INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

A neuron in visual cortex receives input from a particular region of the visual field. Within this region is a primary excitatory area traditionally studied in the literaturethe classical receptive field or CRF. Information must be incorporated from distinct and distant regions of the visual field to create a global visual percept from local features. Although this integration has traditionally been attributed to higher visual areas with larger CRFs, it is now known that neurons in primary visual cortex receive signals, typically suppressive, from a region extending beyond the classical receptive field (Allman et al. 1985; Blakemore and Tobin 1972; DeAngelis et al. 1994; Dreher 1972; Hubel and Wiesel 1968; Levitt and Lund 1997; Nelson and Frost 1985; Sillito et al. 1995). Thus early visual cortical areas such as V1 integrate information from rather large areas of the visual field. To study the limits of early spatial integration, one must determine the nature and extent of the classical central excitatory influence and the more extensive suppressive influence.

Different laboratories have used different methods to measure the CRF. Some used the minimum response field or MRF (Barlow et al. 1967), which estimates the extent of the excitatory influence by marking off the portions of the visual field in which a small edge or bar of light elicits a response from the neuron. Others used expanding patches of drifting grating to estimate the region of summation (DeAngelis et al. 1994; Sceniak et al. 1999). Because the central excitatory region of the receptive field becomes less sensitive farther from the center (Movshon et al. 1978a,b), small isolated stimuli near the insensitive receptive field fringes may only afford subthreshold stimulation that would be undetected using the MRF method but would cause changes in suprathreshold responses in the summation technique. Thus these two methods for measuring receptive field extent typically yield quite different resultsMRF measurements of receptive field size are usually smaller than summation measurements. Moreover, Gilbert et al. (1996) and Kapadia et al. (1999) demonstrated with bar stimuli that summation depends on stimulus contrast, and Sceniak et al. (1999) showed analogous effects that depend on the contrast of grating targets.

Expanding a patch of grating beyond the region of summation often reveals suppression as the stimulus engages the otherwise silent inhibitory surround. Responses to larger stimuli therefore reflect the interaction between excitatory and inhibitory mechanisms with different spatial structure. The challenge we address in this paper is to reconstruct the underlying spatial structure of the excitatory center and inhibitory surround mechanisms and to determine the manner of their interaction. We first show that signals from the surround modulate responses of the center through a divisive gain control. We then construct and test a model based on the ratio of two Gaussian sensitivity distributions that accounts well for variations in receptive field size and suppression evident under different measurement conditions. These variations are well captured by a model in which the spatial extents of the center and surround are stable features of the receptive field; their sensitivities depend differently on stimulus contrast and recent stimulation history. Such a model, while not intended to suggest any particular biophysical implementation, reveals simply that changes in the size of a receptive field can be generated by changing only the sensitivities of center and surround mechanisms that are themselves stable in spatial extent. The extent of these regions is substantially larger than previously thought and leads us to propose a novel interpretation of the role of different neuronal circuits in generating visual cortical receptive fields.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Subjects and surgical preparation

We collected data from simple and complex cells in primary visual cortex of 14 adult Cynomolgus monkeys (Macaca fascicularis) and 5 adult pig-tailed macaques (M. nemestrina). Before surgery, each animal was premedicated with 1.5 mg/kg diazepam or 0.05 mg/kg acepromazine maleate and 0.05 mg/kg atropine sulfate. Each monkey was initially anesthetized with 10.0 mg/kg ketamine HCl. Anesthesia during surgery was maintained by 1.5-3.5% halothane or isoflurane in a 98% O₂-2% CO₂ mixture. Surgery consisted of the placement of cannulae in the saphenous veins of both legs as well as installation of a tracheal cannula. The monkey's head was then placed in a stereotaxic frame, and a small craniotomy was made over parafoveal opercular V1 in one of two locations. The more medial of the craniotomies was made just posterior to the lunate sulcus and about 10 mm lateral to the midline. This type of vertical penetration yielded two, and sometimes three, passes through V1: opercular V1 near the fovea, upper-bank calcarine V1 in the lower visual field, and lower-bank calcarine V1 in the upper visual field. The second type of craniotomy was positioned more laterally and yielded a tangential penetration that remained in opercular parafoveal V1. An agar-filled plastic chamber was placed over each craniotomy to prevent cortical desiccation and to reduce pulsations of the cortical surface. The agar in the chamber was topped with petroleum jelly and/or Parafilm to prevent dehydration and shrinkage of the agar.

Anesthesia was maintained for the duration of each experiment with sufentanyl citrate (4-12 µg/kg/h) in lactated Ringer solution with dextrose (2.5%) administered through one of the leg cannulae. The animal was paralyzed with vecuronium bromide (Norcuron, 0.1 mg/kg), also in lactated Ringer solution, providing a total hourly fluid infusion of 3.25-15.0 ml/kg/h, depending on the animal's weight. The state of anesthesia was continually monitored by electrocardio- and electroencephalography (ECG and EEG), which was recorded from two sites separated along the cranial surface. The level of anesthesia was adjusted when necessary by changing the infusion rate of the anesthetic. The animal was artificially respirated with moist room air at 22-30 strokes per minute, with stroke volume adjusted to keep end-tidal CO₂ between 30 and 36 mmHg. Body temperature was maintained at or near 37.5°C by a thermostatically controlled heating pad attached to a rectal temperature probe. The pupils were dilated with topical atropine sulfate, and the corneas were protected by clear contact lenses (+2.0 diopters). Corrective lenses were used as needed to make the retinae conjugate with the display screen, as determined initially by direct ophthalmoscopy and later by maximizing neuronal responses to sinusoidal gratings at high spatial frequencies. The locations of both foveae were plotted on a tangent screen that was also used for mapping receptive fields.

