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Richard, Bruno, Chadnova, Eva and Baker, Daniel Hart orcid.org/0000-0002-0161-443X (2018) Binocular vision adaptively suppresses delayed monocular signals. Neuroimage. 753 - 765. ISSN 1053-8119

https://doi.org/10.1016/j.neuroimage.2018.02.021

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Richard,Chadnova&Baker(2018),NeuroImagedoi:10.1016/j.neuroimage.2018.02.021

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Binocularvisionadaptivelysuppressesdelayedmonocularsignals

BrunoRichard1,2,EvaChadnova3,&DanielH.Baker1

1DepartmentofPsychology,TheUniversityofYork,Heslington,York,UnitedKingdom2DepartmentofMathematicsandComputerScience,RutgersUniversityNewark,Newark,NewJersey,USA3McGillVisionResearch,DepartmentofOphthalmology,McGillUniversity,Montreal,Quebec,Canadaemail:[email protected]

Aneutraldensityfilterplacedbeforeoneeyewillproduceadichopticimbalanceinluminance,whichattenuatesresponsestovisualstimuliandlagsneuralsignalsfromretinatocortexinthefilteredeye.Whenstimuliarepresentedtoboththefiltered and unfiltered eye (i.e., binocularly), neural responses show little attenuation and no lag compared with theirbaselinecounterpart.Thissuggeststhatbinocularvisualmechanismsmustsuppresstheattenuatedanddelayedinputfromthefilteredeye;however,themechanismsinvolvedremainunclear.Here,weusedaSteady-StateVisualEvokedPotential(SSVEP)techniquetomeasureneuralresponsestomonocularlyandbinocularlypresentedstimuliwhileobserversworeanNDfilterinfrontoftheirdominanteye.Thesedatawerewell-describedbyabinocularsummationmodel,whichreceivedthesinusoidalcontrastmodulationofthestimulusasinput.WeincorporatedtheinfluenceoftheNDfilterwithanimpulseresponsefunction,whichadjustedtheinputmagnitudeandphaseinabiophysicallyplausiblemanner.Themodelcapturedtheincreaseinattenuationandlagofneuralsignalsforstimulipresentedtothefilteredeyeasafunctionoffilterstrength,whilealsogeneratingthefilterphase-invariantresponsesfrombinocularpresentationforEEGandpsychophysicaldata.Theseresultsclarifyhowbinocularvisualmechanisms—specificallyinterocularsuppression—cansuppressthedelayedandattenuatedsignalsfromthefilteredeyeandmaintainnormalneuralsignalsunderimbalancedluminanceconditions.

Keywords: Neutral Density filter, Steady-State Visual Evoked Potential, Binocular Summation, BinocularInteractions,BinocularRivalry,BinocularVision,Luminance,GainControl,Suppression

1Introduction

Neuralandperceptualresponsestovisualstimuliaremodulatedbythemeanluminanceofthevisualfield:underlowluminancelevels,visualresponsesare impoverished and sensitivity to spatial andtemporalcontrastpatternsispoor(DeValoisetal.,1974;Kilpeläinen et al., 2012, 2011; Shapley andEnroth-cugell, 1984; Swanson et al., 1987). Ifluminance is lowered in only one eye (i.e., adichopticluminancechange),thereducedstimulusintensitytothedarkenedeyewill—inturn—alterbinocular function, and hinder performance on aseries of binocular measures including binocularsummation, binocular rivalry, and stereo acuity(Baker, Meese, & Hess, 2008; Baker, Meese,Mansouri, & Hess, 2007; Chang et al., 2006; DeValois et al., 1974; Gilchrist & Pardhan, 1987;Leonards & Sireteanu, 1993; Zhou, Jia, Huang, &Hess, 2013). For example, binocular summationcan be abolished and return to monocular

performancelevelswhentransmittanceisreducedto3%(Bakeretal.,2007b),while theproportionanddurationofdominanceeventsofthedarkenedeyeinbinocularrivalrydecrease inproportiontothe decrement in luminance (Leonards andSireteanu,1993).Thisisthoughttooccurbecausethe reduced responses of the darkened eye pushthe binocular functional balance towards that oftheunaffectedeye.Thatis,interocularinteractionsadaptively suppress signals from the filtered eyeand minimize its contribution to the binocularpercept.Thisprocess issimilartothatthoughttounderlie visual deficits observed in individualswith binocular vision disorders (e.g., amblyopia),andinvestigatingthearchitectureofthisfunctionalbalance may help elucidate the functional visualimbalances experienced by these individuals(Baker, Meese, Mansouri, et al., 2007; Campbell,Maffei,&Piccolino,1973;DeBelsunce&Sireteanu,



1991; Heravian-Shandiz, Douthwaite, & Jenkins,1991;Leonards&Sireteanu,1993;Zhang,Bobier,Thompson,&Hess,2011).An interocular imbalance in luminance limitsbinocular interactions as it reduces the responsemagnitudeandslowstheresponselatencyofcellsselectiveforthedarkenedeye,whichgeneratesanasynchrony between the signals from each eye(Heravian-Shandizetal.,1991;Katsumi,Tanino,&Hirose,1986;Spafford&Cotnam,1989;Wilson&Anstis, 1969). While both the attenuation andslowing of responses can be estimatedpsychophysically (Harker and O’Neal, 1967; Lit,1949;MorganandThompson,1975),theycanalsobedirectlymeasuredinhumanobserverswithEEGmethods, by recording either transient (VEPs) orsteady-stateVisualEvokedPotentials(SSVEPs)tostimulipresentedunderdifferentluminancelevels(Heravian-Shandiz et al., 1991; Katsumi et al.,1986; Norcia et al., 2015; Spafford and Cotnam,1989). Response lags under low transmittanceconditions(1%ora2.0NDfilter)canreachvaluesup to 80ms and a 50% decrease in responsemagnitude in the darkened eye (Chadnova et al.,2018; Heravian-Shandiz et al., 1991; Spafford &Cotnam, 1989). This impairment is generallyabsent when stimuli are presented to both thedarkened and un-filtered eye (i.e., binocularly):transient and SSVEPs show little difference fromnormal viewing conditions, which indicates thatsometypeofcompensatoryneuralmechanismcansuppressthedelayedandattenuatedneuralsignalsfrom the darkened eye (Heravian-Shandiz et al.,1991; Spafford and Cotnam, 1989). Acomprehensive description of the visualmechanism able to maintain normal signaltransmission under binocular viewing wheninterocular responses are asynchronous remainstobedefined.There are cues from previous studies that pointtowards a model architecture able to predict theeffectsofaninterocularluminanceimbalance.Forexample, Chadnova et al. (2018) found that abinocular contrast normalization model, whichreceived as input the temporal signals (stimulusoscillation) filtered by an impulse responsefunction,wasabletodescribetheattenuationanddelayofSSVERs(Steady-StateEvokedResponses,recorded with MEG) generated by a 1.5ND filter(3% transmittance) placed before one eye.However, they frequency tagged their stimuli sothat each eye (the darkened and un-filtered eye)was presented with stimuli that oscillated at

