Five subjects (two females) participated in this study. Subjects were 24–36 years old, right-handed, had normal or corrected-to-normal visual acuity, and were expert at fixating on a central mark while attending to a moving stimulus during visual field mapping experiments. This study was carried out in accordance with the recommendations of the Institutional Review Board (Social and Behavioral Sciences Panel C) at the University of California, Irvine (UCI). All subjects gave written informed consent in accordance with the Declaration of Helsinki prior to the initiation of any experiments.

Each subject participated in two fMRI scan sessions, during which the following data were acquired: 2 T1-weighted in-plane anatomical scans, 4 baseline scans, 8 functional visual field mapping scans, and 1 T1-weighted anatomical volume.

Experiments were performed on the 3T Philips Achieva MR scanner at UCI with an 8 channel SENSE imaging head coil. A high-resolution, whole-brain anatomical dataset was acquired for each subject with the following parameters set to maximize the image contrast between white and gray cortical matter: T1-weighted 3D MPRAGE, 1 mm³ voxels, TR = 8.4 ms, TE = 3.7 ms, flip = 8°, SENSE factor = 2.4. The anatomical volume was corrected for inhomogeneity and linearly transformed with no rescaling and no distortion to align with the Talairach reference brain, using tools from the FMRIB software library¹. This high-resolution anatomical dataset was used to identify the gray matter of the cortical sheet for detailed analysis of the functional measurements.

mrVista is an open-source, Matlab-based, signal-processing software package developed by the Wandell lab at Stanford University that our lab standardly uses for analysis of individual-subject neuroimaging data². In each subject’s high-resolution anatomical dataset, the location of the cortical white matter was identified – or segmented from the overlying gray matter– using the mrVista automated algorithm and expert hand-editing (Teo et al., 1997). The segmented white matter surface was then used to grow a 3–4 mm layer of gray matter. To improve sensitivity and decrease noise, this gray matter was subsequently used to identify which voxels would be analyzed in functional scan measurements (Wandell et al., 2000).

With each functional scan session, one anatomical in-plane dataset was acquired with the same slice prescription as the functional scans but with a higher in-plane spatial resolution (1 mm × 1 mm × 3 mm voxels). As these T1-weighted anatomical images were thus physically in register with the functional scan slices, they were used to align the functional data with the high-resolution anatomical data, first by a manual co-registration and then by a semi-automated, 3D co-registration algorithm, a mutual information method (Maes et al., 1997; Nestares and Heeger, 2000).

Functional MR scans were performed on the same scanner as the anatomical data. For each scan, 35 axial slices were acquired that were oriented close to parallel to the superior temporal gyrus for optimal coverage of the cortex (T2-weighted, gradient echo imaging, TR = 2 s, TE = 30 ms, flip = 90°, SENSE factor = 1.7, reconstructed voxel size of 1.875 × 1.875 × 3 mm, no gap). These parameters were used for all visual stimuli functional scans (i.e., moving bars – experimental scans; expanding rings – baseline scans).

Data from each scan were analyzed voxel-by-voxel with no spatial smoothing. To assess data for potential artifacts from head movements, the mean value maps of the blood oxygenation level dependent (BOLD) signal were compared across all scans within one scan session. Motion correction was not needed for any scans in this study, as all scans had less than one voxel of head motion from these experienced subjects. A high-pass filter was applied to the time series from each scan to remove low-frequency sources of physiological noise. The time series from matching scans (i.e., moving-bar stimulus scans) were then averaged together to form one mean time series for that scan type for each subject; this average time series was then used in the pRF modeling analysis. Following registration to the high-resolution anatomy as described above, each subject’s VFM data were displayed on a 3D rendering of that subject’s cortical surface and on a flattened section of the cortical sheet to allow for optimal delineation of VFM boundaries (Wandell et al., 2000).

The Psychophysics Toolbox (Brainard, 1997; Pelli, 1997) in the Matlab programming environment was used to create stimuli on a Dell Optiplex desktop. A Christie DLV1400-DX DLP projector (spatial resolution: 1024 × 768 pixels, refresh rate: 60 Hz) was used to back-project the stimuli onto a display screen at the head end of the bore of the magnet. An angled front-surface mirror was mounted on the scanner head coil close to the eyes to allow the subjects to view the stimuli with a viewing distance of approximately 70 cm. Surgical tape on the subject’s forehead and padding within the head coil were used to minimize head movements.

