Cross-orientation suppression in human visual cortex

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Cross-orientation suppression in human visual cortex
  Cross-orientation suppression in human visual cortex Gijs Joost Brouwer and David J. Heeger  Department of Psychology and Center for Neural Science, New York University, New York, New York  Submitted 13 June 2011; accepted in final form 17 July 2011 Brouwer GJ, Heeger DJ. Cross-orientation suppression in humanvisual cortex. J Neurophysiol 106: 2108–2119, 2011. First publishedJuly 20, 2011; doi:10.1152/jn.00540.2011.—Cross-orientation sup-pression was measured in human primary visual cortex (V1) to test thenormalization model. Subjects viewed vertical target gratings (of varying contrasts) with or without a superimposed horizontal mask grating (fixed contrast). We used functional magnetic resonanceimaging (fMRI) to measure the activity in each of several hypotheticalchannels (corresponding to subpopulations of neurons) with differentorientation tunings and fit these orientation-selective responses withthe normalization model. For the V1 channel maximally tuned to thetarget orientation, responses increased with target contrast but weresuppressed when the horizontal mask was added, evident as a shift inthe contrast gain of this channel’s responses. For the channel maxi-mally tuned to the mask orientation, a constant baseline response wasevoked for all target contrasts when the mask was absent; responsesdecreased with increasing target contrast when the mask was present.The normalization model provided a good fit to the contrast-responsefunctions with and without the mask. In a control experiment, the tar-get and mask presentations were temporally interleaved, and we foundno shift in contrast gain, i.e., no evidence for suppression. We con-clude that the normalization model can explain cross-orientation sup-pression in human visual cortex. The approach adopted here can beapplied broadly to infer, simultaneously, the responses of severalsubpopulations of neurons in the human brain that span particularstimulus or feature spaces, and characterize their interactions. Inaddition, it allows us to investigate how stimuli are represented by theinferred activity of entire neural populations.functional magnetic resonance imaging; vision; contrast suppression;forward model; primary visual cortex NEURONS IN PRIMARY VISUAL CORTEX (V1) exhibit cross-orienta-tion suppression: a grating orthogonal to a neuron’s preferredorientation (mask) suppresses the response to a simultaneouslypresented grating at the neuron’s preferred orientation (target)(Carandini et al. 1997; DeAngelis et al. 1992; Geisler andAlbrecht 1992; Morrone et al. 1982). Psychophysically, thisleads to impairment in the detection of the target grating, aphenomenon known as cross-orientation masking (Foley1994). The suppression in neural activity is best characterizedas a shift in the contrast gain of the neuron’s response and canbe accurately captured by a model based on contrast normal-ization. This normalization model (Heeger 1992) encompassesa linear receptive field, soft-thresholding, and divisive suppres-sion. The divisive signal increases with the overall contrast inthe stimulus across all orientations and suppresses (or normal-izes) the activity produced by the grating of the neuron’spreferred orientation. The normalization model has been pro-posed to explain stimulus-evoked responses in various corticalareas including V1 (Carandini and Heeger 1994; Carandini etal. 1997; Heeger 1992), MT (Rust et al. 2006; Simoncelli andHeeger 1998), and inferotemporal cortex (Zoccolan et al.2009), multisensory integration in MST (Ohshiro et al. 2011),the representation of value in LIP (Louie and Glimcher 2010),olfactory processing in Drosophila antennal lobe (Olsen et al.2010), and modulatory effects of attention on visual corticalneurons (Reynolds and Chelazzi 2004; Reynolds and Heeger2009). Similarly, the normalization model accurately predictsthe activity of large populations of neurons in cat primaryvisual cortex (measured with electrode arrays) and visuallyevoked potentials in human subjects (Busse et al. 2009).Measuring the responses of distinct subpopulations of neu-rons (e.g., different orientation-selective channels) in the hu-man brain poses a serious challenge. Even though functionalmagnetic resonance imaging (fMRI) allows us to noninva-sively measure human brain