Through ISOI on anaesthetized macaques, we imaged cortical hemodynamic signals for various contour features. The stimulus set included simple contour shapes, including circles and triangles, as well as parts of these shapes, including curves, angles, and short straight lines. As shown in Figure 1C, the contours were presented on a full screen and drifted along one of four or eight directions. Each stimulus condition was presented for 3.5 s and repeated 25–50 times in a random sequence. The light reflectance was imaged through an optical chamber covering parts of V1, V2, and V4 (Figure 1A and B). The exposed V4 region corresponded to the visual field of 0°−10° eccentricity in a lower quadrant. We obtained support vector machine (SVM) maps that compared cortical images collected during two stimulus conditions (Figure 1D–L). In the circle vs. triangle map (Figure 1D), the black and white patches corresponded to regions that preferred circles and triangles, respectively. This V4 pattern significantly differed from the orientation (Figure 1E) and color patterns (Figure 1F) obtained with established methods (Tanigawa et al., 2010; Li et al., 2013). In contrast to V4, we did not observe circle vs. triangle patterns in V1 and V2, or in the cortex anterior to the superior temporal sulcus (Figure 1D). We also examined single-condition maps (stimulus vs. blank); however, the responses were dominated by feature-non-specific activation and the shape-selective response patterns were not apparent (Figure 1—figure supplement 1).

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Similar V4 patterns were observed in the circle vs. triangle (Figure 1D), circle vs. line (Figure 1G), and curve vs. line maps (Figure 1H). Although the strength of the dark patches in the latter two maps appeared weaker, they had similar general layouts and locations as the first one (also see Figure 1—figure supplement 2O–R for enlarged views). This similarity suggests that the key contour feature responsible for these dark patches was the curviness. Therefore, we have henceforth referred to these patches as ‘curvature domains’. These curvature domains contained smaller substructures. For example, a map comparing differently oriented curves showed smaller and weaker patches within the curvature domains (Figure 1I, Figure 1—figure supplement 2). Note that this curve orientation (also called direction) is different from the grating orientation (0–180°) and has a range of 0–360°.

Compared with the curvature domains, triangle-activated cortical regions appeared significantly weaker. In the triangle vs. line (Figure 1J) and angle vs. line maps (Figure 1K), the dark patches (angle-preferring) were apparently more diffused and weaker than those in the circle vs. line or curve vs. line maps (Figure 1G and H). This was also observed in the circle vs. triangle map (Figure 1D), which had fewer and weaker white patches (triangle-preferring) than dark patches (circle-preferring) (also see Figure 1—figure supplement 2G). Moreover, the orientation subdomains observed in the curve-orientation map (Figure 1I) were not present in the angle-orientation map (Figure 1L).

Imaging results of seven hemispheres (cases) of six macaque monkeys were consistent (Figure 2B, Figure 2—figure supplement 1B). We observed curvature domains in the entire exposed V4 surface representing both foveal and peripheral visual fields, but peripheral V4 tend to prefer larger circles (Figure 2—figure supplement 2A–D). Moreover, similar patterns can be repeatedly imaged from the same chamber over months (Figure 2—figure supplement 3). Modification of the experimental conditions (e.g. monocular left- or right-eye viewing conditions or binocular conditions, see Figure 1—figure supplement 2M and N) and noncritical stimulus parameters (e.g. contour brightness, filled disks, and regular vs. random contour arrangements) did not alter the main pattern features (Figure 2—figure supplement 2E–I).

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The curvature domains had an average diameter of 518 ± 25 μm (mean ± s.e.m), which was similar to that of the orientation domains (479 ± 16 μm, p=0.074, paired t-test, n = 7; Figure 2E). The curvature domains occupied 12.1 ± 1.7% of the V4 surface, smaller than the coverage of the orientation domains (22.3 ± 3.7%, p=0.025, paired t-test, n = 7). The intrinsic optical signal amplitude (percentage change), which was measured from the raw subtraction maps, was numerically, but not significantly, larger for the circle vs. triangle maps than the orientation maps (curvature domains: 0.036%, orientation domains: 0.029%, p=0.15, paired t-test, n = 7, Figure 2F).

