psychophysiological modeling current state and future ... · 1 psychophysiological modeling -...

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Psychophysiologicalmodeling-Currentstateandfuturedirections

DominikR.Bach1.2,3,GiuseppeCastegnetti1,2,ChristophW.Korn1,2,4,SamuelGerster1,2,Filip

Melinscak1,2,TobiasMoser1,2

1ClinicalPsychiatryResearch,DepartmentofPsychiatry,Psychotherapy,andPsychosomatics,PsychiatricHospital,UniversityofZurich,Zurich,Switzerland

2NeuroscienceCenterZurich,UniversityofZurich,Zurich,Switzerland3WellcomeTrustCentreforNeuroimagingandMaxPlanck/UCLCentrefor

ComputationalPsychiatryandAgeingResearch,UniversityCollegeLondon,UnitedKingdom

4InstituteforSystemsNeuroscience,UniversityMedicalCenterHamburg-Eppendorf,Hamburg,Germany

Correspondence

DominikR.Bach,DepartmentofPsychiatry,Psychotherapy,andPsychosomatics,PsychiatricHospital,UniversityofZurich,Lenggstrasse31,CH-8032Zurich;

Switzerland.Email:[email protected]

Abstract

Psychologistsoftenuseperipheralphysiologicalmeasurestoinferapsychologicalvariable.Itisdesirabletomakethisinverseinferenceinthemostpreciseway,ideally

standardizedacrossresearchlaboratories.Inrecentyears,psychophysiological

modelinghasemergedasamethodthatrestsonstatisticaltechniquestoinvert

mathematicallyformulatedforwardmodels(psychophysiologicalmodels,PsPMs).

ThesePsPMsarebasedonpsychophysiologicalknowledgeandoptimizedwithrespect

totheprecisionoftheinference.Buildingonestablishedexperimentalmanipulations,

knowntocreatedifferentvaluesofapsychologicalvariable,theycanbebenchmarkedin

termsoftheirsensitivity(e.g.,effectsize)torecoverthesevalueswehavetermedthis

predictivevalidity.Inthisreview,weintroducetheproblemofinverseinferenceand

psychophysiologicalmodellingasasolution.Wepresentbackgroundandapplicationfor

allperipheralmeasuresforwhichPsPMshavebeendeveloped:skinconductance,heart

period,respiratorymeasures,pupilsize,andstartleeyeblink.ManyofthesePsPMsare

taskinvariant,implementedinopen-sourcesoftware,andcanbeusedofftheshelffora

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widerangeofexperiments.Psychophysiologicalmodelingthusappearsasapotentially

powerfulmethodtoinferpsychologicalvariables.

Keywords

analysis/statisticalmethods,autonomicnervoussystem,computationalmodeling,

electrodermalactivity,heartrate,pupillometry

1Introduction

Peripheralphysiologicalmeasurementsareoftenusedtoinferpsychologicalvariables.

Forexample,totestapsychologicalinterventionthatreducesfearmemory,aresearcher

maybeinterestedinquantifyingthestrengthoffearmemoryfromskinconductance

responses(SCR).Thispsychologicalperspectiveistheoppositeofabasic

psychophysiologicalperspective,inwhichresearchersaimtodescribehowpsychologicalvariablesimpactontheperipheralmeasure.Toenableinferenceona

psychologicalvariable,thepsychophysiologicalmappingfromthisvariabletothe

measuredsignal(the"forwardmodel"instatisticalterminology)needstobeknown

withsomecertainty,anditneedstobeexploitedinthebestpossibleway(themodel

needstobe"inverted"),toarriveatthemostpreciseestimateofthepsychological

variable.Thisisthepsychophysiologicalinverseproblem(Figure1a).

Psychophysiologicalmodelingisastatisticalframeworktosolvethisproblemina

principledmanner(Bach&Friston,2013).Itcanprovideexperiment-invariant,off-the-

shelfapplicationsthatimproveoncurrentmethodsforinverseinferenceandthereby

suggestmeaningfulmethodologicalstandardstoenhancereproducibility.

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Indeed,psychophysiologicalmodelingapproacheshavebeenappliedtoanalyzeawide

varietyofexperiments:toinferattentionalvariablesfrompupilresponses(e.g.,deGee

etal.,2017;deGee,Knapen,&Donner,2014),toinferfearlearningfromSCR(e.g.,Bach,

Weiskopf,&Dolan,2011;Bulganin,Bach,&Wittmann,2014;Tzovara,Korn,&Bach,

2018)andstartleeyeblink(Bach,Tzovara,&Vunder,2017),andtoquantifyautonomic

arousalduringperception(e.g.,Bach,Seifritz,&Dolan,2015;Hayesetal.,2013;Koban,

Kusko,&Wager,2018;Koban&Wager,2016;Sulzeretal.,2013),decision-making(e.g.,

Alvarez,etal.,2015;Bach,2015a;deBerkeretal.,2016;Nicolle,Fleming,Bach,Driver,&

Dolan,2011;Talmi,Dayan,Kiebel,Frith,&Dolan,2009),andrest(Fanetal.,2012).

Thisreviewisstructuredinthefollowingway.First,wediscusshowtocompare

methodsforinverseinferenceonpsychologicalvariablesandintroducetheconceptof

predictivevalidity.Wethenpresentpsychophysiologicalmodelingasanovelapproach,

includingaspecificimplementationcreatedbytheauthorstogetherwithrelated

methods.Inthemajorpartofthereview,wegiveatutorial-styleoverviewofthevarious

forwardmodelsandinversionmethodsdevelopedoverthepastdecade,fordifferent

physiologicalmeasures.Thefieldismovingrapidly.Whileninemethodologicalarticles

Figure1.A:Thepsychophysiologicalinverseproblem.Top:psychophysiologicalperspective(forwardinference,e.g.,DoesaversivememoryinfluenceSCR?).Bottom:psychologicalperspective(inverseinference,e.g.,Doesmyprocedureestablishaversivememory,asindexedbySCR?)B:Benchmarkinganinverseinferencemethodbyassessingpredictivevalidity:Whatisthesensitivityforinferringtheeffectofaknownexperimentalmanipulation.

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onthetopicwerepublishedbetween1993-2013,11suchpaperscameoutinthe5

yearssincethelastreviewonthetopic(Bach&Friston,2013).Thislastreview

containedahistoricalperspectiveonthedevelopmentofmodelsforSCRinthe1990s

and2000s(Alexanderetal.,2005;Bach,Flandin,Friston,&Dolan,2009;Barry,

Feldmann,Gordon,Cocker,&Rennie,1993;Limetal.,1997)andontheemergent

critiqueofoperationalism(Green,1992);here,weapproachtheproblemina

systematic,nonhistoricalmanner.

2Predictivevalidity

Allanalysismethodsforpsychophysiologicalsignalsarebasedonsomeknowledge

abouttheforwardmappingfrompsychologytophysiology.Aplethoraof

psychophysiologicalliteraturehasaddressedsuchforwardmappings.However,even

withaperfectforwardmodeltherearedifferentwaysofmakinginverseinference.For

example,onecandefinedifferentpossibletimewindowstodetectanSCRpeakafteran

experimentalevent.Extendingthepeakwindowmayincreasethesensitivityofthe

methodtodetectatrueevent-relatedresponse,butdecreaseitsspecificitybecause

experiment-unspecificpeaksmaybemistakenforevent-relatedones.Crucially,the

optimalbalanceisdifficulttointuitasis,forexample,evidentfromthecoexistenceof

differentpeakdetectionwindowsinanalysisrecommendations(Boucseinetal.,2012),

andsometimesevenwithinthesamelaboratories.Hence,itwouldbedesirableto

quantitativelyevaluateaninverseinferencemethod.

Toassessthequalityofinverseinference,onewouldideallycomparetheinferredwith

theactualvalueofthepsychologicalvariable(i.e.,with"groundtruth").Ofcourse,

groundtruthisneverknownforpsychologicalvariables.1Tosolvethisconundrum,we

havepragmaticallyproposedtouseanexperimentalmanipulationthatcanbeassumed

toinfluencethepsychologicalvariableinacertainwayandisknowntoimpactonthe

peripheralmeasure.Onecanthenevaluatemethodsbytheirsensitivitytodetectthe

impactofthisexperimentalmanipulation(Figure1b).Wehaveintroducedtheterm

predictivevalidityforthismeasure(Bach,Daunizeau,Friston,&Dolan,2010),sinceit

1Thisistrueformanyareasofscienceandtechnology.