activity, each voxel in visualcortex contains a large number of orientation-selective neu-rons, most likely encompassing the full range of possibleorientations, and the voxel’s response amplitudes reflect thepooled activity of all these neurons. Consequently, it has beendifficult to test the normalization model in humans with fMRI,although some progress has been made (Busse et al. 2009;Moradi and Heeger 2009).In the present study, we employed a forward modelingtechnique (Brouwer and Heeger 2009; Kay et al. 2008) totransform voxel responses to orientation-selective channel re-sponses. The analysis relied on the well-established findingthat there are slight biases in orientation preferences acrossvoxels (Freeman et al. 2011; Haynes and Rees 2005a; Kami-tani and Tong 2005). This allowed us to measure cross-orientation suppression and demonstrate the validity of thenormalization model in human visual cortex. MATERIALS AND METHODS Observers and scanning sessions. Four healthy observers betweenthe ages of 24 and 35 yr participated in this study. Observers providedwritten informed consent. Experimental procedures were in compli-ance with the safety guidelines for MRI research and were approvedby the University Committee on Activities Involving Human Subjectsat New York University. Observers had normal or corrected-to-normal vision.Each observer participated in one or two experimental sessions of the weight estimation experiment (see below), consisting of 8–10 runseach, one or two experimental sessions of the main cross-orientationexperiment, and one or two experimental sessions of the controlexperiment (see below), with sessions of each experiment consistingof 8 runs each. Observers also participated in a retinotopic mappingsession and a session in which a high-resolution anatomical volumewas acquired.The weight estimation experiment, the main contrast suppressionexperiment, and the control experiment were performed in separatesessions. We would have preferred to acquire all the data in onescanning session, but the combined number of different conditions Address for reprint requests and other correspondence: G. J. Brouwer, Dept.of Psychology and Center for Neural Science, New York Univ., New York,NY 10003 (e-mail:  J Neurophysiol 106: 2108–2119, 2011.First published July 20, 2011; doi:10.1152/jn.00540.2011.2108 0022-3077/11 Copyright © 2011 the American Physiological Society   onN ov  em b  er 1 1  ,2  0 1 1  j  n. ph  y  s i   ol   o g y . or  gD ownl   o a d  e d f  r  om   between experiments (26) was too high to robustly estimate responseamplitudes for all of these conditions at once. Therefore, we opted todedicate each session to one experiment only, so that the responseamplitudes could be estimated robustly. This does require coregistra-tion of the data acquired in different sessions to align the same voxelsfrom session to session. However, imperfections in the registrationacross scanning sessions were not problematic. The orientation biasesin each voxel reflect a coarse-scale bias for radial orientation acrossthe retinotopic map, not the fine-scale columnar architecture fororientation (Freeman et al. 2011). Consequently, neighboring voxelshave a very similar orientation bias, i.e., very similar channelweightings. Visual stimulus presentation. Visual stimuli were presented with anLCD projector (Eiki LC-XG100; Eiki, Rancho Santa Margarita, CA)with a pixel resolution of 1,024  768 and a 60-Hz refresh rate.Subjects viewed the image from the LCD projector on a rear projec-tion screen placed inside the bore of the magnet at a distance of 57 cm,yielding a field of view of 32  20°. The monitor was calibrated byusing a spectroradiometer (SpectraColorimeter PR650; Photo Re-search, Chatsworth, CA) to achieve a linear gamma.  MRI acquisition. MRI data were acquired with a 3-T, head-onlyMRI scanner (Allegra; Siemens, Erlangen, Germany) using a headcoil (NM-011; NOVA Medical, Wakefield, MA) for transmitting andan eight-channel phased-array surface coil (NMSC-071; NOVA Med-ical) for receiving. Functional scans were acquired with gradient-recalled echo-planar imaging to measure blood oxygen level-depen-dent (BOLD) changes in image intensity (Ogawa et al. 1990). Func-tional imaging was conducted with 24 slices oriented perpendicular tothe calcarine sulcus and positioned with the most posterior slice at theoccipital pole (repetition time, 1.5 s; echo time, 30 ms; flip angle, 75°;2  2  2.5 mm; 64  64 grid size). A T1-weighted magnetization-prepared rapid gradient echo (MPRAGE, 1  1  2.5 mm) anatom-ical volume was acquired in each scanning session with the same sliceprescriptions as the functional images. This anatomical volume wasaligned with a robust image registration algorithm (Nestares andHeeger 2000) to a high-resolution anatomical volume. The high-resolution anatomical volume, acquired in a separate session, was theaverage of several MPRAGE scans (1  1  1 mm) that were alignedand averaged and was used not only for registration across scanningsessions but also for gray matter segmentation and cortical flattening(see below).  