Retinal visual processing constrains human ocular following response

Abstract

Ocular following responses (OFRs) are the initial tracking eye movements elicited at ultra-short latency by sudden motion of a textured pattern. We wished to evaluate quantitatively the impact that subcortical stages of visual processing might have on the OFRs. In three experiments we recorded the OFRs of human subjects to brief horizontal motion of 1D vertical sine-wave gratings restricted to an elongated horizontal aperture. Gratings were composed of a variable number of abutting horizontal strips where alternate strips were in counterphase. In one of the experiments we also utilized gratings occupying a variable number of horizontal strips separated vertically by mean-luminance gaps. We modeled retinal center/surround receptive fields as a difference of two 2-D Gaussian functions. When the characteristics of such local filters were selected in accord with the known properties of primate retinal ganglion cells, a single-layer model was capable to quantitatively account for the observed changes in the OFR amplitude for stimuli composed of counterphase strips of different heights (Experiment 1), for a wide range of stimulus contrasts (Experiment 2) and spatial frequencies (Experiment 3). A similar model using oriented filters that resemble cortical simple cells was also able to account for these data. Since similar filters can be constructed from the linear summation of retinal filters, and these filters alone can explain the data, we conclude that retinal processing determines the response to these stimuli. Thus, with appropriately chosen stimuli, OFRs can be used to study visual spatial integration processes as early as in the retina.

1. Introduction

The ocular following response (OFR) is the initial tracking movement of the eyes elicited at ultra-short latency by the motion of a textured pattern (see Miles, 1998 for review). Early work has concentrated on elucidating its role in gaze stabilization (Busettini, Miles & Schwarz, 1991, Gellman, Carl & Miles, 1990, Masson, Busettini, Yang & Miles, 2001, Miles & Kawano, 1986, Miles, Kawano & Optican, 1986). However, over the years the OFR has also emerged as a powerful behavioral probe for studying the early stages of cortical visual motion processing (Kodaka, Sheliga, Fitzgibbon & Miles, 2007, Miles & Sheliga, 2009).

An extensive body of evidence has been accumulated about cortical direction-selective neuronal machinery that mediates the OFR (see Masson & Perrinet, 2012 for review). However, visual stimuli are processed in the retinogeniculate pathway before direction selectivity appears (in the striate cortex), so in this paper we develop a stimulus intended to probe the contribution of these early processes to the OFR. Figure 1 illustrates the principle that we exploit in this study. It depicts 1-D vertical sinewave gratings. In panels A and B the grating consists of a series of abutting strips in which alternate strips are in counterphase. Panel C illustrates the stimulus that results if all strips are in phase. Several key properties of stimuli in Figure 1 are the same: the total area occupied, the horizontal and vertical extent, the contrast, the distribution of pixel luminance values. The processing of these stimuli in the visual system, however, could result in quite different outcomes. Schematics of two filters—like a 2-D on-center/off-surround classical receptive field (RF) of retinal ganglion cells—are superimposed onto each panel of Figure 1. The size of the lower filter in each pair is substantially larger than the upper one. The output of the lower filter would be close to maximum for the stimuli shown in panels B and C, where as it would be negligible for the stimulus shown in panel A, because in the latter case the dark and bright areas of the grating would largely cancel each other in the on-center as well as in the off-surround of the filter. If such stimuli were subjected to motion, the cortical motion-sensitive circuits would be fed by a strong filter output in cases B and C but not in case A. In contrast, for the smaller upper filter—shown also in a magnified view to the right of Figure 1 panels—the filter output would be the strongest in case A, weaker in case B, and the weakest in case C. In this study we develop a simple model using antagonistic center/surround filters, with properties selected in accord with the known properties of primate retinal ganglion cells. This simple model was able to quantitatively account for the observed changes in the OFR amplitude for stimuli composed of counterphase strips of different heights (Experiment 1), for a wide range of stimulus contrasts (Experiment 2) and spatial frequencies (Experiment 3).

Figure 1.

Stimulus spatial layout in Experiment 1. Gratings were confined to a single rectangular region composed of a variable number of abutting equal-height horizontal strips such that the neighboring strips were always in counterphase. Gratings shown are scaled versions of 0.25 cpd 32% contrast stimuli. The height of a strip equaled ~0.1 times (A; 8 pixels), ~0.78 times (B; 64 pixels), and ~6.23 times (C; 512 pixels) the grating wavelength. Schematics of two 2-D on-center/off-surround classical receptive fields of retinal ganglion cells are superimposed onto the stimuli in each panel: the size of the lower filter in each pair is substantially larger than the upper one. The output of the lower filter would be close to maximum for the stimuli shown in panels B and C, where as it would be negligible for the stimulus shown in panel A, because in the latter case the dark and bright areas of the grating would largely cancel each other in the on-center as well as in the off-surround of the filter. Conversely, for the smaller upper filter—shown also in a magnified view to the right of panels—the filter output would be the strongest in case A, weaker in case B, and the weakest in case C.

Some preliminary results of this study were presented in abstract form elsewhere (Sheliga, Quaia & FitzGibbon, 2011).

2. Experiment 1: OFRs to gratings comprised of counterphase horizontal strips of variable height

2.1. Material and Methods

Most of the techniques were very similar to those used previously in our laboratory (Sheliga, Chen, FitzGibbon & Miles, 2005, Sheliga, Quaia, Cumming & Fitzgibbon, 2012) and, therefore, will only be described in brief here. Experimental protocols were approved by the Institutional Review Committee concerned with the use of human subjects.

2.1.1. Subjects

Three subjects participated in this study: two were authors (BMS and EJF) and the third was a paid volunteer who was unaware of the purpose of the experiments (AGB). All subjects had normal or corrected-to-normal vision. Viewing was binocular.

2.1.2. Eye-movement recording

The horizontal and vertical positions of one eye (right eye in BMS and EJF; left eye in AGB) were recorded with an electromagnetic induction technique (Robinson, 1963) using a scleral search coil embedded in a silastin ring (Collewijn, Van Der Mark & Jansen, 1975), as described by Yang, FitzGibbon, & Miles (2003).

2.1.3. Visual display and the grating stimuli

The subjects sat in a dark room with their heads positioned by means of adjustable rests (for the forehead and chin) and secured in place with a head band. Visual stimuli were presented on a 21″ CRT monitor located straight ahead at 45.7 cm from the corneal vertex. The monitor screen was 400 mm wide and 300 mm high, with a resolution of 1024 × 768 pixels (20.55 pixels/°, directly ahead of the eyes), a vertical refresh rate of 160 Hz, and a mean luminance of 20.8 cd/m². The RGB signals from the video card provided the inputs to an attenuator (Pelli, 1997) whose output was connected to the RGB inputs of the monitor via a video signal splitter (Black Box Corp., AC085A-R2). This arrangement allowed the presentation of black and white images with 11-bit grayscale resolution.