different frequencies (4Hz and 6Hz). While thisallowed them tomeasure independent responsesfrom both eyes under dichoptic viewing, itprevented them from measuring responses to afused binocular stimulus, so they could notmeasure or model normal signal transmission tobinocularly presented stimuli when luminancelevelsdifferbetweentheeyes.Modern models of binocular vision describebinocular combination as a two-stage process ofcontrast gain control, in which normalizedmonocular signals are linearly summed prior toundergoing a second normalization stage.Crucially, the monocular terms in these modelsinclude interocular interactions, which modulatethesignalsfromeacheyebythatoftheothereye(Bakeretal.,2008;DingandSperling,2006;Huangetal.,2010;Meeseetal.,2006;Zhouetal.,2013).This model architecture can account for a widerange of psychophysical phenomena, includingdichoptic masking, binocular summation atthreshold, the converging of monocular andbinocular discrimination thresholds atsuprathreshold contrast levels, and thecombination of dichoptically presented phaseincongruentstimuli(Bakeretal.,2008,2007c;DingandSperling,2006;Georgesonetal.,2016;Heeger,1992;Legge,1984a,1984b;Meeseetal.,2006).Itfollows that this type of model would be ideallysuited todescribe themechanismresponsible formaintaining normal signal transmission whenluminance levelsdifferbetween theeyes. Indeed,this has been demonstrated psychophysically byusingamodifiedversionoftheDingandSperling(2006)binocularcombinationmodeltodefinetheperceptual effects of an imbalance of luminancebetween both eyes on a phase combination task(Zhou et al., 2013). Their model predicted thegradualtransitioninperceivedphasetowardsthatof the un-filtered eye as the transmittance of thefilter in the darkened eye was reduced (i.e.,increasingthedensity).However,giventhenatureof theirparadigm,only thereduction in responseamplitudefromthefilteredeyecouldbeaccountedfor—they couldnot empirically test the abilityoftheir model to explain temporal asynchroniesgeneratedbylowluminanceinthedarkenedeye.Here, we recorded SSVEPs to monocularly andbinocularly presented flickering sinusoidalgratingswhileobserversworeNDfiltersofvarioustransmittances before their dominant eye. Toverify that theattenuationand lagrecorded fromour SSVEPs are representative of the observers’



percept, we measured binocular summation andbinocular rivalry under the same ND filterconditions as the SSVEP portion of our study.Finally,weimplementthetwo-stagecontrastgaincontrolmodelproposedbyMeeseetal.,(2006)inanefforttodefinethemechanismthatsuppressestheattenuatedanddelayedmonocularsignalsfromthe darkened eye in order to maintain normalsignal transmission under binocular viewing. Weadapt thepsychophysical two-stage contrast gaincontrol model to generate neural responseamplitude and latency values under variousmonocularreductionsinluminancebyconvolvingthe inputtothemodelwithanImpulseResponseFunction experimentally derived for thetransmittanceofagivenNDfilter(Swansonetal.,1987),similartopreviousapproachesofmodellingSSVEP amplitude and phase (Chadnova, et al.,2018; Cunningham et al., 2017). As expected,SSVEPamplitudedecreasedandlatencyincreasedas a function of ND filter transmittance formonocularly viewed stimuli, while little changewasobservedunderbinocularviewing,consistentwith previous reports (Heravian-Shandiz et al.,1991;Katsumiet al., 1986; SpaffordandCotnam,1989). These effects were well explained by ourmodel, which generated response amplitude andresponse latencies that that mirrored that of ourobservers both in the monocular and binocularviewing conditions. Additionally, our modelcapturedtheeffectsofadecreaseinluminanceonbinocular summation without any additionalparameter adjustments. Taken together, ourneurophysiological findings, psychophysicalfindings,andmodellingdemonstratethatstandardinterocularinteractionsinbinocularvisionpairedwithresponseattenuationissufficienttomaintainnormal signal transmission from discordant andasynchronousmonocularsignals.2Methods

2.1Participants

Nine observers (2 males: authors BR and DHB),with normal or corrected to normal visual acuityparticipated in this study (Mage = 25 years, SD =4.24). Written informed consent was obtainedfromallparticipants,andexperimentalprocedureswere approved by the ethics committee of theDepartment of Psychology at the University ofYork.

2.2!Apparatus

All stimuli were presented using a gammacorrectedViewPixx3Ddisplay(VPixxtechnologies,Canada)drivenbyaMacPro.Binocularseparationwith minimal crosstalk was achieved bysynchronizingtherefreshrateofthedisplaywiththe toggling of a pair of Nvidia stereo shuttergogglesusingan infra-redsignal.Monitor refreshratewassetto120Hz,meaningthateacheyewasupdated at 60Hz (every 16.67 msec). Displayresolutionwassetto1920X1080pixels.Asinglepixel subtended 0.027° of visual angle (1.63 arcmin) when viewed from 57 cm. The meanluminance of the display viewed through theshuttergoggleswas26cd/m2.EEG signals were recorded from 64 electrodesdistributedacrossthescalpaccordingtothe10/20EEGsystem(Chatrianetal.,1985)inaWaveGuardcap(ANTNeuro,Netherlands).Wemonitoredeyeblinkswithanelectrooculogram,whichconsistedofbipolarelectrodesplacedabovetheeyebrowandatopofthecheekontheleftsideoftheparticipant’sface.Stimulus-contingent triggersweresent fromthe ViewPixx display to the amplifier using aparallelcable.SignalswereamplifiedanddigitizedusingaPCwiththeASAlabsoftware(ANTNeuro,Netherlands). All EEG data were imported intoMATLAB (Mathworks, MA, USA) and analysedoffline.2.3! Stimulus

Stimuliwerefour3cycles/°horizontalsinusoidalgratings,windowedbyaraisedcosineenvelopetosubtend5°ofvisualangleontheretina.Thestimuliwere tiled to have a grating above, below, to theright, and to the left of fixation (see Figure 1).Distance between the centre of the gratings andfixationwassetto5°.Topromotebinocularfusion,two oblique lines crossing at the centre of thedisplay were shown to both eyes throughout theexperiment. To measure contrast responsefunctions, stimulus contrast—expressed indecibels (�∀# = 20 log∗+ �% )—ranged between15.6dB and 39.6dB (6% to 96% MichelsonContrast) in steps of 6dB. Stimulus contrast wasfixed at 39.6dB for SSVEPs measured with NDfilters. The stimulus flicker (on/off contrastmodulation) was set to 5Hz and followed asinusoidal waveform in negative cosine phaserescaled to the range from0-1: stimulus contrastbegan at 0%, increased smoothly to 100%of thenominalmaximum,andthenreturnedto0%overaperiodof200ms(i.e.,1cycle).



Figure1.Examplestimulusdisplay formonocularandbinocularviewingconditions.Undermonocularviewing,onlyasingleeyewaspresentedwiththeflickeringstimuliwhiletheothereyesawascreensettomeanluminancewiththefusioncross.Underbinocularviewingconditions,botheyeswerepresentedwithidenticalstimuliflickeringinphaseatarateof5Hz.Thespatialfrequencyofthesegratingshasbeenadjustedforprintquality.

2.4! Procedures

SSVEPcontrastresponsefunctionsweremeasuredmonocularly (dominant and non-dominant eye)andbinocularly.Stimuliflickeredonscreenfor11secondsandwerefollowedbyascreensettomeanluminance—withthefusioncross—for3seconds.In monocular trials, the un-stimulated eye waspresented with a screen set to mean luminancewith a fusion cross. In binocular trials, observerswerepresentedwithidenticaldisplaystoeacheyethat flickered in-phase—note that as we usedshutter goggles to present stimuli to observers,thereisaslightoffsetbetweenthecontrastofthestimulipresentedtotheleftandrighteyeastheyaresampledfromslightlydifferentpointsalongthesinusoidal modulation. Observers completed 8trialsperstimuluscontrast(15.6,21.6,27.6,33.6,39.6dB)andviewingcondition, foratotalof120trials(~30minutesofviewingtime).Participantsweregiventheopportunitytorestevery30trials.Tomeasuretheeffectsofaninterocularimbalancein luminance on the amplitude and latency ofneural signals, we fitted participants with an NDfilterovertheirdominanteye(measuredwiththeMiles Test; Miles, 1930). Participants viewed thesame sinusoidal gratings as those defined above(onlyatmaximumcontrast:39.6dB)eitherinthefiltered eye alone (monocularly) or binocularly.Presentationdurationandtheinter-trialintervalswere identical to those of the contrast responsefunction measurements. Three neutral densityfilters,withstrength0.6ND(25%transmittance),1.2ND (6% transmittance) and 1.8ND (1.6%transmittance)wereusedtoreducetheluminanceinthefilteredeye.Observerscompleted8trialsfor

