaksineachofthegraphsinFigure 3-8 arenotatthesametimelag.3.3ConclusionsAmplitudeandspiketimingdependentplasticityASTDPrequireslesssupervision|intheformofarticialconstraints|thanSTDPtomaintainaunimodaldistribution.Inpractice,however,ASTDPproducesmorerealisticweightchangeswhensaturationeectsareimplementedontheamountofweightchangeinlargenetworkmodelsdatanotshownsimilartondingspresentedin[ 45 ].ASTDPisanaturalanswertoSTDPstabilityissuesandrequiressimilarcomputationtimeifsubstitutedfortheweightsaturationcalculations.Moreover,amplitudedependentSTDPhasbeenreportedinvitro[ 42 ].Thisdependencyiscriticalforstabilityoftheweightdistribution.However,thisimplementationofASTDPdisregardsthecomplicationsofmultipleinteractingspikes[ 45 121 ].Forthisreason,continueddevelopmentofASTDPmodelswouldberequiredtoreproducethefrequencydependentinductionofLTPshownbyMarkramet.al.[ 102 ].Pre-andpostsynapticspiketrainseectthemean,variance,andskewofthesynapticweightdistributions.Inaddition,multiplicativesynapticmodicationnoisesimilartothatusedin[ 117 ]altersthedistribution;foreverysimulationperformedwiththisadditional 46

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noiseterm,thevarianceoftheweightdistributionincreasedandpositiveskewwasinducedifnotalreadypresent.ThisphenomenonshouldbeinvestigatedfurthertodeterminethenoisedistributionanddependenciesinsynapticmodicationasnoiseisastrongstabilizingforceinamplitudedependentSTDPrules.Indeed,theabilityofsynapsestomaintainmeaningfulweightswithlargeamountsofnoiseshouldbeexplored.SimulatedsynapsesfollowingASTDParehighlyactivitydependentbothwithrespecttotherateofchangeandstablesynapticweight.Nonetheless,synapsesconnectingtwosimulatedneuronswithsimulatedinvivoconductancesmaintainsynapticweightswithoutlargeuctuationsexceptduringsomebursts,datanotshown. 47

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CHAPTER4SELF-REGULATINGINSILICOMODELOFINVITRONEURONALNETWORKSChapterObjective:Chapter 3 providedadescriptionofanovelmethodofimplementingspiketimingdependentplasticity.Inthischapterthecompletemodelofinvitronetworksisdescribed.Neurons,invivoandinvitro,exhibitselfregulationofactivity.Mostnotably,inputismodulatedbyshort-termdepressionandpotentiationofsynapsesandbylong-termactivitydependentAMPAandNMDAreceptorinsertionandremoval.Byincorporatingtheseconceptsintoasimulatednetworkofcorticalneurons,thismodelisabletoreproducethepatternsofactivitymeasuredinvitro.Inter-spikeintervalISI,inter-burstintervalIBI,andsynapticweightdistributionsarecompared.Spontaneousandelicitedactivityproducedbythismodelissimilartotheirinvitrocounter-parts.Finally,theselfregulationincorporatedintothismodelovercomesissueswithinpriormodelsusingstaticweightsduetoanon-uniformnumberofpresynapticcontacts.4.1IntroductionSynchronousnetwork-wideburstingisoneofthemostprevalentpatternsofactivityobservedwithininvitrocultures.Hence,oneoftheprimarygoalsofcreatingamodelofthesenetworksistoreplicatethatpattern.Theexactmechanismsthatproduceburstingarestillamatterofdebate.Frequencydependentsynapseswithleakyintegrate-and-reneuronshavebeenshowninmodelstodemonstrateburstingbehavior[ 103 104 ];while,burstingbehaviorisalsoachievedbymodelingNa+inactivationandslowK+membranecurrents[ 48 107 108 ].Furthermore,Lathemet.al.indicatesburstingbehaviorismodulatedbythefractionofendogenouslyactivecells[ 50 77 ].Hence,modelingburstingphenomenamayprovideinsightsintotheemergentdynamicsofthesenetworksintroducedbyspeciccellularproperties.Correlatingchangesatthesynapselevelinneuronalnetworkstonetworkactivityposessignicantchallengesinvitrobecauseofthenumerousrecordingsitesthatwouldberequired.Modelingenablesresearchersaccesstotheunderlyingvariablesdescribingthesystemallowinganypost-experimentanalysisthatis 48

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desired.Inaddition,theycanaccuratelyreproduceinitialconditionsinsimulation,whichiscrucialwhenstudyingnon-lineardynamicalsystems.However,thepropermathematicaldescriptionofthemodelisimportantwhenattemptingtoreplicatealargerangeofinvitroproperties.Twoofthesepropertiesmaybeparticularlyrelevant:plasticityandhomeostaticregulation.Plasticity.Often,long-termsynapticchangesaremodeledusingaderivationofspike-timingdependentplasticitySTDPinlargenetworkmodels.Generally,STDPrulesgeneratebimodaldistributionsbecausethereisnostableequilibriumstate[ 112 ].Asaresult,abimodaldistributioniscreatedwithsynapticweightsbeingforcedtowardthehighestorlowestvalue,whicharearticiallyrestricted.O'Brienet.al.showedexcitatorypost-synapticpotentialsEPSPstobeunimodallong-taileddistributionsinspinalcorddisassociatedcultures[ 114 ].Articialconstraintsandbiashavebeenaddedtoothermodelsinanattempttobalancethedistributionofweights.Inaddition,O'Brienshowedoverallactivitydependentmodulationofsynapticecacythroughblockadeofexcitatoryandinhibitorytransmitters.Homeostaticregulation.Homeostaticregulationhasbeenproposedasarequirementtobalancelong-termsynapticchanges[ 122 ].Homeostaticregulationmechanismshavebeenshowntoaecttheexcitabilityofratcorticalneuronsinvitro[ 28 ].Indeed,developingnervoussystemsexhibitthishomeostaticplasticitythroughthescalingofAMPAandNMDAcurrentsandbalancingofinhibitionandexcitation;forreview,seeTurrigianoandNelson[ 123 ].Thisselfregulationmechanismsimpliestheconstructionofamodelforneuronalnetworksbyperforminginput-scalingautomatically.Althoughotherself-regulatingmodelsexist[ 117 124 ]thisworkchoosesadierentapproach.Weincorporatesimpliedmodelsofthenetwork'sconstituentsbutrequirethatthemodelsusedincludecriticaldynamicfeatures,whichareexcludedfrommanymodels.Forexample,synapticconductances,frequency-dependentsynapses,amplitude 49

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dependentlong-termplasticity,neuronaldynamics,selfregulation,propagationdelays,andendogenousactivity.Inthiswork,wepresentamodelthatproducessimilaractivitytoinvitroculturesofratcorticalneuronsthatincludesfrequencydependentsynapses,endogenouslyactiveneurons,synapticplasticityrulesdescribedearlierinChapter 3 ,andhomeostaticregulation.Wethendemonstrateourmodel'scompliancewithcurrentexperimentaldataandanalyzetheparametersthatproducethoseresults.4.2AModelofInVitroNetworks4.2.1ModelingtheSpatialPositionofEachNeurononanMEANeuronpositionswererandomlydistributedina2Dplane.Aradiallysymmetricdistributionwasttotheheightofapartialellipticalcross-sectionestimatingawetteddropletofuidonahydrophillicsurfaceusedtoplacecellsduringculturemeasuring3:5mmindiameterandapproximately1:5mminheightwithtotalvolumeequalto20L.Invitroconnectivityiswidelydiscussedinliteraturewherepatterningisused[ 125 ].However,thenetworksusedinthisdissertationarenotpatternedandwehaveonlyafewestimatestobasetheconnectivityofthemodelon[ 14 126 ].Basedonobservationsduringplatingandgrowthofthecultures,weproposeasimpletthatachievesarealisticdistributionofneuronsandagreeswithliteratureonthedistributionofthelengthofconnectionsbetweenneurons.Duringthedisassociationprocess,corticalcellsaresuspendedinsolution.Asmallvolumeofthesolutionisthepipettedontoahydrophilicsurfaceformingacontactanglegreaterthan90.Ifthedropletissmallenough10)]TJ/F15 11.955 Tf 12.833 0 Td[(20Linthiscaseandisnotdisturbedonplacement,thanweassumethatthedropletisradiallysymmetricandtheheightofacolumnofuidabovetheglassdishisapproximatedbyanellipseinacross-section.Then,giventhevolumeofuidandthediameterandheightofthewetteddroplet,theellipsecanbecalculated. 50

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Figure4-1.Ellipticaldropletcross-section.Exampleofthecross-sectionformedbythedropletandahydrophilicsurfacewithellipsesuperimposed.Itispossibletocalculateaandb,givenh,randVthevolumeofthedroplet. Wefurtherassumethatthesolutionishomogenousandtheheightofthecolumnofuid,ataparticularxandy,isproportionaltotheprobabilityofacellsettlingoutofsolutionatthex,ycoordinates.Thus,usingtheseassumptionsweareabletodistributecellsonthesurfaceofasimulatedMEA.Themodelofneuroncellbodypositionsdisregardsthefacttheneuronsarehighlymobileandtendtomovetowardsotherneurons[ 125 ].TheellipseinFigure 4-1 canbetbyndingthesolutiontoEqu. 4{1 fortheminoraxis,b,givenh,r,andV.Themajoraxis,a,canbefoundbyevaluatingEqu. 4{2 .0=2 3b r2 1)]TJ/F21 7.97 Tf 6.586 0 Td[(b)]TJ/F23 7.97 Tf 6.587 0 Td[(h=b21 2r2 1)]TJ/F15 11.955 Tf 11.955 0 Td[(b)]TJ/F22 11.955 Tf 11.955 0 Td[(h=b23 2)]TJ/F15 11.955 Tf 9.73 0 Td[(r2 1)]TJ/F15 11.955 Tf 11.955 0 Td[(b)]TJ/F22 11.955 Tf 11.955 0 Td[(h=b2)]TJ/F22 11.955 Tf 9.73 0 Td[(r23 2)]TJ/F15 11.955 Tf 9.73 0 Td[(2r2b)]TJ/F22 11.955 Tf 9.73 0 Td[(h)]TJ/F22 11.955 Tf 9.73 0 Td[(V{1a=r2 1)]TJ/F15 11.955 Tf 11.955 0 Td[(b)]TJ/F22 11.955 Tf 11.955 0 Td[(h=b21 2{2whereaisthemajoraxisoftheellipse,bistheminoraxis,histhemeasuredheightofthedropletafterplacingonthesurface,ristheradiusofthedropasviewedfromabovetheglasssurface,andVisthevolumeofthedropletused. 51

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Forourcultures,theparametersusedareh=2:0mm,r=3:5mm,andV=20mm3withapproximately10,000-50,000cells.TheresultingsimulateddistributionofcellbodiesareshowninFigure 4-2 .4.2.2IndividualNeuronsFollowinghistologicalassays,themodelincorporates80%excitatoryneuronsand20%inhibitoryneurons[ 8 ].Allneuronsreceivesub-thresholdzeromeanGaussiannoisecurrentwith=70pA.Themodel'sneurondynamicsarederivedfromIzhikevich'swork[ 32 ]whichincludemodelsforanumberofcorticalneurons.Thismodeliscomposedoftwoofthosecelltypes.AnExcititoryRegularSpikingNeurondescribedbyequation 4{3 :_v=:007v2+:7v+16:8)]TJ/F22 11.955 Tf 11.955 0 Td[(u+:01I{3_u=)]TJ/F22 11.955 Tf 9.299 0 Td[(:0006v)]TJ/F22 11.955 Tf 11.955 0 Td[(:03u)]TJ/F22 11.955 Tf 11.955 0 Td[(:036Resetcondition:ifv35thenv=)]TJ/F15 11.955 Tf 9.299 0 Td[(50andu=u+1:0andanInhibitoryFastSpikingNeuronbyequation 4{4 :_v=:05v2+4:75v+110)]TJ/F22 11.955 Tf 11.955 0 Td[(u+:05I{4ifv<)]TJ/F15 11.955 Tf 9.299 0 Td[(55then_u=)]TJ/F22 11.955 Tf 9.299 0 Td[(:2uelse_u=:00025v+553)]TJ/F22 11.955 Tf 11.955 0 Td[(:2uResetcondition:ifv25thenv=)]TJ/F15 11.955 Tf 9.299 0 Td[(45Wherevrepresentsthemembranevoltageinmillivoltsproducedbytransientsodiumcurrentandleakcurrents,uisarecoveryvariablemodelingalltheslowcurrentssuchaspersistentsodiumandpotassium,andIistheinputcurrentproducedbypresynapticneuronsandincludingendogenousnoise.Asanexample,thesimplemodelforaregularspikingRSexcitatoryneocorticalneuroninequation 4{3 istwovariablewithnon-linear 52

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a bFigure4-2.Simulatedandrealneuronpositionsandconnections.aSimulated3:5mmradiusculturewith3connectionsperneuronshown.bPhotoofanMEAwithaneuralculturegrownonit. 53

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Table4-1.Neuronparameters.*Indicatesspontaneouslyring.**AMPAreversalpotentialiscloserto0mV,however,theFSbecomevoltageclamped"near0mVbyhighamplitudetonicexcitatoryconductanceduringbursting. NeuronfdesiredEAMPAEGABAAtypeHzmV**mV ExRS1.2-330.-70.ExRS*2.4-630.-70.InhFS3.6-930.-70. reset.Theparametersoftheseequationsarettorepresentamembranevoltageandrecoveryvariablethatincorporatesthespikingpattern,restingmembranepotential,instantaneousthresholdpotential,rheobase,inputresistance,andmembranecapacitance.Thetwovariabledynamicscanexhibitfeaturessuchasaccommodationandspikefrequencyadaptation.Thedynamicsshownbytheseneuronmodelsarerichandmimictheactivationpatternsshownbyinvivodata.ThesimplemodelspresentedbyIzhikevichareabletoexhibitawiderangeofbiophysicalfeaturesfoundwithincorticalcells.TheIzhikevichcorticalmodelneuronswerealsoadaptedtohaveinput-scaleselfregulationintheformofexcitatoryscaling[ 36 ]inequation 4{5 :I=Nex)]TJ/F21 7.97 Tf 6.586 0 Td[(1Xn=0sgnEAMPA)]TJ/F22 11.955 Tf 10.363 0 Td[(v+Ninh)]TJ/F21 7.97 Tf 6.587 0 Td[(1Xn=0gnEGABAA)]TJ/F22 11.955 Tf 10.363 0 Td[(v+Gaussian=0;=70{5wherethedierentneurontypesscaleanyinputcurrentsupordowndependingontheircurrentringfrequencyandtheirdesiredfrequencygiveninTable 4-1 .4.2.3TheRoleofEndogenouslySpikingNeuronsInaddition,endogenously"spikingneurons[ 50 80 ]werecreatedfromasmallpercentageofregularspikingexcitatoryneurons.Theseendogenouslyspikingneuronsaremodeledasregularlyspikingneuronswithgrowinginputnoisecurrentthatresetsaftertheneuroninitiatesanactionpotentialdescribedbyequation 4{6 : 54

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SpontaneouslyFiringNeuronModicationinitiallysn=1I=Nex)]TJ/F21 7.97 Tf 6.586 0 Td[(1Xn=0+Ninh)]TJ/F21 7.97 Tf 6.586 0 Td[(1Xn=0+maxsn;1Gaussian=0;=70{6_sn=:005sn)]TJ/F15 11.955 Tf 11.955 0 Td[()]TJ/F22 11.955 Tf 11.955 0 Td[(r2Onresetcondition:sn=:3snwhererdenotestheendogenouslyactiveneuron'srelativedesiredringrateie.theneuron'sdesiredringrateisrfmaxandr[:4;1].Thisresettingisnon-linearandthetimetothenextspontaneousactionpotentialisdependentonthehistoryoftheneuron'sinputandactionpotentials.Withoutinput,theendogenouslyactiveneuronsreatapproximately3to5Hz.Thecombinationofinput-scaleselfregulationwithendogenouslyspikingneuronsleadstoheighteningofinputscalesuntilactivitypropagatesthroughouttheentirenetwork.Onceactivityispropagatingthroughthenetwork,theplasticityruleshapessynapticweightsbasedonintrinsicactivitypatterns.4.2.4SynapticConnectivity:ModelingtheStructuralInformationofInVitroNetworksAxonalconnectionsaredeterminedusingadistancedependentgammadistributionforexcitatoryandinhibitorycells.First,thenumberofconnectionsinmadebyaneuronweregreaterforneuronswithagreaternumberofneighbors.Second,connectivityisneurontypedependent;inhibitoryneuronsformlessaxonterminalsthanexcitatoryneurons.Finally,inhibitoryneuronsmakelocalconnections,while,excitatoryneuronsmakemostlylocalconnectionswithseverallongdistanceconnections.Giventheseguidelines,Gammadistributionswereusedfortheconnectionprobabilitiesbetweenneurons.Excitatoryconnectionswereformedusingk=2and=1,whileinhibitoryconnectionsweretestedbyk=2and=2bothbasedonthedistancebetweenwould-bepre-andpostsynapticneurons.Thedistributionswerescaledtomean 55

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probabilitiesof0:7mmand0:4mmforexcitatoryandinhibitoryconnections,respectively.Theresultisthatneuronswillmakemostconnectionslocally,withoutregardforselfconnection[ 126 ],andfewerlongdistantconnections.Theneuronsindenseareasalsohavemoreconnectionsthanthoseinsparseareas.4.2.5SynapticActivationandConductionDelaysSynapticactivationwasmodeledasanimpulseincreaseandexponentialdecayinconductanceratherthanabiexponential[ 64 127 ]forcomputationalsimplicationinequation 4{7 forsynapseconductance:GABAA=6ms{7AMPA=5ms_g=)]TJ/F22 11.955 Tf 9.299 0 Td[(g TYPEOnPresynapticActionPotential:g=g+wwherewisthesynapticweightinnanoseimens.Eachneurontypethengeneratesaspecicconnectiontypetootherneurontypesdescribedearlier.Synapticconnectionsalsoundergoshort-termpotentiationanddepression.Timeconstantsforthesephenomenaareconnectiondependent.ThemodelsimpliesallsynapsesbetweenpairsofneuronclassestobeasingletypealthoughatleastthreetypesofGABAergicsynapsesalonehavebeenidentiedtobesignicantlydierent,[ 128 ].Thedelayfrompresynapticringtopostsynapticactivationisdeterminedbythedistanceseparatingneuronpositionswith.3m/sconductionvelocity[ 129 ],minimumsynapsingtime.75ms,[ 14 ]describestheaveragesynapsingtimeas1.5ms,andarandomadditionaldelayrepresentingtheserpentinepathofneurite 56