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evaluateshowwellthepsychologicalvariablecanbepredicted.2Predictivevalidity

analysishasoftenbeenperformedonacategoricalexperimentalmanipulation(e.g.,

anticipatingthreatorsafetyinfearconditioning).Althoughitmaythusappearonthe

surfacethatpredictivevalidityboilsdowntoclassificationperformance,oneusually

aspirestoinferpsychologicalvariablesonacontinuousscale,sothatthemethod

extendstosituationsinwhichthepsychologicalvariablevariesparametricallyacross

morethantwolevels.Crucially,sincemostpsychophysiologicalmeasuresarerelatively

unspecific,validationexperimentsrequirethattheexperimentalconditionsdifferon

onlyonedimension,thepsychologicalvariableofinterest.Thisistrueforanyinverse

inferencemethod.Onceamethodwithhighpredictivevalidityisidentified,onecan

applythismethodtoother(methodologicallysimilar)experimentstoinferthesame

psychologicalvariable.

Thus,inavalidationexperiment,agoodinferencemethodprovidesanestimatorofthe

(known)psychologicalvariablethathassmallervariancethananyothermethod.Fora

categoricalvalidationexperimentwithtwolevels,thissimplymeans-becausethescale

ofthepsychologicalvariableisarbitrary-thatthestandardizeddifferenceinthe

estimatedpsychologicalvariablebetweenthesetwolevelsshouldbelarge.Thiscanbe

evaluatedbyregardingtheeffectsize,orteststatistic,ortheresidualsumsofsquaresin

apredictivemodel,orthemodelevidenceofthatpredictivemodel.Allofthese

quantitiesaremonotonicallyrelated.Usingmodelevidenceadditionallyallowsusto

makestatementswhethertwomethodsaredecisivelydifferent(Bach&Friston,2013;

seeAppendixEquation1).Atthesametime,thedifferenceintheestimated

psychologicalvariablebetweentworandompartitionsofthesameexperimental

conditionshouldbezeroonaverage.

Predictivevaliditycanbeharnessedtovalidateanyinverseinferencemethod,includingoperationalanalysis.Forthepsychophysiologicalmodelingapproach,someadditional

considerationsarewarranted.Here,psychologicalvariablesareestimatedbyoptimizing

thegoodness-of-fitoftheforwardmodel.Yet,forcomparisonofdifferentmethods,the

goodness-of-fitoftheforwardmodelisnotasuitablecriterion.Thegoaloftheforward

2Becausethepsychologicalvariableisknownapriori,onecouldalsocallit“retrodictivevalidity”.

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modelistopredictthesignal,andthegoalofinferenceistofindthemostprecise

estimateofthepsychologicalvariable.Thesetwogoalscanalignwith,beorthogonalto,

orevenopposeeachother.Intuitively,onecouldassumethat,iftheforwardmodelis

knownwithcertaintyandformulatedinmathematicalterms,oneshouldeasilybeable

toinvertthemapping.However,thereareseveralstatisticalreasonswhythisintuition

isincorrectinthegeneralcase(althoughitmaybecorrectunderspecific

circumstances).First,theforwardmodelmayuseparametersthatoneisnotinterested

ininferring.Forexample,thebestknownforwardmodelforSCRassumesthatthe

strengthoramplitudeofpsychologicalinputintothesystemisdifferentoneachtrial

(Gerster,Namer,Elam,&Bach,2017).However,manyresearchersarenotinterestedin

psychologicalvariablesonatrial-by-trialbasisbutonlyintheaveragepsychological

variablewithinanexperimentalcondition.Thestandardgenerallinearmodel(GLM)

inversionapproachforSCR(Bachetal.2009;Bach,Friston,&Dolan,2013)willnormallyyieldthesameconditionwiseestimates,regardlessofwhetherestimationwas

doneonatrial-by-trialbasisfollowedbyaveraging,oronacondition-by-conditionbasis.

Inthiscase,thesimplermodelyieldsthesameinferenceonthepsychologicalstate,

althoughempiricallyitcannotpredictSCRdatasowell,becauseitwouldassumethe

same(average)SCRamplitudeforeachtrial(Bachetal.,2013).Hence,precisionofthe

forwardmodelandoftheinferenceareunrelated.Anexamplewheretheyareopposed

isgivenbyindividualresponsefunctionsforSCR.Allevidencesuggeststhatthemapping

fromsudomotornerveactivitytoskinconductancedependsonsubject-specific

anatomicalproperties,andisvariablebetweenpersons(Bach,Flandin,Friston,&Dolan,

2010;Gersteretal.,,2017).Hence,aforwardmodeltakingthisheterogeneityinto

accountwillhaveabettergoodness-of-fitthanamodelassumingacanonicalresponse

functionacrosssubjects,aswehavealsoshownempirically(Bachetal.,,2013).Atthe

sametime,itcanbedifficulttoestimatetheshapeofanindividual'strueresponse

functionfromalimitednumberoftrialswithshortintertrialintervals,andensuing"overfitting"canmakeinferenceonthepsychologicalvariableworse,reducing

predictivevalidity(Bach,Friston,&Dolan,2013).

Tosummarize,predictivevalidityallowsastatementonthequalityofinverseinference,

regardlessofthemethodunderstudy.Itcanbeusedtobenchmarkpsychophysiological

models,operationalmethods,orevenmachine-learningmethodsthattrytofind

statisticalregularitieswithoutanyknowledgeofthepsychologicalorbiophysical

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relationships(Grecoetal.,2017;Greco,Lanata,Valenza,DiFrancesco,&Scilingo,2016;

Greco,Valenza,&Scilingo,2016).Asastatisticalframework,ithasapotentialto

improveinverseinference,tostandardizemethodsacrosslaboratories(byselectingthe

bestone),andtoprovideanobjectivemeansforqualitycontrolwithinandbetween

laboratories.Wewillreturntotheselatterpointsinthediscussion.

3PsychophysiologicalModeling

Thegoalofinverseinferenceistofindthebestpossibleestimatorofapsychologicalvariable,fromameasureddatatimeseries.Thisincludesso-calledoperationalmethods,

which"operationalize"(i.e.,equateanoisyversionof)thepsychologicalvariablewitha

singlephysiologicaldatafeature,forexample,apeak-to-troughmeasure.Because

operationalmethodsuseoneoraverysmallnumberofdatafeatures,ratherthanthe

entiretimeseries,theymaysufferfrominformationloss.Psychophysiologicalmodeling

isawayofusinganentiredatatimeseriesforinference(Figure2).Inanutshell,a

psychophysiologicalmodel(PsPM)isaformal,quantitativemodelthatmapsa

psychologicalvariableontoanobserveddatatimeseries.PsPMsarespecifiedin

mathematicalform.TheearliestPsPMsweredevelopedforSCRandexplicitlyconstitutedasequenceoftwomodels(Figure3a):aneuralmodelthatspecifiesthe

mappingofthepsychologicalvariableontosudomotornerveactivity(SNA),anda

peripheral(effectororgan)modelthatspecifieshowSNAmapsontomeasuredSCR

(Alexanderetal.,2005;Bachetal.,2009;Limetal.,1997).ForSCR,thissplitisuseful

Figure2.Operationalanalysis(top)assumesthatselecteddatafeaturesare"equivalent"toapsychologicalvariable,wheretheselectionofdatafeaturesisoftenbasedoninformalmodels.Psychophysiologicalmodelling(bottom)estimatesthemostlikelypsychologicalvariable,giventheentiredatatimeseriesandastandard(experiment-invariant)responsemodel.

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becausetheperipheralmodelcanbeevaluatedonitsownbyintraneuralstimulation

andrecordingsfromwellaccessibleperipheralnerves(Gersteretal.,2017).Forsome

othermeasures,theperipheralmodelcanbeapproximatedbyspecificstimuli,for

example,onecanuseluminancechangestoelucidatepupilmechanics.However,for

mostPsPMsthathavebeencreatedtodate,neuralandperipheralprocessesaremore

difficulttoseparateexperimentallyastheefferentnervesarelessaccessible(atleastin

humans),andincurrentmodelstheyareeithercollapsed,orthedistinctionisonlyused

formathematicalconvenience.

