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Previous Article | Next Article
The Journal of Neuroscience, November 15, 2000, 20(22):8504-8514
Spatial Frequency Maps in Cat Visual Cortex
Naoum P. Issa, Christopher Trepel, and Michael P. Stryker W. M. Keck Foundation Center for Integrative Neuroscience and Department of Physiology, University of California, San Francisco, California 94143-0444
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
Neurons in the primary visual cortex (V1) respond preferentially to stimuli with distinct orientations and spatial frequencies. Although the organization of orientation selectivity has been thoroughly described, the arrangement of spatial frequency (SF) preference in V1 is controversial. Several layouts have been suggested, including laminar, columnar, clustered, pinwheel, and binary (high and low SF domains). We have reexamined the cortical organization of SF preference by imaging intrinsic cortical signals induced by stimuli of various orientations and SFs. SF preference maps, produced from optimally oriented stimuli, were verified using targeted microelectrode recordings. We found that a wide range of SFs is represented independently and mostly continuously within V1. Domains with SF preferences at the extremes of the SF continuum were separated by no more than 3/4 mm (conforming to the hypercolumn description of cortical organization) and were often found at pinwheel center singularities in the cortical map of orientation preference. The organization of cortical maps permits nearly all combinations of orientation and SF preference to be represented in V1, and the overall arrangement of SF preference in V1 suggests that SF-specific adaptation effects, found in psychophysical experiments, may be explained by local interactions within a given SF domain. By reanalyzing our data using a different definition of SF preference than is used in electrophysiological and psychophysical studies, we can reproduce the different SF organizations suggested by earlier studies.
Key words: spatial frequency; visual cortex; cat; area 17; area 18; V1; V2; orientation; ocular dominance; pinwheel; cortical column; cortical map; intrinsic signal imaging
INTRODUCTION
The columnar arrangement of striate cortex is arguably its hallmark and, as a result, much of the work aimed at understanding the mechanisms of vision has focused on characterizing visual cortical columns (for review, see LeVay and Nelson, 1991
). Although the maps of both ocular dominance (LeVay et al., 1978
Optical imaging of intrinsic signals permits the measurement of cortical responses over a large area of cortex (for review, see Bonhoeffer and Grinvald, 1996
A second set of imaging experiments (Everson et al., 1998
To identify the model that best describes the organization of SF preference in the primary visual cortex of the cat, we have used a combination of intrinsic signal optical imaging and multi-unit microelectrode recordings to assess SF preference in V1. We found that a wide range of SF preferences is mapped onto the visual cortex. This representation was mostly continuous, with SF generally changing gradually and progressively in the tangential plane but with occasional linear discontinuities. Tuning curves constructed from optical maps, and confirmed by microelectrode recording, demonstrated that the arrangement of SF preference is derived from a collection of many domains, each of which is selective for a narrow range of SF.
Parts of this work have been published previously in abstract form (Trepel et al., 1999
MATERIALS AND METHODS
Optical imaging of intrinsic signals was used to examine the layout of SF preference in cortical areas 17 and 18 of seven cats between 7 and 16 weeks of age. Previous work has shown that contrast sensitivity reaches adult levels at ~6 weeks of age (Derrington and Fuchs, 1981
Surgical preparation. Animals were initially anesthetized with the inhaled anesthetic isoflurane (3-4% in O2) and, after implantation with a femoral catheter, were switched to a short-lived barbiturate (thiopental). Atropine (0.25-0.4 mg) and dexamethasone (0.4-0.8 mg) were injected subcutaneously to reduce tracheal secretions and minimize the stress response, respectively. A tracheotomy was performed, and a long-lasting barbiturate (sodium pentobarbital) was substituted for thiopental. To assess the anesthetic state of an animal, we continuously monitored its core temperature, electrocardiogram, expired CO2, and peak airway pressure. A feedback-regulated heating pad maintained core body temperature at 37.5°C. Pentobarbital was administered as needed to keep the animal at a surgical plane of anesthesia, determined by the animal's heart rate and peak expired CO2.
