Topographic organization in the brain: Searching for general principles

Abstract

The neurons comprising many cortical areas have long been known to be arranged topographically such that nearby neurons have receptive fields at nearby locations in the world. Although this type of organization may be universal in primary sensory and motor cortex, in the present review we demonstrate that associative cortical areas may not represent the external world in a complete and continuous fashion. After reviewing evidence for novel principles of topographic organization in macaque lateral intraparietal area – one of the most-studied associative areas in the parietal cortex – we explore the implications of these new principles for brain function.

Introduction

In many parts of the mammalian brain spatially adjacent stimuli on sensory receptor surfaces are represented in adjacent positions in cortex, a pattern known as topographic organization. Topographic organization provides invaluable information about brain function and structure. For example, some of the earliest functional characterizations of human primary visual cortex (V1) were based on correlations between visual field deficits and focal lesions in V1 [1–3]. Although crude by today’s standards, these early clinical observations nevertheless helped to confirm some basic facts about V1. First, V1 organization reproduces the spatial organization of the retina (known as retinotopic organization) and, by extension, the visual field (known as visuotopic organization). Second, this part of cortex is clearly involved in visual processing. More recently, the presence of topographic organization has been used to delineate boundaries between cortical areas, with V1 again providing a paradigmatic example. V1 was originally defined by the prominent stripe of myelin in its layer IV, known as the stria of Gennari, which marks the massive input from the lateral geniculate nucleus (LGN) [4,5]. Subsequent neurophysiological studies revealed that this prominent anatomical feature matches the spatial extent of the retinotopic map, reinforcing the use of retinotopy to delineate cortical areas [6]. This matching of retinotopic maps and anatomical boundaries extends to other visual areas [7–9], and the association that the boundaries of topographic maps correspond to those derived from anatomy has also been noted in other sensory and motor areas [10–12].

These observations have helped to establish two fundamental principles about the relationships between topographic organization, anatomical structure, and function in the brain. The first principle is that topographic maps represent their relevant sensory or motor dimensions continuously and completely. The second principle is that topographic and anatomical boundaries align with one another. These principles together form what we term, for simplicity, the standard model of topographic organization (see also [9,13]).

Topography in associative cortex?

While usually not stated explicitly, these basic principles operate as powerful heuristics for understanding brain organization and function. Recently, these principles have guided investigations in both human and non-human primates into the organization of higher-order cortical areas in frontoparietal cortex [14–18]. For convenience, we will use the term “associative cortex” for these areas, although they are likely involved in a much broader range of functional capacities than mere “association”, including transforming sensory information into motor plans [19,20]. Closer scrutiny reveals that these principles may not hold in these areas. In this review, we explore the extent to which these organizational principles generalize (or fail to generalize) beyond sensory and motor cortex to other associative areas of the brain including the parietal cortex by examining the topographic organization of the macaque lateral intraparietal area (LIP), a well-established associative “hub” in the visual processing network that has been extensively studied using anatomical, electrophysiological, and neuroimaging methods [21] (for related discussion, see [22]). We discuss the implications of findings in LIP for understanding the organization and function of other associative cortical areas.

The standard model of topographic organization

The principles outlined

The first principle of the standard model—that topographic maps are largely continuous and complete—can be seen throughout the early visual sensory areas (Figure 1). For example, the cells in V1, which have individual receptive fields each of which covers a relatively small portion of the visual field, are arranged such that cells with adjacent receptive fields occupy adjacent positions along the cortical sheet, thus representing the visual field in a continuous fashion [23]. This locally continuous representation may be interrupted, for example, when only the contralateral half or upper/lower portion of the visual field is mapped (common in early visual and somatotopic areas). A complete representation of visual space only emerges when these partial maps are combined across hemispheres or different sensory areas.

Figure 1.

Retinotopic organization of macaque visual cortex from [54]. A) The legend demonstrates the organization of the visual field in polar coordinates. The dotted lines delineate eccentricity contours with the dark triangles marking the visual periphery. The polar angle coordinates are bounded by meridians that are represented by the dark squares (horizontal meridian), + symbols (upper field vertical meridian), and − symbols (lower field vertical meridian). The eccentricity coordinates are bounded by the triangles, and smaller eccentricities are represented by the dashed lines. B) Flattened schematic representation of visual cortical areas, with simulated coordinates from A) mapped onto each visual area. Note that the represented visual field covers the entirety of each of the visual areas, and that all portions of each visual hemifield are represented in each visual area, even if the area (such as V2) is separated into discontinuous parts.

The second principle of the standard model is that one map completely fills each cortical area, so that topographic map boundaries coincide with areal boundaries. This principle is based on repeated observations in multiple sensory and motor cortical areas that topographic boundaries closely correspond to boundaries defined by anatomical criteria (including cytoarchitecture, myeloarchitecture, and connectivity patterns) and functional criteria such as tuning properties [13,21,24,25]. A logical consequence of this principle is that any individual anatomically- or functionally-defined area will contain no more than a single representation of each point in the visual field or other sensory or motor parameter, and by extension, no more than one distinct topographic map of the same portion of the relevant parameter space. This correspondence principle plays an especially important role in human brain mapping studies, where it is difficult to assess the boundaries between cortical areas in humans using anatomical methods due to their invasive nature. Consequently, establishing topography in the intact human brain using blood-oxygen level dependent functional magnetic resonance imaging (BOLD-fMRI) and other neuroimaging approaches has become the dominant means by which areal boundaries are identified in humans, and often serves as a proxy for these invasive methods [9,14,26–37].