Visual stimulation

Visual stimuli were generated by a Truevision ATVista board or a Cambridge Research Systems VSG 2/2 graphics board and displayed on a Nanao T560i monitor (mean luminance: 33cd/m², frame rate: 106 Hz, subtense: 8-25° visual angle depending on viewing distance). Nonlinearities in phosphor output were corrected by lookup tables.

Sinusoidal gratings were presented alone or in conjunction with another grating (or another pair of gratings) on a gray background with the same mean luminance as the stimulus. The screen contained a mean gray field during inter-stimulus intervals. Stimuli within the classical receptive field (CRF) were contained in a circular window, while stimuli outside the CRF were in an annular window surrounding the CRF or in circular windows outside the CRF. Stimulus windows had rectangular contrast profiles. Simultaneous gratings were sometimes presented by temporally interleaving the two component stimuli in alternate frames, resulting in each grating appearing at half the maximum available contrast (50%). Except in these cases, and when contrast was an experimental variable, gratings were presented at 100% contrast. Simultaneous gratings had the same spatial and temporal frequency but could have their contrasts independently varied. When we presented compound center/surround gratings, stimulus onset of both component gratings was always synchronous.

Unit recording and analysis

We recorded neural activity using tungsten-in-glass electrodes (Merrill and Ainsworth 1972), the initial signals of which were amplified, band-pass filtered, and fed into a time-amplitude window discriminator (Bak Instruments). Action potential pulses from the window discriminator and synchronization pulses from the graphics board were both collected by a computer interface (Cambridge Electronic Design 1401 Plus) and stored with a resolution of 0.25 ms. We measured cell response as either the mean response firing rate minus the mean spontaneous firing rate (for complex cells) or the magnitude of the first harmonic response (for simple cells) at the temporal frequency of drift. Cell class (simple or complex) was determined for each neuron based on which measure of response (mean firing rate or first harmonic response) provided the greatest value during determination of spatial frequency tuning (Skottun et al. 1991).

Experimental design

Each experiment consisted of a number of different stimuli pseudo-randomly ordered in blocks, the number of blocks determining the number of times each stimulus was repeated. Within each block, each stimulus was presented for 1.5-6 s, and experiments contained from two to five blocks. The inter-stimulus interval was typically about 2 s but could be as long as 5 s depending on the time required for the software to generate stimuli of higher complexity.

Receptive fields were initially mapped by hand on a tangent screen, the position and the dimensions of the receptive field being qualitatively determined by listening to the discharge on the audio monitor. We then occluded the nonpreferred eye and used a front-surface mirror to center the receptive field on the monitor. After a brief qualitative determination of the preferred orientation, spatial frequency, and temporal frequency, quantitative assessment of tuning characteristics commenced under computer control.

For each neuron, we first determined the preferred orientation and direction. This was done quantitatively by measuring the response to sinusoidal gratings drifting in different directions, centered on the receptive field as determined by initial mapping. We then determined the preferred spatial frequency by presenting drifting gratings at the neuron's preferred orientation while varying spatial period. Finally, we determined the preferred temporal frequency in a similar manner, using stimuli with the neuron's preferred orientation and spatial frequency.

Histology

At the end of experiments, animals were perfused with 4% paraformaldehyde in saline. The brains were blocked either parasagittally or coronally, and blocks of tissue were cryoprotected by sinking them in a series of sucrose solutions of increasing concentration (10-30%). Blocks were cut into 40-µm sections that were mounted on slides and stained for Nissl substance with cresyl violet.

We reconstructed electrode tracks from cortical slices of each animal by locating lesions made by passing small amounts of current (2 µA, 2-5 s) through the electrode tip and visualizing tissue damage from the passage of the electrode. We confirmed track locations through cortex by comparing them with depths of gray matter/white matter transitions that were noted during each penetration. We determined the laminar location of each cell by overlaying a mosaic image of histological sections with a scaled plot of cell depths along the electrode penetration. Cells were assigned to laminae based on visual inspection of landmarks in the stained sections.

Model fitting

When comparing neuronal responses to model predictions, we used the STEPIT algorithm (Chandler 1965) to minimize the combined ² errors between recorded response magnitudes and model predictions. When a family of curves was recorded, all curves in a family were simultaneously fit, and the minimization algorithm chose the best values for parameters that were not permitted to vary among curves.

We assessed the goodness of each fit by calculating the ² error between the data and the model predictions

(1)

where e_i was the model's expectation of response for the ith stimulus, o_i was the observed response, and _i² was the expected variance of the response.

To avoid unreasonably large errors from randomly small measures of variance, we exploited the observation that the relationship between the variance and mean of cortical neural responses is linear (e.g., Schiller et al. 1976; Tolhurst et al. 1981, 1983; Vogels et al. 1989). We used neuronal spike counts from the pooled responses of each neuron to calculate the constant of proportionality of response variance to response ratethe variance to mean ratio ()for each cell. We then used this ratio to compute the expected variance for each response, thus discounting random fluctuations in variance that could cause inflated error calculations. For simple cells, means and variances were calculated accounting for response phase. ² error was taken as

(2)

in which o is the observed response rate, e is the expected (fit) response rate,  is the variance to mean ratio, t is response duration (required to convert the variance of spike counts to the variance of the response rate), and k is a small factor, calculated for each cell, to prevent responses of zero from producing infinite errors [k = 0.01( max(o))].

This raw ² is not appropriate for comparing models with different numbers of free parameters because of the different numbers of degrees of freedom. To compare fits for models with different numbers of degrees of freedom, we used the normalized ² value, (Hoel et al. 1971):

(3)

where df was the number of degrees of freedom in the model.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

We recorded the responses of 352 neurons in V1. We only included neurons in our analysis that fired at least five spikes/s (334/352 units), and we excluded neurons for which we could not determine the CRF boundaries (see following text, 29/334 units). Fifty-seven percent of receptive fields in our sample were centered within 5° of the fovea, with an additional 9% between 5 and 10°. Eccentricities between 10 and 25° accounted for 19% of our data, and the remaining 15% of receptive fields had eccentricities between 25 and 40°. Simple and complex cells did not respond differently in our experiments, and have been pooled for all analyses.