The animal was placed in a stereotaxic apparatus, and 1% atropine sulfate and 10% phenylephrine hydrochloride were applied to the eyes. To focus the eyes on the stimulus monitor, contact lenses of the appropriate strength were fitted with the aid of a retinoscope or by maximizing visual acuity for each eye as measured by visually evoked potentials (two cats) (Tang and Norcia, 1993
1 · hr
Optical imaging of intrinsic signals. All imaging of V1 was done on the flat part of V1 on the dorsal surface of the lateral gyrus, corresponding to the area in visual field within 10° of the vertical meridian and between the horizontal meridian and 10° into the lower field. Optical images of cortical intrinsic signal were obtained using the ORA-2000 Optical Recording Acquisition and Analysis System (Optical Imaging, Inc., Germantown, NY). Using different tandem lens configurations (Nikon Inc., Melville, NY), both "low-resolution" (50 × 50 mm lenses, 6.0 × 8.0 mm image area) and "high-resolution" (135 × 50 mm lenses, 2.4 × 3.2 mm image area) images could be acquired. The surface vascular pattern or intrinsic signal images were visualized with illumination wavelengths set by a green (546 ± 10 nm) or red (610 ± 10 nm) interference filter, respectively. After acquisition of a surface image, the camera was focused 400-500 µm below the pial surface, an additional red filter was interposed between the brain and slow-scan CCD camera, and intrinsic signal images were acquired. Images were stored as 192 × 144 pixels after binning the 384 × 288 camera pixels by 2.
Visual stimulus patterns were varied according to the stimulus parameter being mapped. Full-field sine and square wave grating stimuli were generated by a VSG 2/3 board (Cambridge Research Systems, Rochester, UK) controlled by custom software. Shutters for the light source, camera, and eyes were controlled by the stimulus and acquisition computers. A typical experiment began with a mapping of orientation and ocular dominance using drifting square wave gratings with a fundamental SF of 0.2 cycles (c) per degree and a temporal frequency of 2.0 c/sec. Stimuli were presented in pseudorandom order separately to the two eyes at eight orientations separated by 22.5°. Gratings reversed their direction of motion every 2 sec and were interspersed with four identical blank screen conditions (both eyes viewing a gray screen). There were therefore a total of 20 stimulus conditions for the gratings plus the blanks. We measured the degree to which both eyes could activate the cortex using the optical contralateral bias index described by Issa et al. (1999)
Spatial frequency mapping required a much larger number of stimulus conditions. A typical experiment involved the binocular presentation of sine wave gratings of eight orientations at six to eight spatial frequencies ranging between 0.1 and 1.84 c/°. Ideally, each mapping run would have randomly interleaved all stimulus conditions, but because the large number of stimulus combinations exceeded the capacity of the optical imaging software, stimulus conditions were distributed among either two or four sets that were run sequentially. Each stimulus set included a wide range of spatial frequencies and orientations and was designed to provide a coarse map on its own before combination with data from the other sets. In addition to the oriented gratings, each stimulus set included five blank stimuli and one grating stimulus that was common to all the stimulus sets. A map from eight orientations and eight spatial frequencies was therefore constructed from four stimulus sets, each of which consisted of 22 conditions: four orientations times four spatial frequencies plus five blanks plus a common condition. Responses to four of the blank stimuli were used to construct an average "blank" image, and the response to the fifth blank stimulus was used to determine the noise level in the data set. The visual stimulus that was common to all the stimulus sets was used to verify the stability of the responses across the sets before combining responses from different sets into a single SF map. If the mean intensity in the active areas of the images produced in response to the common stimulus differed among the stimulus sets by >1 SD, the data set was discarded.
At the beginning of each trial, a stationary grating was presented for 5 sec. The grating then began to drift at a temporal frequency of 2 Hz, and acquisition of 20-25 frames of 250-300 msec duration each began. Within a stimulus set, each of the stimuli was presented 16 times in a different random order, and the different stimulus sets of an experiment were interleaved. Two to four runs of each set were analyzed for each experiment. Images were analyzed using commercial (ORA-2000) and custom software written in the Interactive Data Language (Research Systems, Boulder, CO).