Do these principles apply to associative areas?

It is important to recognize that the standard model is based primarily on data from early sensory areas obtained from non-human species such as the macaque. However, topographic organization of associative areas in macaques may be more complex, with evidence of areas only partially topographically organized (e.g., an eccentricity but no polar angle map has been reported in FEF [38,39]), or with very coarse topography that is inconsistent across studies (e.g., LIP [40,41]). Area LIP is ideal for assessing whether the standard primate model of visual topography can be applied to higher-order areas. Its anatomy and connectivity are well understood (see Box 1). The functional role of LIP has also been intensely investigated (see Box 2). Notably, the anatomically-defined boundaries of LIP do not always appear to be well aligned with boundaries delimited by functional role. For example, numerous single unit recording studies characterize LIP based on a finding of memory activity during a delayed saccade task (e.g., [19,42–45]). These studies consistently report cells extending 3–6 mm along the lateral bank of the IPS. Yet anatomical LIP extends for ~20 mm along this bank [46]. One might therefore look at topography to clarify the functional organization of LIP, and better understand how it relates to underlying anatomy and connectivity. Two single-unit studies previously reported coarse topography in LIP [40,41], and recently there have been two fMRI and one deoxyglucose study also reporting topographic organization but with different features [47–49]. By looking carefully at the evidence for topography that has emerged from these studies and comparing it to the known anatomy and connectivity of LIP, we now report that the standard model of topographic organization (developed largely based on early sensory areas) stands in important need of revision in order to apply to higher-order cortical areas.

Box 1: Anatomy of LIP.

Area LIP is located on the lateral bank of the intraparietal sulcus (IPS) in the parietal cortex. LIP extends from just below the shoulder to the fundus of the IPS, and stretches posteriorly/caudally nearly to the intersection of the parietal-occipital sulcus (POS) and anteriorly/rostrally most of the length of the IPS to its border with the anterior intraparietal area (AIP). It can be subdivided into two anatomically distinct areas, LIPv and LIPd, with the border between the two running almost parallel to the IPS [46,86] (Figure 2A–C; but see [87] and [49]). LIPv can be distinguished from LIPd by its increased density of myelination as well as architectonic differences in a number of its cortical layers ([46,84,86,88], Figure 2D). Connectivity studies indicate that LIP gets much of its input from extrastriate visual areas (including V4 and MT) [63,64,89–91]. It is also reciprocally connected to cortical and subcortical structures involved in the control of eye-movements and attention, including the frontal eye fields (FEF) and Brodmann area 46, with anterior and posterior LIP being reciprocally connected to FEF ventral/lateral and dorsal/medial, respectively [21,64,89,90], and subcortically to the superior colliculus, caudate, and the pulvinar nucleus of the thalamus [90,92,93].

Box 2: Function(s) of LIP.

Early electrophysiological studies of LIP revealed neurons involved in both oculomotor and attentional control [94,95]. The definition of LIP used in most recording studies is a region of neurons on the lateral bank of the IPS with sustained responses to visual stimuli during a remembered saccade task [96]. Functionally defined LIP neurons respond to both visual stimuli and saccadic eye movements, and have medium to large visual receptive fields (5°–30° diameter) mostly distributed in the contralateral visual hemifield [40,50]. However, LIP neurons are not just visually driven. They also demonstrate sustained activity during fixation in an otherwise dark room, provided that subjects are either covertly attending to the receptive field of the neuron or planning an eye movement into the receptive field [94,96]. Lesions to this area produce corresponding deficits in both attention and oculomotor planning [69,97–99]. Controversy persists about the functional role of LIP. Prominent proposals include the idea that it instantiates a “salience map”, according to which LIP neurons represent locations of interest for both attentional control and the planning of eye movements [66]. Others have suggested that LIP subserves oculomotor planning [100], object categorization [101], integrating sensory evidence for making decisions [102], or representing the reward value associated with making a movement decision [103].

Given the uncertainty surrounding LIP function, one interesting yet neglected possibility is that these different functional hypotheses are not mutually exclusive. The above-listed studies implicating LIP in a number of functions often record from neurons with oculomotor delay activity, implying that many of these functions are co-localized in the same neurons [101,102,104]. However, a number of recent studies provide evidence that different populations of LIP neurons may be involved in the control of attention and eye-movements [68,69,105]. A major challenge in assessing these different possibilities arises from the fact that recording locations across these single-unit studies have not been plotted into a common frame. Consequently, it remains difficult to know whether different functions involved the same set of neurons, intermingled but differing neurons, or neurons clustered by function.

Topographic organization of LIP

Current Evidence from single-unit and neuroimaging studies

The topographic organization of LIP has been explicitly targeted in a number of investigations over the past several decades. Using single-unit recordings, Blatt et al. [41] and Ben Hamed et al. [40] each found relatively weak evidence for coarse retinotopic maps in LIP. However, the patterns of topography described in the two studies appear to show no correspondence. Moreover, several hundred single-unit recording studies performed in LIP, some involving hundreds of individual neurons and many focused on their spatial receptive field properties (e.g., [50,51]), have implicitly tested for topography and almost none report even a trend toward global topographic organization (see [52] for one possible exception). From these results, the consensus view among neurophysiologists has been that monkey LIP does not show anything similar to the topography found in primary visual cortex or other extrastriate visual areas (personal communications, Goldberg, Newsome, Crawford, Snyder).