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growthandvarianceinsynapsingtimeandconductionvelocities.Thisdelayisconstantforeachsynapticpathwayoncethemodelhasbeenconstructed.4.2.6SynapticPlasticityClassicspike-timingdependentplasticitySTDPrulesarebasedsolelyonpre-andpostsynapticspiketimingstopotentiateordepresssynapses.Withthismethodofmakinglong-termchanges,synapticweightsareincreasedwhenpresynapticactionpotentialsarecloselyfollowedbypostsynapticactionpotentials;synapticweightsaredecreasedwithconversetiming.Thisrequiresabiasforpotentiationordepressionandamethodtostabilizethelearningrule.However,BiandPoo[ 42 ]haveshownadependenceofthechangeontheinitialamplitudeofthesynapseforpotentiationwherepotentiationisstrongerforweaksynapsesandweakerforstrongsynapses.Withthisrule,describedinChapter 3 andshowninequation 4{8 ,axedpointiscreatedintheweightspace.Amplitudeandspike-timingdependentplasticityrulePandDsaturateatavalueof.01P=20msandD=35ms{8_P=)]TJ/F22 11.955 Tf 9.299 0 Td[(P Pand_D=)]TJ/F22 11.955 Tf 9.298 0 Td[(D DOnPresynapticActionPotential:w=w)]TJ/F22 11.955 Tf 11.955 0 Td[(wDandP=P+:012OnPostsynapticActionPotential:w=w+wPexp)]TJ/F21 7.97 Tf 6.587 0 Td[(3:2wandD=D+:003Inthemodel,excitatoryneuronsexpressAMPAandinhibitoryneuronsexpressGABAA.Onlyexcitatory-excitatoryconnectionsuseASTDPrules.Asaresult,synapticweightswilltendtobedistributednearthexedpoint.Theamplitudeandspike-timingdependentplasticityASTDPruleisstillagreatsimplicationbecauseitignorestheeectofmultipleinteractingspikes[ 45 121 ]. 57

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Table4-2.Synapseparameters.ParametersusedinEquations 4{9 and 4{10 Pre-andpost-UDFsynapticneuronmsms Ex-Ex80%0.50400.500.Ex-Ex20%0.50800.1000.Ex-Inh0.1030.1800.Inh-Ex0.25700.20.Inh-Inh0.25700.20. Synapsesalsoexhibitedshort-termplasticitydependentonthepre-andpostsynapticneurontype,seeTable 4-2 .Duetosimulationtechniqueusedintheimplementationofthemodel,aclosedformsolutionofMarkramet.al.[ 128 ]synapsedynamicsareusedinequation 4{9 ,and 4{10 andparametersinTable 4-2 :Rt+t=1)]TJ/F15 11.955 Tf 11.955 0 Td[()]TJ/F22 11.955 Tf 11.955 0 Td[(Rte)]TJ/F18 5.978 Tf 7.782 3.258 Td[(t D{9wt+t=U)]TJ/F15 11.955 Tf 11.955 0 Td[(U)]TJ/F22 11.955 Tf 11.955 0 Td[(wte)]TJ/F18 5.978 Tf 7.782 3.259 Td[(t FandforPresynapticAPs:Rt+=Rt)]TJ/F20 11.955 Tf 9.409 -0.299 Td[()]TJ/F22 11.955 Tf 11.955 0 Td[(Rt)]TJ/F20 11.955 Tf 9.409 -0.299 Td[(w{10wt+=wt)]TJ/F15 11.955 Tf 9.409 -0.299 Td[(+U)]TJ/F22 11.955 Tf 11.955 0 Td[(wt)]TJ/F15 11.955 Tf 6.752 -0.299 Td[(4.3ResultsUponstartingthemodel,activitydevelopsoverseveralhoursofsimulationtime.Initiallly,synapticweightsandinputscalesaretypicallytoolowforactivitytopropagatethroughoutthenetwork.Theonlyspontaneousactivitythatexistsarethefewactionpotentialsgeneratedbytheendogenouslyspikingneurons.Astheneurons'inputscalesincreaseduetoinactivity,afewneuronsbegintoreinresponsetoinputfromendogenouslyspikingneurons.Duetothesequentialnatureofthisringpatternthesepathwaysarepotentiated.Theseneuronsrecruitmoreneuronstore,andinturnmorepathwaysarepotentiated.Thiseventuallygivesrisetothepropogationoftheactivity 58

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throughouttheentirenetwork,withouthightenedpathways,duetooverlyhightenedinput-scalesandthecascadeofactivity.Thisburstingbeginstocorrect"highlypotentiatedpathwaysusedtoinducetherstbursts.Theburstingalsocorrects"theinput-scales,loweringmanywhileotherscontinuetorise,butataslowerrate.Thenotionoftriggernetworks[ 79 ]canbeusedtoexplaintheonsetofburstingand,toadegree,thesustainedbursting.Burstsoriginatefromahandfuloflocationsinthesimulatedculturedatanotshown.Thetimeframeuptomaturationininvitroculturesismarkedbychangingconnectivity,whichourmodeldoesnotcaptureasconnectivityisxed.Thislikelyexplainsthemodel'srapiddevelopmentstableafter3-4hrs.Moreover,learningandregulatoryratesaremanipulatedtoreducesimulationtime.4.3.1ComparisonofGeneralSpontaneousActivityintheModelVersusInVitroExamplesoftheactivityofinvitroandinsilicoculturesareshowninFigures 4-3 and 4-4 .Asmentionedburstonsetismarkedbyasynchronizedrapidincreaseinringrateandprecursoryspontaneous,asynchronousactivity.Themodelshowsvariationininterburstintervals,burstduration,andburstintensity.ElectroderecordingchannelsaresimulatedtocompareinterspikeintervalsISI.TheresultofonechannelcanbeseeninFigure 4-5 .TheISIdistributionfollowsthatofaLevydistributionasotherworkhasshownforinvitrocultures[ 86 ].Thesimulatedchannelfollowsalevydistributiononlywhenmultipleneuronsaredetectedbythechannel.Withonlyasingleneuron,theprobabilitiesoffastISIslessthan2-3msarezeroasexpectedduetoabsoluterefractoryperiods.TheringrateofthemodelneuronsFigure 4-6 ,afterthetransientphase,arecloselyrelatedtheneuron'sdesiredringrate.TheinterburstintervalIBIofthemodeldiersbetweensimulations,eventhougheachweregeneratedwiththesameparameterdistributions.Burstinginthemodelisalsodiculttoclassifyasitisinvitro.Themodelgeneratesmildpre-burstsynchronizationssimilartoculturednetworks;theseshortpre-burstsynchronizationsoftentriggertheburst 59

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Figure4-3.Variabilityinsimulatednetworkactivity.Theself-regulatingmodelisablereproduceactivityseeninvitro.Theirringrateprolesmimicthosefromculturepre-burst,duringtheburst,andpost-burst.Aswiththelivingnetworks,thesimulatednetworkactivityvariesgreatlybetweeneachculture,"eventhougheachnetworkisgeneratedfromthesameprobabilitydistributions. detectionalgorithm.TheresultisthattheburststatisticsgeneratedautomaticallyseeTable 4-3 indicateshorteraverageburstdurationsandIBIs,andhigherburstratesthanahumanwouldreport.Regardless,themodelburstdurationsareshorterthanthoseseeninvitro[ 3 4 ].Thisislikelyduetothesmallsizeoftheneuralnetworkandthelackofexcitatory-excitatoryconnectionswithfastshort-termdepression,asthelackofactionpotentialsinitiatedaftertheminimumpointintheSTDvariableshowsinFigure 4-10 60

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a bFigure4-4.Spontaneousmodelactivity.Theself-regulatingmodelaisablereproduceactivityseeninvitroboverlongtimescales.Therearesimilarprolestoringsratespre-burst,duringtheburst,andpost-burst. 61

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a bFigure4-5.Inter-spikeintervaldistribution.Theself-regulatingmodelaproducesLevydistributedinter-spikeintervalssimilartothoseofinvitrobcultures[ 86 ]. 62

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Figure4-6.Histogramofringratesinsimulateddish0002.Colorscorrespondtoneurontypewhichdeterminethedistributionofnominalringrates.Thedistributionofringratescloselymatchesthedistributionofdesiredringrates. Table4-3.Self-regulatingmodelburststatistics.Burstraterangesfrom1to1 3Hz,fasterthansomeobservedinvitro. SimulatedMedianburstdurationBurstrateIBIdishsecmin-maxHzsec 00000.060.046-0.0620.5181.9310.90600010.062.052-0.0660.6591.5160.80600020.077.068-0.0860.4062.4650.73800030.062.048-0.1240.9481.0550.58000040.062.050-0.1940.4982.0101.50000050.062.060-0.0640.4612.1680.88600060.066.050-0.1000.8081.2380.44800070.066.062-0.0700.5621.7810.72900080.070.058-0.0880.8181.2230.21800090.101.096-0.1300.3562.8081.639Average0.0690.6031.819 63

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Figure4-7.Burstlengthdependence.Theself-regulatingmodelreectspoorburstdurationdependentpost-burstquiescenceduetothestochasticnatureofburstonset[ 78 ].However,longerburstsarecloselyprecededbyshorterbursts. 4.3.2ComparisonofEvokedActivityEvokedactivitycanvarysignicantly,yetmanyoccurrencesofinvitroactivitycanalsobefoundintheself-regulatingmodelshowninFigure 4-8 .Thedicultyincomparingthesimulatednetworkwiththelivingonesarisesduetothenuancesofeachcultureofinvitroneuralnetworks.Moreover,themodelstrivestoachievesimilaritywithdissociatedculturesascloseasinter-culturesimilarity,nottoreplicateeachculture'spatternofactivityinsimulation.4.3.3AnalysisofModelParametersSynapticecacydistributionisunimodalandlong-tailedaswasshownbyO'Brienet.al.[ 114 ].TheusageoftheASTDPruleinthisnetworkmodelenablesstablevariationofweightsdependentonpre-andpostsynapticAPtimings.Thesynapticweightscanchange 64

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a bFigure4-8.Elicitedmodelactivity.Theself-regulatingmodelaisablereproduceactivityseeninvitrobfromstimulation.Typicallystimulationrapidlyactivatesseveralneuronsfollowedbyalargerburstresponse. 65

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Figure4-9.Unimodalsynapticweightdistribution.Histogramofsynapticweightsinthemodelwithupperandwithoutscalinglower.Long-tailedunimodaldistributionofpeakcurrentinjectioninthemodelissimiliartowhatisseeninvitro.Thelong-taildistributionisemphasizedbydistributionofself-regulatinginput-scaleparameter.Inputscaleparameterishighlyaectedbythelocalityofconnectionsandspatialdistributionofneurons.Onlyplasticsynapsesarehistogrammed. rapidlywithchangesinspiketimingcorrelations.However,mostweightsaremaintainedoverperiodslongerthan15minutes,changinglessthan10%.Casesofspontaneoussynapticweightchangesdooccurinthemodelwithnear100%weightchangespossibleforinitiallylowamplitudesynapsesina15minutetimeperiod.Additionally,somesynapsesaredriventozerounderASTDPandbursting;oncesynapsesarelessthan10)]TJ/F21 7.97 Tf 6.586 0 Td[(3nSitisunlikelythenetworkwillgeneratetherequiredpatternsofactivitytopotentiatethesynapseonceagain.Typically,onlyalimitedsubsetofsynapses0-20%persimulatedcultureareprunedinthismanner. 66

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a b c dFigure4-10.Neuroninputduringbursting.Neuroninputfromexcitationblueandinhibitionredrelatedtoinstantaneousringrateblackduringbursting.Fourtypicalexamplesareshown.Averageringrateisshowningreyforcomparison.Yellowandpurplelinesindicatetheaveragevalueofaerentsynapsedepressionandfacilitationvariables,respectively.Thegureshows4neuronsduringapre-burstsynchronizationandburst.Synchronizationsnotresultinginculture-wideburstingareusuallymarkedbyhigherinhibitorytoexcitatoryratios.Theburstconsistsofapproximatelyseventimesmoreactionpotentials. 67

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Figure4-11.Inputscalecompensation.Inputscaleisinverselyrelatedtothetotalexcitatorysynapticweightexcludingtheactivitydependentup-regulationofexcitatorycurrents.Red,green,andbluedotsindicateinhibitory,endogenous,andexcitatoryneurons,respectively.Brightnessofeachdotrepresentstherelativedesiredringrateofthatneuron.Desiredringratepositivelydrivesinputregulation. Anotherinterestingfeatureofthemodelisthespatialarrangementofthescalingfactors,seeFigure 4-12 .Whilelowscalefactorsarefoundthroughoutthespatialdistributionofthemodel,highscalefactorsoccurpredominatelynearthebordersofthesimulatedculture.Theperipheryofthesimulationhasfewerconnectionsandwouldbealikelycauseofthisphenomena;however,thescalingvariableseemstohaveonlyaslightinversecorrelationwiththenumberofconnectionsnotshown,butamuchstrongercorrelationwithtotalexcitatoryconnectivityFigure 4-11 .Inaddition,largerinputscalingfactorsareassociatedwithnearbyinhibitoryneuronsdistributedthroughoutthespatialdistributionofthenetwork. 68

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Figure4-12.Inputscalespatialdistribution.Greenarelowerscalefactorsandbluearethehighestforexcitatoryneurons.Blackarelowerscalefactorsandredarehighestforinhibitoryneurons.Notethehigherinputscalingneardenserareasofinhibitoryneurons. 4.4DiscussionInthischapter,wedescribedamodelthatincludesfrequencydependentsynapses,endogenouslyactiveneurons,synapticplasticityrulesdescribedearlierinChapter 3 ,andhomeostaticregulation.Intheresults,wecomparedthedistributionofISIsandIBIsproducedbythemodelwiththosefrominvitrocultures.Wefoundthatthemodelproducesactivitywithdistributionssimilartodatafromcultures.Inaddition,thesimulatedsynapticweightsdistributedaccordingtothosemeasuredexperimentallybyO'Brienet.al..Thesesynapticweightswerestableoverhoursasothershaveshowninvitro[ 111 130 ].Overall,thesendingssupportthevalidityofourmodelfortheunderstandingofculturedneuralnetworks.Twoofthekeypropertiesofourmodel,amplitudedependentplasticityandhomestaticselfregulationarediscussednext. 69

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a b c dFigure4-13.Examplesynapticweighttraces.Synapticweightsshowtheabilitytomaintainpotentiatedordepressedsynapticweightsover15minuteperiods.dshowstheatypicalcaseofsynapticweightchange.Notethescaleoftheweightuctuationsinrelationtotheweightdistribution. 4.4.1TheASTDPVersusSTDPArgumentAmplitudedependenceofsynapticweightmodicationleadstocriticalchangesinthepredictionsmadebySTDP.Mostapparently,strongweightsdonotindenitelystrengthenandmostweakweightsdonotindenitelyweaken.Ofkeyimportance,thisinverseamplitudedependenceensuresstabilityinsynapticweightsregardlessofinput/outputsignalsduetothestabilizingforceofnoise.Moreover,amplitudedependentweight 70

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changeshavebeenshowninvitro[ 42 ].Theadditionalcalculationsareminimalandonlyrequiredwhenspikepairingoccursandsynapticchangesaremade.4.4.2SelfRegulationActivitydependentselfregulationofinputscalecanbeusedtoresolveimportantimplementationissueswithneuronalmodels.Themostobviousofwhichisthemultiplicativescalingoftotalsynapticweightduringdynamicchangesinindividualsynapses.Thisscalinghasbeenindicatedtobeactivity-dependentreectingnegativefeedbackinvitroandinvivo[ 89 ].Themodelintroducedhereassumestheactivitydependencyisrelatedtotheringrateoftheneuron[ 107 123 ].However,thedirectdierencefromanominalringratemaynotbethebiologicalfactorinuencinginput-scaling.4.4.3ParameterEectsOneofthekeypropertiesofmanymodelsistheirsensitivitytovariationsinthemodelparameters.Multipletrendswerenoticedwhiledevelopingthemodel.First,frequencydependentexcitatorysynapsesareessentialforstablebursting.Second,inhibitionaddedvariabilitytoburstdurationandinterburstinterval.Third,therelativevaluesfortimeconstantsforexcitatoryshort-termdepressionandinhibitoryshort-termpotentiationcangreatlyshapepre-burstactivityandduration.Fourth,usingasubstantialnumber>20%offacilitatingexcitatory-excitatorysynapsesleadstosuperburststhathavesometimebeenreportedintheliterature[ 4 ].Manyparameterswerevariedwithorwithoutheterogeneityinordertoachievevariabilityininter-burstintervals.HeterogeneityofsynapticdepressionandfacilitationtimeconstantshadlittleeectonIBIvariability.However,variationininterburstintervalwasattainablethroughtheuseofheterogeneityinthedesiredringrateofthesimulatedneurons.Moreover,IBIvariabilityandpositiveskewunimodaldistributedscalingfactorsonlyoccurreliablyinsimulationwithlowdesiredringrates<4Hzforexcitatoryneurons.Lowerdesiredringratesalsotendtoresultinshorterburstdurations. 71