Raw images were normalized by the average of images acquired during the blank screen conditions ("blank normalization") (Crair et al., 1997b
Calculation of spatial frequency maps. Three different types of SF map were constructed to graphically represent SF preferences over a cortical area. In the first type, the "SF map" (see Fig. 5), the preferred SF of a pixel was defined as the SF of the single stimulus condition that produced the strongest response at that pixel among all of the unique combinations of orientation and SF. The color of each pixel was determined by its preferred SF, and lightness and saturation were held constant: red represents a low SF, orange through yellow, green, and blue represent increasing intermediate frequencies, and purple represents the highest SF. In the second type of map, the "SF response map", the preferred SF of a pixel was displayed as above, but the lightness of the pixel was set in proportion to the magnitude of the response to the best stimulus. In SF response maps (see Figs. 2, 3), pixels that are dark have a very small best response. In the third type of map, the "interpolated SF map" (Fig. 5E), the preferred SF of each pixel was determined by interpolating a peak SF from the tuning curve of a single pixel at the optimal stimulus orientation. Therefore, any continuity of SF preference observed in interpolated SF maps cannot be an artifact of the technique used to construct the map but must be a function of the genuine cortical representation of SF preference. The first and third types of SF maps are analogous to the "angle map" used for the display of orientation columns, whereas the second is analogous to the "polar map" (Bonhoeffer and Grinvald, 1996
Because the range of potential SF preference is unbounded, it is possible that none of our stimulus conditions activated certain cortical regions. To prevent these regions from contributing to measurements of the SF map, pixels that had a best response near the noise level were not considered in generating tuning curves of SF preference (see Figs. 4, 7). The noise level was set at a multiple of the SD (
) of the pixel intensities in a blank-normalized blank image: a single-condition image produced by stimulating with a mean-luminance blank screen. Unless otherwise noted, the noise level was set at 2
noise level were considered to have stimulus-dependent activity.
Electrophysiology. To confirm that the optically imaged SF maps corresponded to the neuronal SF selectivity, we made targeted multi-unit recordings using electrolytically sharpened, resin-coated tungsten microelectrodes (1-3 M
). Unit responses were thresholded with a window discriminator to separate spike activity from electrical noise. A computer-based system running custom software presented randomly ordered gratings of different orientations and measured the spike rates of the cells. Once orientation preference was determined, subsequent stimuli consisted of pseudorandomly ordered gratings spanning a range of spatial frequencies presented at the preferred orientation. Blank-screen stimuli were presented interleaved with grating stimuli to provide a measure of spontaneous activity. Electrolytic lesions (4 sec, 4 µA) were made at the beginning and end of a penetration.
Multi-unit recordings were excluded from analysis if one of the following criteria were met: (1) the difference in orientation preference measured electrophysiologically and optically was greater than 11.25° (half the measurement interval); (2) the recording site was not in a superficial layer; or (3) the multi-unit SF tuning curve had multiple peaks. An area of 0.12 mm2 (1.6% of the imaged area) around the targeted site was searched for the best match to the electrophysiologically measured orientation preference. In penetrations for which electrode tracks could not be reconstructed, only sites in the first 400 µm of a penetration were included.
At the end of a recording session, the animal was given a lethal dose of pentobarbital and transcardially perfused with 0.1 M phosphate buffer, followed by 10% paraformaldehyde. After post-fixing and cryoprotecting for at least 1 d in 10% paraformaldehyde-20% sucrose, the visual cortex was sectioned on a freezing microtome. Sections were Nissl stained, and electrode tracks and recording positions were reconstructed from camera lucida drawings.