each ND filter strength and viewing condition(monocularandbinocular),foratotalof48trials—approximately12minutesofviewingtime.Measurementsof the contrast response functionsandtheNDfilterconditionswerecompletedinthisorderduringthesameexperimentalsession.Thus,observerswereadaptedtothemeanluminanceofthe display (26cd/m2) for approximately 30minutes prior to completing the ND filterconditions(withsomevariabilityinthedurationofbreaks taken by observers), which ensuresminimal variability in their sensitivity to light asdark adaptation curves taper after 30minutes inthe dark (Lamb and Pugh, 2004; Pugh, 1975).Stimulus contrast and ND filter strength wererandomized across trials and participants,respectively.Observersweregivennoexplicittaskotherthantofixateatthecentreofthefusioncrossand minimize blinking during stimuluspresentation.3! SSVEPAnalysis

We used whole-head average referencing tonormalizeeachelectrodetothemeansignalofall64electrodes(foreachsamplepoint).Priortodataanalysis, the firstsecondofeachtrial (single trialduration:11seconds)wasdiscarded toeliminateonset transients while the remaining 10 secondswereFouriertransformed.Examplespectrafromasingleobserverforthecontrastresponsefunctionmeasurement and the ND filter conditions areshown in Figure 2A, the scalp distributions ofSSVEP amplitudes at the fundamental frequency(5Hz) for stimuliof increasing contrast inFigure

MONOCULAR BINOCULAR



2B,andNDfiltersofincreasingstrengthsinFigure2C.Across all viewing conditions, the largest andmost reliable Fourier component was at thefundamental frequency of our stimulus flicker(5Hz). Steady-state amplitudes at the thirdharmonic(15Hz)offerednoadditionalinformationto those of the fundamental while the secondharmonic(10Hz)layinthecenterofthealphaband(Strasburger, 1987), which made steady-stateamplitudessmallandquitevariableacrossviewingconditionsandparticipants.WethusconcentratedouranalysesontheamplitudeandphasevaluesofthefundamentalfrequencyanddidnotincludetheFourier amplitude or Fourier phase values fromhigher harmonics in our analyses. We decided toanalyzeSSVEPsatfourelectrodes:Oz,O1,O2,andPOz,concentratedat thebackof thehead(wherethelargestEEGsignalswererecorded;seeFigure2B-C).The Fourier amplitude value for the 5Hzcomponent was averaged using conventionalmethods:we took the coherentaverageofSSVEP

amplitudeacross the fourelectrodes, followedbytrials (n = 8 repetitions), and then took theincoherent average across observers. As Fourierphaseisacircularstatistic,themeanangleofphasevalues for the5Hzcomponent (�)wereaveragedby taking the sum of complex numbers of unitmagnitude �/0 ,�0 = �/023

45∗ , where �4 is themeasuredphaseangleforagiventrial.Thecircularstandard deviation of the average Fourier phase

wascalculatedas��0 = −2 log �0 ,where �0

is the resultant vector length:;

3. Response

delaysweredefinedasthedifferencebetweentheFourier phase angle recorded for viewingconditions with an ND filter and their no filter

counterparts, described by the ratio Δ0 ==>;?≅

=>;Α.

The angular differencewas then averaged acrossobservers in the same manner as defined above,and the resulting valuewas taken as the averageresponse lag in degrees attributable to the NDfilters.

Figure2.AExampleFourierSpectraforSSVEPscollectedfromoneobserver.ThetoprowshowstheFourieramplitudeoffrequenciesup to20Hz for stimuliofdifferent contrasts, fordominanteyemonocular (leftpanel) andbinocular (rightpanel) presentations. The bottom row shows Fourier amplitudes for the ND filter conditions. Fourier amplitude wasgreatestatthefundamentalfrequencyofthestimulusflicker(5Hz),whereasthehigherharmonicamplitudes(10&15Hz)are significantly smaller.B-C Head plots of the average SSVEP amplitude at 5Hz across all 64 electrodes on the scalpaveraged across participants. These head plots clearly illustrate the effect of increasing stimulus contrast on SSVEPamplitudeforbothdominanteyemonocularandbinocularconditions(B),andtheimpactofplacinganNDfilterinfrontofthedominanteyeoftheobserver(C).Thatis,SSVEPamplitude,whichisconcentratedatthebackoftheheadfallsasthestrengthoftheNDfilterincreasesifstimuliareviewedthoughthefilteredeyealone,butnomeaningfulchangeisobservedwhenstimuliareviewedbinocularly.

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4! ModellingtheFourierAmplitudeandPhase

ofSSVEPs

An increase in stimulus contrast leads to anincrease in the amplitude of SSVEPs that is welldefinedbyconventionalmodels(BakerandWade,2017;Brownetal.,1999;Candyetal.,2001;Tsaietal., 2012;ZemonandRatliff, 1984).Traditionally,thesemodelsoperateonan input that is a scalarrepresentation of stimulus contrast, and return avalue that represents the normalized scalarresponseamplitude(Carandinietal.,1997;Heeger,1992),but theycanalsopredict theamplitudeofsingleormultiplefrequencycomponentsinSSVEPsif given a time-varying input. Here, we furtherextend these models to account for the temporaldynamics of SSVEPs (i.e., phase lag) by addingtemporal filters to the two-stage contrast gaincontrolmodelofbinocularcombination(Bakeretal., 2008, 2007a, 2007c; Baker and Meese, 2007;Meese et al., 2006). This produces a timedependent output that allows us to model theeffects of a monocular decrease in luminance onSSVEPamplitudeandphase.Briefly,thismodelhastwo distinct stages of contrast gain control, onebefore and one after binocular combination (seeFigure3A).The first stageof themodel includesmonocular contrast gain control and interocularsuppression followed by linear binocularsummation,whichisdefinedas:

�� =�ΗΙ

� + �Η + �Λ+

�ΛΙ

� + �Λ + �Η (1)

ParametersmandSwerefixedandsetto1.3and1respectively(Bakeretal.,2007;Meeseetal.,2006)whilec(R,L)isthesinusoidalmodulationofstimuluscontrastpresentedtotheobservers’right(R)andleft (L) eye: �(�) = 0.5� (sin 2�� + � + 1). Adefinesthemaximumstimuluscontrast,whilefand�arethetemporalfrequency(5Hz)andphase(0;respectively) of the modulation (identical to thestimulus modulation). The second contrast gaincontrolstageisgivenas:

�[/4 =��∴

� + ��⊥

(2)

wherep,q,andZarefixedmodelparameterssetto7.665,6.5,0.1.Allparametersusedinthecontrastgain control stages of our model were fixed atpreviously reported values (Baker et al., 2008;Georgesonetal.,2016).

