-
1
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
-
2
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.
-
3
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.
-
4
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.
-
5
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”.
-
6
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
-
7
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.
-
8
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.
-
9
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
-
10
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.
-
11
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
LTIsystemwithparameters
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
LTIsystemwithparameters
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
-
12
empiricaldata
RPR Notyetspecified Instantaneousimpulse
LTIwithparametersfrom
empiricaldata
GLM PsPM Bach,Gerster,Tzovara,&Castegnetti,2016
RFRR Notyetspecified Instantaneousimpulse
LTIwithparametersfrom
empiricaldata
GLM PsPM Bach,Gerster,Tzovara,&Castegnetti,2016
RAR Notyetspecified Instantaneousimpulse
LTIwithparametersfrom
empiricaldata
GLM PsPM Bach,Gerster,Tzovara,&Castegnetti,2016
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
-
13
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
19
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
33
TherearegoodempiricalargumentstomotivatetheuseofLTIsystemstomodelthe
34
SNA/SCRrelationship,providedthatSCRdataarehigh-passfiltered.Threekindsoftests
35
havebeenexploitedtoevaluatetheforwardmodel.Indirecttestsmadetheauxiliary
36
-
14
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
61
TheLTImodeldoesnotmaketheassumptionthatSCRshapeisconstantbetween
62
individuals.Onthecontrary,allevidencesuggeststhatthisisnotthecase.Nevertheless,
63
inferencebasedonacanonicalresponsefunctionalreadyprovidesbetterinferencethan
64
operationalmethods.Wehaveshownthatthisinferencecanbefurtherimprovedby
65
allowingsomevariabilitybetweenindividuals,butonlyifthepossibleindividual
66
responsefunctionsareverystronglyconstrainedtoavoidoverfitting(Bachetal.,2013;
67
Staib,Castegnetti,&Bach,2015). 68
69
-
15
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
4.2.2Inferenceonpsychologicalvariables 221
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
4.3.1Forwardmodel 251
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
4.3.2Inferenceonpsychologicalvariables 278
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
4.3.3Futuredirections 287
ElucidatingtheforwardmodelforHPRappearsanimportanttaskbothinthecontextof
288
PsPMsandoperationalapproaches.Thefidelityofinferenceonfearmemoryhasbeen
289
demonstratedinseveraldatasetsbutrequiresindependentconfirmationfromdifferent
290
laboratories.Castegnettietal.(2017)havesuggestedthatfear-conditionedbradycardia
291
couldpotentiallybe-atleastpartly-inducedbyincreasedthoraxpressureinducedvia
292
respirationamplituderesponses;thismaybeanotherinterestingavenueofresearch.
293
294
4.4Respirationmeasures 295
4.4.1Forwardmodel 296
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
4.4.2Inferenceonpsychologicalvariables 314
Itappearsthatfearmemorycanbeinferredfromrespirationamplituderesponses,and
315
predictivevalidityofthisinferenceishigherforaGLMinversionthanpeakscoring
316
(Castegnettietal.,2017);however,itislowerthanformanyotherpsychophysiological
317
measures.AdistinctadvantageoftherespiratoryPsPMcouldbethatitonlyrequires
318
single-chestbeltdata,whichisstandardlyavailableinmanyMRIscanners.
319
320
4.4.3Futuredirections 321
Moreresearchisrequiredtoelucidatetherangeofpsychologicalvariablesthatcanbe
322
inferredfromrespiratorymeasures.Modelingmoresophisticatedrespiratorymeasures
323
couldbeaninterestingpossibility. 324
325
4.5Startleeyeblinkelectromyogram 326
4.5.1Forwardmodel 327
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
4.5.2Inferenceonpsychologicalvariables 344
ThisPsPMwasemployedtoinferfearmemory,bothduringacquisitionandmemory
345
recallunderextinction(Khemkaetal.,2017).Predictivevalidityoftheinferencewas
346
comparedtofourpeak-scoringmethodswithdifferentpreprocessingsteps.Foreachof
347
threeexperiments,adifferentpeak-scoringmethodperformedbest,butacrossall
348
experiments,thePsPMapproachyieldedhighestpredictivevalidity(Khemkaetal.,
349
2017). 350
351
4.5.3Futuredirections 352
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
References 449
Akselrod,S.,Gordon,D.,Ubel,F.A.,Shannon,D.C.,Berger,A.C.,&Cohen,R.J.(1981).
450Powerspectrumanalysisofheartratefluctuation:aquantitativeprobeofbeat-
451to-beatcardiovascularcontrol.Science,213,220-222. 452
Alexander,D.M.,Trengove,C.,Johnston,P.,Cooper,T.,August,J.P.,&Gordon,E.(2005).