Both the curvature and orientation domains represent shape features; therefore, it is logical to expect that they might overlap. However, we observed little overlap between the curvature and orientation domains (Figure 2D). The overlap size was significantly smaller than that expected in a random distribution (p=0.03, paired t-test, n = 7, Figure 2G), which indicates an avoidance tendency between both domains. Moreover, the curvature domains did not overlap with the color domains (p=0.004, paired t-test, n = 7, Figure 2—figure supplement 1F). Contrastingly, the triangle-preferring white patches in the circle vs. triangle maps tended to overlap with the orientation (p=0.003, paired t-test, n = 7; Figure 2—figure supplement 1F) but not the color domains (p=0.17, paired t-test, n = 7; Figure 2—figure supplement 1F).

ISOI used a metabolism-based hemodynamic signal; therefore, the actual neuronal responses and neuron constitution within these domains were unclear. Moreover, ISOI could not provide information regarding the variations in different cortical layers. We then used two-photon calcium imaging to address these questions. Based on the ISOI functional maps, we injected AAV1/9-GCaMP6s virus into multiple locations in two chambers (Cases 3 and 4 in Figure 2A, Figure 3—figure supplement 1). The injections targeted either the centers of the curvature domains or regions outside these domains. We imaged the monkeys under similar anesthesia conditions 1.5 months after the injections. Figure 3C shows an image from Case 3 (red frame in Figure 3A and B, also see Figure 3—video 1) at a 210 μm depth. The center of this image frame contained a curvature domain (Figure 3B). Mapped with both manual and computer-controlled visual stimuli, the population receptive field (RF) of this region was ~4° in size and approximately 7° from the fovea (Figure 4—figure supplement 1A).

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We tested 19 different curved and rectilinear contours, presented at different orientations, which resulted 73 unique stimuli (Figure 6A, also see Materials and methods). Each stimulus contained a single contour element similar to those used in the ISOI experiments (Figure 3—video 1). The stimulus moved across the population RF along a direction randomly chosen. Consistent with the ISOI results (Figure 3B), we observed significant activation of the neurons by circle stimuli (Figure 3D). The whole frame showed a scaled-down response to triangles (Figure 3E). The results demonstrate that different stimuli types mainly affected the population response amplitudes rather than activating different cells within the curvature domain.

We determined the preferences of curved and rectilinear stimuli for each pixel in the two-photon image (Figure 4B). This imaged region showed a preference for curved (red) over rectilinear (green) stimuli. Consistent preference patterns were observed for this two-photon map (Figure 4B) and the ISOI map from the same region (Figure 4A). Similar preference patterns were observed at deeper layers for this (Figure 4B and C) and all five locations imaged at multiple depths (Figure 4D–I, Figure 3—figure supplement 1). Therefore, the curvature domains form a columnar structure within at least the top V4 layers.

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We also performed PCA analysis on the response patterns of all the neurons. This data-driven analysis also revealed a major difference in curved and rectilinear responses, and its association with the neurons’ locations that either inside or outside the curvature domains (Figure 5).

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Although neurons inside the domains exhibited a common preference for curve stimuli, individual neurons showed diverse response properties. Figure 3F shows the responses of 3 example neurons to 14 typical stimuli. Two neurons were selected from the curvature domain showed in Figure 3C (red markers). Both neurons were strongly activated by circle stimuli; however, cell 2 was also activated by multiple other stimuli. Cell 3 were selected from a region highly activated by rectilinear stimuli (Figure 4F arrow) and it showed strong responses to the triangle as well as a 45°-orientated line that resembled an edge of the triangle. Thus, at cellular level, contour-tuning differences exist not only between cells belonging to different functional domains but also between cells within a functional domain. This is further explored in Figure 6.

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We identified 1923 neurons in 10 two-photon imaged locations (Figure 3—figure supplement 1); among them, 788 neurons were in the curvature domains while 1135 neurons were outside of these domains. Despite certain variability due to alignment error, a comparison of the neurons’ calcium responses and their corresponding pixel responses in ISOI maps revealed a general consistency between the two measurements (Figure 4J and K). Figure 4J and K also shows that more neurons had a greater response to curved stimuli than to rectilinear ones (more neurons had a positive Y axis value in both figures). Overall, the neurons with a stronger response to curved stimuli tended to have smaller RFs (Figure 4L and M, Figure 4—figure supplement 1B-E) and greater surround suppression (Figure 4—figure supplement 1F and G), which is consistent with previous findings on the relationship between end-stopping properties and curvature selectivity (Hubel and Wiesel, 1965; Dobbins et al., 1987; Ponce et al., 2017).

