Smith, Earl L., III, Yuzo Chino, Jinren Ni, and Han Cheng. Binocular combination of contrast signals by striate cortical neurons in the monkey. J. Neurophysiol. 78: 366–382, 1997. With the use of microelectrode recording techniques, we investigated how the contrast signals from the two eyes are combined in individual cortical neurons in the striate cortex of anesthetized and paralyzed macaque monkeys. For a given neuron, the optimal spatial frequency, orientation, and direction of drift for sine wave grating stimuli were determined for each eye. The cell's disparity tuning characteristics were determined by measuring responses as a function of the relative interocular spatial phase of dichoptic stimuli that consisted of the optimal monocular gratings. Binocular contrast summation was then investigated by measuring contrast response functions for optimal dichoptic grating pairs that had left- to right-eye interocular contrast ratios that varied from 0.1 to 10. The goal was to determine the left- and right-eye contrast components required to produce a criterion threshold response. For all functional classes of cortical neurons and for both cooperative and antagonistic binocular interactions, there was a linear relationship between the left- and right-eye contrast components required to produce a threshold response. Thus, for example for cooperative binocular interactions, a reduction in contrast to one eye was counterbalanced by an equivalent increase in contrast to the other eye. These results showed that in simple cells and phase-specific complex cells, the contrast signals from the two eyes were linearly combined at the subunit level before nonlinear rectification. In non-phase-specific complex cells, the linear binocular convergence of contrast signals could have taken place either before or after the rectification process, but before spike generation. In addition, for simple cells, vector analysis of spatial summation showed that the inputs from the two eyes were also combined in a linear manner before nonlinear spike-generating mechanisms. Thus simple cells showed linear spatial summation not only within and between subregions in a given receptive field, but also between the left- and right-eye receptive fields. Overall, the results show that the effectiveness of a stimulus in producing a response reflects interocular differences in the relative balance of inputs to a given cell, however, the eye of origin of a light-evoked signal has no specific consequence.
Vision through two eyes is better than monocular vision in several respects. Stereopsis, the relative depth perception that derives from horizontal retinal image disparities, is the most obvious advantage of binocular vision. However, the ability to detect visual stimuli is also better for binocular versus monocular vision, a phenomenon referred to as binocular summation (Blake and Fox 1973; Blake et al. 1981b; Fox 1991). Binocular cortical neurons are the likely substrate for both stereopsis and binocular summation (Hubel and Wiesel 1962, 1968; Joshua and Bishop 1970). Stereopsis is thought to reflect the disparity tuning characteristics of cortical neurons, both their sensitivity to interocular image disparities and the variation in optimal disparities between neurons (Barlow et al. 1967; Pettigrew et al. 1968; Poggio and Fischer 1977; Poggio and Talbot 1981). The degree to which binocular summation exceeds the probabilistic advantages of viewing with two eyes is believed to reflect the manner in which the inputs from the two eyes are combined in individual neurons as well as how the activity of cortical neurons is pooled (Anderson and Movshon 1989; Anzai et al. 1995; Blake et al. 1981a). In the preceding paper (Smith et al. 1997), we examined the binocular disparity tuning characteristics of neurons in the monkey's striate cortex. In this investigation, we address the question of how the contrast signals from the two eyes are combined in individual cortical units.
Although binocular integration is a fundamental aspect of cortical physiology, relatively little effort has been devoted to uncovering the rules by which signals from the left and right eyes are combined. The nature of cortical binocular interactions in individual neurons was first addressed in pioneering studies by Hubel and Wiesel (1959, 1962) of the cat striate cortex. On the basis of comparisons of binocular and monocular responses, Hubel and Wiesel argued that in simple cells the principles of summation and antagonism that characterized the interactions within and between on and off areas in a given receptive field also applied in a similar fashion for dichoptic stimulation. Their observations implied that the inputs from the two eyes exhibited linear spatial summation. However, a cortical cell's binocular response cannot, in a simple scalar way, be reliably predicted from the cell's monocular responses, and numerous subsequent investigations have demonstrated dramatic departures from linear binocular summation (Anzai et al. 1995; Hubel and Wiesel 1970; Pettigrew et al. 1968; Poggio and Fischer 1977). The so-called “obligate” binocular cells, neurons that cannot be excited by monocular stimuli presented to either eye alone, but that show vigorous responses when both eyes are stimulated simultaneously (Poggio 1991), provide a robust example of apparent nonlinear binocular interactions.
Ohzawa and Freeman (1986a,b), in their studies of binocular phase tuning in the cat, provided the most direct and clear-cut evidence concerning the functional way in which cortical neurons combined monocular signals. With the use of a vector summation analysis, they showed that the binocular response amplitudes and phases of cortical simple cells varied as a function of interocular image disparity in a manner that was predicted by a linear model of binocular convergence. Departures from the linear model predictions, when they occurred, could largely be accounted for by a threshold mechanism that was located after the linear combination of monocular signals.
Much less is known about the nature of binocular interactions in complex cells. The vector summation analysis of Ohzawa and Freeman (1986a) was not applicable to complex cells primarily because of the nonlinear nature of their monocular responses. However, Ohzawa and Freeman devised a clever “opposite direction” test that revealed the ability of complex cells to linearly superimpose the two monocular responses. Despite a number of factors that could have potentially interfered with this test (e.g., directional selectivity), the two phase-selective complex cells that were studied exhibited temporal response patterns that suggested that receptive field subunits located before the cell's nonlinear elements combined the signals from the two eyes in a linear manner. However, the results for several non-phase-selective complex cells were not conclusive.