3.1Hybridapproaches

TheempiricaldistinctionbetweenneuralandperipheralmodelsforSCRhasearlyon

motivatedahybridapproach(Alexanderetal.,2005),engendered,forexample,inthe

Figure3.A:Basicformalismofmostpsychophysiologicalmodels.B:Relatedhybridapproaches(e.g.Ledalab,cvxEDA)useastandardresponsemodeltoinfera(noisy)timeseriesofneuralinputs,andselectdatafeaturesofthattimeseriesas"equivalent"tothepsychologicalvariable.C:Lineartimeinvariant(LTI)systemslieatthecoreofallexistingpsychophysiologicalmodellingandhybridapproaches.Aneuralinputisconvolvedwithacanonical(experiment-invariant)responsefunction,toyieldapredictionforthemeasuredsignal.

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softwaresLedalab(Benedek&Kaernbach,2010a,2010b)orcvxEDA(Greco,Valenza,

Lanata,Scilingo,&Citi,2015).Inthisapproach,adeterministicperipheralmodelis

invertedtocomputeanoisySNAtimeseriesfromthetimeseriesofmeasuredSCRdata.

Tomakeinferenceonpsychologicalvariables,somedatafeatures(peak-to-trough

measures)oftheSNAtimeseriesareextracted,inlinewithmoretraditionaloperational

analysis(Figure3b).Thissecondmappingisheuristicallymotivated,notquantitatively

specifiedorevaluated.TwodifferentstudygroupshavecomparedLedalabwithpeak-

to-troughmethodsontheonehandandafullPsPM-basedapproachontheother,in

paradigmswithrelativelyshortintertrialintervals.Onaverage,thehybridLedalab

approachwasfoundtoyieldsimilarpredictivevalidityasdirectlyusingpeak-to-trough

measuresoftheSCRdata,anditspredictivevaliditywassurpassedbyinversionoffull

PsPMs(Bach,2014;Green,Kragel,Fecteau,&LaBar,2014).Systematicevaluationof

cvxEDAhasnotyetbeenconducted.Notably,theseapproachesdifferfromthePsPMapproachalsointheirperipheralforwardmodelsandstatisticalmethodsformodel

inversion.Theycouldpossiblybeextendedtodirectlyestimatepsychologicalvariables,

butretainingtheirspecificforwardmodelsandinversionmethods.

3.2Lineartimeinvariantsystems

AllPsPMsandhybridmodelsthathavebeenproposeduptotodaycontainattheirheart

alineartimeinvariant(LTI)system(Figure3c).ALTIsystemisasystemtheoutputof

whichdoesnotexplicitlydependontime(timeinvariance),andtheoutputtothesumof

twoinputsisjustthesumoftheoutputsoftheindividualinputs(linearity).Thefirst

principleimpliesthatdifferentresponseshapesareexplainedbydifferentinputs.

Accordingtothelinearityprinciple,themagnitudeofaresponsedoesnotdependonthe

baseline.LTIsystemsareunambiguouslydescribedbythemathematicaloperationof

convolution(overlapintegral)ofaninputtimeserieswitharesponsefunction(RF),

whichcorrespondsinsignalprocessingtermstoalinearfilter(seeAppendixEquation2).LTIsystemsconstituteamathematicalsimplificationofrealbiophysicalsystems,

whichcontainmanyparametersthatcannotbeusefullyconstrainedfrommeasured

data.WewillreportforeachmeasurehowcanitbedescribedbyaLTIsystem.

3.3Modelinversion

ManyPsPMsassumethatexperimentaleventsrapidlyengageapsychologicalprocess,

whichthenfeedsintothephysiologicalsystemwithconstantlatencyandshape.Under

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theseassumptions,theamplitudeofthepsychologicalinputcanbeestimatedina

generallinear(convolution)model(Bachetal.,2009),similartostandardapproaches

foranalysisoffMRIs(Friston,Jezzard,&Turner,1994).Inanutshell,theRFisconvolved

withatimeseriesofimpulses(deltafunctions)centeredonexperimentaleventsfor

eachcondition,andtheensuingtimeseriesformcolumnsinthedesignmatrixofa

multipleregressionmodel.Theestimatedcoefficientofanindividualeventcolumn

constitutestheamplitudeestimateforthatcondition(seeAppendixEquation3-5).

Looselyspeaking,theRFisregressedontotheobservedresponse,andtheregression

coefficientistheestimateoftheinputamplitude.Iflatencyand/orshapeofthe

psychologicalinputcannotbeassumedtobeconstant,thentheyneedtobeestimatedas

well,andtheinversionmodelbecomesnonlinear,forexample,inSCRmodelsforfear

conditioning(Bach,Daunizeauetal.,2010)orstartleeyeblinkresponse(SEBR)models

(Khemka,Tzovara,Gerster,Quednow,&Bach,2017).

4Psychophysiologicalmodelsfordifferentmeasurements

Table1givesanoverviewofthedifferentpsychophysiologicalmodelsproposeduntil

today.

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Table1:Psychophysiologicalmodelsdevelopeduntiltoday.PSR:pupilsizeresponses.SCR:skinconductanceresponses.HPR:Heartperiodresponses.RPR:respirationperiodresponses. 1RAR:respirationamplituderesponses.RFRR:respiratoryflowrateresponses.SEBR:startleeyeblinkresponses. 2Measure

ment

Psychological

variable

Neuralmodel Peripheralmodel Model

inversion

Software

implementation

Publishedin

SCR Genericphasicarousal Instantaneousimpulse LTIsystemwithparameters

fromempiricaldata

GLM PsPM Bach,2014;Bach,Flandin,Friston,&

Dolan,2009;Bach,Flandin,Friston,&

Dolan,2010;Bach,Friston,&Dolan,2013

Genericphasicarousal

(validatedforfear

conditioning)

ConstrainedGaussian

impulse

LTIsystemwithparameters

fromempiricaldata

Variational

Bayes

PsPM Bach,Daunizeau,Friston,&Dolan,2010;

Staib,Castegnetti,&Bach,2015

Generictonicarousal

(validatedforanxiety

andcognitiveload)

Gaussianimpulses

withconstantshape

andunconstrained

onset


fromempiricaldata

Variational

Bayes

PsPM Bach,Daunizeau,Kuelzow,Friston,&

Dolan,2011;Bach,Friston,&Dolan,2010

Generic Notspecified LTIsystemwithparameters

fromtheoreticalconsiderations

Deterministic

inversefilter

Ledalab Benedek&Kaernbach,2010a;Benedek&

Kaernbach,2010b

Generic Discreteimpulseswith

unconstrainedonset


fromtheoreticalconsiderations

Convex

optimisation

cvxEDA Greco,Valenza,Lanata,Scilingo,&Citi,

2015

PSR Luminanceadaptation Instantaneousimpulse Combinationof2LTIswith

parametersfromempiricaldata

GLM PsPM Korn&Bach,2016

Attention Instantaneousimpulse LTIwithparametersfrom

empiricaldata

OLSestimation

infrequency

domain

Pupil Hoeks&Levelt,1993

Fearconditioning Instantaneousimpulse LTIwithparametersfrom

empiricaldata

GLM PsPM Korn,Staib,Tzovara,Castegnetti,&Bach,

2017

HPR Notyetspecified Instantaneousimpulse LTIwithparametersfrom

empiricaldata

GLM PsPM Paulus,Castegnetti,&Bach,2016

Fearconditioning Instantaneousimpulse LTIwithparametersfrom GLM PsPM Castegnetti,etal.,2016

