A fundamental organizing principle of sensory cortex is the topographic mapping of stimulus dimensions (Mountcastle, 1957; Kaas, 1997). For instance, visual areas contain maps of the visual field, wherein the spatial arrangement of an image is preserved such that nearby neurons represent adjacent points in the visual field (Inouye, 1909; Holmes, 1918). At a larger scale, multiple visual field maps are arranged in clusters, in which several adjacent polar angle representations share a common eccentricity representation (Wandell et al., 2005, 2007; Kolster et al., 2009). These clusters are thought to form larger, more efficient processing units by sharing computational resources and minimizing the length of axons connecting the portions of the maps with similar spatial receptive fields (Wandell et al., 2005). Furthermore, it has been suggested that clusters, rather than individual visual field maps, organize specializations in cortical function (Bartels and Zeki, 2000). To date, more than 20 visual field maps have been identified in the human brain, several of which are organized into clusters (Wandell et al., 2005, 2007; Larsson and Heeger, 2006; Wandell and Winawer, 2011; Arcaro and Kastner, 2015; Wang et al., 2015; Barton and Brewer, 2017).

Recently, using modified versions of the standard traveling wave method for mapping early visual cortex, several labs have identified representations of polar angle along the intraparietal sulcus (IPS) in posterior parietal cortex and the precentral sulcus (PCS) in frontal cortex (Sereno et al., 2001; Schluppeck et al., 2005; Silver et al., 2005; Kastner et al., 2007; Swisher et al., 2007; Jerde et al., 2012). Not surprisingly, these maps have attracted a great deal of attention given their presumed involvement in a wide range of cognitive and sensorimotor processes, including attention, working memory, and decision-making (Posner et al., 1984; Wilkins et al., 1987; Bechara et al., 1994; Manes et al., 2002; Mackey et al., 2016a, 2016b). Some of these visual maps may correspond to the human homologs of well-characterized areas in the macaque brain that are topographically organized, like the lateral intraparietal area (LIP) and the frontal eye field (FEF). Yet, such inter-species homology and how these maps contribute to different aspects of behavior and cognition remain unknown. This is likely due to our limited understanding of the basic organizing principles of these maps. Further challenges are posed because the maps in parietal and especially frontal cortex have less reliable stimulus-evoked BOLD signals compared to those in visual cortex, are more coarsely organized, and show less consistent topography across subjects. In some cases, it is uncertain as to whether a region merely has a contralateral bias as opposed to containing an actual topographic map (Hagler and Sereno, 2006; Kastner et al., 2007; Silver and Kastner, 2009; Jerde et al., 2012; Patel et al., 2014). Here, we take a step back from trying to understand the functions and instead systematically characterize the basic organizing principles of these putative visual field maps in frontoparietal cortex.

Establishing the organization of maps in parietal and frontal cortex will have several major impacts. First, the identification and better characterization of which maps are human homologs of macaque areas will facilitate better translation of non-human primate models of human cognition to humans. Second, understanding the topography of parietal and frontal maps will enable researchers to aggregate results at the level of individual maps or even small areas within maps, rather than at the level of large regions of cortex, similar to the successes in delineating maps in occipital cortex in animals (Essen and Zeki, 1978; Desimone and Ungerleider, 1986; Gattass et al., 2005) and humans (Sereno et al., 2001; Engel et al., 1997). Indeed, the fundamental reason the visual neurosciences have outpaced the cognitive neurosciences is the ability to reliably define and to study the function of the same areas across individuals and across labs. Such convention facilitates comparisons between studies of different computations and representations across different subject populations and methods of measurement. This effectively creates a worldwide, across-time, collaboration between all labs. As such, the organization of visual field maps in early visual cortex has been well characterized, to the point of enabling the development of detailed templates of the visual field for V1–V3 (Dougherty et al., 2003; Benson et al., 2012, 2014). By contrast, much less is known about the organization of visual field maps in frontoparietal cortex, and thus presents a critical roadblock for understanding their functions.

