# Visual map

Post-publication activity

Curator: Nicholas V. Swindale

The term visual map refers to the existence of a non-random relationship between the positions of neurons in the visual centers of the brain (e.g. in the visual cortex) and the values of one or more of the receptive field properties of those neurons. The term is usually qualified by reference to the property concerned: thus the term retinotopic map refers to the orderly mapping of receptive field position in retinotopic coordinates in a brain region; orientation map refers to the orderly mapping of orientation preference and ocular dominance map refers to the orderly variation in relative preference for stimuli delivered to the contralateral vs. the ipsilateral eye. These quantities can be assigned to neurons in primary visual cortex on the basis of appropriate tests with physiological stimuli such as moving light or dark bars, or sine wave gratings, presented to one or both eyes while the activities of cells are monitored with techniques such as extracellular single unit recording, optical imaging, two-photon confocal imaging or high resolution fMRI. These are not the only quantities that may be mapped: in principle any well-characterised receptive field property is a candidate for mapping in any of the visual areas.

Figure 1: Early, and remarkably accurate (disclaimer notwithstanding) representation of the mapping of visual field regions onto the surface of human primary visual cortex. From Holmes (1918).

## Early Evidence for Retinotopic Maps

The significance of visual maps, and brain maps in general, originates with the 19th century debate concerning localisation of function in the brain. Some of the earliest evidence that brain functions were localised came from experiments and observations by neurologists, notably David Ferrier, Gustav Fritsch, Eduard Hitzig and Hughlings Jackson, suggesting that there was an ordered representation of body parts within motor cortex. This implied that brain functions were localized and not distributed as had earlier been thought. Evidence for the existence of retinotopic maps, and by implication, localisation of function, in the visual cortex came from analyses by the ophthalmologist Tatsuji Inouye and the neurologist Gordon Holmes of visual field scotomas resulting from partial injuries to the visual cortex caused by shell and bullet wounds sustained by soldiers in the Russo-Japanese and First World Wars. These studies showed a predictable relationship between the region of damage in striate cortex and the location of the area of blindness in the visual field (Inouye, 1909; Holmes, 1918). The foveal or macular region was represented on the posterior tip of the occipital lobe, the lower visual fields (or upper half of the retina) were represented dorsal to the calcarine fissure and the upper fields ventral to it. Serial concentric zones of the retina from the macula to the periphery were represented in an ordered sequence from posterior to anterior in the visual cortex ( Figure 1). Modern day measurements have only slightly revised this view and suggest that the area of cortex devoted to the fovea is larger than originally estimated ( Figure 2).

Figure 2: Left: Modern day estimate of the representation of the visual field on the surface of human occipital cortex. The figure shows the medial aspect of the occipital lobe with tissue on either side of the calcarine sulcus pushed apart. Right: representation of visual field coordinates as they would appear on the cortex if completely unfolded and flattened. Numbers show either meridional angle or eccentricity in degrees. The dark circle is the blind spot; HM = horizontal meridian. Note the orthogonal intersections of lines of constant eccentricity and meridional angle. Modified with permission from Horton (2006).

## Quantification of Retinotopic Maps

Retinotopic maps can be characterized quantitatively by the rate of change of position in the cortex as a function of position in visual space, expressed as mm/degree. This quantity is known as magnification factor (M). A high value of M means that a large area of cortex is devoted to analysing a small region of visual space. In primates, M is highest in the fovea and decreases reciprocally with visual field eccentricity. Estimates of its value in the central fovea in humans vary from about 4 mm/deg (Cowey and Rolls, 1974) to about 11 mm/deg (Drasdo, 1977). Individual differences in M and its relation to eccentricity occur (Duncan & Boynton, 2003).

The overall relationship between visual field position and position in the cortex can be described approximately by a complex logarithmic function $$\mathbf{w}=a\log(b+\mathbf{z})$$ where $$\mathbf{w}=(x+iy)$$ gives the position in the cortex in mm, $$\mathbf{z}=re^{i\theta}\ ,$$ where $$r$$ is the visual field eccentricity in degrees, $$\theta$$ is the meridional angle in radians and $$a$$ and $$b$$ are experimentally determined constants. This function, first proposed by Schwartz (1980), describes the type of mapping observed in primary visual cortex (V1) of primates, including humans, including the over-representation of the fovea and the tendency for lines of constant meridional angle and constant eccentricity to be mapped as orthogonally intersecting straight lines on the surface of the cortex ( Figure 2). It however predicts that M is locally isotropic, which is often not the case. Thus there may be a greater rate of change of cortical position for upward movement in the visual field than for movement along the horizontal axis. Such anisotropies have been reported in primary visual cortex; also the retinotopic map in other visual areas such as V2 of primates or area 18 of cats and ferrets can be very significantly anisotropic. The functional significance of these variations is unclear at present.