We extend the two-stage contrast gain controlmodel into a dynamic variant to fit SSVEPamplitudeandphasevaluesbyplacingatemporalfilterpriortothefirstcontrastgaincontrolstageofthe model (see Figure 3A). The form of thetemporalfilters(TF)weretakenfromSwansonetal., (1987), who measured temporal responsefunctions(WatsonandNachmias,1977)inhumanobserversunderdifferentluminancelevels.Placedprior to the first stage of contrast gain control,thesefiltersservetoattenuateandalterthephaseof the sinusoidal input (c) to the model in abiologicallyrelevantmanner.Thetemporal filterswere formed by taking the scaled differencebetweentwofivestageimpulseresponsefunctions(n=5),� �, � = �4α∗�αβχδε � − 1 !,with theirrespectivecornerfrequenciesc1andc2,definedas:(3)

�� = �� ∗, �

�∗− �

� �β, � − �+

�β

Parametert0todefinethelatencydifferenceintheonset of the two filters, while k1 and k2 arenormalizationconstants.To generate SSVEP components from the model,we pass the rectified sinewave through thetemporalfilterandcontrastgaincontrolstagesofthemodel.TheoutputofthemodelisthenFouriertransformedandtheamplitudeandphasevaluesofthe 5Hz component are extracted. In order toadjust the response amplitude of the model tothoseofourSSVEPs,weaddabaselineamplitudevalue, set to the noise level of our EEG data(0.16µV), to the Fourier spectrum. We optimizedthe temporal filters to fit SSVEP amplitude andphase for each viewing condition and observerwith the 5 parameters that define the temporalfilter.ModelfittingwascompletedinMATLABwithfminsearchtominimizethequantity(4)

��=κκλκ = ��/ − ��/β

4

/5∗

Theresultingmodelresponsesforeachparticipantwere then averaged across participants. Weoptimized parameter values for the monocularviewing condition alone, and cross-validated ourparameter estimates by using these to generatebinocular viewing responses and the contrastresponsefunctionsmeasuredwithoutNDfilters.



Figure3.AThearchitectureofthemodifiedtwo-stagecontrastgaincontrolmodel.NDfiltersareplacedbeforethefirstcontrastgaincontrolstage(righteyeinputwithNDfiltersofincreasingstrength,lefteyeinputnoNDfilter).EachNDfiltercontainstheImpulseResponseFunctionthatmodulatestheinputtothemodelaccordingtothetransmittanceofthefilter.Thetemporalfiltersshownrepresenttheparticipantaveragetemporalfilters.Seetextfordetailsontheremainingmodelarchitecture. B The model, which receives as input a temporal waveform (5Hz) outputs a non-sinusoidal temporalwaveform.CThewaveformisthenFouriertransformedandtheamplitudeandphasevaluesofthe5Hzcomponentareextract(showninpolarcoordinates).TheparametersofthetemporalfilterwerefittothehumandatabycalculatingthevectordistancebetweenthecomplexFouriercomponentsat5Hzofthedataandmodeloutput.DThebestfittingtemporalfiltersdefinedbydatafromthemonocularviewingconditionforallNDfilters.

5! ResultsandDiscussion

The average SSVEP amplitude change acrossstimuluscontrastandNDfilterstrength isshownin Figure 4A and 4B respectively. Amplitudeincreasedmonotonicallyasa functionofstimuluscontrast,F(4,32)=5.56,p=.002,�∴

β=.41,andwe

found no difference between SSVEP amplitudemeasured monocularly (dominant and non-dominant eye) or binocularly (interaction effect:F(8,64)=0.58,p= .791;maineffectofocularity:F(2, 16) = 0.54, p = .593). This is expected forstimulipresentedatthecontrastvaluesusedhere(Baker & Wade, 2017; Legge, 1984) because theincreasedexcitationfromstimulatingbotheyesispreciselybalancedbytheinterocularsuppressionbetween the eyes. To generate contrast responsefunctions from our model, we use the temporalfilter estimated from the no ND filter viewingcondition(stimuluscontrast=96%or39.6dB)and

inputted sinusoidal waveforms modulated inamplitude to represent the 5 different contrastlevelsused in this study.Model fitsare shownasthe solid lines in Figure 4A. While the modelcontrastresponsefunctioncouldbeimproved,theycapture the general increase in the amplitude ofSSVEPsasafunctionofstimuluscontrastwell.Wecouldhaveadjustedtheparametersofthemodeltoimprovefits,however,weoptedtokeepthemodelparameters fixed for two reasons. First, themaingoalofthismanuscriptistodefinethedecreaseinneural response amplitude in response to adecrement in luminance, and not the increase inresponse according to stimulus contrast.Additionally, given the already large number ofparametersused todefine the temporal responsefilters(Swansonetal.,1987),wedecidedtokeepall parameters of the two-stage contrast gaincontrol model fixed and similar to previousimplementations(Bakeretal.,2008;Georgesonet

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al., 2016; Meese et al., 2006), and only allow theparameters of the temporal filters to vary whenfittingtheNDfilterdata.Monocular SSVEPs to stimuli presented to thefiltered eye showed a statistically significantdecrease in amplitude as a function of ND filterstrength,F(3, 24) = 4.45,p = .013,�∴

β= .357, and

reachednoise-levelamplitudesatourdarkestfilter(1.8ND). SSVEPs under binocular viewing werestatisticallysignificantlydifferentfromthoseofthemonocular viewing condition, F(1, 8) = 6.50, p =.034,�∴

β= .448). Post-hoc tests show this effect is

predominantly driven by SSVEP amplitudes for a1.8NDfilter,t(8)=-2.97,p=.018,d=-1.87,95%CIof d [-3.36 -0.31], which is in line with previousfindings that have shown severe drops inmonocularamplitudeofERPsandSSVEPsatfilterdensitiesnearorequalto2.0ND(Heravian-Shandizet al., 1991; Spafford and Cotnam, 1989). Theparameters of the temporal response functions(equation 3)were optimized to fit SSVEPs fromthemonocularviewingconditionforeachNDfilterstrength. The best fitting temporal filters (seeFigure 3D) show a progressive drop in peakamplitude in addition to an increase latency in

reachingtheirpeakamplitudeasafunctionofNDfilter strength (from 0.6ND to 1.8ND), whichcapturedthedecreaseinSSVEPamplitudefoundinourobservers.Weusedthesametemporal filtersto generate model predictions for the binocularviewing conditions; the unfiltered eye input wasadjustedbythenoNDtemporalfilter(greylineinFigure 3D) and the filtered eye by the temporalfilter calculated for a given ND strength undermonocular viewing. Thus, binocular viewing datafrom the model was generated with no freeparameters or additional data fitting procedures.Binocular amplitudes decreased slightly when a0.6NDfilterwasplacedbeforethedominanteyeofobservers and tapered off at stronger ND filters,which was well captured by our model. We notehowever, that these effects are not statisticallysignificant (all ps > .05). A small attenuation ofSSVEPamplitudesfordataviewedbinocularlyistobe expected as the filtered eye must exert someinfluence on the binocular percept (Heravian-Shandizetal.,1991;SpaffordandCotnam,1989).However,giventhatthedifferencebetweenthesedatapointsdidnotreachstatisticalsignificance,weare cautious to attribute the small decrease inSSVEP amplitude to the influence of the filteredeye.

Figure 4.Averaged (N = 9) SSVEP amplitudes (μV) measured for sinusoidal gratings of varying contrast (A ContrastResponseSSVEPAmplitude)andtogratingsof96%contrastwithvaryingNDfilterstrength(BNDFilterSSVEPAmplitude).ValuesontheabscissaindicateinAstimuluscontrastindB(loweraxis),andMichelsoncontrast(upperaxis)andinBNDfilterstrength(loweraxis)andresultingilluminationforthefilteredeye(upperaxis).ThegreylinemarksthebaselineSSVEPamplituderecordedwhennostimuliarepresentonthedisplay.Errorbarsandgreyshadedregionsrepresent±1standarderrorofthemean.CurvesrepresentthemodelpredictionsforSSVEPamplitudeacrossstimuluscontrast(A)andNDfilterstrength(B).Themodeloutputforboththedominantandnon-dominanteyeSSVEPamplitudesinA(redandbluelines)overlapperfectlyasthismodelpredictsequalsensitivitybetweentheeyestomonocularstimulipresentedatequalluminancevalues.