To these ends, we focus on characterizing the organization and retinotopic properties of putative visual field maps in frontoparietal cortex. We estimated population receptive field (pRF) parameters in topographic areas in early visual, parietal, and frontal cortices. The pRF method not only estimates a voxel’s polar angle and eccentricity preference, but also its receptive field (RF) size, and has been shown to map topography more accurately than conventional traveling wave methods (Dumoulin and Wandell, 2008). However, two important challenges exist when attempting to identify visual field maps in frontoparietal cortex. First, passive viewing of high-contrast spatial patterns elicits weak and non-systematic responses in frontoparietal cortex (Silver et al., 2005; Saygin and Sereno, 2008). Therefore, identifying visual field maps in higher order frontoparietal cortex requires more cognitively demanding stimulation that taxes attention or memory (Silver et al., 2005; Jerde et al., 2012). Second, the large RF sizes expected in frontoparietal cortex make it difficult for linear RF models to accurately characterize response properties to stimuli that vary in size. To overcome these challenges, we developed a novel, attention-demanding task specifically designed to elicit robust, systematic responses in frontoparietal cortex (Figure 1A). Moreover, we estimated pRFs with a model that accounts for nonlinear responses to stimuli of varying size (Kay et al., 2013; Winawer et al., 2013). Nonlinear spatial summation is more pronounced in extrastriate maps than in V1 and is likely to be even more so in frontoparietal cortices.

Figure 1

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During a single functional neuroimaging session, observers swept their focus of attention across the visual field, while maintaining central fixation, in order to perform a difficult motion discrimination task. The task was designed to tax attentional resources that are presumably controlled by activity in topographic maps in frontoparietal cortex (Figure 1A, Video 1). A bar aperture swept across the visual field in discrete steps, vertically or horizontally traveling in four possible directions: left to right, right to left, top to bottom, bottom to top. The bar was comprised of three rectangular patches, each of which contained a random dot kinematogram (RDK) moving in a particular direction. The central patch contained 100% coherent motion and the two flanking patches contained low coherence motion. Observers pressed a button to indicate which of the two flanking patches (above or below for vertical bars, left or right for horizontal bars) matched the RDK direction of the middle patch. The motion coherence of the flanking patches was staircased to ensure the task remained difficult throughout the duration of the scanning session (75% accuracy).

Video 1

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We used a nonlinear pRF model to predict the BOLD response of each individual voxel to the visual stimulus (Figure 1B). Each model is specified by the center (x,y) and size (σ, or standard deviation of an isotropic 2D Gaussian) of the pRF, and uses a power-law exponent (n) to account for sub-additive spatial summation (Equations 1 and 2). The non-linearity interacts with the Gaussian standard deviation to make an effective pRF size of ${\displaystyle \sigma /\sqrt{n}}$ (Kay et al., 2013; Winawer et al., 2013). We excluded voxels from further analysis if less than 10% of the variance in the time series was explained by the pRF model (Equation 3). We also excluded voxels with pRF centers outside of the limits of our visual display (12 degrees of visual angle). The pRF fitting strategy proposed by Dumoulin and Wandell (2008) was a coarse-to-fine approach, in which the initial coarse fit was solved on time series that were spatially blurred (approximating a Gaussian kernel of 5 mm width at half height) and temporally decimated (2x), and that used gridded parameters rather than searching for the best fit using nonlinear search optimization algorithms; the second stage then used the solution of the grid fit as a seed for a search, and applied this search to the unblurred (in space and time) time series. Here, we used only the first stage (the grid fit), applied to the smoothed and temporally decimated time series. The grid fit is more robust to noise (although also less accurate when noise is low). Our primary goal was to map frontoparietal cortex, where pRFs were expected to be larger, and hence the stimulus relevant signals were expected to be dominated by lower temporal frequencies compared to those of early visual cortex, where pRFs are much smaller. The temporal decimation in the grid fit reduces sensitivity to high temporal frequency noise. Furthermore, in frontoparietal cortex, stimulus-related signals were expected to be less reliable than those in the visual cortex; as a result, the spatial blurring in the grid fit was beneficial. Subsequently, we performed the second stage (search fit) to ensure that our results were not an artifact of artificial structure imposed by the grid fit due to interpolating voxels. We found no discernible differences between the grid and search fits (See Model reliability and comparisons below). The grid included the same set of possible values in the solution as those described by Dumoulin and Wandell (2008), with the addition of the power law exponent, which was gridded to be 0.25, 0.5, 0.75, or 1. A value of 1 indicates a linear fit; values smaller than 1 indicate increasingly more sub-additive spatial summation.

We identified retinotopic maps in early dorsal visual areas (V1, V2, V3, V3A&B) as well as at least four maps along the intraparietal sulcus (IPS0, IPS1, IPS2, IPS3) and two regions with spatial tuning along the precentral sulcus in frontal cortex in each hemisphere of all subjects. The superior portion of the precentral sulcus region contained two distinct visual field maps that we refer to as sPCS1 and sPCS2. Example model fits for voxels in different visual field maps are shown in Figure 1C. Although we were able to observe additional parietal maps in some subjects, we restricted further analysis to maps consistently observed in both hemispheres of every subject. All areas are described in further detail below.