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Duetothedevelopment"oftheburstinginthismodelandthefacilitatingexcitatory-inhibitoryconnections,initializationofthemodelwithhighamplitudeinhibitorycurrentsoftenpreventedburstingfromdeveloping.InvitroactivitydevelopmentisaccompaniedbyCl)]TJ/F15 11.955 Tf 10.986 -4.339 Td[(potentialdevelopment[ 58 59 ]andactivitydependentneuriteoutgrowth[ 131 ]thatcircumventthisissue.Alsoofnote,increasedmembranenoisecurrentmodulatesthespreadoftheweightdistributionduetoitsinteractionwiththeASTDPrule,seeChapter 3 .Increasesinthenoisedecreasevarianceoftheweightdistribution;theconverseisalsotrue.Theeect,however,ismarginalwithrandomlyoccurringburstingactivity.4.4.4FutureWorkWehaveshownthatthemodelcreatesbiologicallysimilarspontaneousactivity.Yet,questionsneedtobeansweredregardingthemodelandstimulationofthemodel.Isthereadistributionofdesiredfrequenciesforeachneurontype?Whatisthetrueoperationalrangeofinput-scaling?Howdoessaturationofthedynamicrangeeectneuronactivity?Isitrealistictohaveproportionallylargecurrentsinjectedbysinglesynapseactivationwhenthereareonlyafewnumberofsynapses?Isitpossibletodetermineaneuron'sscalingfactorinvitrobymeasuringpre-andpostsynapticsignals?Wouldstimulationincreaseringratesand,inturn,decreasescaling?4.4.5SummaryDesigningamodelthatincorporatesthedynamicbehaviorofinvitrocultures,especiallyinresponsetochanginginputconditions,requiresthathomeostaticneuralmechanismsarereproduced.ASTDPandselfregulationaretwoconceptuallyandcomputationallysimplecomponentsthatenablelargenetworkmodelstomorefaithfullyreproduceinvitroactivitythanstaticparametersduringsimulatedexperiments.Theymayalsoleadtonewunderstandingofthedynamicspatio-temporalpatternsgeneratedinvitro. 72

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CHAPTER5SEPARABILITYANDREPEATABILITYOFELECTRICALSTIMULATIONThehumanbraincanrobustlyprocessinputthroughredundancyandparallelism{twofeaturesthatmoderncomputershaveonlyrecentlystartedtobecomemainstream.However,computersarerarelyabletoadapttonewsituationswithoutfurtherprogramming.Thus,creatingahybridneuralcomputerhasbeenheldasanimportantsteptounderstandingcomputationinthebrain.Toimplementoneproposedarchitecture{theliquidstatemachine{forachievingthis,threeassumptionsmustbesatised:seperability,repeatability,andfadingmemory.Usingatemplatebasedclassier,seperabilityandrepeatabilityofelectricalstimulationofdissassosiatedneuralculturesonplanarmultielectrodearraysaredemonstratedthrough99.8%inputreconstructionwhenusingthemostrecentresponsestostimulation.However,classicationperformanceofthestatictemplateshowsgreatererrors;yet,inputreconstructionaverageshigherthan95%usinglow/3HzorhighHzfrequencystimulationof10channels.Highfrequencystimulationisshowntogeneratemorediscriminablelateactivityduetothereducedrecurrentactivity.Twoclassiersarepresentedwithvariableperformancebasedonthevolumeoftrainingdataandstimulationresponsetype.5.1IntroductionDisassociatedneuralculturesinconjuctionwithplanarmicro-electrodearraysMEAshavebeenusedtostudycomputationalandresponsivepropertiesofneuraltissuefordecades[ 23 132 ].Althoughdisassociatedneuralculturesdiercomparedwiththeinvivostructuralorganization,computation[ 133 ]andlearning[ 2 110 130 ]invitrohavebeenreported.Hereweexploreelicitedactivityoftheinvitronetworksforsimplepropertiesrequisiteforthereuseascomputationaldevices.Theessentialpropertyofthebiologicalsubsystemtoachievereliablecomputationistheseparability,whichensurestheoutputtobedecodabledespitethestochasticnatureoftheneuronalnetwork.Separabilitycanbeintuitivelyunderstoodintermsof 73

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aclassicationcontext.Givendierentinputstothesystem,enoughseparationofthescatteredoutputclustersguaranteesthattheoutputcontainsinformationabouttheinput.Infact,wewillshowtheseparabilityforthesetofinputswedenethroughsolvingtheclassicationtask.SeparabilityofstimulationsofdisassociatedcorticaltissueDCTonMEAsusingclassicaltemplatebasedapproaches[ 134 ]isinuencedbyseveralfactorsincludingtherepeatabilityandstationarityofprecisespiketimingsaswellasringrate.Asothershavealsoshown,reliablespikepatternsaregeneratedbytheearlyphaseoftheresponsetostimulation[ 90 ].Interestingly,preciseactionpotentialsreatwelldenedtime-pointsornotatall[ 135 ],thusthedataisconducivetoseparationusingtemplatebasedapproaches.However,wenotedsomeoutputchannels,inresponsetosomestimulatedchannels,appeartohavearepeatableringrateandlackprecisetimingswhileotherchannelshaveconcurrentpreciselytimedresponsesseeResults.Theearlyactivity<20msfromstimulationsinDCTsonMEAsisthoughttooriginatefromneuronsthataredirectlystimulatedoronlycoupledthroughafewsynapses[ 136 ].Jimboet.al.demonstratedatemporallydependentincreaseinspikejitterduetostimulationsthatinducepopulationbursts[ 90 ].Theyindicatethattheincreaseisduetotheactivationofmultiplerecurrentpathways.Wagenaaret.al.showedburstcontrolusingrapidstimulationreducedtheactivationoftheserecurrentpathways[ 83 ].Thus,wehypothesizedmorereliableresponsestostimulationusingrapidmultichannelstimulation.Inaddition,rapidstimulationallowsforhigherdataratesfromacomputationalperspective.Indeed,invivoaerentsensoryconnectionsprovidegreaterthan1 3Hzstimulusratesusedinpreviousinvitroexperimentalprotocols[ 88 ]totheneocortex.Theimportanceofcorrelationsinneuralspiketrainshavebeenaddresspreviously[ 137 ].Herewerelatethenatureoftheelicitedspikingactivitytotheperformanceofcorrelationbasedanddistancebasedmeasuresofinputidentication.Weusetheproposedmethods 74

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toverifytheseparabilityandrepeatabilitypropertiesofthenetworkassumingprecisestimulation-lockedactivity.Twostimulationprotocolsareexplored:onethatelicitsburstingalsoobservedspontaneouslyandonethatattemptstocontrolrecurrentactivityandthusbursting.Thesecomparisonsilluminatethedierencesofspatiallydistinctstimulationandthenonstationarityofelicitedactivity.5.2Methods5.2.1CellCultureNeuronalnetworkswereculturedaccordingto[ 6 ].Briey,embryonicday18Sprague/DawleyorFischer344ratcortexBrainBitsweredissociatedwithWorthingtonPapainDissociationSystem.About20,000-50,000cellswereplatedoneachmicroelectrodearrayMEA,seeFigure 2-1 ,whichwaspre-coatedby100L0.1%polyethyleneiminePEI,Sigmaand10LlamininSigma.TheMEAswerecoveredwithFEPlids[ 6 ],whichreducestheculturemedia'sevaporationwhileallowinggasexchange.Theculturedcellswerekeptinthe35.5C,5%CO2formorethan1month.Halfoftheculturemedia,whichconsistedofDulbeccosmodiedEaglesmediumDMEMGibcocontaining10%inactivatedequineserumHyClone,wasreplacedbiweekly.After30daysinvitro,thespontaneousactivityappearedstable[ 23 ].5.2.2AcquisitionNeuronalactivitywasrecordedextracellularlyusingtheMEAelectrodesandMultiChannelSystems64-channelamplierandacquisitionboardsat25kHz.DatawerecollectedusingaDellPCwithDualIntelXeon2.8GHzprocessorswith3GBRAMoranAppleDualG52.0GHzcomputerwith4GBRAM.Spikedetectionwasperformedatavetimesstandarddeviationthreshold.Alocallineartwasperformedtoremovestimulationartifacts[ 75 ].Post-stimulationblankinglasted2msaftereachstimulation.5.2.3DataandStimulusProtocolsElectricalstimulationofneuralculturesthroughMEAelectrodestypicallyresultsinanevokedburst[ 90 ].Theearlyphaseoftheresponsetostimulationisreliable;whereas, 75

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Figure5-1.Stimuluspatterns.Left:Protocol1,lowfrequencystimulation,1 3Hz.Right:Protocol2,highfrequencystimulation,20Hz.Notethedieringtimescales. Figure5-2.Stimulusblanking.WhenanMEAchannelisstimulatedie.channelA,recordingoftheelectricalsignalsonallchannelsisinhibited.Thus,spikescannotbedetectedonchannelsBorCforashorttime. 76

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thelatephaseishighlyvariable[ 2 ].Inallstimulationprotocols,theamplicationcircuitwasblankedduringstimulationtoavoidexcessstimulusartifact.Thus,2msofresponseislostaftereachstimulationasthecartooninFigure 5-2 depicts.Thus,wherenotmentioned,weusethetimeperiodfrom3msto18msafterstimulationforouranalyses.Twodistinctelectricalstimulationprotocolswereusedforstimulationoftheneuronalnetworks.Protocol1n=7consistedof10repetitionsofstimulationtoeachofthe60MEAchannelsinrandomorderat1 3Hz.Stimulationswerebiphasic200secpulsesat500mV.Stimulationofmostchannelsconsistentlyinducedpopulationburstslastinglongerthan100ms,seeFigure 5-1 .Additionally,theseparabilityofthetwostimulationprotocolsareexaminedinthemodeldevelopedinChapter 4 .Protocol2n=3soughttoeliminateburstingwhenstimulatinginordertoincreasetheinput-outputrateofthesystem[ 83 ].Stimulationof10activechannelsasdeterminedbyvisualinspectionwasrepeated600timesinrandomizedsequences.Theoverallstimulationratewas20Hz.Stimulationswerebiphasic200secpulsesat400mV.Stimulationaftertherstsequencegeneratedactivitythattypicallyendedinlessthan50ms,seeFigure 5-1 .Onlydataaftertherstsecondisusedinthediscriminationtasks,duetotheburstofactivityelicitedbytherststimulation.Previouswork[ 83 ]indicatesincreasedstimulationratesreducetheburstinessofaninvitroculture.Inaddition,theearlyresponsetostimulationisaresultofdirectstimulationorpostsynapticneuronsconnectedthroughonlyafewsynapses.Thus,highlypatternedactivitywillresultfromeachstimulation.However,rapidstimulationwillmitigateburstingfromstimulationwhilestillproducingspecicpatternsofactivity;hence,reliable,patternedactivitywillexistlongerunderprotocol2thanprotocol1.5.2.4ClassicationMethodsAnovelclassicationmethodbasedoncorrelationispresentedhere.ThealgorithmiscomparedtoanL2distancebetweensmoothedspiketrainswhichiswidelyusedincomparingspiketrains[ 138 ].Regardlessofthemethod,thegoalistobeabletodetermine 77

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a bFigure5-3.Representativeexampleofmulti-channel,smoothedPSTHs.Datashownrepresentstheaverageresponseforthe15mspost-stimulationperiodonthecorrespondingchanneloftheMEAfromstimulationonchannel33aand34b.Theresponsetothesamestimulationseenateachrecordingchannelvariesgreatly. whichchannelwasstimulatedwhenparticularoutputpatternsareseenonasetofchannels.Thebasicideaistocreatetemplatesforthesptio-temporalpatternofactionpotentialswithrespecttoeachinput,andlaterselectthemostsimilartemplatewhenanunknownpatternisgiven.Thetemplatesarebuiltfromsmoothedhistogramswithsmallbinsize.5.2.4.1SmoothedPSTHSmoothedhistogramsweregeneratedfromrandomlychosensampledatasetsandaveragedtogether,asshowninEquation 5{1 .Histogramsweregeneratedforeveryinput-outputmapping,i.e.betweeneverystimuluschanneleveryrecordingchannel,seeFigure 5-3 .ThesmoothingfunctionisaLaplacenkernelwithtimeconstant,.Wechoosetobeveryselectivefordierencesintiming,butallowforspikejitter;thus,=.25ms. 78

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Thestandarddeviationofjitterinreliablespiketimingvariesgreatlydatanotshown;usingasmallhassignicanteectwithsmalltrainingsetsizes.SX;Yt=1 NrepsXiejt)]TJ/F24 5.978 Tf 5.756 0 Td[(tij {1whereNrepsisthenumberofrepeatedstimulusresponsesincorporatedintothetemplate.5.2.4.2NormalizationofPSTHforclassicationPropernormalizationofthePSTHsEq. 5{2 allowsdirectcomparisonoftemplatematchingbasedonspiketimesEq. 5{3 regardlessoftheoutputspiketrainthatisunderclassication.Inaddition,removaloflesssignicanttemplates,basedonthecomparisontothemeanandstandarddeviationofthenumberofactionpotentials,reduceserrorintheclassicationseeSection 5.3 .NX;Yt=8>><>>:X;Y ifX;Y<)]TJ/F22 11.955 Tf 11.955 0 Td[(orX;Y=0,SX;Yt X;YifX;Y)]TJ/F22 11.955 Tf 11.955 0 Td[(.{2whereX;YisthetemporalmeanofSX;Yandandisthemeanandstandarddeviation,respectively,ofallX;Y.Templatematchingcanthenbeperformedbysummationofthetemplatevaluescorrespondingtothetimingofalltheactionpotentialsgeneratedbythestimulationunderclassication.Qk=XYXjNk;Ytj{3wheretjisthestim-lockedtimeofthejthactionpotential.ThestimulationisclassiedbythemaximumQkvalue.5.2.4.3L2distanceAsanalternateapproach,L2distancebetweenspiketrains[ 138 ]wereusedtomatchtemplates. 79

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Table5-1.Averageacrossculturesandrepetitionsclassierperformanceincorrectlyidentifyingthestimulatedchannel.Lowfrequencystimulationclassies8stimulationsperinputchannelusing2stimulationsasatemplateall60channelsand10mostactivechannels.Highfrequencystimulationclassies588stimulationsperinputchannelusing10stimulationsasatemplate. ClassicationProtocol1Protocol1Protocol2Method0C,n=7C,n=710C,n=3 Normalization85.9%95.4%96.1%L264.5%89.4%98.1% Dk=s XYZStemplatek;Yt)]TJ/F22 11.955 Tf 11.955 0 Td[(SstimYt2dt{4ThestimulationisclassiedbytheminimumDkvalue.5.3ResultsWeapplythetemplatematchingapproachesfromtheprevioussectiontosatisfyourgoalofndingaone-to-onemappingofstimulustoresponse.Classicationofinputsstimulationsbasedonthespatio-temporaloutputpatternofactionpotentialsisaectedbyavarietyoffactors.Hereweaddresstheclassicationmethods,trainingdatasetsizeinuences,andstimulationprotocoleects.5.3.1InputReconstructionPerformanceThespiketrainsproducedbythetwostimulationprotocolsdieredintheircomposition,asseenbyinspectionoftheactivity.Stimulationprotocol1inducedpopulationburstswhichcausedunreliableresponsesasearlyas13msafterstimulationandmostreliableresponsesendedby20msafterstimulationdatanotshown.Stimulationprotocol2producedthesamereliableresponses;however,unreliableresponsesoccurredlessfrequently.Inaddition,theunreliabletimingofresponsesofprotocol2oftenreliablyoccurredwiththesameringrateduetostimulationofthesamechannel,incontrasttoprotocol1inducingunreliableactivitywithvariedringratesaspartofthepopulationburst.Asaresult,theclassiersusedinthisworkhadvariedperformancedependingonthedataset,seeTable 5-1 80

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Sixtychannelclassicationisamorediculttaskthan10channelsduetoincreasedinputspace.ItshouldbenotedthatunlteredProtocol1dataincludedmid-burststimulationsandnon-responsivestimulationreducingthepotentialforcorrectclassication.However,thisonlyaccountsfor15ofthe600stimulationsonaverage.Selectingdataandusingthetenchannelswiththelargestresponsescomponsatesforboththeseissues;however,withthelimiteddataforProtocol1,onlyalimitednumberofstimulationresponsesmaybeincorporatedinthetemplate.Wesuggestthatthedeteriorationofclassicationforthehighfrequencystimulationwithlaterpost-stimuluswindowsisduetothelackofactionpotentialsseeFigure 5-1 .Whereas,thelowfrequencyperformanceisduetoaccumulationofspikejitterandthegenerationorlackthereofactionpotentialsduetodierenttimings.Interestingly,theL2classieroutperformsbyapproximately10%orbyoneoftentemplatesthenormalizationclassieronthelatelowfrequencystimulationdata.5.3.2SurrogateDataToinsurethereconstructionofstimulatedchannelsthroughoutputspikesisindependentofarticalcorrelations,weshuedthespike-timeandspike-channeldataforbothtrainingandtestdata.Theresultingclassicationofthe20Hzstimulationsdwindledto15.8%and45.3%forthenormalizationandL2methods,respectively.Thisgeneratedsurrogatedatadiscardsconsistentstimulationlockedcorrelationsbutdoesmaintainstimulationlockedchannel-wideaverageringrates.Thus,theL2classier'sringratecomponentisabletomaintainsignicantclassicationperformancesincetheringrateresponsevariesbythechannelstimulated.Thenormalizationmethodperformsnearchance10%sinceringrateinformationisremovedintheformationofthetemplate.Thisisconrmedbypairingrandomchannelsinsteadofshuingchannelswitheachspiketimeresultinginsimilarclassicationperformance.Notshuingthedatausedtogeneratethetemplatehaslittleeectontheclassicationratesforthesurrogate 81

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Figure5-4.Classicationperformancebasedonvaryingthepost-stimuluswindow.Varyingthepost-stimuluswindowusedforthetemplateandclassicationdemonstratesthereliabilityoftimings.Recurrentactivityfromstimulationsinducingbursting.33Hzreducestheabilitytoperformcorrectclassicationtochance0%;however,rapidstimulationminimizestheseeectswithclassicationasymptotingabovechance.Fivestimulationsforeachtemplatewereusedtoclassifyresponsesfrom10channelsProtocol1data,onlythemostactivelyrespondingchannelswereused.Constantwindowof15ms.ThedegradationoftheProtocol2performanceisduetothelackoflateactivityfromstimulatingthechannel.Notethisdropoinperformanceoftheburstinducingstimulationdiersfromthatof[ 90 ];thisislikelyduetothesmalltauusedincreatingthesmoothedPSTHs. 82

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a b cFigure5-5.Trainsetsizedependentclassicationofstimulations.aStimulationprotocol1.bStimulationprotocol1usingresultsforonly10mostactivelyrespondingchannelsthatwerestimulated.cStimulationprotocol2.Colorsrepresentdierentcultures.Solidlinerepresentsperformanceofthenormalizationalgorithm.DottedlinerepresentsperformanceofL2classier.Note:abscissascalesdierduetotheamountofdataavailableinthedierentstimulationprotocols.Thelowesttwolinesinthecentergraphrepresentstheclassiers'performanceonahighlynonstationaryresponses,L2performancewaslesseectedthanthenormalizationmethod.Likely,thisisduetorelativestationarityontheringratewhiletimingswerechanging. testdata.However,assigningrandomspike-timesresultedinclassicationratesforthenormalizationandL2methodsat9.9%and10.2%,respectively.5.3.3TrainingSetSizeIncreasednumberofstimulationsincorporatedintotheclassiertemplatespositivelyaectedperformance.Aplotofthefractionofcorrectlyclassieddataversusnumberof 83

