The functional organization of area V2, II: The impact of ... · The aim of this paper is to examine the relationship between the modular architecture of area V2—its parallel cytochrome

The functional organization of area V2, II:The impact of stripes on visual topography

STEWART SHIPPand SEMIR ZEKIWellcome Department of Cognitive Neurology, University College, Gower Street, London WC1E 6BT, UK

(Received December 28, 2000;Accepted February 15, 2002)

Abstract

We have examined the visuotopic organization of area V2 of macaque monkeys in relation to its modularconstruction, comprising repetitive cycles of stripes running perpendicular to the border with area V1. Receptivefields were plotted in anesthetised animals, mainly using long penetrations parallel to the V1 border crossingseveral stripes in dorsal V2 within the representation of paracentral, inferior visual field. We confirm that each setof modules (thick, thin, and interstripes) mounts an unbroken coverage of the visual field, since there is almostinvariably some overlap between the aggregate fields recorded in successive stripes of the same class, at intervalsof one cycle. Also as expected, penetrations perpendicular to the stripes record changes in eccentricity along anisopolar visual meridian. We measured the size of the point image along such an isopolar meridian in nine cases,and showed that on average it exceeds the length of a typical cycle; again, this implies that no point in spaceescapes analysis by any of the functional modules. The representation of eccentricity across a cycle of stripesresembles a “ratchet” model, in which the gradient of eccentricity across a single stripe exceeds the gradient acrossthe full cycle, leading to discontinuities (“switchbacks”) at the borders between stripes. The shift in eccentricityacross the width of a stripe is sufficient to maintain a virtually continuous map across successive stripes of thesame class; when coupled to receptive field scatter about the mean trend, this creates the overlap of aggregatefields. The presence of topographic discontinuities, in addition to functional ones, at stripe boundaries, reflectsautonomy of function at the local level. At a global level, however, the organization of V2 may promote integrationacross stripes, since the range of visual overlap, and intrinsic connections, exceeds a single cycle. Furthermore,the reduplication of modules along the isopolar axis has the effect of increasing the isopolar magnification factor(mm0deg); the ratio of isopolar to iso-eccentric magnification is approximately 1.5:1, and this elongation abets theexternal configuration of V2 that, stretching concentrically around V1, has long been hypothesized to facilitatefunctional interaction between the two areas.

Keywords: Cytochrome oxidase stripes, Retinotopic mapping, Visual coverage, “Ratchet model” and“switchbacks”, Functional specialization, Functional integration

Introduction

The aim of this paper is to examine the relationship between themodular architecture of area V2—its parallel cytochrome oxidasestripe compartments—and its visual topography. It has alwaysseemed plausible that each compartment may re-represent thevisual field, causing some kind of dislocation, or repetitive fracturewithin the global visual map (Zeki & Shipp, 1989; Roe & Ts’o,1995). The situation is analogous to that in V1 where, at asomewhat finer scale, the visual field is dually represented acrossthe parallel ocular-dominance bands. In V1, the demonstration ofa fragmented but complete visual map, in each eye, is clearest inlayer 4C, where receptive fields are smallest and most exclusivelymonocular (Hubel & Wiesel, 1977; Blasdel & Fitzpatrick, 1984;

Tootell et al., 1988). In V2 binocularity is the rule, of course, buthere it is distinct functions that appear to be regularly compart-mentalized, on a spatial scale that is at least twice as great (Hubel& Livingstone, 1987; Tootell & Hamilton, 1989; Ts’o et al., 1990).The alternating pattern of dissimilar dark stripes interspersed withrelatively regularly sized pale stripes, points, minimally, to atriplicate visual remapping, that we seek to test.

We set out to investigate stripe-related topography by mappingreceptive fields (RFs) along a transect perpendicular to the stripes’axis, through one or more whole cycles. The basic geometry of V2is one in which the stripes traverse its short axis, running from theborder with V1 to the border with V3 (Livingstone & Hubel, 1982;Tootell et al., 1983). The former represents the vertical meridian(VM), and the latter the horizontal meridian (HM) (Cragg, 1969;Zeki, 1969), an organization that has been termed a “2nd-ordertransformation of the visual field” (Allman & Kaas, 1974) owingto its delocalization of the superior and inferior quadrants. It pre-dicts that stripes should describe arcs of iso-eccentricity (Gattass

Address correspondence and reprint requests to: Stewart Shipp, WellcomeDepartment of Cognitive Neurology, University College, Gower Street,London WC1E 6BT, UK. E-mail: [email protected]

Visual Neuroscience(2002),19, 211–231. Printed in the USA.Copyright © 2002 Cambridge University Press 0952-5238002 $12.50DOI: 10.1017.S0952523802191176

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et al., 1981; Rosa et al., 1988)—see Fig. 1—and this appears to beso, at least in the regions studied to date (Roe & Ts’o, 1995).Discontinuity in the global map of V2 that is caused by stripesshould thus be discontinuity of eccentricity, and ideally, the polarangle component of the map might be undisturbed. In previousstudies of fractures, our own brief report emphasized verticaldislocations at stripe borders (equivalent to eccentricity for record-ings located on the VM) whilst Roe and Ts’o employed a scalarmeasure, pooling RF shifts without regard to their exact direction

(Zeki & Shipp, 1989; Roe & Ts’o, 1995). Here we provideadditional data and analysis, to give a fuller account of visualtopography across stripes.

Is a fractured global map, with regular discontinuities (“switch-backs”) at stripe borders an inevitable consequence if multiplerepresentations are to be housed within the same area? As illus-trated below, a hypothetical topographic scheme that lacks frac-tures but maintains an unbroken, uniform visual coverage withineach compartment, may easily be devised. The cost of such ascheme, which restores topographic continuity from one compart-ment to the next, is to impose other constraints upon the localtopography. By contrast, a scheme with fractures allows eachcompartment some form of autonomy in its manner of visualrepresentation, one which may be tailored to its particular func-tion. From this perspective, visual topography represents anothertool by which to characterize the functional diversity of stripes.

Methods

Receptive-field plotting and correction

Preparation and maintenance of animals, and details of the record-ing procedure, are described in the accompanying paper (Shipp &Zeki, 2002). In general, these procedures were tailored to optimizethe study of visual topography. For instance, in order to maximizethe topographic signal-to-noise ratio (“noise” deriving from ir-reducible error in plotting RFs and keeping track of eye position),we made a midline craniotomy and introduced the electrode intodorso-medial V2, as close as possible to the midline in order tomaximize inverse magnification (deg0mm) (Gattass et al., 1981).To ensure an acute angle of approach, so that the electrode wouldrun almost parallel to the cortical surface, it was necessary todispense with a standard recording chamber and seal the corticalexposure with agar alone. Recording sites were studied at intervalsof 100mm. Receptive fields were plotted on a tangent screen at adistance of 114 cm and stored in Cartesian coordinates. RFs wereplotted for both eyes, but the response properties determinedthrough one eye alone. The standard stimulus was a light bar ofluminance 30–60 cdm22 (depending on the operating distance ofthe projector), with contrast over 95% on a background less than1 cdm22. All RFs were plotted as rectangular minimum responsefields, using the best bar stimulus (i.e. adjusted for length, colorand orientation0direction). Although each site was studied rela-tively briefly (15–45 min), it typically took 12 h or so to gatherdata from one or more cycles, often necessitating an overnightbreak in recording (for investigators’ recuperation). In sum, weobtained usable topographic data for nine whole cycles of stripesfrom eight cases altogether (plus numerous partial cycles).

We plotted the foveas using a reversible ophthalmoscope.When a fovea was not visible we approximated its position fromthe radial pattern of blood vessels. Later inspection of the RFscould reveal up to 2 deg interocular discrepancy in the fovealplots—incorrectable since it is not known which fovea is the moreaccurately plotted. To monitor eye movement during the record-ings, we plotted retinal landmarks (easily recognized blood vesselintersections) on the tangent screen along with the foveas. Using areversing ophthalmoscope, the measurement is repeatable to within1 deg. Landmarks were plotted at breaks between penetrations, orat intervals not exceeding 8 h. One experiment was used for trialof a reference electrode at a fixed location in V1; this gave a moreconvenient short-term measure of eye position, but added prob-lems of maintenance over the longer term. On occasion, the main

Fig. 1. The representation of the contralateral superior quadrant by dorsalV2, lying in the lunate sulcus. Top: Schematic view of a left hemispherewith the occipital operculum cut away and stained for cytochrome oxidase,revealing the pattern of V2 stripes lying within the posterior banks of thelunate and inferior occipital sulci. Middle: V2 from the lunate sulcus,rotated so that its visual map is congruent with the visual field. Thehorizontal meridian runs along the fundus of the sulcus, and the verticalmeridian along its lip. Bottom: The image of V2 transformed from Carte-sian to polar coordinates (Adobe Photoshop), and superimposed on a mapof the right inferior quadrant. This mimics the global visual topography inV2, and it can be seen that the stripes roughly describe arcs of iso-eccentricity. It is also evident, however, that if this were an accuratedepiction, each stripe would occupy a discrete segment of the visual field,and any one subset of stripes (e.g. all thick stripes) could not mount auniversal representation of visual space. Hence predictions that the mapwill show local, stripe-related discontinuities.

212 S. Shipp and S. Zeki

electrode in V2 acted as its own reference if a second penetrationrecorded from sites nearby to the first. We also examined the RFplots for any sign of relative movement between the two eyes. Ifa systematic change in interocular disparity was consistent withthe direct measurement of eye position, we used it to “fine tune”the correction and abolish any net drift in interocular disparityover the course of the experiment; there could still be a persistentnonzero value of interocular disparity due to the uncorrected errorin the plots of foveal position.