## Retinotopic Maps outside of Primary Visual Cortex

In primates, including humans, retinotopic maps are present in many, and possibly all, visual areas of the cerebral cortex beyond V1 (Wandell et al., 2007). Retinotopic maps also occur in non-cortical brain structures, notably in the lateral geniculate nucleus and in the superior colliculus of mammals and the optic tectum (which is homologous to the superior colliculus) of lower vertebrates such as fishes and frogs. The factors that lead to the establishment of retinotopic maps in these structures have been intensively studied, especially in the tectum (Luo & Flanagan, 2007). These include the existence of gradients of chemoattractive and chemo-repellent molecules, the ephrins, and of the family of Eph receptors for these substances. These gradients are believed to help establish a rough degree of retinotopic order which is then refined by mechanisms that depend on Hebbian synaptic plasticity and neural activity. Before birth or eye opening the neural activity is spontaneous in origin and, in the retina, takes the form of retinal waves. After eye opening the activity is visually driven.

## Orientation Maps

Evidence for orientation maps in the visual cortex was first obtained in cats by Hubel and Wiesel (1962) and subsequently in macaque monkey (Hubel & Wiesel, 1968). There are two aspects to the order:

• cells in different layers of the cortex, but with similar tangential position e.g. whose cell bodies fall within 30 – 50 um of a line drawn perpendicular to the pial surface, have the same preferred stimulus orientation (i.e. to within ~10 degrees). This constancy across layers is referred to as columnar organization: it is found for other response properties such as ocular dominance and for properties in other sensory and motor areas and appears to be a common feature of cortical organization in higher mammals.
• cells' orientation preferences are locally continuous, so that as a recording electrode is moved tangentially through the cortex (Hubel & Wiesel, 1974) preferences usually rotate, either clockwise or counter-clockwise at a roughly constant rate. The direction of rotation will typically continue unchanged for 1 – 2 mm and then reverse unpredictably. Sudden shifts in preferred orientation of up to 90° also occur.
Figure 3: Predicted layout of orientation preference in visual cortex. Modified from Swindale (1982).
Figure 4: Layout of orientation preference observed in area V1 of macaque monkey. Scale bar = 1 mm. Modified from Blasdel & Salama (1986).

These 1D glimpses of map structure obtained in the 1970s did not clearly reveal the 2D layout, which remained a matter for speculation. A self-organising model of map development proposed by Swindale (1982) introduced the now widely adopted use of a vector (or complex number) to represent orientation values, and a colour cycle (e.g. red = 0° - 30°, orange = 30° - 60°, yellow, green, blue, purple, red etc.). to represent the layout in 2D plots. This model predicted general features of the layout of orientation preference [ Figure 3] that were subsequently confirmed by optical imaging in the primate (Blasdel & Salama, 1986: [ Figure 4]) and by multi-site recording studies in the cat (Swindale et al., 1987). The colour plots show that iso-orientation domains – regions of constant colour – are periodically spaced thin strips with a variable width and pointed terminations, with an average spacing of about 600 um in the primate and about 1200 um in the cat. Also obvious in these images are structures that were termed orientation pinwheels by Bonhoeffer & Grinvald (1991) because of their resemblance to a coloured pinwheel. The center of the pinwheel, where a single set of all the orientations meets, resembles a point singularity in a vector field and can be defined as of positive or negative sign, depending on whether the preferred orientation rotates in a positive or negative direction as a circuit is made in an anti-clockwise direction around the point.

Neither the earlier multi-site recording or optical imaging studies could resolve the preferences of individual neurons with enough detail to be sure that map structure was maintained close to a pinwheel center, however 2-photon recording experiments in cats (Ohki et al., 2006) have confirmed that orientation preferences remain well defined, and spatially ordered, right in to the pinwheel center, meaning that the singularity is as real as is possible, given the neural granularity of the map.

## Ocular Dominance Columns

Figure 5: Pattern of ocular dominance columns observed in humans (top) and macaque monkeys (bottom). Black represents one eye and white the other. The entire area of V1 is shown in both cases. The white region in the center of the pattern is the blind spot. Modified with permission from Adams et al. (2007).
Ocular dominance columns constitute another type of visual map: here preference for stimulation by the contralateral or ipsilateral eye varies across the surface of the cortex with a period of about 1 mm in cats (Shatz et al., 1977) and monkeys (Hubel and Wiesel 1977); the spacing in humans (Adams et al., 2007) is about 2 mm. The overall 2D pattern consists of variably blobby stripes and bands and is strikingly similar in monkeys and humans [ Figure 5]. The bands have a tendency to run horizontally across the visual field in and near the fovea, and circumferentially in the near and far periphery. In one of the most influential experiments done in the history of neuroscience it was shown (Wiesel & Hubel, 1963; Hubel et al., 1977) that closing one eye shortly after birth (monocular deprivation), during a critical period affects the morphology of the columns with those driven by the open eye becoming larger while those driven by the deprived eye become smaller. The factors that affect the development of ocular dominance columns pre- and post-natally, and that mediate the effects of visual deprivation early in life have been the topic of much research (Hooks & Chen, 2007).