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empiricaldata

RPR Notyetspecified Instantaneousimpulse LTIwithparametersfrom

empiricaldata

GLM PsPM Bach,Gerster,Tzovara,&Castegnetti,2016

RFRR Notyetspecified Instantaneousimpulse LTIwithparametersfrom

empiricaldata


RAR Notyetspecified Instantaneousimpulse LTIwithparametersfrom

empiricaldata


Fearconditioning Instantaneousimpulse LTIwithparametersfrom

empiricaldata

GLM PsPM Castegnetti,Tzovara,Staib,Gerster,&

Bach,2017

SEBR Genericstartlereflex Instantaneousimpulse

withvariablelatency

LTIwithparametersfrom

empiricaldata

Template

matching/GLM

PsPM Khemka,Tzovara,Gerster,Quednow,&

Bach,2017

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4.1Skinconductance 3

4.1.1Forwardmodel 4

Skinconductanceisoftenusedtoinferphasicortonicsympatheticarousalgeneratedby 5

awiderangeofpsychologicalstimuliandtasks(Boucsein,2012).Openingofsweat 6

glands,elicitedviathesympatheticnervoussystemwithnegligibleparasympathetic 7

transmission,causesphasicincreasesofskinconductancethataretermedSCR(see 8

Boucsein,2012,forthephysiologyofSCR).SlowCfiberscarryingimpulsestothesweat 9

glandsaretermedsudomotor(SN),andtheiractivitycanbemeasuredbyintraneural 10

recordings.Fromtheirendterminal,theneurotransmitteracetylcholinediffuses 11

throughtheskintoreachsweatglands,aprocessonthetimescaleofuptoasecond.In 12

thehistoryofpsychophysiologicalmodeling,itwasrecognizedearlyonthat 13

nonoverlappingSCRcanbewelldescribedbyasimpleresponsefunction,and 14

overlappingSCRcanbeseenasbeinggeneratedbyaLTIsystem(Alexanderetal.,2005; 15

Bachetal,2009).AllpublishedSCRmodelshavethereforeassumedthatthemapping 16

fromSNAtoSCR(butnotnecessarilyfrompsychologicalvariabletoSNA)iswell 17

describedbyaLTIsystem. 18

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Twotypesofresponsefunctionshavebeenproposed:onebasedonabiophysicalmodel 20

ofthesweatgland,withparameterssetfromtheoreticalconsiderations(Alexanderet 21

al.,2005;Benedek&Kaernbach,2010a,2010b;Grecoetal.,2015),andapurely 22

phenomenologicalfunctionwithparametersfittedtoadatabaseof1,278SCRsfrom64 23

individualsinsixdifferentexperimentalconditions(Bach,Daunizeauetal.,2010;Bach 24

etal.,2009;Bach,Flandinetal.,,2010).Whiletheformerapproachappearstheoretically 25

morerigorous,manyofthebiophysicalparameterswerenotknownfromphysiological 26

researchandhadtobeguessed.Theensuingforwardmodelhasnotbeensystematically 27

evaluated,anditisunclearhowwellthisresponsefunctionfitsactualSCR.Incontrast, 28

thelattermodelisdefinedbyitsfittoempiricaldata.Thisphenomenologicalresponse 29

functionismathematicallydescribedbyaGaussian-smoothedexponential(Bach, 30

Flandinetal.,2010)orathird-order(linear,constant-coefficient)ordinarydifferential 31

equation;seeAppendix-Equation6,7). 32

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TherearegoodempiricalargumentstomotivatetheuseofLTIsystemstomodelthe 34

SNA/SCRrelationship,providedthatSCRdataarehigh-passfiltered.Threekindsoftests 35

havebeenexploitedtoevaluatetheforwardmodel.Indirecttestsmadetheauxiliary 36

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assumptionthatSNburstsfollowexternalstimulationwithconstantshapeandlatency 37

(thisassumptionisnotpartoftheLTIsystem).Thesetestsshowed,thatforshortevents 38

(<1sduration)thatareseparatedbyatleast30s,morethan60%ofthevariancein 39

(high-passfiltered)SCRcanbeexplainedunderaLTImodel(Bach,Flandinetal., 40

2010),supportingtheplausibilityofthetimeinvarianceapproximation.Intheabsence 41

ofstimulation,baselinevarianceexceededtheresidualvarianceunderstimulation, 42

implyingthattheresidualvarianceisduetonoiseratherthanLTIviolations(Bach, 43

Flandinetal.,2010).SCRtopairsofstimuliseparatedbydifferentintervals(2-9s)do 44

notdependontheinterval,inlinewiththelinearityprinciple(Bach,Flandinetal., 45

2010).Amoredirecttestofthetimeinvarianceprincipleisfurnishedbyintraneural 46

recordings,whichshowthat60%-75%ofSCRvarianceisexplainedbyaLTImodelthat 47

takesSNactivityasinput,althoughthisisstillsufferingfrominterferingnon-SN(e.g., 48

vasomotornerve)activity(Gersteretal.,2017).Athirdapproachreliesonintraneural 49

stimulationwhileblockinginterferingnervetrafficbyregionalanesthesia.Here,SNis 50

stimulatedatdifferentrepetitionfrequencies,thussimultaneouslyaddressingthe 51

linearityandtimeinvarianceprinciple.Inthiscase,93%-99%ofSCRvarianceis 52

explainedunderaLTImodelwhenstimulationfrequencyisbelow0.6Hz.Abovethis 53

stimulationfrequency,theLTImodelcannotbeusefullyappliedduetostrong 54

nonlinearities(Gersteretal.,2017);however,thislimitationshouldbelargelyirrelevant 55

formostpsychologicalexperimentswithslowerstimulationrates.Tosummarize,it 56

appearsthatundersuitableconditions,aLTImodelisnotjustanapproximationbut 57

ratheranaccuratedescriptionofbiophysicalrealityintheSNA/SCRsystem.Notably, 58

tonicskinconductancecomponents,whicharefilteredoutinallmodelingapproaches, 59

donotappeartobemodeledbyafiniteLTIsystem. 60

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TheLTImodeldoesnotmaketheassumptionthatSCRshapeisconstantbetween 62

individuals.Onthecontrary,allevidencesuggeststhatthisisnotthecase.Nevertheless, 63

inferencebasedonacanonicalresponsefunctionalreadyprovidesbetterinferencethan 64

operationalmethods.Wehaveshownthatthisinferencecanbefurtherimprovedby 65

allowingsomevariabilitybetweenindividuals,butonlyifthepossibleindividual 66

responsefunctionsareverystronglyconstrainedtoavoidoverfitting(Bachetal.,2013; 67

Staib,Castegnetti,&Bach,2015). 68

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ForthemappingfrompsychologicalvariabletoSNA,threedifferentforwardmodels 70

havebeendevelopedandevaluated.First,shortstimulielicitrapidSNAwithconstant 71

Q6latency(Bachetal.,2009).Itappearsthatthemappingfrompsychologicalvariable 72

toSCRislargelyinvarianttothetypeofexperimentstimulus(aversivewhitenoise 73

bursts,aversiveelectricstimulation,aversivepictures,auditoryoddballs,andavisual 74

detectiontask;Bach,Flandinetal.,,2010),whichmotivatestheuseofthismodelfor 75

phasicarousalindependentoftheelicitingstimulusorexperiment.Forlongerstimulior 76

anticipationofstimuli,amodelwithvariableSNAlatencyandshapecanbeused,and 77

thesetwoparametersareestimatedfromtheexperimentaldata(Bach,Daunizeauetal., 78

2010).Thismodelwasmotivatedspecificallytoanalyzefearconditionexperimentsin 79

whichparticipantsareexposedtoconditionedstimuli(CS),oneofwhich(CS+)predicts 80

anaversiveevent(US).Typically,thereisatimedelaybetweenCS+andUS,andso 81

participantswillanticipatetheUSduringCS+and(toadiminishingextent)duringCS- 82

presentationandexpressSCRatsome(unknownandpossiblyvariable)timepoint 83

duringthisinterval.Notably(anddifferentfrommodelsdiscussedlater),responsesto 84

CS+andCS-arethoughttobegovernedbythesamepsychologicalprocess,buttobe 85

quantitativelydissimilar.Hence,inthisapplicationofthemodel,aconditioned 86

sudomotornerveresponsetoeachCSisestimated,andthedifferenceintheiramplitude 87

betweenCS+andCS-constitutestheinferenceonfearmemory.Finally,toaccountfor 88

spontaneousSCRfluctuations,amodelisproposedinwhichconstant-shapeSNbursts 89

occurwithvariableonsetandamplitude,whichareestimatedfromthedata(Bach, 90

Daunizeauetal.,,2011). 91

92

4.1.2Inferenceonpsychologicalvariables 93

Theconstant-latencyforwardmodelisinvertedinaGLMapproach(Bachetal.,,2009) 94

andhasbeenevaluatedonindependentdatasets(Bach,2014;Bachetal.,2013)in 95

comparisontodifferentpeak-scoringmeasures(Boucseinetal.,2012)andtomeasures 96

fromthehybridLedalabapproach(Benedek&Kaernbach,2010a,,2010b).Predictive 97

validitywasassessedforthecomparisonofnegativearousingversusneutralpicture 98

presentation,positivearousingversusneutralpictures,picturepresentationversusno 99

stimulus,andfearfulversusangryfacepresentation.Predictivevaliditywasdecisively 100

higherfortheGLM-basedapproachonthemajorityofcomparisons,anditwasnever 101

decisivelysurpassedbyanothermethodintheremainingcomparisons(Bach,2014).In 102

anevaluationstudyfromanindependentlaboratory,aGLMapproachhadhigher 103

16

predictivevaliditythanpeak-scoringorLedalabfordistinguishingCS+andCS-in 104

aversivelearning(Greenetal.,,2014).Fordistinguishingfivedifferentphasesofafear 105