Visual field maps were measured using a moving-bar stimulus, which was composed of a dynamic-checkerboard, high-contrast pattern with a spatial frequency of 1 cycle/deg and a modulation metameric to the modulation of a ∼500 nm light (luminance = 140 cd/m²). The bar aperture spanned a visual field subtending a maximum radius of 11° of visual angle with a width that subtended 1/4th of the stimulus radius. The bar was displaced in discrete steps every 2 s in synchrony with the fMRI volume acquisition. Four bar orientations (0, 45, 90, and 135° from vertical) with two motion directions orthogonal to each orientation were used, producing eight different bar configurations and a total presentation time of 192 s at one cycle/scan (no repetition) (Dumoulin and Wandell, 2008, p. 33). Four mean-luminance periods were inserted in the last 12 s of each 48 s period, at a frequency of 4 cycles/scan. At this rate, each mean-luminance presentation replaces a different position of the stimulus. These mean-luminance periods are used with pRF modeling to allow us to capture visuospatial responses more effectively in regions with large receptive fields, as we expected to measure in pSTS. The mean-luminance stimulus changes the response in a particular voxel in a region with small receptive fields (e.g., V1) only when the mean-luminance replaces the bar stimulus at the preferred visual position for that voxel (Dumoulin and Wandell, 2008). In contrast, responses in regions with large receptive fields [e.g., lateral occipital cortex (LO)] decrease across many/all voxels in the region whenever the mean-luminance period occurs. This baseline measurement provided by the mean-luminance period allows us to distinguish the small pRF sizes in areas like V1 from the large pRF sizes in areas like LO and here in pSTS.

Each column of the checkerboard pattern spanned the length of the bar aperture, and each row spanned its width. Adjacent rows appeared to move in opposite directions to each other with a 2-Hz temporal frequency, and the motion direction changed randomly every 2–3 s. Subjects attended to these moving-bar apertures and responded with a button press – not in sync with the visual stimulus position changes or mean-luminance periods – to an intermittent, subtle change in the motion direction of the checkerboard pattern.

We used the pRF modeling method to estimate VFM organization and characteristics for each subject, as described here briefly; for complete details of this analysis method, see Dumoulin and Wandell (2008). The population of receptive fields (RFs) in each voxel of retinotopically organized regions of cortex is expected to have similar preferred centers (i.e., location in visual space driving the peak neural responses) and sizes (i.e., the degrees of visual angle driving significant neural responses), allowing their combined population RFs (pRFs) to be estimated as a single, two-dimensional (2D) Gaussian RF. For each voxel independently in an individual subject’s dataset, the BOLD response to the moving-bar stimulus was predicted by iteratively testing a wide range of possible 2D Gaussian pRFs with parameters of preferred center location (x, y), which are used to determine the traditional eccentricity and polar-angle responses, and spread (σ; standard deviation of the 2D Gaussian), which is used to describe pRF size). The predicted fMRI time series was calculated by convolving the stimulus sequence and BOLD hemodynamic response function (HRF) with each tested pRF (Boynton et al., 1996; Friston et al., 1998). The pRF parameters of position and size ultimately assigned to each voxel minimized the sum of squared errors between the observed and predicted fMRI time series.

As a primary measurement of goodness of fit, each voxel was independently assessed in terms of its percent variance explained, which we converted here to coherence values for comparison with the phase-encoded traveling wave methods used for our baseline measurements (Barton and Brewer, 2015) as well as numerous previous visual field mapping studies (for reviews, see Wandell et al., 2007; Brewer and Barton, 2012b). All voxels considered for further analysis displayed statistically significant responses to the moving-bar stimulus, with a coherence measurement of the BOLD signal of at least 0.25 (see section below for further discussion of coherence measurements). Eccentricity and polar angle [tan^-1(y/x)] coordinates were derived from the 2D Gaussian pRF models and were used to plot the VFM representations on the cortical surface for each subject. The pRF sizes were measured as a function of eccentricity for each VFM, collapsed across subjects. As with all visual field mapping measurements, there may be interactions in the most peripheral measurements with large receptive fields centered in the further periphery that overlap the stimulus edge. These interactions may affect the pRF center and size measurements in complicated ways in the most peripheral measurements; thus, we routinely crop our data in by at least 1°. In this study, we only report measurements for eccentricity bins including data out to 10° of eccentricity rather than the full 11° radius of the stimulus.

A traditional measure of statistical significance used in visual field mapping, coherence is equal to the amplitude of the BOLD signal modulation at the stimulus frequency divided by the square root of the power of the BOLD modulation at all other frequencies except the first and second harmonics (Engel et al., 1994, 1997; Wandell et al., 2007; Brewer and Barton, 2012b, 2014). Here, coherence was converted from the variance explained of the pRF model fit (Barton and Brewer, 2015). Our coherence threshold of 0.25 is on the conservative side of statistical significance thresholds in visual field mapping studies. For this study, we also empirically validated this threshold by measuring the coherence of the noise activity elicited by our baseline stimulus (see below for details) (Barton and Brewer, 2015).