To our knowledge there is no direct information on the integration of monocular signals in binocular cells in the monkey striate cortex. In the present study we used the vector summation analysis described by Ohzawa and Freeman (1986a) to examine binocular spatial summation in cortical simple cells. In addition, we employed a test of binocular contrast summation that can be applied to almost any cortical cell, both simple and complex cells, both phase-specific and non-phase-specific complex cells, and even cells in which the binocular response is dominated by non-phase-specific binocular suppression. This test, which involves measuring a cell's responses for a series of dichoptic gratings that vary in the ratio of contrasts presented to the two eyes, is analogous to psychophysical paradigms that have been used to measure binocular summation contours in human (Anderson and Movshon 1989) and monkey observers (Ridder et al. 1990). Some of these results have been presented previously in abstract form (Smith et al. 1992).
The nature of binocular interactions was assessed in individual striate cortex neurons in anesthetized and paralyzed macaque monkeys (n = 11) with the use of extracellular microelectrode recording techniques. The subjects, surgical preparation, apparatus, and general recording procedures were identical to those described in detail in the preceding paper (Smith et al. 1997). All experimental and animal care procedures were in compliance with the policies of the American Physiological Society and the National Institutes of Health Guide for the Care and Use of Laboratory Animals.
For each neuron, the optimal monocular stimuli were first determined by measuring orientation response functions and spatial frequency tuning functions for each eye with the use of drifting sine wave gratings. The cell's disparity tuning function was determined by measuring the cell's responses as a function of the relative interocular spatial phase of dichoptic stimuli consisting of the optimal monocular gratings. For descriptive and analytic purposes, the disparity tuning functions were fit with a single cycle of a sine wave (Ohzawa and Freeman 1986a). The sine wave's amplitude was used to calculate the degree of binocular interaction [binocular interaction index (BII) = amplitude of the fitted sine wave/average response amplitude]. A signal-to-noise ratio (S/N = amplitude of the fitted sine wave/residual root mean square error of the fit) was calculated to determine the adequacy of the fitted sine wave in describing a cell's phase tuning characteristics.
Binocular contrast summation was investigated in simple and complex neurons with the use of a series of dichoptic stimulus pairs that had different interocular contrast ratios. For these experiments, only stable, well-isolated neurons that exhibited robust responses were considered. Typically, we studied cells that had maximal response rates for high contrasts that were greater than ∼20 Hz. It was necessary to be selective because these experiments required a substantial amount of time to complete and employed a range of low contrasts that were ineffective in many neurons with lower response rates. In the most commonly used experimental paradigm, data were collected for seven interocular contrast ratios; the left-to-right stimulus contrast ratios were 1:10, 1:3.2, 1:1.7, 1:1, 1.7:1, 3.2:1, and 10:1. For each interocular contrast ratio and for the monocular stimulus conditions that were included in the parameter file, data were obtained for eight different contrast levels in 2.5-dB steps. The absolute contrast range depended on the neuron's contrast sensitivity, but the maximum available contrast was 0.3. The temporal frequency for all the stimuli was 3.12 Hz. The orientation, spatial frequency, and interocular spatial phase disparity were set at the optimal values for each neuron. Thus during a given experiment the neuron's responses for a total of 73 stimuli (56 binocular stimuli, 8 monocular stimuli for each eye, and a 0 contrast control) were accumulated in a randomly interleaved sequence. The goal was to determine for each interocular contrast ratio the stimulus contrasts required to produce a criterion response amplitude. These contrasts were then employed to construct binocular interaction contours similar to those used to analyze psychophysical binocular interactions (Anderson and Movshon 1989; Ridder et al. 1988).
In all experiments, the data were collected with the use of a multiple histogram design (Movshon et al. 1978a) in which responses were collected for 30–60 stimulus cycles for each stimulus. The amplitudes and phases of the appropriate temporal-response components in the peristimulus time histograms (PSTHs) were determined by Fourier analysis. The amplitude of the first harmonic component was used as the response measure for simple cells, whereas for complex cells, the amplitude of the average discharge rate was used as the measure of response strength (Skottun et al. 1991).
Vector model of binocular spatial summation
For cortical simple cells, the vector summation analysis of Ohzawa and Freeman (1986a) was employed to determine whether the phase tuning data were in agreement with a linear model for binocular spatial summation. According to the model of Ohzawa and Freeman, the signals representing the stimulus intensity values over local space and recent time from the left and right eyes are combined by linear summation before the cell's spike-generating mechanism. Consequently, responses to dichoptic stimuli can be predicted from the spatial transfer function of the composite binocular receptive field produced by combining the monocular receptive field profiles. The exact shape of the binocular receptive field reflects the monocular receptive field structures and the effective interocular receptive field disparity, where disparity is defined along the axis perpendicular to the cell's preferred orientation. The effective binocular disparity can be varied by changing interocular alignment or alternatively by changing an object's relative interocular retinal image disparity, as in the dichoptic phase tuning experiments.
Graphically, the predicted binocular response is obtained by vector summation of the monocular responses (Ohzawa and Freeman 1986a). Figure 1 A shows in polar coordinates the expected monocular left- and right-eye responses measured for a hypothetical simple cell. In our disparity tuning experiments, the spatial phase of the grating presented to the left eye was held constant and the relative binocular disparity was varied by systematically changing the spatial phase of the right eye's grating. For this example, it was assumed that the responses to stimulation of the left eye (K L) had a response phase of 30° (α) and an amplitude of 50 spikes/s, 2.5 times larger than the right-eye response. Because the left-eye stimulus is identical for all stimulus pairs, the left eye's response vector would remain constant. The right eye's input would be constant in amplitude (20 spikes/s), but its response phase would vary systematically with the relative spatial phase of the grating stimulus. In the polar coordinate system, the right eye's input would be represented by a series of vectors (K R) that differed in their angular orientation (δ). Because the relative spatial phase of the right eye's grating was varied over 360° in the phase tuning experiments, the family of right-eye vectors would describe a circle. The binocular response amplitudes (K B) and phases can be predicted by adding the right- and left-eye vectors graphically. Assuming that the effects of any subsequent nonlinear mechanisms are negligible, the binocular responses would fall on a circle with a radius equal to the right eye's response; the position of the circle would be determined by the left eye's amplitude and phase. Maximum binocular facilitation would occur when the left- and right-eye response phases were identical. When the left- and right-eye response phases differed by 180°, maximum binocular inhibition would occur.