453Separatingindividualskinconductanceresponsesinashortinterstimulus-
454intervalparadigm.JournalofNeuroscienceMethods,146,116-123.
455
Alvarez,R.P.,Kirlic,N.,Misaki,M.,Bodurka,J.,Rhudy,J.L.,Paulus,M.P.,&Drevets,W.C.
456(2015).Increasedanteriorinsulaactivityinanxiousindividualsislinkedto
457diminishedperceivedcontrol.Translationalpsychiatry,5,e591.
458
Bach,D.R.(2014).Ahead-to-headcomparisonofSCRalyzeandLedalab,twomodel-
459basedmethodsforskinconductanceanalysis.BiolPsychol,103C,63-68.
460
Bach,D.R.(2015a).Anxiety-LikeBehaviouralInhibitionIsNormativeunder
461EnvironmentalThreat-RewardCorrelations.PLoSComputBiol,11,e1004646.
462
Bach,D.R.(2015b).AcostminimisationandBayesianinferencemodelpredictsstartle
463reflexmodulationacrossspecies.JTheorBiol,370,53-60. 464
Bach,D.R.,Daunizeau,J.,Friston,K.J.,&Dolan,R.J.(2010).Dynamiccausalmodellingof
465anticipatoryskinconductanceresponses.BiolPsychol,85,163-170.
466
Bach,D.R.,Daunizeau,J.,Kuelzow,N.,Friston,K.J.,&Dolan,R.J.(2011).Dynamiccausal
467modelingofspontaneousfluctuationsinskinconductance.Psychophysiology,48,
468252-257. 469
Bach,D.R.,Flandin,G.,Friston,K.J.,&Dolan,R.J.(2009).Time-seriesanalysisforrapid
470event-relatedskinconductanceresponses.JNeurosciMethods,184,224-234.
471
Bach,D.R.,Flandin,G.,Friston,K.J.,&Dolan,R.J.(2010).Modellingevent-relatedskin
472conductanceresponses.InternationalJournalofPsychophysiology,75,349-356.
473
Bach,D.R.,&Friston,K.J.(2013).Model-basedanalysisofskinconductanceresponses:
474Towardscausalmodelsinpsychophysiology.Psychophysiology,50,15-22.
475
Bach,D.R.,Friston,K.J.,&Dolan,R.J.(2010).Analyticmeasuresforquantificationof
476arousalfromspontaneousskinconductancefluctuations.InternationalJournalof
477Psychophysiology,76,52-55. 478
Bach,D.R.,Friston,K.J.,&Dolan,R.J.(2013).Animprovedalgorithmformodel-based
479analysisofevokedskinconductanceresponses.BiolPsychol,94,490-497.
480
-
27
Bach,D.R.,Gerster,S.,Tzovara,A.,&Castegnetti,G.(2016).Alinearmodelforevent-
481relatedrespirationresponses.JNeurosciMethods,270,147-155.
482
Bach,D.R.,Seifritz,E.,&Dolan,R.J.(2015).TemporallyUnpredictableSoundsExerta
483Context-DependentInfluenceonEvaluationofUnrelatedImages.PLoSOne,10,
484e0131065. 485
Bach,D.R.,&Staib,M.(2015).Amatchingpursuitalgorithmforinferringtonic
486sympatheticarousalfromspontaneousskinconductancefluctuations.
487Psychophysiology,52,1106-1112. 488
Bach,D.R.,Tzovara,A.,&Vunder,J.(2017).Blockinghumanfearmemorywiththe
489matrixmetalloproteinaseinhibitordoxycycline.MolPsychiatry.
490
Bach,D.R.,Weiskopf,N.,&Dolan,R.J.(2011).Astablesparsefearmemorytracein
491humanamygdala.JournalofNeuroscience,31,9383-9389. 492
Barbur,J.L.,Harlow,A.J.,&Sahraie,A.(1992).Pupillaryresponsestostimulusstructure,
493colourandmovement.OphthalmicPhysiolOpt,12,137-141. 494
Barry,R.J.,Feldmann,S.,Gordon,E.,Cocker,K.I.,&Rennie,C.(1993).Elicitationand
495habituationoftheelectrodermalorientingresponseinashortinterstimulus
496intervalparadigm.InternationalJournalofPsychophysiology,15,247-253.