Defining visual cortical areas. Primary visual cortex was definedby standard retinotopic mapping methods (Engel et al. 1994, 1997;Larsson and Heeger 2006; Sereno et al. 1995). Visual area boundarieswere drawn by hand on the flat maps, following published conven-tions (Larsson and Heeger 2006), and the corresponding gray mattercoordinates were recorded. Stimuli and experimental protocols. Stimuli were contrast-revers-ing sinusoidal gratings (spatial frequency: 1 cycle/° of visual angle;temporal frequency: 1.33 cycles/s), within an annular aperture (innerradius: 0.5° of visual angle; outer radius: 8° of visual angle) atdifferent orientations (weight estimation experiment) and/or differentcontrasts (cross-orientation suppression and control experiments). Themean luminance of the stimulus and background was 526 cd/m 2 . Atmaximum contrast, the minimum luminance of the stimulus was 31cd/m 2 and the maximum luminance 1,083 cd/m 2 . In the weightestimation experiment (Fig. 1  A ), we presented stimuli at maximumcontrast, with six different possible orientations (0°, 30°, 60°, 90°,120°, and 150°). In the cross-orientation suppression experiment (Fig.1  B ), we presented a vertical (0°) target grating at five differentcontrasts (1.56%, 3.125%, 6.25%, 12.5%, and 50%) either in isolation(target-only condition) or superimposed with a horizontal (90°) mask grating of a constant contrast of 50% (target  mask condition). Size,extent, and spatial and temporal frequencies of the stimuli wereidentical to those in the weight estimation experiment. In the controlexperiment, we used identical gratings; however, the target and mask were temporally interleaved: the target grating modulated from zerocontrast to the maximum contrast and back to zero contrast, followedby the mask grating, which modulated from zero contrast to themaximum contrast and back to zero contrast. Two of these cyclesmade up each stimulus presentation. In addition, we doubled thecontrasts of the target stimuli (3.125%, 6.25%, 25%, and 100%) andthe mask stimulus (100%) to compensate for the 50% reduction induty cycle compared with the cross-orientation suppression experi-ment.Stimuli were presented for 1.5 s in randomized order, interleavedwith interstimulus intervals (ISIs) that ranged from 3 to 6 s, in stepsof 1.5 s. In the weight estimation runs, all six possible orientationswere presented eight times in each run, along with eight blank trials.This created a total of 56 trials per run (including blank trials), withone run lasting 5 min and 42 s. In the cross-orientation suppressionand control experiments, all 10 different stimuli (5 different contrasts,target-only/target  mask condition) were presented 6 times in eachrun, along with 6 blank trials. This created a total of 66 trials per run(including blank trials), with one run lasting 6 min and 42 s.Observers performed a two-back detection task continuouslythroughout each run to maintain a consistent behavioral state and toencourage stable fixation. A sequence of digits (0 to 9) was displayedat fixation (each appearing for 400 ms). The observer’s task was toindicate, by means of a button press, whether the current digitmatched that from two steps earlier. We have used this or a similarprotocol in previous fMRI experiments and have found that themeasured fMRI responses are more reliable under these conditions,even though the subjects’ attention is diverted away from the targetstimuli in the periphery. Without any attentional control, or if subjectsare attending the peripheral/parafoveal target stimuli, we (and others) Fig. 1. Stimulus and experimental protocol. Stimuli were contrast-reversingsinusoidal gratings, within a annular aperture. A : in the weight estimationexperiment, stimuli were full-contrast gratings, with 6 different orientations.ISI, interstimulus