However, Ohzawa and Freeman (1986a) also showed that if the binocular response was measured after the action of a significant threshold mechanism, the locus of binocular responses would assume an elongated, teardrop shape that was aligned with the origin. These shape alterations can be produced by reducing the amplitudes of all of the binocular vectors by a constant amount equivalent to the action of the threshold mechanism (Fig. 1 B). In addition, expansive nonlinearities that characterize simple cell responses (Albrecht and Geisler 1991; Heeger 1992a) would further accentuate the elongation of the plot. Thus, if this type of model can adequately account for the combination of monocular signals in monkey simple cells, then binocular phase tuning data should assume either a circular shape or an elongated teardrop shape when plotted on polar coordinates.
Figure 2 illustrates the vector summation analysis for a simple cell that appeared to show linear binocular spatial summation. This cell was strongly dominated by the right eye, but, as reflected by the systematic changes in the PSTHs for the binocular phase tuning experiment, the cell exhibited strong binocular interactions. When the binocular responses of this cell are plotted as vectors in polar coordinates, the phase tuning data approximate a circle. So in addition to combining the inputs from the two eyes in a linear manner, the influence of nonlinear mechanisms was minimal in this cell. For example, this cell's spike-generating mechanism must have had a relatively low threshold, despite the fact that the cell showed very little maintained activity.
Although we found a number of simple cells that demonstrated approximately circular vector summation plots, a variety of different response patterns were observed in our sample (n = 107). Figure 3 shows the vector summation plots for a series of simple cells that were selected to illustrate the range of response patterns. Figure 3, A and B, illustrates the data for two cells that were effectively monocular. The simple cell in Fig. 3 A showed a circular vector summation plot centered on the origin of the polar coordinate system. There was no response from the left eye. The monocular right-eye response amplitude was 47.2 spikes/s. The average binocular response amplitude was 47.6 ± 3.2 (SD) spikes/s and the phase of the response varied systematically with the relative spatial phase of the stimulus presented to the right eye. Figure 3 B shows data for a monocular cell excited by the left eye. Because the spatial phase of the grating presented to the left eye was the same for all stimulus pairs, the binocular response amplitudes and phases were essentially constant. All the data points clustered around the monocular left-eye response.
Within the population of binocular simple cells, the phase tuning data for the majority of cells showed clear departures from a circular shape (Fig. 3, C–H). These departures, which appeared to reflect the nonlinearities described above, were evidenced by an elongation of the plots along the left eye's response vector. There were no apparent qualitative differences between cells with relatively circular summation plots and those with obviously elongated plots. However, in general the cells with elongated vector summation plots showed evidence of significant threshold and/or expansive nonlinearities. These cells, which typically exhibited no background activity, were often excited by only one eye under monocular stimulus conditions, but they showed large, systematic changes in binocular response amplitude as a function of the relative interocular phase disparity. If these cells responded to monocular stimuli in both eyes, the monocular response amplitudes were typically very low relative to the maximum binocular response.
Binocular interaction contours: contrast summation
Figure 4 A illustrates a geometric model that has been used to analyze behavioral binocular contrast summation data in humans (Anderson and Movshon 1989; Legge 1984) and monkeys (Ridder et al. 1988). The abscissa and ordinate represent, respectively, the normalized left- and right-eye stimulus contrasts. Data points at 1.0 on the horizontal and vertical axes represent the monocular detection thresholds; points between the axes represent the left- and right-eye contrast values at threshold for dichoptic stimuli. Several potential forms of binocular combination are shown. In the case of linear summation, thresholds for dichoptic gratings that had different interocular contrast ratios would fall along the diagonal line connecting the monocular thresholds. In this case, a decrease in contrast to one eye would be counterbalanced by a functionally equivalent increase in contrast to the other eye. However, behavioral data in humans and monkeys with normal binocular vision typically fall near an arc that has a radius of 1.0, i.e., binocular sensitivity for stimuli with equal monocular contrasts exceeds monocular sensitivity by (Anderson and Movshon 1989; Harwerth and Smith 1985; Legge 1984; Ridder et al. 1988).
Figure 4 B shows how this geometric model applies to the contrast response data obtained from cortical neurons for dichoptic gratings that have different interocular contrast ratios. In this context, the abscissa and ordinate represent the left- and right-eye contrasts required to elicit a criterion response amplitude. The lines radiating from the origin represent dichoptic stimuli that have different interocular contrast ratios. In our experiments, responses were measured at five to eight contrasts levels for each interocular contrast ratio and the “threshold” contrasts required to produce a criterion response were calculated from hyperbolic functions fit to the contrast response data. This paradigm is analogous to behavioral experiments in which the left- and right-eye contrasts are covaried in a fixed ratio to determine a subject's detection threshold.
The filled circles in Fig. 4 B show the pattern of contrast combinations that would produce a criterion response in a hypothetical cell that combined contrast signals from the two eyes in a linear manner. The data fall on a straight line connecting the monocular contrast thresholds. In this specific example, the cell had an interocular difference in the monocular contrast thresholds as expected in a cell with unequal ocular dominance. If the contrast axes are normalized to this cell's monocular contrast thresholds, the binocular data would fall on a line with a slope of −1.0, i.e., with absolute contrast axes, a straight line, regardless of its slope, would correspond to linear summation. An advantage of this approach is that a quantitative indication of how well a cell's response complies with a linear model can be determined by simple linear regression.