Curvature domains imaged with curves and circles in ISOI were generally similar (e.g. Figure 1G and H). However, individual neurons inside the curvature domain often showed different responses to these two stimuli. Figure 6A,C and E shows response matrices of three example neurons selected from the curvature domains. Each neuron showed a wide response spectrum to the 73 contour stimuli. To analyze different responses to curves and circles, we labeled neurons that exhibited significant orientation tuning to curves as ‘curve-orientation-preferring neurons’ (e.g. Figure 6A and B) and those with stronger responses to circles than to curves as ‘circle-preferring neurons’ (e.g. Figure 6E and F). Some neurons that met both criteria were labeled ‘dual-preference neurons’ (e.g. Figure 6C and D). Note that after dual-preference neurons were isolated into a separate group, the earlier two groups no longer contained dual-preference neurons. PCA analysis of response patterns for neurons inside curvature domain also showed differences between circle-preferring neurons and curve-orientation-preferring neurons (Figure 6—figure supplement 1). Among the 788 neurons imaged inside the curvature domains, circle-preferring comprised 25.6% (202), dual-preference comprised 14.4% (113), and curve-orientation-preferring neurons comprised 19.2% (151), with the rest not passing the statistical tests. The corresponding proportions of these three groups in the 1135 neurons outside the curvature domains were 7.3% (83), 1.8% (20), and 11.7% (133), respectively (Figure 6I). As expected, the summed proportion of these three types of neurons was larger inside the curvature domains (59.1%) than the outside (20.8%). The ratio of circle-preferring to curve-orientation-preferring neurons also appeared to be larger inside (1.35) than outside (0.62) the curvature domains.

When neurons were labeled according to their preferences, there was a tendency of spatial clustering according to their types (Figure 6G). Moreover, the curve-orientation-preferring neurons further clustered based on their preferred orientations (Figure 6H), which is consistent with the ISOI results (Figure 1I, Figure 1—figure supplement 2A–D). The average distances for within-group neuron pairs were shorter than the average distance between two randomly selected neurons (Figure 6J). Periodicity analysis shows the size of curve-orientation subdomain was around 360 μm (Figure 6—figure supplement 2).

Circle-preferring neurons also showed some interesting features. Figure 6K plots average responses to different contours for circle-preferring neurons (red) and curve-orientation neurons (green). For each stimulus, neurons’ maximum orientation-responses were averaged. For circle-preferring neurons, their responses increased approximately linearly with the length of the circle fragment. This was not the case for curve-orientation neurons. Also, their responses to closed shapes seemed to be proportional to the general similarity between the shape and the circle. As a comparison, Figure 6L plotted their orientation-averaged responses. The two curves are similar to those in Figure 6K, except that the green curve becomes lower on the left side, reflecting the modulation of curve orientation on the responses of the curve-orientation-preferring neurons.

So far, we have shown the common response properties for neurons within the curvature domains and their subdomains. To have a full picture of the neuronal constituents within these functional domains, we examined the diversity of neuronal tunings inside the curvature domains.

In Figure 7, we show single-neuron response matrices from three example two-photon sites, including a circle-preferring site (A), a curvature-orientation-preferring site (B) and a rectilinear-preferring site (C). The location of these sites can be found in Figure 6G. For each site, 10 example neurons are shown. For the circle-preferring neurons (A), they prefer circles much better than the half circles. Their responses patterns also exhibited certain diversity, including some neurons responded modestly to the 90°-angle stimuli (cell 8–10) while others did not. They could respond well (cells 1, 2, 3, 5, 7, 9) or modestly (cells 4, 6, 8, 10) to hexagons. For cells in curve-orientation-preferring site (Figure 7B), response diversity appeared even larger. Different neurons showed strong selectivity to the trefoil shapes (cells 1, 4), or particular 90° angles (cell 3). Different degrees of circle-preference were also apparent among these neighboring neurons.

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The rectilinear site shown in Figure 7C was also located in an orientation domain that preferring the 45° orientation. Many cells responded well to the triangles and the 45°-oriented lines. Some cells also responded to the 45°-orientated ovals and flat curves, likely due to their general orientation appearance. However, neighboring neurons could respond strongly to one of these stimuli (e.g. cell 1 to oval, cells 2 and 3 to triangle, cell 4 to line) but much weaker to others. Some neurons (e.g. cell 9) exhibited a wider range of preferred shapes than their neighbors.