Visual cortex

As an important control, our methods revealed the functional organization and pRF properties typically observed in early visual cortex. Polar angle and eccentricity representations revealed the expected patterns in V1, V2d, V3d, and V3A&B (Figure 2A and B; Figure 2—figure supplement 1). The progression of these areas begins medially from the occipital pole in the calcarine sulcus with V1, and extends dorsally and laterally along the surface of the cortex. V1 contains a continuous angular representation of the contralateral hemifield, beginning at the upper vertical meridian (UVM) on the lower bank of the calcarine sulcus, and progressing to the lower vertical meridian (LVM) along the inferior-to-superior direction. V2 sits adjacent to the LVM border of V1, and begins a reversal of polar angles representing half of the contralateral hemifield and progressing to the horizontal meridian (HM). V3 sits adjacent to the HM border of V2, beginning another angle reversal back towards the LVM, and also represents half of the contralateral hemifield. Finally, V3A begins along the border of V3 in the periphery (but not fovea), and contains a full and continuous angular representation of the contralateral hemifield from the LVM to the UVM. V3B is adjacent to V3A, divided by a shared foveal representation, as reported previously (Press et al., 2001; Wandell et al., 2005).

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Together, these maps form two distinct visual field map clusters. A cluster is comprised of a group of angle representations that all share a confluent fovea (Wandell et al., 2005; Kolster et al., 2009). Within a cluster, the boundaries of adjacent angle representations can be defined by reversals in polar angle progression or eccentricity. For example, the boundary between V1 and V2 is identified by a polar angle reversal at the LVM, as described above. V1, V2, and V3 share a common foveal representation centered near the occipital pole that extends towards the collateral sulcus. V3A and V3B comprise a second cluster because they share another foveal representation, anterior to and distinct from the foveal representation shared by V1, V2, and V3. They are divided by an eccentricity reversal rather than by a polar angle reversal.

Moving up the hierarchy of early visual cortex, from V1 to V3A&B, pRF parameters begin to differ systematically. For example, pRF sizes at a given eccentricity generally increased across visual field maps, and within each visual field map in visual cortex, pRF size increased monotonically with eccentricity (Figure 2C). Consistent with previous studies investigating spatial summation in pRFs (Kay et al., 2013), we found that in extrastriate maps, the pRF models show more sub-additive spatial summation, indicated by a smaller power law exponent. The fraction of voxels with the minimal pRF exponent allowed by our grid search (0.25) was least in V1 (33%), and substantially higher in extrastriate areas (68% in V2; 80% in V3; 77% in V3A&B).

Parietal cortex

We found clear patterns of systematic organization in eccentricity and polar angle representation in the intraparietal sulcus (Figure 3; Figure 3—figure supplement 1). Beginning with IPS0 and progressing through IPS3, each map contains a full representation of the contralateral hemifield, while the polar angle reversals demarcate the boundaries of each individual map. Additionally, each successive map lies anterior to the visual field map before it. Starting with the most posterior map, IPS0 lies at the intersection of the parietal-occipital sulcus and the intraparietal sulcus, adjacent to the UVM representation of V3A&B. The angular representation systematically progresses from the UVM to the LVM, where another angle reversal takes place, creating the posterior border of IPS1. The angular gradient of IPS1 sweeps from the LVM back towards the UVM, where it borders IPS2. IPS2 then contains an angular progression from the UVM to the LVM, where it borders IPS3. IPS3 then contains an angular progression from the LVM to the UVM.

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Using these novel methods, we discovered that maps along the IPS are organized into two clusters of visual maps. IPS0 and IPS1 share a confluent fovea, while IPS2 and IPS3 share another distinct foveal representation (Figure 3). Notably, we find that the direction of the eccentricity gradient shared by IPS0 and IPS1, as well as that shared by IPS2 and IPS3 is the same. In both clusters, there is a mediolateral representation of eccentricity, where the foveal region is found near the fundus of the intraparietal sulcus, and then parafoveal-to-peripheral representations progress medially towards the medial wall (Figure 3—figure supplement 1). However, unlike maps in early visual cortex, parietal visual field maps did not allow us to measure pRF sizes with sufficient accuracy. Estimates of pRF size for nearly all voxels in parietal visual field maps were ~12 degrees, even for voxels with pRF centers at the fovea. As 12 degrees is both the maximum stimulus extent in our experiment and the upper boundary of our grid fit, it is likely that these pRF size estimates are a floor on the true size, rather than an accurate measure of the pRF size of voxels in this region. However, these measurements do indicate that the sizes of pRFs in parietal cortex are large, and probably larger than 12 degrees.