Recently, however, neuroimaging studies have reported evidence for topography [47–49]. Interestingly, this more recent evidence does not strictly follow the standard model of topographic organization that has been observed in sensory and motor areas. We compare results across five recent studies and review these deviations from the standard model below.

Aligning data for cross-study comparison

As outlined above, the first principle of topographic organization holds that topographically-organized brain areas contain largely continuous maps of the relevant sensory modality. Based on this principle, we might therefore expect LIP to contain an orderly and continuous map of the contralateral hemifield with eccentricity and polar angle represented along orthogonal axes. To explore this possibility, we first projected data from all of the studies into a common reference frame (Figure 3). To accomplish this we projected the data directly to the F99 atlas or approximated its projection based on anatomical features such as the IPS fundus and shoulder (see Figure 3 caption for more details). As a result, the accuracy of the matches varies from extremely precise to approximate. Figure 3 already reveals several surprising aspects of the topographic organization of LIP.

Figure 3.

Topographic organization of LIP from five studies. Data transferred to flattened segment of F99 macaque atlas, with LIPv and LIPd borders from [46]. For Patel et al. the data were directly projected from the F6 atlas used in the study to the F99 surface. In the two other imaging studies (Figures 3C–E), the data alignment was approximated by matching anatomical markers such as the fundus of the IPS with the F99 surface. In the single-unit recording studies (Figures 3A and B), alignment was achieved by matching the illustrated coronal sections to the coronal sections of the F99 macaque atlas, and used these aligned slices to anchor the projections to the F99 surface. Because of potential scale differences between the two species (and between fixed versus in vivo brains) we relied more heavily on anatomical features than stereotaxic coordinates. Primary colors represent stimulation in the upper (red) or lower (blue) visual fields or at the horizontal meridian (green). Light blue represents stimulation at fixation or at the fovea, orange represents parafovea (<7° eccentricity), lighter polar angle colors 7°–15° eccentricity, and darker colors >15° eccentricity.

Polar-angle maps

All five topographic mapping studies report the presence of a polar angle map in posterior LIPv. In particular, stimuli presented in the contralateral upper visual field, lower visual field, and along the horizontal meridian elicit the strongest responses in spatially segregated but adjacent populations of LIP neurons. The approximate layout of polar angle is congruent across three of the five studies [40,47,48]. In these three studies, the upper and lower contralateral peripheral visual fields are represented at the posterior end and middle of LIPv, respectively, so that the upper to lower field axis runs posterior to anterior (Figures 3B, D and E). The other two studies [41,49] also support a map of polar angle topography, but the polarity of the map is reversed compared to the other three studies (Figures 3A and C).

Foveal representation

In striking contrast to the clear evidence for a continuous map of polar angle, the evidence for a continuous map of eccentricity is poor. Three of the five studies--Ben Hamed et al., Arcaro et al., and Blatt et al.--argue for an eccentricity axis running dorsal-ventral, perpendicular to the polar angle axis, with the fovea represented dorsally [40,41,48]. If correct, LIP would then contain a full retinotopic map of the contralateral hemifield, following the standard model of topographic organization. However, neither Blatt et al. [41] nor Ben Hamed et al. [40,53] actually found a systematic ordering of neurons with respect to the eccentricity of their receptive fields as has been described in single-unit studies of visual cortex [54], and Arcaro et al. [48] found that the location and size of the dorsal foveal representation varied across animals and even across hemispheres within a single animal. Moreover, Patel et al. [47] found no evidence of an eccentricity axis and Savaki et al. [49] reported evidence of an axis with the opposite orientation to those described above.

A more consistent finding is the existence of a foveal representation in anterior LIP. In Figure 3, four of the five studies find foveal/fixation (blue) and parafoveal (orange) representations that lie anterior to the peripheral representation, either entirely within LIPv or straddling the LIPv/d border. The fifth study likely did not find this representation because they did not record far enough anteriorly [41]. This representation is almost certainly not one end of an eccentricity axis; if it were, then the polar angle and eccentricity axes would lie nearly parallel to one another. A more likely explanation is that this anterior foveal representation is separate from the posterior polar-angle map, with no continuous map connecting the two. Indeed, Arcaro et al. show that when eccentricities from fovea out to the periphery are sequentially stimulated, the foveal representation does not appear to be continuous with the more posterior peripheral field map ([48], Figure 3E). Consequently, the current weight of evidence suggests that LIP contains a separate foveal representation that is anterior to and discontinuous from a posterior polar angle map. As for a dorsal-ventral eccentricity axis, the evidence for this remains weak. An eccentricity axis may be present but variable from hemisphere to hemisphere [48], or the posterior map may, like the topographic map reported in FEF, reflect only a single dimension [38,39].

LIP vs. V1

In summary, to the extent that it exists, the topographic organization of macaque LIP does not match the clear organization found in early visual areas such as V1. In V1, polar angle and eccentricity are mapped out along perpendicular axes [7,9]. In LIP, however, the evidence for an eccentricity axis perpendicular to the polar angle axis is weak, while evidence of a discontinuous foveal representation is much stronger. LIP therefore appears to violate the first principle of the standard model of topography as it fails to have the requisite continuous topographic organization.