The analysis of cyclic mapping in V2

Our aim was to tell how the visual field representation is seg-mented across regular cyclic alternation of functionally distinctcompartments. Mean RF size, scatter, and net RF shift werecomputed for a unitary cycle, and for each of its four stripes. Wethen tested for retinotopic overlap between corresponding points inadjacent cycles (e.g. thin stripe to thin stripe), and for discontinu-ities and0or overlaps within a cycle.

The calculation of receptive-field size, scatter,and magnification factorRF size was defined as the square root of the field’s area.

Scatter was determined by the displacement of an RF center fromits “predicted” position, assuming a linear path through the visualfield as the electrode is pushed through the cortex. The latter wasestimated using a least-squares regression of theX andY coordi-nates of the RF center against electrode depth. The outcome issimply illustrated by a “trend-plot” (e.g. Fig. 5) which links theobserved position of each field to its “predicted” position along thevector of topographic drift computed by the regression procedure.The RMS scatter of the “n” units recorded in a single penetrationwas computed as

RMS scatter (single penetration)

5 [(Ssquare displacement0n 2 2!102,

~n 2 2) being the degrees of freedom, in the manner of a statisticalmean-square.

Shifts in RF location were measured as the distance betweenthe “predicted” (regressed) positions of the first and last cells in adefined group of units (e.g. a whole cycle or one of its componentstripes). Because single stripe and full cycle regressions predictdifferent positions for any given unit’s RF, the cyclic shift is notnecessarily equal to the sum of the four component stripe shifts.We were interested, principally, in shifts occasioned by movingperpendicular to the stripes. Due to the configuration of stripes inV2, this demands an analysis of shifts in eccentricity. However, forthose penetrations that passed near to and parallel with the V1border, we substituted an analysis of elevation up the VM, sincechanges in elevation (but not eccentricity) are independent of theexact location determined for the fovea. Standard linear magnifi-cation factors (mm0deg) were computed for the axis perpendicularto the stripes after accounting, trigonometrically, for the angle ofthe electrode track to this axis. Since we are considering visualfield coverage, we also work in terms of inverse magnification,otherwise referred to as “slope” (deg0mm) in our standard plots ofstripe related topography. The slopes of individual stripes werecompared to that of their parent cycle, and the population dataevaluated by binomial statistics. The raw datum for this procedurewas the binocular average of the RF center plotted through eacheye; for comparability, the illustrations also display “binocular”

RFs, calculated as the spatial average of the two monocular fields,after all appropriate correction for ocular drift (see above).

Analysis of visual field coverage and overlapWe used several means to measure the overlap between the

visual representations in separate stripes. In terms of area (deg2),overlap between the aggregate RFs of two stripes was expressed asa fraction of the mean RF area of all the component RFs of thatpair of stripes. The aim is to collate data across individuals withsimilar but not identical recording sites, so this normalizing pro-cedure helps to correct for variations in the scale of representation(i.e. variations in magnification) due to differences in eccentricity.Overlap might, in principle, be expressed as a fraction of theaggregate RF area itself, but the resulting normalization is lessrobust since aggregate RF area is prone to additional variabilitydependent on RF scatter, and the unit sample size from each stripe.Other, linear, analyses of RF coverage were based on RF size andthe eccentricity component of RF location. Thelinear point image(the extent of cortex receiving input from a notional visual point)was compiled from a full cycle of stripe RF data. Aggregate RFsize was computed as mean RF size plus the diameter of anenvelope encompassing 95% of all that cycle’s units in a standardscatterplot—a diagram showing the distribution of all RF centersabout their predicted location (e.g. Fig. 5). The point image(notionally, of any point in the target cycle) was taken to be theratio of the aggregate RF size to the shift in eccentricity recordedacross that cycle—and the aim was to test whether the point imageexceeds one cycle in size (see Fig. 4).

“Slope,” “scope,” and “smear” indicesThese indices were computed separately for each class of

stripe, and measure the relative contributions of visual mapping,and RF size and scatter, toward an uninterrupted coverage of thevisual field by that set of stripes. The visual mapping is the shift ineccentricity across the width of the stripe; RF size and RMS scatterare as defined above. The denominator, cyclic shift, estimates theunit of visual space that is each stripe’s duty to cover. Each of theseparameters is calculated independently for each eye, before aver-aging to yield a binocular value. Then

Slope index5Stripe shift,

Cyclic shift,

Scope index5Stripe shift1 (23 RMS scatter)

Cyclic shift,

Smear index5mean RF size1 (23 RMS scatter)

Cyclic shift.

Values above 1.0 imply unbroken coverage of the visual field bythe associated set of stripes, according to one or other hypotheticalmodels of V2 topography (see Fig. 7). Values below 1.0 mightfalsify a particular model. Note that, using RMS scatter, the scope(5 scatter1 slope) and smear indices provide a conservativemeasure of RF dispersion.

Results

Determination of stripe boundaries

In part I of this report, we allocated about 20% of units to marginalzones, to avoid possible contamination of stripe classes by errorsof stripe assignment. The current exercise, to examine the visual

Area V2. II: The impact of stripes on visual topography 213

topography of functionally distinct modules in V2, requires aforced-choice allocation of every receptive field to one stripe oranother. Logically, having established that stripes are functionallydistinct entities (Shipp & Zeki, 2002), the physiology data can beallowed to resolve the ambiguity inherent in histological borders.Thus, where possible, functional transitions at or within the mar-ginal zone were used to allocate all marginal units to one or otherof their neighboring stripes. Many of these transitions were “the-matic,” in that they followed the gross characteristics of a stripe,for example, a transition to spectral sensitivity at a thin stripeborder, or to orientation sensitivity at a thin0interstripe border.Unexpectedly, several borders between thick stripes and inter-stripes were localized by “non-thematic” transitions of orientationsensitivity, involving minority, local patches of nonoriented cellsin one or other stripe. These are listed in Table 1. Interstripe0thickstripe borders were also localized by the onset of direction sensi-tivity, or changes in the preferred local orientation. It is worthnoting that the physiological data, by itself, does not yield acoherent set of stripe borders, for there are some transitionsinternal to stripes, and some stripe borders lacking any suchtransition. The final borders that were used were thus histologicalones, tightened by physiological criteria. There was one exception,where the “thematic” functional border of a stripe occurred outsidethe histological marginal zone (case SP34, noted in the legend toFig. 10). In this circumstance, it was deemed most logical to allowthe functional border to override the histological one, since the aimof the exercise is to examine visual topography of separate func-tions (and since there is always the possibility of minor, unrecov-

erable error in electrode track reconstruction). In other words, thehistological borders may serve as proxies for some functionaltransitions that we may have missed (due to our limited stimulusrepertoire), but should not override those that emerge plainly.

Overlapping representations from stripe to stripe

How can we be sure that each set of stripes contains a continuousand unbroken visual map? We develop a number of indirect testsbelow but, where there are sufficiently rich recordings from singlestripes, the simplest test is to check that aggregate fields recordedin successive stripes of the same type are not too isolated fromeach other. Fig. 2 shows an example: five penetrations madeparallel to the axis of the stripes, in which the most medial andlateral recordings were assigned to thick stripes. The aggregateRFs of these two thick stripe locations, roughly one cycle apart, arevirtually juxtaposed. Each might be considered as a sample from adiscrete point in the course of a cycle and, although there is nodirect overlap, the gap of “unrepresented” space between them istiny. Thus, at least in this part of V2 in this animal, little or noregion of visual space is likely to escape a “thick stripe” analysis.The same conclusion pertains for two successive interstripes,whose aggregate RFs actually show substantial overlap. The re-maining penetration was at a thin0interstripe border. It was theonly one to display wavelength selectivity, and its fields overlapped those of all the other penetrations, suggesting—asanticipated—that there is substantial overlap in the visual coverageof separate functions within a cycle.

Table 1. Physiological properties of all stripe borders illustrated in Figs. 8–12a

Physiological Transition

Fig. Case

Border:K 0I0N0I0K

& depth From To CategoryHistologicalverification

8 SP03 I0K 1050 null Y8 SP03 K0I 1950 oriented nonoriented NT Y8 SP03 I0N 2750 nonspectral spectral T Y9 SP07 K0I 30001 oriented not recorded null Y9 SP07 I0N 5000 not recorded oriented null Y9 SP07 N0I 5850 nonoriented oriented T Y9 SP07 I0K 6450 null Y9 SP07 K0I 7650 direct nondirect T Y9 SP07 I0N 8350 oriented nonoriented T Y

10 SP34 N0I 1250 nonoriented; spectral oriented; nonspectral T N10 SP34 I0K 1950 null Y10 SP34 K0I 3250 varied oriented & nonoriented regular oriented. NT Y10 SP34 I0N 4250 oriented; nonspectral nonoriented; spectral T Y10 SP34 N0I 5250 nonoriented; spectral oriented; nonspectral T Y10 SP34 I0K 6050 nonoriented oriented NT Y11 SP42 I0K 650 nondirectional directional T Y11 SP42 K0I 3000 varied orientation (peri-horizontal) regular orientation (peri-vertical) NT Y11 SP42 I0N 4150 oriented nonoriented T Y11 SP42 N0I 5550 oriented; nonspectral nonoriented; spectral T Y11 SP42 I0K 6350 mainly nonoriented oriented NT Y12 SP43 K0I 1500 oriented nonoriented NT Y12 SP43 I0N 2200 nonspectral spectral T Y12 SP43 N0I 3150 spectral nonspectral T Y12 SP43 I0K 3850 oriented nonoriented NT Y12 SP43 N0I 9300 nonoriented; nonspectral nonoriented; nonspectral null Y12 SP43 I0K 9800 nonoriented oriented NT Y

aBorders are described by their medial0lateral stripes and recording depths. Physiological transitions are briefly described, andcategorized as “Thematic” (T) if in accord with general stripe characteristics. Nonthematic borders (NT) generally involve patches ofnonoriented cells in either a thick stripe or an interstripe. Null borders, with no recorded physiological discontinuity, were uniformlyoriented and nonspectral, unless specified otherwise. All borders (with one exception) coincide with histological margins of stripes.