Maps in parietal cortex, like extrastriate maps in visual areas, showed a systematic sub-additivity in spatial summation. The vast majority of voxels were best fit by a pRF model with the minimal pRF exponent allowed by our grid (IPS0: 73%; IPS1: 75%; IPS2: 81%; IPS3: 89%). These results are comparable to the low exponent found in measurements of ventral occipitotemporal face-selective regions (0.20, 0.16, 0.23 in three face-selective ROIs) (Kay et al., 2015).

Frontal cortex

We also discovered that visual field maps in frontal cortex are organized by polar angle as well as by eccentricity. Although polar angle representations have been described before (Kastner et al., 2007; Saygin and Sereno, 2008; Jerde et al., 2012), representations of eccentricity have remained undiscovered until now. Two regions of frontal cortex along the PCS exhibited spatial tuning: one in the superior portion (sPCS) and another in the inferior portion (iPCS). Each region contains a gradient of eccentricity with a central foveal representation that radiates towards the periphery. In the sPCS, the fovea is represented in the fundus of PCS where it intersects the superior frontal sulcus. This organization was consistent across both hemispheres in all subjects (Figure 4). The discovery of the foveal representation in a location common across subjects allowed us to separate the region into two visual field maps, identifiable in each subject. We refer to these new maps as sPCS1 and sPCS2, consistent with naming visual field maps according to their anatomical location (Larsson and Heeger, 2006; Arcaro et al., 2009). Both sPCS1 and sPCS2 contain a full and continuous representation of the contralateral hemifield (Figure 5; Figure 5—figure supplement 1). The superior border of sPCS1 begins at the LVM and continues to the UVM, where an angle reversal occurs, signaling the border of sPCS2. sPCS2 then contains an angular progression from the UVM back to the LVM. The inferior portion of the PCS (iPCS) also contained spatial representations and was distinct from the sPCS cluster (Figure 5; Figure 5—figure supplement 2). The foveal representation in the iPCS is located at the junction of the PCS and the inferior frontal sulcus. Although the topography in the iPCS region was not sufficiently regular across subjects to propose a generalized map schema, the eccentricity representation was regular in that peripheral representations typically surrounded a foveal representation. Further, while the map organization was less clear than the sPCS maps, both in terms of consistency across subjects and structure within a subject, the visual field coverage nonetheless showed a systematic representation of the contralateral visual field, similar to sPCS1 and sPCS2, which we return to in the next section (Visual field coverage density and laterality). Moreover, the iPCS maps were as accurate as the sPCS maps in terms of cross-validated prediction error and were also as lateralized, as we describe below (Model reliability and comparison, Visual field coverage laterality and density). These results indicate that the iPCS map, like the sPCS maps, contains a clear representation of spatial information.

Figure 4

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As was the case in parietal cortex, in frontal cortex, estimates of pRF size were large and pRF exponents small for nearly all voxels. Size estimates were limited by the field of view of our display and the analysis method. Most pRFs in frontal cortex had a size estimate at the upper bound of our analysis (12 deg) and an exponent at the lower bound (0.25; iPCS: 78%; sPCS1: 82%; sPCS2: 75%). As discussed in the next two sections, the large pRF size does not indicate a failure to estimate spatial tuning, as indicated by the cross-validated model fits and the laterality indices. Nonetheless, future studies with larger displays are probably needed to estimate pRF size in these regions accurately.