LIP also appears to violate the second principle of the standard model, according to which each cortical area contains one and only one map, and this map completely fills that area such that map and areal boundaries coincide. The edges of the topographic map in LIP do not appear to align with any areal boundaries, but instead enclose only a portion of LIPv, and may even cross over into the territory of LIPd. The lower edge of the map does consistently align with the LIPv/VIP border across the studies surveyed above. Yet critically, the upper edge aligns with the LIPv/LIPd border in at most three of the five studies, and in no case do the anterior and posterior edges of the map align with the anterior and posterior LIP borders. Furthermore, while three of the five studies find a polar angle map with a similar orientation, the other two studies find a polar angle map with nearly the opposite orientation, raising the possibility of multiple polar angle maps within LIP. The implications of these findings are discussed below.

Finally, it is worth emphasizing that the absence of a topographic map in no way implies an absence of a complete representation of visual space. Representations do not need to be topographically mapped. Individual cells can have spatially selective responses without being topographically organized across the cortical surface.

DISCUSSION

Interpreting findings about LIP topography

Single-unit studies

The literature prior to the publication of the imaging studies indicates that LIP topography is weak. Ben Hamed et al. state that, "LIP does not appear to contain a continuous and orderly retinotopic organization" (p. 142, [40]), and instead emphasize a patchy clustering of cells with similar properties. This evidence for topography is weakened further by the fact that the coarse topography the two electrophysiological studies describe are exactly opposite in polarity and therefore contradictory. Due to the language in the Blatt et al. abstract, this point of discordance was not widely appreciated (Blatt et al. report that the "upper field representation was concentrated in the rostral [anterior] two-thirds of LIP, while [the] lower field representation was restricted to the caudal [posterior] two-thirds of LIP" (p. 430, [41]); however, their abstract describes the reverse polarity).

Neuroimaging studies

Against this default negative view about LIP topography, the three recent primate neuroimaging studies using different methods all demonstrate clear topographic mapping in LIP [47–49]. Savaki et al. [49] imaged the accumulation of tritiated deoxyglucose in post-mortem brain slices from animals who performed multiple back-and-forth saccades. Patel et al. [47] used BOLD-fMRI to image responses while animals performed a difficult peripheral attention task. Arcaro et al. [48] also used BOLD-fMRI, but employed a markedly different task in which a pie-shaped flashing checkerboard was swept in a circle while animals fixated central crosshairs. Despite the difference in methods and discrepancies in the eccentricity axis detailed above, there were clear similarities across all three studies. In each study, the deep and posterior portion of LIP (roughly corresponding to the posterior portion of LIPv) mapped the periphery, while a point midway to anterior LIP (close to the LIPv/LIPd border) mapped stimuli placed at or near fixation.

At first glance, it appears that the single-unit and imaging studies are inconsistent within and between modalities; however we believe that these discrepancies can be explained. Below we briefly highlight the three major discrepancies about topographic organization in LIP that stand in need of resolution and sketch potential explanations. First, LIP topographic map appears to be less coarse with neuroimaging as compared to single-unit studies. Second, the emerging picture of discontinuous topographic organization in LIP differs in important ways from the standard model. Third, two of the studies report results that are almost exactly the opposite of the results in the remaining three studies, opening up the possibility that LIP may contain more than one map. All of these issues present difficulties that the field must somehow reconcile.

Single-unit recording versus neuroimaging

The natural conclusion to draw from the conflicting literature is that LIP is only weakly topographically organized. However, while a few neuroimaging studies have been inconclusive about topographic organization [55,56], most of them do report clear evidence for topography. What might explain this discrepancy?

A simple explanation is that imaging essentially “low-passes” spatial information, and so may be sensitive to coarse topography that is difficult to see with higher spatial resolution methods such as single-unit recording. As an intuitive example, consider how an image in a pointillist painting made up of many small dots is indecipherable when viewed up close (high spatial resolution), but patently obvious when viewed from a distance (low spatial resolution). LIP may similarly show no spatial organization at a fine scale ("up close") such that receptive fields of sampled single units exhibit no discernible regularity. Nevertheless, when viewed at a lower spatial resolution, relatively subtle biases in receptive field distributions may sum to produce clear topography. For example, consider two adjacent square millimeters of cortex, one containing 45% upper field and 55% lower field receptive fields, and the other containing the reverse proportion. At high resolution, such a bias would require sampling of over 200 cells from each region to discern a statistically significant difference (Chi-squared test). At low resolution, however, a significant difference would be easily discernible. There are ~100,000 cells in one cubic millimeter of tissue, so an imaging method with a resolution as small as 150 microns would be sufficient to register significant topography in this scenario. Therefore, one explanation for the apparent ease of finding topography using imaging compared to single unit recording is that imaging is better suited to detecting coarse patterns.

Another possible explanation for the greater ease in identifying topography using imaging compared to single-unit recording could arise due to differences in what the different methods are measuring (see Box 3). These potential differences have important implications for comparing and interpreting studies of topographic organization collected with different methods. For example, if topography is present in the inputs to LIP, or even in both the inputs and in small local interneurons that are not easily recorded using extracellular electrodes, then the neuroimaging methods used by Patel et al., Arcaro et al., and Savaki et al. would reveal the topographic organization whereas single-unit recording studies would be less sensitive [47–49]. By considering the different sensitivities of different techniques, one can see how apparent conflicts about topographic organization can be rendered consistent. Below we explore in more detail the possibility that different elements of a neural circuit may reflect different topographic organizations.

Box 3: Differences in the neural signals measured by single-unit recording and neuroimaging methods.

