The effect of stimulus strength on binocular rivalry rate in healthy individuals: Implications for genetic, clinical and individual differences studies

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Binocular rivalry (BR) occurs when conflicting images concurrently presented to corresponding retinal locations of each eye stochastically alternate in perception. Anomalies of BR rate have been examined in a range of clinical psychiatric conditions.
  Contents lists available at ScienceDirect Physiology & Behavior  journal homepage: The e ff  ect of stimulus strength on binocular rivalry rate in healthyindividuals: Implications for genetic, clinical and individual di ff  erencesstudies Phillip C.F. Law a, ⁎ , Steven M. Miller a,b , Trung T. Ngo a,c,d a  Monash Alfred Psychiatry Research Centre, Monash University Central Clinical School and The Alfred Hospital, Melbourne, Australia b  School of Psychological Sciences, Monash University, Melbourne, Australia c Genetic Epidemiology Laboratory, QIMR Berghofer Medical Research Institute, Brisbane, Australia d  Mater Research Institute-UQ, Neurosciences&Cognitive Health Program, Faculty of Medicine, University of Queensland, Brisbane, Australia A R T I C L E I N F O  Keywords: Binocular rivalry rate endophenotypeMixed perceptsStimulus strengthDrift speedAperture sizeIndividual di ff  erencesLevelt A B S T R A C T Binocular rivalry (BR) occurs when con 󿬂 icting images concurrently presented to corresponding retinal locationsof each eye stochastically alternate in perception. Anomalies of BR rate have been examined in a range of clinicalpsychiatric conditions. In particular, slow BR rate has been proposed as an endophenotype for bipolar disorder(BD) to improve power in large-scale genome-wide association studies. Examining the validity of BR rate as a BDendophenotype however requires large-scale datasets ( n  = 1000 s to 10,000 s), a standardized testing protocol,and optimization of stimulus parameters to maximize separation between BD and healthy groups. Such re-quirements are indeed relevant to all clinical psychiatric BR studies. Here we address the issue of stimulusoptimization by examining the e ff  ect of stimulus parameter variation on BR rate and mixed-percept duration(MPD) in healthy individuals. We aimed to identify the stimulus parameters that induced the fastest BR rateswith the least MPD. Employing a repeated-measures within-subjects design, 40 healthy adults completed four BRtasks using orthogonally drifting grating stimuli that varied in drift speed and aperture size. Pairwise compar-isons were performed to determine modulation of BR rate and MPD by these stimulus parameters, and individualvariation of such modulation was also assessed. From amongst the stimulus parameters examined, we found that8 cycles/s drift speed in a 1.5° aperture induced the fastest BR rate without increasing MPD, but that BR rate withthis stimulus con 󿬁 guration was not substantially di ff  erent to BR rate with stimulus parameters we have used inprevious studies (i.e., 4 cycles/s drift speed in a 1.5° aperture). In addition to contributing to stimulus optimi-zation issues, the  󿬁 ndings have implications for Levelt's Proposition IV of binocular rivalry dynamics and in-dividual di ff  erences in such dynamics. 1. Introduction Binocular rivalry (BR) is an intriguing visual phenomenon in whichcon 󿬂 icting images presented to each eye are perceived in alternationrather than being superimposed. For example, simultaneously pre-senting a vertical grating to one eye, and a horizontal grating to theother eye, induces perception of the vertical grating for a few seconds,followed by perception of the horizontal grating for a few seconds, andso on (Fig. 1). BR and other perceptual rivalry types such as ambiguous 󿬁 gures have previously been examined, particularly with respect toalternation rate, in the context of clinical psychiatric disorders from theearly to mid-20th Century (e.g., [14,17,20,21,25,27,37,51,58,74]). Themodern clinical focus on BR emerged with reports from Australia thatBR rate was slow in the