All other topographic data came from penetrations orientedperpendicular to the stripes. Here, the sample obtained from eachstripe normally spans its full width. To compare across cases andnormalize for variations due to eccentricity, overlaps are expressedas a fraction of the local mean RF area. The analysis was per-formed separately for each eye, then averaged (Fig. 3). The mean

overlap over an interval of one cycle was 0.7 RFs, and samplesfrom pairs of thick, thin, and interstripes did not differ~F5 0.4,P . 0.5). Like the result in Fig. 2, this larger body of evidencesuggests that each set of stripes mounts an independent, unbrokenrepresentation of the visual field. As anticipated, samples at smallerintervals show progressively greater overlap: 1.2, and 1.6 RFs for

Fig. 2. (a) Case LV85: Five penetrations (arrowheads) were made parallel to the stripes, each traversing about 1 mm of V2 beforeentering V1. The pattern of stripes is obscure in the most superficial section (39), through layer 2, but gradually resolves through layers3 and 4 (sections 35 & 31). Only penetrations 2 and 6 are directly visible, as indicated by marking lesions (arrows). The bottom threesections (31, 25, & 21), shown at lower magnification, help to identify thick (K) and thin (N) stripes, by tracing the pattern throughto its excursion down the bank of the lunate sulcus, where stripes are easily distinguishable. Stripes in the region of the penetrationshad to be identified by the principle of alternation alone (signified by lower case lettersn & k!. (b) Receptive fields plotted in fivepenetrations made parallel to the stripes, close to the border with V1. The RFs belonging to each stripe are shown, shaded, against abackground of the outlines of the RFs recorded in all five stripes. These are “binocular average” fields, displayed as an equally weightedaverage of the fields recorded separately in the two eyes. Note the systematic increase in elevation, from left to right, as the recordingsites shift laterally, closer to central vision. Note also that in this, as in subsequent illustrations, that there are likely to be residual smallerrors (1 deg–2 deg) in foveal location.


the half-, and quarter-cycle data, respectively. The half-cycle dataare expanded (Fig. 3), to compare the overlap between thick andthin stripes, and between pairs of interstripes separated by either asingle thick or thin stripe. The values obtained did not differsignificantly ~F5 1.0, P . 0.1). Notably, the overlap betweensuccessive interstripes is similar to that between mixed pairs ofthick and thin stripes, and exceeds the overlap of thick to thick orthin to thin. So, if the two interstripes in a cycle serve duplicatefunctions, they would seem to cover the visual field in greaterdepth than either set of thick or thin stripes.

An alternative model, prompted by findings in Roe and Ts’o(1995) and Shipp and Zeki (2002), is that the interstripes areweakly asymmetric, each being biased in character toward the darkstripe on its medial margin. The final component of Fig. 3 lendspartial support, showing that the overlap between immediatelyadjacent stripes is also weakly asymmetric. To be more stringent,the comparison is restricted to thick and thin stripes lying eitherside of the very same interstripe, and shows a slightly greateroverlap of an interstripe with its medial neighbor (but more evidentfor thick medial neighbors than thin); a one-tailed, paired,t-testyields t 5 1.8, P , 0.05.

Are cycles of stripes discrete units of function?We might picture a single cycle of stripes as a discrete unit of

function, that is, one that contains all the neural components

necessary for processing a discrete sector of the visual field. If adiscrete cycle were to be a physiological reality, there should becorresponding sharp discontinuities in visual representation, whereone cycle gives way to the next: most adjacent stripes should showalmost 100% overlap in their visual representations but, at a givenpoint in the cycle, repeated from one cycle to the next, the overlapshould be closer to zero. The result of Fig. 3 outlaws this picture,because it shows uniform stripe–stripe overlap across the cycle; inother words, there is no fixed point at which one discrete cycle canbe said to end, and another to begin. Two simple conclusionsfollow; firstly, that a single cycle is a purely notional entity, witharbitrary start and end points; and secondly, that the visual seg-mentations achieved by each set of stripes are imperfectly regis-tered, or out of phase with each other. We refer to the latter as a“phase-shifted” model.

The cycle and the linear point image

Although a cycle of stripes may have arbitrary start and end points,the dimensions of a cycle should still be commensurate with the“grain size” of visual analysis in V2. Hence we expect a notional“point” in the visual field to be represented, in all modalities(motion, color, etc.) across a stretch of cortex no smaller in extentthan a single cycle. In other words, we expect that the size of thecortical point image (McIlwain, 1986) should exceed the length ofa single cycle in the axis perpendicular to the stripes.

It is conventional to calculate a linear point image as (Dowet al., 1981)

Point image (mm)5 Aggregate RF size (deg)

3 magnification factor (mm0deg).

Or, using cycles as the unit of distance

Point image (cycles)5 Aggregate RF size (deg)

3 magnification factor (cycles0deg)

5aggregate RF size (deg)

Shift per cycle (deg).

Fig. 4 illustrates this relationship schematically. Fig. 5 shows itsdetermination using RF size, scatter, and topographic shift mea-sured over the course of a single cycle. The shift per cycle is thenet change in eccentricity of RF centers recorded while traversingone cycle of stripes (identified histologically); if recording nearand parallel to the V10V2 border this corresponds to a shift alongthe VM. And, if cycles are not discrete, it should not matterbetween which specific points the cycle is measured (e.g. mid-K tomid-K, or N0I border to N0I border, etc.). Aggregate RF dependson the size and scatter of RFs, but its specific definition issomewhat arbitrary. Here, we noted the vertical span that includes95% of RF scatter, and calculated aggregate RF size as the sum ofthis value and the mean RF size. Values were calculated in eacheye, then averaged.

The full data from nine separate cycles (recorded in eighthemispheres) are given in Table 2, variations in cyclic shift andaggregate field size being illustrated graphically in Fig. 6. Some ofthis variability reflects individual differences, but it can also beseen that the cyclic shift and aggregate RF size are generally largerat the higher eccentricity (measured in number of cycles from the

Fig. 3. The overlap between aggregate receptive fields, calculated as thearea in common to both aggregate fields, divided by the mean RF sizethroughout both samples; values are obtained separately for each eye, thenaveraged. The leftmost triplet of columns shows overlap at intervals of 1.0,0.5, or 0.25 stripe cycles. The next set of columns shows full cycle overlapsampled between interstripes (I–C–I) thick stripes (K–K) and thin stripes(N–N). The middle set of four columns shows four sets of half-cycleoverlaps: K–N is thick to lateral neighboring thin stripe; I–(N)–I isinterstripe to lateral neighboring interstripe, separated by a thin stripe; N–K& I–(K)–I similar. The final two pairs of columns are quarter-cycleoverlaps (i.e. adjacent stripes)—the members of each pair show the meanoverlaps made by thick or thin stripes with the specific interstripe sand-wiched between them. Numbers above each column are sample size; errorbars are6 SEM.


lateral apex of V2, which coincides with central vision). The toppart of Fig. 6 shows the ratio of aggregate field size to the cyclicshift of each cycle, giving the point image in units of cycles. Thevalues obtained ranged from 0.7 to 2.5, with a geometric mean of1.43. The mean value is sufficiently close to unity to imply that thepoint image is indeed commensurate with the size of one cycle.And, because it slightlyexceedsunity, we can reiterate that suc-cessive cycles seem to map overlapping segments of the visualfield, ensuring topographic continuity.

The nature of mapping within stripes

So far we have established that each of the three sets of stripessupports a continuous retinotopic map, and that the three maps areinterlaced with a shift of phase from one to the next. The lattersuggests some form of discontinuity in the maps at the interfacebetween stripes. We now proceed to evaluate this possibility, andto examine the nature of visual maps internal to a stripe.

Fig. 7 illustrates some of the schemes that we might entertain.Model A is the phase-registered model we rejected above; theothers are varieties of phase-shifted model. In model B, the phaseshift is introduced without any form of mapping internal to thestripe (each stripe has zero slope); the number of discontinuities isincreased four-fold but, on average, each one is four times smaller.Model C (a “ramp” model) eliminates the discontinuities by settingeach stripe to have an identical internal slope. Models A, B, and Call share constraints on the aggregate RF size (labelled “smear” inFig. 7): in order to close gaps in the visual field between succes-sive stripes of the same class, its magnitude must be no less thanthe visual size of the cycle; but furthermore, in order to provideuniformly dense coverage of the visual field, it should exactlymatch the visual size of the cycle. Hence, in each of models A, B,and C, smear is set equal to shift per cycle. Model D (“ratchet”)removes this constraint by setting the slope within each stripesufficiently steep to match the shift per cycle; so here the shift per

stripe and shift per cycle are of equal magnitude. This introducessharp discontinuities (switchbacks) between the maps of eachstripe, but the aggregate RF (or smear) is now free to adopt anysize, without inducing gaps or uneven coverage of the visual field;so, in this model, smear could conceivably differ across the threetypes of stripe.

