ATTENTIONAL FUNCTIONS

IN DORSAL AND VENTRAL

SIMULTANAGNOSIA

John DuncanMRC Cognition and Brain Sciences Unit, Cambridge, UK

Claus BundesenUniversity of Copenhagen, Denmark

Andrew Olson and Glyn HumphreysUniversity of Birmingham, UK

Robert WardUniversity of Wales, Bangor, UK

Søren KyllingsbækUniversity of Copenhagen, Denmark

Monique van RaamsdonkAVV Transport Research Centre, Rotterdam, The Netherlands

Chris RordenMRC Cognition and Brain Sciences Unit, Cambridge, UK

Swarup ChavdaQueen Elizabeth Medical Centre, Birmingham, UK

Whole report of brief letter arrays is used to analyse basic attentional deficits in dorsal and ventral vari-ants of simultanagnosia. Using Bundesen’s Theory of Visual Attention (TVA), a number of previoustheoretical suggestions are formalised and tested, including primary deficit in processing more than onedisplay element, attentional stickiness, foveal bias, and global weakness of the visual representation.Interestingly, data from two cases, one dorsal and one ventral, show little true deficit in simultaneousperception, or selective deficit in those TVA parameters (short-term memory capacity, attentionalweighting) specifically associated with multi-element displays. Instead there is a general reduction inspeed of visual processing (processing rate in TVA), effective even for a single display element butcompounded when two or more elements compete.

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� 2003 Psychology Press Ltdhttp://www.tandf.co.uk/journals/pp/02643294.html DOI:10.1080/02643290342000041

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Correspondence should be addressed to John Duncan, MRC Cognition and Brain Sciences Unit, 15 Chaucer Road, CambridgeCB2 2EF, UK (Email: john.duncan@mrc-cbu.cam.ac.uk).

This work was supported by grants from the Human Frontier Science Program, the Wellcome Trust, the Danish ResearchCouncil for the Humanities, and the Carlsberg Foundation. We thank Jan Catalan for testing the controls in Experiments 1 and 4.

INTRODUCTION

Simultanagnosia and its variants

Impairments in seeing several things at once—thedifferent objects of a cluttered visual scene, com-ponents of a picture, or letters of a word—definethe clinical term “simultanagnosia.” Often, suchimpairments have been interpreted as an atten-tional restriction—an exaggeration of normal limitson the ability to identify several different things atonce. In this paper, we use a theory of normalattentional functions—Bundesen’s (1990) Theoryof Visual Attention, or TVA—to analyse impair-ments in simultanagnosia.

In the literature, the general term simultanag-nosia has been used to describe two somewhatdifferent types of patient (Farah, 1990). In “dorsalsimultanagnosia” or Bálint’s syndrome (seeBálint, 1909/1995; Friedman-Hill, Robertson, &Treisman, 1995; Humphreys, Romani, Olson,Riddoch, & Duncan, 1994; Luria, 1959), there aregenerally bilateral parietal or occipito-parietallesions. In addition to impairments in visuallyguided reaching, stimulus localisation and eyemovement control, patients experience severerestriction in visual awareness. Bálint’s patient, forexample, would often identify only one of twointersecting shapes drawn on a blackboard,remaining unaware of the other’s presence untilprompted, while Luria’s patient explained that hecould not mark the centre of a cross because, as hispencil approached the page and entered awareness,the cross itself disappeared from view. In “ventralsimultanagnosia” (see Kinsbourne & Warrington,1962; Levine & Calvanio, 1978), there is usually asingle left occipital lesion. In this case, complaintsof restricted awareness are less dramatic, butinclude an inability to “make sense of ” a picturebecause only parts are noticed and, conspicuously, atendency to read words letter by letter (hence theterm “pure alexia” also used to describe patients ofthis sort). The bulk of this paper presents a detailedanalysis of a single dorsal simultanagnosic patient,GK (Humphreys et al., 1994). For comparison, lesscomplete data are presented for a ventral patient,MP.