RESULTS
We have defined the SF preference of a small region of cortex corresponding to a pixel in our maps as the SF of the single stimulus that best activated the pixel, among all the combinations of orientation and SF presented. The maps of SF preference constructed using this definition are very different from previously published maps (Hubener et al., 1997
Gross structure of the SF map
We used low-resolution images of cortical intrinsic signals to study the gross structure of the map of SF preference. The map shown in Figure 1 is consistent with the known layout of SF across the cat's lateral gyrus (Movshon et al., 1978b
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Figure 1. The area 17/18 border is revealed by SF sensitivity. Top row, Polar orientation maps constructed from responses to eight differently oriented sine wave gratings at the specified SF. Hue represents orientation preference, and color lightness represents degree of tuning. For low SFs, area 17 is dark, indicating weak or poorly tuned responses to oriented gratings, but area 18 is active and well tuned. For intermediate SFs (0.43 and 0.70 c/°) both areas 17 and 18 are active and well tuned. At higher SFs, a pattern complementary to that seen at low SFs develops, with area 17 active and area 18 inactive. The polar map from stimuli at 3.0 c/° is not shown because there was no stimulus-dependent response. Bottom row, The left panel shows the vascular pattern in the region of cortex imaged. The lateral (Lat) and posterior (Post) directions are marked. Scale bar, 1 mm (applicable to all images). The middle panel is an SF response map in which color represents preferred SF, and brightness represents response intensity. The right panel shows the cumulative distribution of preferred SFs in V1 and V2 (plotted semilogarithmically). For comparison, the cumulative distribution of SF preferences from single-unit recordings made by Movshon et al. (1978b)
To determine whether optical mapping of SF preference can be used to quantify the distribution of neuronal SF preferences, we compared SF preferences measured in the maps shown in Figure 1 with the distribution of SF preferences from the populations of single units in areas 17 and 18 reported by Movshon et al. (1978b)
Fine structure of the SF map
We then used high-resolution maps of V1 (Figs. 2, 3) (see Fig. 5) to study the fine structure of SF organization in V1. Figure 2 shows how such SF maps were constructed from single-condition images. The cortical responses to each of six spatial frequencies at a single orientation are shown in Figure 2A. In these single-condition images, areas of the cortex that are preferentially responsive to certain spatial frequencies are dark in a few of the panels and light in all of the others. A single-orientation SF response map, shown in Figure 2A, center panel, was constructed by color-coding a pixel based on the SF at which the pixel was most active. The plots in Figure 2A, bottom center panel, show SF tuning curves, which graph absolute optical response as a function of stimulus spatial frequency, for the pixels at the three positions indicated on the single-orientation SF map in the center panel. These tuning curves show that individual regions of cortex respond strongly only to a very narrow range of SFs and that all of the SFs used can produce strong cortical responses.
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Figure 2. A high-resolution spatial frequency map. A, A single-orientation SF map. Grayscale images are single-condition images showing the cortical response to single sinusoidal grating stimuli, each with an orientation of 45°, and the SF indicated in the panel. Dark regions in these images are active; all six images were scaled to the same absolute range of intrinsic signal intensities. The middle panel was constructed by color-coding each pixel according to the SF of the stimulus condition that most effectively drove the neurons at that pixel position. The brightness of a pixel corresponds to the response strength of the pixel. Spatial frequency tuning curves for the three points marked on the single-orientation SF map are shown in the middle panel in the bottom row. The maximum response level is similar for the three tuning curves, although the points prefer very different spatial frequencies. Absolute response is shown as 10,000 times the difference between the optical signal produced in response to a stimulus and the signal produced in response to a blank screen. B, An all-orientation SF map. The eight panels surrounding the middle panel are the single-orientation SF maps constructed from the orientation shown on the panel and the spatial frequencies shown in A. The middle panel was constructed by color-coding each pixel according to the SF of the stimulus condition that most effectively drove the neurons at that pixel. Orientation pinwheel centers are marked with asterisks. Color-lightness code for SF and response strength are as shown in A, except that maximum response for the middle panel is 4.9 × 10
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Figure 3. Multi-unit recordings validate spatial frequency maps. A, Microelectrode penetrations were targeted to specific SF domains in area 17. Microelectrode penetrations were made at the locations marked by black circles on the SF response map. In the optical and electrophysiological tuning curves, relative activity is plotted as a function of SF (line graph) and orientation (polar plot); for each tuning curve, the maximum response was set to a value of 1, and the minimum response was set to 0. Note that the penetrations shown are in "intermediate" SF domains (between 0.3 and 0.8 c/°). Orientation pinwheel centers are marked with asterisks. B, Preferred SF derived from optical maps plotted against preferred SF measured from unit recording. To show each data point, points that overly each other have been plotted adjacent to each other. A linear fit had a correlation coefficient r = 0.86 for 19 cells. The mean difference in orientation preference between optical and electrophysiological measurements was 4.2 ± 3.3° (mean ± SD). Scales are linear.