Thus, for neighboring neurons, although their general shape preferences were similar, which constitute the basis of the ISOI signals, their contour response patterns still vary from cell to cell, and some of the differences were substantial. The degrees of such diversity also seem to be related to the types of these sites in V4.

Shape-related responses of neurons in curvature domains, rectilinear domains, and those outside of these two were summarized in Figure 8. In the orientation-sorted average response matrices, curvature neurons showed much higher response amplitudes, and larger differences between curved and rectilinear responses, than the other two types of neurons. Nevertheless, these neurons also responded to rectilinear stimuli, for example the triangles, at about half of the response amplitude. Interestingly, neurons in rectilinear domains did not show prominent differences in their responses to rectilinear and curved stimuli. This is also consistent with the weak rectilinear domains in ISOI imaging (Figure 1D). Figure 8D further illustrates the differences among three regions, in which the size and color of the shapes are proportional to the response magnitudes of the first rows in the response matrices in A–C.

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Animals were sedated with ketamine (10 mg/kg) or Zoletil (tiletamine HCl and zolazepam HCl, 4 mg/kg) and transferred to the lab. They were artificially ventilated on a stereotaxic and anesthetized with isoflurane (1.5–2.5%) during surgery. A 22–24 mm (diameter) circular craniotomy and durotomy were performed (center location, 30–37 mm from midline, 15–24 mm from posterior bone ridge) to expose visual areas V1, V2, and V4 (illustrated in Figure 1A). ISOI was performed right after the surgery (see below). Then, one of two types of protocols was chosen: For cases only used for ISOI, we implanted an optical chamber and recovered the animal. For cases used for two-photon calcium imaging, we injected virus into the visual cortex, placed back the bone and sealed the craniotomy (described below). After 1.5 months, we reopen the craniotomy and implanted an optical chamber for the following weekly based two-photon imaging experiments. The same type of chronic chamber was used for ISOI and two-photon imaging (Li et al., 2017). The inside diameter of the chamber was 13–16 mm, thickness of the glass is 0.18 mm. Case 2 was only imaged once and then used for other studies thus no chamber was implanted.

ISOI were performed either right after the surgery (without a chamber), or on a weekly-base after a chamber was implanted. Imaging usually lasted for 8 hr. Right before the imaging, anesthesia was switched from isoflurane to a mixture of propofol (induction 2 mg/kg, maintenance 2 mg/kg/hr) and sufentanil (induction 0.15 μg/kg, maintenance: 0.15 μg/kg/hr) (in four cases), or to Zoletil (tiletamine HCl and zolazepam HCl, induction 4 mg/kg, maintenance 1.25 mg/kg/hr, in three cases). The monkeys were immobilized with vecuronium bromide (induction 0.25 mg/kg, maintenance 0.05 mg/kg/hr) to prevent eye movements. Anesthetic depth was assessed continuously via monitoring the electrocardiogram, end-tidal CO₂, blood oximetry, and body temperature. Eyes were dilated (atropine sulfate, 0.5 mg/ml) and fit with contact lenses of appropriate curvatures to focus on a stimulus screen 57 cm from the eyes.

Images of reflectance change (intrinsic hemodynamic signals) corresponding to local cortical activity were acquired (Imager 3001, Optical Imaging Inc) with 632 nm illumination. Frame size was 540 × 654 pixels, representing either 15.5 × 19 mm or 18 × 22 mm of imaged area, depending on the lenses chosen. For each trial, imaging started 0.5 s before the stimulus onset and collected at 4 Hz frame rate. Each visual stimulus was presented for 3.5 s. The total imaging time for each trial was 4 s, during which 16 frames were imaged. Interstimulus intervals were at least 6 s. Stimulus conditions were displayed in a randomized order.