Spatial distribution of excitatory and suppressive influences

We obtained estimates of CRF extent, surround extent, and surround suppression from stimulus expansion tuning curves. Figure 1A () shows an example of a stimulus expansion tuning curve for a simple cell. The response of the neuron is plotted as a function of grating patch diameter. Patches of drifting grating were centered on the CRF and presented at the neuron's preferred orientation, spatial and temporal frequencies. The diameter of a patch of grating was systematically varied over a range of eight or nine logarithmically spaced values. Stimulus diameters ranged from 0.15 to 15.7° of visual angle. Diameter tuning curves followed a typical pattern, of which Fig. 1A () is representative. For very small stimuli, responses were low. Responses increased with stimulus diameter and were suppressed for the largest stimuli. For our analysis, we took the grating summation field (GSF) as the diameter of the smallest stimulus that elicited at least 95% of the neuron's maximum response (1.3° in this example).

View larger version (13K): [in this window] [in a new window]   Fig. 1. Example diameter tuning curves for circular and annular patches of grating. Responses of 4 neurons are shown to patches of circular grating () and annular patches of grating (). A: typical diameter tuning curves. The smallest diameter at which responses to circular patches stopped increasing was our initial measure of receptive field extent, the grating summation field (GSF). The smallest inner diameter at which the neuron ceased responding to the annular stimulus was the annular minimum response field (AMRF). We extracted the diameter of the surround from our data as the smallest circular patch diameter at which the suppressive influence asymptoted. Suppression was the relative reduction in response from the neuron's maximum response to this asymptotic response. For some neurons (B-D), we were unable to extract all parameters because there was no suppression (B), no response saturation (C), or no suppression asymptote (D).

Stimulation by the large grating patches usually caused a measurable reduction in response. Suppression increased as the stimulus continued to extend into the receptive field periphery until further expansion into the surround no longer produced additional suppression. We took the inhibitory surround extent as the diameter of the smallest stimulus for which the neuron's response was reduced to within 5% of its asymptotic value for the largest gratings. For 29 of 334 units, there was neither suppression nor response saturation for our largest stimuli, and we were therefore unable to estimate the extent of the CRF. An example of such a data set is drawn in Fig. 1C. These cells were not included in further analyses. For some other neurons (123/305 units), the suppression saturation point was not reached (Fig. 1D). For these cells, we considered the extent of the surround to be the diameter of the largest stimulus presented. We occasionally observed nonmonotonic suppressive effects (De Valois et al. 1985), but the magnitudes of these effects and their frequency of occurrence were not substantial enough to affect our primary findings.

Surround suppression strength for each neuron was calculated from the diameter tuning curve as the reduction from the maximum response to the asymptotic response for large stimuli. We computed a suppression index, SI, which expressed suppression as a fraction of the optimal response

(4)

where R_opt is the maximum response, and R_supp is the suppressed response (Fig. 1A).

In most cases, the patch diameter tuning experiment included a second set of stimuli, consisting of drifting gratings in an annular window centered on the receptive field. The outer diameter of the annulus was fixed at the largest value possible on our display, whereas the inner diameter assumed the same values as the circular patch diameters. Figure 1, , shows responses to the annular stimuli as a function of increasing inner diameter. Responses to annuli with the smallest inner diameters (leftmost ) approximated responses to the largest circular patches of grating (rightmost ), as expected. Progressing from left to right in the plot, the inner edge of the annulus withdrew from the center of the CRF, and the response of the neuron decreased, eventually reaching the spontaneous rate when the CRF was no longer stimulated. We estimated the extent of the CRF as the point at which the response to the annular stimulus reached a value of at most 5% of the neuron's maximum response to a circular patch of grating. We called this estimate the annular minimum response field or AMRF.

We compared the empirically derived extents of the center and surround influences for the 260 neurons (of 305) for which suppression was greater than 10%. Figure 2 shows the distribution of GSF diameters and surround diameters for four different ranges of eccentricities (cf. Levitt and Lund 2002). The average GSF diameter for small eccentricities (eccentricity µ = 2.4°,  = 1.2°) was 0.8° and increased to 2.1° for the largest eccentricities (eccentricity µ = 29.6°,  = 2.8°). These means were significantly different (t-test, P 0.001). The average surround diameter for low eccentricities was 2.5° and increased to 6.9° for the largest eccentricities. These means were also significantly different (t-test, P 0.001). The distributions cumulated along the diagonal of each panel in Fig. 2 show the ratios of surround to GSF extent. These distributions do not differ from one another, and over all eccentricities the geometric mean ratio was 3.2 ± 2.0 (mean ± SD) (cf. Li and Li 1994; Maffei and Fiorentini 1976).

View larger version (16K): [in this window] [in a new window]   Fig. 2. Center and surround extents extracted from data. Each panel shows the diameter of the surround plotted against the diameter of the center for each of 4 ranges of eccentricities. Marginal histograms show, for each panel, the distribution of GSF diameters (right) and the distribution of surround diameters (top). The ratio of surround to center extent is plotted in the histogram on each diagonal. , the geometric mean in each distribution. We included neurons for which there was a measurable (at least 10%) degree of suppression (n = 260). Both GSF diameter and surround diameter increased with eccentricity, although the ratio of surround to center diameter (relative surround extent) was fairly constant across eccentricities.