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SSVEPphaseangles,whicharerepresentativeofameasureof the response latencyof anoscillatorymechanism (Strasburger, 1987), for stimuli ofvarying contrast and luminance are shown inFigure5Aand5Brespectively.Dataareshowninpolar coordinates, where the radial componentdepictsSSVEPamplitude(asinFigure4)andtheangular axis shows the Fourier phase angle(estimated response latency, inferred from theperiodicityofourstimuli,areshowninparenthesesin Figure 5B). Standard error of the cross-participantmeanSSVEPamplitudeandphasearerepresentedasellipses.Thesemi-majoraxisoftheellipserepresentsthestandarderroroftheFourierphase angle, and its semi-minor axis, that of theFourier amplitude. As Fourier phase is a circularvariable, these polar plots should be read asfollows:valuesatornear0ontheangularaxishaveaphaseangle like thatof thesinusoidal flickerofthestimulus(i.e.,nearinstantaneousresponsestothe stimulus), while values with greater phaseangles lag behind that of the stimulus flicker(approximately16msper30⁰step).Fourierphaseisdefinedmodulo360⁰,thus,phaseanglesat lowstimuluscontrast—thatlienear0—shouldnotbeinterpreted to have near instantaneous responselatencywiththestimulusflicker,butinsteadphaselagsthatapproachorareslightlygreaterthanafullstimulus flicker cycle (i.e., response latency of200ms).ThephaseangleofSSVEPs is inversely related tostimulus contrast, Χβ(8) = 44.70, p < .001, butunaffected by the viewing condition (whetherstimuli are viewed monocularly or binocularly;effect of eye: Χβ(4) = 6.47, p = .167, interactioneffect:Χβ(8)=6.37,p=.606),whichisexpectedinasampleofnormalobservers(Meeseetal.,2006;Zhangetal.,2011).Responselatencywasshortest(100ms) for gratings of maximum contrast (i.e.,39.6dB), and increased as contrast decreased,reaching response latency values near 200ms atourloweststimuluscontrast(15.6dB).Aresponselatency of 100ms for stimuli of high contrastcorresponds well with previous EEG reports(Heravian-Shandiz et al., 1991; Spafford andCotnam, 1989), however, response latencies forlowerstimuluscontrastvaluesdoexceedthoseofpreviousfindings,whichmaybeattributedtotheir

useoftransientVEPstoinferlatencyasopposedtoSSVEPs.This isbecausethe latter includesbothapuredelayofsignaltransmission(i.e.,opticnervetransmission) and the contributions of anoscillatory mechanism (Heravian-Shandiz et al.,1991; Spafford and Cotnam, 1989; Strasburger,1987;Vialatteetal.,2010).

Response latency to our stimuli increased asluminance decreased when viewed monocularly,but was unaffected when stimuli were viewedbinocularly. Monocular response lags, whichrepresentthedifferenceinlatencybetweentheno-filter and ND filter conditions increasedproportionally to ND filter strength (M0.6ND =11.49ms,SD=31.46;M1.2ND=27.99ms,SD=41.95;M1.8ND=82.99ms,SD=40.84),andwasstatisticallysignificantly different from the no filter responselatencyataNDfilterstrengthof1.8,t(8)=2.03,p=.038, . Binocular response lags remained near avalueof0acrossallNDfilterstrengths,(M0.6ND=-3.67ms,SD=25.80;M1.2ND= -6.47ms,SD=30.90;M1.8ND = -15.63ms,SD =36.94; allps> .05).Mostimportantly, the increase in response latency formonocular viewing, and the absence of an effectunderbinocularviewingwerewellcapturedbyourmodel.Asareminder,weonlyfittheparametersofthetemporalfilterstothemonocularviewingdata,andusethesamefilterstopredicttheattenuationand response latency of the filtered eye underbinocular viewing. The temporal filter estimatedfor themonocularno filterconditionwasusedtodefine the input to the unfiltered eye underbinocularviewing.Thus,theinputtotheunfilteredeye in our model was faster and of greateramplitudethanthatofthefilteredeye.Thisleadstorelativelygreaterinterocularsuppressionfromtheunfiltered eye onto the filtered eye and abinocularly summed output that is mostrepresentativeoftheunfilteredeyeresponses.TheabilityofourmodeltogeneratebinocularresponselatenciesthatareunaffectedbyNDfilterssuggeststhat neural responses to dichoptic stimuli can besufficientlyexplainedbyadjustingatemporalfilterto reflect neurophysiological responses todecreasingamountsofillumination.Anyadditionalchanges to interocular interactions (as proposedbyZhouetal.,2013)arenotnecessary.



Figure5.APolarrepresentationoftheresultingSSVEPFourieramplitudeandphasefromthecontrastresponseconditions.Underallthreeviewingconditionsshownhere,SSVEPamplitudeincreasedaccordingtostimuluscontrast,whileSSVEPphasedecreased(responselatencyshortened).Ellipseerrorareasrepresent+/-onestandarderrorofthemeanforFourierphase(semi-majoraxis)andamplitude(semi-minoraxis).Theblacklineandshadedregionindicatethebaselineamplitude(0%contrast)anditsrespectivestandarderror.Thecurrentarchitectureofthemodelisnotdesignedtogenerateachangeinphaseanglegivenachangeinstimuluscontrastasouraimherewastodefineinterocularinteractionsthatresultfromachangeinluminance,thusnomodelfitsarepresentedinthischart.Valuesinthepolarplotsindicatetheaverageresponselatency (standard deviation in parentheses) for each stimulus contrast. B Polar plots of the relative phase lags(�3ρ �4λ3ρ)formonocularandbinocularviewingconditions.CirclemarkersshowtheobserverphaselagforagivenNDfilterstrength(withthecorrespondingFourieramplitude),whilesquaremarkersshowthemodeloutputaveragedacrossall participants. Response latency is presented in parentheses beneath the phase angle. Monocular response latencyincreasesasafunctionofNDfilterstrengthincomparisontothatmeasuredwithoutanNDfilter.Underbinocularviewingconditions,nochangeinresponselatencyisobserved.StandarderrorsofbothFourieramplitudeandphaselagaredrawnasellipsesaroundthedatapoint.Observerstandarderrorisdepictedbyshadedellipses,whilemodelstandarderrorisshownbytheoutlinedellipses.ThegreylinemarkstheSSVEPamplitudeofthenofilterconditionformonocular(right)and binocular viewing (left), while the black line and shaded area indicate the baseline amplitude and its respectivestandarderror.

Human Data

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6! PsychophysicalMeasures

AninterocularimbalanceinluminanceinducedbyaNDfilterwillattenuateandlagSSVEPstostimulipresented only to the filtered eye, but has littleeffect when stimuli are presented to both eyes.Whether these effects are representative of theobservers’ percept, however, must bedemonstratedpsychophysically.Thus, in additiontoourSSVEPexperiment,observerscompletedtwopsychophysical experiments that bringbehaviouralsupporttothetwo-stagecontrastgaincontrolmodelusedtoexplaintheeffectsdescribedabove. Additionally, we demonstrate that ourmodel architecture is well-suited to explain notonly the neural responses to stimuli presentedabove, but effects of monocularly decreasingluminance on psychophysical performance.Participants completed two psychophysicalparadigms that have previously been used tomeasurethehindranceofaninterocularimbalancein luminance on performance: a binocularsummationexperiment(Bakeretal.,2007b)andabinocular rivalry experiment (De Belsunce andSireteanu, 1991; Leonards and Sireteanu, 1993).Performanceonthesetasksisknowntobesubjectto interocular interactions, and thus, anybehavioural change attributed to the ND filter intheseparadigmsfurthersupportsthesuppressiveeffects of binocular vision on delayed monocularsignalswedefinedabove.Weimplementthemodelin the binocular summation experiment, butpresent only the psychophysical findings of ourbinocular rivalry experiment, as the dynamicproperties of binocular rivalrywould require toolargeachange toourmodellingarchitecture,andaddnofurtherinsighttoourfindings.