Fig. 8 illustrates the construction of charts in the format ofFig. 7 from our RF data. Each of the stripes in this cycle (identifiedhistologically in Fig. 8b) appear separately, in a plot of eccentricityagainst electrode depth. Typically, if analyzed separately, the re-sults from each eye differ a little; this might, in part, reflect asystematic organization of retinal disparity between the two eyes,but for present purposes we treat it as topographic noise, probablycompounded by random error in plotting fields, and eye position.To reduce noise, we plot binocular-average eccentricity againstrecording depth, and show binocular-average RF outlines. Binoc-ular averaging slightly enhances the correlation between eccentric-ity and cortical distance, to yield the results we report (seeFigs. 9–12 for further examples). In brief, we compare the slope ofeach stripe to that of its parent cycle to determine which of themodels in Fig. 7 is most accurate, and whether the same modelapplies equally to all three stripe classes.

Overall, we have measured the gradient in eccentricity (“slope”)across 36 stripes from seven animals in which a single penetrationtraversed at least one full cycle, so permitting comparison of thelocal slope across each stripe to the slope across the cycle as awhole (see Fig. 13 and Table 3). In almost all cases (34036, 94%),eccentricity fell as the stripe was traversed medio-laterally, whichwe treat as a “positive” slope. Furthermore, a significant majority,29036 (81%) of these stripes had a slope which exceeded thatobtaining for the cycle as a whole~P , 0.0005, one-tailed, on thenull hypothesis that this fraction should be 50%). The proportionof steeper slopes was similar in each class of stripe. Table 4 detailssome control procedures, where we subjected other coordinates(e.g. polar angle; interocular disparity of eccentricity) predicted to

Fig. 4. A schematic plot of visual representation across several cycles of stripes to show the relationship between aggregatereceptive-field size and point image. The bold line shows the mean trend of RF centers, in the dimension perpendicular to the stripes;the shaded region on either side of the line indicates the extent of the local aggregate RF. The linear point image is the extent of cortexrepresenting a virtual point on the (vertical) visual axis. The diagram shows how the slope of the trend, that is, visual shift per cycleis equal to the quotient (aggregate RF size)0(point image).


bear no relation to the stripe architecture, to a similar analysis. Inall of these controls data from individual stripes behaved more likerandom subsamples of the parent cycle, so highlighting the stripes’particular relationship to the mapping of eccentricity.

Thus far, the analysis offers initial support to the “ratchet”model (Fig. 7D). Yet, as the various models demonstrate, there aremany potential combinations of the two factors—slope and smear—

that would endow a set of stripes with an unbroken visual map. Itis thus important to examine these factors more closely acrossindividuals, to see if they may differ between thick, thin, andinterstripes. Figs. 8–12 illustrate the prevailing tendency for themap within a single stripe to have a slope greater than that of thewhole cycle, and the associated discontinuities (“switchbacks”)between adjacent stripes. However, there are also instances of near

Fig. 5. Topographic trend and scatter for one cycle of stripes in V2 (case SP43). At left, the mean trend of RF centers (asterisks), asdetermined independently through the contralateral and ipsilateral eyes. The RF centerX andY coordinates are regressed separatelyon to recording depth along the electrode track, to yield estimates of the mean topographic location at each site (bold line) and scatter(the fine line linking each RF center to the projected location of that recording site). The central cross marks an arbitrary location(0.0 deg,24.5 deg) to aid interocular comparison of the slant and location of the mean trends. At right, scatterplot showing thedistribution of all RF centers about their projected location (the origin of the plot for each eye). The diagram yields estimates of thecyclic shift and vertical span of (95% of ) RF centers. It is pure coincidence that, for this example, both values5 1.0 deg in theipsilateral eye. For the contralateral eye, cyclic shift5 1.0 deg, 95% vertical span5 0.60 deg.

Table 2. Data for nine cycles of stripes in Fig. 6a

Case nEccentricity

(cycles)

ET distanceperpendicular

(mm)

Cyclicshift(deg)

Magnification(mm0deg)

RF size(deg)

95%scatter(deg)

AggRF

(deg)

Pointimage

(cycles)

SP34 32 4.000 3900 1.01 3.85 0.95 0.87 1.82 1.80SP36 31 4.125 4229 0.71 5.92 0.90 0.89 1.79 2.51SP07 25 4.250 3500 1.24 2.82 1.04 1.15 2.19 1.76SP35 30 5.000 3932 1.23 3.21 0.91 0.75 1.66 1.36SP43 40 5.125 3791 1.02 3.70 0.72 0.80 1.52 1.49LV85 63 5.125 4000 2.99 1.34 0.94 1.69 2.63 0.88SP07 30 5.250 5400 2.88 1.88 0.88 1.18 2.05 0.71SP42 57 5.250 4710 2.17 2.17 1.33 1.19 2.52 1.16SP03 31 5.500 3517 1.24 2.84 1.06 1.69 2.75 2.22

aEccentricity is the distance of the cycle center, in cycles, from the apex of V2. The point image size is calculated from RF mean sizeplus dispersion (i.e. 95% scatter) divided by the cyclic shift in visual eccentricity. Linear magnification (mm0deg) is based on thecorresponding distance along the electrode track (ET), i.e. the component perpendicular to the stripe axis.


continuity (fitting a “ramp” model), for example, between thethird, fourth, and fifth stripes in Fig. 12. Overall, there is sufficientcase–case variability in topographic organization that a brief in-spection reveals no ready distinction between the internal maps ofthick, thin, or interstripes. Our next step was thus to pool dataacross individuals, in order to form a picture of an “average” V2.Fig. 14 shows the result of this exercise, using the same format asthe models of Fig. 7.

The average V2 bears a close resemblance to the “ratchet”model (Fig. 7D). The slope of the map differs across the threeclasses of stripe, and the presence of switchbacks is obvious.However, the relative slopes are not set strictly by the relativewidths of the stripes, and they are all a little less steep thanpredicted. This means that, although the visual map is virtuallycontinuous across each set of stripes, scatter of RFs about the mean

slope might remain an important factor in ensuring overlap fromone stripe to the next of the same class—the key constraint that the“ratchet” model is designed to eliminate. The discrepancy betweenthe modelled and observed slopes is less marked in thick than inthin stripes, and least for the pair of interstripes on the left half ofFig. 14, which are treated as identical and sharing visual coverage.Alternatively, if the two interstripes are treated as distinct classes,and averaged separately (as for the pair at right in Fig. 14), it islogical to regard each as mounting independent coverage of thevisual field. The predicted slopes are now still steeper than theobserved interstripe slopes, the discrepancy exceeding that per-taining to thin stripes. We now evaluate these differences morequantitatively.

Slope, scope, and smear indices

We used these indices (see Methods for formulae) to assess therelative roles of mapping (stripe shift) and RF scatter and size, inspatial coverage. The slope index compares the shift across a stripeto the shift between adjacent cycles (cyclic shift). Hence the“ratchet” model would predict a slope index of 1.0 for each stripe(as shown in Fig. 7). The scope index includes, in addition, theeffects of RF scatter. If the slope index is less than 1.0, then thescope index should exceed 1.0 to eliminate gaps in coverage of

Fig. 6. Summary of the receptive-field topography in nine cycles, recordedin eight separate hemispheres. The diagram shows the aggregate RF sizewithin each cycle (shaded zones) in relation to the shift in eccentricity(indicated by the slope of the central bold line). These values are generallygreater at more medial recording locations (leftward—indexed here asnumber of cycles from the lateral apex of V2). The plots for each cycle arearbitrarily displaced in the vertical axis, to avoid overlap. The top part ofthe figure charts the ratioaggregate RF size: cyclic shift, which gives thesize of the point image in units of cycles; points (open circles) areregistered with the middle stripe0stripe border of their corresponding cycle.

Fig. 7. Schematic depiction of four alternative models for the topographyof field representation in V2 with respect to its stripes. The horizontal axisis cortical distance perpendicular to the stripes; the vertical axis is eccen-tricity. All models display the same cyclic shift, that is, the same displace-ment between equivalent points in adjacent cycles. A: Phase-registeredmodel; B: Phase-shifted model with zero slope intrinsic to a stripe. C:Phase-shifted (“ramp”) model with uniform slope across the cycle, toensure continuity from one stripe to the next (i.e. between immediatelyneighboring stripes). D: Phase-shifted (“ratchet”) model with steeper slopes,to ensure continuity from one stripe to the next of the same class. See textfor further details.


the visual field. A scope index5 2.0 implies that the visualterritory of a stripe is 100% overlapped by the pair of like,neighboring stripes (50% from one side, 50% from the other). Thethird, “smear,” index is most relevant to the “ramp” model, and

was compiled from RMS scatter and mean RF size, to record thedispersion of visual field coverage about a point in each stripemap. Models A, B, and C in Fig. 7 are all illustrated with smearindex5 1.0.