Examining distributions of GSF diameter and surround diameter by cortical lamina showed slightly larger receptive field diameters in layer 6, while surrounds appeared smaller for layer 2/3 neurons. Despite visible trends, homogeneity for these distributions could not be rejected on the basis of a ² test. Sceniak et al. (2001) observed significantly larger receptive field sizes in layer 6 and smaller receptive fields in layer 3B. They also showed that layer 2/3a surrounds were smaller, although not significantly. They did observe, however, that layer 2/3a surrounds were significantly smaller than layer 6 surrounds. As our penetrations often went through the operculum into the calcarine sulcus, we were unable to use a canonical depth grid for unbiased layer placement and instead had to rely on visual inspection of electrode tracks (see METHODS). Thus we were unable to systematically differentiate layers with typically vague borders, and so we cannot rule out the possibility of some laminar differences.

On average, neurons were suppressed by 38% of their maximum firing rate by stimuli extending beyond their classical receptive fields. Figure 3B shows the distribution of suppression indices for all neurons. Only a very small number of neurons (2 of 106 with sufficient spontaneous activity) were suppressed below spontaneous firing rate by large patches of grating, even though stimulating the surround often suppressed responses to stimuli within the receptive field. This suggests that inhibitory influences from the surround act by modifying gain, not by subtraction.

View larger version (15K): [in this window] [in a new window]   Fig. 3. Distribution of surround suppression for 305 neurons for which there was either suppression or response saturation for the largest patches of grating. Suppression is expressed as a suppression index (SI)the fractional reduction in the neuron's maximum response. Neurons were suppressed by an average of 38% of their maximum response by stimuli extending beyond the GSF.

When analyzed by lamina, suppression was slightly stronger on average for cells in layer 4ab and weaker for cells in layer 6. This trend was not significant based on a ² test. Sceniak et al. (2001) found a similar trend in their data set to be significant.

Along with the AMRF and GSF determined from responses to gratings, we also qualitatively assessed the MRF with bars of light. This gave us three independent measures of receptive field extent. We compared qualitative estimates of the MRF with GSF diameters for 217 neurons. The GSF was, on average, about twice the diameter of the MRF. For 162 neurons, AMRFs were on average 47% larger than GSFs.

For simple cells of a particular preferred spatial frequency, variations in GSF size should be related to variations in spatial frequency selectivityspecifically, cells with large GSFs relative to the period of their preferred frequency are best stimulated when a relatively large number of cycles of the preferred grating fall within their receptive fields. Such cells should have narrow spatial frequency bandwidths, while cells with relatively small GSFs should have broad bandwidths. This trend could be easily seen in our data: the correlation between spatial bandwidth (in octaves) and the ratio of GSF diameter to preferred spatial period was 0.40 (n = 123, P 0.001). A similar trend would be expected also for orientation bandwidth (cf. De Valois et al. 1985), and we found a similar relationship in our data (r = 0.35, n = 118, P 0.001). We conclude that measured variations in GSF diameter correspond to functional summation zones within cortical receptive fields that are related to their spatial selectivity.

More than half of our neurons tested with the annular stimuli (150/255) had AMRFs that were larger than their GSFs, meaning that an annular stimulus placed entirely outside the receptive field measured with a patch of grating could still elicit a response. The behavior of these neurons gave us an important clue about the relationship between center and surround mechanisms. Consider the example cell whose data are shown in Fig. 4. Responses to circular patches of grating are plotted as  and responses to annuli are plotted as ; the shaded area represents the difference between the two estimates of receptive field extent. For this neuron, the GSF was 1.3° in diameter, meaning that increases in outer diameter beyond this value caused response to decrease. However, the response to an annular grating began to increase when the inner diameter was made smaller than 2.7°. Thus the region of the receptive field covered by an annulus whose inner and outer diameters were 1.3 and 2.7° had an influence on response that depended on the pattern of stimulation of other parts of the receptive field. The schematics at the top and bottom of Fig. 4 make this explicit by showing the effect of this annulus on response. When added to the optimal circular patch of grating, the annulus caused a 20% reduction in response, but when added to the ineffective annular grating, the same annulus increased the neuron's firing rate to about 30% of its maximum. We interpret this to mean that in the region defined by this annulus, the neuron's response depended on a combination of influences from the excitatory center mechanism and the suppressive surround. The balance between the excitatory and inhibitory regions determined whether a stimulus would excite or suppress.

View larger version (31K): [in this window] [in a new window]   Fig. 4. Certain regions of the receptive field yield different responses depending on stimulus context. , responses to a circular patch of grating; , responses to an annular patch of grating. Shading indicates the area outside the GSF from which an annular stimulus still elicited a response. Stimulation of this shaded area yielded suppression when the center was being stimulated by a grating with a diameter of 1.3° and excitation in the presence of an annular patch of grating with an inner diameter of 2.7°. This suggests that the excitatory and inhibitory influences of the receptive field are independently regulated, their balance determining the overall effect of stimulation.

We conjecture that center and surround responses arise from independent mechanisms, the gains of which are independently regulated. A stimulus in the center reduces center sensitivity, allowing surround suppression to dominate in the transitional annulus. Similarly, a surround stimulus reduces surround sensitivity, allowing the center to dominate in the transitional annulus. This explains why adding the annulus to the center causes suppression while adding it to the surround causes excitation and suggests that it might be fruitful to try to explain other complex features of responses with a model in which the sensitivity of the center and surround mechanisms are independently regulated. Before building such a model, however, it is necessary to know the form of the interaction between center and surround signals.

Contrast response of the center and surround

Given independent center and surround mechanisms, suppression from the surround will manifest itself in the neuron's contrast response. Suppression might be either divisive or subtractive, requiring responses at different stimulus contrasts to differentiate the two. Characterizing changes in a neuron's contrast response will tell us whether the influence from the surround should be modeled as a divisive or subtractive suppression.