## Other Properties Represented in Visual Maps

A number of other properties are systematically mapped in the primary visual cortex of cats and ferret: these include spatial frequency and direction preference. Candidate properties include colour (in primates) and stereoscopic disparity and there may be others. In infero-temporal (IT) cortex there is evidence for ordered columnar representations of higher-order visual features (Tsunoda et al., 2001). Limits on the number of map dimensions that might simultaneously be present in any one cortical area have been explored in computer simulations (Swindale, 2000); the real number is not known.

## Theoretical Approaches

The consequences of having multiple overlaid maps of different properties were realised by Hubel and Wiesel (1977) who speculated that maps ought to be superimposed in ways that would allow combinations of features such as eye and orientation preference to be equally well represented over all positions in visual space. They also speculated that continuity in the layout of columns for different features would minimise connection lengths by bringing functionally related groups of cells close together in the cortex. These two ideas form the basis for a theoretical understanding of cortical maps that has been extremely fruitful (Durbin and Mitchison,1990). In this approach, cortical maps are regarded as a dimension-reducing projection from a set of points or manifold in a multi-dimensional feature space onto the 2D surface of the cortex. The axes of the feature space are the parameters which vary in the maps, e.g. retinal position, orientation angle, spatial frequency etc. The projection is assumed to be made subject to the two constraints identified by Hubel and Wiesel: completeness and continuity. Completeness specifies that all functionally relevant points in the space should be mapped; this constraint is sometimes equivalently referred to as coverage uniformity. Continuity specifies that neighbouring points in the cortex should be mapped, as far as possible, to neighbouring points in the feature space. These constraints act in opposition and models that achieve projections subject to a balance between them reproduce many of the morphological features of real visual cortex maps and the structural relationships between them (reviewed in Swindale, 1996; Goodhill, 2007). There are experimental confirmations of many of the predictions of the models; in particular, there is evidence that maps of ocular dominance, orientation, and spatial frequency preference in cat visual cortex are arranged in ways that optimise coverage (Swindale et al., 2000).

## Comparative Studies

Most information about visual maps has come from studies of areas 17 and 18 of cats and ferrets and V1 of primates such as the macaque. While the organisation of corresponding visual areas in cat and ferret appears similar there are differences between maps in these species and those found in primate V1. Notably, maps of direction preference seem to be absent in primate V1 but are present in both areas 17 and 18 of cats and ferrets. In several species of primate, cytochrome oxidase (CO) stains of area V2 (which is probably not homologous to area 18 of non-primate species) show a system of alternating darkly stained thick and thin stripes, each roughly 1 - 2 mm wide, containing high levels of the enzyme. Between each pair of thick and thin stripes is a third type of palely stained stripe containing lower levels of CO. The three types of stripe are known as thick, thin and pale stripes. Each seems to contain maps of different functional properties - stereoscopic disparity in the thick stripes, colour in the thin stripes and orientation in the pale stripes (Roe and Ts'o, 1995; Lu and Roe, 2007). Human V2 also contains stripes of high and low CO density but alternations in width of the dark stripes are not present raising the possibility that the functional organisation is different from that of other primates (Adams et al., 2007). Area MT (or V5) of macaque monkey contains a well organised map of direction preference and probably also of stereoscopic disparity. Homologies between areas such as V2 and MT in primates (and the types of maps within these areas) and areas in non-primate species such as the cat are possible but speculative at present. Retinotopic maps are present in the visual areas of lower mammals such as rats and squirrels but other properties, such as ocular dominance and preferred orientation appear to vary randomly with position (Van Hooser et al., 2005). The functional significance of these species variations is unclear at present.

## Significance of Visual Maps

Many uncertainties remain concerning the functional and biological significance of visual maps including

• the number and types of properties that may be mapped in specific areas in particular species
• the structural details of individual maps and their geometrical relationships with others in the same cortical area
• the extent to which columnar organization holds
• the extent to which map properties may be modifiable by experience
• the developmental mechanisms leading to map formation

New techniques, such as 2-photon confocal microscopy and high-resolution fMRI may help answer some of these question in the future. At present, a reasonable consensus exists that a major function of visual maps, and probably brain maps in general, is to minimise the connection lengths of axons and dendrites (Chklovskii & Koulakov, 2004). This has an obvious evolutionary advantage since it will reduce the overall volume and weight of the brain and increase the speed of processing. It follows if it is assumed that connections are most likely to be made between groups of neurons with similar functional properties, and in proportion to the degree of similarity. One reason for the success of dimension-reduction models may therefore lie in their implementation of the continuity constraint since this leads directly to minimisation of wirelength (Durbin & Mitchison, 1990).

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Internal references

• John Dowling (2007) Retina. Scholarpedia, 2(12):3487.