generalizationexperiment,peakscoringappearedtohavehigherpredictivevalidity 106

(Greenetal.,2014).However,notethatthepredictivevalidityevaluationassumesthat 107

distinguishabledifferentpsychologicalstatesarecreatedbytheexperiment,whichis 108

lesswellestablishedforthelattermanipulation.Thisstudydidnotallowforassessing 109

whetheranymethodwasdecisivelybetterorworsethananother.3 110

111

Theflexible-latencyforwardmodelisinvertedinavariationalBayesapproach(Bach, 112

Daunizeauetal.,2010)andwasevaluatedonindependentfearconditioningdatasets 113

(Staibetal,2015)incomparisontodifferentpeak-scoringmeasures(Boucseinetal., 114

2012)andtomeasuresfromthehybridLedalabapproach(Benedek&Kaernbach, 115

2010a,2010b).PredictivevaliditywasassessedforthecomparisonofCS+versusCS-, 116

andwasfoundtobedecisivelyhigherforthemodel-basedapproachthanforpeak- 117

scoringorLedalabmeasures(Staibetal.,2015). 118

119

Finally,theflexible-onsetmodelisinvertedwiththesamevariationalBayesapproach 120

(Bach,Daunizeauetal.,2011)andcanbeusedtoinfertonicarousal,whichisoften 121

operationalizedasthenumberofspontaneousskinconductancefluctuations(Boucsein 122

etal.,2012).Thismethodwasevaluatedwithrespecttodistinguishingpublicspeaking 123

anxietyfromrestornonpublicspeakinganxiety,andmentalloadfromrest.Predictive 124

validityofthemodel-basedapproachandofanautomatedpeak-countmeasurewas 125

comparable(Bach&Staib,2015).Furthermore,undertheperipheralLTImodel,the 126

areaunderthecurveofatimeseriesequalsthenumberofspontaneousfluctuations 127

timestheiramplitude.Whilethisrelationhasbeenempiricallyvalidated,thesamestudy 128

alsoshowedthatthenumberofspontaneousfluctuationsaloneallowsbetterinference 129

ontonicarousalthantheareaunderthecurve(Bach,Friston,&Dolan,2010). 130

131

4.1.3Futuredirections 132

3Bayesfactorsarereportedinthisstudyaswell,buttheyarenotcomparablebetweenthemodelsevaluated.Comparisonofmodelevidenceisonlypossibleifthedependentvariableinthemodelisthesame(Burnham&Anderson,2004)butGreenetal.(2014)useestimatesofpsychologicalstateasdependentvariable,whichareobviouslydifferentbetweenmethods.

17

Theconstant-latencyGLMapproachappearsfairlymature.Ithasbeenoptimizedwith 133

respecttomodelcomplexityanddatapreprocessing(Bachetal.,,2013)andevaluated 134

bytwodifferentlaboratories(Bach,2014;Greenetal.,2014).Currentresearchfocuses 135

onincrementalimprovements,suchasdatapreprocessingandmodelingof 136

nonlinearitiesunderspecificconditionssuchasrapideventsuccession,orwhenthe 137

sweatductsqualitativelychangetheirresponsebehavior(Tronstad,Kalvoy,Grimnes,& 138

Martinsen,2013). 139

140

Theflexible-latencymodelisalsoinamaturestageandhasbeenoptimized(Staibetal., 141

2015),butaformalevaluationbydifferentresearchlaboratoriesislacking.Intermsof 142

theforwardmodel,aquestionremainsastounderwhatconditionsadditional 143

complexityaffordedbyestimatingresponselatencyimprovesinferenceonthe 144

psychologicalvariable(i.e.,Whatisthelevelofvariabilityinresponselatencythat 145

shouldmotivatepreferringthismethodtotheconstant-latencyGLMapproach?).This 146

questionisawaitingempiricalinvestigation.Aweaknessoftheflexible-latencymodelis 147

itscomplexity,suchthatitisimpossibletoestimateallparametersatthesametimeon 148

standardPCsandclustercores.Parametersarethereforeestimatedinatrial-by-trial 149

fashionsuchthatestimationerrorsthatoccurinonetrialwillpropagateintothenext 150

one.Whilesometechnicaltricksreduceadetrimentalimpactofthissequential 151

estimation,itmaybepossibletoimproveonparameterestimationwithaglobal 152

optimizationmethodthatevaluatestheentireparameterspaceatthesametime. 153

154

Finally,theflexible-onsetmodelistheleastmatureandhasbeenevaluatedononlya 155

smallnumberofquestionsanddatasets;thereisroomforoptimizationofthismethod. 156

157

BeyondSCR,othermeasuresalsoallowinferenceonSNAand,thus,onthesame 158

psychologicalvariables.Itremainstobedeterminedwhethermeasuressuchasskin 159

potentialandskinsusceptance(Tronstadetal.,2013)orthememristorpropertiesofthe 160

skin(Pabst,Tronstad,&Martinsen,2017)yieldadditionalinformationorcanhelp 161

reducenoiseintheinverseinference. 162

163

4.2Pupilsize 164

4.2.1Forwardmodel 165

18

Awiderangeofpsychologicalvariablesimpactsonpupilsize(e.g.,deGeeetal.,2014; 166

Joshi,Li,Kalwani,&Gold,2016).Pupilsizeiscontrolledbytwoantagonistmuscles:the 167

radialM.dilatatorpupillae,whichreceivessympatheticinnervationviapreganglionic 168

neuronsfromthespinalcordandpostganglionicneuronsfromthesuperiorcervical 169

ganglion,andthecircularM.sphincterpupillae,whichreceiveparasympatheticinput 170

frompreganglionicneuronsin 171

theEdinger–Westphalnucleuswithinthemidbrainandpostganglionicneuronsinthe 172

ciliaryganglion(McDougal&Gamlin,2008).TheEdinger–Westphalnucleusreceives 173

bothluminance-mediatedinputsfromtheretinaandappearstorelayinputsthatarenot 174

relatedtoluminance(e.g.,fromthelocuscoeruleus;Joshietal.,2016;Liu,Rodenkirch, 175

Moskowitz,Schriver,&Wang,2017).Thisinnervationmotivatesusingluminance 176

changestoprobethebiophysicsofphasicpupilresponses.Thefactthatthepupilis 177

controlledseparatelybybothbranchesoftheautonomicnervoussystem,andby 178

antagonisticmuscleswithdifferentmechanicalproperties,alreadysuggeststhatpupil 179

responsesmaybestbemodeledbytwoparallelLTIsystems.Asaparsimonious 180

description,amodelisproposedthatdoesnotsplitthesystemintocontributionsofthe 181

twomusclesbutratherseparatesaslowerdilation/constrictionresponsefromafaster 182

componentthatonlyoccursforconstrictions(seeAppendixEquation9,10and 183

parametersforPSR_dilandPSR_con;Korn&Bach,2016).Interestingly,theformer 184

componentdirectly(exponentially)relatestoluminance,whilethecontributionofthe 185

lattercomponentappearsindependentfromtheamountofluminancechange(Korn& 186

Bach,2016).Becauseofthedifferenttimeconstantsofthetwosystems,themodel 187

makesaninterestingcounterintuitiveprediction:lightflashesshouldleadtopupil 188

constriction,butbriefdarknessperiodsshouldalsoleadtoconstriction,whenthefaster 189