The visual stimuli consisted of 1-D vertical gratings with sinusoidal luminance profiles (0.25 cpd; 32% contrast) which extended the full width of the display (47°) and underwent successive ⅛-wavelength shifts each video frame (20 Hz temporal frequency). The gratings were ~25° in height and centered vertically at a subject’s eye level. On any given trial, gratings were composed of a variable number (from 1 to 128) of abutting equal-height horizontal strips such that the neighboring strips were always in counterphase (180° phase difference). The height of a strip could range from ~0.05 times (~0.2°; 4 pixels) to ~6.23 times (~25°; 512 pixels) the grating wavelength in octave increments. See Figure 1A–C for examples. Each block of trials had 16 randomly interleaved stimuli: 8 strip heights and 2 directions of motion (leftward vs. rightward).

2.1.4. Procedures

All aspects of the experimental paradigms were controlled by two PCs, which communicated via Ethernet using the TCP/IP protocol. One of the PCs was running a Real-time EXperimentation software package (REX) developed by Hays, Richmond and Optican (1982), and provided the overall control of the experimental protocol as well as acquiring, displaying, and storing the eye-movement data. The other PC was running Matlab subroutines, utilizing the Psychophysics Toolbox extensions (Brainard, 1997, Pelli, 1997), and generated the visual stimuli.

At the beginning of each trial, the grating patterns appeared (randomly selected from a lookup table) together with a target spot (diameter, 0.25°) at the screen center that the subject was instructed to fixate. After the subject’s eye had been positioned within 2° of the fixation target and no saccades had been detected (using an eye velocity threshold of 18°/s) for a randomized period of 600 to 1100 ms the fixation target disappeared and motion began. The motion lasted for 200 ms, at which point the screen became a uniform gray (luminance, 20.8 cd/m²) marking the end of the trial. After an inter-trial interval of 500 ms a new grating pattern appeared together with a central fixation target, commencing a new trial. The subjects were asked to refrain from blinking or shifting fixation except during the inter-trial intervals but were given no instructions relating to the motion stimuli. If no saccades were detected for the duration of the trial, then the data were stored to disk; otherwise, the trial was aborted and subsequently repeated within the same block. Data were collected over several sessions until each condition had been repeated an adequate number of times to permit good resolution of the responses (through averaging).

2.1.5. Data analysis

The horizontal and vertical eye position data obtained during the calibration procedure were each fitted with second-order polynomials which were used to linearize the horizontal and vertical eye position data recorded during the experiment proper. The linearized eye-position signals were smoothed with an a causal 6^th-order Butterworth filter (3 dB at 30 Hz) and mean temporal profiles were computed for each stimulus condition. Trials with saccadic intrusions (that had failed to reach the eye-velocity cut-off of 18°/s used during the experiment) were deleted. Because the OFRs elicited by some stimuli could be very weak and/or show directional asymmetries (e.g., Quaia, Sheliga, Fitzgibbon & Optican, 2012), the mean horizontal eye position with each leftward motion stimulus was subtracted from the mean horizontal eye position with the corresponding rightward motion stimulus: the “mean R-L eye position”. Velocity responses (the “mean R-L eye velocity”) were estimated from differences between samples 10ms apart (central difference method), and evaluated every 1ms. Response latency was estimated by determining the time after stimulus onset when the mean R-L eye velocity first exceeded 0.1°/s. The initial OFRs to a given stimulus were quantified by measuring the changes in the mean R-L eye position signals—“OFR amplitude”—over the initial open-loop period, i.e., over the period up to twice the minimum response latency. For all of the data of a given subject, the measurement window always commenced at the same time after the stimulus onset (“stimulus-locked”), the actual time being determined by the shortest response latency. The duration of the window for a given subject was the same across all experimental conditions.

2.2. Results

Figure 2A shows mean R-L eye velocity profiles over time obtained from subject BMS in response to stimuli of different strip height (noted by grayscale coding of velocity traces). The OFRs increased for strip heights up to 2–3°, whereas further height increase led to a significant decline in the OFR magnitude. Also as the strip height got larger, the OFR latency decreased until reaching a plateau for strip heights of 2–3° or more. Figures 2B and 2C quantify these observations for three subjects.

Figure 2.

OFRs to stimuli of different strip height. (A) Mean R-L eye velocity profiles over time for subject BMS. Different strip heights are grayscale coded (see the insert). Abscissa shows the time from the stimulus onset; horizontal dotted lines represent zero velocity; horizontal thick black line beneath the traces indicates the response measurement window. Each trace is the mean response to 133–140 repetitions of the stimulus. (B) OFR amplitude: Dependence on strip height for subjects AGB (red filled diamonds, 129–141 trials per condition; SDs ranged 0.010–0.024°), BMS (black filled circles, 133–140 trials per condition; SDs ranged 0.010–0.021°), and EJF (blue filled squares, 58–71 trials per condition; SDs ranged 0.013–0.027°). (C) OFR latency: Dependence on strip height for subjects AGB, BMS, and EJF. Colors and symbols as in B.

2.2.1. A Simple Model: antagonistic center/surround RFs

In order to evaluate the role of early visual neurons in generating our responses, we attempted to model the responses quantitatively with a simple Linear-Nonlinear (LN) model. These models, consisting of a linear filter followed by an output nonlinearity (typically an exponent) have been widely used to describe the response of neurons in the retina, LGN, and striate cortex. First we attempt to describe the responses with linear filters that resemble retinal ganglion cell RFs. For this we use a difference of two 2-D Gaussian functions (Enroth-Cugell & Robson, 1966, Rodieck, 1965): Difference of Gaussians model (DOG; Figure 3A):

$$F_{\mathit{DOG}}=A_{C}exp\left[-\frac{X^2}{2{\sigma }_{Cx}^2}-\frac{Y^2}{2{\sigma }_{Cy}^2}\right]-A_{S}exp\left[-\frac{X^2}{2{\sigma }_{Sx}^2}-\frac{Y^2}{2{\sigma }_{Sy}^2}\right]$$ (1)

Figure 3.