6.2! BinocularSummation

6.2.1! StimulusandProcedures

Stimuli were 3 cycles/° horizontal sinusoidalgratingswindowedbyaraisedcosineenvelopetosubtend5°ofvisualangleontheretina(identicaltothose of the SSVEP study). Monocular andbinocular contrast detection thresholds weremeasured with a 2-AFC staircase procedure (3-down, 1-up), which adjusted contrast inlogarithmic steps around threshold (step-size =3dB;seeBaker,Meese,Mansouri,etal.,2007).Onanygiventrial,observerswerefirstpresentedwithablankscreenandfixationcrossinthecentreofthedisplay for 500ms. Two 200ms intervals werepresented in succession, interlaced by a blankscreen for 400ms; one interval contained the

stimulus, while the other was blank. Like in theSSVEPexperiment,targetcontrastwastemporallymodulated according to a full cycle of a raisedsinusoidalwaveformduringthestimulusinterval:contrastbeganat0%,andincreasedto100%ofitsnominalmaximum,andreturnto0%overaperiodof200ms.Observerswereaskedtoindicatewhichofthetwostimulusintervalscontainedthetarget.Theonsetofastimulusintervalwaspairedwithatone to minimize observer uncertainty. Contrastdetection thresholds were determined by Probitanalysis,andtakentobethe75%correctpointonthefittedfunction.Therewerenineconditionsinthisstudy:contrastdetection thresholds of thenon-filtered eyewereonly measured once, while the filtered eye andbinocular conditions were each repeated fourtimes(nofilter,andatallthreeNDfilterslevels).Asin the EEG portion of this study, observerscompletedthenofilterconditionsbeforerepeatingthe experimentwithND filters.This ensures thatobservers were dark adapted when measuringdetectionthresholdsunderlowilluminationlevels.Observers completed three staircases percondition, which were subsequently combined toestimatethresholds.6.2.2! ResultsandDiscussion

Average monocular and binocular contrastdetection thresholds (CS) and summation ratios(�� = ��#/4λδ ��σλ4λδ(3λ4αρλΙ/4τ4ε)) for all ND

filterstrengthsareshowninFigure6A.Binocularsummation—withnofilterplacedbeforethenon-dominanteye—wasapproximatelylinear(SR=2),slightlyhigherthanthetypicallyreportedratiosof1.4 - 1.8 (Baker et al., 2007c; Blake et al., 1981;CampbellandGreen,1965;Legge,1984b;Meeseetal.,2006;MeeseandBaker,2013).Wefoundthatattenuatingtheresponsesofastimulusbyreducingits luminance with ND filters decreased thebinocular advantage and reached monocularperformance levels at dense ND filters. This isexpected when measuring contrast detectionthresholds as the relative sensitivity of each eyeinfluencesbinocularcontrastsensitivity(Bakeretal., 2007b; Nes et al., 1967). However, binocularcontrast sensitivity never fell below that of themonocularcontrastsensitivityfromtheunfilteredeye,suggestingminimalornobinocularinhibitionfrom difference in luminance between both eyes(i.e.,we findnoevidenceofFechner’sparadox inoursubjects;GilchristandPardhan,1987).



Figure6.(A)Contrastdetectionthresholds(left)measuredmonocularlyandbinocularly,andbinocularsummationratio(right) across allND filter conditions of this study. Contrast detection thresholds for the non-dominant eyewere onlymeasuredatbaseline(nofilter),andaredrawnasalineacrossallNDfiltervaluesforreference.Errorbarsrepresent+/-1standard error of the mean (error for the non-dominant line is represented as a shaded region). Summation ratiosdecreased as a function of filter density, and reached monocular levels (no summation) for filters of 1.8ND.B Modelpredictions of monocular and binocular contrast detection thresholds across all ND filter conditions (Left). Modelthresholds were generated by feeding inputs varying in contrast, and selecting an arbitrary cut-off value (k = 1) thatindicatedtargetdetection.Whilethethresholdvaluesgeneratedbythemodeldonotmatchhumanobserverthresholds,theinfluenceoftheNDfilterontargetdetectioniscapturedwellbythetemporalfiltersweestimatedfromourEEGdata.(Right)ThemodelsummationratiosacrosstheNDfilterconditions.ThedecreaseinsummationasafunctionofNDfilterstrength iswell captured by themodel.However, it is incapable of capturing the unusually large summation ratioweobtainedwithnoNDfilters.

Binocular summation is well described byphysiologicalsummation–thelinearcombinationof normalized monocular signals (Baker et al.,2007b; Georgeson et al., 2016; Meese and Baker,2011). This is a fundamental component of ourmodel as it defines the impeding effects of NDfilters on the amplitude and phase of SSVEPs. Itthus follows that our general model architectureshould also be able to account for thepsychophysical binocular summation datacollectedhere.Wedonotattempttofitthemodel

parameters to the binocular summation datashownhere,butinsteadfeedtheEEGmodelwithasingle cycle of a sinusoidal waveform of varyingamplitude(tosimulatedifferentstimuluscontrastvalues),identicaltothepsychophysicalproceduresof this study. The effects of the ND filter weremodelledwiththetemporalfiltersoftheEEGstudy.Togeneratecontrastdetectionthresholds(Ct)fromourmodel response (i.e., amplitude),we selectedan arbitrary model criterion value (k= 1) todeterminepredictionsforwhich

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� = ��(�ε). (5)

The model predictions are shown in Figure 6B.Whilethemodeldetectionthresholdsdonotmatchthoseofhumanobserversinmagnitude,theydoinkind. The model predicts a similar increase inthreshold for both the monocular and binocularviewing conditions as a function of the ND filterstrength,andconsequently,adecreaseinbinocularsummation that mirrors – in the ND filterconditions-thatofourhumanobservers,reachingmonocular levels of summation at anND filter of1.8.Aninterestingobservationwiththismodeltypeisthat the binocular summation ratio (the ratio ofbinocular to monocular contrast detectionthresholds)isgivenby21/m=1.7or4.6dBwhenmis set to 1.3 (Baker et al., 2007a). While thisapproximates binocular summation well in mostcases,binocularsummationwithnoNDfilterwasunusually high in our sample: the baselinebinocular summation ratio was greater than thetypicallyreportedvalueandquasi-linear(SR=2.14or 6.61dB). A summation ratio this high isuncommonanditisplausiblethatthefilteredeyeofourobserverswasstrengthenedbytheNDfilterinstudiesconductedpriortothesummationstudy(e.g., the EEG experiment), as short monoculardeprivation (or partial occlusion) is known toincreasethecontributionofthefilteredeyetothebinocularpercept(Zhouetal.,2013).However,itisdifficulttoascertainhowmuchinfluencethismayhave had on our quasi-linear summation ratio asmonocular deprivation requires a substantiallylonger occlusion period (~2.5 hours) than thatundergone by our observers in the experimentprecedingthisone(12minuteswith filters in theEEG experiment). We also find no difference inmonocularcontrastsensitivitybetweenthefilteredandunfilteredeyewithnoNDfilterthatwouldbeindicativeofastrengtheningofthefilteredeyebyNDfilters(seeFigure6).Aswedonotattempttofit the responses of the model to the binocularsummationdatabyadjustingthemparameter,andkeep it set to 1.3, our model is incapable ofgeneratingbinocularsummationwithnoNDfilteras high as that of our human observers.Nevertheless,wedemonstrateherethatthemodelarchitecture we have created to describe thechanges in SSVEP amplitude and phase valueswhenluminanceisimbalancedbetweenbotheyescanalsocapturegeneralchangesinpsychophysicalmeasurements of binocular summation. The dataandmodelpredictionsfurtherdemonstratehowasevereluminanceimbalancebetweentheeyescan

makeasystemappearmonocular,despitehavingabinoculararchitecture.