We define a VFM in accordance with very exact criteria: (i) a VFM comprises two orthogonal, non-repeating topographical representations of visual space: eccentricity and polar angle; (ii) each of these topographical representations must be organized as a generally contiguous, orderly gradient; (iii) each VFM should represent a substantial portion of sensory space – e.g., a hemifield of the visual field (VFMs vary in the degree to which their pRFs extend into ipsilateral space, so we ignore extent of ipsilateral representation in this definition); and (iv) the general features of each VFM should be consistent across individuals (Sereno et al., 1995a; DeYoe et al., 1996; Van Essen, 2003; Brewer et al., 2005; Wandell et al., 2007; Brewer and Barton, 2012b).

An eccentricity or polar-angle gradient is one of the most highly organized features of the cortical surface ever measured using fMRI. Such gradients are identified by trained experts using colors that represent stimulus values because human visual pattern recognition is still necessary, even with the best efforts to date to perform computer-based atlas fitting (Dougherty et al., 2003; Brewer and Barton, 2012b). The fact that human recognition is involved has led to a critique that researchers are “reading tea leaves” when performing gradient identification, implying that it would be too easy for a biased researcher to mistake spurious gradients arising from noise for signal from a true gradient. Thus, it is important to estimate just how unlikely it is for an organized gradient to arise from noise in an area of cortical surface the size of a VFM. In other words, we can estimate the probability that a VFM gradient is observed under the null hypothesis that pRF centers are distributed randomly.

For such a gradient to arise, a large number of voxels must be organized such that they span an entire range of pRF centers in sensory space, in order from one boundary to the other (from lowest to highest eccentricity or from upper to lower vertical meridian for polar angle). An eccentricity gradient can be modeled as an M by N matrix of voxels, where each column spans the entire range of eccentricities (Figure 1). For simplicity, we consider the case where the eccentricity representation is evenly distributed across the M rows of each column, such that each row in a gradient represents 1/M of the total eccentricity range E_min to E_max. Let each voxel’s eccentricity value e be drawn from distribution E ∼ uniform (E_min, E_max). Eccentricity values for voxels in rows R₁, …, R_M must fall within intervals [E_min + (R – 1)^∗ ((E_max – E_min) / M), E_min + R ^∗ ((E_max – E_min)/M)]. The probability of observing a voxel with eccentricity value e appropriate for its row is therefore 1/M. The probability p of observing all voxels which meet the criteria for an eccentricity gradient is therefore (1/M)^(M∗N). It follows similarly for a polar angle (or other sensory) gradient.

For a conservative estimate, we chose a VFM surface area of ∼220 mm², which is approximately the smallest reported size of individual-subject measurements for the V3v quarterfield (Dougherty et al., 2003; Brewer and Barton, 2014). Each voxel measures 1.875 mm × 1.875 mm × 3 mm. Assuming an equal number of voxels contribute their 1.875 mm × 1.875 mm (3.52 mm²) and 1.875 mm × 3 mm (5.625 mm²) sides to the VFM surface area, the effective surface area per voxel is 4.57 mm². We can approximate the mean VFM with a 7 × 7 matrix of 4.57 mm² units with a total surface area of 224 mm². Therefore, the probability of observing either an eccentricity or polar-angle gradient in that cortical area is (1/7)^(7∗7), or 3.89^∗ 10^-42 (Figure 1A).

Of course, that scenario entails little tolerance for error. In reality, no gradient is perfect, and it is actually the human experts’ ability to see gradients through some noise that gives them the advantage over computer-based atlas fitting. Consider the case where each voxels’ acceptable range of eccentricity values is tripled from 1/M to 3/M. The probability p of a gradient arising from noise keeping the other parameters the same becomes (3/7)^(7∗7), or 9.31 ^∗ 10^-19, which is much higher than the 1/M case, but still remote. Note that an example 3/M gradient is rough, but still identifiable (Figure 1B). We think that this should form a rough upper limit on the acceptable error. As such, that probability is what we use for observing a gradient given the null hypothesis that the gradient emerged spontaneously from random noise. Even a higher amount of “allowed error,” quintupling from 1/M to 5/M, yields a remote probability of a spurious gradient (5/7)^(7∗7), or 6.91 ^∗ 10^-8. Note that there is little resemblance between Figures 1A,C; at best, the example 5/M gradient is a noisy bifurcation of the stimulus space, and therefore too liberal an estimate of acceptable error.

At this point, five further details about the probability estimate require discussion. First, all the voxels considered above are significantly active voxels, which means that all estimated probabilities just discussed are given that some sort of pRF model fit was possible for the voxels in the first place. In other words, these voxels are systematically, reliably activated by standard visual field mapping stimuli, and it is only the interpretation of the pattern of these significantly active voxels that is addressed by this probability estimate.