Although the intent of this analysis was to determine whether the initial convergence of inputs from the two eyes follows linear summation, it is important to keep in mind that this experiment measures neuronal output following the action of several nonlinear mechanisms. Current models of striate neurons (e.g., Carandini and Heeger 1994) posit that after the initial input stage, which is assumed to be linear, the responses of cortical neurons are normalized with respect to stimulus contrast and rectified, and the overall firing rate is set by an expansive component so that a cell's firing rate depends approximately on the squared output of the underlying linear stage (Albrecht and Geisler 1991; Heeger 1992a,b). However, because these nonlinearities occur after the input stage and act on the combined left- and right-eye signals, the potential masking effects of these nonlinearities can be negated by defining threshold with the use of a constant suprathreshold response amplitude that falls within the rising portion of the cell's contrast response function. Assuming that the action of these nonlinearities is stable during our experiment, then it is reasonable to expect that a constant criterion firing rate would reflect a constant combined level of input from the two eyes. Of course, a given absolute level of input could be obtained via many different ratios of left- and right-eye inputs. The specific ratios of left- and right-eye inputs, as reflected by the interocular ratio of the stimulus contrasts required to produce the criterion firing rate, would then define the manner in which the inputs from the two eyes were combined.
Binocular summation contours: excitatory binocular interactions
Binocular summation contours were investigated in 16 simple cells. Figure 5 illustrates the results for a typical simple cell. Although under monocular conditions this neuron was only weakly excited by stimuli presented to the right eye, the disparity tuning function (Fig. 5 D) revealed a high degree of binocular interactions. For the experiment with asymmetric contrasts, an optimal phase disparity of 45° was used for all stimulus pairs. The PSTHs obtained for the highest contrasts at each interocular contrast ratio are shown in Fig. 5 A. An important feature of the PSTHs was that a single, discrete peak was found in each histogram. During the experiments, we closely monitor the PSTHs, particularly for monocular stimuli, for any changes in response phase. Residual disjunctive eye movements orthogonal to the grating's orientation would produce changes in response phase and alter a cell's optimal phase disparity, thus confounding the binocular measures. If any sign of eye movements was observed, the ongoing experiment was stopped and steps were taken to stabilize the eyes. Fortunately, contaminating eye movements were rarely observed during an experimental run.
The contrast response functions measured for each interocular contrast ratio are shown in Fig. 5 B, where the amplitude of the Fourier fundamental is plotted as a function of stimulus contrast. For the dichoptic stimuli (filled symbols), the abscissa represents the contrast for the dominant left eye. Each function was fitted with a hyperbolic function of the form where C is contrast, R max is the maximum response amplitude, C 50 is the contrast required to produce a response equal to 50% of the cell's maximum response, and n is an exponent that reflects the rate at which the function changes (Albrecht and Geisler 1991; Albrecht and Hamilton 1982; Heeger 1992a,b; Naka and Rushton 1966). Although the monocular contrast response functions indicated that stimulation of the nondominant right eye was ineffective, the systematic displacement of the dichoptic contrast response functions along the abscissa reveals the influence of the nondominant eye. In Fig. 5 C, the contrast response functions have been replotted on a relative contrast axis and individual curves were shifted along the abscissa to facilitate comparisons of the shapes of the functions. With the use of a criterion response amplitude of 7 spikes/s (dashed lines), threshold contrast levels were obtained for each contrast ratio and the right- versus left-eye thresholds were plotted for each ratio to produce a binocular interaction contour (Fig. 5 E). By linear regression, the data for this neuron were well fit by a straight line; the coefficient of determination, r 2, was 0.94. The slope of the best fitting line was −0.5, reflecting the fact that this cell was dominated by the left eye. By extrapolation to the abscissa, the monocular contrast threshold required to produce the criterion response for the right eye could be predicted to be a contrast of ∼43%.
For a given neuron, the dichoptic contrast response functions for different interocular contrast ratios were similar in shape. As a consequence, the slope of the binocular interaction contour was not dependent in a critical manner on the exact criterion response amplitude that was used to determine the threshold contrasts. Figure 6 A shows the contrast response functions for another simple cell that demonstrated response saturation for both monocular (○, □) and binocular (•, ▪, ▴, ▾, ♦) stimulation. The functions have been arranged on a relative contrast axis for clarity. The dichoptic functions have been arranged so that the right-eye to left-eye contrast ratio decreased from 10 to 0.1 from left to right. Figure 6 B shows a series of binocular interaction contours that were generated for four different criterion response amplitudes ranging from 5 to 28 spikes/s. For criterion amplitudes of 5 and 10 spikes/s, the slopes of the binocular interaction contours were −1.4 and −1.9, with the linear model accounting for 88% and 87% of the variance, respectively. The criterion amplitudes of 15 and 28 spikes/s were selected to illustrate that apparent departures from the linear model occur when the criterion amplitude falls within the rising portion of the contrast response function for some contrast ratios, but in the region of response saturation for others. However, in these instances, if regression analysis is restricted to data derived from the rising portions of the response functions, the binocular interaction contours exhibit comparable slopes and a linear fit accounts for a high degree of the variance (15 spikes/s, slope = −2.2, r 2 = 0.94; 28 spikes/s, slope = −1.76, r 2 = 0.94). For all the binocular interaction contours shown below, we employed relatively low, but clearly reliable, criterion response amplitudes that avoided the saturated portions of contrast response functions.
The binocular interaction contours were qualitatively similar for all of the binocular simple cells that we studied. Figure 7 shows the interaction contours for four additional simple cells that were selected to illustrate some of the quantitative between-cell differences. For every simple cell's interaction contour, the calculated coefficient of determination for a linear fit was quite high (r 2 ranged from 0.79 to 0.94). The interaction contours for all of the simple cells that were studied with the use of optimal interocular phase disparities demonstrated negative slopes that indicated cooperative binocular interactions. There was a rough correlation between the slope of the interaction contour and the cell's ocular dominance; left-eye-dominated cells showed slopes flatter than −1.0, whereas right-eye-dominated cells had slopes steeper than −1.0.