Modeling the OFRs. (A–C) antagonistic center/surround RF model. (C–D) V1 RF model (Gabor). (A) Difference of Gaussians function (DOG). The “on”-center of a filter is an area where the DOG function stays positive. (B) Normalized response power of 2D circular antagonistic center/surround filters of different “on”-center diameters for stimuli of different strip heights (grayscale coded; see insert). Power is normalized by the maximal response to the one-strip grating. (C) Dependence of the normalized power upon the stimulus strip height: the stimulus with maximal absolute power was set to have a power of 1. Black continuous line: DOG model; Experiment 1. Gray continuous line: Gabor filters; Experiment 1. Black dotted line: DOG model; Counterphase Configuration; Experiment 3. Black dashed line: DOG model; Gap Configuration; Experiment 3. (D) Normalized power of the Gabor filters of different central spatial frequencies for stimuli of different strip heights (grayscale coded; see insert). Power is normalized by the maximal response to the one-strip grating. See text for details.

We define the “on”-center of a filter as the area where the DOG function stays positive (Figure 3A). Assigning equal standard deviations (SDs) to the horizontal and vertical Gaussian envelopes (σ_Cx = σ_Cy and σ_Sx = σ_Sy) would result in circular filters, while non-equal Gaussian SDs in two cardinal dimensions would result in elliptical filters. The SD of the surround Gaussian envelope was always five times that of the center (σ_Sx = 5σ_Cx and σ_Sy = 5σ_Cy), which corresponds to the mean value of the center/surround classical RF diameter ratio found for primate ganglion M-cells (~4.8; Croner & Kaplan, 1995). ¹ Similar center/surround diameter ratios were reported for feline X-cells (Cleland, Levick & Sanderson, 1973, Linsenmeier, Frishman, Jakiela & Enroth-Cugell, 1982). The volume under the center 2-D Gaussian surface was set to twice that of the surround Gaussian (A_C ≈ 50A_S in Equation 1), again in accordance with the values reported for primate ganglion cells (Croner & Kaplan, 1995).

A sinewave grating of certain spatial frequency would activate filters having a range of sizes. The filter response depends on both spatial frequency and strip size in a way that makes it necessary to consider a range of filter sizes in accounting for the response to any one stimulus. To estimate a response of a population of filters at one scale, we convolved each of our eight stimuli with this filter, and then took the sum of squares of the convolution (filter power). Before combining across filters, we adjust for the fact that the OFRs displays a band-pass dependence on spatial frequency (Quaia et al., 2012, Sheliga et al., 2005), scaling the filter power value in each channel according to the observed spatial frequency tuning: see Appendix for details. Figure 3B shows these scaled model responses for circular filters of different sizes to each of the stimuli we used. As strip height becomes smaller, there is a progressive leftward shift of the peak. To assess the total filter output for a given stimulus, we summed the power of 121 filters whose “on”-center diameters were spaced by 1/16 of the octave and ranged from 2.6 min of arc to 7.9°:² this is equivalent to calculating the area under the curve for each trace in Figure 3B. The black continuous line in Figure 3C shows the dependence of such total filter output on strip height. One feature of the empirical data is not captured simply by the filter response: at large strip sizes the OFRs were actually smaller than at the optimal strip size (see Figure 2B). In order to accommodate this feature we included a normalizing term that depended on strip height. For any given filter, we fit the OFR amplitudes with the following equation:

$$\mathrm{R}={\mathrm{P}}^A\ast \frac{K}{1+B\ast \text{SH}}$$ (2)

where R is the OFR amplitude, SH is the strip height³, P is the total filter output, and A, K, and B are free parameters. The term P^A * K represents the response of LN filters that resemble retinal ganglion cells. The terms K and A determine the peak response magnitudes and the rate of rise with strip height, respectively. We chose the term 1 + B*SH to describe attenuation for large strip sizes for its simplicity: it introduces only one free parameter, B, that determines the extent of suppression by large strip sizes.

Equation 2 provided good fits for the OFR dependences on strip height. When the filters were circular, the coefficients of determination (r²) of Equation 2 fits equaled 0.965, 0.967, and 0.927 for subjects AGB, BMS, and EJF, respectively. These fits are shown by continuous black lines in Figure 4A–C. Filters’ ellipticity ratios (height/width) had minor effects on the goodness of fits: four-fold changes in the ratio—from 0.5 to 2—lowered r² values by 3–6% in different subjects. To ensure that this result was not sensitive to our simple model for normalization, we used a model with no normalization (setting B to zero in equation 2), and fit this only to the data for strip heights up to and including the maximum (<1 cycle of the grating period, see Figure 4). These fits were also extremely good - r² equaled 0.966, 0.976, and 0.931 for subjects AGB, BMS, and EJF, respectively. Finally we discuss below a different model (Ratio of Gaussians; ROG) for explaining the response decline at large strip heights.

Figure 4.

Equation 2 fits for the OFR amplitude data of Experiment 1. The dependence of the OFR amplitude on the strip height—black filled circles—is replotted from Figure 2B. Black continuous lines: fits obtained using 2D circular antagonistic center/surround filters. Black dotted lines: fits obtained using Gabor filters. Gray continuous lines: ROG model fits (see text). (A) subject AGB, (B) subject BMS, (C) subject EJF.

2.2.2. A Simple Model: V1 simple-cell RFs

We used 2-D Gabor functions to model spatial properties of striate cortex simple cells’ RFs (Jones & Palmer, 1987, Ringach, 2002):

$$F_{\mathit{Gabor}}=Aexp\left[-\frac{X^2}{2{\sigma }_x^2}-\frac{Y^2}{2{\sigma }_y^2}\right]cos(2\pi fX)$$ (3)

For each frequency, we used five different Gaussian envelopes, with horizontal SDs (σ_x; width) of 0.1, 0.2, 0.3, 0.4, or 0.5 times the Gabor central wavelength (covering ~93% of the n_x values in Ringach, 2002 neuronal sample). The vertical Gaussian SD (σ_y; height) for each filter was set to 1.07 times σ_x (median value of n_y/n_x ratio in Ringach, 2002). As with the DOG model above, filter outputs at each scale were normalized to produce the observed spatial frequency tuning to single strips. Individual traces in Figure 3D show the normalized power of the Gabor filters of different central spatial frequencies for stimuli of different strip heights. Each point on these curves is the summed response of the five filters with different σ_x. For lower-strip-height stimuli power maximums shifted rightward. To assess the total filter output for a given stimulus, we summed the power of 89 filters whose central spatial frequencies were spaced by 1/16 of the octave and ranged from 0.0625 cpd to 2.8 cpd: this is equivalent to calculating the area under the curve for each trace in Figure 3D. The gray continuous line in Figure 3C shows the dependence of such total filter output on strip height.

Equation 2 provided good fits for the OFR dependences on strip height: the r²s equaled 0.920, 0.909, and 0.854 for subjects AGB, BMS, and EJF, respectively. These fits are shown by dotted black lines in Figure 4A–C. The goodness of fits would further improve if we were to use solely the filters whose σ_x equaled 0.1 (or 0.2): the r²s would reach 0.969 (or 0.964), 0.963 (or 0.957), and 0.920 (or 0.910) for subjects AGB, BMS, and EJF, respectively.