6.3! BinocularRivalry

6.3.1! StimulusandProcedures

Stimuliweretwo3cycles/°oblique(45°and135°)sinusoidal gratings windowed by a raised cosineenvelopetosubtend5°ofvisualangleontheretina.Dichopticpresentationofbothgratings(45°totheright,135°totheleft)wasaccomplishedwiththesame stereo shutter goggles as described above(seeFigure7A;apparatuswasidenticaltothatofthe SSVEP study). Stimuli were presented at thecentreofthedisplayforadurationof60seconds,duringwhichobserverscontinuouslyindicatedtheorientation of the perceptually dominant gratingvia button press. All participants completed therivalrytaskfourtimes,oncewithoutanNDfilterinfrontofthedominanteye,andthenonceforeachND filter strength (filter strength order wascounterbalancedacrossobservers).6.3.2! ResultsandDiscussion

Under normal binocular viewing,we find a smalldominant eye effect of rivalry. The stimuluspresentedtothedominanteyeoftheobserverwasperceivedapproximately25%moreoftenthanthatofthenon-dominanteye(ln(ratio)=0.17,SDln(ratio)= 0.32, logit d = .121), an effect often found inbinocular rivalry studies (Bartels and Logothetis,2010). Importantly, the proportion of dominanceeventsinthefilteredeyefellrapidlyasafunctionof ND filter strength. Perceptual dominance ofstimulipresentedtothefilteredeyeoccurredhalfasoftenasthoseoftheunfilteredeyewitha1.8NDfilter (ln(ratio) = -0.67, SDln(ratio) = 0.37, logit d =.336; seeFigure7B).Thedurationofdominanceevents in the filtered eye also decreased as afunction of ND filter strength. The histograms inFigure 7C show distributions of dominancedurations (pooled across all observers) for eacheyeatthefourNDfilterstrengths.Atbaselineandwitha0.6NDfilter,thedistributionsofdominanceeventsofeacheyeoverlapsignificantly(no filter:KS=0.133,p=.424;0.6ND:KS=0.181,p=.076).As the strength of the ND filter is increased,dominanceeventsinthefilteredeyedecreasedinduration, which shifted the distribution towardsthe leftwhile that of theunfiltered eye remainedunchanged(1.2ND:KS=0.252,p=.004;1.8ND:KS=0.598,p<.005).UnlikeourSSVEPandbinocularsummationdata,wechosenottomodeltheeffectsofND filterson thenumberofdominanceeventsand dominance duration in our binocular rivalry



data.There existmodels of binocular rivalry thatare structurally similar to the psychophysicalmodelwepresenthere(Wilson,2007,2003),buttheir implementation would have necessitatedsignificant changes to the model architecture inaddition toa seriesof additionalparameters thatdefine the complex dynamics of binocular rivalrythatgobeyondthegoalsofthismanuscript.Adecreaseinthenumberofdominanceeventsandtheir duration across filter strength is similar tofindingsofbinocularrivalryinobserverswithpoorbinocularity (e.g., amblyopia; De Belsunce &Sireteanu, 1991), and corroborate previousfindingsthatusedsimilarmethodology(LeonardsandSireteanu, 1993).Additionally, these findingsclarify the influence of the ND filter on thebinocular summation of monocular signals thatdiffer in luminance. It is thought that binocularrivalryisdriven,inpart,byinterocularcompetitionwhereby one eye will temporarily exert greatersuppressionontheother,resultingititsperceptual

dominance (Nichols & Wilson, 2009; Wilson,2003). As the suppressive signals from thedominanteyesubside(duetoadaptation;Wilson,2003,2007),theothereyebeginstoexertalargersuppressivesignalandbecomesdominant,andthisprocess repeats until the stimuli are removed orcan be binocularly fused. We show here thatreducing the luminance input to one eye (whilemaintaining contrast) alters the oscillations inperceptual dominance observed in rivalry as thefilteredeye’ssignalbecomestooweaktoexertanymeaningful influence on the responses of theunfiltered eye. The imbalance of interocularsuppression from decreased illumination thusseems a likely candidate as a mechanism thatgeneratesthechangesinSSVEPamplitude.Thatis,theamountofsuppressionreceivedbythefilteredeye from the unfiltered eye in rivalry is directlyproportional to the attenuation of signal input, afinding congruent with our SSVEP results andmodel.

Figure7.AStimulipresentedtoobserversintherivalrytask.BProportionofdominanceeventsacrossfilterstrengths.Proportion scoreshavebeen log transformed, and thusa ratioof1 (nodifference in thenumberofdominanceeventsexperiencedbybotheyes)isequaltoavalueof0.Errorbarsrepresent+/-1standarderrorofthemean.CDominancedurationhistogramsfordominanceeventsinthefiltered(coloured)andunfiltered(gray)eyeforallNDfilterconditions.Eventdurationswerecollapsedacrossallobservers(N=9)tomakethehistograms.ThedurationofdominanceeventsinthefilteredeyedecreasedinproportiontothestrengthoftheNDfilter,leadingtoaleftwardshiftinthedistribution.

Perceptual Dominance Duration Distributions

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7! Discussion

Animbalanceinluminancebetweentheeyeshasadetrimentaleffectonpsychophysicalperformanceforaseriesofbinocular tasks(Bakeretal.,2008;Changetal.,2006;Gilchrist&Pardhan,1987;Zhouet al., 2013), which is related to the decreasedamplitudeandslowedonsetofresponsesinearlyvisual pathways under reduced illumination(Heravian-Shandiz et al., 1991; Katsumi et al.,1986;Spafford&Cotnam,1989;Wilson&Anstis,1969). Interestingly, a dichoptic decrement inluminanceonlyimpactsneuralresponsestostimulipresented to the filtered eye alone (i.e.,monocular), while responses to binocularlypresented stimuli suffer little from theimpoverished input from the filtered eye. Theunalteredresponsestobinocularlyviewedstimuliare thought to represent the influence ofinterocular interactions, which suppress thedelayedandattenuatedsignal from thedarkenedeye.Wetestedthisproposedarchitecture,whichislikethatdefinedbyMeeseetal.(2006),withSSVEPand psychophysical data measured whilstobserversworeNDfiltersofvaryingtransmittancebefore their dominant eye. We find that placingbiophysicallyplausibletemporalfilterspriortothefirst contrast gain control stage is sufficient toaccount for the attenuation and lag generated bytheNDfilter.Our study replicates earlier findings that thedarkening of stimuli with progressively strongerNDfilters leadstoadecreaseinSSVEPamplitudeand lag in the SSVEP phase when stimuli arepresented monocularly (Heravian-Shandiz et al.,1991; Spafford and Cotnam, 1989). SSVEPamplitudesdecreasedasfilterstrengthincreased,reachingnoise levelsata filterstrengthof1.8ND,comparable to amplitudes measured from otherstudies with filter strengths that exceed 1.2ND(previousstudiesuseda1.0anda2.6NDfilterandwethusestimatethemagnitudeoftheireffectsatourNDfilterlevels;Heravian-Shandizetal.,1991;Spafford&Cotnam,1989).Responselatencyinthefilteredeye increasedaccordingto filterstrength,generating progressively greater asynchroniesbetween the response latency of the filtered andunfiltered eyes. The increase in response latencyrecordedherewasgreaterthanthoseofpreviousreports, which have typically found delays ofapproximately 35ms for ND filter strengths of1.5ND(Heravian-Shandizetal.,1991;SpaffordandCotnam,1989).Whileresponse latencymeasured