Single-unit recording techniques (used by Blatt et al. and Ben Hamed et al.) measure action potentials originating in the axons of neurons [40,41]. It is likely that single-unit recording mainly picks up action potentials coming from large cell bodies (e.g., those of pyramidal cells) or from their proximal axons. By contrast, the BOLD response is not known to be markedly differentially sensitive to large neurons. While the neural basis of the BOLD signal remains subject to intense debate, the consensus view is that BOLD-fMRI (used by Arcaro et al. and Patel et al.) is primarily sensitive to dendritic currents and not axonal potentials [47,48,106]. The evidence for this view is based on the idea that local field potentials are likely driven by spatially-aligned and temporally synchronized dendritic currents rather than by action potentials [107], and that the correlation between BOLD and LFP remains even when action potentials are abolished [108–110]. A parallel argument applies to the 2-deoxyglucose imaging method of Savaki et al., which measures energy consumption and so would, like BOLD-fMRI, be more sensitive to synaptic and dendritic events than single-unit recording techniques [49,110,111].

Distorted and discontinuous topographic organization in LIP

In early visual areas, there is a single continuous map of the visual field, and within this map, representations of polar angle and eccentricity axes lie orthogonal to one another. The results of all five studies discussed above show that this is not the case in LIP. Instead, there are spatially separate representations of the periphery and fovea (Figure 3). The foveal representation cannot be construed as comprising one end of the eccentricity axis, since within the representation of the periphery, the eccentricity axis is either weakly organized or altogether absent. We suggest that these departures from the standard model are related to the fact that LIP is involved in directing gaze and attention. For this purpose, the processing requirements for the fovea and the periphery are different, and consequently, it is computationally efficient to segregate these two representations (see Box 4 for additional discussion of topography and efficiency constraints).

Box 4: Theoretical arguments for the existence of topographic organization.

There are at least two non-exclusive reasons that topographic organization may exist. First, it may reflect a developmental accident. The mechanisms that guide axons from one structure to another structure during development may incidentally preserve the relative positions of those axons with respect to one another, thus preserving topographic organization [112,113]. This cannot be the full story, however, since there are instances of topography that this cannot explain. For example, consider axons from the dorsal root ganglia that carry fine touch information from the periphery up to the brainstem. When these axons enter the dorsal columns, they do so dermatome by dermatome. Because dermatomes overlap, the representation of the body surface is not one-to-one. However, within the dorsal column they re-sort themselves back into a single continuous topographic representation [114]. This cannot be explained, for example, as a mere side-effect of guidance factor concentration gradients that maintain a micro-scale organization as they direct the axons to enter and synapse in the dorsal column nuclei.

A second reason for the existence of topography is that it may provide substantial functional benefits. Brain volume is driven largely by the volume of axons. Since travel down the birth canal limits skull size, reducing axon length provides space for more neurons [115,116]. In addition, shorter connections conserve metabolic resources and reduce processing time [117]. The correct type of topography can provide these benefits. Total axon length is minimized when computational units (neurons) that share dense connectivity with one another are clustered together [58,117–119]. For example, one way to compute changes in intensity values in an image (large changes are often associated with object edges or boundaries) involves local comparisons of the intensity values of a number of nearby pixels. Critically, because this algorithm only requires information about neighboring pixels, total wire length can be minimized by mapping neighboring parts of the image or input space onto neighboring computational units. Early visual processing similarly involves the computation of local features (e.g., orientation, visual motion, speed). Thus placing neurons with adjacent or overlapping receptive fields as closely together as possible will minimize total axon length and thereby save space, metabolic resources and time [58,119].

Topographic distortions and computational efficiency

How might a distorted topographic map result in more efficient computation? First of all, continuity-preserving distortions such as the cortical magnification for the fovea in V1 [57], which are presumed to reflect changes in the number of neurons devoted to representing that portion of the sensory dimension, are perfectly consistent with the nearest neighbor rule for computational efficiency. However, the topographic map in LIP does not preserve continuity and so violates this rule. According to the effective wire length argument, discontinuous topographic maps in LIP and elsewhere in the brain must therefore reflect situations in which proximity along the represented dimension (e.g., sensory receptor or bodily surface) is no longer the primary determinant of computational traffic (see Box 5 for additional discussion of discontinuous topographic maps in somatosensory cortex).

Box 5: Topographic map discontinuities in somatosensory cortex.

The hand representations in primary somatosensory cortex (SI) provide a clear example of topographic map discontinuity as adjacent body surfaces are represented in non-adjacent cortical loci [85,120]. A minimally distorted topographic representation would map each finger with something like adjacent and concentric rings representing progressively more proximal portions of the finger, incorporating both ventral and dorsal surfaces especially the fingertip (Figure 4A). Yet the hand representation in SI is actually organized so that the ventral surfaces of each finger are side-by-side (Figures 4B and C). This likely reflects the fact that local computations across the ventral surfaces of adjacent fingers are at least as common as computations between the ventral and dorsal surfaces of each individual finger (see [121]). More dramatic map discontinuities in SI include the representation of the posterior and anterior portions of the hindleg which is interrupted by the representation of the foot [85,122], and the representation of the hands in cortical tissue adjacent to the representation of the face [123]. While the latter reflects in part the separation between spinal and cranial pathways, one might speculate that such discontinue also shaped by the functional advantages this organization brings about by minimizing the effective wire length between these two representations. Organisms use their forelimbs to bring food to their mouths, and therefore computations involving the fingers and the face are quite frequent. Over millions of years of evolution, this could explain why the two representations have ended up side-by-side in cortex

More generally, a neural population arranged across the cortical sheet that minimizes effective connection length could be described as efficiently representing, without distortion, the information or parameter space relevant to that particular computation [58]. As we move from early areas subserving basic sensory processing into higher-order areas involved in sensorimotor transformations and more complex cognitive functions, we should therefore expect to leave behind simple organizational schemes (e.g., retinotopy, somatotopy) in favor of more complex topographic representations whose apparent distortions and discontinuities actually reflect, in scrutable or inscrutable ways, the computations being performed in those areas (for related discussion, see [59]).