2.3. Discussion of Experiment 1

The main objective of this experiment was to evaluate the impact of antagonistic center/surround neuronal filters in the retinogeniculate pathway on OFRs. A model that simply sums the responses of center/surround filters and includes divisive normalization reproduced the OFR magnitudes for a large set of visual stimuli. This outcome does not imply that cortical processing has no role in the OFR. Rather, for this particular stimulus, the increasing response with increasing strip height are largely explained by the effect of this stimulus in the retina. Indeed, the stimulus was constructed with this goal in mind. If the strips are small enough, then having adjacent strips in counterphase would be expected to silence retinal ganglion cells. We show that the results are also compatible with filters typical of cortical simple cells. But since these linear filters can be constructed from the DOG filters we use to model retinal processing, and the DOG filters reproduce the same results, its seems likely that it is the retinal filtering that produces this effect. This suggests that this stimulus allows us to observe properties of the OFR that reflect retinal processing.

The existing electrophysiological evidence indicates that elliptical RF centers—mean minor/major axis ratios of 0.7–0.8—are frequently observed in retinal ganglion cells of cats (Hammond, 1974, Levick & Thibos, 1982, Soodak, Shapley & Kaplan, 1987) and primates (Passaglia, Troy, Ruttiger & Lee, 2002), as well as in the primate LGN (Kremers & Weiss, 1997, Smith, Chino, Ridder, Kitagawa & Langston, 1990). Our model does not, however, seem to be particularly sensitive to this aspect of retinal RF properties and easily accommodates the fact that the RF shapes of the vast majority of neurons in the retina deviate from circularity.

To obtain good fits for the whole OFR amplitude dataset we had to introduce an additional term into the fitting equation — $1+B\ast \text{SH}$ — which would account for a sizeable (up to 18–25%) decline in the OFR amplitude observed at large strip heights. A somewhat similar observation was made in one of our previous studies (Sheliga, FitzGibbon & Miles, 2008): the OFRs to full-screen stimuli were usually markedly weaker than the OFRs to stimuli having an identical horizontal and vertical extent but composed of 15 strips separated by gaps of mean luminance. In the current paper, however, we are able to make a step further and show that the strength of inhibition is a simple function of the strip height. The neural substrate of this “inhibitory” effect is likely to be cortical, perhaps through the end-stopped neurons in the striate cortex (Hubel & Wiesel, 1965) and/or the local inhibitory surround mechanisms in area MT (Born & Bradley, 2005). One interesting possibility in regard to suppression comes from studies that showed the existence of the suppressive surround mechanisms in V1 neurons (Cavanaugh, Bair & Movshon, 2002a, Sceniak, Ringach, Hawken & Shapley, 1999). Similar observations were also made at the LGN level (extra-classical receptive field of Solomon, White & Martin, 2002). The Ratio of Gaussians (ROG: Cavanaugh et al., 2002a) model was very successful in describing the rise and fall in the activity of single units in response to drifting sinusoids of different sizes. We, therefore, tested this model with our OFR dataset. We set the ratio of the 2D “surround” vs. “central” Gaussian envelopes to 3:1, in accordance with values derived in the single cell (Cavanaugh et al., 2002a) as well as the psychophysical (Nurminen, Kilpelainen, Laurinen & Vanni, 2009) studies. We fit the OFR amplitudes with the following equation (after Cavanaugh et al., 2002a):

$$\mathrm{R}=K\ast {\left(\sum _{n=1}^{89}\frac{{L^2}_C}{1+k_S\ast {L^2}_S}\right)}^A$$ (4)

where R is the OFR amplitude, L²_C is the sum of squares of the convolution with the ROG “central Gaussian”, L²_S is the sum of squares of the convolution with the ROG “surround Gaussian”; A, K, and k_S are free parameters. A and K determine the peak response magnitude and the rate of rise with strip height, respectively, while k_S is the gain of the surround mechanism (the gain of the central mechanism was always set to one). To calculate the total ROG output we summed the output of 89 ratios: the “central Gaussian” standard deviations ranged from 1.8 min of arc to 1.3° (spaced by 1/16 of the octave), while the “surround Gaussians” standard deviations in each individual ratio were three times that of the “central” one.

Equation 4 provided good fits for the OFR dependences on strip height: the r²s equaled 0.944, 0.948, and 0.902 for subjects AGB, BMS, and EJF, respectively. These fits are shown by continuous gray lines in Figure 4A–C, and best-fit values of free parameters are listed in Table S1 of the Supplementary Material. The ROG model correctly located the maximums of the OFR dependencies, though the shape of the declining arm of the dependences did not quite match that of the experimental data.

Although we needed to include a model of normalization to fit all of the data, our conclusions do not depend upon the choice of model. It is the rising portion of responses in Figure 4 that constrains the model for the linear filter. Consequently, in subsequent experiments, we omitted the largest two strip heights, which cause the greatest response reduction.

3. Experiment 2: Contrast

In Experiment 1 a simple model based on the output of filters that resemble ganglion cells successfully reproduced the OFR magnitudes as a function of strip height. If these functions reflect retinal processing, it should be possible to extend the findings across a broader range of stimuli. Experiments 2 and 3 explore a range of contrasts and spatial frequencies, respectively, and ask if this framework still holds. In Experiment 1 we showed that the ellipticity ratios of filters had minor effects on the goodness of fits, and so in Experiments 2 and 3 we used only circular filters in our models.

3.1. Material and Methods

Many of the methods and procedures were identical to those used in Experiment 1, and only those that were different will be described here.

3.1.1. Visual stimuli

The visual stimuli consisted of 1-D vertical sinewave gratings as in Experiment 1. On any given trial, gratings were composed of a variable number (from 1 to 32 in octave increments) of abutting equal-height horizontal strips such that the neighboring strips were always in counterphase. The total stimulus height in this experiment was fixed, so the height of a strip could range from ~0.05 times (~0.2°; 4 pixels) to ~1.56 times (~6.2°; 128 pixels) the grating wavelength. All gratings had spatial frequency of 0.25 cpd; their contrasts ranged from 4% to 64% in octave increments. Each block of trials had 60 randomly interleaved stimuli: 6 strip heights, 5 contrasts, and 2 directions of motion (leftward vs. rightward).