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trainingdataintheaveraged,smoothedPSTHisshowninFigure 5-5 .ThenormalizationalgorithmoutperformstheL2distancemeasureonstimulationprotocol1.Whenstimulatingaccordingtoprotocol2,theL2distancemeasureoutperformsthenormalizationmethodexceptforsmalltrainingsetsizes<5.Performancedierencesbetweenstimulationprotocolsweredierentiatedbyreprocessingstimulationprotocol1datausing1 6ofthestimulatedchannelsselectedbythemostactivechannels.Figure 5-5 showstheL2methodperformanceisprotocoldependentandmoresensitivetotheincreasedinputparameterspacethanthenormalizationmethod.However,theperformancemaybeduetothelackofdatainprotocol1;thetrainingsetsizewasalwayslessthanorequalto5duetoprotocollimitations.Incontrasttotheincreaseinperformanceassociatedwithadditionalrepetitionsofthestimulationinthetemplate,increasingthepost-stimuluswindowlengthdoesnotindenitelyincreaseclassicationperformance.Indeed,aplotofwindowsizeversusperformanceisnotmonotonicallyincreasingseeFigure 5-6 andpeaksatapproximately5-10ms.Figures 5-4 and 5-6 takentogetheragreewiththehypothesisthathighfrequencystimulationreduceserroraccumulatedthroughrecurrentactivity.5.3.4TrainingSetSamplingandNonstationarityCleartemporally-dependenttrendswerenoticedintheanalysisofthehighfrequencystimulusresponsesovertheavailabledatasets.Thesametrendswerenotnoticedwiththelowfrequencystimulusresponses;althoughsamplesoftheProtocol1dataaresparseandsubtlecorrelationswouldbeindiscernible.Thus,onlythestationarityofProtocol2arementionedandclearlyshowninFigure 5-7 .Alargeportion>70%foreachcultureofmisclassicationsoccurredduringtheinitialminuteofhighfrequencystimulation;indeed,greaterthan90%ofmisclassicationsoccurredinthersttwominutesofdata.Thistimeframecoincideswithmanychangesinspiketimings.Thechangesintheresponsetostimulationovertimeoccursmostoftenduringtherst60seconds.Asaresult,thetemplateismorerepresentativeofthelatter4minutes 84

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Figure5-6.Averageperformanceofclassierswithvariedstimulationandwindowsize.AnalysisconditionsarethesameasinFigure 5-4 exceptthepost-stimuluswindowalwaysbeganat3msandisvariable.Observethesharperlatephasedeclineofclassicationperformancewiththelowfrequencystimulationcomparedtohighfrequencystimulation. asshowninFigure 5-7 .Toelucidatehowsimilarconsecutivestimulusresponsesareandthusagrossmeasureofplasticchangeseectclassicationoverlongtimeperiods,thetenpreviousstimulationsperchannelareusedasthetemplate.Theperformanceofthenormalizationclassierusingthisslidingtemplateis99:770:07%correctn=3.ContrastedwiththenumbersinTable 5-1 andconsideringthekernelsize=0:25ms,theperformanceindicatesthatthechangesintimingsofactionpotentialsaresmallbetweenconsecutivestimulations.Changesinresponsetohighfrequencystimulationoccurswithmanyofthechannels.Thechangesaremanifestastheoriginationorterminationofpreciselytimedspikesorasashiftintheprecisetimingeitherearlierorlater.Duetothesechangesselectingtherst 85

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Figure5-7.Rapidstimulationnonstationarity.Alterationsintheringpatterntimingseecthowwelleachtrialmatcheswiththetemplate.Upper:RasterofactivityfromrepeatedstimulationofMEAelectrode.Notethechangesinactionpotentialprecisetimings.Lower:Comparisionofthetemplateandrepresentativematchfromlast4minutesandbeginningminute.Linesmoothedtemplate,dashedsmoothedstimulationfromlastminute,dottedsmoothedsimulationfromrstminute. stimulationsforthegenerationofthetemplateforcomparisonsresultsinalargernumberofmisclassicationsthanrandomlyselectingstimulationsforthetemplate.Consideringallthedata,itisessential{tousethesetemplatematchingalgorithmsbasedonprecisetimings{thatthetemplateincorporatestimulationsfromeachperiodoftimewhiletimingsarechanging.5.3.5SeparabilityofStimulationsInSilicoProtocol1and2werereproducedwiththemodeldevelopedinChapter 4 .TheL2classierwasusedtodeterminetheseparabilityofthestimulationsinthemodelduetothelargevariancesofspiketimingwithbothearlyandlateresponses.Protocol1demonstrated80.8%separabilityofstimulusresponseswhilethestimulationsinprotocol2datawereabletobedeterminedwith76.6%accuracy.Whencomparedwiththevalues 86

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fromTable 5-1 ,thesevaluesindicatethattheseparabilityofthestimuliaresignicantlylessfromthemodel.Therelativeinput-outputclassicationfromthemodelshowsthatevenlargevariancesinAPtimingsareclassiablewithmultichannelreadouts.Protocol1responseshadsignicantlyhigherresponsevariabilityinthemodelthaninvitro,withrespecttoprecisionofactionpotentialsdetectedatthereadout.TheseresponsescanbecontrastedinFigures 5-8 and 5-7 .Fromthisdiscrepancy,wedeterminedthattheratioofinputfromstimulationtoneuronmembranenoisewasthemostlikelycause.Wethenperformedtwofollowupsimulations:wesimulatedsomeexcitatory-excitatorysynapsesthatuseddepressionrecoverytime-constantsof30msandreducedmembranenoiseto=20pA.Theformerhadonlyaminimaleectonvarianceofprecise"APs.However,thelatterreducedthelatencyandvarianceofevokedAPsseeFigure 5-8 andincreasedclassicationto98.5%correct.Additionally,reductionofneuralnoiseenabledmultiplepreciselytimedevokedAPstobedetectedonseveralchannels.Thisseparabilityisremarkableespeciallywithnodirectdetection"ofdirectlystimulatedneurons,ie.everyevokedAPinthemodelisconnectedwiththestimulatedneuronsatleastmonosynaptically,whereasinvitroclassicationincludesAPsdetectedfromdirectneuralstimulation.Bothprotocol1and2showearlyresponsereliabilityseeninvitro.However,themodeldemonstratesincreasedvarianceintimingofactionpotentialswithlowertemporalproximitytothestimulation.Thisisnotalwaysthecaseinvitroalthoughitistypical.5.4ConclusionsInthischapter,wehaveshowntheseparabilityofstimulationsoninvitroandinsiliconeuralnetworks.Thetwostimulusprotocolsenabledustocontrastthedynamicsgeneratingthisactivity.Forexample,invitrohighfrequencystimulationislessseparablewithshortwindowsizesthanthelowfrequencystimulation,howevertheconverseistrueforlongwindowsizesseeFigure 5-6 .Asweintendedtoactivateshort-termdepression 87

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a bFigure5-8.Modelrapidmultichannelstimulusresponse.Responsesfrom600stimulationsofsimulatedMEAchannela,=70pA;b,=20pA.Notethelowreliablityofsomeresponsesandthelargevarianceintimingswithlargeamountsofnoise.Withlowernoise,multipleprecisepostsynapticactionpotentialsaredetectedearlyintheresponse. 88

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duringprotocol1,apossibleexplanationisthatsynapticecacyisreducedduringhighfrequencystimulationwhereasitisrecoveredduringtheearlyresponsetolowfrequencystimulation,thuslowfrequencystimulationdemonstratesbetterearlyreliability.However,astheresponsecascadesthenonlineardynamicscausethenetworktoproduceapatternthatdivergesfromthepreviousstimulation,thusreducingthereliabilityofpreciselytimedactionpotentials.Incontrast,thelatephaseofhighfrequencystimulationissuppressedduetoshort-termdepressionandonlygenerateaspecicpatternwithnearlyconstantseparability.5.4.1SeparabilityandReliabilityofElectricalStimulationSimilartoauditorystimulusresponsesinvivo[ 135 ],earlyresponsestohighfrequencyelectricalstimulationinvitrooccurwithprecisetimingornotatall.Inaddition,earlyresponsesfromstimulationareveryreliableontheshortterm;however,overthescaleoftensofseconds,changesintimingsoccurduringrapidstimulation.Incontrast,theerrorsinclassifyinglowerfrequencystimulationsProtocol1arenotskewedtowardaparticulartimeperioddespitethelowfrequencystimulationsbeingsimilarlywellclassiedusingtheequivalentnumberofstimulationsinthetemplateandthelongerexperimentaltimescale.However,thismaybeasparsesamplingissueduetothelackofdata.Theearlyresponsetolowandhighfrequencystimulationishighlyseparable.Indeed,highfrequencystimulationisespeciallysowhennonstationarityisaccountedforwithclassicationabove99.5%.However,thelatephaseofthestimulationprotocolsusedintheseexperimentsshowthattheburstingresponsesarenotseparableusingtheprecisetimingsofactionpotentials,time-lockedtostimulation,likethetwoclassiersinthisexperiment.Although,signicantbutnotremarkableseparabilityispresentusinglatephaselowfrequencystimulationresponse.Thesendingsareinlinewithcurrentdataregardingelectricalstimulation[ 55 90 ].AnMEAselectrodeactivatesnearbytissuewithasucientlylowactivationthreshold{mostofwhichareaxons.Axonsthenpropagateorthodromicandantidromicaction 89

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potentialstotheextentoftheaxonalarborization[ 56 ],thus,activatingspecicsynapseswithspecictiming.Inturn,aparticularpatternisgenerated.However,spikejitterandunreliablevesicularreleaseamongotherreasons[ 33 79 81 139 ]accumulatesdownstreamerrortrialbytrialvariationsinthepattern.Withouthighlyrecurrentactivity,thesevariationsintimingpropagateonlyforashorttime.Thus,evenasingleearlyresponseisrepresentativeofthepatternseenfromeachrepeatedstimulation.5.4.2ComputationalPerspectiveTheperformanceachievedwiththesimpleclassiersinthisstudyshowthehighlyseparableandrepeatablenatureofelectricalstimulationofdisassociatedneuraltissueonMEAs.Inmatchingspiketrainstotemplates,thenormalizationmethodemphizetheimportanceoftheportionofpatternsthatexist.Inaddition,iftheextraspikesarenoise,thedegreetowhichtheymatchtheothertemplatesisminimalandismitigatedbycombiningmultiplereadouts.WiththeL2classier,missingspikeshaveanegativeeect;however,asinvivodatashowstheoverallpatternthetemporalrelationofthespikesthatdoexistmaybemoreimportantthananindividualspikebeingmissing[ 135 ].Thus,theL2methodisbetteratmatchingringratesandhighlysparsestimulusresponses,butoftenrequiresseveralexamplesofoutputspiketrainstoprovideclassicationattainablebythenormalizationmethod.Aftertheseexperiments,itwasfoundthatremovingemptyresponsesfromthetemplateincreasedtheperformanceofthenormalizationclassieronProtocol2data.Highfrequencyinputhasimprovedreliabilityminimallatephasewithreducedrecurrentactivity,isbetterfromaninputdatarateperspectiveincreasesthroughput,andismorelikelytoproduceinteractingresponsesie.overlapingactivityduetostimulationthanslowerstimulationcounterparts.RapidstimulationavoidsacascadeofrecurrentactivationmaintaininglargeportionofAPsduetostimulationrelativetorecurrentactivityie.theactionpotentialstriggeredbythestimulationoftheneuronswithaxonswithin20-40micrometersversustheactionpotentialsinitiatedby 90

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post-stimulusactivity.Assumingpathwaychangesare{toalargedegree{atthesynapticlevel,thenthenumberofAPsduringthereliableperiodismuchgreaterthantheburstAPs.Assumingtimingbasedsynapticchanges[ 42 ],increasingstimulationrateshouldincreasetheabilityofthenetworktoestablishtemporalcorrelationsintheinputduetoshorterdelaysbetweeninputandlessrecurrentactivitytherebyintroducingspecicactionpotentialpatterns[ 43 ].However,highfrequencyinputalsoreducestheactivitylengthsomanyactivityfromconsecutivestimulationsmaynotdirectlyinteractthroughAPsorbeabletobeseparatedbasedonlateportionssincethereisnoactivity.5.4.3FutureWorkManyphenomenareportedinthisworkshouldbeinvestigatedfurther.Forexample,howcanactionpotentialtimingschangewhilemaintaininghighprecisionsuchasseeninFigure 5-7 ?Dothesechangespersist?Preliminarydatasuggestsnot.Jimboet.al.[ 87 ]leadsustoconcludethatsomeformofchangedoespersist.Howcanwetrackthesechangesbothintimeandprecision?Thequestionremains:whatinformationisbeingencodedandhowcanitbemanipulated?Thehighfrequencystimulationusedintheexperimentproducedfewinteractionsbetweenstimulithatwasnoticeablebyvisualinspectiondatanotshown.Wouldincreasingthestimulationratechangethis;forexample,bytheexistenceofpersistentactivityfromonestimulationtothenext?Fromhere,wecontinuetoexamineadditionalbehaviorsofthemodelunderstimulation.Inthenextchapter,wediscussplasticityofsynapticweightsandmodulationofproberesponses.Inaddition,weshowexperimentalresultsnotattainableinvitroandexplaintheimplicationsofthedata. 91

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CHAPTER6SIMULATEDINVITROPLASTICITYInthischapter,weexplorethemodeldevelopedinChapters 3 and 4 .Theabilityofthemodeltorespondtostimulationinamannersimilartoinvitronetworksiscentraltoitsutility.Stimulationprotocolsfromotherworksareexaminedtovalidatethemodelandinvestigatethechangesinnetworkunderlyingthechangesinactivity.Wealsodiscussspontaneouschangesanditsimplicationswhenattemptingtodeterminethechangesincurredbystimulation.6.1IntroductionPlasticityofneuronalnetworksiswidelydiscussedinvitroandinvivoasaconsequenceofresearchrelatingittolearning[ 2 87 103 130 133 140 { 144 ].Thereare,however,numerousmeansbywhichneuronsexhibitplasticity.Oftenthesechangesinaneuroncanbetracedbacktosynapticchanges.Recordinginformationtotracksynapticchangesistediousandyieldslittleinformationotherthanwhatcanbeimpliedbydierencesinsynapticactivation.Giventhenumeroussynapsesinvolvedinthesmallestmaintainableneuralnetworks,modelingisperhapsthesimplestsolutiontodeterminethealterationsintheentirenetwork.Withinvitromodels,oneisabletoinvestigatethenetworksdynamicsinexquisitedetail.Allvariablescanbetrackedandanalyzedoveranylengthoftimemakingexperimentspossibleinsilicobeforetechnologyenablestheminvitroorinvivo.Thenumerousaspectsandparametersoftheneuronalnetworksmayobfuscateexperimentalquestionsthatcanbesimpliedanddirectlyimplementedandtestedinsimulation;forexample,onemaywishtoperformanexperimenttounderstandtheinteractionsoftimingplasticitywithactivity-dependentAMPAtrackingwithouttheeectsofotheractivity-dependentphenomena.Theboonfromrealisticnetworkmodelswouldbetoexplain,indetail,emergentpropertiesfoundwithresponsetoexperimentalstimulation. 92

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Inthepastdecade,threeestablishedexperimentalprotocolshavedemonstratedtheabilitytoelicitchangesinthedynamicsofdissociatedcorticalnetworks[ 83 87 88 ].Tetanic,pairedrare-frequent,andrapidmultichannelstimulationalterinvitronetworksstimulationresponses;however,thosechangehavenotbeenreproducedinamodel.Theseparadigmsinduceaspectrumofplasticeectsthathavesupposedexplanations.Thegoalofthisworkistovalidatethemodelandtofurtherexplainthephenomenashowntoresultfromrapidmultichannel,tetanicsinglechannel,andpairedchannelrare-frequentstimulation.Weisolatethechangesresultingfromstimulationbycomparisonwithspontaneouslyoccurringchanges.Inaddition,wereexaminetheapproachofprobingtoevaluatethechangesinvitroanddiscusstheresultsofthestimulations.6.2SimulationsThemodeldevelopedinourpreviousworkseeChapter 4 wasemployedtoexaminenetworkphenomenanotedbyotherwork.Briey,thenetworksimulationsusedinthischapterarecomprisedof500neuronsand300,000synapses.Neuronsmayhavepolysynapticconnectionswithotherneurons.Synapsearefrequencydependentandmaintainlong-termchangesgovernedbyamplitudeandtimingdependentplasticityASTDP.Aspatialdistributionofneuronsisfollowedthatresemblesthatofdissociatedinvitronetworks.Inaddition,themodelisusedheretodierentiatespontaneouslyoccurringplasticity.Theseexperimentalprotocolsrequirestimulationofthesimulatednetwork;thestrategyforelectricalstimulationisnotedinAppendix B .Thefollowingsubsectionsoutlinethestimulationprotocolstested.6.2.1RapidMultichannelStimulusWagenaaret.al.[ 83 ]employedrapidmultichannelstimulationtodesynchronizeinvitronetworkactivity.Theyappliedawiderangeofstimulationfrequenciesandnumberofstimulationchannels,however,thisworkusesonlyoneprotocolP1:20Hzstimulation 93