interval. B : in the cross-orientation suppression experiment,stimuli were vertical target gratings with different contrasts either in isolation(target-only condition) or superimposed with a high-contrast, horizontal, mask grating (target  mask condition). In the control experiment (not shown) weused identical gratings, but the target and mask were temporally interleavedand doubled in contrast.2109CROSS-ORIENTATION SUPPRESSION IN HUMAN VISUAL CORTEX  J Neurophysiol • VOL 106 • NOVEMBER 2011 •   onN ov  em b  er 1 1  ,2  0 1 1  j  n. ph  y  s i   ol   o g y . or  gD ownl   o a d  e d f  r  om   have reported large and highly variable (trial to trial) attentionaleffects in visual cortex (Gandhi et al. 1999). Diverting attention awayfrom the target stimuli yields a measure of the stimulus-evokedresponses that is not confounded with such attentional modulation.Moreover, the single-unit and multiunit electrophysiological measure-ments of cross-orientation suppression and normalization have mostlybeen performed with anesthetized animals, i.e., without attending thetarget stimuli. Diverting attention to fixation allowed us to compareour results with these above-mentioned studies.  Response time courses and response amplitudes. fMRI data werepreprocessed with standard procedures. The first four images of eachrun were discarded to allow the longitudinal magnetization to reachsteady state. We compensated for head movements within and acrossruns with a robust motion estimation algorithm (Nestares and Heeger2000), divided the time series of each voxel by its mean imageintensity to convert to percentage signal change and compensate fordistance from the RF coil, and linearly detrended and high-passfiltered the resulting time series with a cutoff frequency of 0.01 Hz toremove low-frequency drift. A V1 region of interest (ROI) wasdefined, separately for each observer, with retinotopic mapping pro-cedures (see above). The aperture for the stimuli in the experimentsreported in this study was identical to the aperture of the checkerboardstimuli used during retinotopic mapping, ensuring that the V1 ROIcontained only voxels to which the stimulus was visible. The hemo-dynamic impulse response function (HIRF) for the V1 ROI wasestimated with deconvolution (Dale 1999) using the same procedurethat we have described in detail previously (Brouwer and Heeger2009).The response amplitudes for each trial type (contrast-orientationcombination) were computed separately for each voxel in the V1 ROIand separately for each run by linear regression. A regression matrixwas constructed for the ROI by convolving the ROI-specific HIRFand its numerical derivative with binary time courses corresponding tothe onsets of each trial type (with 1s at each stimulus onset and 0selsewhere). For the weight estimation experiment, this resulted in aregression matrix with 12 columns: 6 columns for the HIRF con-volved with each of the 6 stimulus onsets and 6 columns for theHIRF-derivative convolved with each of the 6 stimulus onsets. For thecross-orientation suppression and control experiments, the regressionmatrix had 20 columns: 10 columns for the HIRF convolved with eachof the 10 stimulus onsets (5 contrasts, with or without the mask) and10 columns for the HIRF-derivative convolved with each of the 10stimulus onsets. Each column of the regression matrix was linearlydetrended and high-pass filtered, identically to the preprocessing of the fMRI measurements. Response amplitudes were estimated bymultiplying the pseudoinverse of this regression matrix with themeasured (and preprocessed) fMRI response time courses. The values(beta weights) obtained for the derivative regressors were discardedafter response amplitudes were estimated (Brouwer and Heeger 2009).We included the HIRF-derivative in the regression, even though theassociated beta weights were discarded, because the HIRF of anindividual voxel may have differed from the mean HIRF of the V1ROI. The HIRF and its derivative are not mutually orthogonal, soincluding the derivative in the regression accounted for some of thevariance in the measured response time courses and affected the res-ponse amplitudes associated with the HIRF. The variance of theestimated response amplitudes across runs was indeed smaller withthe derivative included than without it. We thus obtained, for eachvoxel and each run, one response amplitude measurement for each of the different trial