heritable psychiatric condition, bipolar disorder(BD), relative to healthy individuals (e.g., [53,68])  —  a  󿬁 nding that hassince been independently replicated in populations from Japan [57],New Zealand [82] and China [87]. Following Pettigrew and Miller's [68] srcinal study on BD, otherclinical psychiatric conditions have been examined including schizo-phrenia and major depression [39,53], autism spectrum conditions[4,26,42,71 – 73], attention de 󿬁 cit hyperactivity disorder (e.g., [3,6]), andgeneralized social anxiety disorder [5]. Although some researchers (e.g.,[82]) have attempted to use the same testing protocol as that of Pettigrewand Miller [68], so that data may be directly compared between clinicalstudies, other researchers have employed di ff  erent test protocols (e.g.,shorter viewing durations, di ff  erent stimulus characteristics, di ff  erent 1 June 2017; Received in revised form 15 August 2017; Accepted 26 August 2017 ⁎ Corresponding author at: Level 4, 607 St Kilda Road, Melbourne, VIC 3004, Australia.  E-mail address: (P.C.F. Law). Physiology & Behavior 181 (2017) 127–136Available online 30 August 20170031-9384/ © 2017 Elsevier Inc. All rights reserved. M R  response options), making comparisons di ffi cult. Such issues becomeparticularly relevant when considering potential applications of BR  󿬁 nd-ings in genetic studies of clinical psychiatric disorders.Pettigrew and Miller [68] and Miller et al. [53] demonstrated high sensitivity and reliability of the BR rate trait in BD. This earlier workwas followed by a large twin study demonstrating high heritability of the trait and con 󿬁 rming its high reliability ([54]; see also [76]). This heritability study supported the srcinal proposal [68] that slow BRcould be used as an endophenotype for BD (reviewed in [59,60]). En-dophenotypes  —  or intermediate phenotypes  —  can enhance power ingene- 󿬁 nding studies of complex psychiatric diseases by using the re-levant quantitative trait to classify a genotype as a ff  ected rather thanmanifestation of the clinical disorder (see [30,31,33,43]). However,such application requires large-scale studies of thousands to tens of thousands of subjects (see [24,36,45,50,86]). Elsewhere we have dis-cussed prospects for an online platform of BR testing to address theselarge sample-size requirements [46]. Such a platform not only facil-itates the collection of very large sample-sizes, but also enables theprospect of standardized BR testing across clinical conditions and re-search centres, for purposes of direct comparison between clinicalstudies.For any such endeavor striving for large-scale, standardized BR testingin clinical conditions, the optimal stimulus parameters also require ex-amination. Changing stimulus parameters can change the signal strengthof the stimulus or its  stimulus strength , which can in turn modulate BR rate.For example, higher contrast, faster drift speed, and brighter luminanceare all considered to induce greater stimulus strength (see below).However, the sensitivity function of stimulus-strength rate modulations isnot always monotonic (e.g., [44]). In the study by Pettigrew and Miller[68], a high-strength stimulus (i.e., orthogonally drifting gratings of highspatial frequency; 8 cycles/°) induced signi 󿬁 cantly slower BR rate in agroup of euthymic subjects with BD relative to healthy controls, with widegroup separation. The  󿬁 nding was independently replicated using thesame high-strength stimulus [82] and using an intermediate-strength sti-mulus [57]. Following Pettigrew and Miller's [68] srcinal study, a sub- sequent study by Miller et al. [53] using a low-strength stimulus (i.e.,stationary gratings of lower spatial frequency; 4 cycles/°) also demon-strated signi 󿬁 cantly slower BR rate in BD than in healthy individuals,though with less evident group separation. Comparing the data in thesetwo studies (i.e., [53,68]) suggested that the greater group separation intheearlierstudymayhavebeenduetothehigh-strengthstimuliproducingafasteraverageBRrateinhealthyindividuals,whileBDsubjectsremainedrobustly slow whether viewing