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spreadrandomlyover10channels.Thisstimulationwassucienttocontrolburstinginmostcases.Wagenaaroeredthatthisprotocoldistruptsburstingbydesynchronizingmanypartsofthenetwork.Thisisaccomplishedbyforcingtherefractorystateofthenetworktobeinvariousstatesofrecoverydependentonthelaststimulations.PreviouslyseeChapter 5 ,weshowedthatthenetworkstillhasasurgeofactivity,seenonmostchannels,asaresultofeachstimulation;however,thisexcitationisofmuchshorterdurationthanatypicalburstresponse.Wealsonotedchangesinpreciselytimedactionpotentialsoverthespanoftheexperimentthatalsoemergeinthemodel.6.2.2TetanicStimulusJimboet.al.[ 87 ]inducedplasticitythroughrepeatedtetanizationofasinglechannelP2TET.Totestthechangesduetostimulation,all60channelsareprobedP2PROBEbeforeandafterthetetanization.ThisexperimentalprotocolP2demonstratednetworkwidepotentiationordepressionofresponsesduetothestimulationofaparticularchannel.Jimboadvocatesthechangesinthenetworkaretheresultoflong-termsynapticchangesandnotesthatinitialburstresponses-40msshowpotentiation,whereastheactivityafter40mstendtobedepressed.Theyspeculatethatthemeasurableincreaseinresponseistheresultofseveralsynapsesinapathwaypotentiating.Thelatedepressionoccursbecauseofthelackofcorrelationoftheactivitytothestimulus.Oursimulationsshowchangesoccurringinthemodelandthesamestimulationchanneldependentnetworkwideincreaseordecreaseinresponse.6.2.3PairedRare-FrequentStimulusEytanet.al.[ 88 ]showedalterationsinnetworkoutputoverminutesbyusingloworhighfrequencystimulation.Singlechannelhighfrequency1 2to1 5Hzleadtodepressionofthestimulusresponse.Conversely,singlechannellowfrequency1 20to1 50HzleadtopotentiationofthestimulusresponsewhenaccompaniedbyasimultaneoushighfrequencystimulationP3. 94

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Figure6-1.Variationinspontaneousnetworkactivitypriortosimulatedexperiments.Thesimulationsusedallthesameprobabilitiesfortheconstructionofthenetworkandindividualcomponentsperformthesame,yetwidedierencesinspontaneousactivitycanbeseenbetweenthevesimulatedcultures. Eytantheorizesthatthereasonthisoccursisduetodepressionoflocalizedexcitatoryanddistributedinhibitoryresourcesbyfrequentstimulation,thustherarestimulusactivatesthelocalnon-depressedexcitatoryanddistributeddepressedinhibitorynetworkandtheresultisanoverallincreaseinactivitytorarestimulation.Habituationandsensitizationofresponsesfrequentlyoccursinexperimentsandunderstandingthesechangesisimportanttointerpretationofproberesponsesusedtodetermineresponsechangesinvitro. 95

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6.3ResultsEachnetworkinstantiationdevelopedthroughspontaneousactivitypriortotheexperimentalprotocols.TheactivityjustpriortoexperimentalstimulationisshowninFigure 6-1 andisconsistentwithinvitronetworkactivity.Furthersimulationofthespontaneousactivitywasconductedinunisonwiththeexperiments;thisdataisanalyzedforabaselineplasticitycomparisoninafollowingsubsection.6.3.1SpontaneousPlasticityInChapter 4 seeFigure 4-13 ,mostsynapticweightsinthemodeluctuatebutmaintainlessthan10%changefromtheaveragevalueover15minutesandlonger.Somespontaneouschangesdooccurbutonlyatslowrates<.04nS/min.GiventheASTDPrule,onewouldexpectstrongweightstodepressandweakweightstopotentiatespontaneously,however,Figure 6-5 showsthisdoesnotnecessarilyoccur.ManyweightchangesoccurinconcertwithchangesinotheraerentoreerentweightsofaneuronseeFigure 6-2 .Indeed,aerentsynapsesareregulatedinunisonbyexcitatoryscalingandeerentsynapsesareactivatedinclosetemporalproximityduetothestructureandtransmissionofneuronsandactionpotentials.Thisphenomenahasinterestingimplicationsforlearningandadaptationinthesenetworksespeciallyhowpropagationoflearningatonesynapsespreadstocompetingconnections.6.3.2ProbePlasticityStimulationofmodelresultsinsignicantchangesintheweightsasillustratedbyTable 6-1 .Withoutstimulation,themodeldemonstratesremarkablestability.Theuseofprobestodetermineconnectivityseemsinnocuous,however,thedatashowchangesinsynapticweightsasaresultoftheprobesthemselves.P2PROBEhasalargereectonthenetworksthanP2TETdoesafterward.Probeshavedualeectsduetodirectstimulationinthemodel.First,probesinduceburststhatoriginateinawaythatdiersfromspontaneousbursts.Thiscanchangethenumberofactionpotentialsgeneratedbyneuronsand,thus,theirself-regulatory 96

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a b c dFigure6-2.Spontaneousuctuationsinsynapticweightsthroughoutthesimulatednetwork.Mostsynapticweightschangeinconcertwithothers,aerentoreerent.Theframesfroma,b,c,todrightindicatethesummationofweightchangesbetweenneuronsoverconsecutive15minuteperiods.Thisshowsthereductionoflargeweightchangesovertime.Thescaleofredtogreentobluerepresentsincreases,nochange,anddecreasesinweightsrespectively. 97

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Figure6-3.Histogramsofplasticsynapticweightsduringspontaneousactivity.Histogramsareshownataninitialtimepointupperand30minuteslaterlower.Synapticweightsarecolorcodedbyinitialhistogrambin.Thehistogramsshowthedistributionofsynapticweightsandthatmostweightschangebyatmostonebin.05nS.Ifsynapseschangedbylargeamounts,onewouldexpecttoseethecolorsdistribute,forexample,agreenorredblockmightappearinthe[0.5]nSinterval.Thisisnotthecase. excitatoryscalefactor.Second,thestimulationofthenetworkintroducesnewtimingsofpre-andpostsynapticneurons,resultinginashiftintheunderlyingASTDP-basedsynapticweights.Inturn,thesecumulativeaerentchangesproducetheoppositeeectintheexcitatoryscalingsothatasimilarlevelofinputismaintained,eectivelycausingachangeinthescaledweightofothersynapsesnotnecessarilyaectedbytimings.6.3.3RapidMultichannelStimulationPlasticityAlthoughnotreectedinthedatashownhere,initialexperimentshadnoteworthyfailurerateoftherapidmultichannelstimulationtocontrolbursting.Increasingthe 98

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a bFigure6-4.BurstcontrolusingrapidmultichannelstimulationP1.arasterplotshowsthenetworkbeforestimulation.Duringstimulationb,thenetwork'smedianringrateFRishigherbutthepeakringrateduringburstingissuppressed. 99

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a bFigure6-5.Stabilityoflargeandsmallsynapticweightsandtheeectofstimulation.Spontaneousactivityhaslittleeectonthesynapticweightovertimea.However,P1inducesarapidconvergencebinpotentiatedanddepressedsynapsesfollowedbyslowerchangesinecacy.Typicallyunscaledsynapticweightsshowonlyminimaldriftoverlongperiodsoftimeduringspontaneousactivity.Oneneuronssynapsesofinitialweights[.1,.15]and[.65,.7]nS. 100

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a bFigure6-6.Eectofhighfrequencystimulationonconnectivity.Coloringindicatesweightchangeaandscaledweightchangeb.Dish-widedepressionofsynapsesoccurs.Synapticweightsarecorrected,withmanyincreasingordecreasing,howeverscalingisuniversallyreduced. 101

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Table6-1.Portionofsubstantialplasticweightchanges>:1nS.Notethebalanceofpotentiationanddepressioninspontaneousactivity.Whilemoststimulationprotocolsinducemoredepressionthatpotentiation,P2TETdemonstratesmorepotentiationthandepression.Inaddition,thecomparisionofthepercentofdepressedandpotentiatedsynapsesdemonstratesaninvertedrelationshipbetweenscaledandunscaledweightvalues. ExperimentDepressed%Depressed%Potentiated%Potentiated%Durationincl.scalingw/oscalingincl.scalingw/oscaling Spont.min1.00.50.30.51.20.90.30.4Spont.min1.90.80.91.22.22.00.90.9Spont.min4.03.01.51.63.33.61.61.3P1min45.417.814.53.11.10.715.04.1P2PROBE0min18.912.58.05.67.34.410.55.9P2TETmin3.12.54.32.611.95.63.22.1P2PROBE0min14.67.64.83.15.24.17.13.5P2min21.612.89.94.89.95.113.66.0P3min18.211.610.97.310.78.412.36.0 Figure6-7.Eectofhighfrequencystimulationonplasticsynapticweights.HistogramofplasticsynapticweightsbeforeupperandafterlowerrapidmultichannelstimulationP1. 102

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radiusofstimulation,andthusthenumberofneuronsstimulated,orselectionofhighlyinnervatedstimulationchannels,eliminatedburstcontrolfailureFigure 6-4 .PlasticityofstimulusresponsetimingsshowninvitroinFigure 5-7 wasobservedinthemodellessfrequentlyandonlywithhighlyvariableresponses.Thestimulationmodelusedinthisworkdeliversthesamepatternofsynapticactivationduringeachstimulus,however,short-andlong-termplasticityinsynapticecacyresultsinvariationofpostsynapticinputs.Asaresult,severalpreciselytimedactionpotentialsaregeneratedalongwithlessreliablevariably-timedAPs.Stimulationinducednetwork-widedepressionunderP1.However,theunderlyingweightvariablesaremodiedinasymmetricmannerseeTable 6-1 .Thus,mostofthedepressionresultfromthereductionoftheexcitatoryscalingcomponent.6.3.4TetanicPlasticitySince,Jimboet.al.showedthatmostofchangeinresponseoccurredafter20ms,itislikelythatthephenomenaorignatesinthepolysynapticpathwaysofthenetworkand,thus,weanticipatethatchangesinweightsdirectlymediatedbysinglesynapsesshouldnotillustratetheprobe-responsechanges.Indeed,acorrespondencebetweenthetwographsinFigure 6-10 donotexist.Moreover,thecorrespondencedoesnotexistfortheinitialresponseeitherthatwouldbeexpected.Toinvestigatethisphenomenafurther,weexaminedneuronswithlargeresponsechanges.Suprisingly,eachof15neuronswiththelargestchangesinresponsewereinhibitoryneuronsanddidnotdemonstrateanylong-termplasticityofitsaerentsynapseswiththeexclusionofexcitatoryscaling.Ifexcitatoryscalingwasresponsibleforthesechanges,allresponseswouldbeexpectedtoincreaseordecreasetogether.Inhibitoryneuronstypicallyreat2-3timesthefrequencyofexcitatoryneuronsinthemodeland,thus,demonstratesensitivitytodierencesininputfromthenetwork.Inaddition,increasesanddecreasesinresponsetostimulationofchanneldonotcorrespondtothechangesinthetotalsynapticweightsdirectlystimulatedbytheelectrode.Furthermore, 103

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a bFigure6-8.EectoftetanicstimulationonthenetworksimulationasdeterminedbyprobesofsimulatedMEAchannels.Bluevaluesindicateareductionintheaverageresponse,whereasredshowincreasescoloraxesindicatechangeinthenumberofactionpotentialsdetected.Twoexamplesofhowtypicalresponsestostimulationofaparticularchannelareeitherallpotentiatedordepressed.Inaddition,neuronswithlargeresponsedierencesshowbothlargedecreasesandincreases. 104

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a b c dFigure6-9.Eectoftetanicstimulationonsynapticweightsinnetworksimulation.Bluevaluesindicateareductionintheweight,whereasredshowincreases.anostimulus.bafterP2PROBE.cafterP2TET.daftersecondP2PROBE. re-simulationofthesameexperimentonthesamenetworkdierentnoiseseed,samedistributionresultsinadierentproberesponseplot.Thisevidencemightindicatethatthesechangesaretheresultofsamplingofvariationsofactivity,however,weknowthatsynapticchangesdooccur.Samplingofthesynapticcurrentshowsthatnetworkinputtothoseneuronshasincreasedforlargeincreasesintheprobe-responseplot.Infact,there-simulationofP2showsthatweightchangesproducedbythestimulationsaresimilargivenadierentnoiseseed.Inaddition,thechangeinproberesponseplotsaveragedover10repetitionsaremutedduetoinverted 105

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a b c d e fFigure6-10.ReproducibilityoftheeectsofP2stimulation.Upperleftandmiddleleftexampleproberesponseplotspairedwithweightchangeplotsforthesamestimulationandnetwork,upperrightandmiddlerightrespectively.Lowerleftistheprobe-responseplotaveragedover10repetitionsoftheexperiment.Lowerrightanotherweightchangeplotforcomparisionwiththeaveragedresponse.Notethecorrespondencebetweenweightchangeplots;repetitionswithdierentrandomseedsresultsinsimilarweightchangeseventhoughtheproberesponseplotdoesnotclearlyshowthis.Theaveragedproberesponseplotismutedindicatingminimalcorrespondencebetweentrials. 106

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Figure6-11.Modulationofstimulusresponsebyprioractivity.Thestimulusresponseisdominatedbyshort-termvariablesthataredeterminedbyactivity.Theshapeofthecurveformedbythedataisreminiscentofinter-pulseintervalcurvesseenexperimentally.Shownarepre-tetnusupperandpost-tetnuslowerdata. overlappingresponsesontheplotspromotingthenotionthatthedierencesaredotonoiseorhighlydivergent.Moreover,theaveragedplotdidnotrevealsimilaritywiththechangesinweights.Thus,probeseitherreecttheshort-termdynamicsofthenetworksordistributedand/orminutedierencesinsynapticconnectionsgreatlymodifytheproberesponseasmightbeexpectedaccordingtothedivergenceofdynamicalsystemsfrominitialconditions.Regardless,P2inducesreliablechangesinsynapticpathwaysbetweenstimulationelectrodesandoutputneurons.Asainitialtestofthesourceofresponsevariabilityseen,wecomparedthemagnitudeoftheresponsethenumberofAPswiththeelapsedtimesincetheonsetofthelast 107

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Figure6-12.Inuenceofshort-termdynamicsonburstresponse.Usingmeandataovertheentirenetworkoftwooftheeighttimescalesrepresentedinsynapticshort-termvariables,thenetworkformsatrajectoryinstatespaceandisdispersedalongthetrajectorydependentontheaggregateexcitatory-to-excitatoryconnectionsstrengthindicatedbycolorsbluetored,lowtohighassociatedwitheachstimuluschannel. burst,seeFigure 6-11 .Thereisacleardependencyoftheactivitypriortothestimulusonthestimulusresponse.Moreover,whenconsideringtheshort-termdynamicsinvolvedinthismodulationtherearedistincttrendsinthedatawithrespecttoelectricalstimulationactivatingexcitatorypathwaysandthemagnitudeoftheresponseFigure 6-12 .6.3.5PairedRare-FrequentStimulationAdaptationPairedlowandhighfrequencystimulationonaverageproduceslargernormalizedresponsestotherarestimulusthantothefrequentstimulusinthemodel.Additionally,theresponsetorarestimulusisaugmentedasEytanet.al.showed.Inthemodel,the 108

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Figure6-13.Eectofpairedrare-frequentstimulation.Thisplotshowstheincreaseintheresponsetorare1 30Hzstimulationrelativetoabaselineaverageat2minuteswhendeliveredwithafrequent1 3Hzstimulus. variabilityoftheresponseproduceslargevariationoftherelativeresponsewhenusingasingletime-pointcomparison,thus,weaveraged3responsesfromthe1 30Hzstimulationspriortothe2minutetime-pointusedasareferencebyEytanet.al..Theeectisnotaspronouncedinthemodelasitisinvitro;a15-20%increaseinresponsivenessisobservedascomparedto30-40%increaseinvitro[ 88 ].Theincreaseinthesimulatedresponseisonlyseenrelativetorarestimulationafterfrequentstimulation.Ifabaselinerarestimulationisestablishedbeforetheexperiment,theinitialwindowaverageslowerthanthebaselineandtheremainderofthewindowismarginallyaboveunityrelativeresponsiveness.Theplasticeectishighlyvariableandeachinstancedoesnotdemonstrateasmoothincreaseinresponsiveness.Instead,wenotedthatindividualtrialstypicallypotentiateinlargejumpsinresponse. 109

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Figure6-14.Histogramofplasticsynapticweightsbeforeupperandafterlowerpairedrare-frequentstimulationP3. Theincreaseinoursimulatedresponseisencouraging,Eytanet.al.supposedthatthisphenomenawaspossiblethroughahighlyinterconnectedinhibitorysystemincludinggapjunctions.However,themodeldoesnotincludegapjunctions;thismaybeareasonforthediscrepancyintheaugmentationoftheresponse.Anotherpossibledierenceisthesizeanddensityofsimulatedculture,asonly500neuronsweresimulated.Inthemodel,responsesthataugmentcoincidewithadepressionofexcitatoryinputontoinhibitoryneuronswithadditionallargechangesinsynapsesaectsbybothstimuluschannels,seeFigure 6-15 .6.4DiscussionThemodelproposedinChapter 4 hasenabledexperimentationandanalysisofsimulatedcultureswithresultsequitabletothelivingnetworks.Furtherinspectionof 110

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Figure6-15.Localizedsynapticandscalingchanges.Coloredpointsindicatethechangeincollectivescaledsynapticstrengthwithredandblueindicatingincreasesanddecreases,respectively.Postsynapticneuronsaresortedintotwogroupsexcitatoryleftsideandinhibitoryrightside.Additionally,presynapticneuronsaregroupedintofourcategoriesfromtoptobottomdeterminedbyiftheyarestimulatedby:frequentstimulus,bothstimuli,rarestimulus,orneitherstimulus. themodelispossible,whichhasleadtosignicantenhancementoftheunderstandingofinteractionsbetweenneuronsinthesenetworks.Forexample,wedemonstratedthattheproberesponsedoesnottypicallyindicatethesynapticweightsbetweenthestimulationelectrodeandtheoutputneuron,asthetechniqueisoftenusedfor.Wealsoshowthatthethreestimulationprotocolsexaminedherechangesynapticweightsthatareotherwisestableforhours.Theseaccomplishmentsshowthevalidityofthesimulatedself-regulatingnetworkandthebenetsofmodeling. 111