types (6 orientations or 10 combinations of contrast  condition). Voxel selection. To maximize the signal-to-noise ratio in thecross-orientation suppression and control experiments, we selectedvoxels that showed the highest differential responses between orien-tations (Fig. 2  A ). Specifically, we computed the ANOVA F  -statistic of response amplitudes in the weight estimation experiment across ori-entations for each voxel. Voxels were included whose F  -statistic wasabove the median F  -statistic of all voxels in the V1 ROI, selecting50% of the srcinal voxels for the subsequent analysis of the re-sponses in the cross-orientation suppression and control experiments.The median split was arbitrary and was used solely to remove noisyvoxels. A range of  F  -statistic thresholds (25th—75th percentile)yielded similar results and supported the same conclusions.  Baseline removal. Before the channel responses were computed, abaseline was removed from each voxel’s response, separately for eachrun, in each scanning session. Specifically, let v be the number of voxels and c the number of conditions (e.g., orientations/contrasts),giving us, for each run, a matrix of estimated response amplitudes B of size v  c . For each B , we computed the mean voxel responsesacross all stimulus conditions, yielding a vector m of mean responseamplitudes of length v (1 per voxel). This vector was normalized to aunit vector and removed by linear projection from the responses to each Fig. 2. A : voxel selection. Distribution of  F  -statistic values taken from V1 of 1representative subject. The F  -statistic quantifies how well a single voxel differen-tiates between stimulus orientations: a voxel with a low F  -statistic ( left  ) shows nosignificant bias for orientation, while a voxel with a high F  -statistic ( right  ) showsa clear (and significant) tuning, centered on 60°. fMRI, functional magneticresonance imaging. B : orientation decoding with the forward model. The accuracyof orientation decoding using the forward model is plotted against the accuracyusing a conventional classifier. Each data point represents a scanning session. Theforward model reduced the high-dimensional (no. of voxels) voxel space to alow-dimensional (no. of channels  6) channel space. This dimensionality reduc-tion did not result in a considerable loss of information. The decoding accuracieswere nearly the same, but the conventional classifier utilized all the information inthe full, high-dimensional voxel space. Classification was performed with a 8-waymaximum likelihood classifier, implemented by the Matlab (Mathworks) function‘classify’ with the option ‘diaglinear’.2110 CROSS-ORIENTATION SUPPRESSION IN HUMAN VISUAL CORTEX  J Neurophysiol • VOL 106 • NOVEMBER 2011 •   onN ov  em b  er 1 1  ,2  0 1 1  j  n. ph  y  s i   ol   o g y . or  gD ownl   o a d  e d f  r  om   stimulus condition: B  B  m ( m T B ). The baseline removal was doneas an additional preprocessing step before transforming the voxel re-sponses to the channel responses (described next); this analysis step wasnot performed when computing the mean responses across voxels. Forward model. Following our previous work on color vision(Brouwer and Heeger 2009), we used a forward model of orientationtuning to separate the voxel responses into a smaller number of channel responses, each tuned to a different orientation. The forwardmodel assumed that each voxel contained a large number of orienta-tion-selective neurons, each tuned to a different orientation. Wecharacterized the orientation selectivity of each neuron as a weightedsum of six hypothetical channels, each with an idealized orientationtuning curve (or basis function) such that the transformation fromorientation to channel outputs was one-to-one and invertible. Theshape of the tuning curves was selected (as described below) so thatthe response tuning of any one neuron could be expressed as aweighted sum of the six basis functions and these basis functionswould closely resemble measured neural tuning curves. We furtherassumed that the response of a voxel was proportional to the summedresponses of all the neurons in that voxel. This assumption is justifiedby the observation that the residual hemodynamic responses havebeen shown to be tightly linked with spiking activity, after removingthe baseline response component (see DISCUSSION ). The underlyingorientation tuning curve of each neuron was presumed to be a propertyof