Second, the probability estimate assumes that each voxel’s pRF model fit is independent of its neighbors. This assumption could be violated by the model itself, but because each voxel is evaluated independently, with no smoothing of any kind, and no motion correction, the pRF model fit of one voxel has no influence on its neighbors (Dumoulin and Wandell, 2008; Brewer and Barton, 2012b). This assumption could also be violated by the fact that we are measuring BOLD activity in each voxel. In visual cortex, the point spread function is estimated to be 1–2 voxels (3.5 mm), indicating that the raw activity of one voxel leaks somewhat to its neighbors (Engel et al., 1997). However, under the null hypothesis of our probability estimate, a group of voxels with random stimulus preferences would influence their neighbors randomly as well, which would not meaningfully change our probability estimates.

Third, we performed the calculation assuming an even distribution of pRF fits across the stimulus space, but VFMs along dorsal and ventral pathways, for example, have been shown to have clear differences in cortical magnification (e.g., Brainard, 1997; Kastner et al., 2001; Press et al., 2001; Huk et al., 2002; Dougherty et al., 2003; Brewer et al., 2005; Wandell et al., 2007; Brewer and Barton, 2012b). In such cases, the number of rows is larger than the number of evenly divided intervals, meaning that the exponential component M is now larger than the denominator of 1/M or 3/M, above. Thus, our probability estimate of a gradient arising from random noise is likely too high, and therefore more conservative.

Fourth, our estimation is based on a rectangle, and VFMs typically are trapezoidal or shaped like a pie slice. Our estimates are meant to be just that, but even if the “columns” of our model do not form a perfect rectangle, but broaden toward the periphery, the difference in probability is marginal, because most surface area lost on one end is gained on the other.

Fifth, so far we have only discussed one gradient arising in a cortical area, but two are necessary to define a VFM hemifield. The odds of two gradients arising in one hemisphere using the 3/M model for this size of VFM, are (9.31 ^∗ 10^-19)², or 8.67 ^∗ 10^-37. Thus, the probability of measuring 2 gradients using the 3/M model for a VFM with a surface area of approximately 224 mm² in each of 10 hemispheres, as we report for each of the VFMs presently measured, is (8.67 ^∗ 10^-37)¹⁰, or 8.67 ^∗ 10^-370.

As noted above, each VFM is expected to represent the contralateral hemifield and be organized such that it contains two orthogonal gradients of visual space representation: one of eccentricity, one of polar angle. The eccentricity and polar-angle gradients must be orthogonal to one another in order to create a complete representation of a contralateral hemifield of visual space. Two such hemifields, one in each hemisphere, then form a complete VFM. To measure whether two such gradients are orthogonal to one another, we identified a vector from the center of mass of the lowest eccentricity from fixation to the highest (an eccentricity vector) along a constant, iso-angle line and from the lower vertical meridian to the upper vertical meridian (a polar-angle vector) along a constant, iso-eccentricity line on the flattened cortical surface and computed the rotational offset between the two vectors (Barton et al., 2012). VFMs with orthogonal gradients (i) should have vectors offset rotationally by about 90° from one another, whereas randomly distributed gradients (ii) should have no consistent arrangement (high standard error, no meaningful average), parallel gradients should have no difference (0°) in vector offset (iii) and anti-parallel gradients should be 180° offset (iv).

The coverage of visual space in a particular VFM is what portion of visual space evokes significant responses from the voxels composing that VFM. The concentration of pRFs for a given VFM is then defined as the number of pRFs within that map that respond to each portion of visual space (Dumoulin and Wandell, 2008; Amano et al., 2009). To identify these two aspects of each VFM, we first identify the pRF coverage of each voxel within a VFM for each visual location. Across the visual field, we assign a binary value of 1 or 0 for each voxel in that VFM, where 1 denotes the visual position as being within the pRF for that voxel, and 0 denotes that location as being outside of that voxel’s pRF. These values are summed and normalized within VFMs to a value between 0 and 1, where 1 corresponds to the highest concentration of pRFs representing that visual field position and 0 to no pRF coverage at all. An image plotting visual space is then created using these normalized values for each spatial location, coded by a colormap. Values above 0 (cyan to red) indicate at least some pRF coverage at a given spatial location, with increasing values indicating more pRFs covering that location, to a maximum concentration for that particular map, at 1 (bright red). Visual field coverage plots thus provide an improved visualization of which portions of visual space are represented by a particular VFM with information about both the pRF center and the spread (coverage across visual space by the group of neurons within each voxel).