3.2. Results

3.2.1. OFR amplitude

Figure 5A–C summarizes the OFR amplitude results for all three subjects, plotting them as a function of strip height. Data for each stimulus contrast are color- and symbol-coded, and it is apparent that for each one of contrasts that were used, increasing the strip height initially led to a substantial increase in the OFR magnitude followed by a decline, just as in Experiment 1⁴. Fitting the data using Equation 2 resulted in high r² values: median r² 0.977, ranging from 0.906 to 0.992. These fits are shown by color-matching continuous lines in Figure 5A–C.

Figure 5.

Effect of strip height on OFRs to stimuli of different contrast. (A–C) OFR amplitude: Dependence of mean OFR amplitude on strip height for subjects AGB (A), BMS (B), and EJF (C). Symbols: experimental data for different contrasts (see insert). Continuous lines: Equation 2 fits. Dotted lines: Equation 6 fits with only parameter A free to change with contrast. Subject AGB (66–77 trials per condition; SDs ranged 0.012–0.027°), subject BMS (81–86 trials per condition; SDs ranged 0.013–0.027°), subject EJF (76–101 trials per condition; SDs ranged 0.016–0.027°) (D, E, and F) Dependence of best fitting parameter for Equation 2—A, K, and B, respectively—on stimulus contrast. (G) Relationship between best-fit parameters A and K. Note log ordinate. (H) Dependence of parameter A in Equation 6 on stimulus contrast when it was the only parameter free to change with contrast (symbols; continuous lines) or when both parameters—A and B—were set free (dotted thin lines).

Careful examination of the fitted parameters (Figure 5D–F) revealed two interesting properties. First, although all three parameters changed with contrast, two of the parameters were closely related. Figure 5G plots K against A, where the relationship is well described by:

$$K={\mathrm{k}}_1\ast exp({\mathrm{k}}_2\ast A),$$ (5)

where k₁ and k₂ are two constants. Incorporating this relationship, Equation 2 becomes:

$$\mathrm{R}={[exp({\mathrm{k}}_2)\ast \mathrm{P}]}^A\ast \frac{{\mathrm{k}}_1}{1+B\ast \text{SH}}$$ (6)

so that now only two parameters (A and B) are allowed to vary with contrast. The term k₁ is an arbitrary scale factor that converts from the units we used to compute filter output. The term k₂ is a scale factor that determines the maximum OFR amplitude for any strip height or contrast. We refit the data using this equation (after finding the best values of k₁ and k₂ for each subject), and found that there was little change in the quality of the fits, with a median drop in r² of only 0.4% (range 0% to 2.8%).

Secondly, although there are systematic changes in the value of B with contrast (Figure 5F), this has little effect on the overall quality of the fits. As a result, when we fixed the value of B in Equation 6 (choosing the value that gives the best fit overall), there was little effect on the fits, causing a further reduction in r² of 1.0% (range 0% to 19.2%). Compared to fits obtained with Equation 2 an overall drop in the fits’ r² values was still small: median 1.7%, ranging from 0.1% to 19.4%. The largest errors occurred for the lowest contrast used, 4%. At such low contrast, the OFRs are quite small and so it is hard to be sure whether this really reflects a change in visual processing at the low contrast. The fits with only one parameter free to change with contrast are shown with dotted lines in Figure 5A–C. Values of k₁, k₂, and B are listed in Table S2 in the Supplementary Material. Figure 5H shows how the parameter A varies with contrast, when all the other parameters were held fixed. These dependencies were very well fit by a power function using the following expression (Sheliga, Fitzgibbon & Miles, 2009):

$$K\ast {\mathrm{C}}^{-n}+A_0$$ (7)

where K is a scaling coefficient, C is the stimulus contrast, n is an exponent, A₀ is an asymptote (r² were 0.999 for all three subjects). Fits are shown by continuous lines in Figure 5H, and the best-fit coefficients can be found in Table S3 of the Supplementary Material. Thin color-matched dotted lines in Figure 5H describe dependences (r²>0.997) which would result if the value of B were allowed to change with contrast. Thus the response across the entire range of strip sizes and contrasts can be described by our simple model (Equation 2) provided we allow changes in contrast gain. Figure 5 allows us to use the OFR to estimate these changes in contrast gain for human subjects.

For each given strip height the OFR amplitude dependence on contrast can also be very well described by the Naka-Rushton equation (Naka & Rushton, 1966):

$$R_{max}\frac{C^n}{C^n+C_{50}^n}$$ (8)

where R_max is the maximum attainable response, C is the contrast, C₅₀ is the semi-saturation contrast (at which the response has half its maximum value), and n is the exponent that sets the steepness of the curves. The continuous smooth lines in Figure 6A–C are the best fit curves using Equation 8 and are excellent approximations to the data (median r² 0.996, ranging from 0.927 to 0.999). Figure 6D–F shows that C₅₀ and n decreased substantially, whereas R_max slightly increased, as the strip height grew up to ~0.2–0.4% of the sinewave cycle, which was followed in the vast majority of cases by a plateau in values of all three parameters⁵.

Figure 6.

Effect of contrast on OFRs to stimuli of different strip height. (A–C) OFR amplitude: Dependence of mean OFR amplitude on stimulus contrast for subjects AGB (A), BMS (B), and EJF (C). Symbols: experimental data for different strip heights (see insert). Continuous lines: Equation 8 fits. (D, E, and F) Dependence of Equation 8 best-fit parameters—R_max, C₅₀, and n, respectively—on strip height. Note that panels D through F plot n/10 instead of n in order to permit all three parameters to share similar range of values along the ordinate axis. (G–I) The OFR latency plotted as a function of normalized stimulus power for subjects AGB (G), BMS (H), and EJF (I). Colored symbols (see insert): dependence on total filter output. Gray symbols: dependence on a single strip filter output (see text). Black continuous lines: Equation 9 fits.

3.2.2. OFR latency

Figure 6G–I summarizes the OFR latency data for all three subjects. The latency is plotted as a function of normalized total filter output (on a log abscissa). Color- and symbol-coding refer to stimuli of different strip height. Two main observations are evident. Firstly, regardless of strip height an increase in the power of the stimulus is accompanied by a decrease in latency. Secondly, the data points for the two thinnest strip conditions are located visibly above [and to the left] from the other strip conditions. That is, reductions in power caused by very small strip heights produce different latencies than equivalent reductions in power caused by reducing contrast. If, however, the latency data were replotted in respect to the normalized filter output from a single strip⁶, all strip conditions would converge into a single dependence—see gray symbols in the background of Figure 6G–I—which is well fitted with a power function, as in Equation 7:

$$K\ast {\mathrm{P}}^{-n}+L_0$$ (9)

where K is a coefficient, P is the single-strip filter output, n is an exponent, L₀ is an asymptote, and the plots include these fits (r² were 0.847, 0.841, and 0.883 for subjects AGB, BMS, and EJF, respectively) as black continuous lines whose best-fit parameters are listed in Table S4 in the Supplementary Material. Note that this equation is closely similar to Equation 2, used to fit the response amplitudes, with two differences. First Equation (9) requires the term L₀ to account for fixed delays. And second there is no normalization term (i.e. B in Equation 2 is set to zero) reflecting a real difference in the data – while large strip heights lead to a reduction in response amplitude, they do not increase latencies (compare Figures 2B and 2C). The same equation using the true filter power (not just a single strip) provides an extremely good description of the latency data if a different value of K (while L₀ and n are fixed) is allowed for each contrast (r² > 0.9 in all subjects).