Virus injection and two-photon imaging procedures were similar to those described in Li et al., 2017. In two cases (Case 3 and Case 4), we injected 500 nL AAV9.Syn.GCaMP6S.WPRE.SV40 (CS1282, titer 3.34e13 GC/ml, Addgene), or AAV1.Syn.GCaMP6S.WPRE.SV40 (v25497, titer 2.5e13 GC/ml, Addgene) into 10–15 cortical locations at a depth of 500 μm. After virus injection, cortex was covered with a piece of artificial dura. And the remaining dura was covered and glued to the top of the artificial dura with medical adhesive (Beijing Compont medical devices Co. Ltd). The original bone was placed back, secured with titanium lugs and bone wax in the gap. The scalp was sutured. A second surgery was performed 1.5 months later, in which the old craniotomy was reopened and an optical chamber was implanted for the following ISOI and two-photon imaging.

Two-photon calcium imaging was performed on a weekly-base after the chamber implanting. Animal anesthesia and preparation were the same as those in the ISOI experiments. Two-photon microscope was a Brucker Ultima IV Extended Reach (Bruker Nano Inc). Laser was generated with a Chameleon Ultra II (Coherent Inc). The excitation wavelength of the laser was set at 980 nm. Scanning frame rate was 1.3 Hz in a galvo scanning mode. Under a 16X objective (0.8 N.A., Nikon), 515 × 512 pixel images were collected, representing a 830 × 830 μm cortical surface. Imaging was continuous and the beginning of each stimulus presentation was synchronized with the beginning of a frame scanning.

As the microscope was vertical, we rotated the stereotaxic and the animal for ~45° so that the chamber plane was perpendicular to the laser beam. We imaged 10 cortical locations in the two virus-injected chambers (Figure 3—figure supplement 1A and E). Images were normally collected at a depth between 210 and 350 μm from the cortical surface. In six locations, we imaged at two depths, a depth around 230 μm and a depth around 310 μm (Figure 3—figure supplement 1D and H). During the imaging session, slow drifts of cortex in the imaging window was observed. The drift was normally less than 50 μm in the X-Y plane and less than 150 μm along the Z-axis in a course of 6–8 hr. We closely monitored the cell features during the imaging and adjusted position of the focal plane accordingly. Drifts in the X-Y plane were further corrected in offline data analysis (described below). In addition, population receptive field locations were re-plotted every 1–1.5 hr in order to check the stableness of the eye positions. In half of the experiments, some eye drift (1–2°) was detected during the imaging session. If drift was larger than 1°, we repeated the last stimulus run at the new receptive field position. If the drift was smaller than 1°, we adjusted the stimulus location for the following stimuli and continued the imaging. Replication of two-photon imaging of the same neuron population were tried but was not systematically tested. A general replication of the population-level responses was qualitatively observed.

Visual stimuli were generated using ViSaGe (Cambridge Research Systems Ltd.) and presented on a CRT monitor positioned 57 cm from the eyes. The stimulus screen was gamma corrected and worked at 100 Hz refreshing rate. We compared contour preference maps obtained with monocular and binocular conditions in Case 1 (Figure 1—figure supplement 2M and N), as well as two monocular conditions in Case 4 and did not find obvious differences. Since ISOI signal is normally stronger in binocular condition, all but one case (Case 5) were imaged in binocular conditions. For orientation and color preference maps, full-screen drifting sinewave gratings were used. The mean luminance was 28.9 cd/m². Gratings of two SF (0.25 and 1 c/deg, except for Case 6 in which only 0.25 c/deg were tested) and two (45° and 135°, for Cases 5 and 6) or four orientations (0°, 45°, 90°, and 135°, for other five cases) were tested. Gratings were drifting at 4°/s along a random direction perpendicular to its orientation and were presented in a random order. The initial phases of the gratings were also randomly selected.

For contour shape preference maps (e.g. Figure 1D–L), drifting contour patterns were used. Each contour element was ~2.5° and placed in a 3 × 3° grid (Figure 1C). The white contour lines was 0.2° in width and had a luminance of 111.2 cd/m². The dark background had a luminance of 20.6 cd/m². For each trial, a contour pattern was presented and drifted at one out of four or eight directions for 3.5 s at a speed of 4°/s. Interstimulus intervals were 6 s, during which a gray screen (20.6 cd/m²) was presented. The initial phase (i.e. relative position) of the pattern was random. Each stimulus was repeated for 25–50 times. The essential stimuli (e.g. circle, triangle, gratings) was obtained in all seven cases (Figure 2—figure supplement 1), new stimuli were added in later cases and are described in the Results whenever is necessary.