responseinducedbythereturntolightprecedestheslowerresponseinducedbythe 190

darknessperiod.Indeed,thispredictionwasconfirmedbyexperimentalobservationin 191

ourownlaboratory(Korn&Bach,2016)andbyothers(Barbur,Harlow,&Sahraie, 192

1992).Thisforwardmodelexplainedaround60%ofsignalvariance,speakingtothe 193

validityofLTIapproximation(Korn&Bach,2016).Furthermore,itwasusedtoinferthe 194

neuralinputintothepupilsystemfordifferentpsychologicaltasks(visualdetection, 195

auditoryoddballdetection,listeningtoemotionalwords).Theinferredinputlatency 196

meaningfullyrelatedtoknownunderlyingpsychologicalprocesses(Korn&Bach,2016). 197

Thisalsosuggeststhatthefasttimecourseofpupilresponsesimpliesanecessityto 198

buildneuralforwardmodelsthataretosomeextentspecifictothepsychological 199

19

processstudied-different,forexample,fromtheunspecificSCRmodels-becausethe 200

timeconstantsofthepsychologicalprocessesdiffer.Onesuchmodelwasdevelopedfor 201

fearconditioning(Korn,Staib,Tzovara,Castegnetti,&Bach,2017).Here,wefoundthat 202

CS-responsesaredifferentbetweenexperiments,dependingontheperceptualmodality 203

andphysicalpropertiesoftheCS.However,theaddedimpactoftheCS+wasrather 204

constantacrossexperimentsandcouldbemodeledwithaconstant-latencyCS-evoked 205

neuralinputthatpeaksbetweenCSandUS(Kornetal.,2017).Thisneuralinput 206

appearedtobetime-lockedtotheCS,fordifferentintervalsbetweenCSandUS. 207

DifferentfromSCRmodels,thismeansthatthereisnocommonCSresponsethatdiffers 208

onlyinamplitudebetweenconditions.Instead,themodelseekstoestimatetowhat 209

extentaspecificCS+componentisexpressedoneach(CS+andCS-)trial.SincethisCS+ 210

componentmaynotbeorthogonaltotheexperiment-specificCSresponse,thismeans 211

thatallestimates(CS+andCS-)areonlyinterpretableuptoaconstant:itispossibleto 212

interpretdifferencesbetweentrialsets,ortemporalchangesintheestimatedCS 213

response,butnotthemagnitudeofresponseestimatesforindividualtrialsor 214

conditions.Formathematicalconvenience,neuralandperipheralmodelarecollapsed 215

intooneresponsefunction,whichmakesGLMinversionpossible(Kornetal.,2017;see 216

AppendixEquation9andparametersforPSR_FC).Anotherpsychologicalmodelwith 217

similarstructurebutadifferentresponsefunctionwasproposedtocapturetheimpact 218

ofattentiononpupilsize(Hoeks&Levelt,1993). 219

220


PupilPsPMshavebeenusedfortwopurposes.Thefirstisdirectinferenceona 222

psychologicalvariable.InferenceonCS+memoryinfearconditioningisimplementedin 223

aGLMinversionapproach,andyieldspredictivevaliditysuperiortopeakscoringor 224

area-under-the-curvemeasures(Kornetal.,2017).Giventheshortlatencyandsignal- 225

to-noiselevelssimilarorbetterthanSCR,inferencecanbeperformedonasingle-trial 226

level.Similarly,inferenceonattentionhasbeenusedinnumerousstudies(e.g.,deGeeet 227

al.,2014,2017;Knapenetal.,2016),althoughtoourknowledgethismethodhasnot 228

beensystematicallyinvestigatedandvalidatedbeyondtheinitialdevelopmentdataset 229

(Hoeks&Ellenbroek,1993;Hoeks&Levelt,1993).Anotherapplication,distinctfromall 230

othermodelspresentedinthisarticle,istoinferthetimecourseofapsychological 231

process.Thisispossiblebecauseluminance-relatedresponsesaremediatedbynear- 232

instantaneousneuralactivityandtherebyallowcharacterizingpupilbiomechanics. 233

20

Comparingameasuredpupiltimecoursewiththetimecourseofaluminance-related 234

responsethereforeaffordsestimatingtheneuralinputintothepupillarysystem,and 235

thusmakesinferenceonthedynamicsoftheunderlyingpsychologicalprocess(Korn& 236

Bach,2016). 237

238

4.2.3Futuredirections. 239

Pupil-sizemodelingisarelativelynewapproachandrequiresfurtherstudy. 240

Importantly,anindependentvalidationofpsychologicalinferenceisyetlacking.PsPMs 241

existforluminance-conditioned,fear-conditioned,andattention-relatedresponses,and 242

appeartocruciallydependonthetimingofthepsychologicalprocessunderstudy. 243

Potentially,pupil-sizemodelingthusoffersamoreprecisewindowintothetemporal 244

dynamicsofcognitiveprocessesthanmanyotherpsychophysiologicalvariables.Finally, 245

alotofresearchiscurrentlybeingdoneonpupilsizeanditsrelationtocognitive 246

processes,inhumansandotherspecies(e.g.,Eldar,Cohen,&Niv,2013;Joshietal., 247

2016).Itislikelythatnewmodelsandmethodswillemanatefromthisbasicresearch. 248

249

4.3Heartperiod 250


Heartrateorheartperiodareoftenusedtoinferemotionalarousal,forexample,while 252

watchingpicturesorduringfearconditioning(Berntson,Quigley,&Lozano,2007; 253

Bradley,Codispoti,Cuthbert,&Lang,2001)andcanbemeasuredwith 254

electrocardiogramorpulseoxymeters.Cardiacrhythmisgeneratedlocallyintheheart, 255

butmodulatedunderslowersympatheticandfasterparasympatheticinfluence 256

(Akselrodetal.,1981).Sympatheticstimulationfrequencyappearstolinearlyscalewith 257

heartperiodchanges,notheartrate(Berntson,Cacioppo,&Quigley,1995).Therefore 258

currentPsPMsforphasiccardiacresponsesmodelheartperiod,whichismappedonto 259

thefollowingRspikeandlinearlyinterpolated.Itappearsthatvariousshortstimuli 260

inducephasicheartperiodresponses(HPR),andsixresponsecomponentscouldbe 261

identifiedinasystematicinvestigationseeAppendixEquation8andparametersfor 262

HPR_E1-E6).However,neitherthisstudynorpreviousresearchbasedonoperational 263

methodsallowadefiniteconclusionastowhichpsychologicalvariablesinfluenceeach 264

ofthecomponentsandrelatedly,whetherthesecomponentsareindependently 265

controlled.Incontrast,awell-replicatedphenomenonisfear-conditionedbradycardia 266

21

(Castegnettietal.,2016).Thisbradycardiaresponseappearstobeaddedtoastimulus- 267

specificHPRthatoccursforbothCS+andCS-infearconditioning,similartowhatis 268

observedforpupilsizeandwiththesamelimitationsforinterpretationofresponse 269

estimates.However,differentfrompupilresponses,itappearstobetime-lockedtothe 270

USwhentheCS-USintervalisvaried(Castegnetti,Tzovara,Staib,Gerster,&Bach,2017; 271

Castegnettietal.,2016).Furthermore,relatingthebradycardiaresponsetothefirst 272

responsecomponentelicitedbyshortstimulirevealedaputativeneuralinputthat 273

peaksattheUS(Castegnettietal.,2016).Pragmatically,thePsPMforfear-conditioned 274

HPRcollapsesaneuralandperipheralsystemintooneresponsefunction,allowingGLM 275

inversion(seeAppendixEquation9andparametersforHPR_FC). 276

277


TherangeofpsychologicalvariablesthatcanbeinferredfromphasicHPRtoshort 279

stimuliappearsunclearatpresent.Fear-conditionedbradycardiaisanotable,well- 280

studiedexception.UsingtheGLMapproach,fearmemorycouldbeinferredwithhigher 281

predictivevaliditythanwithpeak-scoringmethods(Castegnettietal.,2016).Unlikefor 282

SCRandPSR,attemptstoperformsingle-trialanalysesinourownlaboratoryhavenot 283

succeeded,probablybecauseheart-periodtimeseriesaredominatedbyrespiratory 284

arrhythmia,andmanytrialsarerequiredtoreducetheimpactofthisnoisecomponent. 285

286


ElucidatingtheforwardmodelforHPRappearsanimportanttaskbothinthecontextof 288

PsPMsandoperationalapproaches.Thefidelityofinferenceonfearmemoryhasbeen 289

demonstratedinseveraldatasetsbutrequiresindependentconfirmationfromdifferent 290

laboratories.Castegnettietal.(2017)havesuggestedthatfear-conditionedbradycardia 291