that neuron, such that it did not depend on the stimulus (the neuron’sresponse was presumed to depend on the stimulus, but the under-lying tuning curve was presumed to be independent of the stimulus).Hence, the weights on each voxel likewise were presumed to beindependent of the stimulus.Each basis function was a sinusoid raised to the fifth power.Raising to the fifth power made the tuning curves narrower andthereby comparable to physiological findings. A tuning curve with anypossible orientation preference (i.e., intermediate to the 6 basis func-tions) can be expressed exactly as a weighted sum of the six basisfunctions (Freeman and Adelson 1991). We evenly spaced the sixbasis functions along the orientation axis, so that one channel re-sponded maximally to the vertical target stimulus and another channelresponded maximally to the horizontal mask stimulus.In the first stage of the analysis, we used the data from the weightestimation experiment to estimate the weights on the six hypotheticalchannels separately for each voxel. With these weights in hand, thesecond stage of analysis computed the channel outputs associated withthe spatially distributed pattern of activity across voxels evoked by thestimuli in the cross-orientation suppression and control experiments.This allowed us to transform the voxel responses to the channelresponses, each tuned to a different orientation. Let k  be the numberof channels, m the number of voxels, and n the number of repeatedmeasurements (i.e., 6 orientations times the number of runs for theweight estimation experiment). The matrix of estimated responseamplitudes in the weight estimation experiment ( B w , m  n ) wasrelated to the matrix of hypothetical channel outputs ( C w , k   n ) bya weight matrix ( W , m  k  ): B w  WC w ( 1 )The least-squares estimate of the weights was computed with linearregression: W ˆ   B w C wT  C w C wT   1 ( 2 )The channel responses ( C c ) associated with the cross-orientationsuppression and control experiment responses ( B c ) were estimated byusing the weights ( W ˆ  ): C ˆ  c   W ˆ  T W ˆ    1 W ˆ  T B c ( 3 )For these matrices to be invertible, the number of voxels must begreater than the number of channels, and there must be an unevenweighting of the orientation channels in at least a subset of the voxelsso that the voxels exhibit sufficiently different responses to thedifferent orientations (specifically, the space spanned by the voxelresponses must be at least as large as the number of channels). Theserequirements posed no difficulty for our analysis. First, the averagesize of V1 across subjects, at our scanning resolution, was  800voxels, much larger than the number of channels. Second, there arestable biases in the responses of voxels to different orientations,exhibiting a robust, coarse-scale, radial organization (Freeman et al.2011). We combined the intermediate channels (not tuned to eitherhorizontal or vertical) such that responses from the two channelsclosest to the horizontal channel were estimated separately but lateraveraged together to form one single intermediate channel and re-sponses from the two channels closest to the vertical channel wereestimated separately but later averaged into another intermediatechannel. For each main experimental session, the estimated channelresponses were then averaged across runs, separately for each stimu-lus condition, within that session. Finally, we computed the mean andSE of the channel responses across subjects, separately for eachstimulus condition and separately for the cross-orientation suppres-sion and the control experiment. Weight estimation stability and forward model fit. The forwardmodel provided a good fit to the orientation biases in the voxelresponses. We evaluated this in several ways. First, the average r  2 value (explained variance of the fit) for the weight estimation exper-iment was 0.76 across the subjects. This was much larger thanexpected by chance ( P  0.001). Second, we used decoding accuracyto assess the model fit. Within-session accuracy for decoding orien-tation from the voxel responses was around 68%, well above thechance level of 16% ( P  0.001). Decoding accuracies obtained withthe forward model were highly correlated to those obtained with aconventional classifier (Fig. 2  B ). This demonstrates that there waslittle or no information lost by replacing the voxel responses with thechannel responses, i.e., by reducing the