To measure surface area, the boundaries of each VFM were first identified on a 2D flattened region representing the cortical surface of an individual hemisphere, as described above. Because the process of flattening a section of the cortical sheet unavoidably distorts distance and area measurements, the 2D coordinates were first mapped back to the 3D manifold. The surface area was then measured along the 3D cortical manifold at the division between gray and white matter, which allows more reliable boundary definition than the outer surface of the gray matter or any particular cortical layer (Teo et al., 1997; Wandell et al., 2000). For extended details about the algorithm used in these measurements, see (Dougherty et al., 2003). The surface area of each VFM was measured in individual subjects and then averaged across subjects by VFM.

We also characterized each VFM across subjects in terms of the average percentage of the surface area as a function of eccentricity from fixation. The measurement of the distribution of surface area using pRF centers representing particular regions of visual space is analogous to the measurement of cortical magnification, but takes into account not only the dimension of magnification along iso-angle lines, as does cortical magnification, but also along iso-eccentricity lines (Dougherty et al., 2003; Brewer and Barton, 2012b, 2014).

In order to empirically validate the coherence threshold used in the VFM measurements, we also measured cortical responses to a baseline stimulus composed of expanding rings presented under low light – scotopic – conditions (Barton and Brewer, 2015). Scotopic conditions during scanning were created by blacking out all light sources in the scanner room and placing neutral density filters over the projector’s wave guide to achieve a luminance of 0.003 cd/m². Before the baseline scans, subjects dark-adapted for 35–40 min, and all subjects reported being unable to perceive the stimuli for rings within the central 3° of visual angle. Under scotopic conditions, the cortical regions representing the central 3° of visual angle receive little-to-no stimulation, as this luminance level is too low to activate the cone-only fovea (Hadjikhani and Tootell, 2000; Baseler et al., 2002; Dougherty et al., 2003; Duffy and Hubel, 2007; Hubel et al., 2009).

The expanding-ring stimulus comprised the same high-contrast, flickering, black and white checkerboard patterns as the moving-bar stimulus, but subtended only a maximum radius of 3° of visual angle. The checkerboard was organized as a dartboard pattern with a radial spatial frequency of 5 cycles/deg and an angular frequency of 12 cycles/2π. Each stimulus had a 45° duty cycle, spanning appropriate eccentricities in 12 steps. Seven cycles were completed in each scan, creating a 7 cycles/scan traveling wave of activity. No mean-luminance periods were inserted. Other details of the ring stimulus matched that of the moving-bar stimulus.

Subjects maintained fixation on a large central cross that spanned the diagonals from each corner of the field of view. The lines of the fixation cross were approximately 0.5° thick and were present throughout each scan. This thin, large fixation cross allows subjects to maintain fixation under scotopic conditions under which the central 3° of visual angle – the fovea – is not activated. Subjects were instructed to perform the same motion perception attentional task as for the moving-bar stimulus. As the subjects could not perceive the stimulus, they could not successfully perform this task, but it served to engage the subjects’ attention to the central 3° of their visual fields. Subjects were trained on this type of fixation and this attention task with identical stimuli under photopic conditions (luminance = 140 cd/ m²) and with other scotopic scans in which the visual stimuli spanned 7.4° and 11° of visual angle and thus were visible outside of the foveal region (Barton and Brewer, 2015).

Field-standard, visual field mapping, traveling-wave analyses were performed on the baseline stimuli using mrVista and the same functional data analysis as described above (for additional discussion, see Engel et al., 1994; Sereno et al., 1994, 1995a; DeYoe et al., 1996; Brewer et al., 2002; Dougherty et al., 2003; Brewer et al., 2005; Wandell et al., 2007; Brewer and Barton, 2012b). Our measurements show a maximum baseline noise level for coherence from these traveling wave measurements of 0.15, well below our statistical threshold of coherence (co) = 0.25 used for the moving-bar pRF analysis.

Consistent with previous work, our VFM measurements demonstrated the presence of the V3A/B cloverleaf cluster located dorsally, adjacent to V3d and/or LO-1 along the TOS (Figures 2, 3 and see Table 1 for Talairach coordinates) (Smith et al., 1998; Press et al., 2001; Brewer et al., 2005; Tyler and Wade, 2005; Wandell et al., 2005; Larsson and Heeger, 2006; Brewer and Barton, 2012b). The average coherence of our measurements of each of these two VFMs was far above our chosen coherence threshold (co ≥ 0.25) and measured baseline noise (co ≤ 0.15) (Figure 4). V3A and V3B form a radially orthogonal cluster with the foveal representation in the center and increasingly peripheral representations along the outer sections of the cluster. Because the V3A/B cluster contains only two VFMs, the visual field representations appear to curve to split a ventral peripheral eccentricity reversal, a lower vertical meridian polar angle reversal, or both with V3d and/or LO-1 (Brewer et al., 2005; Tyler and Wade, 2005; Wandell et al., 2005). V3A is positioned along the medial aspect of the TOS and shares the dorsal border of V3d (Figure 2). V3B joins V3A at the foveal representation and extends peripherally across the lateral aspect of the TOS. The exact position of V3B in relation to the dorsal border of V3d varies across subjects; V3B shares a border as described above with only V3d, with V3d and LO-1, or with only LO-1, depending on the size and location of the other VFMs in the visual hierarchy of each subject (Press et al., 2001; Larsson and Heeger, 2006). The dorsal portions of each VFM represent the upper visual quarterfield and border the posterior parietal VFMs along the IPS (Silver et al., 2005; Swisher et al., 2007; Silver and Kastner, 2009).