The asymmetric contrast paradigm was also applied to one simple neuron that appeared to be monocularly driven on all preliminary tests. During the experiments to measure orientation and spatial tuning functions for each eye, the left-eye response did not differ from the cell's maintained firing rate. Figure 8 illustrates the disparity tuning function (A), contrast response functions (B), and the binocular interaction contour (C) for this neuron. As expected, there were no systematic variations in the binocular response amplitude as a function of spatial phase (BII = 0.10; S/N = 0.9). And as shown in Fig. 8 B, all of the dichoptic contrast response functions superimposed on the right eye's function, whereas the monocular left-eye responses were equivalent to the maintained firing rate at all contrast levels. The response phases for suprathreshold dichoptic stimuli were also well matched to those for monocular right-eye stimuli. For a criterion amplitude of 5 spikes/s, the right eye exhibited a contrast threshold of ∼7%. The interaction contour conformed to a vertical line that indicated that the binocular threshold was independent of the left-eye contrast, i.e., no binocular interactions were observed.
Binocular interaction contours were measured for 16 binocular complex cells that showed cooperative binocular interactions. Seven of these neurons were phase-specific complex cells (BII ≥ 0.3); nine of the complex cells showed non-phase-specific interactions (Ohzawa and Freeman 1986b; Smith et al. 1997). Figure 9 shows the main results for a representative phase-specific complex cell. For all interocular contrast ratios, the PSTHs were dominated by the elevation in average firing rate that is characteristic of complex neurons (Skottun et al. 1991). For the dichoptic functions in Fig. 9 B, the abscissa represents the stimulus contrasts presented to the dominant left eye. Cooperative interactions between the inputs from the two eyes are evidenced by the leftward displacement of the dichoptic contrast response functions from the monocular left-eye function. The binocular interaction contour (Fig. 9 E), which was derived for a criterion response amplitude of 22 spikes/s, was well fit by a straight line with a slope of −0.4 (r 2 = 0.96).
The binocular interaction contours of four other phase-specific complex cells are shown in Fig. 10. For our sample of phase-specific complex cells, the BII values obtained from the disparity tuning functions ranged from 0.37 to 1.43. The slopes of the interaction contours that were obtained at the optimal relative interocular phases all had negative slopes. In comparison with simple cells, phase-specific complex cells generally exhibited more balanced ocular dominances and the slopes of the interaction contours were closer to −1.0. More importantly, the interaction contours were well fit by the linear model, with r 2 values ranging from 0.81 to 0.96.
For the nine complex cells that were classified as non-phase specific, the calculated BII values ranged from 0.01 to 0.23. However, no qualitative or quantitative differences were noted between the binocular interaction contours obtained from non-phase-specific and phase-specific complex cells. Figure 11 shows the interaction contours measured for four representative non-phase-specific complex cells. These cells were usually well driven by monocular stimuli presented to either eye and the interaction contours all showed moderate negative slopes. In all non-phase-specific complex cells, a linear fit could account for a high degree of the variance, with the r 2 values ranging from 0.82 to 0.99.
The linear regression analysis included in the preceding figures shows that a linear model describes the binocular data very well. However, a stronger test of whether binocular contrast summation is linear can be made by normalizing the contrast axes to the monocular threshold contrasts and fitting the data with a more general equation of the form where L c and R c represent the left- and right-eye stimulus contrasts and n is the summation exponent. If summation is linear, the value for n should be 1.0. It was possible to perform this analysis on seven of the units that we studied. Limitations in the maximum available stimulus contrast prevented accurate measurement of the monocular thresholds for both eyes in other cells.
Figure 12 shows the binocular summation contour for a non-phase-specific complex cell plotted on absolute (A) and normalized contrast axes (B). In the normalized plot the binocular data cluster around the line with a slope of −1.0 ( ). In agreement with the idea that the binocular contrast summation is linear, the best-fitting summation function represented by the dashed line had an exponent value of 0.94. The n values for the seven analyzed units ranged from 0.91 to 1.47 with a mean value of 1.14 ± 0.21. Four of the seven units had n values within 0.1 of 1.0. Although the number of cells is too low for a rigorous statistical analysis, the available data support the linear summation model. Clearly, the n values for all units fall well below those that characterize behavioral binocular summation contours, i.e., values of 2 or quadratic summation (Anderson and Movshon 1989; Legge 1984; Ridder et al. 1988).
Binocular contrast summation contours: antagonistic binocular interactions
Binocular suppression is a common phenomenon in monkey cortical neurons (Poggio and Fischer 1977; Smith et al. 1997). During the disparity tuning experiments, the majority of binocular simple cells and phase tuned complex cells showed binocular suppression for phase disparities that were 180° away from the optimal phase values, i.e., binocular response amplitudes below the monocular response amplitude for the dominant eye. In addition, a number of non-phase-specific complex cells exhibited binocular suppression at all interocular phase disparities (Smith et al. 1997). We investigated the manner in which antagonistic signals from the two eyes were integrated in two complex cells that exhibited non-phase-specific suppression and in two simple cells that were stimulated at nonoptimal phase disparities.