Figure 5A shows three ways in which a neuron's contrast response might be changed by stimulating the receptive field surround. A horizontal shift in the neuron's contrast response curve represents a change in the neuron's response with stimulus contrasta change in contrast gain. Changing contrast gain does not typically affect a neuron's maximum firing rate but effectively scales contrast for the neuron. A vertical scaling of the curve represents a change in response dependent on the neuron's firing ratea change in response gain. This gain change does not alter the range of contrasts to which a neuron responds but simply scales responses at all contrasts. Changes in both contrast gain and response gain are divisive forms of suppression. A third possibility is subtraction in combination with a threshold that reduces responses the same amount at all contrasts. To determine which of these three forms of suppression best characterized surround influences, we considered three models. The first model accounts for surround suppression through a divisive change in the neuron's response gain. This response gain model is

(5)

in which R is the neuron's response, K(c_s) is the scaling factor dependent on surround contrast, c_c is the center contrast,  sets the neuron's contrast gain, and  sets the slope of the neuron's contrast response function in log-linear coordinates. In this model, contrast response is scaled by a single factor K(c_s) that depends on surround contrast.

View larger version (18K): [in this window] [in a new window]   Fig. 5. Different forms of surround suppression. A: 3 ways in which a neuron's contrast response can change. The bold curve represents a neuron's unmodified response to stimuli at different contrasts. The two thinner solid curves represent 2 divisive forms of suppression. A change in contrast gain (thin gray curve) is a divisive suppression that effectively scales stimulus contrast for the neuron. A change in response gain (dashed curve) is a divisive suppression that scales responses equally at all contrasts. The 3rd type of suppression shown is subtractive (thin black curve), which suppresses the same amount at all contrasts. B: responses and fits for 2 sample cells (left and right) to models accounting for surround suppression either by division (top and middle) or subtraction (bottom). The circles in each panel represent responses to a compound center/surround stimulus in which we varied the contrast of each component grating independently. The abscissa designates the contrast of the center patch of grating, while the shading of each circle denotes the contrast of the surround stimulus with darker shades representing higher contrasts (lightest to darkest circles = 0, 3, 6, 12, 25, and 50% contrast, respectively). Responses decrease as surround contrast increases (lighter to darker circles). Solid curves are fits of the 3 models. Top panels show fits to the response gain modelmodeled contrast responses are vertically scaled versions of one another. Cell 2 (right) was fit best by the response gain model. Middle panels show fits to the contrast gain modelsurround contrast shifts the curves horizontally. Cell 1 (left) was best fit by the contrast gain model. Bottom panels show fits to the subtractive model, which performed reasonably for both cells. Inset in each panel is the 2 error normalized by the degrees of freedom in each model (). C: comparison of for 3 models. Axis units are normalized, making the total value for all 3 models equal 1. The distance of a point from each bounding axis represents its for the fit to that model. Points in the center of the plot represent data fit equally well by all 3 models. Points near a bounding axis represent cells for which that model performed better than the others. The response gain model performed best, indicated by the number of points nearest that axis. When we took response phase into account for simple cells, the response gain and contrast gain models performed equally well. The subtractive model on average did the poorest job accounting for surround suppression.

The second model also accounts for the surround influence with divisive suppression, but through a change in contrast gain

(6)

For the contrast gain model, the response-scaling factor K is fixed, but the contrast gain parameter (c_s) depends on surround contrast.

The third model assumes a subtractive influence from the surround

(7)

in which k₀(c_s) is a response offset that depends on surround contrast. The maximum operation simply imposes a floor at 0 on the response. Each of these models is based on the familiar Michaelis-Menten equation, which well describes the contrast/response relationship in visual cortical neurons (Albrecht and Hamilton 1982).

We collected families of contrast response curves from 66 neurons. We presented center and surround gratings at the neuron's preferred orientation, spatial frequency, and temporal frequency. In these and other experiments, we used our measurements of the GSF and AMRF to make conservative choices for the center and surround regions. We always chose center stimuli to be equal to or smaller than the GSF diameter, reasoning that they were thus confined to a region in which the center mechanism was dominant. To be certain that the surround stimulus did not encroach on the center, we always chose surround stimuli to be annuli whose inner diameter was either the AMRF diameter or the GSF diameter, whichever was larger.

We independently varied the contrasts of the center and surround stimuli and for each neuron obtained a family of six contrast response curves. The data (circles) in Fig. 5B are examples of families of contrast response curves recorded from two neurons. Each set of points shows the response of the neuron to increasing center contrast in the presence of a single surround contrast. The shading of the points in each curve represents surround contrast: white for 0% surround contrast to black for 50% surround contrast. Responses of a simple cell are shown on the left. For this neuron, an increase in surround contrast caused a rightward shift in the contrast response curve as indicated by the disappearance of response saturation at higher surround contrasts. For the responses of the complex cell shown on the right, there was a change in slope and a loss of response saturation, suggesting that none of the three models would completely account for the effect of increasing surround contrast.

We fit our models to the response magnitudes of our contrast response curve families. Sample fits of each model for two cells are shown in Fig. 5B as solid curves. The top panels show fits to the response gain model, the center panels show fits to the contrast gain model, and the bottom panels show fits to the subtractive model. The shading of each curve indicates surround contrast, with darker shades representing higher contrasts. Each panel gives for that model's fit to the responses (see METHODS). The neuron for which the contrast response curve shifted horizontally with surround contrast (left) was best fit by the contrast gain model. On the other hand, the neuron for which responses seemed to scale vertically with surround contrast (right) was best fit by the response gain model. The subtractive model also provided good fits in both cases, but in neither case was the best. Although the models provided good fits qualitatively, the were often well above 1 (e.g., for contrast gain in cell 1). This was often due to model deviations from the large number of small responses at low contrast; response variances were proportionately low and thus provided greater penalties when fitting.