As illustrated in Figure 5A, the low-to-high vectors for each gradient were reliably offset by roughly 90° in both VFMs, confirming that each VFM contains orthogonal eccentricity and polar-angle gradients. We were able to clearly identify two orthogonal gradients to define both V3A and V3B in all 10 hemispheres of our five subjects, and all VFMs contained hemifield representations of the contralateral visual field (Table 2). As seen in the visual field coverage plots of Figures 6A,B, the centers and spreads of all the significantly active voxels (co ≥ 0.25) fell within the contralateral visual field with a little overlap into the ipsilateral field along the vertical meridian especially near the fovea, as expected for these regions (Baizer et al., 1991; Ejima et al., 2003).

The surface area of the full V3A/B cluster ranged across subjects from 308 mm² to 628 mm² (mean: 464 mm²; SEM: 59 mm²; Figure 7A and Table 3). This average cluster surface area is similar to that reported for the V3d quarterfield (Dougherty et al., 2003). The V3A and V3B maps were very similar in size to each other within subjects, and the average sizes across subjects and hemispheres were nearly the same (Figures 7B,D), with an average area of 232 mm² for V3A (SEM: 29 mm²) and 233 mm² for V3B (SEM: 31 mm²). There were no significant differences in surface area between hemispheres for each VFM (Figure 7E; V3A: p = 0.89; V3B: p = 0.83). Given these mean surface areas for V3A and V3B, our example probability calculation for a VFM with a surface area of 220 mm² can be used for these maps. We thus reject the null hypothesis that the two gradients in each V3A/B VFM observed in 10 hemispheres arose out of random noise.

For analysis of the measurements of pRF sizes and the distribution of the representation of visual space (i.e., % surface area distribution), we divided up the eccentricity representation in each VFM in each hemisphere of each subject into 10 regions of interest (ROIs) spanning 1° of visual angle along the eccentricity gradient from 0 to 10°, centered on every half degree. Each measurement was drawn from these 10 eccentricity-band ROIs for each subject and then averaged across hemispheres and subjects. We found that V3A and V3B exhibited increasing pRF sizes as a function of eccentricity (Figures 8A,B); this is similar to the V1-hV4 VFMs in early and mid-level visual cortex, which have generally small pRF sizes that increase more eccentric from fixation (Smith et al., 2001; Dumoulin and Wandell, 2008; Barton and Brewer, 2015). The average pRF radius for the cluster ranged from ∼2° in the measurements of the more foveal eccentricities to ∼6° in the measurements of the more peripheral eccentricities (Figure 8A). V3B had slightly larger pRF sizes (∼1–2°) than V3A for the peripheral half of the measurements (5–10° of eccentricity). Conversely, the percentage of the surface area increases more eccentric from fixation, demonstrating a larger representation of the more peripheral regions (5–10°) that is remarkably different from the foveal expansion of the V1-hV4 VMFs (Figure 9) (Dougherty et al., 2003; Ejima et al., 2003; Brewer et al., 2005; Wandell et al., 2007; Brewer and Barton, 2012a). These measurements are consistent with the expectations for expanded peripheral representations of visual space along the mid- and high-level regions of the dorsal stream (Baizer et al., 1991; Huk et al., 2002; Swisher et al., 2007; Kolster et al., 2009, 2010; Silver and Kastner, 2009).