Topographic separation of foveal and peripheral representations

In early visual areas, the only prominent distortion in retinotopy is cortical magnification, the relative expansion of areas close to the fovea, as if the visual field were being viewed through a fisheye lens. Based on the computational considerations outlined above, what distortions might we expect as we move away from the sensory periphery to neural systems involved in directing gaze and attention? One possibility is that computations involving foveal input might differ from computations that involve peripheral input. In support of this idea, studies suggest that foveal and peripheral distractors can have qualitatively different effects on the control of visual attention [60–62]. Therefore, it is not unreasonable to posit that the machinery for processing foveal versus peripheral visual inputs might become distinct in gaze or attention control areas, leading to a separate foveal topographic representations.

The imaging studies we have reviewed all suggest that LIP may contain two representations of the visual field that are discontinuous from one another. The first, at the posterior end of LIP, represents the visual periphery in polar angle coordinates but without a clear eccentricity axis. The second, at the anterior end of LIP, represents the fovea. LIP-FEF connectivity data provide further support for this idea. Monkey FEF contains a clear and continuous mapping of eccentricity from lateral (foveal) to medial (peripheral). However, the projections from FEF to LIP do not follow the possible superficial-to-deep axis eccentricity axis described by Arcaro et al. and others [40,41,48]. Instead, lateral/foveal FEF is more strongly connected with anterior LIP, and medial/peripheral FEF is more strongly connected to posterior LIP [63,64]. This is inconsistent with the superficial-to-deep eccentricity axis in LIP first proposed by Blatt et al., and instead supports a posterior representation of the periphery and an anterior representation of the fovea [41].

We propose that this discontinuity reflects fundamental processing differences for foveal compared to peripheral stimuli in LIP. Visual features within or very near the fovea might belong to the stimulus currently being fixated, or might be a stimulus of interest that can be inspected with only a minimal and perhaps low cost shift in spatial attention. Alternatively, inspection of a stimulus in the periphery would require the additional computation of targeting a saccade. Given the differences in the computations required to attend to something in the fovea versus the periphery, it may be advantageous to separate the circuitry underlying these two type of attention, resulting in separated foveal and peripheral representations.

In summary, the separation of the foveal representation from the peripheral map in LIP is a marked departure from the distortions observed in early visual areas, and likely represents a change in the types of computations occurring in LIP. These changes may emphasize interactions between neurons at the fovea or in the periphery but decreased interactions between the fovea and periphery, and this topographic organization may reflect the most efficient configuration of these neurons.

Multiple topographic maps in LIP

Functional and topographic subdivisions of LIP

As described above, of the five studies of topography in LIP, the polar angle axis runs posterior to anterior in three studies but anterior to posterior in the other two (Figure 3). What could account for these discordant results? We suggest that there may be two distinct topographic maps of polar angle in LIP, whose relative levels of activity depend on the particular task being performed. In the three studies which report a posterior to anterior polar axis (Figures 3B, D, and E), animals were required to maintain fixation and ignore salient peripheral stimuli. In each case, the peripheral stimuli were designed to be exogenously salient, and in some cases they were task-relevant, but in all three of these studies the animals were explicitly trained not to saccade to these stimuli. As a result, these animals were performing an attentional rather than oculomotor task. In contrast, in the other two studies (Figures 3A and C), animals were not trained to fixate and there was no requirement to suppress saccades towards a peripheral stimulus. Savaki et al. [49] used a simple oculomotor task in which animals moved their eyes to a peripheral target as soon as it appeared. Blatt et al. [41] presented peripheral stimuli to lightly sedated animals whose eyes were mechanically restrained. Although the animals were unable to move their eyes, one might reasonably assume that oculomotor circuitry was nevertheless engaged by the peripheral stimuli, since these animals were never trained to suppress saccades. It is even conceivable that, to the extent that a distinction can be made, the low level of sedation might have interfered more with attentional over saccadic circuits. Therefore, the maps uncovered by Blatt et al. [41] and Savaki et al. [49] may correspond to a population of neurons within LIP primarily involved in oculomotor planning, whereas the maps uncovered by the other three studies may correspond to neurons primarily involved in orienting spatial attention. This possibility of multiple maps within LIP breaks the second principle of topographic organization that one anatomically defined area contains one topographic map, and opens up the possibility that LIP and associative areas contain multiple subunits, each representing separate functions.

Adjacent vs. overlapping topographic maps

Where are these maps located relative to one another? The three attention maps (Figures 3B, D, and E) and one of the two oculomotor maps all appear to be located in posterior LIPv. The Blatt et al. [41] map appears to be posterior to the other four and straddling the LIP/cIPS border. Averaging the locations of the two oculomotor maps suggests that the oculomotor map lies slightly in front of the attentional map (Figure 5A). A variant of this configuration is that the Blatt et al. [41] map may lie posterior to the attention map (corresponding to the "CIP-2" map described by Arcaro et al. [48]) and the Savaki et al. [49] map anterior to the attention map. This may explain the differing orientations of the eccentricity axes between the two studies.