Experimental investigations of simultanagnosiahave typically compared identification of singly andmultiply presented letters, forms, or drawings (e.g.,Coslett & Saffran, 1991; Kinsbourne &Warrington, 1962; Levine & Calvanio, 1978).Though some deficit is often apparent for even onestimulus presented alone, apparently greater diffi-culties are seen when several stimuli must be identi-fied at once. The patients of Kinsbourne andWarrington, for example, sometimes failed to iden-tify both letters of a pair even when these wereshown for 1000 ms or more. As we shall see, TVAallows us to distinguish and evaluate a variety ofalternative “attentional” explanations for results ofthis sort. Indeed, it provides an integrated frame-work within which several theoretical approachesto the problem of simultanagnosia can be formal-ised, related, and tested.

Theory of Visual Attention (TVA)

In contrast to many serial models of attention (e.g.,Treisman & Gelade, 1980), TVA is based onparallel, competitive processing (Rumelhart, 1970).Objects or elements in the visual field compete foraccess to a visual short-term memory (VSTM).Their competitive strength or weight is determinedin part by task context, allowing preferentialprocessing of relevant or target elements. Inprevious work, the empirical motivation for thevarious components of TVA has been considered indetail, and the theory fit to data from a wide varietyof attentional paradigms including partial andwhole report, visual search, redundant targetdetection, and cued reaction time (Bundesen, 1990,1998). In this section we give an outline ofthe theory and the component functions itdistinguishes.

Much of the theory can be understood in thecontext of a simple divided attention task, wholereport (Sperling, 1960). In whole report, the partici-pant is shown a brief array of letters, shapes, orother elements. Commonly, the array is followed bya backward mask intended to interrupt processing.The task is simply to identify and report asmany array elements as possible. Performance ismeasured as a function of the number of elements

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in the array and the stimulus onset asynchrony(SOA) between array and mask.

Exponential processing timesConsider first the simple case of a display consistingof a single element i. According to TVA, thiselement can be identified when an appropriatecategorisation is entered into VSTM. A basicassumption of the theory is exponentially distrib-uted processing time: The probability of identifica-tion Pi as a function of time t is described by theequation

Pe

i v t ti

� ��

11

0( )(1)

Example functions are shown in Figure 1; similarreal data are provided by Bundesen (1998).Equation 1 has two parameters. The first, t0, repre-sents a minimum exposure duration required beforeprocessing can begin. In Figure 1 it has a typicalvalue of 20 ms. Although t0 is important in fittingreal data, its interpretation is of no concern here.Instead we are concerned with the rate parametervi, determining how quickly performance increasesonce processing has begun. Numerically, vi is theslope of the identification function at t0. Functionsfor three values of vi are illustrated in Figure 1. For

a single-element display, vi may be taken as ameasure of sensory efficiency, determined by suchfactors as stimulus discriminability, retinal eccen-tricity, etc.

Competitive modulation of rateIn TVA, competitive processing is implementedthrough modulation of rate parameters (v values) inmulti-element displays. Specifically, each element iin a display of n elements is given an attentionalweight, wi. Its processing rate is then determined bythe equation

v sw

wi i

i

jj

n�

�

�1

(2)

In this equation, si is the v value for element ipresented alone. It thus represents basic sensoryefficiency for that element. The weight ratio wi/�wj

measures how strongly processing rate is reduced bycompetition from other elements in the display. Fora display consisting of n equally weighted elements,for example, v values for each element are theirsingle-element values multiplied by 1/n. By wayof illustration, Figure 1 shows the consequences ofmultiplying a basic v value of 24 elements/s by1/2 (array of 2 equally weighted elements) or 1/4(array of 4 equally weighted elements). As thenumber of array elements is increased, the rate ofprocessing any given element (and hence the proba-bility that it will be identified at any given exposure)goes down.

For a multi-element display, v values for eachelement can be estimated (see later) from functionsrelating the probability of identifying that elementto exposure duration. A useful measure of overallprocessing rate is then capacity C, defined as thesum of v values for all display elements. This defini-tion of capacity brings an interesting property: Ifbasic sensory efficiency si is approximately constantacross elements, then it follows that C will also beapproximately constant across variations in boththe number of elements and their attentionalweighting. Since weight ratios wi/�wj for theelements of a display always sum to 1, it followsfrom Equation 2 that v values for these elements

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Figure 1. Example identification functions for three differentprocessing rates (vi = 6, 12, 24 elements/s).

will always sum to si. In this sense C—measured bysumming empirical v values for the differentelements in a display—may be taken as a basicprocessing capacity that can be arbitrarily dividedby variations in attentional weighting.