Our fMRI measurements also revealed a new cluster of VFMs along the posterior aspect of the superior temporal sulcus (STS). This pSTS cluster contains four radially orthogonal hemifield VFMs, which we have termed pSTS-1, pSTS-2, pSTS-3, and pSTS-4, according to recent convention (Figures 10, 11) (Brewer et al., 2005; Kolster et al., 2010). The average coherence of each of these four VFMs was again clearly above our chosen conservative coherence threshold (co ≥ 0.25) and measured baseline noise (co ≤ 0.15) levels (Figure 4). The pSTS cluster tends to lie along the fundus and posterior bank of the superior portion of the STS and does not border any heretofore discovered VFM or cloverleaf cluster (Figure 10C). By convention, PSTS-1 is defined as the map with its posterior border lying in the middle of the posterior patch of lower vertical meridian representation (cyan/blue), bordering pSTS-4, and with its anterior border lying in the middle of the dorsal patch of upper vertical meridian representation (magenta/red), bordering pSTS-2. pSTS-2 is then the VFM anterior to pSTS-1 and dorsal to pSTS-3, which in turn borders pSTS-4 posteriorly. Compared to early and mid-level VFMs, the range of visual space representation (i.e., color span) was compressed, as expected for such small VFMs containing fewer voxels with relatively large pRFs; see below for further discussion. Even so, the boundary reversals between maps were clearly identifiable for all hemispheres in which we could define the pSTS cluster (9/10 hemispheres).

As illustrated in Figure 5B, the low-to-high vectors for each gradient were again reliably offset by roughly 90° in both VFMs, confirming that each VFM contains orthogonal eccentricity and polar-angle gradients. We were able to identify two orthogonal gradients to define all 4 VFMs in 9 hemispheres of our five subjects (e.g., 36 maps out of a possible 40); one subject (S5) lacked a clearly definable pSTS cluster in the left hemisphere. Out of the 36 measured maps, the majority spanned a full hemifield. For each individual VFM, 2–3 out of the 10 hemispheres had a compressed color range with a prominent representation of one quarterfield (e.g., only lower or upper visual field), but only a few voxels representing the other quarterfield (Table 2). As seen in the visual field coverage plots of Figures 6C–F and in the pRF size measurements of Figures 8A,C, all the pRFs within pSTS were close to the larger size seen in the peripheral regions in mid and early visual cortex, as expected for higher-order visual processing (Baizer et al., 1991; Ejima et al., 2003; Van Essen, 2003). The coverage plots further demonstrate the more peripheral pRF concentration in pSTS. There was still only a little overlap into the ipsilateral field along the vertical meridian especially near the fovea as measured with our stimuli; it is possible that some ipsilateral inputs also exist that were not strong enough compared to the contralateral inputs to be picked up by our measurements (Baizer et al., 1991; Ejima et al., 2003; Silver et al., 2005; Swisher et al., 2007; Silver and Kastner, 2009; Brewer and Barton, 2012b).

The surface area of the full pSTS cluster ranged across subjects from 388 mm² to 764 mm² (mean: 534 mm²; SEM: 66 mm²; Figure 7A and Table 3). This average cluster surface area is similar to what we measured for the V3A/B cluster, but note that the 4 VFMs in the pSTS cluster are then smaller than the 2 VFMs in the V3A/B cluster. The pSTS maps were very similar in size to each other within subjects, and the average sizes across subjects and hemispheres were comparable (Figures 7C,D), with an average area of 135 mm² for pSTS-1 (SEM: 24 mm²), 147 mm² for pSTS-2 (SEM: 21 mm²), 138 mm² for pSTS-3 (SEM: 12 mm²), and 113 mm² for pSTS-4 (SEM: 21 mm²). There were no significant differences in surface area between hemispheres for each VFM (Figure 7F, pSTS-1: p = 0.06; pSTS-2: p = 0.36; pSTS-3: p = 0.64; pSTS-4: p = 0.25).

For these slightly smaller pSTS VFMs of mean surface area of ∼133 mm², we can approximate the mean VFM with a 6 × 6 matrix of 4.57 mm² units with a total surface area of ∼165 mm² (Figure 1). Therefore, the probability of observing either an eccentricity or polar-angle gradient in that cortical area is now (1/6)^(6∗6), or 9.70 ^∗ 10^-29. If we again triple the acceptable range of eccentricity values from 1/M to 3/M, the probability p of a gradient arising from noise keeping the other parameters the same becomes (3/6)^(6∗6), or 1.46 ^∗ 10^-11. For this smaller-sized VFM, the odds of two gradients arising in one hemisphere using the 3/M model are (1.46 ^∗ 10^-11)², or 2.12 ^∗ 10^-22. This probability of a two-gradient map arising from noise is slightly higher than for V3A/B as expected for a smaller VFM composed of fewer voxels, but still very remote. In addition, we were able to measure complete pSTS clusters of 4 VFMs in 9 out of 10 hemispheres, as noted above (Table 2). The probability of measuring 2 gradients using the 3/M model in each of 9 hemispheres is (2.12 ^∗ 10^-22)⁹, or 8.56 ^∗ 10^-196. We thus reject the null hypothesis that the two gradients in each pSTS VFM observed in 9 hemispheres arose out of random noise.