Each model provided adequate fits to responses from most neurons (mean  = 2.15 for response gain, 2.24 for contrast gain, and 2.38 for subtraction). We compared the three models on the basis of their values, which accounted for differences in the number of degrees of freedom. We made a three-way relative comparison (Fig. 5C) by plotting a point in a triangular space in which the distances of a point from the three edges were in proportion to the values for the three models indicated by the edge labels. If all three values of were equal for a neuron, its point would lie at the center of the triangle. If the for only one of the fits was zero, the point would lie on the edge corresponding to that fit. The point for each cell therefore lies in the triangle closest to the edge corresponding to the model that provides the best fit for its data. The distribution of points favors the response gain model, while fewer than 25% of neurons were best described by a subtractive change in response. When we fit the simple cell subpopulation of our sample (23/66 units) to forms of the models that accounted for the effects of contrast gain on response phase (Carandini et al. 1997b), the numbers of units better described by the contrast gain model (10/23) and by the response gain model (13/23) were roughly equal.

The subtractive model, when compared with the two divisive forms of suppression, performed best in less than a quarter of the neurons. In addition, fits to a model which used both contrast gain and response gain to account for surround suppression produced an improvement in (mean = 1.82), suggesting that using both of these forms of divisive gain provides a better description of the data than either one alone. Because previous results have suggested that suppression is mediated by divisive changes in gain (DeAngelis et al. 1994; Sengpiel et al. 1998; Somers et al. 1998), we conclude that the influence of the surround is best considered as some form of divisive or modulatory suppression. We considered two different forms of divisive interaction, contrast gain and response gain. Our laboratory has previously shown that contrast gain models account well for suppressive effects within the classical receptive field (Carandini et al. 1997b). In the case of surround suppression, however, our analysis suggests that the response gain model provides a better description. For the purposes of the remaining work in this paper, the two models are equivalent; more refined experiments are needed to decide which description is more accurate.

Stability and independence of center and surround mechanisms

Recall that stimulus context appears to differentially set the gains of the center and surround (Fig. 4) and that we have just concluded that the surround acts through some divisive form of suppression. We now describe and test a receptive field model that assumes independent center and surround mechanisms in which the surround influences responses through a divisive gain control. This model is intended to provide a simple explanation of changes in receptive field size by using mechanisms with spatially constant dimensions.

Based on the general shape of diameter tuning curves, we modeled the sensitivity distribution of each mechanism with a one-dimensional Gaussian envelope of sensitivity. Integration of this one-dimensional Gaussian corresponds to integrating a two-dimensional envelope of the form

(8)

where r is radius and  is the SD of the Gaussian envelope. This envelope determined the spatial extent of the receptive field mechanisms. It is important to understand that the Gaussian envelopes do not describe the spatial weighting function of the receptive field but only the envelope of that function. So for a linear approximation to a simple cell, the center envelope would correspond to the Gaussian envelope of a Gabor filter (Movshon et al. 1978a). For a complex cell, the center envelope would correspond roughly to the receptive field map obtained from a line weighting function (Movshon et al. 1978b). Figure 6 shows a schematic of this model. The left portion of the model shows the overlapping one-dimensional sensitivity envelopes. We calculated the activity of each mechanism by taking the integral under each Gaussian envelope covered by a stimulus placed over their common centers. The model divides the output of the center mechanism by the output of the surround mechanism; the gain for each mechanism is independently controlled by the gains k_c and k_s. This divisive interaction of center and surround mechanisms formed a ratio of Gaussians (RoG). To model responses to circular patches of grating we take

(9)

where

(10)

and

(11)

in which x is stimulus diameter, k_c and k_s are the gains of the center and surround mechanisms, and L_c and L_s are the summed squared activities of the center and surround mechanisms, respectively. The spatial extents of the center and surround components were represented by w_c and w_s. We always constrained w_c < w_s.

View larger version (7K): [in this window] [in a new window]   Fig. 6. The ratio of Gaussians (RoG) model. We constructed the RoG model from independent and spatially stable center and surround components. We modeled each component as a Gaussian envelope of sensitivity incorporating the spatiotemporal tuning characteristics of a neuron. Each component had an independently controlled gain, and the surround affected the model cell's response through divisive suppression. The model is instantiated in Eq. 9 through 11.

This model implements a general divisive normalization, so Eq. 9 differs from previously considered divisive models (Eqs. 5 and 6), which capture particular kinds of divisive normalization (changes in response gain and contrast gain). Rather than explicitly describe the neuron's contrast/response relationship, we devised a new model according to a more generalized concept of divisive normalization as illustrated in Fig. 6. This generalized RoG model is similar to the one used by Chen et al. (2001) to model the effect of patches of grating flanking the CRF on a neuron's contrast response.

Changes in receptive field structure with contrast

Sceniak et al. (1999) and Kapadia et al. (1999) have recently demonstrated that the spatial extent of the receptive field appears to change with stimulus contrast: at lower contrasts, neurons prefer larger stimuli. Although at first it might appear that the underlying mechanisms must grow as contrast decreases (Sceniak et al. 1999), we decided to use our model to test whether simply changing the gains of fixed center and surround mechanisms could account for changes in measured receptive field extent with contrast. Figure 7 illustrates the manner in which receptive field extent can change assuming spatially stable center and surround mechanisms. The center and surround mechanisms (gray lines) are identical in each panel save for their gains, which are represented by the thickness of the lines. We calculated the resulting apparent receptive field (solid black line) by dividing the center mechanism by the surround mechanism, and imposing a response threshold (dashed black line). The boundaries of the resulting receptive field (shaded area) are designated by the dotted vertical lines, and the width of the receptive field is noted in each panel along with the relative gain of the surround mechanism. For strong surround gains, the resulting receptive field is small. As surround gain decreases, more of the receptive field is uncovered, resulting in an expansion of the measured receptive field. This receptive field expansion is purely a function of the changing balance between center and surround gains.