A further understanding of C can be obtained byconsidering another standard score in whole report;the mean total number of elements reported foreach exposure duration t. As we have seen, vi foreach element i is the slope of the function relating Pi

to t at t0. As the sum of these v values, C accordinglymay be visualised as the corresponding slope of thefunction relating the mean total number of itemsreported to t at t0 (see Figure 3). Independent ofvariations in the number of display elements orattentional weighting, higher values of C meanfaster processing, and a steeper initial increase innumber of elements reported per unit time.

VSTM capacity (K)One further limitation is needed to understandwhole report performance with displays of morethan four or five elements. As exposure durationincreases, the number of elements reported reachesan asymptote in the region of three to four(Coltheart, 1972; Sperling, 1967). FollowingSperling, TVA interprets this asymptote as thecapacity of VSTM, denoted K. Thus only the firstK elements to complete processing can be stored inVSTM and made available for report.

In this sense processing in TVA can be under-stood as a race between display elements. Processingspeeds for each element are set by Equations 1 and2. The first K elements to complete processing areavailable for report; subjectively they are “attended”and reach awareness. Remaining elements aresubjectively “unattended” and lost.

Depending on array size, accordingly, two sepa-rate factors contribute to conventional “dividedattention decrement,” or loss of performance as thenumber of attended objects increases (Broadbent,1958; Treisman, 1969). For all array sizes, reducedv values associated with increasing n mean slowerprocessing for each element, and reduced chance ofcorrect identification before a display terminates(Equation 2). For array sizes above K, in addition,further elements cannot be stored once VSTM is

filled. As considered in detail by Bundesen (1990),Equations 1 and 2, augmented by a limited VSTMcapacity K, allow TVA to produce excellent fits towhole report data gathered across wide variations innumber of array elements n and exposure durationt. These fits concern not simply the mean numberof elements reported, but the whole distribution offrequencies of report of 0, 1, . . ., n elements for all nand t combinations.

Attentional weightingAbove we considered the case of equal attentionalweighting in a multi-element display. The pointof attentional weighting, however, is to givesome elements priority over others. Returning toEquation 2, an element with high weight isprocessed relatively well (numerator of weight ratiolarge), and interferes strongly with processing ofother elements (large contribution to denominatorof all weight ratios). An element with low weight isprocessed poorly (numerator of weight ratio small),and interferes little with processing of otherelements (little contribution to denominator ofweight ratios).

In TVA, any form of attentional priority can beimplemented by differential attentional weighting.In general, weight setting is the mechanism for top-down control, or attentional priority for inputs ofrelevance to current behaviour. For presentpurposes, the most important aspect of attentionalweighting will be priority for one region of space,implemented by giving elements in the favouredregion increased weights relative to elementselsewhere.

Attentional functions in simultanagnosia

The attraction of TVA lies in its potential to distin-guish and relate a number of separate componentsof attentional function. In principle, this shouldtake us far beyond the simple idea that some visualdisorder involves “impaired attention.” Theapproach is illustrated by a recent analysis of wholereport and related deficits in patients with rightparietal lobe lesions and variable degrees of leftneglect (Duncan, Bundesen, Olson, Humphreys,Chavda, & Shibuya, 1999). In addition to the

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expected rightward attentional bias (higher weightsfor right field elements), we found major, bilateralreductions in C and modest reductions in K. Incontrast to these impairments, there was a strikingbilateral preservation of top-down control, orattentional priority, for targets when arrayscontained a mixture of targets to be reported andnontargets to be ignored. The results show that theperceptual impairments of left neglect patientsderive not just from rightward bias, but fromsubstantial bilateral reductions in the total rate ofinformation uptake. They show also that not allaspects of attentional function are impaired in thecontralesional field.