The binocular interaction data obtained at a nonoptimal phase disparity for one of the simple cells are shown in Fig. 13, left. Although this cell was not driven by the monocular left-eye stimuli, the disparity tuning function (Fig. 13 A) revealed a moderate degree of modulation (BII = 0.24; S/N =3.5) with an optimal phase disparity of ∼330°. The binocular interaction experiment was conducted with the use of a relative interocular phase disparity of 225°, a disparity that produced a binocular response equal to ∼60% of the maximum binocular response. Figure 13 B shows the contrast response functions measured at each of the interocular contrast ratios. The contrast response functions obtained for dichoptic pairs with right-to-left eye contrast ratios of 10/1 and 3.16/1 virtually superimposed the monocular function for the dominant right eye. However, as the right-to-left eye contrast ratio was reduced further, there was a reduction in the slope of the function and a progressive decrease in response amplitude. The binocular interaction contour was determined with the use of a criterion response amplitude of 7 spikes/s. Under monocular stimulus conditions, the right eye had a contrast threshold of 3.7%. However, in contrast to interaction contours measured at the optimal stimulus disparities, this cell's interaction contour (Fig. 13 C) had a steep, positive slope. As the left eye's contrast component was increased, the contrast of the right eye's stimulus also had to be increased to produce the criterion response, i.e., the stimulus in the left eye reduced the effectiveness of the right-eye stimulus. These antagonistic interactions were, however, well described by a linear function (r 2 = 0.98).
Figure 13, middle and right, shows the results for the two complex cells that exhibited non-phase-specific suppression. As shown by the phase tuning functions (top), the binocular response amplitudes for both neurons were not substantially affected by the relative interocular spatial phase of the dichoptic gratings, but the binocular firing rates were clearly below those produced by stimulating the dominant eye alone. The contrast response functions for the asymmetric, dichoptic grating pairs were measured at relative phase disparities of 337.5 and 292.5° for units 184L40 and 184L42, respectively. The results were similar for both cells. The dichoptic contrast response functions (▪, ▴, ▾, ♦, ⬡) were displaced to the right of the functions for the dominant right eyes and there was a progressive reduction in contrast gain as the relative contrast of the stimulus presented to the left eye was increased. The binocular interaction contours had steep positive slopes, again indicating that to reach the criterion response levels, an increase in right-eye contrast was needed to counterbalance an increase in left-eye contrast. For both complex cells, the interaction contours were adequately fit with a straight line (r 2 = 0.94 for unit 184L40, r 2 = 0.87 for unit 184L42).
Optimal phase disparities versus contrast
An assumption implicit in our binocular contrast summation paradigm is that the optimal stimulus parameters were invariant with respect to stimulus contrast and, in particular, to the interocular contrast ratio. This is a reasonable assumption with respect to a cell's optimal orientation and spatial frequency (Albrecht and Hamilton 1982; Sclar and Freeman 1982; Tolhurst and Movshon 1975). However, because stimulus contrast can influence behavioral (Harwerth and Levi 1978; Harwerth et al. 1980) and neurophysiological response latencies (Carandini and Heeger 1994; Dean and Tolhurst 1986; Shapley and Victor 1978), and because we employed drifting stimuli, it was necessary first to determine whether a cell's optimal interocular spatial phase was influenced by absolute contrast and/or interocular contrast asymmetries. In the cat striate cortex, Freeman and Ohzawa (1990) found that interocular contrast ratios as large as 10/1 did not influence the degree of modulation found in a cell's disparity tuning function. However, Freeman and Ohzawa did not systematically evaluate potential changes in optimal phase.
The effects of absolute contrast levels on the phase tuning functions of a simple cell and a phase tuned complex cell are shown in Fig. 14. During these experiments, equal contrast stimuli were presented to both eyes. In these representative examples from a sample of five simple cells and three complex cells, the general shape of the phase tuning function did not vary with contrast. Neither the relative degree of binocular interaction, as reflected by the BII (Ohzawa and Freeman 1986a,b), nor the optimal relative interocular spatial phase varied substantially with stimulus contrast.
The effects of interocular contrast asymmetries on a cell's optimal phase disparities were evaluated by measuring phase tuning functions simultaneously for a series of interleaved stimulus pairs that had different interocular contrast ratios. Specifically, the contrast was fixed at 12% for the left eye, but varied from 4.7% to 30% in the right eye. Figure 15 shows the results for representative simple (n = 5) and complex cells (n = 7). As revealed in the monocular contrast response functions for the right eyes (Fig. 15, left), contrast was varied in the dominant eye for the simple cell (top) and in the nondominant eye for the complex cell (bottom). Regardless of whether the dominant or nondominant eye's contrast was varied, the disparity tuning functions were similar in shape for all contrast ratios. As expected, systematic changes in the maximal binocular firing rate varied with the contrast presented to the right eyes. However, the relative degree of binocular interactions and the optimal stimulus phases did not vary substantially over the contrast range that we investigated. We did observe latency changes in the monocular responses of simple cells as a function of contrast. The simple cell shown in Fig. 15 A exhibited an increase in response phase lag for monocular right-eye stimuli of 16° as the contrast was reduced from the highest to the lowest values. Similar changes in phase lag have been observed in both cat and monkey simple cells for comparable contrast ranges (Carandini and Heeger 1994; Dean and Tolhurst 1986). However, the increase in response latency was not sufficient to produce significant changes in the cell's optimal disparity. But note that there was a subtle shift to higher relative spatial phases in the trough of this cell's tuning function as contrast was decreased.
Figure 16 summarizes the effects of interocular contrast differences on phase tuning. Figure 16, top and bottom, shows, respectively, the calculated BII (see Smith et al. 1997 for details) and the optimal phase angles plotted as a function of the interocular contrast ratio for individual cells. For both simple (filled symbols) and complex (open symbols) cells, neither the relative depth of modulation in the disparity tuning function nor the optimal phase disparity was affected by asymmetric stimulus contrasts. Also note that the results for a given cell were quite repeatable. The bottom pairs of open symbols in each graph show the results from the same cell obtained in two separate experiments in which the same stimulus parameter file was used. Despite the fact that these experiments were separated by >1 h, there was good correspondence between the two experiments in the BII and, in particular, in the optimal stimulus phase.