497
Benedek,M.,&Kaernbach,C.(2010a).Acontinuousmeasureofphasicelectrodermal
498activity.JournalofNeuroscienceMethods,190,80-91. 499
Benedek,M.,&Kaernbach,C.(2010b).Decompositionofskinconductancedataby
500meansofnonnegativedeconvolution.Psychophysiology,47,647-658.
501
Berntson,G.G.,Cacioppo,J.T.,&Quigley,K.S.(1995).Themetricsofcardiac
502chronotropism:biometricperspectives.Psychophysiology,32,162-171.
503
Berntson,G.G.,Quigley,K.S.,&Lozano,D.(2007).CardiovascularPsychophysiology.In
504J.T.T.Cacioppo,L.G.;Berntson,G.G.(Ed.),HandbookofPsychophysiology.NewYork
505City:CambridgeUniversityPress. 506
Boiten,F.A.,Frijda,N.H.,&Wientjes,C.J.(1994).Emotionsandrespiratorypatterns:
507reviewandcriticalanalysis.IntJPsychophysiol,17,103-128. 508
Boucsein,W.(2012).Electrodermalactivity.NewYorkSpringer.
509Boucsein,W.,Fowles,D.C.,Grimnes,S.,Ben-Shakhar,G.,roth,W.T.,Dawson,M.E.,&
510
Filion,D.L.(2012).Publicationrecommendationsforelectrodermal
511measurements.Psychophysiology,49,1017-1034. 512
Bradley,M.M.,Codispoti,M.,Cuthbert,B.N.,&Lang,P.J.(2001).EmotionandMotivation
513I:DefensiveandAppetitiveReactionsinPictureProcessing.Emotion,1,276-298.
514
Brown,J.S.,Kalish,H.I.,&Faber,I.E.(1951).Conditionedfearasrevealedbymagnitude
515ofstartleresponsetoanauditorystimulus.JournalofExperimentalPsychology,
51641,317-328. 517
Bulganin,L.,Bach,D.R.,&Wittmann,B.C.(2014).Priorfearconditioningandreward
518learninginteractinfearandrewardnetworks.FrontiersinBehavioral
519Neuroscience,8,67. 520
Castegnetti,G.,Tzovara,A.,Staib,M.,Gerster,S.,&Bach,D.R.(2017).Assessingfear
521learningviaconditionedrespiratoryamplituderesponses.Psychophysiology,54,
522215-223. 523
Castegnetti,G.,Tzovara,A.,Staib,M.,Paulus,P.C.,Hofer,N.,&Bach,D.R.(2016).
524Modelingfear-conditionedbradycardiainhumans.Psychophysiology,53,930-
525939. 526
deBerker,A.O.,Rutledge,R.B.,Mathys,C.,Marshall,L.,Cross,G.F.,Dolan,R.J.,&
527Bestmann,S.(2016).Computationsofuncertaintymediateacutestress
528responsesinhumans.NatCommun,7,10996. 529
-
28
deGee,J.W.,Colizoli,O.,Kloosterman,N.A.,Knapen,T.,Nieuwenhuis,S.,&Donner,T.H.
530(2017).Dynamicmodulationofdecisionbiasesbybrainstemarousalsystems.
531Elife,6. 532
deGee,J.W.,Knapen,T.,&Donner,T.H.(2014).Decision-relatedpupildilationreflects
533upcomingchoiceandindividualbias.ProceedingsoftheNationalAcademyof
534SciencesoftheUSA,111,E618-625. 535
Eldar,E.,Cohen,J.D.,&Niv,Y.(2013).Theeffectsofneuralgainonattentionand
536learning.NatureNeuroscience,16,1146-1153. 537
Fan,J.,Xu,P.,VanDam,N.T.,Eilam-Stock,T.,Gu,X.,Luo,Y.-j.,&Hof,P.R.(2012).
538Spontaneousbrainactivityrelatestoautonomicarousal.TheJournalof
539Neuroscience,32,11176-11186. 540
Friston,K.J.,Jezzard,P.,&Turner,R.(1994).AnalysisoffunctionalMRItime-series.Hum
541BrainMapp,1153-171. 542
Gerster,S.,Namer,B.,Elam,M.,&Bach,D.R.(2017).Testingalineartimeinvariant
543modelforskinconductanceresponsesbyintraneuralrecordingandstimulation.
544Psychophysiology. 545
Grassmann,M.,Vlemincx,E.,vonLeupoldt,A.,&VandenBergh,O.(2015).Theroleof
546respiratorymeasurestoassessmentalloadinpilotselection.Ergonomics,1-9.