3.3. Discussion of Experiment 2

The results of Experiment 2 confirm the conclusion that a model comprised of a layer of antagonistic center/surround filters reproduces the OFR amplitudes for a large set of visual stimuli, which now extends to stimuli of different contrasts. The effects of contrast could all be captured quantitatively by a single varying term that presumably reflects contrast gain. Higher contrast gain produces a steeper initial rise in response as a function of strip height, which can be seen in Figures 5A–C. The changes in contrast gain we infer from these fits are similar to those reported in primate retinal ganglion M-cells (Croner & Kaplan, 1995, Kaplan & Shapley, 1986) and their targets in the LGN (Derrington & Lennie, 1984, Solomon et al., 2002). This raises the possibility that shape of the response curves in Figure 5 at least partly reflects retinal processing. Our results show that the inhibitory term —parameter B of Equation 2—changed very little in fits for stimuli of very different contrasts. At first sight this seems at odds with our suggestion that this reflects cortical processing, where surround suppression is weaker at low contrast (e.g., Sceniak et al., 1999). However, it is important to note that any inhibition observed here depends upon surround suppression that is specific for the relative phase of center and surround. Surround inhibition elicited by gratings at any phase will be activated at all strip heights. In the striate cortex, it is clear that on average surround suppression is the strongest for in-phase surrounds, but there is nonetheless substantial suppression for out of phase surrounds (Cavanaugh, Bair & Movshon, 2002b), although with single bar stimuli the suppression is strongly depended on phase (Yazdanbakhsh & Livingstone, 2006). How this phase-specific component of surround suppression varies with contrast has not yet been studied physiologically as far as we are aware.

Interestingly, in all subjects the best-fit Naka-Rushton parameters generally showed little change for stimuli in which the height of a strip was larger than ~0.2–0.4 of the sinewave cycle (Figure 6D–F). These observations parallel the latency data: for strip heights exceeding ~0.4 of the sinewave cycle the OFR latencies were rather constant (note how in Figure 6G–I black open squares, blue open circles, and violet filled squares are all clustered together) ⁷. These observations, presumably, all reflect the fact that the filter output changes little over this range (at 0.4 of the sinewave cycle the filter output reached ~75% of maximum value). When plotted as a function of the total filter output, the latency data points for the two thinnest strip conditions were visibly separated from the other data (green circles and orange diamonds; Figure 6G–I). That is, reductions in power caused by very small strip heights produce different latencies than equivalent reductions in power caused by reducing contrast. We do not have a well justified explanation for this, but we speculate that it might be explained by spatial summation. In our retinal ganglion cell model the filters that are centered on a strip junction are silent, so that after filtering the stimulus consists of separate strips. For a response to be triggered, it might be sufficient that only one such locus were to exceed a certain threshold, and this moment would mark when the response is triggered. The amplitude of the response, on the other hand, is determined by a read-out of total stimulus-related neuronal activity accumulated till the moment the trigger arrived. According to this explanation, the latency should depend upon the power contained within a single strip, and it turns out that this does provide a much better description of the data (grey symbols in Figure 6G–I). Of course many other explanations are possible – it may also be the effect of contrast gain control on latency. Also of note is the similarity of Equations 2 and 9: both are power functions, but Equation 9 lacks the normalization term (1 + B*SH). The normalization mechanisms seem to reduce response amplitudes, but they do not increase latencies.

4. Experiment 3: Spatial Frequency

In this experiment we explore how well our simple model can account for changes in the OFR with spatial frequency (SF). Because this stimulus is similar to one that we have used in a previous study (Sheliga et al., 2008), in which strips were separated by uniform grey “gaps”, we also include this condition for comparison, and to see if the modeling framework developed above can also account for these data.

4.1. Material and Methods

Many of the methods and procedures were identical to those used in Experiments 1 and 2, and only those that were different will be described here.

4.1.1. Visual stimuli

Two stimulus configurations were used in this experiment—Counterphase Configuration (as the one used in Experiments 1 and 2) and Gap Configuration (a new configuration which was not used in the first two experiments, but is similar to the stimulus used in Sheliga et al. 2008)—which were run in separate experimental sessions.

Counterphase Configuration: Figure 7A–E

The visual stimuli consisted of 1-D vertical sine wave gratings confined to a horizontally elongated rectangular patch. On any given trial, this patch was composed of a variable number (from 1 to 16 in octave increments) of abutting equal-height horizontal strips such that the neighboring strips were always in counterphase. Gratings had a fixed contrast of 32%; their SFs ranged from 0.0625 to 1 cpd in octave increments. For a given SF the stimulus height was fixed, so that the height of a strip ranged from ~0.1 times to ~1.56 times the grating wavelength. Each block of trials had 50 randomly interleaved stimuli: 5 strip heights, 5 SFs, and 2 directions of motion (leftward vs. rightward).

Gap Configuration: Figure 7F–J

The visual stimuli consisted of 1-D vertical sine wave gratings occupying a variable number (from 1 to 16 in octave increments) of horizontal strips separated vertically by mean-luminance gaps. On a given trial gratings in each strip had the same phase, and both the strips and gaps between them had equal height.⁸ Gratings had contrast of 32% and their SFs ranged from 0.125 to 1 cpd in octave increments. For a given SF the overall stimulus vertical extent was fixed, so that the height of a strip ranged from ~0.1 times to ~1.56 times the grating wavelength. Each block of trials had 40 randomly interleaved stimuli: 5 strip heights, 4 SFs, and 2 directions of motion (leftward vs. rightward).

When comparing the Gap Configuration with the Counterphase Configuration, there are two possible ways to match stimuli. One possibility is to match the total stimulus height, in which case the Gap stimulus would have lower contrast energy. The other possibility is to keep the number of horizontal lines with sinusoidal modulation constant, in which case the Gap stimulus will have double the height. We chose the second of these, as illustrated in Figure 7.

Figure 7.