View larger version (11K): [in this window] [in a new window]   Fig. 7. Stable center and surround mechanisms can account for changes in receptive field size. Each panel shows a schematic representation of the Gaussian center and surround components in our RoG model (solid gray curves). Line thickness represents the relative gains of each component. The gain of the center component is held constant for each panel, but the gain of the surround changes from 3 (A) to 1 (B) to 0.1 (C). We calculated the resulting receptive field profile (solid black curve) by dividing the center mechanism by the weighted surround mechanism as in the RoG model. After imposing a response threshold (dashed line), we measured the width of the receptive field (shaded area). As surround gain decreased, the size of the resulting receptive field increased from 1 when surround gain was 3, to 1.8 when surround gain was virtually absent. The weakening of the surround allows the fringes of the receptive field to become responsive, increasing its apparent size.

We measured grating diameter tuning curves at different stimulus contrasts for 79 neurons in primary visual cortex. As stimulus contrast decreased, not only did responses decrease, but also the shape of the diameter tuning curves changed, resulting in a preference for larger stimuli (data in Fig. 8, A-C). For stimuli at the lowest contrast (6%, lightest points in Fig. 8, A-C), GSF diameters were on average about 2.5 times those measured at high contrast (darkest points), confirming the results of Sceniak et al. (1999) and Kapadia et al. (1999).

View larger version (17K): [in this window] [in a new window]   Fig. 8. Receptive field size changes with stimulus contrast. A-C: responses of a single cell (filled circles) are duplicated in each panel. We have plotted response as a function of stimulus diameter, the shading of each circle representing stimulus contrast (darker circles indicate higher contrast: 6, 13, 25, 50, and 100% contrast, respectively). As stimulus contrast decreased, responses decreased more for small stimuli than for large, resulting in a shift in diameter tuning. Solid curves show the fits for each of 3 versions of the RoG model: uniform, gain, and size. The shading of each line indicates stimulus contrast. The uniform model only varied the gain of the center component in the RoG model, whereas both center and surround gains varied in the gain model. In the size model, the extent of the center component varied with stimulus contrast as well. The normalized 2 error for each fit () is shown in each panel. Both the gain and size models captured the change in receptive field size with contrast, but was smaller for the gain model, indicating that changing the width of the center mechanism yielded no substantial improvement in fit quality. C: comparison of among the 3 models for 79 neurons (see Fig. 5 for explanation of axes). Although each model often provided fits of similar quality (points near the center), the majority of points are closer to the axis for the gain model, indicating that the model with spatially stable center and surround components accounted for the data best. Permitting mechanism width to vary in the size model did not improve fit quality when taking into account the number of free parameters in each model.

These data demonstrate that the area of summation of V1 cells changes with stimulus contrast. To determine whether this change in spatial summation required a change in the spatial extents of the underlying mechanisms, we fit three forms of our ratio of Gaussians model to families of diameter tuning curves showing receptive field expansion. In the first form of the model, we permitted only the central gain parameter, k_c, to vary with contrast. We designated this the uniform model because changing only the center gain produces a family of curves that are scaled versions of each other. In the second form of the model, the surround gain parameter, k_s, was also permitted to vary with stimulus contrast while the widths of the sensitivity envelopes were held constant. This was the gain model, as it permitted center and surround gains to be independently regulated. In the final form of the model, we additionally permitted the width of the center sensitivity envelope (w_c) to change with contrast. We called this the size model, as it allowed the changing extent of the center mechanism to help explain receptive field expansion.

The fits of each version of the model to the responses of the sample neuron are also plotted in Fig. 8, A-C. Fits are plotted as solid curves in each panel, the shade of each curve corresponding to stimulus contrast. The top panel shows the fit to the uniform model, the middle panel shows fits to the gain model, and the third panel shows fits to the size model.

When only center gain was allowed to vary (Fig. 8A), the curves produced by the uniform model were vertically scaled versions of each other. As expected, the uniform model was unable to account for the shift in optimal stimulus diameter with changes in contrast. When surround gain was also permitted to vary in the gain model (Fig. 8B), the curves accounted well for the reduction in response and for the shift in GSF diameter. When additionally the extent of the center spatial envelope was permitted to vary in the size model (Fig. 8C), fit quality again visibly improved.

Mean were 0.99 for the uniform model, 0.86 for the gain model, and 1.14 for the size model. Thus all three forms of the model provided acceptable accounts of most of the data. The mean was lower for the gain model than for the uniform model, indicating an improvement in fit quality, even taking into account the addition of the extra varying parameter. However, when the center mechanism width was allowed to vary as well in the size model, there was an increase in the , implying that although the absolute error decreased when adding this parameter to the model, this reduction in error did not warrant the extra parameter.

Figure 8D shows a three-way comparison of among models (see Fig. 5C). The points fall predominantly in the sector for the gain model in which center and surround gains only (k_c and k_s) were permitted to vary with contrast, indicating that this model provided the best overall description of the data. Permitting the center mechanism width to also vary with contrast in the size model did not provide better fits than the gain model. Thus the model providing the most parsimonious explanation of the data was the gain model, in which changes in receptive field extent were accounted for by independent changes in gain of spatially fixed center and surround mechanisms. The gain parameters in this model accounted for the changes in mechanism activity with contrast and thus reflect each mechanism's sensitivity to contrast. The way that the balance of the gains in the model creates changes in receptive field size is the one schematized in Fig. 7. At high contrasts, the surround is relatively strong and suppresses weak responses from the flanks of the center mechanism. At low contrasts the surround is relatively weak, and this suppression is relaxed, allowing more of the center to be seen.