with steady-state measures are generally greaterthan those measured with ERPs (Strasburger,1987; Vialatte et al., 2010), one other study hasestimated response latency from the phasecomponentofsteady-states(e.g.,SSVERinMEG)of38mswitha1.5ND filter (Chadnovaet al., 2018).However,methodologicaldifferencesincludingthetype of stimulus (sinusoidal gratings VS noise),absolute(mean)luminance,andstimuluscontrast(96%VS32%) canaccount for thedifferences infindings between studies. Importantly, previousstudiesfound,aswedid,nochangeintheresponselatency in binocular viewing conditions, whichsuggestthisviewingconditionisnotaffectedbythetemporal asynchronygeneratedwithanND filter(GilchristandPardhan,1987;Heravian-Shandizetal.,1991;SpaffordandCotnam,1989).We do observe a small decrease in SSVEPamplitudes that levelled-off at a filter strength of1.2ND in our binocular viewing condition. Whilethiseffectwasnotstatisticallysignificant,thesmalldecrease is congruent with previous reports of amild drop in neural response amplitude tobinocularlyviewedstimuliwhentheluminanceinone eye is decreased (Heravian-Shandiz et al.,1991; Spafford and Cotnam, 1989). These effectsmay be attributed to a slight disruption inbinocular summation from the attenuated andasynchronous input fromthe filteredeye. Indeed,binocular contrast sensitivity was evidentlyaffectedbythemonoculardecrease in luminance,which impeded binocular summation. That said,the decrease in SSVEP amplitude for binocularlyviewedstimuliwassignificantlymilderthanthatofbinocular summation. This is to be expected asbinocular summation is most evident whenmeasuredatcontrastdetectionthresholdwhileourSSVEP study presented sinusoidal gratings set at96%contrast(Meeseetal.,2006;MeeseandBaker,2011). It is also important to caution any directinterpretationbetweenneuralandpsychophysicalresponses: SSVEP amplitude can be highlycorrelated with observer percept (Norcia et al.,2015),butarebynomeansadirectrepresentationof percept (Timora and Budd, 2013). Multiplefactors that contribute to an observers’ contrastdetection thresholds that are not necessarilymeasurable with SSVEPs (e.g., decision criteria).Still,itislikelythesummationofmonocularsignalswillbeimpededbyadifferenceinluminanceevenwhen stimuli are presented well above contrastdetection thresholds, albeit to a milder extent(Meeseetal.,2006;MeeseandBaker,2011).



We postulated that a mechanism that maintainsnormal signal transmission under our binocularviewingconditionscanbedescribedbyastandardbinocular summation model that adaptivelysuppresses the delayed and attenuated signal viainterocularsuppressiveterms(Bakeretal.,2008;Meeseetal.,2006),andfoundthismodeldescribedthe effects of an ND filter on the neural andpsychophysical data well. The only additionbrought to this model architecture werebiophysicallyplausibletemporalfilterspriortothemonocular contrast gain control stage to fit thetime sensitive SSVEPdata. These temporal filtersadjusted the magnitude of input for a given NDfilter strength according to a set of biophysicallyrelevant parameters defined by Swanson et al.(1987) for different illumination conditions. Themodel generated normal signal transmissionregardlessofNDfilterstrengthwhenstimuliwereviewed binocularly as the faster onset of the nofilter temporal filter ensured it took precedenceovertheslowerfiltersoftheNDconditionswhenthe inputs frombotheyeswere linearlysummed.Thisadjustmenttoourmodelisatemporalvariantof an attenuation parameter that decreases thevalueoftheinputtooneeye,whileleavingallotherproperties of the binocular summation modelintact(Bakeretal.,2008).Responseattenuationisknown todescribevariouspsychophysicaleffectsin observers with poor binocularity, includingdichoptic masking and binocular summation(Bakeretal.,2008,2007b).Here,wedemonstratehow to extend response attenuation to becometime sensitive, and further, showed that normalinterocular interactions paired with responseattenuation are sufficient to account for thestability of response latencies under binocularviewingbyadaptivelysuppressingtheattenuatedanddelayedresponsesfromthefilteredeye(Bakeret al., 2007b; Sengpiel et al., 1995; Zhou et al.,2013).Thatsaid,ourmodellingapproachdoesnotpreclude the use of additional or weightedsuppressiveterms(Bakeretal.,2008;Huangetal.,2011; Zhou et al., 2013), the inclusion of othertemporal filters between the monocular andbinocular summation stages (Cunningham et al.,2017),oranyincrementsinadditiveinternalnoisefromareductioninluminance(Lietal.,2015;Pelli,1990).However,theabilityofourmodeltomirrortheresponsepatternsmeasuredwithtwodifferentparadigms(EEGandpsychophysics)suggestsit isunnecessarytoincludeanyadditionalparameterstoimprovemodelfit.Itmaybeoffutureinteresttoverify how the different approaches to the

combination of monocular responses fare incomparisontothemodeldefinedhere.

7.1Conclusion

The amplitude and onset of neural responses tovisuallypresentedstimuliissubjecttoilluminance:underlowluminanceconditions,neuralresponsesshow increased lag and decreased amplitudeproportionaltothedecrementinluminancetotheeye (Gilchrist and Pardhan, 1987; Heravian-Shandizetal.,1991;HeronandDutton,1989;Hessetal.,1980;MorganandThompson,1975;Spaffordand Cotnam, 1989). If stimuli are presentedbinocularly,theimpactonneuralresponsesismild:responseamplitudemayshowasmalldecrement,while response phase will remain mostlyunchanged relative to their baseline (no filter)counterparts.Whiletheeffectsofanimbalanceinluminance between both eyes has been well-described with psychophysical andneurophysiologicalmeasures,lessisknownaboutthe underlying mechanism responsible for theseeffects.Wepostulate that a binocular summationmodel (Meese et al., 2006), which linearlycombines the normalized input from each eye(with interocular suppression) prior to a secondnormalization stage, would be able to maintainnormal signal transmission under binocularviewing when monocular responses areasynchronousanddiffer inamplitude.Ourmodelwas able to fit both our neural (SSVEPs) andpsychophysical data well, indicating that simpleresponse attenuation is sufficient to generate themonocular and binocular response patterns thatoccur under different monocular illuminationconditions.Ourfindingsmayofferinsightonfutureclinicalstudiesthatmeasurebinocularfunctioninindividuals with poor binocularity. That is, ifattenuation alone contributes to monoculardeficits (as observed here), then ND filters canserve as an adequate simulation tool to replicatethe visual deficits in individuals with poorbinocularity (e.g., amblyopia; Harrad et al., 1996;Sengpiel, 2014). This has already been proposedwith psychophysical findings (see Baker et al.,2008), and it would be interesting to conduct asimilarstudytooursinasampleofindividualswithamblyopia. This could serve to 1) verify whetherthey resemble our normal observers wearing anNDfilterbeforetheirdominanteye;and2)whetherplacinganNDfilterinfrontoftheirfellowfixingeyeof amblyopes could equate the amplitude andresponse latency between the eyes, similar topreviouspsychophysicalfindings(DeBelsunceandSireteanu,1991).



8Funding

This work was supported in part by a WellcomeTrust (ref:105624)grant, through theCentre forChronic Diseases and Disorders (C2D2) at theUniversityofYork,awardedtoDHB.

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binocular vision adaptively suppresses delayed monocular...

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