Figure 5.

Possibilities for LIP topographic organization. A) Separate maps for attention and saccades. B) Overlapping attention and saccade maps.

A second possibility is that the attention and oculomotor maps overlap one another (Figure 5B). Attention and oculomotor control are intimately connected [65,66], and studies of LIP have found an intermingling of neurons involved in oculomotor control and covert shifts of attention [67,68]. Selective inactivation of LIPv affects both saccades and covert visual search [69]. However, the lesion effects on saccades and attention can be dissociated from one another by varying eye position, suggesting that the circuitry subserving the two functions are at least partially distinct [69]. If separate circuits co-exist in LIPv to subserve these two functions, it is conceivable that the topographic organization of the two overlapping circuits might not be aligned with one another. In this case, one might reasonably speculate that the topography measured in vivo in the behaving animal depends on precisely which circuit was being activated during the experiment.

Mechanistic consequences of overlapping topographic maps

A variation on this theme is that the inputs and outputs of even a single neural circuit may not be topographically aligned. For example, a circuit involved in mediating overt shifts of gaze or covert shifts of attention might receive two spatial inputs, one encoding the current attentional locus and the other encoding the desired future locus. This might be useful, for example, in computing head- or bodycentered vectors, or for transiently remapping activity [70,71]. One can imagine that the two inputs (current and future attentional loci) might each be only coarsely topographically mapped, such that any one neuron (or cluster of neurons) would receive information from a highly distributed region of space. Topography might be evident at low, but not high, resolutions. If the goal is to compute shifts in spatial location, it might be advantageous for the two topographies to be out of register with one another. Different tasks might emphasize either the current or future attentional locus (e.g., perhaps the representation of the future location is more strongly represented in the case of an overt compared to a covert shift). This could lead to different apparent topographies, depending on the particular task at hand. As another example, the same neuronal circuit might be involved in either activating or suppressing saccadic eye movements, depending on the task demands. The function of the circuit might depend on the current task demands, such that the topography of its output might be in alignment with the topography of its input in some states but dissociated from it in others.

What purpose might this decoupling of inputs and outputs serve? Studies of neural plasticity suggest it may reflect the rapid reconfiguration of circuitry needed to support the current task. These rapid reconfigurations may be mediated by selective activation or inhibition of cortico-cortical connections, as it is much faster to activate or deactivate these connections than it is to phagocytize old connections and grow new ones [72]. Studies of functional organization in temporarily blinded human subjects [73,74], and in macaque areas 7a and DP [75], support this concept since large-scale functional reorganization occurs too rapidly to be mediated by the growth of new cell processes. Thus, the topographic maps found in LIP and other associative areas may use selective activation and deactivation to respond to rapidly changing task demands [72].

In summary, the apparent conflicts between studies on polar-angle map orientation may reflect the fact that different tasks were being performed. The two distinct maps revealed by the five studies may lie side by side, or they may overlap one another. Overlapping maps might occur if, for example, inputs, outputs or other circuit elements are partially shared by the circuits in question.

Open questions about LIP topography

A number of issues concerning the topographic organization of LIP remain unclear. The first issue is whether attention and oculomotor maps are overlapping or adjacent within individual macaques. Another issue is whether an eccentricity axis exists in the posterior topographic map, and if so, to confirm the orientation of this axis. Yet another issue is whether the anatomical subdivision LIPd also contains topographic maps like LIPv. Although LIPd is clearly involved in oculomotor planning [69], no topographic map has been found within this anatomical subdivision of LIP; the presence or absence of topographic maps in certain functional areas may help reveal the functional utility of topographic organization. Despite these open questions, the differences in topographic mapping across studies should not be dismissed out of hand. Instead, differences in tasks and methodologies should be carefully considered as potential drivers capable of revealing true differences in topography. Associative cortical areas may support more than one function, and therefore may contain multiple topographic maps, as many as one for each function. This functional multiplicity may be supported by re-weighting across multiple inputs and multiple outputs from individual neural circuits, or re-weighting the relative activity of different circuits that are interdigitated across the cortical surface. If the topography of these different elements are not aligned with one another, then we may find violations of the standard model of a single topographic map per brain area.

Conclusion: Revising the principles of topographic organization

We describe five findings in this review that suggest that some of our deep-seated assumptions about topographic organization in the brain do not generalize beyond early sensory and late motor areas. We show that the fovea and periphery are mapped in entirely separate locations in LIP (Figure 3); a polar angle map may exist without a clear eccentricity map (Figure 3); the maps we observe may depend on the particular task being performed (Figures 3 and 5); areas may contain more than one topographic map (Figure 5); and, most speculatively, multiple topographic maps may sometimes overlie one another (Figure 5B).

Revised principles of topographic organization

We propose that the first principle of topography, rather than requiring each map to reflect the entirety of a particular sensory or motor dimension, may instead be modified to accommodate continuous mappings of a subset of that dimension, with the extent determined by the precise functional demands of the particular circuit. An important consequence of this is that we should expect a spectrum of types of topographic organization across brain areas with different functional profiles. We suggest that the second principle, which requires that a single map occupy the entirety of a single anatomically-defined area, be understood to apply only to early sensory and late motor areas. Topographic maps in parts of cortex that serve more intermediate functions should encompass all of the neurons performing a single unified function, but this does not necessitate anatomical or even spatial separation of each map.