To construct an SF response map that summarizes SF preference over all orientation domains (Fig. 2B, center panel), we color-coded each pixel according to the SF that best stimulated it among all of the eight single-orientation maps. The color of a pixel in the all-orientation SF response map therefore represents its preferred SF at its preferred orientation. In the map shown in Figure 2B, center panel, nearly the entire cortex is brightly colored, indicating that it was activated well by one or more of the combinations of SF and orientation presented. The all-orientation SF map represents SF preference as has traditionally been defined by electrophysiologists, that is, SF preference at the preferred orientation.
To ensure that SF maps represent cortical SF preference, we concluded most experiments with targeted multi-unit recordings. We recorded multi-unit responses in the supragranular layers to sinusoidal gratings at a range of spatial frequencies, all at the preferred orientation (Fig. 3A). The three receptive fields illustrated show a progression of preferred orientation and SF from the top to the bottom penetration. When the best orientations from the electrophysiological and optical tuning curves were similar, the peak spatial frequencies were also similar (Fig. 3B). Although SF preference sometimes varied along the course of penetrations deeper into the cortex, we did not systematically investigate the possibility of a laminar organization of spatial frequency. From these results, we conclude that the optically derived map accurately represents the SF preference of the neurons in superficial cortical layers.
The most notable feature of the SF maps shown in Figures 2, 3, and 5A-D is the wide range of SF preferences. Within V1, there are cortical domains that respond best to very low (0.2 c/°), very high (>1.0 c/°), and all intermediate SFs. Figure 4A shows the result of averaging SF tuning curves for all the pixels with a given SF preference. For each SF in the stimulus set, there is a unimodal tuning curve centered at the SF. These multi-pixel tuning curves are similar to the tuning curves for individual pixels shown in Figure 2A. The tuning curves derived from the optical data had bandwidths (full-width at the half height) between one and two octaves, similar to the range of bandwidths found with single-unit measurements of SF preference (Movshon et al., 1978b
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Figure 4. Intermediate SF domains are independent of neighboring high and low SF domains. A, Average tuning curves at each SF peak for the SF map shown in Figure 2. Average tuning curves were constructed after first normalizing the response at each pixel such that 1 represents the maximum response of a pixel, and 0 represents the theoretical response of the cortex to a blank image. Tuning curves from all pixels that had the same peak SF preference and those whose peak response exceeded the 2
The weighting factor, f, varied from 0 to 1; each curve has a different value of f. TC0.2 was the tuning curve measured for pixels with a best response at 0.2 c/° (red curve in A), and TC0.95 was the tuning curve measured for pixels with a best response of 0.95 c/° (purple curve in A).
It has been suggested previously on the basis of intrinsic signal imaging that there are only high (~0.8 c/°) and low (~0.2 c/°) SF domains in cat V1 (Shoham et al., 1997
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Figure 5. SF maps show linear discontinuities. A, An SF map produced in response to the eight SF stimuli marked on the color bar below the panel; the SF scale shown on this color bar is shared with E. Orientation pinwheel centers are marked with asterisks in A-D. The area marked by a square is shown rotated in Figure 3. B-D, The SF map in B was produced in response to six SFs (0.2, 0.35, 0.5, 0.7, 0.95, and 1.2), marked with short lines on the second color bar. The SF maps in C and D were produced in response to the seven SFs marked on the second color bar. E, The interpolated SF map constructed from the same data used to make the SF map in A. F, Spatial frequency profile along the transect marked by the black line in E and H. SF preference varies smoothly over this region. G, Spatial frequency profile along the transect marked by the white line in E and H. SF preference varies continuously over the initial segment of this transect but shifts at a fracture in the SF map. H, Spatial gradient of SF preference. Pixels at which SF preference varies rapidly are shown in red. Areas in which the spatial gradient is small are shown in blue.