Visual stimuli used for two-photon imaging were generated in a similar way as those in the ISOI imaging and presented on a 21-inch LCD monitor (Dell E1913Sf) positioned 57 cm from the eyes. The stimulus screen was gamma corrected and worked at 60 Hz refreshing rate. All stimuli were bright stimulus (80.8 cd/m²) on a gray (13.2 cd/m²) background and presented monocularly to the left eye.

Population RF location was first mapped manually with a 2–3° circular patch of square-wave gratings, during which cortical fluorescent response was monitored. Then the RF were systematically mapped at the potential region with a single 2–3° patch of stimulus presented on a grid of 5 × 5 locations. Each position was tested with a square-wave grating, a random dot patch, and a circle, each moved at one out of four directions (45°, 135°, 225°, 315°) at 4°/s speed. Each stimulus was presented for 1.5 s. Interstimulus interval was 0.5 s. Population RF center (normally 5–7 degrees eccentricity) was then analyzed online based on cortical responses to these stimuli.

To obtain detailed RF size information, we presented circular patches of square-wave gratings (SF = 1 c/degrees, TF = 4 c/s, duty cycle = 0.2) of six different sizes (0.5°, 1°, 2°, 4°, 8°, 12°) at the population RF center mapped before. Each stimulus was drifted along one of eight directions, and presented for 2 s with a 3 s interval. Each stimulus was repeated for seven times. From these stimuli, a size-tuning curve was calculated, which normally peaked at patch sizes of 2°–3.5°. Population RF size was then defined as twice of this size (i.e. 4°–7°).

To test the contour-shape preferences of the neurons, we presented single contour elements in the population RF. Single contour element was the same as those used in the ISOI experiments. The size of the contour was adjusted to 40% of the population RF. Each stimulus was presented for 2 s, during which it first appeared in the center of the population RF and drifted along one of eight directions (randomly selected). After it moved to the edge of a virtual window equal to the population RF diameter, it disappeared and reappeared in the opposite side of the window, and continue its motion along the same direction (illustrated in Figure 3—video 1). The speed of the contour movement was adjusted to (half of the diameter of the population RF)/s. The interstimulus intervals were 3 s. Each stimulus was usually repeated for 10–15 times. As shown in Figures 6A, 19 different contour shapes were used, most of them was presented in four orientations, two stimuli were presented in two orientations (square, hexagon), and one stimulus (half circle) was presented in eight orientations. This made up 73 different stimulus conditions. We also included four identical circles instead of 1 to be comparable to other stimuli’s four orientations. The final stimulus matrix contained 76 stimuli.

ISOI data analysis was performed using MatLab 2017 (The MathWorks, Natick, MA). We first obtained ΔR/R response to each stimulus using following formula ΔR/R=(R_8-16 - R_1-4)/R_1-4, in whichR_8-16 is the average of frames 8–16, R_1-4 is the average of frames 1–4. The ΔR/R frames for each trial were then used for following analysis.

We used a pattern classifier (support vector machine, SVM) for calculating contrast maps between ΔR/R frames of two stimulus conditions. Compared with simple subtraction maps, SVM weight map achieved a higher signal-noise ratio by suppressing blood vessel noise and low-frequency noises (Xiao et al., 2008; Chen et al., 2016). The Matlab SVM program was provided by Chih-Jen Lin (LIBLINEAR: A Library for Large Linear Classification, 2008; available at https://www.csie.ntu.edu.tw/~cjlin/liblinear/).

For each SVM map (e.g. Figure 1D–L), it was first Gaussian low-pass filtered (size = 5 pixels, std = 1), then clipped at 0 ± 8 SD for display, in which SD was the standard deviation of the background pixels values (blood vessel pixels and outside-chamber pixels, determined based on the blood vessel maps like the example shown in Figure 1B). For display purposes, the original map size (540 × 654 pixels) was cropped to 540 × 540 pixels by trimming off some background regions on the two edges.

To separate domain region from non-domain regions (e.g. Figure 2D), we used 0 ± 2 SD as the threshold levels and discarded resulting regions containing less than 50 pixels. Curvature domains were identified as the dark regions in the circle vs. triangle maps. Domain coverage in Figure 2D and the neuron classification in Figures 5–8 were all based on this method. Only in estimating domain sizes (Figure 2E), we used a watershed method in order to deal with the ‘connected domain’ problem (see below). Orientation domains were identified as both the dark and white regions in the orientation maps. Color domains were identified as both the dark and white regions in the color vs. luminance maps. To compare with two-photon results (e.g. Figure 4J and K), regions in the SVM map that aligned with the two-photon imaging area were extracted and resized (bicubic interpolation) to 512 × 512 pixels for further analysis.