547
Greco,A.,Guidi,A.,Felici,F.,Leo,A.,Ricciardi,E.,Bianchi,M.,Bicchi,A.,Citi,L.,Valenza,
548G.,&Scilingo,E.P.(2017).Musclefatigueassessmentthroughelectrodermal
549activityanalysisduringisometriccontraction.ConfProcIEEEEngMedBiolSoc,
5502017,398-401. 551
Greco,A.,Lanata,A.,Valenza,G.,DiFrancesco,F.,&Scilingo,E.P.(2016).Gender-specific
552automaticvalencerecognitionofaffectiveolfactorystimulationthroughthe
553analysisoftheelectrodermalactivity.ConfProcIEEEEngMedBiolSoc,2016,
554399-402. 555
Greco,A.,Valenza,G.,Lanata,A.,Scilingo,E.,&Citi,L.(2015).cvxEDA:aConvex
556OptimizationApproachtoElectrodermalActivityProcessing.IEEETransBiomed
557Eng. 558
Greco,A.,Valenza,G.,&Scilingo,E.P.(2016).Investigatingmechanicalpropertiesofa
559fabric-basedaffectivehapticdisplaythroughelectrodermalactivityanalysis.Conf
560ProcIEEEEngMedBiolSoc,2016,407-410. 561
Green,C.D.(1992).OfImmortalMythologicalBeasts:OperationisminPsychology.
562Theory&Psychology,2,291-320. 563
Green,S.R.,Kragel,P.A.,Fecteau,M.E.,&LaBar,K.S.(2014).Developmentandvalidation
564ofanunsupervisedscoringsystem(Autonomate)forskinconductanceresponse
565analysis.IntJPsychophysiol,91,186-193. 566
Hayes,D.J.,Duncan,N.W.,Wiebking,C.,Pietruska,K.,Qin,P.,Lang,S.,Gagnon,J.,Bing,
567P.G.,Verhaeghe,J.,Kostikov,A.P.,Schirrmacher,R.,Reader,A.J.,Doyon,J.,
568Rainville,P.,&Northoff,G.(2013).GABAAreceptorspredictaversion-related
569brainresponses:anfMRI-PETinvestigationinhealthyhumans.
570Neuropsychopharmacology,38,1438-1450. 571
Hoeks,B.,&Ellenbroek,B.A.(1993).Aneuralbasisforaquantitativepupillarymodel.
572JournalofPsychophysiology,7,315-315. 573
Hoeks,B.,&Levelt,W.J.M.(1993).PupillaryDilationasaMeasureofAttention-a
574QuantitativeSystem-Analysis.BehaviorResearchMethodsInstruments&
575Computers,25,16-26. 576
Joshi,S.,Li,Y.,Kalwani,R.M.,&Gold,J.I.(2016).RelationshipsbetweenPupilDiameter
577andNeuronalActivityintheLocusCoeruleus,Colliculi,andCingulateCortex.
578Neuron,89,221-234. 579
-
29
Khemka,S.,Tzovara,A.,Gerster,S.,Quednow,B.B.,&Bach,D.R.(2017).Modelingstartle
580eyeblinkelectromyogramtoassessfearlearning.Psychophysiology,54,204-214.
581
Knapen,T.,deGee,J.W.,Brascamp,J.,Nuiten,S.,Hoppenbrouwers,S.,&Theeuwes,J.
582(2016).CognitiveandOcularFactorsJointlyDeterminePupilResponsesunder
583Equiluminance.PLoSOne,11,e0155574. 584
Koban,L.,Kusko,D.,&Wager,T.D.(2018).Generalizationoflearnedpainmodulation
585dependsonexplicitlearning.ActaPsychol(Amst),184,75-84. 586
Koban,L.,&Wager,T.D.(2016).Beyondconformity:Socialinfluencesonpainreports
587andphysiology.Emotion,16,24. 588
Korn,C.W.,&Bach,D.R.(2016).Asolidframeforthewindowoncognition:Modeling
589event-relatedpupilresponses.JVis,16,28. 590
Korn,C.W.,Staib,M.,Tzovara,A.,Castegnetti,G.,&Bach,D.R.(2017).Apupilsize
591responsemodeltoassessfearlearning.Psychophysiology,54,330-343.
592
Lang,P.J.,Bradley,M.M.,&Cuthbert,B.N.(2005).Internationalaffectivepicturesystem
593(IAPS):Affectiveratingsofpicturesandinstructionmanual.TechnicalReportA-6.
594Gainesville,FL:UniversityofFlorida. 595
Lim,C.L.,Rennie,C.,Barry,R.J.,Bahramali,H.,Lazzaro,I.,Manor,B.,&Gordon,E.(1997).