high- or low-strength stimuli. On this in-terpretation, BD subjects would be relatively insensitive to stimulus-re-lated BR rate modulation compared with healthy individuals (discussed in[53]; see also [59]), and therefore viewing of higher-strength stimuli shouldmaximizegroupseparation.However,thiscomparisonbetweenthedata of Miller et al. [53] and Pettigrew and Miller [68] is limited by the fact that control subjects were  di  ff  erent   between the two studies, as werethe BD subjects. What is needed to directly assess the hypothesis that in-dividualswithBDhaverobustlyslowBRrates(i.e.,relativelyinsensitivetostimulus-related BR rate modulation) is varying stimulus strength in the  same  BD and control subjects (i.e., a within-subject design).Here we report a within-subject study in healthy individuals thataims to determine whether viewing higher-strength stimuli  —  usinggrating drift speed as the stimulus strength factor  —  can induce fasterBR. The predominance of drifting gratings over stationary gratings in-creases with drift speed ([83]), suggesting that changing from sta-tionary to drifting stimuli increases stimulus strength (in accordancewith [48]; see below). It is not clear, however, whether the sensitivityfunction for drift speed is non-monotonic and whether gratings driftingat 4 cycles/s as used in previous studies [54,68,82] are the peak of sucha non-monotonic function. Hence 8 cycles/s gratings are also assessedin the current study to examine whether this particular drift speeddrives BR rate faster than 4 cycles/s gratings, or whether the 4 cycles/sgratings represent a ceiling e ff  ect for BR rate. Here we report a com-paratively large within-subject BR dataset of healthy individuals( n  = 40) to directly assess and clarify the e ff  ect of stimulus strength onBR rate.The study protocol also enabled assessment of a secondary aim, i.e.,the e ff  ect of stimulus size on mixed-percept duration (MPD). MPD is thetotal time spent perceiving mixed percepts in a given BR viewingperiod, and provides a measure of the degree of perceptual mixingbetween each eye's presented image. BR rate is derived by dividing thetotal number of perceptual alternations by the total BR viewing period,excluding responses to mixed percepts. As such, reducing an in-dividual's total MPD provides more data on which to base the calcu-lation of BR rate and thus improves accuracy of the BR rate measure.There have been reports that smaller BR stimuli between 0.5° and 2° of visual angle increase exclusive percept visibility ([63]; see also [8,78]), which corresponds to a shorter MPD. The current study thus aimed toexamine whether reducing the size of a BR stimulus from 1.5° [53,54]to 1° or 0.5° of visual angle would produce a shorter MPD. We did notassess stimuli subtending larger than 1.5° so as to avoid inducing alonger MPD. Furthermore, because earlier studies examining the e ff  ectof stimulus size on exclusive visibility used only small samples([8,64,78];  n  = 3 and 4 and 11, respectively), the current study em-ployed a comparatively large dataset ( n  = 40) to clarify the e ff  ect of stimulus size modulation on MPD. However, interpretation of theseMPD data will require caution as the mixed-percept response optionalso included subjects' erroneous responses (see Methods andDiscussion).The current experiment is also relevant to the historical literaturebecause stimulus-related modulation of BR temporal dynamics has beena focus for rivalry researchers since Breese [12] (see also Wade & Ngo,[84]) and especially since the seminal four-proposition framework of BR dynamics by Levelt [48]. Recently reviewed in detail by Brascampet al. [11], these propositions have mostly been examined experimen-tally by assessing contrast-modulated dominance duration (i.e., thetime a percept maintains exclusive dominance). Such experiments in-volve keeping constant the stimulus strength presented to one eye,while manipulating the stimulus strength presented to the other eye(see Levelt's Proposition III discussed in [11]). Relevant to the currentstudy, Levelt's Proposition IV holds that increasing the stimulusstrength  matched between both eyes  should induce a faster BR rate, andthis has indeed been observed using dominance duration as the de-pendent variable and contrast as the stimulus strength factor (e.g.,[2,12,13,19,69]). Moreover, two earlier reports indicated that Fig. 1.  