As regards simultanagnosia, it seems possiblethat each of the major components of TVA could inprinciple contribute to difficulties in processingsimultaneous inputs. At the same time, deficits ineach component should be associated with theirown, characteristic data pattern. In this section, weoutline possible deficits according to TVA andrelate them to previous findings.

VSTM capacity (K)Taken at face value, simultanagnosia suggests aprimary deficit in processing any additionalelement in a visual display after the first. Such adeficit is implied, for example, by the proposal thatperception could be “sticky,” or hard to move fromone focus to another (see, e.g., Kinsbourne &Warrington, 1962). In TVA, the most straight-forward way to implement such a deficit is reduc-tion in K. A K value of 1, for example, would leaveprocessing of a single display element normal, butrender report of two or more elements impossible.1

For variants of whole report, reductions in Kshould affect the asymptote rather than the initialslope of the function relating mean number ofelements reported to exposure duration. For thecase of K = 1, performance should increase steeplyuntil one item is reported on every trial, but remainconstant at this value over substantial further

increases in exposure. Given normal attentionalweighting, the position from which the singlereported element is drawn should vary somewhatrandomly across trials.

Perhaps the closest approximation to this datapattern was described for a single patient by Coslettand Saffran (1991). In this patient there were bilat-eral occipitotemporal lesions, with extension intothe inferior parietal lobule on the right. Displays ofa single picture were identified at an exposure(40 ms, unmasked) comparable to that required bynormal controls. When two pictures were shownsimultaneously, however, the patient alwaysreported one, but rarely two, until exposures roseto 1 s or more. The single reported object camerandomly from all four display positions employed(above, below, and to left or right of fixation). Forthis patient, the results indeed suggest primaryreduction in K and hence pure deficit in processingany display elements beyond the first.

Processing rate (C)Reductions in C imply that all visual processing—even the processing of single elements—should beslowed. In fact, several previous interpretations ofsimultanagnosia have this character. Luria (1959),for example, proposed a general weakening of visualtraces in Bálint’s syndrome, accompanied bymutual inhibition such that all but the strongestcompetitors were lost. Bálint (1909/1995) similarlyproposed a general weakening of visual representa-tions, affecting even single objects but most severewhen two or more were present at once.

For variants of whole report, reductions in Cimply reduced initial slope in the function relatingnumber of elements reported to exposure. Impor-tantly, this deficit should be similar across varia-tions in the number of display elements, extendingeven to displays of a single object.

Perhaps surprisingly, few studies of simultanag-nosic deficits have involved serious investigation ofsingle-element processing; emphasis has instead

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1TVA does not deal in detail with report of elements from VSTM, and how this frees the store for further inputs. The assumption

is, however, that very substantial exposure durations—above the range of most experiments—will be needed before more than Kelements can be reported from any one display.

gone to the conspicuous difficulty with multi-element arrays. At the same time, it is clear fromseveral reports that single-element processing cancertainly be abnormal in both ventral (Kinsbourne& Warrington, 1962) and dorsal (Bálint,1909/1995) simultanagnosics. Without a detailed,quantitative comparison, it is hard to establishwhether observed deficits for multi-element arraysare in fact out of line with single-element perfor-mance. From previous data, accordingly, it is hardto determine the contribution of C to simultanag-nosic deficits; and in this sense, indeed, whether theterm “simultanagnosia” is always apt for thesepatients.

Attentional weighting: Positional biasParticular difficulty with multi-element displayscan also be a reflection of disordered attentionalweighting. As an extreme case, consider two displaylocations, for one of which the attentional weight isvery much higher than the other. Elements in eitherlocation will be processed normally when they arepresented alone. In the absence of attentionalcompetitors, attentional weights are of no signifi-cance (Equation 2). When elements are present inboth locations, however, only the element in thepreferred location will be easily identified. In theextreme case, the weight ratio may be so large as toreduce the v value for the nonpreferred locationtowards zero.

Assessing this possibility requires separatescoring of display elements in each possible posi-tion. For a multi-element (but not a single-element) display, the prediction is that v valuesshould be unusually high in some positions butunusually low or close to zero in others.