Fig. 8. (a) The receptive-field topography across one cycle of stripes incase SP03. Top: The binocularly averaged RFs belonging to each stripe(shaded) shown against the total field outlines for the full cycle. Middle:The topographic trend of the binocular average field centers (calculatedseparately for each stripe, as the regression of eccentricity on recordingdepth). The overall trend for the whole cycle is calculated from the sameset of receptive fields, but shown over a slightly longer distance, forclarity of presentation. From left-to-right, the penetration follows amedial-to-lateral direction. There is a gap in the recording sequence of500mm following a lesion at depth 2500. Bottom: RF properties of eachcell. Key: concentric circles—nonoriented; solid bars—orientation se-lective, slant of bar matches preferred orientation; dashed bars—orientation biased; x symbol—orientation not classified. Arrows indicateposition of lesions.(b) Identification of stripes for receptive fields shown in Fig. 8 (electrodetrack 2) and Fig. 16 (track 1). The two, parallel tracks are separated by1 mm along the stripe axis: Track 1, with 24 units in 2800mm, passesthrough the external margin of V2 into V1 (top); Track 2, with 32 unitsin 3900mm, skims the crown of the postlunate gyrus and just reaches intothe lunate sulcus (middle). The first recorded units are marked by whitearrowheads; dark arrowheads indicate track-marking lesions. The secondlesion in track 1 is in V1. The third lesion in track 2 marks the terminationof recording. Most of track 2 passes through layers 5 and 6; the light areajust beyond the third lesion is white matter. The top and middle elementscorrespond to the boxed region of the lower image, a composite of a pairof sections passing through more superficial layers of the lunate sulcus,and shown at lower magnification to facilitate stripe identification. Thereis an unmistakable sequence of K and N stripes in the depth of the sulcus,but toward its rim, medially (leftward), an adjacent pair of N and Kstripes undergo a bifurcation. The sibling stripes are provisionally iden-tified by maintaining the sequence of alternation (as signified by lowercasen andk!. Both tracks 1 and 2 intersect the most medial sibling, takento be a thin stripe.


We determined these indices for every stripe and Table 5reports the average value for each type of stripe (plus supportingdata). Let us first compare thick and thin stripes, which havesimilar slopes. The slope index is below unity for both classes ofstripe, but although the slopes are therefore not quite as steep aspredicted by the “ratchet” model, consideration of the standarderrors (Table 5) suggests that the difference is not significant. Thusthe ratchet model cannot be disproved. It is possible that themapping may also rely on scatter to achieve continuity and, in boththick and thin stripes, the scope index is comfortably in excess ofunity. Both sets of stripes should thus have a continuous distribu-tion of RF centers along the isopolar visual axis, with plenty ofoverlap from one stripe to the next of its class.

As above, data from the interstripes have been treated accord-ing to two alternative hypotheses: as if alternate interstripes arefunctionally distinct, or as if all interstripes are functionally equiv-

alent. For the former the interstripe data are pooled into separate Im

and Il categories, then analyzed like thick or thin stripes; data forthe latter are pooled across all interstripes (Ip), but each comparedto half the shift of the associated cycle. The outcome is that, treatedindividually, Im and Il stripes are not too dissimilar to each other,but are inferior to thin stripes in their visual field coverage.Nonetheless, each has a scope index slightly in excess of unity, sothere are no major gaps in the distribution of RF centers. Thismeans that, topographically, an alternate set of interstripes canmount a full coverage of the visual field—and hence there are nofirm topographic grounds for debarring the idea that the twointerstripes within a cycle might be differently specialized infunction. Alternatively, if treated as identical in function, thespatial coverage of the interstripes surpasses that of the thickstripes. Indeed, the slope index of the pooled data is about equal tounity, suggesting that the “ratchet” model is a reliable description

Fig. 9. The receptive-field topography across two cycles of stripes in case SP07. Conventions follow Fig. 8. There is a gap in therecording sequence of 2000mm at a depth of 3200 to 5200mm (rapid advance of electrode occasioned by onset of small monocularRFs at 3300, wrongly assumed to indicate that the electrode had passed from V2 into V1). The penetration traverses two full cycles,whose overall slopes are shown separately. Note reverse slope in second N stripe at a depth of 8350–9350mm. See Fig. 1 of thecompanion paper for these stripes’ anatomy.


of interstripe topography if these stripes do all perform equivalentfunctions.*

Finally, recall that for the “ramp” model (Fig. 7C), the con-straint is on smear, which must exceed the cyclic shift in order toeliminate gaps in field coverage. Smear is provided not only by RFscatter, but also by the bodies of RFs (which of course are not merepoints, but possess a finite area). The smear index is comfortablygreater than 1.0 in all types of stripe, so a “ramp” topographywould not be prohibited by inadequate RF size and scatter. Yet theramp model provides a poor fit to the data in general—as if theavoidance of local discontinuities, that it achieves, is unimportant.

Statistical comparison of stripes’ topography

The data summarized in Table 5 were formally tested for differ-ences between stripes, using a two-way ANOVA (factors of case,and stripe—K, Im, N, & I l ). The stripe width data (determinedfunctionally) gaveF3,155 7.4,P , 0.005, confirming the variationin width that is evident anatomically. None of the RF measures andnone of the three indices yielded so significant a result. The mostextreme were for RF scatter~F3,155 3.6,P , 0.05) and stripe shift~F3,15 5 2.9, P , 0.1) reflecting a higher degree of scatter, andshift, in thick stripes (Table 5). Therefore, the stripes we examined

were not formally distinct and it is evident that a larger sample sizemay be required for statistical confirmation of any topographicdifferences between them.

Analysis of switchbacks at stripe borders

The switchbacks of a “ratchet” model imply that the local func-tional domains have a degree of topographic autonomy from eachother. Is there any regular variation across a cycle, or localcorrelation between the size of a switchback and the sharpness ofany transition in RF properties? We measured the magnitude of theswitchback at all four classes of stripe borders (K0I, I 0N, N0I, &I0K), also noting whether there was an obvious local transition inRF properties (Table 6). Differences in switchback size were testedby using ANOVA across all four classes, and a specifict-testgrouping K0I and N0I in comparison to I0K and I0N (to test the“medial neighbor” hypothesis, that each interstripe has a closerfunctional association with its medial dark stripe). Neither test waspositive ~P . 0.5, andP . 0.1, respectively), so this procedureproduced no further evidence for asymmetry within the stripecycle. Equally, switchback size was not firmly correlated with thepresence or absence of a functional discontinuity (such as a changein wavelength and0or orientation selectivity at a thin stripe border)or whether the discontinuity was “thematic” (e.g. lack of orienta-tion selectivity at an interstripe border, for a “non-thematic” dis-continuity): borders with a thematic discontinuity had largerswitchbacks on average (Table 6), but the effect was not signifi-

*The slope index produced by this numerical analysis is an arithmeticmean, and hence slightly greater than the equivalent that can be derived byinspection of Fig. 14, which illustrates geometric means.

Fig. 10. The receptive-field topography across almost two cycles of stripes in case SP34. Conventions follow Fig. 8 (except that thevisual field map is shown as an inset, lower right). When defined functionally, the medial (leftmost) thin stripe includes two units,around depth 1000mm, that histologically are N0I marginals, and two further nonoriented units that, histologically, are I-stripe cells.Elsewhere, histological and functional borders are consistent. There is a small gap in the recording sequence of 300mm, postlesion,at a depth of 3100mm. See Fig. 3 of the companion paper for these stripes’ anatomy.


cant~P . 0.1). It is worth noting that functional continuity in ourdataset is not a guarantee of functional continuity at the stripeborder in question, since we did not test all possible stimuli. Acrossall stripe borders, the grand mean switchback size was 0.44 deg,approximately 40% of the mean shift per cycle.

Stripe substructure

Stripes themselves are composed of different functional cell types,a functional substructure that may possess its own subordinatetopography. In general, our sampling was too coarse to support arigorous analysis at this smaller scale, but some individual exam-ples, where we encountered runs of cells with similar selectivity,are worth examining. Fig. 15 reexamines a track with specializedsubdivisions of the initial thick stripe and interstripe. The keyfeature is a run of six successive directional cells on the medialedge of the thick stripe, showing a 1.9-deg shift in eccentricityover 550 um. The shift over the whole cycle was 2.2 deg, so thissmall group of directional cells, by itself, has a slope index of 0.88,comparing favorably to the slope index of the thick stripe as awhole, 0.26 (the remainder of the stripe undergoes a topographicreversal). Notably, though, the preferred direction of each cell wasnot uniform, so we are still some way from demonstrating com-plete coverage for any specific direction of motion. Pursuing this

theme, the rest of the thick stripe, and the next interstripe, aredivided into stretches of similar tuning specificity—but for orien-tation, not direction. These groups cover rather smaller segmentsof field (0.4 deg or less), but the general pattern is suggestive ofmultiple component topographies for the representation of eachorientation. The final example comes from a thin stripe. It wasrecorded in case SP03 in a penetration that, failing to traverse awhole cycle (Fig. 8 part 2), has not so far figured in the analysisof topography. The 12 units in this sequence provided severalsmall runs of similar wavelength tuning (Fig. 16—see legend fordetails). Again, there are switchbacks in the mapping of eccentric-ity, a sign perhaps that each subcomponent has an independenttopography. The shift within each group is as much as 1.0 deg, anappreciable fraction of the likely, overall shift per cycle.

Discussion

Many cortical areas may have a modular construction, but no-where is this more emphatic than area V2, whose striped archi-tecture spans all layers and can be visualized by studies ofhistochemistry, connectivity, single-unit physiology, and func-tional imaging (Peterhans, 1997; Roe & Ts’o, 1997). In manyways, the modules of V2 continue the specialized functions of theirantecedents in V1. But if V2 is to function as more than the sum

Fig. 11. The receptive-field topography across one cycle of stripes in case SP42. Conventions follow Fig. 8. See Fig. 15 for a finergrained analysis of the initial K and I stripes. See Fig. 2 of the companion paper for these stripes’ anatomy.


of its parts, there must be inter-modular interactions. The anatom-ical substrates for such activity are known to exist (Shipp & Zeki,1989; Levitt et al., 1994; Malach et al., 1994). The aim of thispaper is to explore the way the separate modules fit together,locally, to make up a global area; it can be instructive to comparewhat is actually observed with hypothetical alternative modulararchitectures. The underlying thesis here, as elsewhere, is that thekey to any “global” function of V2 lies in the interaction of itsspecialized modular operations.