Stimulus spatial layout in Experiment 3. Sample gratings are scaled versions of 0.25 cpd 32% contrast stimuli. (A–E) Counterphase Configuration: Gratings were confined to a single horizontal strip, composed of a variable number of abutting equal-height horizontal strips such that the neighboring strips were always in counterphase. (F–J) Gap Configuration: Gratings occupied a variable number of horizontal strips separated vertically by mean-luminance gaps. Gratings in each strip had the same phase, and grating-containing strips and gaps between them had equal height. The height of a strip equaled ~0.10 times (A and F; 8 pixels), ~0.19 times (B and G; 16 pixels), ~0.39 times (C and H; 32 pixels), ~0.78 times (D and I; 64 pixels), and ~1.56 times (E and J; 128 pixels) the grating wavelength.

4.1.2. Data analysis

We again used the “stimulus-locked” OFR amplitude measures, but for stimuli of different SF the measurement window could commence at a different moment in time after motion onset, the actual time being determined by the shortest OFR latency recorded for each SF. The duration of the window for a given subject was, nevertheless, always the same throughout the experiment.

4.1.3. Model considerations

For each SF, we calculated the normalized power of all stimuli, expressing it as a fraction of the power of a single-strip grating of this SF. For the single strip case, both configurations consist of a single patch of grating of the same size, so both conditions are normalized to the same maximum. Figure 3C provides examples for circular filters in the Counterphase (dotted lines) or Gap (dashed lines) Configurations.

Because we normalized filter responses within each SF, we did the same for the OFRs within each SF, expressing them as a fraction of the response to a single-strip grating⁹. Prior to this normalization we also applied a scaling to remove any effects of day-do-day variation, as the data for the Gap Configuration was collected on different days from the data for the Counterphase Configuration. However, both stimulus sets contained one stimulus—the single-strip stimulus—that was the same size. We therefore scaled the responses so that same stimulus gave an identical mean response¹⁰.

For stimuli of different SF the strip height—SH in Equation 2—was expressed as a fraction of the sinewave grating period and, therefore, regardless of stimulus SF the strip height values fed into Equation 2 were the same and equaled ~0.1, ~0.19, ~0.39, ~0.78, and ~1.56.

4.2. Results

Figure 8A–C summarizes the OFR amplitudes as a function of SF and strip height, for the Counterphase Configuration (like that used in Experiments 1 and 2 above). For each SF, the shape of these response curves is broadly similar to that observed in Experiments 1 and 2. The continuous lines show fits to these data using Equation 2, and these fits describe the data well (median r² 0.968, ranging from 0.879 to 0.989). Responses to the Gap Configuration are shown in Figure 9A–C. The continuous lines again show fits to these data using Equation 2 (median r² 0.955, ranging from 0.877 to 0.996). In the Counterphase Configuration, filters centered on a boundary will be inactive because of cancellation of responses from each half of the filter. This is why responses were very small for small strip heights. For the Gap Configuration this cancellation does not take place, so the decline in response at low strip heights is much less dramatic. Dashed and dotted black lines in Figure 3C compare these filters’ responses.

Figure 8.

OFRs to stimuli of different spatial frequency: Counterphase Configuration. (A–C) OFR amplitude: Dependence of mean OFR amplitude on strip height for subjects AGB (A), BMS (B), and EJF (C). Symbols: experimental data for different spatial frequencies (see insert). Continuous lines: Equation 2 fits. Dotted lines: Equation 12 fits, when—for a given stimulus spatial frequency—A was constrained to be the same for Counterphase and Gap Configurations. Subject AGB (173–193 trials per condition; SDs ranged 0.016–0.029°), subject BMS (173–180 trials per condition; SDs ranged 0.015–0.027°), subject EJF (136–162 trials per condition; SDs ranged 0.012–0.024°). (D–F) OFR latency dependence on strip height for subjects AGB (D), BMS (E), and EJF (F).

Figure 9.

OFRs to stimuli of different spatial frequency: Gap Configuration. (A–C) OFR amplitude: Dependence of mean OFR amplitude on strip height for subjects AGB (A), BMS (B), and EJF (C). Symbols: experimental data for different spatial frequencies (see insert). Continuous lines: Equation 2 fits. Dotted lines: Equation 12 fits, when—for a given stimulus spatial frequency—A was constrained to be the same for Counterphase and Gap Configurations. Subject AGB (167–179 trials per condition; SDs ranged 0.015–0.027°), subject BMS (172–180 trials per condition; SDs ranged 0.018–0.032°), subject EJF (135–164 trials per condition; SDs ranged 0.017–0.028°). (D–F) OFR latency dependence on strip height for subjects AGB (D), BMS (E), and EJF (F).

There are substantial changes in overall response magnitude with spatial frequency (Figure 8). In order to analyze the effect of strip height across frequency, we therefore normalized the response amplitudes for each frequency, dividing by the response to a single strip. The fit parameters B and K then showed a tightly linearly relationship (r²>0.997 in the Counterphase Configuration; r²>0.993 in the Gap Configuration), that is:

$$K=k_1\ast B+k_2$$ (10)

where k₁ and k₂ are two constants. Incorporating this relationship, Equation 2 becomes:

$$\mathrm{R}={\mathrm{P}}^A\ast \frac{k_1\ast B+k_2}{1+B\ast \text{SH}}$$ (11)

so that now only two parameters (A and B) are allowed to vary with SF. Because of the normalization, for the one-strip stimulus Equation 11 requires k₁ * B + k₂ to be equal to 1 + B*SH, since for this stimulus R=1 and P=1. To keep this requirement regardless of the value of B, k₁ should be equal to one, while k₂ should be equal to SH₁, where SH₁ is the strip height of a one-strip stimulus. Equation 11 is then transformed into

$$\mathrm{R}={\mathrm{P}}^A\ast \frac{1+B\ast {\text{SH}}_1}{1+B\ast \text{SH}}$$ (12)

For both stimulus Configurations, Equation 12 fits displayed a marginal overall drop in the r² values when compared to those obtained with Equation 2: median 0.2%, ranging from 0.0% to 0.7%. If the differences between the Gap Configuration and the Counterphase Configurations are explained entirely by differences in the filter responses, then it should be possible to fit the data for both conditions with a single set of parameters. In fact, when we tried to do this, fits were substantially worse (median r² 0.790), but this was largely attributable to differences in suppression at large strip sizes, which in our model is controlled by parameter B, and probably reflects cortical processing. When we constrained A to be the same for both conditions, allowing only B to vary, the fits were very good (median r² 0.935, dashed lines in Figures 8 and 9). Figure 10B shows the values taken by B in these fits: there is little variation with SF, but they are higher for the Gap Configuration than for the Counterphase Configuration, suggesting that the former elicits stronger surround suppression or end-stopping in cortical neurons. Although these fits fixed the value of A across Gap and Counterphase conditions, different values were used for each SF: Figure 10A. These SF-dependent changes in A are idiosyncratic, but seem to indicate that changes in SF, in addition to changing response magnitude, alter somewhat the rate at which the relative response grows with stimulus strength (captured by parameter A).