Binocular rivalry. Presenting dissimilar imagessimultaneously  —  such as rightward-drifting verticalgratings and downward-drifting horizontal gratings  —  oneto each eye (i.e., dichoptic presentation), causes eachimage to stochastically alternate in perception. Mixed orpiecemeal percepts (i.e., portions of both eyes' presentedimages are simultaneously visible) occur occasionallyduring the transition between perception of the presentedimages. Arrows adjacent to the presented stimuli denotethe direction of grating drift.  P.C.F. Law et al.  Physiology & Behavior 181 (2017) 127–136 128  increasing stimulus strength matched between both eyes up to a certainlevel  —  where spatial frequency was the stimulus strength factor  — produced more BR alternations in a given observation period, but thenumber of alternations decreased beyond that level [44,64]. There hasalso been mention in the literature, based only on unanalysed data andlimited pilot observations, of greater stimulus strength (using driftspeed) presented to both eyes inducing a faster BR rate [61]. Other thanthese pilot observations however, to our knowledge no study has yetproperly examined Levelt's Proposition IV using drift speed as the sti-mulus strength factor. The experimental protocol of the current studythus enabled direct testing of Levelt's Proposition IV with this stimulusstrength factor, albeit within a restricted range of drift speeds.Finally, compared with typical psychophysics experiments, the rela-tively large sample size in the current study enables, for the  󿬁 rst time,assessment of individual di ff  erences in stimulus-related modulation of BRrate. The issue of individual di ff  erences in psychophysical and visualfunctions has been a topic of resurgent interest and enables new means of probing genetic and environmental in 󿬂 uences on sensory and perceptualsystems, as well as neurobiological and pathophysiological mechanismsunderlying such in 󿬂 uence (e.g., [15,32,40,41,49,65,67,85]). 2. Methods  2.1. Participants Forty naïve healthy adults aged between 20 and 66 years (meanage=34.4 ± 12.7years; 21 males) with normal or corrected-to-normalvision (6/9 or better in both eyes) participated in the study. Written, in-formed consent was obtained in the presence of a witness prior to testingaccording to a protocol approved by the Alfred Human Research EthicsCommittee and Monash University Human ResearchEthics Committee. Theresearch was conducted in accordance with the Declaration of Helsinki.Visual acuity was assessed with a Snellen chart from a distance of 3m.Reduced visual acuity decreases an individual's perceived contrast andspatial frequency of the stimulus and thus reduces BR rate ([22]; see also[35]). Handedness was assessed using the Edinburgh Handedness Inventory[62]. All participants had their medical and psychiatric history screenedusing a brief questionnaire and the Mini International NeuropsychiatricInterview [77] to exclude individuals with a psychiatric disorder (e.g., BD,schizophrenia, major depressive disorder), neurological disorder (e.g., epi-lepsy), brain injury, or visual disorders (e.g., strabismus, amblyopia, colorvision de 󿬁 ciency). Subjects were also screened to exclude individuals with 󿬁 rst-degree relatives diagnosed with a psychiatric disorder.State, trait, and clinical ratings were examined along with psycho-metric measures prior to the testing session for all subjects. Trait andstate anxiety were assessed with the State-Trait Anxiety Inventory(STAI; [79]; mean = 33.50 ± 8.59 and 24.25 ± 8.44, respectively).Depressive state was assessed with the Montgomery-Åsberg DepressionRating Scale (MÅDRS; [55]; mean = 1.48 ± 2.61). Subjective moodwas assessed with a 10-point self-report visual analogue scale (1 =  ‘ theworst you have ever felt ’  to 10 =  ‘ the best you have ever felt ’ ;mean = 7.45 ± 1.24).  