To document this point, Fig. 9A shows how the average center signal (k_c) across neurons develops with increasing contrast in the gain model. Because contrast was not explicit in our model, it has been absorbed into the gain parameters that thus capture the way that signals depend on contrast. We plot means of signal values normalized by their maximum for each neuron. At low contrasts, the signal of the center component was weak, and it increased with contrast. Figure 9B shows the average development across neurons of the surround signal (k_s) with contrast. Surround signals were also weak at low contrasts and also increased for high contrast stimuli. The key to understanding the changing role of the two mechanisms with contrast is to visualize the relative sensitivity of each mechanism to contrast. We gauged the relative effect of surround suppression in a manner analogous to the measurement of suppression in diameter tuning curves by measuring the suppressive influence relative to the excitatory influence. Without suppression, the overall response to large (infinite) diameter stimuli is proportional to k_c. With divisive suppression, the response was proportional to k_c/(1 + k_s). Expressing suppression as a fractional reduction in response, we obtain

(12)

where S is the suppression value. Because we constrained k_s > 0, it must be that 0 < S < 1. Figure 9C shows that relative surround gain S fell from its high contrast value of about 0.65 to near zero at low contrast. We conclude that the influence of the surround was, on average, drastically weaker at lower contrasts than at high, and that this difference in the contrast gain characteristics of center and surround mechanisms is what causes the apparent change in receptive field size with contrast.

View larger version (10K): [in this window] [in a new window]   Fig. 9. Changes in RoG model parameters with contrast. We extracted center and surround gain parameters from fits to the gain RoG model for 79 cells. Because contrast was not explicit in our model, it has been absorbed into the gain parameters, labeled center and surround signals in the figure. Thus the center and surround gain parameters are expected to increase with contrast. What is interesting is the comparison between the two. For each neuron, we normalized the gain parameters to their maximum value, and averaged these normalized quantities for all neurons. A and B: center signal increases with contrast more than surround signal. C: we expressed the asymptotic influence of the surround as the expected reduction in model activity (see Eq. 12). The relative influence of the surround increases with contrast, suggesting that the surround is less sensitive than the center at lower contrasts.

Changes in receptive field structure with adaptation

Encouraged by our finding that changes in spatial summation with stimulus contrast are accounted for by changes only in contrast gain, we turned our attention to the question of how other changes in gain might affect receptive field structure. Cortical cell responses fall during prolonged stimulation with high contrast targets, because of a change of contrast gain (Sclar et al. 1989; Vautin and Berkley 1977). We earlier speculated that the center and surround gains might be independently controlled by adaptation (Fig. 4). We now test this conjecture by asking whether the gain model just described can be used to account for the effects of adaptation over the 1.5- to 6-s duration of each of our stimulus presentations.

Figure 10 shows an analysis of the time course of the responses of a complex cell to patches of grating of different diameters. Mean responses are plotted in the left panel as a grating diameter tuning curve, and the time histograms for each response are plotted in the right panel. In the diameter tuning curve, the responses to stimuli with diameters of 0.69 and 2.78° (A and B) are highlighted with circles. Mean response rates to these two stimuli were similar (13.8 and 14.1 spikes/s, respectively), but the histograms show the responses to have very different time courses (right, indicated by the , A and B). In the first 2,000 ms, the response to the smaller diameter stimulus (A) was greater than the response to the larger stimulus (B), and this relationship reversed in the second 2,000 ms, when the response to the smaller stimulus diminished.

View larger version (24K): [in this window] [in a new window]   Fig. 10. Time course of responses depends on stimulus diameter. Responses to patches of grating with different diameters are shown for a complex cell. Left: we have plotted response as a function of stimulus diameter. The time course of each response in the left panel is shown in the panel on the right, with responses to smaller stimuli at the top. Responses with similar mean firing rates (A and B, left) had very different time courses (A and B, right). The response to the smaller stimulus (A) started strong, then faded over 2 s. The response to the larger stimulus was initially lower than the response to the smaller stimulus, but maintained its response rate for 4 s. This resulted in a preference for the smaller stimulus at the beginning of the response and for the larger stimulus at the end of the response.

To track the time course of responses, we divided spike trains into fixed-duration epochs. We determined the duration of the epoch by first examining the distribution of cycle drift periods for all cells. We chose a canonical epoch duration of 640 ms, which was short enough to provide reasonable temporal resolution of response trends over time, yet long enough to usually provide reliable response rates within a single epoch. Figure 10, right, shows a series of alternating shaded and unshaded areas, representing the time windows used. Each time window has been given a label (t1-t7) for later reference.

We used spikes beginning 150 ms after the stimulus appeared. This offset accounted for response latencies and minimized the influence of response transients in the first time window. Stimulus duration varied from 1.5 s to over 5 s, yielding from two to eight response epochs. Within each time epoch, we calculated the neuron's response to gratings of different diameters. We organized these responses into families of patch diameter tuning curves with one curve for each time epoch. For this analysis, we used data from 208 units that were studied with suitable stimulus epochs and which had measurable suppression (greater than 10%).

Temporal partitioning of responses yielded a family of grating diameter tuning curves for each neuron. A family of such curves is shown in Fig. 11A for a single example cell. Stimulus duration was about 5 s, so temporal partitioning at 640 ms resulted in a family of seven diameter-tuning curves for this cell. The diameter-tuning curve for the earliest time window (t1) is plotted as the topmost curve (shaded line) in Fig. 11A. The shading of the points on each curve represents the relative time of the responses, with lighter points denoting later times. The neuron's baseline is plotted as the first point in each curve, at 0° diameter and has been carried across each curve as a dashed line. Because curves from subsequent time windows have been shifted down for visibility, they can be compared by using the dashed baseline as a reference.

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