Two versions of this hypothesis may be relevantto simultanagnosia. The first is simple unilateralextinction, or deficit in processing inputs from oneside of space in the presence of simultaneous,competing inputs on the other. Since elements oneither side are processed well when they occuralone, such a deficit strongly implies unequalattentional weights on the two sides (see Duncan etal., 1999). Ventral simultanagnosics—with theircharacteristic left occipital lesion—have indeed

been reported to favour left field items (Kinsbourne& Warrington, 1962; Rapp & Caramazza, 1991),in line with the more general finding that contra-lesional extinction is extremely widespread follow-ing many different kinds of unilateral brain damage(Bender, 1952; Vallar, Rusconi, Bignamini,Geminiani, & Perani, 1994). Despite their bilaterallesions, lateral biases can also be seen in dorsalsimultanagnosics, Bálint’s (1909/1995) patient,for example, showing a clear preference for theright.

For dorsal simultanagnosia, a strong preferenceis also often noted for objects at the fovea (Bálint,1909/1995; Hécaen & De Ajuriaguerra, 1954).Indeed, this is what Bálint meant by his term“psychic paralysis of gaze”-a capture by the object atthe fovea so strong that it could not easily bebroken. Others, too, have seen Bálint’s syndrome asa form of bilateral extinction of objects in bothperipheral visual fields (e.g., Harvey & Milner,1995). Such ideas imply strongly imbalancedattentional weight for foveal and peripheral inputs.

SummaryEvidently, TVA suggests a range of separate basicdeficits that could underlie or contribute to simul-tanagnosia. Each, furthermore, finds some supportin the literature, implying that simultanagnosiamay often not be a unitary deficit, or that its causemay be different in different variants.

TVA also defines characteristic data patterns foreach possible basic deficit. In the experiments thatfollow, we use several versions of whole report,comparison of single- and multi-element displays,and separate scoring of display positions to distin-guish deficits in VSTM capacity K, processing rateC, and spatial attentional bias.

DORSAL SIMULTANAGNOSIA

The patient

GK, a former businessman, suffered two strokes atthe age of 46. The resulting lesions, reconstructedfrom an MRI scan taken 9 years post-stroke, are

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shown in radiological convention (left–rightreversed) in Figure 2. Like other cases (Bálint,1909/1995; Friedman-Hill et al., 1995), GK’sdamage is complex but with bilateral involvementof the inferior parietal lobule. In the right hemi-sphere there are two lesions, one in the peri-Sylvianregion, affecting primary sensorimotor cortex andparts of the inferior parietal lobule, and the otheraffecting a large region of the medial occipital lobe,including parts of striate and extrastriate cortex.In the left hemisphere there is a single lesion,

predominantly parietotemporal but extending backtowards the occipitotemporal junction.

GK has the classical symptoms of Bálint’ssyndrome. He has a severe simultanagnosia,commonly reporting only one of two objects ina display even with an exposure of up to 2 s(Humphreys et al., 1994). His descriptions ofcomplex pictures make reference to only a few ofthe objects present, so that he is often unable tograsp the meaning of the scene as a whole. He hasoptic ataxia, showing misreaching to objects under

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Figure 2. Lesions for dorsal (GK) and ventral (MP) patients, traced onto standard slices from Gado, Hanaway, and Frank (1979). The 10slices from Gado et al. are illustrated at bottom; only slices 3–8 are used here. The left of each slice represents the right hemisphere. Slicetemplates from “Functional Anatomy of the Cerebral Cortex by Computed Tomography,” by M. Gado, J. Hanaway, and R. Frank, 1979,Journal of Computer Assisted Tomography, 3, 1–19. Copyright 1979 by Lippincott, Williams & Wilkins. Adapted with permission.

visual guidance; reaching under proprioceptiveguidance is somewhat better. Visual perception ofspatial location is also very impaired when assessedby verbal report. As in Bálint’s (1909/1995) patient,there is a tendency to left-sided extinctionunder bilateral stimulus presentation (Gilchrist,Humphreys, & Riddoch, 1996). Despite intactvisual fields, measured with Goldman perimetry,GK is registered as functionally blind and walkswith a cane.

The present experiments were carried out 7(Experiments 1 and 4), 9 (Experiment 2), and 12(Experiment 3) years post-stroke. GK’s generalsymptoms appeared to be stable over this period.