high-dimensional voxel datawith the lower-dimensional space of six channels. Third, we foundthat the best-fit weights were stable across scanning sessions ondifferent days (Fig. 3  A ). We used data from one weight estimationsession to calculate the weights and then applied those weights tomeasure how well they fit the data from a second weight estimationsession. This revealed r  2 values (mean 0.54) that were still signifi-cantly larger than expected by chance ( P  0.001). In addition,orientation decoding (using the forward model and estimated weights)was also stable across sessions (Fig. 3  B ). We used data from oneweight estimation session to calculate the weights and then appliedthese weights to decode orientation from a second weight estimationsession. Session-to-session decoding accuracies were  50% on aver-age, much larger than expected by chance ( P  0.001). Finally, the“preferred orientations” (determined using the best-fit weights) of voxels were stable from session to session (Fig. 3 C  ). We computedthe preferred orientation for each voxel as follows. The six channelswere tuned for six different orientations. This provided us with sixunit vectors, of unit length, each pointing to the preferred orientationof one orientation channel in the forward model. We multiplied eachof these vectors with each of the six corresponding estimated weightsand computed the vector sum of the resulting six vectors. The angleof the resulting vector sum was taken to be the “preferred orientation”of that voxel. This calculation was repeated for each voxel in twoseparate sessions. Preferred orientations were highly correlated acrosssessions, for all subjects, significantly higher than what would beexpected by chance ( P  0.01).  Main experiment forward model fit. After estimating the weights,how well did the forward model fit the voxel responses from the mainexperiment and the control experiment? If there was no neuronalinteraction (i.e., suppression) between the vertical and horizontalgratings, a plaid would evoke channel responses that are the sum of the channel responses evoked by the vertical and horizontal gratingsin isolation. Such a scenario would have allowed us to determine the 2111CROSS-ORIENTATION SUPPRESSION IN HUMAN VISUAL CORTEX  J Neurophysiol • VOL 106 • NOVEMBER 2011 •   onN ov  em b  er 1 1  ,2  0 1 1  j  n. ph  y  s i   ol   o g y . or  gD ownl   o a d  e d f  r  om   fit between channel responses computed from the voxel responses andpredicted channel responses. This was not possible, however, becauseof suppression. We therefore used a different approach to determinethe quality of the forward model fit in the main experiment. Thechannel responses were computed by multiplying the voxel responseswith the inverse of the weight matrix (from the weight estimationexperiment). We then computed a set of predicted voxel responses bymultiplying the channel responses with the weights and comparedthem with the measured voxel responses. Specifically, we determinedthe proportion of the variance in the voxel responses that wasaccounted for by the forward model (i.e., r  2 ). The resulting r  2 valueswere then compared with a null distribution of  r  2 values computed byrandomly shuffling the weights between the voxels. We found that the r  2 values for both the main and control experiments (in all subjects)were modest (mean r  2  0.33) but significantly above the 99thpercentile of the null distribution.  Normalization model and fitting procedures. The normalizationmodel (Heeger 1992) was used to fit the channel responses from thecross-orientation suppression experiment and the control experiment.The model for the cross-orientation suppression experiment includedcross-orientation suppression terms. The response of each channel r  i as a function of target and mask contrast was modeled as: r  i  r  max  c t n v i    t   c m n v i    m     c t2  c m2  n    n   b ( 4 )where c t is the target contrast, c m is the mask contrast, v i is the tuningcurve of the i th channel,   t is the orientation of the target grating, and   m is the orientation of the mask grating. For the channel tuned to thetarget orientation, v i (   t )  1 and v i (   m )  0 (the channel did notrespond to gratings orthogonal to its preferred orientation). In thechannel tuned to the orientation of the mask grating, v i (   t )  0 and v i (   m )  1. The intermediate channels are associated with intermedi-ate values for v i (   t ) and v i (   t  ). The model had four parameters,   , n , r  max , and b , determining, respectively, the gain, slope, saturation, andbaseline of the resulting contrast-response functions. For the channelresponses during the control experiment, we used a modified versionof the model without cross-orientation suppression: r  i  r  max  c t n v i    t  c t n    n  c m n v i    m  c m n    n   b ( 5 )Thus in this modified version we weighted the normalizing signalsrcinating from each grating by the contrast energy of that grating,while in the cross-orientation suppression experiment we normalizedthe channel activity by the summed contrast energy of all gratings,regardless of the channel’s sensitivity to those gratings. We fitted thechannel responses simultaneously from both the cross-orientationsuppression and control experiments to all contrasts and both condi-tions (target only, target  mask). We used a single n , r  max , and b , butallowed   to vary between the two experiments. Thus there were fivefree parameters (   main,   control, n , r  max , and b ). In addition, wefitted the models to each experimental data set separately, to deter-mine which version (with or without cross-orientation suppression)was more appropriate for the data from each experiment.Statistical significance of the model fits was determined withcross-validation. We divided the data from each experiment in half.Both models were fitted to the first half of the data. Using the resultingparameters, we created predicted channel responses and computed theamount of variance in the remaining half of the data explained by thepredicted channel responses ( r  2 ). Repeating this procedure a largenumber of times with different (random) subdivisions of the datagenerated distributions of  r  2 values, one distribution for each versionof the model (with and without cross-orientation suppression). Takingthe ratio between these two distributions generated a new distributionfor which we determined the median and 5th and 95th percentiles. If the r  2 values were not statistically different, the distribution of theirratios would have been centered on 1, with the 5th percentile beingsmaller and the 95th percentile being larger than 1. If, for thedistribution of ratios for model A over model B , we found that the 5thpercentile was larger than 1, we concluded that model A provided astatistically better fit to the data than model B . If, on the other hand,the distribution of ratios for model A over model B yielded a 95thpercentile smaller than 1, we concluded that model B provided astatistically better fit to the data than model A . Fig. 3. Stability of weight estimation across sessions. A : estimating the weights in one session and then applying these weights to fit the data of a secondsession revealed r  2 values significantly higher than chance: the mean r  2 value was 0.54, many standard deviations away from the null distribution of  r  2 values. The null distribution was obtained by shuffling the weights between the voxels. B : accuracy of the forward model in decoding orientation in onesession, using weights estimated from a different session. Decoding accuracy was significantly higher than expected by chance: the mean accuracy of 0.56was in the 99.75th percentile of the null distribution. The null distribution was obtained by shuffling the weights between the voxels. C  : session-to-sessioncomparison of the preferred orientation. Each data point represents a voxel. The preferred orientation (a continuous measure) of each voxel was computedby using the response amplitudes to each stimulus orientation in the weight estimation experiment. Points cluster around the diagonal, indicating that thepreferred orientations of most voxels were stable between sessions. The size of each point represents r  2 , the proportion of the variance in the voxel’sresponse time course that was accounted for by the regression model (i.e., the regression matrix and hemodynamic impulse response function that wasused to estimate the response amplitudes). Voxels with a robust responses to the stimuli (higher r  2 values) tended to have stable weights across sessions(closer to the diagonal).2112 CROSS-ORIENTATION SUPPRESSION IN HUMAN VISUAL CORTEX  J Neurophysiol • VOL 106 • NOVEMBER 2011 •   onN ov  em b  er 1 1  ,2  0 1 1  j  n. ph  y  s i   ol   o g y . or  gD ownl   o a d  e d f  r  om 
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