Figure 10.

Counterphase vs. Gap Configuration. Dependence of best fitting parameters for Equation 12—A (A) and B (B)—on stimulus spatial frequency for subjects AGB (red filled diamonds), BMS (black filled circles), and EJF (blue filled squares). For a given spatial frequency parameters A was constrained to be the same, while B was allowed to be different (see insert in panel B), in Counterphase and Gap Configurations.

In the Counterphase Configuration, the OFR latency becomes shorter with increasing strip height, reflecting the stronger filter response. This saturates once strip height exceeds ~0.4 of carrier cycle or more (Figure 8D–E). For the Gap Configuration, where small strip heights produce much larger filter responses, the latencies are close to the asymptotic value even at small strip heights (Figure 9D–E).

4.3. Discussion of Experiment 3

In Experiment 3 we varied 16-fold the SF of visual stimuli and showed that a model based on the antagonistic center/surround filters whose sizes were inversely proportional to stimulus SF was able to quantitatively reproduce the experimentally observed OFR amplitudes.

In Experiment 3 stimulus height was scaled with SF. Calculating the total filter response to these different stimuli requires making assumptions about the distribution of the filters, which are certainly not uniform. Firstly, at a given retinal eccentricity the quantity of filters which would respond to stimuli of different SF is most likely not the same: numerous studies have reported that RF size increase with retinal eccentricity in primate retinal ganglion cells (Croner & Kaplan, 1995, Crook, Lange-Malecki, Lee & Valberg, 1988, De Monasterio & Gouras, 1975, Hubel & Wiesel, 1960), as well as in the LGN (Derrington & Lennie, 1984, Kremers & Weiss, 1997, Solomon et al., 2002). Secondly, as described in Section 4.1.1., the total stimulus size varied with SF. Since it is known that the density of ganglion cells falls markedly from the fovea to the peripheral retina (Perry & Cowey, 1985), any quantitative comparison of the number of filters activated by stimuli of different SF becomes even more problematic.¹¹ In order to avoid these complications, within each SF, we normalized the filter response by the maximal filter response to that stimulus (composed of a single strip). Having normalized the filter responses in this way, we also normalized the OFR response amplitudes for each SF, so that our fitted curves describe the relative shape of the OFR response, not its absolute magnitude. Despite this normalization, we had to allow parameter A to vary with SF to produce good fits. That is, the rate at which responses grow with strip height does seem to change with spatial scale, in addition to changes in response magnitude. However, these changes do not follow a very consistent pattern across subjects.

Parameter B did not change much with SF, but was consistently larger for the Gap than the Counterphase Configuration (by a factor of 1.5 on average, see Figure 10B), i.e. the inhibitory term was stronger in the Gap Configuration. This may reflect some property of cortical mechanisms producing surround suppression. In particular, it will depend critically on whether or not surround suppression is phase-sensitive. If an out-of-phase surround produces equally strong suppression as an in-phase surround, then surround suppression will be strong in all of our counterphase stimuli, but it will not change much with strip size, and so a small value of B is expected. But it may also be a consequence of retinal processing: filters that are centered on a strip junction in the Counterphase Configuration are silent. The total contrast energy after filtering is therefore somewhat smaller in the Counterphase Configurations. In estimating parameters K and A this filter response is incorporated in the model, but the denominator in Equation 2 depends on the strip height in the stimulus, not the filter response. (We did try various models using filter response in the denominator, but none were as successful as Equation 2).

5. Concluding Remarks

The OFR has proven to be a useful behavioral tool for isolating and investigating neural mechanisms involved in the early cortical processing of visual motion (Masson & Perrinet, 2012, Miles & Sheliga, 2009). In this paper we introduced a new stimulus (abutting counterphase strips) in which the retinal response should be very sensitive to strip height. Larger strip heights should produce larger retinal responses, and they also produced larger OFRs. A simple model based on center-surround RFs produced an excellent quantitative description of the data across a range of strip sizes, contrasts, and SFs. This suggests that visual processing of these stimuli in the retina plays a critical role in determining OFRs. A model based on cortical simple cell RFs also accounted for the data, but since these can be constructed from the linear summation of our retinal filters, we suggest that the retinal filter represents the critical step. Although the OFRs is activated by visual stimulus motion, this paper shows that the earliest levels of visual processing, which are not direction-selective, have a great impact in determining what is fed to the cortical direction-selective machinery. Besides the theoretical significance of these findings, this suggests that OFRs might also have a potential diagnostic value in clinical studies of abnormal function in ganglion cells, especially the magnocellular pathway (e.g., glaucoma; Shabana, Cornilleau Peres, Carkeet & Chew, 2003).

• Human OFRs were studied using narrow sinusoidal strip in counterphase

• Retinal receptive fields were modeled as a difference of two 2-D Gaussian functions

• Non-oriented center/surround antagonistic filters (retina, LGN) accounted for the data

Appendix

It is well established that for a 1D vertical sinewave grating, the OFR amplitudes show Gaussian dependence on stimulus log spatial frequency (SF). It was shown to be true for a grating occupying the whole screen (Sheliga et al., 2005) as well as for a one restricted to just a thin elongated horizontal strip centered at eye level (Quaia et al., 2012). However, the exact form of the dependence on SF depends on several stimulus properties, including eccentricity (Quaia et al., 2012) and size (Sheliga et al., 2012).

Therefore, in order to estimate the impact filters of different spatial frequency on the OFR, we used the responses recorded in Experiment 3, in which the stimulus consisted of a single strip whose height scaled with SF (i.e. the height expressed in periods of the grating was constant). With these stimuli we again find that the OFR amplitude dependence on stimulus log spatial frequency is very well captured by Gaussian functions: the r² of fits equaled 0.999, 0.965, and 0.990 for subjects AGB, BMS, and EJF, respectively (Figure A1).

Figure A1.

OFR dependence on stimulus spatial frequency for subjects AGB (red filled diamonds, 173–187 trials per condition; SDs ranged 0.025–0.033°), BMS (black filled circles, 175–179 trials per condition; SDs ranged 0.026–0.032°), and EJF (blue filled squares, 137–162 trials per condition; SDs ranged 0.023–0.029°). Color-matched continuous lines: Gaussian fits.

We therefore used these fits to differentially scale the outputs of filters of different SFs. For each filter we first take the sum of squares of the convolution with the stimulus, and then multiplied this sum by the value of our fitted Gaussian for that frequency.