596Decomposingskinconductanceintotonicandphasiccomponents.International
597JournalofPsychophysiology,25,97-109. 598
Liu,Y.,Rodenkirch,C.,Moskowitz,N.,Schriver,B.,&Wang,Q.(2017).Dynamic
599LateralizationofPupilDilationEvokedbyLocusCoeruleusActivationResults
600fromSympathetic,NotParasympathetic,Contributions.CellRep,20,3099-3112.
601
Lonsdorf,T.B.,Menz,M.M.,Andreatta,M.,Fullana,M.A.,Golkar,A.,Haaker,J.,Heitland,I.,
602Hermann,A.,Kuhn,M.,Kruse,O.,MeirDrexler,S.,Meulders,A.,Nees,F.,Pittig,A.,
603Richter,J.,Romer,S.,Shiban,Y.,Schmitz,A.,Straube,B.,Vervliet,B.,Wendt,J.,
604Baas,J.M.P.,&Merz,C.J.(2017).Don'tfear'fearconditioning':Methodological
605considerationsforthedesignandanalysisofstudiesonhumanfearacquisition,
606extinction,andreturnoffear.NeurosciBiobehavRev,77,247-285.
607
McDougal,D.H.,&Gamlin,P.D.R.(2008).Pupillarycontrolpathways.
608Nicolle,A.,Fleming,S.M.,Bach,D.R.,Driver,J.,&Dolan,R.J.(2011).Aregret-induced
609
statusquobias.JournalofNeuroscience,31,3320-3327.
610Pabst,O.,Tronstad,C.,&Martinsen,O.G.(2017).Instrumentation,electrodechoiceand
611
challengesinhumanskinmemristormeasurement.ConfProcIEEEEngMedBiol
612Soc,2017,1844-1848. 613
Paulus,P.C.,Castegnetti,G.,&Bach,D.R.(2016).Modelingevent-relatedheartperiod
614responses.Psychophysiology,53,837-846. 615
Ritz,T.,Kullowatz,A.,Goldman,M.D.,Smith,H.J.,Kanniess,F.,Dahme,B.,&Magnussen,
616H.(2010).Airwayresponsetoemotionalstimuliinasthma:theroleofthe
617cholinergicpathway.JApplPhysiol(1985),108,1542-1549. 618
Simmons,J.P.,Nelson,L.D.,&Simonsohn,U.(2011).False-PositivePsychology:
619UndisclosedFlexibilityinDataCollectionandAnalysisAllowsPresenting
620AnythingasSignificant.PsychologicalScience,22,1359-1366. 621
Staib,M.,Castegnetti,G.,&Bach,D.R.(2015).Optimisingamodel-basedapproachto
622inferringfearlearningfromskinconductanceresponses.JNeurosciMethods,255,
623131-138. 624
Sulzer,J.,Sitaram,R.,Blefari,M.L.,Kollias,S.,Birbaumer,N.,Stephan,K.E.,Luft,A.,&
625Gassert,R.(2013).Neurofeedback-mediatedself-regulationofthedopaminergic
626midbrain.Neuroimage,83,817-825. 627
-
30
Talmi,D.,Dayan,P.,Kiebel,S.J.,Frith,C.D.,&Dolan,R.J.(2009).Howhumansintegrate
628theprospectsofpainandrewardduringchoice.JournalofNeuroscience,29,
62914617-14626. 630
Tronstad,C.,Kalvoy,H.,Grimnes,S.,&Martinsen,O.G.(2013).Waveformdifference
631betweenskinconductanceandskinpotentialresponsesinrelationtoelectrical
632andevaporativepropertiesofskin.Psychophysiology,50,1070-1078.
633
Tzovara,A.,Korn,C.W.,&Bach,D.R.(2018).HumanPavlovian 634
fearconditioningconformstoprobabilisticlearning.PLOS 635
ComputationalBiology,14,e1006243.
636Vlemincx,E.,VanDiest,I.,&VandenBergh,O.(2015).Emotion,sighing,andrespiratory
637
variability.Psychophysiology,52,657-666.
638Wuyts,R.,Vlemincx,E.,Bogaerts,K.,VanDiest,I.,&VandenBergh,O.(2011).Sighrate
639
andrespiratoryvariabilityduringnormalbreathingandtheroleofnegative
640affectivity.IntJPsychophysiol,82,175-179. 641
Yeomans,J.S.,Li,L.,Scott,B.W.,&Frankland,P.W.(2002).Tactile,acousticandvestibular
642systemssumtoelicitthestartlereflex.NeurosciBiobehavRev,26,1-11.
643
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)