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6.4.1UtilityoftheModelTheactivityreproducedbythemodelcloselyresemblesthatseeninvitrowithrespecttobothspontaneousandelicitedactivity.Wewereabletoexaminechangesinthemodelthatarenotreadilyobservableinvitro.Theseunderlyingchangesinthemodeldeservefurtherscrutinyinvitro.Remarkably,mostsynapsesinthemodelarestabileovertime,withonly8%onaveragedeviatingmorethan.1nSduringonehourofsimulation.Thisstabilityallowsforrelativelysimplecomparisonofpre-andpost-experimentnetworkstatesoflong-termregulatoryvariables.Severalrevelationsofthemodelwereexpectedincludingthestabilityofsynapticweightsandsignicantchangesinsynapticweightasaresultofstimulation.However,thisimmutabilityofsynapticweightshadyettobeshowninmodelsexhibitingplasticweights.Thisbehaviorhasbeenanticipatedbyothers[ 111 130 ]inculturelargelyderivedfromobservationsofthestabilityofburstactivitystructureandspiketimings.Amajorityofelectricalstimulationexperimentsevokechangesineectivityconnectivitywithonlyafewexceptions[ 144 ].6.4.2PlasticityDuetoStimulationAllofthestimulationprotocolsexploredhereelicitplasticityinthesimulatednetworksinexcessofchangesseenspontaneously.Typicallysynapticchangesfromstimulationbalancemanyweights,however,somepotentiatedordepressedsynapsesarefurthermagnied.Rapidmultichannelstimulationleadtoasharpnarrowingofthesynapticweightdistributionanddepressionofexcitatoryinputscalefactors.Inthisstate,thenetworkresemblesthesimulationsoonafterinitializationofthemodelandearlysimulation.Thiswouldindicatethattheseparabilityandreliabilityofrapidmultichannelstimulationislargelystructuredbasedonthexedconnectionsinthenetwork.Eventhoughlargeweightchangesoccurinthemodel,onlyaminimalamountofplasticityisseenintheprecisetimingsofactionpotentials. 112

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Theactualmeasureofaproberesponseplotisdebatable.Themodelandinvitrodatasuggestthattheincreaseinactionpotentialsisduetoanincreaseininputfromthenetworkandthathighringrateneuronsdemonstratethemostsensitivitychangesininput.Thus,theprobesaremeasuringareliablechangeinthenetworkfromthestimulatedchannelintotherecurrentstructureofthenetworkandnottheconnectivityfromthechanneltoaspecicneuron.However,ouranalysisdidnotshowanycorrespondencebetweenthecumulativechangesinsynapticweightsdirectlyactivatedbythestimulationchannelandthegeneralincreaseinresponsestimulation.Followingthislogic,theprobemusteitherbemodulatedbythecurrentstateofthenetworkorbyspecicdistributedpathwaysthataresensitivetosmalldierencesinsynapticweightsie.thesmalldierencesinrepetitionsoftheexperiment.Itmaybepossibletoforcethestateofthenetworkbyusingrapidstimulationie.followingtheburstcontrolparadigmtoprobethenetworkbeforeandafterstimulation.WhileweareabletodemonstrateanincreaseinresponsetorarestimulusthatEytanet.al.showed,thechangeisonlyrelativetothetime-point2minutesintotheexperiment.Assuch,theincreaseinrelativeresponsivenessappearstooccurasahabituationtothefrequentstimulus.Interestingly,manychangesinweightsareshownwithdepressionoccurringmoreoftenthanpotentiation,however,thereispositiveshiftinthesynapticweighthistogrampeak.Thismayindicatelocaldepressionofexcitatoryscalingtothefrequentstimulus,asaresulttherestofthenetworkbeginstoslightlyincreasescaling.Thus,stimulationoftherarechannelbeginstoslightlyincreaseresponsewithoutinducinglocaldepressionbecauseoftherarityofthestimuli.6.4.3FutureWorkLookingattheeectofthestimulationprotocols,wenoteonespecictrendthatdemandsfurtherexploration.Slowandfaststimulationofmanychannelsie.P2PROBEandP1leadtoanegativeshiftinthepeakofthesynapticweightshistogram,whereasslowandfaststimulationofoneortwochannelsie.P2TETandP3resultedinapositive 113

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shiftinthepeakofthesynapticweightshistogram.Thishypothesishasimportantrepercussionssuchaslimitthenumberofinputsforlong-termstimulationprotocolsandcouldbetestedwithadditionalsimulations.Sincewehaveseenchangesinthenetworksduetoallstimulationsincludingprobes,furtherworkshouldexploremorelocalizedstimulationmethodstoassertainthereeectsonthesimulatednetworks.Naturally,themodelshouldbeusedtoanalyzeotherstimulationprotocolssuchasthatusedbyChaoet.al.[ 103 ].Correlatedstimulationscanbeexploredfortheeectsofpositiveandnegativetimingstosynapticweights. 114

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CHAPTER7CONCLUSIONSForyearscomputerscientistshavestriventocreatecomputerswiththesamecognitiveabilitiesashumans.However,manyattemptshavefallenshortofsuchloftygoals.Today,scientistsandengineersoftenlooktobiologyforinspirationtocreateeloquentsolutionstotasks.Forcomputationandlearning,thismeansstudyingneuronalnetworkstoelucidateandunderstandhowtheyworkinunisontoachievetheirremarkableaptitude.Theadventofinvitroneuralculturesgrownonelectrodearrayshascreatedtheabilitytochronicallystudycomputationalanddynamicpropertiesofneuronalnetworks.Inthiswork,amodelwasdevelopedthatfacilitatesexperimentationandunderstandingofneuralcultures.Furthermore,understandingthesenetworkswillfacilitatethedevelopmentofcrucialtechnologieslikebrain-machineinterfacesandneuralprosthetics.Theknowledgegainedbydecipheringcomputationandlearningatfundamentallevelscanbeappliedtoencodinganddecodingofneuraldata,crucialforanybraininterfaceddevice.Inaddition,therelevancetodataprocessingisenormous,duplicatingtheexibilityandcomprehensionthathumanspossessisfarointhefuturegivencurrenttechnology.7.1CriticalAssessmentThisstudyhighlightsimportantcharacteristicsofinvitroneuralnetworksfordevelopmentofmodelsanddirectcomparisontothecultures.Thenecessityofeachcomponentofthemodelismadeevidentbythoroughexaminationofthebehavioroftheculture.Theeectsofstimulationaretiedbacktothemodel;wendrapidinputisnecessarytolimittheburstingbehavioroftheinvitromodelnetwork.AmplitudeandspiketimingdependentplasticityASTDP,developedinChapter 3 ,maintainsanunimodalsynapticweightdistributionthatisnecessaryforcompliancewithinvitroexperimentalevidence.Inpractice,ASTDPcanproduceslargerapidweightchangeswhenthepre-andpostsynapticspikepatternschange.However,noiseinnetworks 115

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ofneuronscanprovidestrongfeedbackformaintainingasynapticweight.ASTDPisanaturalanswertoSTDPstabilityissuesandrequiressimilarcomputationtimeifsubstitutedfortheweightsaturationcalculations.Activitydependentselfregulationofinputscalecanbeusedtoresolveimportantimplementationissueswithneuronalmodels,likethatintroducedinChapter 4 .Weshowedmultiplicativescalingoftotalsynapticweightduringdynamicchangesinindividualsynapsesisabletobothregulatepostsynapticneuronringratesandenabletheinteractofscaledaerentsynapticweights.Thisscalinghasbeenindicatedtobeactivity-dependentreectingnegativefeedbackinvitroandinvivo[ 28 89 ].Moreover,ournetworkmodeldemonstratesinvitrolikewithrespecttoISIs,IBIs,andweightdistributionsactivityandstability.Chapter 5 showedthattheearlyresponsetolowandhighfrequencystimulationishighlyseparable.Indeed,highfrequencystimulationisespeciallysowhennonstationarityisaccountedforwithclassicationabove99.5%.However,thelatephaseofthestimulationprotocolsusedintheseexperimentsshowthattheburstingresponsesarenotseparableusingtheprecisetimingsofactionpotentials,time-lockedtostimulation.Although,signicantbutnotremarkableseparabilityispresentusinglatephaselowfrequencystimulationresponse.SimulatedinvitroplasticityisshowninChapter 6 withthemodelwedevelopedinChapters 3 and 4 .Themodelwasdemonstratedtoreproduceaburstcontrolscheme,changesinproberesponsebeforeandaftertetnus,andanaveragedincreaseinresponsivenesstoararestimuluswhenpairedwithafrequentstimulus.Weshowedconsiderablevariationinproberesponsesacrosssimulationsevenwhenthereareconcurrentsimilarchangesinsynapticweightsinallsimulations.Theseaccomplishmentsshowthevalidityofthesimulatedself-regulatingnetworkandthebenetsofmodeling.Designingamodelthatincorporatesthedynamicbehaviorofinvitrocultures,especiallyinresponsetochanginginputconditions,requiresthathomeostaticneural 116

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mechanismsarereproduced.ASTDPandself-regulationaretwoconceptuallyandcomputationallysimplecomponentsthatenablelargenetworkmodelstomorefaithfullyreproduceinvitroactivitythanstaticparametersduringsimulatedexperiments.Theymayalsoleadtonewunderstandingofthedynamicspatio-temporalpatternsgeneratedinvitro.7.2FutureWorkThebulkofthisdissertationisfocusedonthedevelopmentandvalidationofanaccuratenetworkmodel.However,wedidbegintousethefullpotentialofthismodeltoilluminatealterationsinnetworkbehavior.Ofcourse,thereareseveralexperimentsthatcouldbedonetocontinuethisworkinthefuture.ThismodelcouldbeusedtoexplorecompetitionbetweenASTDPbasedsynapsesinmoredetail.Someresearchersarguethatcompetitionisnecessaryforlearning[ 112 ]atsynapses;othershavestated[ 115 117 ]thatSTDPcreatescompetitionbetweensynapseswhileamplitudedependentrulesdonot.However,thenetworkmodelemployedinthisresearchneverusesASTDPalone,onlyinconjunctionwithhomeostaticscalingofexcitatoryinput.Thus,multiplicativescalingisonlyusedforaportionofthesynapsesandlikely,creatingcompetition.Indeed,thereispartialevidenceforthisinChapter 6 ,theexperimentalchangesinweightsindicatethatscalingcompensatesforchangesinlong-termsynapticvariablesandbydoingsowilleectivelydepresssynapsesthatdonopotentiateorpotentiatesynapsesthatdonotdepress.Inaddition,Froemkeet.al.[ 45 ]demonstratedmorerealisticweightchangeswhensaturationormultipleinteractingspikeeectsareimplemented.Thisisanimportantquestiontoaskasburstpatternsofinvitronetworksmakethosemodelsofspike-timingplasticityrulesrelevant.Alongthesametheme,themodelcouldbetestedforitsabilitytoidentifycorrelationsintwospiketrains.Atthesinglesynapselevel,thiswasshowninChapter 3 .However,usingelectrodebasedstimulation,itremainstobeseenhowtheencodingoccursandwhereinthenetworkitismanifestduetothemultitudeofpathwaysconnectingone 117

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channeltoanother.Similarly,afeedbackloopcouldbemadetotestthenetworksabilitytoassociateitownoutputswithinputs.Forexample,thestimulationtraininputintothenetworkcouldbegeneratedbythetimedelayedcombinationofoneormanyoutputchannels.Thenthequestioncouldbeposedwhethersynapsesbetweenoutputneuronsandtheinputneuronsarechanged,andhowthenetworkconductiondelayofthesynapticpathwaysarerelatedtothetimedelayoftheinput.Anotheruseofthemodelistotestifthestructureoftheinvitronetworkagainstasimulatedcorticalstructure.Thehypothesiscouldbetestedwhetherthereasontheculturesburstisbecauseofthelackofstructureorbecauseofthelackofinput.Additionally,asimulatedcorticalstructure,likeafeedbackloop,couldbeusedunderbackgroundinputtolearntogenerateAPsforparticularinputpatternssimilartoShahafandMarom[ 130 ].7.3SignicanceandContributionTheworkpresentedheremarksmanyessentialadvancementsinmodelingneuronalnetworks.Previously,networkmodelsreliedsolelyonSTDPforlong-termsynapticchangeswithfewexceptions[ 117 145 ].Inaddition,scarcelyanynetworkmodelsusehomeostaticregulation[ 103 ].Tosummarize,thisworkisthersttoincorporaterealistic,dynamicneuronswithhomeostaticscalingcoupledbyfrequencydependentsynapsesthatundergoamplitudedependentlong-termchanges.Furthermore,theuseofadaptingendogenouslyactiveneuronsisnovel.Other,morehypothetical,contributionsthismodelmakestothescienticcommunityarepotentialwaysfordescribingneurondisbursement,connectivity,andstimulusonanMEA.Theideaofusingalocalellipticaltawetteddropletisnotnew;but,theideatouseitforthesettlementofcellsduringcultureis.Inaddition,connectivitydistributionsweredevelopedindependentlyfromobservationsincultureliteratureandbymorphologicalknowledgeofcelltypes.Thisworkshowsthefunctionalityofthesedistributionsbutdoesnotprovetheiraccuracy.Rigorousattentionwasalsodevotedtothedevelopmentof 118

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modelingstimulationonMEAswithminimalcomplexity.Whileithasbeenknownthatelectricalstimulationactivatesaxonsandlowthresholdtissueatreasonablestimulationlevels,thiswaslargelyignored,withrespecttonetworkmodels,beforethisworkasidefromtomographyexperiments.Themodeldemonstratedinthisdissertationisabletomimicseveralmodesofactivityobservedinvitroincludingtypicalmatureburstingpatternsandsuperbursting.Thecomponentsofthemodelareselectedandbuiltfromsimpleandexperimentallyexposedbehaviorsofthenetworkconstituents.Observationofthespontaneousactivityalonehasenabledustounravelthesecretsunderlyingthenetwork'sstability.Anothernoveltyofthisresearchisthevalidationthatwasperformedonthemodel.Mostoftenneuronalnetworkmodelsaredevelopedtomimicaringpatternordistribution,ortobeusedtocreateanoutputforaspecicinput.Thismodelwasdevelopedforthepurposeofunderstandingtheunderlyingdynamicsthatalterthenetworkbehavior.Severalstimulationschemeswerereproducedinvitroandinsimulationtoverifytheplausibilityofthemodel.Indoingso,wediscoveredremarkablecharacteristicofthenetworkmodelthatmaybeappliedtotheoriesoftheoperationofculturednetworks. 119

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APPENDIXAEFFICIENTIMPLEMENTATIONOFNETWORKSIMULATIONSimulatingneuronalnetworkmodelscanbeanarduoustaskwithoutthepropersegmentationoftheproblem.Axonalconnectionsareanexcellentsegmentationpointbecauseofthesparsecodingofactionpotentialsie.binarywithrareeventsandthelackofdynamicchangesmodeledinaxonsseeFigure A-1 .Exploitingtheparallelisminherentinneuralnetworkscanleadtoanecientimplementationoftheequationsgoverningthemodel,however,minimizingthenumberofcalculationsismoreimportanttoimproveperformanceofthesimulations.Unfortunately,integrationbytimestepsisrequiredwhenanalyticalsolutionsarenotpossible.Asidefromtheintegrate-and-reIFmodel,mostneuronmodelsdonothaveclosedformsolutions.Inaddition,simulatedgaussianmembranenoisepreventstheuseofclosedformsolutionsasthisrequirestheintegrationofthenoisesignalwithrespecttotheneurondynamics.Thus,thetime-complexityoftheneuronsimulationisbasedontheoperationspertimestepandthesizeofthetimestepsthatmaybeusedwhilemaintainingaccuracyandstabilityofthemodel.Theusageofcompartamentalmodelsfornetworksimulationsisimpracticalfortheobservanceoflargenetworklevelphenomena.Hence,simplicationtacticsforthosemodelsarenotdiscussedhere.Instead,weassumeallsynapsesaremanifestontheactionpotentialinitiationsite,suchthatthereiszerodelaybetweensynapticinputandtheneuronbutthereisatimedelayfromtheneurontosynapticoutputs.Simplesynapticactivitycanbesimulatedasaresultofpre-andpostsynapticactionpotentials.Ifthisactivityisnotinuencedbysubthresholdsomaticactivity,thenintegrationofsynapticvariablesmustonlyoccuruntilsteadystateisreachedapproximatelyvetimesthelongesttimeconstant.Asanalternative,synapsesthathaveclosedformsolutions,andthetimecoursesofthereconductancesarethesame,canbecalculatedonlyattimepointsthatsynapsesarealteredandanuniedcalculationfor 120

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FigureA-1.Divisionpointforparallelnetworkmodelsimulation.Incomputingterms,thispointistheminimalistsignal:sparse1or0coding.Since,eithertheneuronredornot;thiscanbesimpliedtoneuronnumberandtimeofeachactionpotentials. fort=1totimesteps foreachsynapse ifexistsAP=t-conductiondelay+synapticdelay updatesynapsefortimejumpfromlastsynapseevent perform"pre"synapseeventcalculations end end foreachneuron performsingletimestepcalculationforneuron ifneuronspiked forallinputsynapsesofthisneuron updatesynapsefortimejumpfromlastsynapseevent perform"post"synapseeventcalculations end end end end FigureA-2.Pseudocodeofmodelrunloop.Implementationoftherstinternalloopismostecientifitisactionpotentialdriven,insteadofperformingthecheckforallsynapses. synapseclassescanbeincorporatedintothepost-synapticneuronsthatisupdatedateverytimepoint.Thisreducesthenumberofcalculationsbyapproximatelyanorderofmagnitude,sincefullsynapsecalculationscanjumpfromonedelayedpre-orpostsynapticactivationtothenextbasedonthetimingeg.Figure A-2 121

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APPENDIXBSIMULATINGELECTRICALSTIMULATIONPropagationofelectricalstimulationofexcitableneuraltissuehasbecomeasignicantfactorinunderstandinginvitroandinvivoneuralinterfaces[ 55 56 ].Researchersnowunderstandthatusingminimallevelsofcurrentisimportantinpreservingthehealthoftissuenearthestimulationsite.Inaddition,neuralaxonsinitiateactionpotentialsinresponsetostimulationbeforeotherportionsoftheneuron,sincetheaxonhasthelowestactivationthreshold[ 56 ].Thus,onemayassumethatmostneuraltissuestimulatedinvitro,whenusingtheminimalstimulustoinitiateaburst,isaxonal.Giventhisinformation,weproposeanewstimulationmethodthatdiersfromothermethodsofnetworkmodelstimulation.Mostmodels[ 103 ]activatecellbodiesnearMEAchannelswhenastimulationoccurs.Primarily,thissimplicationismadeforcomputationalease;however,anotherruntimecombinatoriallysimplemethodispossiblebasedonthestimulationofaxons.Inaddition,theeectivespreadofthecurrentinjectionsimulatedbystimulatingsomasisgrosslyinaccurate.Moreover,stimulationofaxonspredictsamorereliablepatternofactivationofaxonterminalsandthussynapses.Thishighreliabilityisseenexperimentally[ 90 139 ]Chapter 5 .Indeed,thesomaticstimulationmodelalsofailstopredictchangesintimingsofsynapticactivationattheextentoftheaxonalarborsastheinducedactionpotentialpropagatesorthodromicallyandantidromicallycomparedwiththoseproducednaturally"attheaxonhiloc.Astimingsarecrucialtounderstandingchangesinvitro,thesomaticstimulationmodelisill-equipedtorecreateexperimentalprotocols.Usingtheaxonstimulationmodel,manymoreneuronsareexcitedthanwiththesomastimulationmodel.UsingthenetworkconnectivitydevelopedinChapter 4 andtheaxonalstimulationmodel,the500neuronmodelresultsinelectrodestimulationsactivatingapproximately5-10%ofneurons.Simultaneousexcitationof5-10%ofthenetworkresultsinapopulationburstwhenthenetworkisnotinarefractorystate.This 122