To determine whether SF domains are organized in a continuum, similar to the organization of orientation domains, we constructed finer maps of SF by interpolating the preferred SF of each pixel from its individual SF tuning curve. No spatial filtering was done on the map. Such an interpolated SF map is shown in Figure 5E. Two types of transition between regions of different SF preference are apparent in this map: smooth transitions and abrupt transitions (fractures). Throughout most of the map, SF preference varies smoothly. Figure 5F shows an SF profile in which SF decreased gradually and progressively over a distance of 750 µm. The range of SFs covered in this smooth progression spanned four of the SFs included in the stimulus set. In contrast, the SF profile shown in Figure 5G provides an example of a fracture in the SF map; SF preference shifted from 1.2 to 0.64 c/° over the course of a few pixels. The pattern of SF gradient can be seen in Figure 5H, in which large areas with small spatial gradients are interrupted by lines of high gradient corresponding to the fractures. There is no correspondence between the vascular pattern seen on the vascular map and the lines of high SF gradient, ensuring that the abrupt changes in SF preference observed are not vascular artifacts. Spatial frequency preference in area 17 is therefore continuous over most of the cortex but has distinct linear discontinuities.
Compared with the relatively regular patterns of ocular dominance and orientation columns, SF domains are irregularly spaced. This irregular pattern precluded our measuring the periodicity of SF domains using Fourier techniques, and it means that measurements of average SF domain density are not representative of the local organization of SF domains. To estimate the distance a dendritic tree would have to cover to span the entire range of SF preferences, we measured the distance between pixels preferring 0.2 c/° and pixels preferring other SFs. The average distance between a pixel preferring 0.2 c/° and the nearest pixel with a specified SF preference was proportional to the specified SF. A logarithmic relationship fit the distribution of distances well [distance(mm) = 0.10 · ln(SF) + 0.17; r2 = 0.89]. On average, the distance from a pixel preferring 0.2 c/° to the nearest pixel preferring 1.2 c/° was 196.8 ± 15.1 µm (mean ± SEM); in all cases, a pixel preferring 1.2 c/° could be found within 610 µm of any pixel preferring 0.2 c/°. For a periodic pattern, such as ocular dominance or orientation maps, the corresponding measurement would represent something less than half the columnar repeat distance. The fact that the measured distance between pixels of low and high spatial frequency preference is somewhat smaller than half the repeat distances reported for ocular dominance and orientation (Crair et al., 1997a
Relationships among the spatial frequency, ocular dominance, and orientation maps
Previous imaging studies have found specific relationships between different cortical maps (Obermayer and Blasdel, 1993
0.8 c/°) SF domains was much larger than in intermediate SF domains; in low domains there were 3.3 pinwheels/mm2, in intermediate domains there were 1.7 pinwheels/mm2, and in high domains there were 2.8 pinwheels/mm2 (measured in six maps from five cats). The distribution of pinwheel centers over the three SF ranges was significantly different than expected for a uniform distribution [
2(2) = 6.81; p < 0.05; n = 82 pinwheels over 35.4 mm2]. Because the measured positions of pinwheel centers can vary slightly depending on details of how they are identified, we also looked at the distribution of SFs in the nine pixels around the pinwheel centers (corresponding to an area of 2500 µm2). This analysis showed a similar, albeit not statistically significant, correlation between high and low SF domains and pinwheel centers [2.9, 1.7, and 2.9 pinwheels/mm2 in low, intermediate, and high SF domains, respectively;
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Figure 6. Comparison of orientation and ocular dominance maps with the spatial frequency map. A, Orientation preference is represented by color in this smoothed angle map. The color bar represents orientation preference in degrees. The length of the color bar corresponds to 1 mm. This orientation map was constructed using square wave gratings of fundamental SF 0.2 c/°. B, SF map with iso-orientation contour lines overlaid. Points at which iso-orientation contours converge are the orientation pinwheel centers. Note that the color under most pinwheel centers is red or purple, indicating an association between pinwheel centers and regions of low (red) and high (purple) SF preference. C, In this ocular dominance ratio map, dark areas are dominated by the ipsilateral eye, and light areas are dominated by the contralateral eye. The grayscale bar shows the deviation of pixel intensities ( ×104) from 1.0, the value corresponding to equal activation by the two eyes. D, SF map with ocular dominance contours overlaid. No clear association was observed between the SF and ocular dominance maps. The legend shows the SF preference color code for the SF map shown in B and D.