Overall, the results of these experiments indicate that contrast signals from the two eyes are combined in a simple linear manner by cortical cells. A major finding of this study was that there were no qualitative differences in the rules of combination exhibited by the different functional classes of cortical cells. Even though the overall responses of many cortical cells, in particular complex cells, are dominated by response nonlinearities, the inputs from the two eyes are apparently combined linearly. In addition, both cooperative and antagonistic binocular interactions reflect the linear combination of left- and right-eye contrast signals.
Polar plots of the phase tuning data for simple cells showed that both the amplitudes and temporal phases of binocular responses were in agreement with the predictions of a linear spatial summation model (Ohzawa and Freeman 1986a) in which spatial summation occurred both within each monocular receptive field and between the receptive fields in each eye. In essence, a simple cell's binocular response reflects the relative distribution of light in on versus off subregions across both the left- and right-eye receptive fields together. In this respect, the polarity of a stimulated area is critical; however, the eye of origin of a light-evoked signal has no specific consequence. Thus the vector summation analysis provides a quantitative basis for the cooperative interactions observed by Hubel and Wiesel (1968) in monkey simple cells on simultaneous stimulation of on or off subregions in both eyes with small bars of light and for the mutually antagonistic interactions found on simultaneous stimulation of opposite polarity subregions.
In agreement with the vector summation analysis, the analysis of the binocular interaction contours demonstrated that contrast signals from the two eyes are combined in a linear manner in monkey simple cells. As would be expected in the case of linear spatial summation between the receptive fields in the two eyes, dichoptic stimuli presented at the optimal spatial phases produced additive interactions, whereas stimuli presented 180° from the optimal disparity resulted in linear subtractive interactions. A satisfying aspect of the binocular interaction contours is that correspondence between a linear model and the experimental data could be easily quantified by linear regression. For each simple cell, even those that showed elongated vector summation plots, the binocular interaction contours were well fit by a straight line.
As described in the preceding paper (Smith et al. 1997), the relative phase tuning properties of monkey simple cells are qualitatively similar to those of simple cells in the cat's striate cortex (Chino et al. 1994; Ohzawa and Freeman 1986a). Likewise, the vector summation analysis indicated that the integration of left- and right-eye signals in individual simple cells is qualitatively comparable in cats and monkeys. However, by comparison with the data presented by Ohzawa and Freeman (1986a) for the cat, it would appear that a higher proportion of monkey simple cells show elongated polar plots. The higher proportion of elongated plots in the monkey could reflect an interspecies difference in the slope of the contrast-response functions of cortical neurons (Albrecht and Hamilton 1982). It is also possible that binocular responses in monkey simple cells are effectively influenced to a greater degree by a threshold mechanism. The observation that so-called obligate binocular cells are apparently more common in the monkey (Poggio and Fischer 1977; Poggio and Talbot 1981) than in the cat (Gardner and Raiten 1986) suggests that the responses of monkey striate neurons are influenced to a higher degree by a threshold mechanism.
In contrast to simple cells, complex cells are characterized by nonlinear, rectified responses throughout their receptive fields, they are comparatively insensitive to the spatial phase of a grating within their receptive field, and their responses to drifting gratings are dominated by an increase in the cell's average firing rate (Hubel and Wiesel 1968; Movshon et al. 1978b; Skottun et al. 1991). Many of these response properties are captured by multistage receptive field models that are composed of a number of discrete, but spatially overlapping, subunits. These subunits, which can have different response polarities, are assumed to exhibit linear spatial summation within and between spatially separated antagonistic subregions. The spatial structure of the individual subunits thus provides for the spatial frequency selectivity of complex cells. And even though the subunits encode visual information in a linear manner, the overall responses of complex cells are typified by nonlinear spatial summation because the outputs of the subunits undergo half-wave rectification before being combined (Movshon et al. 1978b; Spitzer and Hochstein 1985). Important issues are at what stage in this model and in what manner the contrast signals from the two eyes are combined.
In the cat, binocular interactions in phase-specific complex cells could be accounted for by linear spatial summation within the receptive field subunits before the nonlinear rectification process (Ohzawa and Freeman 1986b). The binocular interactions contours obtained from phase-selective complex cells in the monkey are consistent with the binocular model of Ohzawa and Freeman for phase-specific complex cells. Accordingly, the interocular disparity tuning of phase-specific cells in the monkey would come about because the left- and right-eye subunits pairs in these cells have the same optimal relative disparity. The linear summation observed in the binocular interaction contours would reflect the fact that the left- and right-eye contrast signals were combined at the subunit level before the cell's nonlinear stage. The anatomic identity of these subunits is not known. However, several observations support the long-held view (Hubel and Wiesel 1962) that simple cells may be the origin of the complex cell's receptive field subunits. For example, in both simple cells and phase-specific complex cells, disparity selectivity is orientation dependent (Smith et al. 1997).