Visual field coverage laterality and density

A pRF model summarizes the sensitivity of a single cortical site (for example, a voxel) to positions in the visual field. By combining the pRFs across sites within a region of interest, one can visualize the field of view of the region of interest, also called the visual field coverage (Amano et al., 2009; Winawer et al., 2010; Wandell and Winawer, 2015). The visual field coverage is typically computed as the envelope of the pRFs within an ROI. Here, we took the mean of the pRFs rather than the envelope, thereby scaling the visual field coverage by the density of pRFs at any particular location in the visual field (cortical magnification), which we refer to as the coverage density. In the V1-V3 maps, the coverage density plots show a nearly total contralateral bias, as well as bias toward the fovea over the periphery (Figure 6A). As we only estimated pRF models in the dorsal visual maps of V2 and V3, coverage was limited to the lower quadrant of the contralateral visual field as expected. The contralateral and foveal biases in early visual cortex reflect three aspects of the pRF models: (1) the centers are in the contralateral visual field, (2) the pRF sizes are relatively small, and (3) the largest number of pRF centers are close to the fovea. In V3A&B, the coverage density is wider and extends slightly into the ipsilateral visual field, as the result of larger pRF sizes. This observation was used previously to distinguish area MST from area MT in the human visual system (Huk et al., 2002; Amano et al., 2009). In parietal cortex (IPS0-IPS3) and frontal cortex (iPCS and sPCS1&2), the coverage is also centered in the contralateral hemifield, but increasingly extends into the ipsilateral field, again reflecting the larger pRF sizes. Similar to visual cortex, the coverage density is highest near the fovea, indicating a qualitative similarity in cortical magnification between frontoparietal cortex and visual cortex. The visual field coverage is evident at the individual level as well as the group level, and is supported by viewing the pRF centers as well as the coverage density (Figure 6B).

Figure 6

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We quantified the degree to which visual areas have lateralized pRFs using a laterality index (Equation 4). In agreement with the coverage density plots, the laterality index shows that early visual cortex is highly lateralized, whereas successive maps from parietal to frontal cortex become less and less lateralized (Figure 6C). Additionally, there is larger subject-to-subject variability in the lateralization index in parietal and frontal areas compared to visual cortex. In summary, although maps in frontal and parietal cortex have very large pRFs compared to those in visual cortex, the spatial tuning is sufficiently reliable to show clear lateralization, complete hemifield visual coverage, and maps that are organized in an orderly topographic manner.

Model reliability and comparison

Reliably mapping topography in frontal and parietal cortex depends on nonlinear models of pRFs. We compared performance of the nonlinear pRF model to two other models: a linear pRF model (Dumoulin and Wandell, 2008) and a simple contralateralized response model. Comparisons with the linear model allowed us to see how much, if any, improvement in accuracy was gained by allowing for sub-additive spatial summation. Comparing with the lateralized response model allowed us to investigate whether our results indicate systematically organized maps as opposed to noisy representations of lateralized responses, with no spatial tuning other than a preference for the contralateral hemifield. The lateralized model predicted a uniform response amplitude whenever any portion of the stimulus was in the contralateral visual field, and zero response otherwise.

In order to compare model performance, we used a leave-one-out cross-validation procedure, which provides no advantage to models with additional parameters. The models were solved using two of the three stimulus types as training data (narrow, intermediate, or wide bars), and the remaining stimulus type as test data, iterated by leaving out each of the three stimulus types. We defined accuracy as the variance explained for the left-out data, averaged across the three cross-validation iterations. The ordinal ranking of the three models was the same in all 11 areas tested: the nonlinear model explained the greatest amount of variance, followed by the linear model, and then the lateralized response model (Figure 6D). The quantitative advantage of the nonlinear model over the linear model was smallest in V1, and larger in other maps. The improvement in performance from the nonlinear over the linear model demonstrates the benefits of including a parameter to estimate sub-additive spatial summation. This is particularly true for maps in frontal and parietal cortex, where pRFs are large and response nonlinearity estimations were at our measurement boundary. The contralateral model was much worse than either of the Gaussian models (linear or nonlinear) in visual cortex, a result of the relatively small pRFs in those areas, yet even in parietal and frontal areas, where pRFs were much larger, the contralateral model was worse than the non-linear pRF model in every area tested. This result strengthens the claim that the observed responses are spatially tuned, and not merely due to a non-specific preference for contralateral stimuli.

In order to investigate the reliability of newly discovered visual field map clusters in precentral sulcus and intraparietal sulcus, we performed a test-retest analysis on two subjects. Importantly, we found that visual field map structure (that is, polar angle and eccentricity gradients) were consistent across sessions in both subjects (Figure 7). Both the location of the fovea along the eccentricity gradient and the map borders between sPCS1 and sPCS2 were remarkably consistent across sessions. Similarly, along the intraparietal sulcus, the foveal location and angle boundaries were the same across the two sessions in both subjects. Therefore, the structure of visual field map clusters in frontoparietal cortex is stable across scanning sessions.