Concepts of multiple representation

Contingent upon the fact that stripes are differently specialized isthe notion that each set should mount a full, independent coverageof the visual field. Even if virtually axiomatic, this is the obviousstarting point in the examination of topographic data. The simplesttest is whether the aggregate fields recorded from stripes at aninterval of one cycle overlap with each other. Almost invariably,they do; furthermore the allocation of visual space to each stripeseems relatively efficient, as the amount of overlap is typically lessthan the area of an average receptive field.

We performed two further analyses to complement this result.These used linear measures of mapping along the isopolar visualfield axis that runs perpendicular to the stripes. Firstly, poolingdata from a single stripe cycle (a thick, a thin, and two interstripes),we calculated the size of the linear point image (McIlwain, 1986)in several individuals and showed that, on average, it exceeds thedimensions of the cycle. Thus, a single visual point is processed

throughout the course of a cycle: were this not generally the case,one would begin to suspect that some points in space might beomitted from some subset of processing operations, wherever thedimensions of the cycle exceeded the point image in question.Secondly, we pooled data across thick stripes, thin stripes, etc.from different individuals, for separate analysis of the mapping ofvisual space by each cycle element. We calculated what we havetermed a “scope index”, in order to compare the map in each typeof stripe to the map in its parent cycle. Unlike the above twoprocedures, the scope index ignores RF area0size, and measuresonly the distribution of RF centers, parameterized into componentsof “map” and “scatter”. A scope index in excess of 1.0, which wasthe result in all three classes of stripe, indicates that the spread ofRF centers across a single stripe is sufficient to match the shift invisual location from one cycle to the next (a “cycle-step”), result-ing from the global map in V2. And, if this is true for any givenstripe in relation to its parent cycle, there should be no gapsbetween the coverage of that stripe and the next one of the sameclass, residing in the adjacent cycle.

Maps within maps

At the next level of analysis, it has to be considered that stripes areundoubtedly coalitions of distinct functions. Within thick stripes,for instance, there are instances of orientation, direction and stereo-depth sensitivity (Hubel & Livingstone, 1987; Peterhans & von derHeydt, 1993; Roe & Ts’o, 1995)—and each must be expressedcontiguously across the visual field. In turn, a map of directions

Fig. 12. The receptive-field topography in case SP43. The electrode traversed a single cycle of stripes before entering V1, and thencrossing white matter before reentering V2 within the posterior bank of the lunate sulcus. The second K stripe of the first phase isincompletely sampled; the second phase of V2 begins in an N stripe, about 5.5 stripes distant. Conventions follow Fig. 8. There is agap in the recording sequence of 350mm, postlesion, at a depth of 2050. See Fig. 4 of the companion paper for these stripes’ anatomy.


must include components tuned to each different direction. It is notnecessary to enumerate all possible elemental maps to concludethat a single penetration cannot hope to monitor them all indepen-dently. Therefore, we have to ask how satisfactorily a limited

Fig. 13.Summary of stripe slopes in comparison to their parent cycles. The greater variability of the former is evident. In contrast toFigs. 8–12, the data shown here are corrected for oblique electrode trajectories that are not exactly at 90 deg to the stripes, so that the“slope” corresponds to the linear inverse magnification factor in the axis perpendicular to stripes, concerning change in eccentricity.

Table 3. Summary of stripe slope dataa

(A) Stripe type (B) Probability

K I N P . 0.05 P , 0.05 Total

Steeper 9 13 7 15 14 29Shallower 3 2 2 5 2 7All 12 15 9 20 16 36

aGiven are numbers of stripes with slopes steeper, or shallower than theslope of the cycle in which they occur, classified (A) as thick (K), inter (I),or thin (N); (B) according to the significance (i.e. P-value arising from a2-tailedt-test) for the difference in slope between each stripe and its parentcycle. Excluded are stripes with fewer than five recorded RFs, and stripesfrom subtotal cycles.

Table 4. Details of control analysisa

(A) Slope (B) Probability

Steeper Shallower P . 0.05 P , 0.05

Eccentricity 29 7 20 16y coordinate 29 7 21 15polar angle 17 19 30 6x coordinate 16 20 26 10x disparity 18 18 29 7y disparity 17 19 31 5e disparity 17 19 30 6

aComparison of eccentricity (andy coordinate) with other elements oftopography that are not predicted to be organized in relation to the stripearchitecture of V2. The latter include the binocular mean polar angle andx coordinate, and interocular disparity ofx, y, ande (eccentricity) coordi-nates. (A) relative slope: comparison of a stripe to its entire parent cycle;for x, y, ande disparity, the parent cycle slope is zero; for polar angle andx coordinate, the parent slope is nonzero where the electrode track is notfully perpendicular to stripes. (B) numbers of stripes with slopes that do notdiffer from the parent cycle slope~P . 0.05), or are significantly steeperor shallower~P , 0.05) (2-tailedt-test). In both respects, (A) and (B) the“control” elements of stripe topography are essentially random.


sample (e.g. thick stripe RFs) can represent a compendium ofseparate maps. The analyses we performed would work best if allthe component maps are freely interspersed at a cellular level. Thisscheme supposes one “master” thick stripe map, constituting mul-tiple directions, disparities, and orientations at each point. As theelectrode traverses this map, the functional class that is sampledvaries randomly, but the RF locations of each class stand in foreach other and the resulting plots of mapping and scatter are notsystematically distorted. This scheme represents a hypotheticalideal, for it is known that functions do cluster on a subordinate

scale (Tootell & Hamilton, 1989; Ts’o et al., 1990; Malach et al.,1994; Roe & Ts’o, 1995). In our experiments, RF location wassampled at intervals of 100mm, so the scale of clustering has to beseveral fold larger in order to potentially distort the emergent thickstripe map. If this was generally the case, we would expect to seeit in the RF data, in the form of regular offsets, or reversals ofslope, within single stripes. Such features have been reportedpreviously (Roe & Ts’o, 1995), and there were occasional clearexamples in our own data (Figs. 15 and 16): in Fig. 15, forinstance, an unusually long run of directional cells yields a localanomaly in topography, such that the total thick stripe sequence isbetter modelled as separate components. In general, however, thisis not characteristic of our results, and it would seem that the scaleof functional clustering within stripes is not so much coarser thanthe scale of our sampling.

The local construction of V2

The borders of individual stripes are notoriously indistinct. Even inoptimally stained cytochrome oxidase tissue, it is essentially arbi-trary to locate a border to better than6100mm. Are the functionalboundaries between stripes equally blurred? It is worth recalling,in this context, that Roe and Ts’o (1995) reported sequences ofcolor cells spanning a greater width than the corresponding histo-logical thin stripe, apparently loosening the correlation betweenhistology and physiology. In the companion paper, marginal zonesbetween stripes were treated as a separate category. But this wasprimarily to safeguard the properties of stripe “cores” from con-tamination by uncertain placement of the border, possibly com-pounded by limitations in electrode track reconstruction. For thepresent analysis it was necessary to dispense with marginal zones,and we have segmented the recordings using a combination ofhistological and functional criteria to discern stripe boundaries. Inabout 80% of cases, there was some evident physiological discon-tinuity coincident with the histological border; for example, the on-set of wavelength or orientation selectivity, or perhaps a pronouncedshift in the preferred orientation. Some of these physiologicaltransitions (which we labelled “non-thematic”) were discordantwith the major characteristics of the stripes in question. In theremainder of cases, the division was purely histological, as thephysiology appeared uniform in the factors we tested. A physio-

Fig. 14. Topography of an “average” V2, compiled from the full cyclesillustrated in Figs. 8–12. The slopes, shifts, and width for each stripe shownhere are the geometric means of these values, which conserve the relation-ship [mean slope]5 [mean shift]0[mean width]. The smear (depicted bythe diffuse grey band) is set equal to the mean RMS scatter either sideof the central trend line). The slope in all three types of stripe is greaterthan that pertaining across the cycle as a whole, leading to obviousdiscontinuities—“switchbacks”—between stripes. But the stripe slopes arenot quite as large as those predicted by a “ratchet” model (Fig. 7D), inwhich each stripe is credited with a shift equal to the whole cycle shift. Theaverage data, and the modelled slopes, are shown in two variants: at left,equivalent (pooled) interstripes (Ip) , dividing visual coverage equallybetween them; at right, distinct interstripes, derived from separate averag-ing of the Im and Il components (and hence with different widths, shifts,and slopes), and mounting separate visual coverage.