2.2. Study protocol Participants abstained from consuming ca ff  einated drinks, tobacco,and alcohol for 4 h prior to testing given their known e ff  ects on BR rate[7,18,28,52,75]. All participants completed BR tasks under the super-vision of an experimenter throughout the testing session to ensure taskcompliance (see Section 2.3). The BR measures reported in the currentstudy were obtained along with eye-movement task measures. The eye-movement tasks were completed separately and counterbalanced withthe BR tasks across participants to avoid potential order e ff  ects. Ana-lyses presented in the current study relate only to the BR data. The eye-movement data providing evidence for no relationship with BR rate arereported elsewhere [47].  2.3. Binocular rivalry task: apparatus and experimental protocol BR stimuli were generated with custom software programmed usingPsychtoolbox-3 [10,66] in conjunction with MATLAB ™  (MathWorksInc., Natick, MA, USA). The speci 󿬁 c square-wave stimuli were greenrightward-drifting vertical and downward-drifting horizontal gratings.The stimuli had a spatial frequency of 5.33 cycles/°, were isoluminantbetween the two eyes, and were presented in a circular aperture on ablack background (stimulus contrast = 0.99). Drift speed was either 4or 8 cycles/s. The luminance of all stimuli (mean = 4.8 cd/m 2 ) and thebackground (0.35 cd/m 2 ) was measured using a LS-100 luminancemeter (Konica Minolta Sensing Americas Inc., Ramsey, NJ, USA)through passive polarizer  󿬁 lters. The four BR stimulus conditions were:(i) 4 cycles/s drift speed in an aperture subtending 1.5° of visual angle;(ii) 8 cycles/s drift speed in an aperture subtending 0.5° of visual angle;(iii) 8 cycles/s drift speed in an aperture subtending 1° of visual angle;and (iv) 8 cycles/s drift speed in an aperture subtending 1.5° of visualangle.Subjects were instructed to blink naturally and record what theyobserved passively (i.e., not to preferentially respond to any of thepercepts or try to in 󿬂 uence their perceptions). Subjects pressed oneraised key (V) on a standard keyboard in response to the left eye'spresented image, and an adjacent raised key (B) in response to the righteye's presented image. A third response option (spacebar) was used toindicate response error or the perception of either mixed (e.g., check-erboard or mosaic image) or unusual percepts (e.g.,  󿬁 lled circle ordouble images). BR testing was conducted in a quiet, dimly illuminatedroom. BR behavioral data collection was run with custom softwaregenerated in MATLAB ™  (MathWorks Inc., Natick, MA, USA) forWindows 7 ™  on the customized PC (see below).After familiarizing subjects with the BR task, the BR testing sessioncomprised  󿬁 ve 7-min blocks (see Fig. 2), each comprising four 100-strials. The blocks were separated by 110-s rest breaks and the trials 30-srest breaks. The  󿬁 rst few minutes of BR viewing have been character-ized by increases in BR rate within individuals [1,16,29,34,35,80].However, BR rates stabilize with longer BR viewing periods [53,54],yielding a more accurate measure of an individual's BR rate. Therefore,the  󿬁 rst block served to adequately stabilize BR rates for the remaining Breaks 1 (stabilization)7minBreaks30s100s12342 minTRIALSBLOCKS 2 2 min 3 2 min 4 2 min 5 Fig. 2.  Binocular rivalry testing protocol. Each blockcomprised 7 min of rivalry viewing across four 100-s trials,with rest breaks interspersed between the blocks and trials(2 min and 30s, respectively). Each of the 40 subjectscompleted all four stimulus conditions (grey blocks). Foursubgroups ( n  = 10) were each run on a di ff  erent stimuluscondition in blocks 1 – 2, followed by the remaining (re-spective) three stimulus conditions in test blocks 3 – 5 incounterbalanced order across subjects within each sub-group. Therefore, each of the 40 participants completed allfour BR stimulus conditions.  P.C.F. Law et al.  