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percentageiscanwidelyvarydependingontheshapeoftheaxonsmodeledandtheradiusinwhichtheelectricalstimulationactivesthoseaxonsinthismodel,20m.Simpleaxonalstimulationmodelmethods: Pre-calculatethedistancethatthestimulationlevelusedwouldinitiateandactionpotentialinanearbyaxon. Basedonthemodelusedforaxonshape,calculateallaxonswithinthestimulationradiusofeachelectrode.Astraightpathbetweensomasofconnectedneuronswasusedinourmodel;thisishighlysimplistic. Calculatetheconductionandsynapticdelayfromthepointofstimulationoftheaxontoeachofthepostsynaptictargetsgiventheaxonshape.Astraightpathbetweenstimulationpointandthepostsynapticneuronwasusedinourmodel.Again,thisishighlysimplied,butdoesachievethegoalofintroducingnewtimingsbetweenaxonterminalsofastimulatedneuron. Intheimplementationofthemodel,aparticularstimulationistreatedthesameasanactionpotentialgeneratedbythenetwork,butwithmanymoresynaptictargets.Benetsofaxonalstimulationmodel: Fastimplementationofstimulus. Representsantidromicpropagation. Flexibleanddierentoutcomesforaxonalshapeandlayout. Stimulatesreasonablenumberofneuronsleadingtoburstofactivity.Shortcomingsofaxonalstimulationmodel: Mustprecalculatebasedonxedstimulationlevelforeeciency. Ignoresaxon'sabsoluterefractoryperiod. Ignoresstimulatedneuron'saerentsynapses.Canbeovercomewithadditionalprogramming. Doesnotinducerefractorystateinstimulatedneuron. 123

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REFERENCES [1] R.P.VillarrealandJ.E.Steinmetz,Neuroscienceandlearning:lessonsfromstudyingtheinvolvementofaregionofcerebellarcortexineyeblinkclassicalconditioning.,"JExpAnalBehav,vol.84,no.0022-5002,pp.631{52,2005. [2] S.MaromandG.Shahaf,Development,learningandmemoryinlargerandomnetworksofcorticalneurons:lessonsbeyondanatomy,pp.63{87,CambridgeUniversityPress,2002. [3] J.vanPelt,P.S.Wolters,M.A.Corner,W.L.C.Rutten,andG.J.A.Ramakers,Long-termcharacterizationofringdynamicsofspontaneousburstsinculturedneuralnetworks.,"IEEETransBiomedEng,vol.51,no.0018-9294,pp.2051{62,2004. [4] D.A.Wagenaar,J.Pine,andS.M.Potter,Anextremelyrichrepertoireofburstingpatternsduringthedevelopmentofcorticalcultures,"BMCNeuroscience,vol.7,no.11,2006. [5] M.A.Lebedev,J.M.Carmena,J.E.O'Doherty,M.Zacksenhouse,C.S.Henriquez,J.C.Principe,andM.A.L.Nicolelis,Corticalensembleadaptationtorepresentvelocityofanarticialactuatorcontrolledbyabrain-machineinterface.,"JNeurosci,vol.25,no.1529-2401,pp.4681{93,2005. [6] S.M.PotterandT.B.DeMarse,Anewapproachtoneuralcellcultureforlong-termstudies,"JournalofNeuroscienceMethods,vol.110,pp.17{24,2001. [7] C.A.BatesandR.L.Meyer,Theneurite-promotingeectoflamininismediatedbydierentmechanismsinembryonicandadultregeneratingmouseopticaxonsinvitro.,"DevBiol,vol.181,no.0012-1606,pp.91{101,1997. [8] J.E.HuettnerandR.W.Baughman,Primarycultureofidentiedneuronsfromthevisualcortexofpostnatalrats,"JournalofNeuroscience,vol.6,no.10,pp.3044{3060,October1986. [9] K.NakanishiandF.Kukita,Intracellular[Cl)]TJ/F15 11.955 Tf 7.084 -4.339 Td[(]modulatessynchronouselectricalactivityinratneocorticalneuronsinculturebywayofGABAergicinputs,"BrainResearch,vol.863,pp.192{204,2000. [10] A.M.Habets,A.M.VanDongen,F.VanHuizen,andM.A.Corner,Spontaneousneuronalringpatternsinfetalratcorticalnetworksduringdevelopmentinvitro:aquantitativeanalysis.,"ExpBrainRes,vol.69,no.0014-4819Print,pp.43{52,1987. [11] M.Ichikawa,K.Muramoto,K.Kobayashi,M.Kawahara,andY.Kuroda,Formationandmaturationofsynapsesinprimaryculturesofratcerebralcorticalcells:anelectronmicroscopicstudy.,"1993. 124

PAGE 125

[12] K.Muramoto,M.Ichikawa,M.Kawahara,K.Kobayashi,andY.Kuroda,Frequencyofsynchronousoscillationsofneuronalactivityincreasesduringdevelopmentandiscorrelatedtothenumberofsynapsesinculturedcorticalneuronnetworks.,"NeurosciLett,vol.163,no.0304-3940Print,pp.163{5,1993. [13] F.vanHuizen,H.J.Romijn,A.M.Habets,andP.vandenHoo,Acceleratedneuralnetworkformationinratcerebralcortexcultureschronicallydisinhibitedwithpicrotoxin.,"ExpNeurol,vol.97,no.0014-4886Print,pp.280{8,1987. [14] K.NakanishiandF.Kukita,Functionalsynapsesinsynchronizedburstingofneocorticalneuronsinculture,"BrainResearch,vol.795,pp.137{146,1998. [15] Y.Ben-Ari,Developingnetworksplayasimilarmelody.,"2001. [16] J.vanPelt,I.Vajda,P.S.Wolters,M.A.Corner,andG.J.A.Ramakers,Dynamicsandplasticityindevelopingneuronalnetworksinvitro.,"2005. [17] A.N.VanDenPol,K.Obrietan,andA.Belousov,Glutamatehyperexcitabilityandseizure-likeactivitythroughoutthebrainandspinalcorduponrelieffromchronicglutamatereceptorblockadeinculture.,"1996. [18] B.K.RhoadesandG.W.Gross,Potassiumandcalciumchanneldependenceofburstinginculturedneuronalnetworks.,"1994. [19] R.E.Harris,M.G.Coulombe,andM.B.Feller,Dissociatedretinalneuronsformperiodicallyactivesynapticcircuits.,"2002. [20] M.Meister,L.Lagnado,andD.A.Baylor,Concertedsignalingbyretinalganglioncells.,"1995. [21] X.Leinekugel,R.Khazipov,R.Cannon,H.Hirase,Y.Ben-Ari,andG.Buzsaki,Correlatedburstsofactivityintheneonatalhippocampusinvivo.,"2002. [22] D.A.Wagenaar,Z.Nadasdy,andS.M.Potter,Persistentdynamicattractorsinactivitypatternsofculturedneuronalnetworks,"PhysicalReviewLettersE,vol.73,2006. [23] H.Kamioka,E.Maeda,Y.Jimbo,H.P.C.Robinson,andA.Kawana,Spontaneousperiodicsynchronizedburstingduringformationofmaturepatternsofconnectionsincorticalcultures,"NeuroscienceLetters,vol.206,pp.109{112,1996. [24] E.A.Neale,W.H.Oertel,L.M.Bowers,andV.K.Weise,Glutamatedecarboxylaseimmunoreactivityandgamma-[3h]aminobutyricacidaccumulationwithinthesameneuronsindissociatedcellculturesofcerebralcortex.,"JNeurosci,vol.3,no.0270-6474Print,pp.376{82,1983. [25] H.Markram,M.Toledo-Rodriguez,Y.Wang,A.Gupta,G.Silberberg,andC.Wu,Interneuronsoftheneocorticalinhibitorysystem,"NatureReviews,vol.5,pp.793{807,October2004. 125

PAGE 126

[26] L.F.Abbott,J.A.Varela,K.Sen,andS.B.Nelson,Synapticdepressionandcorticalgaincontrol,"Science,vol.275,pp.220{224,January1997. [27] R.AzouzandC.M.Gray,Cellularmechanismscontributingtoresponsevariabilityofcorticalneuronsinvivo,"JournalofNeuroscience,vol.19,no.6,pp.2209{2223,March1999. [28] N.S.Desai,L.C.Rutherford,andG.G.Turrigiano,Plasticityintheintrinsicexcitabilityofcorticalpyramidalneurons,"Nature,vol.2,no.6,pp.515{520,1999. [29] R.K.Ellerkmann,V.Riazanski,C.E.Elger,B.W.Urban,andH.Beck,Slowrecoveryfrominactivationregulatestheavailabilityofvoltage-dependentNa+channelsinhippocampalgranulecells,hilarneuronsandbasketcells,"JournalofPhysiology,vol.532,no.2,pp.385{397,2001. [30] A.Toib,V.Lyakhov,andS.Marom,InteractionbetweendurationofactivityandtimecourseofrecoveryfromslowinactivationinmammalianbrainNa+channels,"JournalofNeuroscience,vol.18,no.5,pp.1893{1903,March1998. [31] M.Giugliano,P.Darbon,M.Arsiero,H.Luscher,andJ.Streit,Single-neurondischargepropertiesandnetworkactivityindissociatedculturesofneocortex,"JournalofNeurophysiology,vol.92,pp.977{996,March2004. [32] E.M.Izhikevich,DynamicalSystemsinNeuroscience:TheGeometryofExcitabilityandBursting,MITPress,2006. [33] M.N.ShadlenandW.T.Newsome,Thevariabledischargeofcorticalneurons:Implicationsforconnectivity,computation,andinformationcoding,"JournalofNeuroscience,vol.18,no.10,pp.3870{3895,May1998. [34] G.J.StuartandB.Sakmann,Activepropagationofsomaticactionpotentialsintoneocorticalpyramidalcelldendrites,"Nature,vol.367,pp.69{72,January1994. [35] I.Timofeev,F.Grenier,andM.Steriade,Impactofintrinsicpropertiesandsynapticfactorsontheactivityofneocorticalnetworksinvivo,"JournalofPhysiology,vol.94,pp.343{355,2000. [36] R.MalinowandR.C.Malenka,Ampareceptortrackingandsynapticplasticity,"AnnualReviewsinNeuroscience,vol.25,pp.103{126,2002. [37] M.J.E.Richardson,O.Melamed,G.Silberberg,W.Gerstner,andH.Markram,Short-termsynapticplasticityorchestratestheresponseofpyramidalcellsandinterneuronstopopulationbursts,"JournalofComputationalNeuroscience,vol.18,pp.323{331,2005. [38] M.Tsodyks,K.Pawelzik,andH.Markram,Neuralnetworkswithdynamicsynapses,"NeuralComputation,vol.10,pp.821{835,1998. 126

PAGE 127

[39] R.S.ZuckerandW.G.Regehr,Short-termsynapticplasticity,"AnnualReviewsinPhysiology,vol.64,pp.355{405,2002. [40] J.A.Varela,K.Sen,J.Gibson,J.Fost,L.F.Abbott,andS.B.Nelson,Aquantitativedescriptionofshort-termplasticityatexcitatorysynapsesinlayer2/3ofratprimaryvisualcortex,"JournalofNeuroscience,vol.17,no.20,pp.7926{7940,October1997. [41] L.F.AbbottandS.B.Nelson,Synapticplasticity:tamingthebeast,"NatureNeuroscience,vol.3,pp.1178{1183,2000. [42] G.BiandM.Poo,Synapticmodicationsinculturedhippocampalneurons:Dependenceonspiketiming,synapticstrength,andpostsynapticcelltype,"JNeurosci,vol.18,no.24,pp.10464{10472,1998. [43] G.BiandM.Poo,Distributedsynapticmodicationinneuralnetworksinducedbypatternedstimulation.,"Nature,vol.401,no.0028-0836,pp.792{6,1999. [44] R.C.Froemke,M.-M.Poo,andY.Dan,Spike-timing-dependentsynapticplasticitydependsondendriticlocation.,"Nature,vol.434,no.1476-4687,pp.221{5,2005. [45] R.C.Froemke,I.A.Tsay,M.Raad,J.D.Long,andY.Dan,Contributionofindividualspikesinburst-inducedlong-termsynapticmodication,"JNeurophysiol,vol.95,pp.1620{1629,2005. [46] O.PaulsenandT.J.Sejnowski,Naturalpatternsofactivityandlong-termsynapticplasticity,"CurrentOpinioninNeurobiology,vol.10,pp.172{179,2000. [47] S.Yang,Y.Tang,andR.S.Zucker,SelectiveinductionofLTPandLTDbypostsynaptic[Ca2+]ielevation,"JournalofNeurophysiology,vol.81,pp.781{787,1999. [48] R.J.Butera,J.Rinzel,andJ.C.Smith,Modelsofrespiratoryrhythmgenerationinthepre-botzingercomplex.i.burstingpacemakerneurons,"JournalofNeurophys-iology,vol.81,pp.382{397,1999. [49] C.M.Colbert,J.C.Magee,D.A.Homan,andD.Johnston,Slowrecoveryfrominactivationofna,"JournalofNeuroscience,vol.17,no.17,pp.6512{6521,September1997. [50] P.E.Latham,B.J.Richmond,P.G.Nelson,andS.Nirenberg,Intrinsicdynamicsinneuronalnetworks.i.theory,"JournalofNeurophysiology,vol.83,pp.808{827,2000. [51] H.Markram,A.Roth,andF.Helmchen,Competitivecalciumbinding:Implicationsfordendriticcalciumsignaling,"JournalofComputationNeuroscience,vol.5,pp.331{348,1998. 127

PAGE 128

[52] T.H.Murphy,L.A.Blatter,W.G.Wier,andJ.M.Barabans,Spontaneoussynchronoussynapticcalciumtransientsinculturedcorticalneurons,"JournalofNeuroscience,vol.12,no.12,pp.4834{4845,December1992. [53] D.F.Owens,L.H.Boyce,M.B.E.Davis,andA.R.Kriegstein,ExcitatoryGABAresponsesinembryonicandneonatalcorticalslicesdemonstratedbygramicidinperforated-patchrecordingsandcalciumimaging,"JournalofNeuroscience,vol.16,no.20,pp.6414{6423,October1996. [54] E.M.Izhikevich,Simplemodelofspikingnetwork,"IEEETransactionsonNeuralNetworks,2004. [55] L.G.NowakandJ.Bullier,Spreadofstimulatingcurrentinthecorticalgreymatterofratvisualcortexstudiedonanewinvitroslicepreparation,"JournalofNeuroscienceMethods,vol.67,pp.237{248,1996. [56] L.G.NowakandJ.Bullier,Axons,butnotcellbodies,areactivatedbyelectricalstimulationincorticalgraymatter:I.evidencefromchronaxiemeasurements,"ExperimentsinBrainResearch,vol.118,pp.477{488,1998. [57] B.Hutcheon,P.Morley,andM.O.Poulter,DevelopmentalchangeinGABAAsynapsefunctioninratcorticalneuronsreceptordesensitizationkineticsanditsrolein,"JournalofPhysiology,vol.522,no.1,pp.3{17,2000. [58] M.OuardouzandB.R.Sastry,Activity-mediatedshiftinreversalpotentialofGABA-ergicsynapticcurrentsinimmatureneurons,"DevelopmentalBrainResearch,vol.160,pp.78{84,2005. [59] D.F.Owens,X.Liu,andA.R.Kriegstein,ChangingpropertiesofGABAAreceptor{mediatedsignalingduringearlyneocorticaldevelopment,"JournalofNeurophysiology,vol.82,pp.570{583,1999. [60] L.H.FinkelandG.M.Edelman,Interactionofsynapticmodicationruleswithinpopulationsofneurons.,"ProcNatlAcadSciUSA,vol.82,no.0027-8424,pp.1291{5,1985. [61] W.Senn,H.Markram,andM.Tsodyks,Analgorithmformodifyingneurotransmitterreleaseprobabilitybasedonpre-andpostsynapticspiketiming,"NeuralComputation,vol.13,pp.35{67,2000. [62] M.V.TsodyksandH.Markram,Theneuralcodebetweenneocorticalpyramidalneuronsdependsonneurotransmitterreleaseprobability,"ProceedingsoftheNationalAcademyofSciences,vol.94,pp.719{723,January1997. [63] B.W.Connors,R.C.Malenka,andL.R.Silva,Twoinhibitorypostsynapticpotentials,andGABAAandGABABreceptor-mediatedresponsesinneocortexofratandcat,"JournalofPhysiology,vol.406,pp.443{468,1988. 128