Table 5. Mean values for the data underlying the “average V2” (Fig. 14),and supporting the calculation of slope, scope and smear indicesa

Thick Im Thin Il I p

Slope (deg0mm) 0.91 0.83 0.94 0.54 0.68Stripe width (mm) 1209 731 847 773 752Stripe shift (deg) 0.94 0.55 0.78 0.42 0.49Mean RF size (deg) 1.06 1.07 0.87 1.05 1.06RMS scatter (deg) 0.45 0.30 0.34 0.28 0.29Slope index6 SEM 0.946 0.21 0.616 0.21 0.836 0.31 0.546 0.28 1.146 0.33Scope index6 SEM 2.006 0.61 1.236 0.38 1.636 0.62 1.186 0.52 2.416 0.61Smear index6 SEM 2.336 0.94 1.716 0.44 1.766 0.63 1.806 0.61 3.516 0.72

aStripe widths are the change in electrode depths between physiological transitions, corrected for nonperpendicular electrode angles.Shift values are shifts in eccentricity, and slope is inverse magnification. Ip is pooled interstripe data, equal to the average of Im andI l for receptive-field data, and the sum (i.e. twice the average) of Im and Il for the indices. Note: (i) The table shows arithmetic meanvalues, that are uniformly greater than the geometric mean values illustrated in Fig. 14; (ii) these are mean absolute values, i.e. thenegative shift and slope of one thin stripe in this sample is treated as positive.


logical transition may have been present in a nontested modality,disparity selectivity being one obvious example (Hubel & Living-stone, 1987; Peterhans & von der Heydt, 1993; Roe & Ts’o, 1995).

The aim of the precise segmentation was to search for visualswitchbacks at functional0stripe borders, as predicted by a “ratchet”model of stripe topography (see Fig. 7D), in which the gradient ofthe map across each stripe exceeds the gradient of the global map.

Having noted previously, the qualitative basis for a “ratchet”topography in V2 (Zeki & Shipp, 1989), we have now subjected alarger dataset to a more systematic analysis (e.g. averaging mon-ocular data to reduce noise and resolving topographic shifts intoiso-eccentric and isopolar vectors). The procedure differs from thatused by Roe and Ts’o (1995) who plotted only a scalar quantity, thevisual displacement of successive RFs from the first field recorded.

Table 6. Data for magnitude of switchback at 25 stripe borders, grouped (A) by stripe type;(B) by the presence/absence of an associated functional discontinuity; and(C) by the presence/absence of an associated “thematic” functional discontinuitya

Switchback (deg)Stripe border(medial0lateral) n

% Functionaldiscontinuity

(%)

% “thematic”discontinuity

(%) Mean, SD

A: thick0inter 5 100 20 0.46, 0.58A: inter0thin 6 100 100 0.52, 0.38A: thin0inter 7 86 86 0.44, 0.28A: inter0thick 7 57 14 0.33, 0.31B: mostly inter0thick 4 0 0 0.38, 0.21B: mixed 21 100 67 0.45, 0.42C: thick0inter & inter0thick 7 100 0 0.36, 0.52C: mixed 14 100 100 0.49, 0.35

aA “thematic” functional discontinuity is one that might be predicted on the basis of the stripes’ gross functional characteristics.Note: These are mean absolute values, discounting the direction of shift between stripes.

Fig. 15. A reexamination of the topography of the initial stripes in case SP42, at a higher level of resolution. Units 1–5 (featuring 3wavelength tuned cells) belong to an interstripe, that was not sampled across its full width. The subsequent thick stripe and interstripehave been segmented according to the tuning and specificity of cell groups. The thick stripe has three segments K(a), K(b), and K(c)delineated by grey-shaded columns. The second I stripe has two segments I(a) and I(b). Notable are units 6–11 in the K stripe, a groupof directionally tuned cells with a topography distinct from their neighbors; the other groups (12–18 & 20–27 in the K stripe, 29–33& 34–39 in the following I stripe) are segmented on the basis of similarity of preferred orientation. These subgroups have preferredorientations within spans of 60 deg, 60 deg, 30 deg, and 30 deg, respectively.


They were thus able to diagnose the presence of visual disconti-nuity across stripe borders, without further characterizing thedetails of topography. Our own analysis finds that stripe bordersare particularly associated with breaks in the representation ofeccentricity, and that these are significantly greater than any dis-ruption in the representation of polar angle, for instance, or dis-continuity in interocular disparity.

The size of switchbacks is related to the gradient of the submapacross stripes. We measured the latter using the “slope index”(which discards RF scatter and compares the shift in RF locationacross a stripe to that across its parent cycle). Ideally, the ratchetmodel predicts a slope index of 1.0 in each stripe, and switchbacksequal to 50% of the cycle step on average. The mean values forthese parameters, across all stripes, were 0.97 and 40%. Variationbetween the three classes of stripe was not statistically significant.However, it is worth noting that the slope index of interstripesslightly exceeds 1.0, if the pair within a cycle are treated asfunctionally equivalent with equal shares of visual representation(and hence their internal map compared to half a cycle-step); thequestion of whether interstripes are, in fact, identical in function isconsidered in the companion paper (Shipp & Zeki, 2002). Themean slope indices of thick and thin stripes were below 1.0, whichcould mean that the submaps of these two classes are partiallyreliant on RF scatter to achieve visual continuity. However, theshortfall in slope index was not great, and it is worth noting thatthe general effect of any interference from multiple submappingwithin a stripe is to boost scatter and reduce the estimated slope ofa single submap (the thick stripe reanalyzed in Fig. 15 provides anobvious example). On balance, we feel that the ratchet modelprovides a good fit to our data, and should not, on this evidence,be rejected in favor of more complex alternatives.

Typically, therefore, we observed both functional and topo-graphic discontinuities at stripe borders. This pattern of organiza-tion is reminiscent of (cat) V1, where fractures in the local maps oforientation tend to coincide with steeper local topographic gradi-ents, but where regions of continuity in the representation oforientation also tend to be more uniform in their spatial locations

(Das & Gilbert, 1997). Although the functional discontinuities inV2 may be intermodal (e.g. from color to orientation) as well asintramodal (one orientation to another), it is generally true in bothV1 and V2 that the fractures in functional and topographic mapscoincide. It is noteworthy that theoretical models for developmentof multidimensional maps across a two-dimensional cortical sur-face based on the original Kohonen algorithm (Kohonen, 1982)did not express this property: instead, these models predicted thatshifts in orientation and in spatial coordinates would be anti-correlated (Durbin & Mitchison, 1990; Obermayer et al., 1990;Swindale & Bauer, 1998). In a similar vein, there is no theoreticalobstacle to a perfectly smooth (“ramp”) model of V2 topography(see Fig. 7C), that can deliver full visual coverage to all stripeclasses without fracturing the global visual map along stripeborders. If these models are inaccurate, it may be because they lacka Hebbian-like element in the determination of local circuitry, onethat acts to promote links between RFs of similar response selec-tivity and spatial location (Mitchison & Swindale, 1999). Forinstance, a more recent model of the results of Das and Gilbertuses rules governing the implementation of intrinsic connections(e.g. connections between like oriented units) to simulate thecortical map in V1 (Ernst et al., 1999). The basic idea is that thedeterminants of synapse formation may act to stabilize, rather thandispel, discontinuities in developing cortical maps, perhaps en-abling initial fractures in one system to spread to another.

In conclusion, therefore, one implication of the ratchet modelis that fuzzy cytochrome oxidase stripe borders (our “marginalzones”) do not appear to be functionally significant features ofthe stripe architecture: we have no evidence that the interfacebetween stripes is a zone with a special set of properties, thatmight be particularly significant with regard to integration ofneighboring functions. Rather, any integrative actions wouldseem to be conducted across the body of stripes (and evidentlythis must be true of any interactions of thick and thin stripes,which commonly do not abut). Pursuing this train of thought,we switch our attention to the global, rather than local, charac-teristics of a striped architecture.

Fig. 16. Possible subsegmentation of a thinstripe, according to spectral tuning. Conven-tions follow Figs. 8 and 15. Units 3–7 allshowed a preference for LW light; units 10–13comprised two units with a preference for MW,and two with a preference for SW light. Thesetwo sequences display a typical switchbacktopography, as if representing separate visualmaps. Units 14–15 also had LW preference;the intervening units 8–9 were not spectrallytuned. The subsequent interstripe appears tohave a featureless, “flat” topography.


The global construction of V2

The basic idea to be examined here is that the striped architectureof V2 represents a “design” in which the multiple maps, beinginterlaced only along one axis of V2 (the axis parallel to the V1border or, in visual field terms, the isopolar axis), exert a conse-quent anisotropy in the isopolar and iso-eccentric magnificationfactors, in the overall shape and dimensions of V2, and in itsinternal and external relationships. This involves a working as-sumption that the design of V2 is uniform throughout the cerebralhemisphere—a notion that has yet to be proven since most studiesof topography concern only the relatively central zone locatedwithin the lunate sulcus.

Magnification factorsIt is apt to set the scene by analogy to V1, whose interlaced

ocular-dominance (OD) stripes should give rise to an anisotropicglobal map—with magnification perpendicular to OD stripes dou-ble that parallel to stripes—unless the map internal to an OD stripeshowed some compensation, that is, a relative compression of themagnification across its width (Hubel & Freeman, 1977; Hubel &Wiesel, 1977). From their 2-deoxyglycose (2DG) retinotopic data,Tootell et al. (1988) concluded that such compensation was eitherabsent, or at best partial, since the overall cortical representationwas certainly greater in the dimension perpendicular to OD stripes.This concurs with the earlier finding of Van Essen et al. (1984) thatthe local isopolar to iso-eccentric magnification ratio is close to 2,along the inferior and superior VM (where OD stripes tend to beorderly and arranged perpendicular to the V10V2 border), but notalong the HM (where the arrangement is more jumbled).

The simplest model of V2 would be that the three-fold remap-ping, expressed by its cytochrome stripes, triples the magnificationfactor for the isopolar versus iso-eccentric axis. A departure fromthis expected 3:1 ratio could imply (1) that unitary functional mapsinside a stripe are not isotropic, or (2) that there is additionalremapping internal to stripes, acting to distort the 3:1 ratio. Pre-vious estimates of the isopolar to iso-eccentric ratio of magnifica-tion factors are very inconsistent: 1.5:1 reported for V2 in Cebusmonkey (Rosa et al., 1988) and 6:1 for the macaque (Roe & Ts’o,1995).