To estimate domain sizes (e.g. Figure 2E), neighboring domains were often connected and we separated them using a watershed algorithm. First, the image values were reversed to make the negative domains positive. Then we located the strongest response pixel, and cut out a 31 × 31 (0.9 × 0.9 mm) pixel region around this pixel. For all pixels in this square that had a value lower than 0+2SD, they were set as 0+2SD. The response pattern was fitted with a two-dimentional Gaussian. An oval was obtained from the two-dimentional Gaussian with a threshold so that the oval had half of its pixels valued larger than 0+2SD (and the other half pixel all had values of 0+2SD). This oval was taken as the representation of this curvature domain. Before search for the next domain, the pixels in the oval region in the original map was set as 0+2SD. The searching stopped until no more pixels had value larger than 0+2SD. In addition, small domains had fewer than 75 pixels were not included in the size analysis. Individual domain size was described as the diameter of an equivalent disk. Domain sizes were then averaged according to map types and cases. To measure the map strength of a functional map (e.g. Figure 2F), we calculated the differences of average pixel values in white and dark domains in the subtraction map, using the domain masks described above. For example, the map strength of a 45° vs. 135° orientation map was calculated as the subtraction between the average pixel values of 135° domains and the average pixel values of 45° domains in the 45°−135° subtraction map.

Two-photon data analysis was performed using MatLab 2017 (The MathWorks, Natick, MA). Image alignment and cell identification algorithms were modified from those used in Li et al., 2017. To correct slow cortex drifts and biological movements (likely due to heart pulsation and artificial ventilation) within the X-Y plane (normally less than 20 pixels during the whole imaging session, typically five pixels), we first obtained a frame template by averaging 1000 frames from a chosen session, then all frames of that experiment, and frames from other days of the same cortical layer, were aligned to this template using a cross-correlation method.

Fluorescent images (e.g. Figure 3C) were obtained by averaging all collected two-photon images during the imaging session, including the baseline and response images. Response images (e.g. Figure 3D and E) were obtained by subtracting the baseline image (average of the two frames before the stimulus onset) from the response image (average of the second and third frames after the stimulus onset).

Cell bodies were first identified based on their responses to each visual stimulus. We first averaged all repeats for a stimulus, then obtained a subtraction image by subtracting the baseline image (average of 2 immediate pre-stimulus frames) from the response image (average of frames 2 and 3 after the stimulus onset). This subtraction image was then filtered using two separate Gaussian filters: G1 (size = 7 pixels, std = 1.5) and G2 (size = 15 pixels, std = 7). Then the subtraction map of G1-G2 was used for cell extraction. The cells extracted in this way had smooth edges and filled cell-body. For each cell, the cell body identified from its best-responsive stimulus was used as its cell body and was used to calculate its responses in all the other stimuli.

A cell was identified if more than 30 connected pixels had values larger than mean+2.75SD, in which SD is the standard deviation of the pixel values of the whole filtered subtraction image. After cell locations were determined, we calculated fluorescence responses for cells to each stimulus using following formula: ΔF/F0=(F-F0)/F0, in which F is the average pixel value covered by the cell in the response image, and F0 is average pixel values in the baseline image. A cell was included for the following analysis if any of its stimulus responses (ΔF/F0) was larger than 0.3 for the stimuli tested.

A cell was identified as a curve-orientation-preferred cell (e.g. Figure 6A–D) if its responses to eight curve orientations passed the Rayleigh test for circular uniformity (Fisher, 1993) at a significant level of p<0.05. Then we fitted the responses with a modified von Mises function (Mardia, 1972):

where θ is the orientation of curve (0–360°); θp is the preferred orientation; a0 is the baseline offset; (b1, b2) and (c1, c2) determine the amplitude and shape of the tuning curve, respectively. Fitting parameters were obtained with a least-square nonlinear regression method (nlinfit in Matlab, Mathworks). Goodness of fit (R²) values were >0.7 for all neurons which have significant orientation tuning to curve (n = 417). Cells’ preferred orientations were then calculated from the fitting curve (Figure 6B).