Physiology & Behavior 181 (2017) 127–136 129  four test blocks and familiarize the subject with the task to diminish thee ff  ects of any response errors. To avoid potential order e ff  ects, the fourBR stimulus conditions were counterbalanced across four subgroups of subjects ( n  = 10 each). Each subgroup was run on a di ff  erent BR sti-mulus condition for Blocks 1 – 2. For Blocks 3 – 5, participants withineach subgroup completed the remaining (respective) three BR stimulusconditions, which were counterbalanced across participants within thesubgroup. Therefore, each of the 40 participants completed all four BRstimulus conditions.All BR stimuli were dichoptically presented on a specialized 19-inchdual-screen liquid crystal display monitor (True3Di ™ ; SharperTechnology Inc., Palo Alto, CA, USA; 60 Hz frame rate, 1280 × 1024pixel resolution). Each screen was directly behind one of two linearpolarizers oriented at right angles to each other, and a half-silveredmirror (beam-combiner) oriented at a 45° angle was between the po-larizers. To induce BR, con 󿬂 icting images of a BR stimulus were in-dependently and simultaneously presented at corresponding centralpositions on separate screens that projected each image in orthogonalplanes (angles) of polarization. One image is transmitted through thehalf-silvered mirror while the adjacent image is re 󿬂 ected o ff   the mirror,resulting in an interleaved (superimposed) stimulus of two orthogonallypolarized images when naturally viewed (see [46]). Subjects viewed thepolarized stimulus through passive linear polarizer  󿬁 lters at eye levelfrom a distance of 3 m, resulting in the presentation of con 󿬂 ictingimages to corresponding retinal locations of both eyes. Each polarizer 󿬁 lter was tuned to a distinct plane of polarization that enabled theexclusive presentation of one image to one eye while blocking its pre-sentation to the other eye. The result is that simultaneously, the left eyealways viewed vertical gratings and the right eye always viewed hor-izontal gratings. The True3Di ™  monitor used to present BR stimuli wasconnected to a customized PC (Vostro 460 mini-tower; Dell Inc., RoundRock, TX, USA). This PC was  󿬁 tted with a Gigabyte ™  ATI Radeon HD6850 video card, 8GB RAM, and Cooler Master ™  eXtreme Power Plus700 W power supply unit. These modi 󿬁 cations were to enable adequateprocessing capacity by the PC as it was concurrently connected to boththe True3Di ™  monitor for BR stimuli presentation and a 24-inch single-screen liquid crystal display monitor (P2412H; Dell Inc., Round Rock,TX, USA; 60 Hz frame rate, 1280 × 1024 pixel resolution) for dis-playing the trial-based BR data collection protocol.The passive linear polarizer method for dichoptic viewing hasnegligible crosstalk and, when viewed with the head in neutral position,there is minimal ghosting (i.e., the subjective perceptual consequenceof crosstalk, whereby there is faint perception in one eye of the othereye's intended image; see [46]). To ensure BR viewing was not in 󿬂 u-enced by the e ff  ects of ghosting, subjects were instructed to (i) not tiltor rotate their head, and (ii) view the BR stimulus through the centre of the polarizer  󿬁 lters.  2.4. Data analysis Analysis of participants' BR data employed custom software devel-oped in MATLAB ™  (MathWorks Inc., Natick, MA, USA). BR rate wascalculated by dividing the total number of perceptual alternations bythe total time of BR viewing (expressed in Hz), excluding mixed orunusual percepts and erroneous responses (i.e., incorrectly pressed keyresponses) which were indicated by pressing the spacebar. Along withBR rate, MPD was assessed, however MPD is only an approximation of the total time spent perceiving mixed percepts because the spacebarresponse was also used to indicate response error and unusual percepts.Pressing of the spacebar not only initiated onset of a recorded MPDinterval, it was also designated by the data analysis program to dis-regard the immediately previous recorded response to a perceivedimage (in case the spacebar had been pressed to indicate a previouslyerroneous response). Notwithstanding the necessary cautious inter-pretation due to the con 󿬂 ation of MPD with response errors, in a