A correlation between the positions of ocular dominance column peaks and orientation pinwheel centers has been observed in cat V1 (Crair et al., 1997a
The dependence of spatial frequency preference on stimulus orientation
Our characterizations of SF preference presented thus far have relied on a definition of SF preference that does not assume that SF preference is constant across all stimulus orientations. Specifically, SF preference has been defined only at a single orientation, the preferred orientation of a pixel. Other studies of SF preference have averaged responses over all orientations (Tootell et al., 1981
To test explicitly whether SF preference measured optically is independent of stimulus orientation, we constructed SF tuning curves at a variety of stimulus orientations. Figure 7A-C compares responses to different SFs for stimuli at the preferred orientation of each pixel with responses to stimuli at orientations that differ from the preferred by 22 or 45°. Each panel shows responses compiled from all of the pixels in the map of the case illustrated in Figure 2 that prefer a low SF (A), an intermediate SF (B), or a high SF (C) at their optimal orientation. In every case, the strongest response by far occurs at the preferred orientation (curves marked 0), and it is clear that the tuning curve for SF is much broader at off-peak orientations. C shows that the peak response shifts to progressively lower SFs as the stimulus orientation changes from the optimal. D plots the change in the preferred SF as a function of stimulus orientation for all of the pixels in the map. For the regions of cortex that preferred high SFs, the curves fall off sharply as orientation changes in either direction, indicating preference for lower SFs at nonoptimal orientations. This behavior is predicted by linear models of simple cell receptive fields (Webster and De Valois, 1985
0.35 c/°) do not fall off as orientation changes. Overall, the assumption that SF tuning is independent of stimulus orientation is wrong; there are systematic shifts in SF preference at off-peak orientations.
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Figure 7. The effect of stimulus orientation on spatial frequency preference. A, Average SF tuning curves for all pixels that respond most strongly to gratings with an SF of 0.2 c/°. Each tuning curve is constructed at a different stimulus orientation. The tuning curve labeled 0 is constructed from responses at preferred orientation of the pixels. The curves labeled 22 and 45 were constructed from responses of these same pixels to gratings presented at 22 or 45° from the preferred orientation. For each point in a tuning curve, only genuine responses were considered, using pixels whose response exceeded a 4
The independence of orientation preference from stimulus spatial frequency
Consistent with single-unit studies (Webster and De Valois, 1985
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Figure 8. The effect of stimulus spatial frequency on orientation preference. The six angle maps in the top two rows were constructed using sinusoidal gratings with the SF shown with each map. Black areas in these maps had a peak activity below the 2
Computation of spatial frequency maps using other algorithms
The choice of analysis procedure affects the appearance of SF maps. The two previous groups that reported on SF tuning using optical imaging (Hubener et al., 1997
Figure 9, A and B, compares an SF map constructed using the procedure described for Figure 5E (selecting the preferred orientation and estimating an SF preference based on the SF tuning curve; Fig. 9A) to an SF map constructed by first averaging responses over all orientations and then estimating an SF preference based on the resulting SF tuning curve (Fig. 9B). Unlike the pattern of SF domains in Figure 9A, SF domains in Figure 9B are arranged in SF pinwheels, similar to those described by Everson et al. (1998)
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Figure 9. Comparison with previous analyses of optical SF responses. A, An interpolated SF map constructed using the techniques described in Materials and Methods. B, An interpolated SF map constructed by first averaging over all orientations and then interpolating between SFs to get the preferred SF. SF pinwheels similar to those found by Everson et al. (1998)
The SF maps produced by Shoham et al. (1997)
Cocktail-blank normalization has two effects on the SF maps. First, it preferentially reduces responses to intermediate SFs. As an example of this problem, consider the effect of cocktail-blank normalization on the responses of three pixels (their responses to stimuli of low, intermediate, or high SF are given in parenthesis): one that prefers a low SF (response of 1, 0.5, and 0), one that prefers an intermediate SF (response of 0.5, 1, and 0.5), and one that prefers a high SF (response of 0, 0.5, and 1). Normalizing the peak response of each pixel by its average response reduces the peak response for the pixel that prefers an intermediate SF (peak response intensities after normalization of 2, 1.5, and 2 for the pixel that prefers a low, intermediate, and high SF, respectively).