Experiment 1

In Experiment 1 we focused on the capacity param-eters K (VSTM capacity) and C (processing rate).The task was whole report. To minimise any impactof lateral attentional bias, stimulus displays werevertical columns of five letters presented in eitherthe left or right visual field. For each participant(GK and a group of seven age-matched controls),data were collected at three exposure durations,each used both with and without backward masks,aiming for a broad spread of performance.Following each display, participants were asked toreport just the identities (not locations) of as manyletters as they could.

For each participant, fits to TVA were obtainedby estimating a total of 13 parameters. The detailedfitting procedure has been described elsewhere(Duncan et al., 1999); in brief, for any combinationof parameters, the theory can be used to calculatethe probability of the exact report observed on eachtrial, and best fitting parameters were chosen asthose for which, across trials, the joint probability ofall observed reports was maximal.

First there are two parameters concerned witheffective processing times for each display. The firstof these, t0, was defined earlier as the minimumexposure duration required before processing canbegin. The second, �, is an estimated additionalduration available when displays are unmasked;a detailed justification for this treatment of

unmasked displays is provided by Bundesen (1990).For a true exposure duration of t, effective exposureduration was thus calculated as t – t0 for maskeddisplays, and t – t0 + µ for unmasked displays. Foreach participant, data were thus available for sixeffective exposure durations, for both left- andright-field arrays. Though important in datafitting, parameters t0 and � are of no immediatetheoretical interest here. In the data-fitting proce-dure, they were constrained to be the same forarrays on either side.

Second, there are 10 v values, one estimated foreach possible letter position (five vertical positionsin each hemifield.) As processing rate parameters, vvalues reflect how quickly performance improves asa function of effective exposure duration, separatelyfor letters in each display position. Theoretically(see Equation 2), v values are jointly determined bysensory efficiency and attentional weighting. As wehave described, total processing rate or capacity Cfor any array is defined as the sum of v values for allelements in that array. By summing the estimated vvalues we thus obtained separate values of C for left(CL) and right (CR) field arrays.

The final parameter is K, the capacity of VSTM.In line with our previous findings for both neglectpatients and controls (Duncan et al., 1999), K wasconstrained to be the same for the two hemifields.As we have seen, K represents the upper limit oneach participant’s whole report performance.According to TVA, it should correspond both tothe asymptote of the function relating meannumber of letters reported to exposure duration,and to the maximum number of letters reported ona single trial. In practice, the second of these isespecially significant in fitting trial-by-trial data;typically, the data show the same maximumnumber of letters reported across a range ofdifferent exposure durations, and this numberstrongly determines the best-fitting estimate of K.Noninteger values of K are treated as probabilitymixtures; for example, a value of 3.7 is treated as amixture of trials in which K = 3 with probability 0.3and K = 4 with probability 0.7. The result inpractice is that K, rounded up to the nearest integer,corresponds to the maximum number of letters everreported on a single trial.

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Method

Participants. In addition to GK, data were gath-ered for seven healthy controls, four women andthree men, aged between 52 and 80 years (mean68).

Task and procedure. The experiment was con-trolled by an IBM-PC compatible computerrunning custom software. Stimuli were presentedon a standard monitor with black background. Asno chin rest was used for precise control of viewingdistance, reported visual angles are approximate.

The initial part of each trial was an unscored taskdesigned to encourage central fixation. The trialbegan with a central white fixation dot. When theexperimenter pressed a key, this dot was replacedfor 300 ms by a central white digit, 0.3° in height,which the participant immediately read aloud. Insome sessions with GK, the experimenter watchedthe patient’s eyes to ensure that no detectablemovements occurred between this central task andthe subsequent display. In fact, GK had no diffi-culty maintaining fixation; no trials were excludedbecause of detected eye movements.