Although the opposite-direction drift test of Ohzawa and Freeman (1986b) did not provide conclusive evidence of how binocular convergence occurred in non-phase-specific complex cells, our binocular interaction contours clearly indicate that the contrast signals from the two eyes are combined linearly. However, for non-phase-selective cells, it is not known at what stage within the cell's receptive field organization these interactions occur. Our data are in agreement with two possible convergence models described by Ohzawa and Freeman (1986b). It is possible that, as with phase-specific complex cells, the inputs from the two eyes are combined at the subunit level. Uniformity is a benefit of this convergence model. In this respect, phase tuning in the complex cell population appears to be continuously distributed; there are no apparent qualitative differences between phase-specific and non-phase-specific complex cells (Smith et al. 1997). The absence of phase tuning in non-phase-specific cells could be attributed to variations in the optimal disparity between subunits (Ohzawa and Freeman 1986b). However, it is also possible that binocular convergence could occur after the nonlinear rectification stage, but before the cell's threshold mechanism or its expansive response nonlinearity. In this scenario, the subunits would be essentially monocular. After rectification, the outputs of left- and right-eye subunits would be added together in manner similar to that described for the nonlinear subunits in Y-type retinal ganglion cells (Hochstein and Shapley 1976). Rectification before binocular convergence would preclude normal disparity selectivity. In this case, the key point provided by the binocular interaction contours is that the contrast signals from the two eyes to a given non-phase-specific complex cell would have a functional equivalence. Because signals related to stimulus polarity are lost after rectification, inputs from one eye could not cancel inputs from the other eye; thus only cooperative interactions would be possible. A decrease in the excitatory input from one eye could be counterbalanced by a functionally equivalent increase from the other eye. There is, however, an important distinction between this form of binocular convergence and that found in simple cells and phase-specific complex cells. In this case, binocular interactions would reflect linear summation of the contrast signals from the two eyes rather than linear spatial summation between the receptive fields in the two eyes. This idea supposes that the rectified responses of the subunits would be a linear function of contrast, an assumption that has been included in complex cell receptive field models (Spitzer and Hochstein 1985). In this regard, it is important to note that the responses of nonlinear subunits in Y retinal ganglion cells show a linear dependence on contrast (Hochstein and Shapley 1976). In light of the diversity of complex cell types, it is likely that binocular convergence is accomplished in more than one way.
Binocular convergence after the subunit rectification stage, but before the cell's spike-generating mechanism, is also consistent with data from complex cells that exhibited non-phase-specific suppression. Typically, under monocular stimulus conditions, these cells are only excited by stimuli presented to one eye, i.e., before rectification, the subunits receive stimulus-evoked excitatory inputs from only one eye. Inhibitory input from the nondominant eye, the strength of which would be linearly dependent on stimulus contrast, could be combined in a linear fashion with the excitatory rectified input from the subunits before the cell spike-generating mechanism. The nature of this inhibitory input is not known. It is possible, as suggested by Ohzawa and Freeman (1986b), that this antagonistic input results from intracortical signals from other complex cells that are monocularly innervated by the nondominant eye.
Binocular contrast summation
Psychophysical binocular summation at contrast detection threshold is assumed to reflect binocular interactions in striate neurons (Anzai et al. 1995; Fox 1991). In this respect, it is interesting that monkey cortical neurons show linear binocular summation, whereas behavioral binocular summation in both monkeys (Harwerth and Smith 1985; Ridder et al. 1988) and humans is incomplete and, instead, approximates quadratic summation (Anderson and Movshon 1989; Legge 1984). In this respect, Anzai et al. (1995) have also shown that binocular summation in individual cat cortical cells exceeds behavioral summation. The “distribution” model for binocular integration proposed by Anderson and Movshon (1989) provides a reasonable explanation for the apparent discrepancy between the behavior of monkeys and their cortical physiology. In fact, the model of Anderson and Movshon posits a pool of binocular cortical neurons that reflect the basic properties that we observed in this study. Specifically, the model of Anderson and Movshon includes a neuronal population that individually combines contrast signals from each eye in a linear manner and that as a group exhibit cell-to-cell variations in the slopes of their binocular interaction contours. According to the model of Anderson and Movshon, a neuron's relative contrast sensitivity in the two eyes would basically reflect the relative number and effectiveness of the inputs that it receives from the two eyes. In other words, the contrast threshold measured through a given eye would vary with ocular dominance and be reflected in the slope of the cell's binocular interaction contour. Cells that had interaction contours with slopes near −1, i.e., cells with equal monocular contrast thresholds, would be optimally stimulated by dichoptic stimuli that presented equal contrasts to the two eyes. It would be expected that behavioral detection of equal-contrast, dichoptic stimuli would be dominated by this subset of binocular neurons, whereas cells that were strongly dominated by one eye (the model of Anderson and Movshon did not include exclusively monocular neurons) and had interaction contours that were either very flat or very steep would be optimally stimulated by dichoptic stimuli with large interocular contrast asymmetries. These cells would constitute an independent detection channel that would be expected to dominate behavioral detection of monocular stimuli and binocular stimuli with large contrast asymmetries. Thus the behavioral binocular summation contour would deviate from linear summation because monocular contrast thresholds mediated via cortical channels composed of cells with asymmetric ocular dominances would be lower in absolute terms than the monocular contrast thresholds mediated via channels with balanced ocular dominances. The limited data set in these studies does not allow us to address this question, but it is clearly testable.
In summary, the mixing of inputs from the two eyes to produce binocular neurons in the monkey striate cortex appears to follow the same rules of combination that underlie many of the distinctive response features of cortical neurons. Selectivity for stimulus spatial frequency (Movshon et al. 1978a), orientation (Ferster 1981, 1988; Hubel and Wiesel 1962), and direction of movement (Albrecht and Geisler 1991; Heeger 1993; Jagadeesh et al. 1993; Reid et al. 1991) can, to a first approximation, be accounted for by a linear summation of input signals before a cell's nonlinear mechanisms. Likewise, our results suggest that before spike generation the postsynaptic potentials produced by visual stimulation of a given eye reflect the strength of the stimulus and the relative number and effectiveness of inputs from the stimulated eye and are combined in a nondiscriminating, linear manner with postsynaptic potentials produced by stimulation of the other eye.
We thank W. Ridder III and K. Kitagawa for help in some of the recording experiments.
This work was supported by National Institutes of Health Research Grants EY-03611, EY-08128, and RR-07146 and funds from the Greeman-Petty Professorship of the University of Houston Endowment.
Address reprint requests to E. L. Smith III.
- Copyright © 1997 the American Physiological Society