The present data are largely in agreement with the earlier report(Rosa et al., 1988). The issue of different species is probablyunimportant, given that V2 in Macaca and Cebus are approxi-mately equal in size and dimensions (Rosa et al., 1988). We findan average isopolar magnification of 3.1 mm0deg for dorsal V2,over an eccentricity range of 2–5 deg. Rosa et al. (1988) summa-rize isopolar magnification according to the equation:

M 5 10.31~eccn!21.04.

This givesM 5 3.29, and 2.80 mm0deg at eccentricities of 3.0 degand 3.5 deg, respectively—effectively an identical result. We didnot attempt to measure iso-eccentric magnification directly, but itis simple to estimate it in principle from the quadrantic map of V2,running between the HM and VM. All we need to know is thewidth ~w! of V2, which is about 10 mm on average [about 8–9 mmon flatmounted cortex (Olavarria & Van Essen, 1997), so about10 mm in reality, allowing for histological shrinkage]. Hence,

Magnification5width of V2

90 deg arc of iso-eccentric perimeter

5w

0.5{p{ecc.

Predictions for iso-eccentric magnification calculated in this wayare compared with the values determined by Rosa et al.’s empiricalformula in Table 7, showing very good agreement. At 3.5-degeccentricity, for instance, the value is about 1.8 mm0deg, so ourdirect estimate of the isopolar : iso-eccentric ratio of magnificationfactors (at 3.5-deg eccentricity) is 3.0801.825 1.70

Roe and Ts’o (1995) report values for iso-eccentric (inverse)magnification of 1.5–2 deg0mm (i.e. an along-stripe magnificationof 0.7–0.5 mm0deg). This estimate was derived from a single pairof electrode tracks, 1 mm apart, both of which passed across a thinstripe and an interstripe. However, at a separation of 1 mm alongthe length of the stripes, the distance between aggregate RFs islikely to be influenced by local map distortions accompanyingsubstripe clustering of function. Certainly, a value of 0.7 mm0degseems to underestimate magnification in the iso-eccentric axis—implying for instance, a total width of about 4 mm for V2 at aneccentricity of 3.5 deg, according to the simple formula above. Afurther consequence is the notion of a 6:1 asymmetry in isopolar toiso-eccentric magnification, stemming from their magnificationacross a stripe (1.0–1.5 mm0deg) being approximately twice thatalong a stripe: Roe and Ts’o assumed that three interleaved iso-tropic maps would yield a 3:1 ratio, doubling to 6:1 if there is atwo-fold internal stripe anisotropy.

An expansion of magnification in the axis across a single stripewould be unexpected, and might imply a further remapping offunction in this dimension (i.e. additional to that between stripes),as Roe and Ts’o suggest. Previously, Rosa et al. had adoptedprecisely analogous, but opposite reasoning, in a model stipulatingremapping of separate functionsalongstripes, in order to accountfor the global magnification ratio being less than 3:1, that is,almost 1.5:1. Both models assume that a submap inside a stripe hasisotropic magnification, but there is no compelling reason that thismust be so. We can confirm a global magnification anisotropy ofaround 1.5:1, but do not believe that it provides a firm constraintover the order, geometry or isotropy of functional maps internal tostripes.

The asymmetric dimensions of V2 andits external relationshipsIf the width of dorsal V2 is 10 mm, its length is about 4–5 times

greater (Olavarria & Van Essen, 1997). Is this asymmetry in theoverall dimensions entirely due to remapping between stripes, and

Table 7. Iso-eccentric magnification over the range 2–6 dega

Iso-eccentric magnification factor(mm0deg)

Eccentricity(deg)

(a)Empirical formula

(b)Schematic formula

2.0 3.47 3.183.0 2.26 2.123.5 1.92 1.824.0 1.66 1.595.0 1.31 1.276.0 1.08 1.06

a(a) according to the empirical formula of Rosa et al. (1988)M 5 7.23~ecc!21.06;.(b) according to the formulaM 5 2w~p{ecc!21, wherew 5 width of V2,usingw 5 10 mm (see text for explanation).


a consequent anisotropy of magnification that is minimally 1.5-fold? Integration of Rosa et al.’s formula for isopolar magnifica-tion (cited above) over the range 1–60 deg, gives about 42 mm;add 3–4 mm for the central 1 deg and the total length roughlymatches the anatomical measurement from flatmounted tissue.However, even if magnification in the isopolar and iso-eccentricdimensions were equal, the overall dimensions of dorsal V2 wouldstill be notably asymmetric: integration of Rosa et al.’s formula foriso-eccentric magnification (imagine that it also describes isopolarmagnification) over 1–60 deg gives an overall length of about34 mm (after adding 4 mm for the central 1 deg). Hence, aquadrantic representation with isotropic magnification gives rise toan area whose long and short axes are at least 3:1 in relative length.It is fair to conclude that the striped architecture of V2 furtherdistends this shape, but not that it is the sole responsible factor.

The reason for the separation of the superior and inferiorquadrants may be that it permits V2 to adopt a concentric confor-mation around V1, as if to facilitate (by physical proximity)interrelationships between homotopic parts of the visual field inthe two areas—possibly at the cost of defacilitating internal rela-tionships in V2 (i.e. between points either side of the HM) (Allman& Kaas, 1974). This interpretation initially arose for the smoothbrained owl monkey—and the inference is still sounder in ma-caque, or Cebus monkeys, where cortical folding brings large partsof V1 and V2 into apposition on opposite walls of a gyrus. Thus,the subdivision of V2 into iso-eccentric stripes acts in harmonywith the quadrantic delocalization. A hypothetical alternative—isopolar stripes spanning the long axis of V2—would tend tocounteract the effect of the second-order transform, acting to swellthe width of V2 and to cut the length of its border with V1. Theargument might be extended to encompass V3, which has a similar(albeit mirror-image) visual field transform to V2 (Zeki, 1969;Newsome et al., 1986; Van Essen et al., 1986; Gattass et al., 1988).There is a great deal of recurrent circuitry between the three areas,and much simultaneous activity (Munk et al., 1995; Nowak et al.,1995; Schmolesky et al., 1998; Schroeder et al., 1998). For in-stance, the latency of activity in layers 4, 3, and 2 of V2 is similarto that of supragranular neurons of V1 (Nowak et al., 1995). Soone possible factor governing the global architecture of stripes inV2 could be a constraint on interareal connectivity, acting tomaximize the brain proximity of processing related to the samepart of space, and perhaps to facilitate transareal synchronizationof activity (Engel et al., 1991; Bressler, 1996; Traub et al., 1996).

Stripe geometry and internal relationshipsEqually, it is worth considering how the striped architecture

affects internal processing within V2. Many anatomical studiesagree that the (patchy) fields of intrinsic connections found tosurround a focus of tracer deposition are oval in shape, with thelong axis extending medio-laterally, that is, perpendicular to thestripes (Rockland, 1985; Cusick & Kaas, 1988; Amir et al., 1993;Lund et al., 1993; Levitt et al., 1994; Malach et al., 1994). Hencethe overall span of the field of connectivity may approximatesymmetry in its visual dimensions. The majority of connectionsoccur within 2.5 mm of the injection site, and they represent allpossible stripe–stripe interactions within the context of a singlecycle (Levitt et al., 1994; Malach et al., 1994). The absolute rangecan exceed 4 mm, commensurate with communication betweenadjacent cycles, for example, between successive thin stripes(Livingstone & Hubel, 1984; Cusick & Kaas, 1988). In principle,intrinsic connections between two stripes of the same class shouldcost more than connections along a single stripe, in terms of a

greater length of wiring (about 50%), and inherent timing delay,per unit of visual field traversed. Due to the ratchet topography ofV2, there is less iso-polar:iso-eccentric asymmetry in the shorterrange connections between dissimilar stripes.

Does this have any particular impact on visual function? If so,the prediction is for asymmetry between the isopolar and iso-eccentric dimensions of the visual field, manifest in homogenousinteractions (i.e. between similar stripes in adjacent cycles). Apotential outcome is that the neighborhood for local, cooperativeinteractions might be more extensive in the iso-eccentric axis.However, although cooperative effects involving motion and ste-reo are known to exist (Westheimer, 1979; Williams et al., 1986;Nawrot & Sekuler, 1990), their spatial geometry has not beenextensively tested. An obvious scenario might concern optic flow,since the conformation of stripes in V2 would seem to favor theanalysis of rotation (iso-eccentric motion) over expansion (iso-polar motion); yet the example is purely conjectural, as its eco-logical benefit is unclear, and V2 is not known to be a keycomponent in optic flow analysis. Also, it has to be noted that theiso-eccentric0isopolar visual geometry of stripes is less precise inventral V2 than dorsal V2: in ventral V2, some stripes curve awayfrom V1, to run almost parallel to the anterior border of V2 withV3 (Olavarria & Van Essen, 1997). In short, the evolutionaryimpetus provided by stripes that traverse the short, rather than longaxis of V2—or indeed, in preference to a blob0matrix pattern—isunclear. It could involve either the internal or external relationshipsof V2 (or both), but the question does seem worth posing, if onlyas a tool to probe the factors determining global cortical architecture.

Acknowledgments

We thank Ian Wilson for technical assistance. This work was supported bythe Wellcome Trust, UK.

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