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Although pRF accuracy differs considerably between nonlinear and linear models, it is not dependent on using the grid or search fit. In the traditional pRF fitting procedure outlined in Dumoulin and Wandell (2008), pRF parameters are determined by a two-stage coarse-to-fine fitting procedure in which a grid fit is performed to generate a seed for the search fit. To investigate whether our use of the grid fit instead of the full two-stage process impacted our results, we compared our results to results from the two-stage fitting procedure. Using the same cross-validation procedure outlined above to compare nonlinear and linear models, we compared nonlinear model solutions between the grid fit and search fit. The two models—grid fit and search fit—solved on the training data both made predictions for the identical, left-out, unsmoothed test data. The grid fit performed numerically, but not statistically, better than the search fit in every ROI (Figure 7—figure supplement 1). Additionally, there is little to no difference in visual field map structure, polar angle gradients, or eccentricity gradients between the grid fit and search fit.

Together, these observations, coupled with our newly discovered systematic organization of frontal and parietal maps, demonstrate the existence of topographically organized visual field maps in frontoparietal cortex. Moreover, the facts that the pRF model solutions cross-validate well and are stable over time strongly indicate that the visual field maps are reliable and that our methods for measuring and modeling them are accurate.

Positioning of frontoparietal visual topographic maps in the context of other mapping schemes

Next, we wondered how the locations of these visual maps might correspond to previous anatomical designations of the lateral frontal cortex and posterior parietal cortex. To address this, we transformed and spatially aligned the maximum probability map of visual topography (PMVT; Wang et al., 2015) and the multi-modal parcellation of brain areas (MMP; Glasser et al., 2016) to each subject’s native space. We were then able to compare the overlap of each subject’s frontal and parietal topographic areas with these maps. Figure 8 depicts the results of the overlap. Our IPS0-IPS3 maps tend to overlap with maps from both of these sources. However, the correspondence between specific areas is systematic neither across hemispheres nor across subjects. For instance, IPS3 from PMVT has some overlap with subject 2’s left hemisphere IPS3, but not with any of the other subjects’ hemispheres. Similarly, ‘LIPd’ and ‘LIPv’ from the MMP show little correspondence to our retinotopically defined IPS visual maps. In the lateral frontal cortex, we see better correspondence between our sPCS2 maps and the ‘FEF’ areas designated in the PMVT and MMP maps. However, this correspondence is better in the left hemisphere than in the right for some reason, and it often includes sPCS1 and misses large portions of sPCS2. MMP areas 6a and 6d typically encompass most of our sPCS1, which mostly straddles these two areas, especially in the left hemisphere.

Figure 8

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Using novel procedures, we precisely characterized the topographic organization of visual field maps in human frontoparietal cortex, including four visual field maps along the IPS and two spatially tuned regions along the PCS. Each of these maps contains a representation of the full range of polar angles in the contralateral visual field; they are topographically, not simply contralaterally, organized. By combining pRFs across voxels within visual maps, we demonstrate that these maps tile the complete contralateral hemifield in an orderly manner. As expected, the pRF sizes in frontoparietal cortex are larger than those in early visual cortex. We also demonstrate previously unreported representations of eccentricity along the precentral sulcus, and replicate previous findings of eccentricity gradients along all IPS (Swisher et al., 2007). Furthermore, we show that a spatially tuned region of the superior precentral sulcus is organized into at least two distinct visual field maps (referred to here as sPCS1 and sPCS2), each representing the entire contralateral visual field in an orderly manner. Interestingly, the visual maps in both parietal and frontal cortex are organized into clusters of polar angle maps sharing the dimension of eccentricity, similar to visual cortex (Wandell et al., 2005). Two maps in frontal cortex and two pairs of maps in parietal cortex form clusters of polar angle gradients that share a foveal to peripheral representation. Together, these data clearly describe the topographic structure of the visual maps in human frontoparietal cortices.

Following standard practices of reproducible research, the data (Mackey et al., 2017) and software (Winawer et al., 2017) are publicly available.

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Author details

1. Wayne E Mackey

   Center for Neural Science, New York University, New York, United States

   Contribution

   WEM, Conceptualization, Data curation, Formal analysis, Validation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0002-1577-9235

2. Jonathan Winawer

   1. Center for Neural Science, New York University, New York, United States
   2. Department of Psychology, New York University, New York, United States

   Contribution

   JW, Conceptualization, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0001-7475-5586

3. Clayton E Curtis

   1. Center for Neural Science, New York University, New York, United States
   2. Department of Psychology, New York University, New York, United States

   Contribution

   CEC, Conceptualization, Data curation, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   clayton.curtis@nyu.edu

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0003-0702-1499

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