This first effect, the reduction in response to intermediate SFs, can be seen for the data shown in Figure 9D (compare with C, which has no cocktail-blank normalization or averaging over orientations). The open symbols in Figure 9E show the mean response intensities in domains that prefer different SFs for the map in 9C. The strongest responses occur at intermediate SFs. The open symbols in Figure 9F show the same plot for the map in Figure 9D. It is clear that the strongest response occur at the extremes of the SF range in this plot. Thus, the combined effect of averaging over all orientations and cocktail-blank normalization is to reduce the apparent response strength of the pixels that prefer intermediate SFs.
The second effect of cocktail-blank normalization is that apparent response intensities are dependent on the specific set of stimuli used. Because the cocktail blank (which is the mean image to which all images are normalized) is composed of the responses to a specific set of stimuli, changing the stimulus set changes the apparent responses. To demonstrate this dependence, we recalculated the mean response strengths for the data presented in Figure 9, C and D, using the range of SFs studied by Shoham et al. (1997)
DISCUSSION
Four rules characterize the organization of SF preference in V1. First, cells with SF preferences between 0.2 and 1.8 c/° are clustered into domains with other cells of similar SF preference. Cells in these domains respond well only to spatial frequencies within one to two octaves of the preferred SF. Second, these SF domains are organized into a map that is locally continuous across V1, although the spatial gradient of SF preference is not constant, and there are often clear fractures in the SF map before the entire range of SF preference is represented. Third, although SF domains are irregularly spaced, the distance between domains of very different SF preference conforms to the hypercolumn description of cortical organization. Finally, cortical domains containing cells that prefer the extremes of the SF continuum, either very low or very high spatial frequencies, tend to colocalize with the pinwheel center singularities in the cortical map of orientation preference.
Several observations confirm that the optically derived maps accurately represent the SF preference of neurons in V1. First, the same optical data that we analyzed for SF also produced maps of orientation preference that were consistent with the known cortical organization. Second, the observed SF maps were consistent with the gross layout and distribution of SF preference in visual cortex as demonstrated by previous electrophysiological and optical imaging experiments (Movshon et al., 1978b
Comparison with previous imaging studies of spatial frequency maps in V1
The maps of SF preference described here differ from the results of previous imaging studies. In one such study, Everson et al. (1998)
Shoham et al. (1997)
Several differences in experimental protocols and in analytic procedures may account for the differences between the SF maps described here and those of Shoham et al. (1997)
The final procedural difference is in the type of image normalization used in constructing maps of SF preference. Both Shoham et al. and Hubener et al. used cocktail-blank normalization, whereas we used blank stimulus normalization. Cocktail-blank normalization can accentuate differences in responses to certain stimuli, but it can also obscure genuine responses (compare the conclusions of Crair et al., 1997b
Despite disagreement between our results and those of Shoham et al. (1997)
Implications for development of receptive fields and cortical maps
Geniculocortical X and Y cells have different SF tuning characteristics. The response of the Y cell to visual stimuli has a low SF cutoff (corner frequency of first harmonic response of 0.4 c/°) (Derrington and Fuchs, 1979
What might be the value of the relationship between low and high SF domains and orientation pinwheels found in the present study and by Hubener et al. (1997)
If the relationship between the orientation and SF maps is consistent across species, it may provide an important constraint to models of V1 development. Predicting the shape of the orientation map alone is not sufficient to validate the assumptions of a model; nearly any mixture of spatially periodic orientation domains will produce a pinwheel-like structure (Rojer and Schwartz, 1990
Comparison with microelectrode and behavioral studies of spatial frequency in V1
The range of SF preferences found in optical maps is consistent with the findings of many electrophysiological and behavioral studies on SF preference in the cat. There is a wide range of preferred SFs among neurons in V1 (Movshon et al., 1978b
Implications for cortical processing in V1
The clustering of cells with similar SF preferences in a continuous map in V1 is consistent with features of SF adaptation observed in human psychophysical studies (for review, see Shapley and Lennie, 1985