couldpotentiallybe-atleastpartly-inducedbyincreasedthoraxpressureinducedvia 292

respirationamplituderesponses;thismaybeanotherinterestingavenueofresearch. 293

294

4.4Respirationmeasures 295


Mostrespiratorypsychophysiologyresearchhasfocusedonhowpsychologicalstates 297

onatimescaleof10-20suptominutesinfluencerespirationparameters(Boiten, 298

Frijda,&Wientjes,1994;Grassmann,Vlemincx,vonLeupoldt,&VandenBergh,2015; 299

Ritzetal.,2010;Vlemincx,VanDiest,&VandenBergh,2015;Wuyts,Vlemincx,Bogaerts, 300

22

VanDiest,&VandenBergh,2011),butrelativelylittleisknownaboutphasic 301

respiratoryresponses.PsPMshavebeendevelopedforrespiratoryperiod,respiratory 302

amplitude,andrespiratoryflowrateresponsestobriefexternalevents,allmeasured 303

withasimplesingle-chestbeltsystemasstandardlyemployedinfMRIlaboratories(see 304

AppendixEquation8andparametersforRPR,RAR_E,andRFRR).Externaleventscause 305

responsesinthesethreemeasuresthatarecapturedwithLTIsystems,butasyetitis 306

notclearwhichpsychologicalstatescouldbeinferredfromtheseresponses(Bach, 307

Gerster,Tzovara,&Castegnetti,2016).Incontrast,wehaveshowninseveral 308

experimentsthataCS+infearconditioningelicitsabiphasicrespiratoryamplitude 309

responsethatcanbemodeledinaLTIsystem,thusallowingGLMinversion(Castegnetti 310

etal.,2017)(seeAppendixEquation9andparametersforRAR_FC).Theapproachand 311

itsinterpretationaresimilartothatforpupilsizeandheartperiod. 312

313


Itappearsthatfearmemorycanbeinferredfromrespirationamplituderesponses,and 315

predictivevalidityofthisinferenceishigherforaGLMinversionthanpeakscoring 316

(Castegnettietal.,2017);however,itislowerthanformanyotherpsychophysiological 317

measures.AdistinctadvantageoftherespiratoryPsPMcouldbethatitonlyrequires 318

single-chestbeltdata,whichisstandardlyavailableinmanyMRIscanners. 319

320


Moreresearchisrequiredtoelucidatetherangeofpsychologicalvariablesthatcanbe 322

inferredfromrespiratorymeasures.Modelingmoresophisticatedrespiratorymeasures 323

couldbeaninterestingpossibility. 324

325

4.5Startleeyeblinkelectromyogram 326


Differentfromthepreviouslydiscussedmeasures,whichareunderthedirectinfluence 328

ofapsychologicalvariable,theimpactofpsychologicalvariablesonstartleeyeblinkis 329

onlymodulatoryandrequireselicitationofastartleresponsetorevealit.Thisstartle 330

eyeblinkresponse(SEBR)itselfhasratherstereotypicaldynamics,whileitsamplitudeis 331

modulatedbydifferentpsychologicalvariables(Yeomans,Li,Scott,&Frankland,2002). 332

Thismodulationhasbeensuggestedtobalancetheprotectiveutilityofthestartle 333

responsewithitsmetabolicandopportunitycost(Bach,2015b).Importantly,SEBR 334

23

dissociatesCS+andCS-infearconditioning,aphenomenontermedfear-potentiated 335

startle(Brown,Kalish,&Faber,1951).APsPMwasdevelopedtomodeltheimmediate, 336

briefSEBRtostartleprobesintheabsenceofanypsychologicalmanipulation(Khemka 337

etal.,2017).Thismodelexplainedabout60%ofsignalvarianceunderLTIassumptions. 338

Forinference,theneuralinputwasallowedaflexiblelatency,tobettercaptureslight 339

latencyvariationbetweenindividualsandtrials(Khemkaetal.,2017).Ascommoninthe 340

literature,themodelassumesthattheshapeofSEBRisindependentofthepsychological 341

orcognitivestate,whichonlyimpactsonitsamplitude. 342

343


ThisPsPMwasemployedtoinferfearmemory,bothduringacquisitionandmemory 345

recallunderextinction(Khemkaetal.,2017).Predictivevalidityoftheinferencewas 346

comparedtofourpeak-scoringmethodswithdifferentpreprocessingsteps.Foreachof 347

threeexperiments,adifferentpeak-scoringmethodperformedbest,butacrossall 348

experiments,thePsPMapproachyieldedhighestpredictivevalidity(Khemkaetal., 349

2017). 350

351


TheimpactofdifferentpreprocessingmethodsonSEBRanalysisappearsnotwell 353

understood.ThisleadstoaheterogeneouspicturewhencomparingPsPMwithdifferent 354

peak-scoringmethods,andshouldbeafocusoffutureresearch.Startle-independent 355

eyeblinksareatypicalsourceofnoiseinSEBRresearch,andmodelingtheseeyeblinks 356

couldbeanimportanttopicforfurtherinvestigation. 357

358

4.6Combiningpsychophysiologicalmodels 359

Inpsychophysiologicalresearch,differentmeasurementmethodsareoftenused 360

simultaneously(inthespiritofconvergentoperationalization),butnotcommonly 361

combinedforstatisticalinferenceonapsychologicalvariable.InaPsPMapproach,this 362

maybeapossibilityandcouldimproveinferenceundercircumstanceswhereseveral 363

measuresareindicativeofthesamepsychologicalvariable.Inordertoenablesuch 364

combination,itwouldbedesirabletoclarifyqualitativelythattwomeasuresare 365

impactedbythesamepsychologicalvariable,andtoinvestigatequantitativelythe 366

dimensionalstructureofthesemeasuresacrossdifferentindividuals. 367

368

24

3695Discussion 370

Psychologicalinvestigationreliesonsolvingtheinverseproblem:makinginferenceon 371

essentiallyunobservablepsychologicalvariables.Psychophysiologybenefitsfrommany 372

decadesofresearchontheforwardmappingfrompsychologicalvariablesonto 373

physiologicalmeasures.Thishasallowedthebuildingofpreciseandexplicitforward 374

models,whichcanbespecifiedinmathematicalformandinvertedtoyieldinferenceon 375

thepsychologicalvariable:psychophysiologicalmodeling.Buildingonsimple 376

experimentalmanipulationsthatyieldaknownpsychologicalstate,methodscanbe 377

evaluatedintermsoftheirpredictivevalidity(i.e.,thefidelitywithwhichtheyrecover 378

theknownstate).Thisallowscomparisonofoperationalaswellasmodel-based 379

methodsandhasrevealedthatinmanycasesPsPMsallowmorepreciseinferencethan 380

traditionaloperationalmethods,forexamplepeakscoring. 381

382

Asalimitation,thisconclusionisbasedonalimitednumberofstudiesanddatasets, 383

mostofwhich-withoneexception(Greenetal.,2014)-comefromourlaboratoryand 384

arethusbasedonthesamerecordingequipmentandrathercomparableexperimental 385

procedures.ItispossiblethatthePsPMsandinversionmethodsdevelopedinthis 386

contextoverfittheseexperimentalcircumstancesanddonotgeneralizewelltodata 387

acquiredindifferentcontexts,forexample,usingdifferentexperimentaltimingsor 388

involvingothertypesofartifacts.Notably,thesamelimitationappliestothevarietyof 389

operationalmethodsthathaveoftenbeendevelopedinandforspecificlaboratories 390

suchthatamultitudeofoperationalanalysismethodscoexistsintheliterature.Wehave 391

providedexamplesforapplicationofthePsPMsindifferentlaboratories,whichprovides 392

circumstantialevidencethatoverfittingisnotamajorissuefortheapproachpresented 393

here.However,toentirelyruleoutsuchpossibility,itwouldbedesirabletocomparethe 394

PsPMswithdifferentoperationalanalysesmethodsinmanyexperimentalsituations. 395

396

Researchonpsychophysiologicalmodelingunderlinesthenecessityforprecise 397

specificationofforwardmodel,andthusforthedetailedandmeticulousworkofbasic 398

psychophysiology.TheapplicationofPsPMsremainsrestrictedtosituationsinwhich 399

thismappingiswellknown.Indeed,PsPMsexistonlyforasmallnumberof 400

experimentalscenarios.However,theseincludestandardexperimentssuchasfear 401

conditioningandpictureviewing,andmaywellcomprisealargeproportionofapplied 402

25

psychophysiologyresearch.Forthese,PsPMsofferimprovedinferencecomparedto 403

currentlyusedmethods.Forexploratoryresearch,operationalmethodswiththeir 404

flexibilitymaybemoreappropriate.However,asanadvantageofmodel-basedmethods 405

theirprecisespecificationimplementationreducesresearcherdegreesoffreedom. 406

Analysisflexibilityisaproblemrecognizedacrosstheentirefieldofpsychology 407

(Simmons,Nelson,&Simonsohn,2011)andpossiblymoreprevalentwithflexible 408

operationalmethods.Whilestandardizationofmethodsisanongoingeffort(Boucsein 409

etal.,2012;Lonsdorfetal.,2017),PsPMoffersrationalcriteriabeyondcommunity 410

consensusforchoosingthestandards,namely,thequalityoftheinference.Notably,all 411

methodsdiscussedinthisreviewareavailableinopen-sourcetoolboxes,mostofthem 412

intheMatlab-basedPsPMtoolbox(pspm.sourceforge.net). 413

414

Asaframeworkforevaluatingmethods,wehaveproposedtobenchmarktheir 415

predictivevalidity,thatis,theirabilitytorecoverknownpsychologicalstates(Bach& 416