givenobservation period, a relatively short MPD corresponds to a relativelygreater amount of data being collected for calculating BR rate, thusre 󿬂 ecting a more representative and accurate measure of an individual'strue BR rate.Predominance is the prevailing dominance of one image over theother in a given observation period, and was calculated by dividing thetotal time spent perceiving the vertical grating by the total time spentperceiving the horizontal grating (in seconds). The resulting ratio valuewas log-transformed (PR log ) to account for the disproportionate nu-merical representation in predominance (i.e., any value > 1 for oneimage cf. values between 0 and 1 for the other image). As such, wherethere is no perceptual predominance, PR log  equals zero, whereas PR log values less than zero or greater than zero indicate a perceptual pre-dilection towards the horizontal grating or vertical grating, respec-tively. Individuals' BR rate, total MPD, and PR log  were calculated foreach trial. For each individual, the mean BR rate, total MPD, and meanPR log  were calculated for all trials. The stabilization block was excludedfrom analysis. Statistical analyses were performed with PASW Statistics17 and R (version 3.2.5; [70]). 3. Results 3.1. Stimulus-strength modulation of binocular rivalry rate BR rate was compared between the stimulus conditions to examinestimulus-strength modulation e ff  ects. Normality was violated for thedistributions of BR rate (Shapiro-Wilk test;  p  < 0.05). A Friedman testwith BR rate as the dependent variable and stimulus conditions as theindependent variable showed a signi 󿬁 cant di ff  erence in BR rate acrossthe stimulus conditions (  p  = 3.40 × 10 − 10 ). Pairwise comparisons Table 1 Binocular rivalry (BR) rate, mixed-percept duration (MPD) and log-transformed predominance ratio (PR log ) for all stimulus conditions.Median ±  MAD 4 c/s, 1.5° 8 c/s, 1.5° 8 c/s, 1° 8 c/s, 0.5°BR rate (Hz) 0.47 ± 0.12 0.52 ± 0.10 0.48 ± 0.11 0.40 ± 0.11MPD (s) 62.81 ± 41.17 60.23 ± 35.41 71.37 ± 33.46 110.17 ± 49.61PR log  0.09 ± 0.12 0.09 ± 0.17 0.02 ± 0.16 0.11 ± 0.13Mean ±  SD 4 c/s, 1.5° 8 c/s, 1.5° 8 c/s, 1° 8 c/s, 0.5°BR rate (Hz) 0.53 ± 0.22 0.57 ± 0.24 0.54 ± 0.23 0.43 ± 0.16MPD (s) 72.12 ± 53.09 74.34 ± 69.35 87.03 ± 73.98 123.05 ± 72.59PR log  0.08 ± 0.23 0.13 ± 0.28 0.01 ± 0.31 0.14 ± 0.45c/s: cycles/s. °: degrees of visual angle in a circular aperture.  MAD : median absolute deviation.  SD : standard deviation. Hz: hertz. s: seconds.  P.C.F. Law et al.  Physiology & Behavior 181 (2017) 127–136 130  showed that BR rate for a 1.5° aperture stimulus was signi 󿬁 cantly fasterat 8 cycles/s than at 4 cycles/s (  p  = 3.43 × 10 − 3 ; Bonferroni-adjusted α : 0.05/6 Wilcoxon signed rank tests = 8.33 × 10 − 3 ; see Table 1 andFig. 3a). In contrast, BR rate for a 0.5° stimulus was signi 󿬁 cantly slowercompared with 1° and 1.5° stimuli drifting at 8 cycles/s(  p  = 3.70 × 10 − 6 ), and compared with a 1.5° stimulus drifting at4 cycles/s (  p  = 1.32 × 10 − 5 ). There was no signi 󿬁 cant di ff  erence inBR rate between a 1° aperture stimulus drifting at 8 cycles/s and a 1.5°stimulus drifting at 4 or 8 cycles/s (  p ≥ 5.91 × 10 − 2 ). The results forthese comparisons remained non-signi 󿬁 cant at a less conservative  α  of 0.05. 3.2. Individual variation in stimulus-strength modulation of binocular rivalry rate To examine the individual variation in stimulus-strength modula-tion of BR rate, an individual's ratio of BR rates (r-BR) was calculated bydividing BR rate for 8 cycles/s by that for 4 cycles/s (in a 1.5° aperture).The resulting value was log-transformed (r-BR log ) to account for thedisproportionate numerical representation in BR rate, i.e., anyvalue> 1 for one direction of stimulus-strength modulation whereasvalues are between 0 and 1 for the other direction. As such, where thereis no stimulus-strength modulation of an individual's BR rate, r-BR log equals zero, whereas r-BR log  less than zero or greater than zero in-dicates a slower or faster BR rate with faster drift speed, respectively.Increasing drift speed from 4 to 8 cycles/s in a 1.5° aperture was foundto induce a faster BR rate in a majority of individuals (r-BR log  > 0 in70% of subjects; see Fig. 4). However, it is also evident that severalindividuals showed exactly the reverse e ff  ect of a slower BR rate as driftspeed increased (r-BR log  < 0 in 27.5% of subjects), while one in-dividual showed no modulation of BR rate (r-BR log  = 0). 