A cell was determined as circle-preferred cell if it met following two criteria: 1. The cell’s response was significantly modulated by contour types (bar, 90°-angle, triangle, curve, each was represented by its optimal oriented stimulus, and circle, p<0.05, one-way ANOVA) and its maximum response was to the circle. 2. The cell’s response to the circle was significantly larger than its response to the curve of its preferred orientation (p<0.05, paired t-test).

In calculation of the preferential responses to two contours (e.g. Figure 4J and K), we first normalized the cell’s ΔF/F0 responses to the whole stimulus set to 0–1, then the differences of the responses to the two types of stimuli were calculated.

To measure cell RF sizes (e.g. Figure 4L and M), we first performed a two-way ANOVA analysis (with repetition) for the cell’s responses to square-wave gratings of 6 different sizes and eight different moving directions. If the size factor is significant (p<0.05), then we fitted a ratio of Gaussian function (Cavanaugh et al., 2002) to the direction-averaged size tuning curve:

where x is the stimulus diameter, k_c and k_s are gains for the RF center and surround, L_c and L_s are the total squared responses of the center and surround, and wc and ws are the size of the center and surround (wc <ws). Fitting parameters were obtained with a least-square nonlinear regression method (nlinfit in Matlab, Mathworks). The optimal stimulus size was determined as the diameter corresponding to the peak response in the fitted function. Goodness of fit (R²) values were >0.7 for all neurons that had significant size tuning to square wave gratings (n = 1493), and 95% (1418/1493) of these neurons had a preferred stimulus size between 0.5° and 12°. If a cell’s responses were not modulated by stimulus size (i.e. size factor was not significant in the two-way ANOVA analysis), then this cell was not included in the RF size related analysis. Surround suppression index (e.g. Figure 4—figure supplement 1F) was calculated from the size tuning curve as (maximum response – minimum response)/maximum response, in which minimum response was the least response obtained for stimulus size larger than that of maximum response (maximum surround suppression).

Pixel-based contour-preference maps (e.g. Figure 4B) were a combination of a gray value (G) map and a red/green hue map. For each pixel, we first calculated a shape preference index: SPI = abs(ΔFcc-ΔFbat)/max(ΔFcc,ΔFbat), where ΔFcc is the maximum fluorescence increase to curves and circles (red framed ones in Figure 3F), ΔFbat is the maximum fluorescence increase to bar, angle and triangle (green framed ones in Figure 3F). Then we calculated the gray value as: G = 200xSPIxFp/Fp_f, where Fp is the maximum of the fluorescence values in the response images to all five types of stimuli, Fp_f is the average of all pixels’ Fp in the same frame. Hue for a pixel is red if its ΔFcc is larger than ΔFbat, and is green if not.

PCA results were shown in Figure 5 and Figure 6—figure supplement 1. For each neuron, its response matrix was normalized to 0–1. Its responses to different orientations were sorted, so that for each contour, 0° represented its highest response and 135° for the lowest (thus no longer correspond to the stimulus icons). Only neurons tested with the full stimulus set were analyzed (n = 1556). The responses of these neurons were arranged as a 2D matrix, and the mean response to each stimulus was subtracted before the PCA analysis was performed. In Figure 5E, the color of the neurons was determined based on their coordinates on PC1.

All t-tests and paired t-test are two-tailed.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

This work was supported by the National Natural Science Foundation of China (31530029 and 31625012 to HDL and 31800870 to RT) and the China Postdoctoral Science Foundation (2018M631373 to RT). We thank Dr. Shiming Tang for valuable technical support on two-photon imaging. Lab members Jie Lu, Yan Xiao, Chen Fang, Kun Yan, Jingting Xu, Heng Ma, Jiayu Wang, Pengcheng Li, Chen Liang, and Wenhao Zhao provided technical assistance.

Animal experimentation: All procedures were performed in accordance with the National Institutes of Health Guidelines and were approved by the Institutional Animal Care and Use Committee of the Beijing Normal University. Protocol number: IACUC(BNU)-NKCNL2016-06.

1. Received: April 2, 2020
2. Accepted: November 18, 2020
3. Accepted Manuscript published: November 19, 2020 (version 1)
4. Version of Record published: December 1, 2020 (version 2)

© 2020, Tang et al.

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