Friston,2013).Wenotethatthisframeworkhaspotentiallymanymoreapplications 417

thanevaluatingPsPMsorcomparingthemtooperationalmethods.Forexample,it 418

allowspoweranalyses.Ifthefidelityofamethodisknowninastandardexperiment,it 419

isoftenpossibletoderivebest-caseadditionalassumptionsthatdefineminimum 420

samplesizesrequiredtoachieveadesiredpowerlevel.Wehaveprovidedan 421

experimentalexampleforthisinthecontextofaninterventiontoreducesynaptic 422

plasticityduringfearconditioning,asmeasuredwithSEBR(Bachetal.,2017).Asan 423

importantinsight,poweranalysisbasedonpredictivevalidityresearchhasrevealed 424

thattherequiredsamplesizes-especiallywhenusingtraditionaloperationalmethods- 425

canbemuchhigherthanwhatisthestandardinthefield.Consequently,studiesnot 426

basingtheirsamplesizeonthisorotherformalanalysesmaybeunderpowered. 427

Anotherpotentialapplicationisqualitycontrol.Labscancomparetheirmeasurement 428

methodsbetweeneachother,assuremeasurementfidelityovertime,orbenchmark 429

researchtrainees,usingpredictivevalidityofstandardmeasures.Finally,apotentially 430

powerfuluseofthisframeworkistheoptimizationofexperimentaldesign.Iftheeffect 431

ofastandardexperimentonapsychologicalvariableisknownapriori,thenonecan 432

chooseanexperimentaldesignthatbestallowsdetectingthiseffect.Asanexample,this 433

approachcanhelptofindtheoptimalbalanceofretentiontrialstomeasurefear 434

memoryrecall,forwhichwehaveprovidedanempiricalexample(Khemkaetal.,2017). 435

436

26

Tosummarize,thefieldofpsychophysiologicalmodelingismovingrapidlyandhasin 437

partsalreadymatured.Withthesedevelopments,wehopetohaveprovidedtask- 438

unspecifictoolsthatfreeresearchers'resourcesfromhavingtodevelopdataanalysis 439

proceduresforeverystudy,andinsteadfocusonthepsychologicalorcognitive 440

questionstheywanttoanswer. 441

442

Acknowledgments 443

Theauthorsthanktheircolleagueswhoovertheyearshelpedestablishingthesoftware 444

PsPMandthemethodsdescribedinthisreview:JeanDaunizeau,RaymondJ.Dolan, 445

GuillaumeFlandin,KarlJ.Friston,GabrielGräni,SaurabhKhemka,PhilippC.Paulus, 446

LinusRüttimann,MatthiasStaib,AthinaTzovara. 447

448

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644

645Appendix 646

647

Modelevidence 648

Toquantifymodelevidence,PsPMusesthefollowingidentitytocomputeAkaike 649

InformationCriterion(AIC): 650

wherenisthenumberofdatapointsinthepredictivemodel,Listhemaximumofthe 651

likelihoodfunction,andkthenumberofparametersinthepredictivemodel.kis 652

constantforallmethodsthatareevaluatedinamethodscomparison.Thepredictive 653

modelusestheaprioridefinedpsychologicalvariableasdependentvariable(this 654

ensuresitisthesameacrossallmethods),andthedesignmatrixcontainstheestimated 655

psychologicalvariableand(possiblysubject-specific)interceptterms. 656

657

LTIsystems 658

Lineartimeinvariantsystemsaredefinedbythefollowingconvolutionoperation: 659

whereu(t)istheinputintothesystemattimet,histheimpulseresponsefunction(RF), 660

andτisadummyvariableoverwhichintegrationisperformed.Notethatsinceweare 661

dealingwithacausalsystem(i.e,.intime),wehaveexplicitlysetthelowerlimitofthe 662

!"# = −2 ln ! + 2! = ! ln !""! + 2! (1)

! ! = !×ℎ = ! ! − ! ℎ ! d!!

! (2)

31

integraltozero,suchthataninputthatoccursaftertcanhavenoimpactuponthe 663

outputattimet. 664

665

GLM 666

AGLMcanbewrittenas 667

whereYisthevectorofobservations,βisavectorofinputamplitudeparameters,andϵ 668

istheerror.Xisthedesignmatrixinwhicheachcolumnisobtainedbyconvolving 669

impulsefunctionsatknowntimepointswitheachcomponentoftheRF.Eachcolumn 670

takestheform: 671

where!!(!)istheneuralinputwithunitamplitudeforconditioni,andjistheindexof 672theRFcomponent.Finally,Xalsocontainsacolumnfortheintercept.Themaximum- 673

likelihoodamplitudeestimates!canbecomputedusingtheMoore-Penrose 674pseudoinverse!!,forexampleimplementedintheMatlabfunctionpinv.m: 675

676

Skinconductanceforwardmodel 677

(a)PhenomenologicalRFdescribedasaGaussian-smoothedexponential: 678

withestimatedparameters:!! = 3.0745 !forpeaklatency;! = 0.7013fordefinitionof 679therisetime;!! = 0.3176 and!! = 0.0708todefinethetwodecaycomponents. 680(b)PhenomenologicalRFdescribedasthird-order(linear,constant-coefficient)ordinary 681

differentialequation: 682

with!! = 1.342052,!! = 1.411425,!! = 0.122505,!! = 1.533879 683 684

! = !" + ! (3)

! = !!(!)×ℎ!(!) (4)

! = !!! (5)

ℎ ! ∝ ! ! − !!

!!! ! + !! ! !",

! ≥ 0,

! ! = 12!" !! !!!!

!!!! ,

!! ! = !!!!

(6)

! = !!! + !!! + !!! − ! ! − !! = 0 (7)

32

ModelswithGaussianresponsefunctions 685

Gaussianfunction: 686

Parametersseetable(HPR_E1-6:constant-latencyheartperiodresponses;RPR: 687

respirationperiodresponses;RAR_E:constant-latencyrespirationamplituderesponses; 688

RFRR:respiratoryflowrateresponses). 689

Responsefunction(RF) ParametersofGaussianFunction

!(mean) !(standarddeviation)HPR_E1 1.0 1.9

HPR_E2 5.2 1.9

HPR_E3 7.2 1.5

HPR_E4 7.2 4.0

HPR_E5 12.6 2.0

HPR_E6 18.85 1.8

RPR 4.20 1.65

RAR_E 8.07 3.74

RFRR 6.00 3.23

690

Modelswithgammaresponsefunctions 691

Gammafunction: 692

Parametersseetable(HPR_RC:fear-conditionedheartperiodresponses;PSR_dil: 693

luminance-evokedpupildilation;PSR_con:luminance-evokedpupilconstriction;PSR_FC: 694

fear-conditionedpupilsizeresponses;RAR_FC:fear-conditionedrespirationamplitude 695

responses;SEBR:startleeyeblinkresponses).Notethattheamplitudeparameterisleftfree 696

forallmodelsotherthantheluminancemodelsinwhichithasaphysicalinterpretation. 697

698

Responsefunction(RF) ParametersofgammaFunction

!(shape) !(scale) !!(onset) !(amplitude)

! = 1! 2! !! !!!

!!!! (8)

! = ! − !!!!!!!

!!!!!

!!Γ ! (9)

33

HPR_FC 48.5 0.182 -3.86 -

PSR_dil 2.40 2.40 0.2 0.77

PSR_con 3.24 0.18 0.2 0.43

PSR_FC 5.94 0.75 0.002 -

RAR_FC(early) 2.570×10! 3.124×10!! −8.024×10! -RAR_FC(late) 3.413 1.107 7.583 -

SEBR 3.5114 0.0108 -

699

Modelforsteady-statepupilsize 700

701where!isthezscoredsteady-statepupildiameterand!!is the respective illuminance 702level in (in [!"] ). The parameter values are: 703! = 49.79;! = −0.50 !!" ;! = −1.05. 704 705 706

! !! = ! + !!!!! (10)

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