3.3. Covariance of binocular rivalry rate between stimuli Spearman's  ρ  correlations were performed to assess the similarity (orcovariance) of individuals' BR rates between all stimulus conditions. Therewas a pattern of signi 󿬁 cant, high positive correlations in BR rate betweenall stimulus conditions ( ρ  = 0.79 – 0.91,  p ≤ 1.04 × 10 − 9 , one-tailed;Bonferroni-adjusted  α : 0.05/6 Spearman's  ρ  tests = 8.33 × 10 − 3 )  —  in-dicating that individuals' BR rates strongly covaried across the stimulusconditions. In addition, a signi 󿬁 cant high intraclass correlation indicatedlowvariance(orhighclustering)inBR ratewithineach stimulus condition( r   = 0.95,  p  = 8.70 × 10 − 37 ; average measures, two-way mixed model).These  󿬁 ndings indicate that the observed di ff  erences in BR rate betweenthe stimulus conditions can be attributed to the manipulation of stimulusstrength factors. 3.4. Stimulus-strength modulation of mixed-percept duration MPD was compared between the stimulus conditions to examine sti-mulus-strength modulation e ff  ects on this BR measure. Normality wasviolated for the distributions of MPD (Shapiro-Wilk test;  p  < 0.05). AFriedman test with MPD as the dependent variable and stimulus condi-tions as the independent variable showed a signi 󿬁 cant di ff  erence in MPDacross the stimulus conditions (  p  = 8.61 × 10 − 6 ). Pairwise comparisonsshowed that MPD for an 8 cycles/s stimulus was signi 󿬁 cantly shorter in a Fig. 3.  Column scatter plots showing (a) binocular rivalry (BR) rate and (b) mixed-per-cept duration (MPD) for the four stimulus conditions. Each solid black dot on the scatterplots represents an individual data point within the respective stimulus condition. Dashedhorizontal lines denote the group median value (in accordance with non-parametricstatistics) with the numerical value shown above each line. Horizontal brackets above apair of column scatter plots denote a signi 󿬁 cant statistical di ff  erence between the twostimulus conditions for the corresponding BR measure,  p  < 8.33 × 10 − 3 (Bonferroni-adjusted  α  of 0.05/6 Wilcoxon signed rank tests). * denotes a signi 󿬁 cant statistical dif-ference between a particular stimulus condition and all the other stimulus conditions inthe respective scatter plot,  p  < 8.33 × 10 − 3 (Bonferroni-adjusted  α  of 0.05/6 Wilcoxonsigned rank tests). s: seconds. c/s: cycles/s. Stimuli drifting at 8 c/s in a 1.5° apertureproduced the fastest BR rate and the shortest MPD (see Discussion). Fig. 4.  Individual variation in stimulus-strength modulation of binocular rivalry (BR)rate. The log-transformed ratio of BR rates (r-BR log ) is indicated on the ordinate (  y axis ),with each data point of r-BR log  presented in ascending order on the abscissa  (x axis) . r-BR log  is calculated by dividing BR rate for 8 cycles/s by that for 4 cycles/s (in a 1.5°aperture stimulus) and log-transforming the resulting ratio value. A r-BR log  value of zerodenotes no stimulus-strength modulation of BR rate, whereas r-BR log  values less than zeroor greater than zero denote a slower or faster BR rate with greater stimulus strength,respectively. Increasing stimulus strength, through increasing the drift speed from 4 to8 cycles/s in a 1.5° aperture stimulus, produced a faster BR rate (i.e., a r-BR log  > 0;Levelt's Proposition IV) in a majority of healthy individuals ( n  = 28 or 70%). However,several individuals ( n  = 11 or 27.5%) exhibited a reverse e ff  ect, i.e., a slower BR rate asdrift speed increased (i.e., r-BR log  < 0), and one individual showed no modulation of BRrate (r-BR log  = 0).  P.C.F. Law et al.  Physiology & Behavior 181 (2017) 127–136 131
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