PAGE 129

[64] A.Destexhe,Z.F.Mainen,andT.J.Sejnowski,MethodsinNeuronalModeling,chapterKineticModelsofSynapticTransmission,pp.1{25,MITPress,1998. [65] M.HausserandA.Roth,Estimatingthetimecourseoftheexcitatorysynapticconductanceinneocorticalpyramidalcellsusinganovelvoltagejumpmethod,"JournalofNeuroscience,vol.17,no.20,pp.7606{7625,October1997. [66] G.DaoudalandD.Debanne,Long-termplasticityofintrinsicexcitability:learningrulesandmechanisms.,"LearnMem,vol.10,no.1072-0502,pp.456{65,2003. [67] C.Koch,chapterSynapticInteractionsInaPassiveDendriticTree,pp.115{141,September1997. [68] H.LuscherandM.E.Larkum,Modelingactionpotentialinitiationandback-propogationindendritesofculturesratmotoneurons,"JournalofNeuro-physiology,vol.80,pp.715{729,1998. [69] G.J.StuartandM.Hausser,DendriticcoincidencedetectionofEPSPsandactionpotentials,"NatureNeuroscience,vol.4,no.1,pp.63{71,January2001. [70] Y.Shu,A.Hasenstaub,A.Duque,Y.Yu,andD.A.McCormick,Modulationofintracorticalsynapticpotentialsbypresynapticsomaticmembranepotential,"Nature,2006. [71] T.ZadorandC.Koch,BiophysicsofComputation:InformationProcessinginSingleNeurons,chapterSynapticPlasticity,pp.297{323,OxfordUniversityPress,1999. [72] J.-V.LeBeandH.Markram,Spontaneousandevokedsynapticrewiringintheneonatalneocortex,"ProceedingsoftheNationalAcademyofSciences,vol.103,no.35,pp.13214{13219,August2006. [73] M.H.MohajeraniandE.Cherubini,Spontaneousrecurrentnetworkactivityinorganotypicrathippocampalslices,"EuropeanJournalofNeuroscience,vol.22,pp.107{118,2005. [74] M.Sur,P.E.Garraghty,andA.W.Roe,Experimentallyinducedvisualprojectionsintoauditorythalamusandcortex.,"1988. [75] D.A.Wagenaar,T.B.DeMarse,andS.M.Potter,Meabench:Atoolsetformulti-electrodedataacquisitionandon-lineanalysis,"inProc2ndIntlIEEEEMBSConfonNeuralEng,2005,pp.518{521. [76] E.Maeda,H.P.Robinson,andA.Kawana,Themechanismsofgenerationandpropagationofsynchronizedburstingindevelopingnetworksofcorticalneurons.,"JNeurosci,vol.15,no.0270-6474,pp.6834{45,1995. [77] P.E.Latham,B.J.Richmond,S.Nirenberg,andP.G.Nelson,Intrinsicdynamicsinneuronalnetworks.ii.experiment,"JournalofNeurophysiology,vol.83,pp.828{835,2000. 129

PAGE 130

[78] J.Tabak,W.Senn,M.J.O'Donovan,andJ.Rinzel,Modelingofspontaneousactivityindevelopingspinalcordusingactivity-dependentdepressioninanexcitatorynetwork,"JournalofNeuroscience,vol.20,no.8,pp.3041{3056,April2000. [79] C.Yvon,R.Rubli,andJ.Streit,Patternsofspontaneousactivityinunstructuredandminimallystructuredspinalnetworksinculture.,"ExpBrainRes,vol.165,no.0014-4819,pp.139{51,2005. [80] J.Streit,A.Tscherter,andP.Darbon,AdvancesinNetworkElectrophysiologyUsingMulti-ElectrodeArraysetrogradesignalingatcentralsynapses,chapterRhythmGenerationinSpinalCultures:IsIttheNeuronortheNetwork,pp.377{408,KluwerAcademic/PlenumPublishers,2006. [81] P.Darbon,L.Scicluna,A.Tscherter,andJ.Streit,Mechanismscontrollingburstingactivityinducedbydisinhibitioninspinalcordnetworks.,"EurJNeurosci,vol.15,no.0953-816X,pp.671{83,2002. [82] I.Timofeev,F.Grenier,M.Bazhenov,A.R.Houweling,T.J.Sejnowski,andM.Steriade,Short-andmedium-termplasticityassociatedwithaugmentingresponsesincorticalslabsandspindlesinintactcortexofcatsinvivo.,"JPhysiol,vol.542,no.0022-3751Print,pp.583{98,2002. [83] D.A.Wagenaar,R.Madhavan,J.Pine,andS.M.Potter,Controllingburstingincorticalcultureswithclosed-loopmulti-electrodestimulation.,"JNeurosci,vol.25,no.1529-2401,pp.680{8,2005. [84] S.B.Bausch,S.He,Y.Petrova,X.-M.Wang,andJ.O.McNamara,Plasticityofbothexcitatoryandinhibitorysynapsesisassociatedwithseizuresinducedbyremovalofchronicblockadeofactivityinculturedhippocampus.,"2006. [85] M.Tsodyks,T.Kenet,A.Grinvald,andA.Arieli,Linkingspontaneousactivityofsinglecorticalneuronsandtheunderlyingfunctionalarchitecture,"Science,vol.286,pp.1943{1946,December1999. [86] V.Volman,I.Baruchi,E.Persi,andE.Ben-Jacob,Generativemodellingofregulateddynamicalbehaviorinculturedneuronalnetworks,"PhysicaA:StatisticalMechanicsanditsApplications,vol.335,no.1-2,pp.249{278,2004. [87] Y.Jimbo,T.Tateno,andH.P.C.Robinson,Simultaneousinductionofpathway-specicpotentiationanddepressioninnetworksofcorticalneurons,"BiophysicalJournal,vol.76,pp.670{678,1999. [88] D.Eytan,N.Brenner,andS.Marom,Selectiveadaptationinnetworksofcorticalneurons,"JournalofNeuroscience,vol.23,no.29,October2003. 130

PAGE 131

[89] G.G.Turrigiano,K.R.Leslie,N.S.Desai,L.C.Rutherford,andS.B.Nelson,Activity-dependentscalingofquantalamplitudeinneocorticalneurons.,"Nature,vol.391,no.0028-0836Print,pp.892{6,1998. [90] Y.Jimbo,A.Kawana,P.Parodi,andV.Torre,Thedynamicsofaneuronalcultureofdissociatedcorticalneuronsofneonatalrats,"BiologicalCybernetics,vol.83,pp.1{20,2000. [91] E.M.Izhikevich,Whichmodeltouseforcorticalspikingneurons?,"IEEETransactionsonNeuralNetworks,vol.15,no.5,pp.1063{1070,September2004. [92] J.Tabak,J.Rinzel,andM.J.O'Donovan,Theroleofactivity-dependentnetworkdepressionintheexpressionandself-regulationofspontaneousactivityinthedevelopingspinalcord.,"2001. [93] J.Streit,Regularoscillationsofsynapticactivityinspinalnetworksinvitro,"JNeurophysiol,vol.70,pp.871{878,1993. [94] J.TabakandP.E.Latham,Analysisofspontaneousburstingactivityinrandomneuralnetworks.,"2003. [95] W.Maass,T.Natschlager,andH.Markram,Real-timecomputingwithoutstablestates:anewframeworkforneuralcomputationbasedonperturbations.,"NeuralComput,vol.14,no.0899-7667,pp.2531{60,2002. [96] P.Darbon,C.Pignier,E.Niggli,andJ.Streit,Involvementofcalciuminrhythmicactivityinducedbydisinhibitioninculturedspinalcordnetworks.,"2002. [97] T.PoggioandV.Torre,Avolterrarepresentationforsomeneuronmodels.,"BiolCybern,vol.27,no.0340-1200Print,pp.113{24,1977. [98] W.R.SoftkyandC.Koch,Thehighlyirregularringofcorticalcellsisinconsistentwithtemporalintegrationofrandomepsps,"JournalofNeuroscience,vol.13,no.1,pp.334{350,January1993. [99] A.L.HODGKINandA.F.HUXLEY,Aquantitativedescriptionofmembranecurrentanditsapplicationtoconductionandexcitationinnerve.,"JPhysiol,vol.117,no.0022-3751Print,pp.500{44,1952. [100] C.MorrisandH.Lecar,Voltageoscillationsinthebarnaclegiantmuscleber.,"BiophysJ,vol.35,no.0006-3495Print,pp.193{213,1981. [101] R.FitzHugh,Impulsesandphysiologicalstatesinmodelsofnervemembrane,"Biophys.J.,vol.1,no.445-446,1961. [102] H.Markram,J.Lubke,M.Frotscher,andB.Sakmann,RegulationofsynapticecacybycoincidenceofpostsynapticAPsandEPSPs,"Science,vol.275,pp.213{215,January1997. 131

PAGE 132

[103] Z.C.Chao,D.J.Bakkum,D.A.Wagenaar,andS.M.Potter,Eectsofrandomexternalbackgroundstimulationonnetworksynapticstabilityaftertetanization,"Neuroinformatics,vol.3,no.3,pp.263{280,2005. [104] E.Persi,D.Horn,V.Volman,R.Segev,andE.Ben-Jacob,Modelingofsynchronizedburstingevents:Theimportanceofinhomogeneity,"NeuralCom-putation,vol.16,pp.2577{2595,2004. [105] W.W.LyttonandT.J.Sejnowski,Simulationsofcorticalpyramidalneuronssynchronizedbyinhibitoryinterneurons,"JournalofNeurophysiology,vol.66,no.3,pp.1059{1079,September1991. [106] E.M.Izhikevich,J.A.Gally,andG.M.Edelman,Spike-timingdynamicsofneuronalgroups,"CerebralCortex,vol.14,pp.933{944,2004. [107] R.J.Butera,J.Rinzel,andJ.C.Smith,Modelsofrespiratoryrhythmgenerationinthepre-botzingercomplex.ii.populationsofcoupledpacemakerneurons,"JournalofNeurophysiology,vol.81,pp.398{415,1999. [108] C.A.delNegro,S.M.Johnson,R.J.Butera,andJ.C.Smith,Modelsofrespiratoryrhythmgenerationinthepre-botzingercomplex.iii.experimentaltestsofmodelpredictions,"JournalofNeurophysiology,vol.86,pp.59{74,2001. [109] M.Giugliano,M.Arsiero,P.Darbon,J.Streit,andH.Luscher,AdvancesinNetworkElectrophysiologyUsingMulti-ElectrodeArrays,chapterEmergingnetworkactivityindissociatedculturesofneocortex:novelelectrophysiologicalprotocolsandmathematicalmodelling,pp.243{273,KluwerAcademic/PlenumPublishers. [110] T.B.DeMarse,D.A.Wagenaar,A.W.Blau,andS.M.Potter,Theneurallycontrolledanimat:biologicalbrainsactingwithsimulatedbodies,"AutonomousRobots,vol.11,no.5,pp.305{310,2001. [111] J.Rolston,D.Wagenaar,andS.Potter,Preciselytimedspatiotemporalpatternsofneuralactivityindissociatedcorticalcultures.,"2007. [112] S.Song,K.D.Miller,andL.F.Abbott,Competitivehebbianlearningthroughspike-timing-dependentsynapticplasticity.,"NatNeurosci,vol.3,no.1097-6256,pp.919{26,2000. [113] Y.DanandM.-M.Poo,Spiketiming-dependentplasticity:fromsynapsetoperception.,"PhysiolRev,vol.86,no.0031-9333,pp.1033{48,2006. [114] R.J.O'Brien,S.Kamboj,M.D.Ehlers,K.R.Rosen,G.D.Fischbach,andR.L.Huganir,Activity-dependentmodulationofsynapticampareceptoraccumulation.,"Neuron,vol.21,no.0896-6273,pp.1067{78,1998. [115] H.CateauandT.Fukai,Astochasticmethodtopredicttheconsequenceofarbitraryformsofspike-timing-dependentplasticity.,"NeuralComput,vol.15,no.0899-7667,pp.597{620,2003. 132

PAGE 133

[116] T.Toyoizumi,J.-P.Pster,K.Aihara,andW.Gerstner,Generalizedbienenstock-cooper-munroruleforspikingneuronsthatmaximizesinformationtransmission.,"ProcNatlAcadSciUSA,vol.102,no.0027-8424,pp.5239{44,2005. [117] M.C.vanRossum,G.Q.Bi,andG.G.Turrigiano,Stablehebbianlearningfromspiketiming-dependentplasticity.,"JNeurosci,vol.20,no.1529-2401,pp.8812{21,2000. [118] A.Kepecs,M.C.W.vanRossum,S.Song,andJ.Tegner,Spike-timing-dependentplasticity:commonthemesanddivergentvistas.,"BiolCybern,vol.87,no.0340-1200,pp.446{58,2002. [119] W.Senn,Beyondspiketiming:theroleofnonlinearplasticityandunreliablesynapses.,"BiolCybern,vol.87,no.0340-1200,pp.344{55,2002. [120] A.Destexhe,M.Rudolph,J.M.Fellous,andT.J.Sejnowski,Fluctuatingsynapticconductancesrecreateinvivo-likeactivityinneocorticalneurons.,"JNeurosci,vol.107,no.0306-4522,pp.13{24,2001. [121] H.-X.Wang,R.C.Gerkin,D.W.Nauen,andG.-Q.Bi,Coactivationandtiming-dependentintegrationofsynapticpotentiationanddepression.,"NatNeurosci,vol.8,no.1097-6256,pp.187{93,2005. [122] K.D.Miller,Synapticeconomics:competitionandcooperationinsynapticplasticity.,"1996. [123] G.G.TurrigianoandS.B.Nelson,Homeostaticplasticityinthedevelopingnervoussystem.,"NatRevNeurosci,vol.5,no.1471-003XPrint,pp.97{107,2004. [124] Z.Liu,J.Golowasch,E.Marder,andL.F.Abbott,Amodelneuronwithactivity-dependentconductancesregulatedbymultiplecalciumsensors.,"JNeurosci,vol.18,no.0270-6474Print,pp.2309{20,1998. [125] Y.NamandB.C.Wheeler,Multichannelrecordingandstimulationofneuronalculturesgrownonmicrostampedpoly-D-lysine,"in26thAnnualInternationalConferenceoftheIEEEEMBS,2004,pp.4049{4052. [126] O.She,I.Golding,R.Segev,E.Ben-Jacob,andA.Ayali,Morphologicalcharacterizationofinvitroneuronalnetworks,"PhysicalReviewLettersE,vol.66,2002. [127] A.Destexhe,Z.F.Mainen,andT.J.Sejnowski,Anecientmethodforcomputingsynapticconductancesonakineticmodelofreceptorbinding,"NeuralComputation,vol.6,pp.14{18,1994. [128] H.Markram,Y.Wang,andM.Tsodyks,Dierentialsignalingviathesameaxonofneocorticalpyramidalneurons.,"1998. 133

PAGE 134

[129] H.KawaguchiandK.Fukunishi,Dendriteclassicationinrathippocampalneuronsaccordingtosignalpropagationproperties,"ExperimentsinBrainResearch,vol.122,pp.378{392,1998. [130] G.ShahafandS.Marom,Learninginnetworksofcorticalneurons.,"JNeurosci,vol.21,no.1529-2401,pp.8782{8,2001. [131] A.VanOoyen,J.VanPelt,andM.A.Corner,Implicationsofactivitydependentneuriteoutgrowthforneuronalmorphologyandnetworkdevelopment.,"JTheorBiol,vol.172,no.0022-5193Print,pp.63{82,1995. [132] J.L.NovakandB.C.Wheeler,Multisitehippocampalslicerecordingandstimulationusinga32elementmicroelectrodearray.,"JNeurosciMethods,vol.23,no.0165-0270,pp.149{59,1988. [133] M.E.Ruaro,P.Bonifazi,andV.Torre,Towardtheneurocomputer:Imageprocessingandpatternrecognitionwithneuronalcultures,"IEEETransactionsonBiomedicalEngineering,vol.52,no.3,pp.371{383,March2005. [134] M.Tatsuno,P.Lipa,andB.L.McNaughton,Methodologicalconsiderationsontheuseoftemplatematchingtostudylong-lastingmemorytracereplay.,"2006. [135] P.ReinagelandR.C.Reid,Preciseringeventsareconservedacrossneurons.,"JNeurosci,vol.22,no.1529-2401,pp.6837{41,2002. [136] D.A.Wagenaar,J.Pine,andS.M.Potter,Eectiveparametersforstimulationofdissociatedculturesusingmulti-electrodearrays.,"JNeurosciMethods,vol.138,no.0165-0270,pp.27{37,2004. [137] S.NirenbergandP.E.Latham,Decodingneuronalspiketrains:Howimportantarecorrelations?,"ProceedingsoftheNationalAcademyofSciences,vol.1000,no.12,pp.7348{7353,June2003. [138] M.C.W.vanRossum,Anovelspikedistance,"NeuralComputation,vol.13,no.4,pp.751{764,2001. [139] D.S.Reich,J.D.Victor,B.W.Knight,T.Ozaki,andE.Kaplan,Responsevariabilityandtimingprecisionofneuronalspiketrainsinvivo.,"1997. [140] Y.Jimbo,H.P.Robinson,andA.Kawana,Strengtheningofsynchronizedactivitybytetanicstimulationincorticalcultures:applicationofplanarelectrodearrays.,"IEEETransBiomedEng,vol.45,no.0018-9294Print,pp.1297{304,1998. [141] E.Maeda,Y.Kuroda,H.P.C.Robinson,andA.Kawana,Modicationofparallelactivityelicitedbypropogatingburstsindevelopingnetworksofratcorticalneurones.,"EuropeanJournalofNeuroscience,vol.10,pp.488{496,1998. 134

PAGE 135

[142] I.SuzukiandK.Yasuda,Detectionoftetanus-inducedeectsinlinearlylined-upmicropatternedneuronalnetworks:applicationofamulti-electrodearraychipcombinedwithagarosemicrostructures.,"2007. [143] T.TatenoandY.Jimbo,Activity-dependentenhancementinthereliabilityofcorrelatedspiketimingsinculturedcorticalneurons.,"BiolCybern,vol.80,no.0340-1200Print,pp.45{55,1999. [144] D.A.Wagenaar,J.Pine,andS.M.Potter,Searchingforplasticityindissociatedcorticalculturesonmulti-electrodearrays.,"2006. [145] E.M.Izhikevich,Solvingthedistalrewardproblemthroughlinkageofstdpanddopaminesignaling.,"2007. 135

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BIOGRAPHICALSKETCHKarlPaulDockendorf,thesonofPaulandElaineDockendorf,wasborninGainesville,Florida.HegrewupinOcala,FloridaandgraduatedfromForestHighSchoolin2000.HereceivedhisBachelorofScienceincomputerengineeringfromtheUniversityofFloridainDecember2003andhisMasterofEngineeringinelectricalandcomputerengineeringfromtheUniversityofFloridainMay2004.Hisresearchinvolvedrobotics.Afterreceivinghismastersdegree,Karlbeganworkonhisdoctoralresearch,whichinvolvedneuralcomputationalmodeling.HisPh.D.inbiomedicalengineering,withaspecializationinneuralengineering,wasconferredbytheUniversityofFloridain2008. 136