To examine pSTS cluster pRF sizes and % surface area distributions, we again divided up the eccentricity representations into 10 eccentricity-band ROIs. We found that all 4 pSTS VFMs have pRF sizes that change little as a function of eccentricity (Figures 8A,C), and the surface area distribution is weighted heavily to the periphery, similar to the higher-order regions along the dorsal processing stream like the hMT+/TO cluster (Figures 9A,C) (Baizer et al., 1991; Brewer et al., 2002; Huk et al., 2002; Kolster et al., 2009, 2010; Brewer and Barton, 2012b). The average pRF radius for the cluster ranged from ∼4° to ∼6° across the measured eccentricity range (Figure 8A). Within the central 6°, the measurements of the individual VFMs had higher variability in pRF size than the outer range from 6 to 10° of eccentricity (Figure 8C). Note that there are no pRF centers that fall within the 0.5 eccentricity bin due to the relatively large pRF sizes within the pSTS cluster (Brewer and Barton, 2014, p. 212). In the more peripheral range, the 4 pSTS VFMs all had very similar pRF sizes of ∼4°. This increased foveal variability is not surprising, given the large shift in the % surface area to representations of the more peripheral regions (5–10°; Figures 9A,C); there were only a small number of foveal voxels within the central 6° from which to draw pRF size measurements for these VFMs. In addition, higher-order processing regions like we expect pSTS to be are often more significantly affected by alterations in attention. It is possible that the variability in pSTS foveal pRF sizes is due to different attentional or cognitive states among the subjects (Baizer et al., 1991; Silver et al., 2005; Silver and Kastner, 2009; Haak et al., 2012a); however, all subjects were successfully performing our visuospatial attentional task (Barton and Brewer, 2015). As in the V3A/B cluster, these measurements of a magnified peripheral representation are consistent with the expectations for expanded peripheral representations of visual space along the mid- and high-level regions of the dorsal stream (Baizer et al., 1991; Huk et al., 2002; Swisher et al., 2007; Kolster et al., 2009, 2010; Silver and Kastner, 2009).

If cloverleaf clusters are fundamental to the human visual system, they should not only be seen throughout the visual hierarchy as we see here in mid- and higher-level visual cortex, but should also be reliably consistent and functionally differentiable (Wandell et al., 2005, 2007; Kolster et al., 2009, 2010; Barton et al., 2012; Brewer and Barton, 2012b). To characterize the reliability of these measurements, we performed an even-odd, split-half analysis of the functional scans for each subject (Figure 12; e.g., Swisher et al., 2007). First, note the relatively strong average even-odd correlations for eccentricity and polar angle in Figure 12A. The pRF model fits the pRF center in visual space to each voxel based on a 2D Gaussian pRF with a given size about the center. The average Pearson correlation coefficients of the eccentricity and polar angle pRF center fits for the V3A/B cluster are 0.77 (p < 0.01) and 0.79 (p < 0.01), respectively, and 0.46 (p < 0.01) and 0.51 (p < 0.01), respectively, for the pSTS cluster. Next, note the very similar average coherence across VFMs in Figure 12B. BOLD responses in these VFMs are not only well above threshold, but also consistent from scan to scan. Finally, note that the average pRF sizes for V3A and V3B are also very similar between the even and odd scans (Figure 12C). pSTS has slightly higher variability in the even-odd comparison of average pRF sizes, but this is not unexpected given the inclusion of the rather variable foveal measurements observed in each of the pSTS VFMs, as described above. Thus, each split-half measurement is remarkably reliable, especially when we consider the differing anatomical locations and functional characteristics of the VFMs presently evaluated (Callinan et al., 2003; Dougherty et al., 2003; Brewer and Barton, 2012b).

To examine whether the clusters are also functionally differentiable, first note that VFMs within a cluster have very similar total surface areas (Figure 5), and each cluster’s total surface area is consistent across subjects (Table 3). In addition, each cloverleaf cluster can be functionally differentiated by its pattern of coherence measurements (Figure 4), pRF sizes (Figure 7), and distribution of % surface area as a function of eccentricity (Figure 9). Note in particular that the distributions of pRF sizes have two patterns here: either the sizes remain roughly the same size across eccentricities as in the pSTS cluster, or they increase with more peripheral eccentricities as in the V3A/B cluster. Also note that there are two patterns of surface area distributions as eccentricities increase: the distribution gradually increases (V3A/B) or sharply increases (pSTS). These distinctions indicate that VFMs within individual cloverleaf clusters are not only anatomically, but also functionally related (Brewer et al., 2005; Wandell et al., 2005, 2007; Kolster et al., 2009, 2010; Moradi and Heeger, 2009; Brewer and Barton, 2012b).