Examples of the revised principles in other associative areas

These modified principles may also apply to the organization of prefrontal cortical areas as well. Macaque FEF is one clear example. FEF is functionally defined as an area on the anterior bank of the arcuate sulcus in which electrical stimulation results in both saccades and shifts in attention [38,76,77]. This area has two striking features. First, within FEF there is a clear eccentricity axis of organization, but no clear orthogonal polar angle map [38,39], fitting the first principle of the modified criteria. Second, while the functionally defined borders correspond to those of the eccentricity map, they do not match any architectonic borders —one recent parcellation scheme splits the functional area across four architectonic divisions [46,78]. This fits with the second modified principle.

Area 46d potentially serves as another example. Area 46d (Area 46 dorsal to the principal sulcus) is an area involved in maintaining spatial working memory in delayed saccade tasks [79,80]. This area is reciprocally connected to retinotopically and non-retinotopically organized areas [80,81]. While no single-unit study has provided evidence of topographic organization in dorsolateral prefrontal cortex, reversible inactivations with muscimol that induce deficits in a memory saccade task reveal a topographic map in Area 46d [82]. Muscimol, a GABAa agonist, will inhibit not just the pyramidal output neurons that would normally be recorded from, but also any topographically arranged inputs projecting to Area 46d. So, it is possible that single-unit recording studies have not found topographic organization because the outputs themselves may not be arranged topographically even if the inputs are. This area then may serve as an example of the second principle, in which a functionally unified population of neurons is topographically organized and overlapping with other neurons with different (or no) topographic organization, though this clearly needs to be investigated further.

Advantages of the revised principles

One major advantage of the revised organization principles over the current model is that they gracefully accommodate more complex forms of topographic organization of the sort observed in associative areas including parietal cortex. Another advantage of the revised principles is that they are more inclusive. In particular, they subsume the more restrictive principles at the core of the standard model derived from sensory and motor areas. Now those original principles can be more appropriately understood as special or limit cases. As brain research continues to shift from its original focus on the sensory and motor periphery (e.g., early visual and late motor areas) to brain areas and networks involved in more complex modes of cognition, it is incumbent on us to consider more flexible models of how neural populations underlying these computations may be distributed across the cortical surface. The revised organizing principles provide a much more suitable framework/foundation for this kind flexible model.

Having a coherent set of general principles of topographic organization is a pressing objective for contemporary neuroscience. With the emergence of multi-unit recording, higher-resolution neuroimaging, and interventional methods such as optogenetics, topographic organization in both non-human primates and humans has is more easily observed and interrogated than ever before. Consequently, it has never been more important than now to understand what topographic organization does (and does not) tell us about brain function and structure. We believe that by keeping these principles in mind, the importance and complexity of topographic organization in the brain can be more readily appreciated and understood.

Figure 4.

Possible topographically-organized hand representations. A) Schematic of minimally distorted, topologically intact hand representation. Color gradient indicates dorsal/ventral surface locations on digits (D₁-D₅) from distal (red) to proximal (green). B) Schematic of actual topographically-discontinuous hand representation found in somatosensory cortex. Color gradient indicates locations on ventral digit surfaces from D₅ (red) to D₁ (green). C) Hand representation in somatosensory areas 3b and 1 of the owl monkey (adapted from [85]).

Box 6: Defining ‘area’.

The definition of ‘area’ is fraught with difficulty. Cortical areas are typically defined in terms of architectonics, connectivity, functional characteristics, topography, or some combination of these [21]. In primary sensory and motor cortex, the task of identifying areas is greatly simplified by the fact that all of these standard approaches can be used more or less interchangeably to deliver comparable answers about areal boundaries. In associative cortical areas like LIP, this neat alignment breaks down. In human neuroscience, the problems associated with defining cortical areas is compounded by the fact that information about architecture and connectivity is largely unavailable because the invasive techniques required to attain this information cannot be deployed. In light of these difficulties, one option is to jettison talk of cortical areas entirely (e.g., [9]). Another option (the one we prefer), which is consistent with much of the field (e.g., [21]), is to retain the term 'area' but also acknowledge that the construct is more nuanced than is often assumed. According to this view, one may operationally define an ‘area’ as any cortical territory that can be consistently segregated from a neighboring territory by any combination of architectonics, connectivity analysis, functional characteristics, and topography. This way of defining areas will often result in multiple functionally and topographically defined areas contained within a single architectonically defined area. This likely implies that these functionally and topographically defined areas share similar neuronal circuit architecture for performing different functions.

This definition of an area will impact the interpretation of human studies of cortical organization, since topography is often used to partition cortex into areas [9]. For instance, the multiple topographic maps in human parietal cortex may each belong to functionally distinct but related areas, and like the multiple topographic maps in LIPv, may share similar architectonic features, such as dense myelination. The existence of partial topographic maps may also explain the relative weakness of eccentricity topography in human parietal cortex--only one parietal topographic mapping study has reported an eccentricity axis of organization [124] whereas multiple others have not (see for instance [26,125]).

Highlights.

• Topography is fundamental to cortical organization

• Topography organization of LIP differs in important ways from other visual areas

• Differences may underlie computational flexibility in LIP and other multimodal areas

• We propose two new principle of topographic organization for multimodal areas