The fixation point reappeared while the digitresponse was given; following this, a secondkeypress from the experimenter initiated the mainstimulus display. When the key was pressed, thefixation point disappeared immediately, and thedisplay itself appeared 100 ms later. It was a columnof five letters, centred on the horizontal meridian,2.4° to left or right of fixation. The height of eachletter was 0.5°; the whole column measured 6.4°with letters equally spaced. Letters were drawnfrom the set ABEFHJKLMNPRSTWXYZ; indifferent trial blocks, they were either all red or allgreen. After a predetermined exposure duration,the display was immediately replaced by either ablank screen (unmasked exposures) or a 500 msmask. The mask consisted of separate characters ineach possible display location (i.e., two columns offive characters to left and right). Each maskcharacter was a white square, 0.75° in height, with ahorizontal line connecting the midpoints of leftand right sides, a vertical line connecting midpointsof top and bottom sides, and diagonal lines

connecting opposite corners. The task was simplyto name as many letters as possible, in any order.Only identities, not locations, were reported.Responses were unspeeded, and typed into thecomputer by the experimenter as they were given.Participants were asked to report only letters theywere fairly sure they had seen.

Exposure durations were set in an initial practicesession, aiming for a broad spread of performance.Three exposures were chosen for each participant(Table 1), each used both with and without masks.For each participant there were accordingly 12 trialtypes (2 sides × 3 exposures × 2 mask conditions),presented equally often and in random order in eachblock.

Each participant was tested over a number ofsessions on different days. The number of trialscompleted on any given day varied widely. In total,GK completed 516 scored trials, while the numberfor controls ranged from 504 to 535.

ResultsResults for all participants appear in Figure 3 overthe next four pages. For each participant, data areshown separately for displays in left (left panels) andright (right panels) visual fields. Upper panels showmean number of letters correctly reported on eachtrial as a function of effective exposure duration.Data are shown separately for masked (opensquares) and unmasked (filled diamonds) displays,with effective exposure durations calculated asdescribed above. Solid lines show fits from TVA.Middle panels show proportions of trials with

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Table 1. Experiment 1: Exposure durations

Participant Exposure durations (ms)

PatientGK 157, 200, 400

ControlsCX 43, 86, 157JT 43, 86, 157FS 86, 157, 300PK 43, 86, 157RC 43, 86, 157RK 43, 86, 157RP 43, 86, 157

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Figure 3. Experiment 1: Data for patient (GK) and controls (remainder), separately for left (left panels) and right (right panels) visual fields. Upper panels: Mean number of lettersreported as a function of effective exposure duration; open squares—masked exposures; filled diamonds—unmasked exposures; solid line—fit from TVA. Middle panels: Proportions of trialswith 0, 1, . . ., 5 letters correctly reported for each effective exposure (increasing duration from left to right); for clarity, proportions below .10 are unlabelled. Bottom panels: Proportioncorrect as a function of effective exposure for each array position (order of positions from top to bottom—squares, diamonds, circles, triangles, crosses).

0, 1, . . ., 5 letters correct, separately for each of thesix effective exposure durations (within each panel,durations in increasing order from left to right).Lower panels show proportion of correct reports forletters in each array location, again as a function ofeffective exposure duration.

The data show several important features ofGK’s whole report deficit. The first concerns rateof processing, captured in TVA by the parametersCL and CR. The strong impression is that, bycomparison with controls, processing rate was verymuch slowed in GK, with only very gradualimprovements in performance as exposure durationincreased (Figure 3, top panels). The secondconcerns maximum number of letters reported,captured in TVA by VSTM capacity K. Whilethree or more letters were frequently reported by allcontrols (Figure 3, middle panels), GK fairly oftenreported two letters but very rarely three. Finally,GK’s deficit concerned all display positions (Figure3, bottom panels), with no evidence that pooroverall performance resulted from excellent scoresin certain positions at the expense of very poorperformance elsewhere.

As described above, TVA was fitted to data foreach participant and visual field. Best-fittingparameters for each data set appear in Table 2. In

line with the above impressions, overall processingrates CL and CR were at least an order of magnitudelower in GK than controls. Separately for CL andCR, differences between GK and controls weretested by between-groups ANOVA (N = 1 for GKand N = 7 for controls), following a log transforma-tion to eliminate outliers in the control distribution.Both differences were significant, F(1, 6) = 35.0, p <.001 (1-tailed) for CL, F(1, 6) = 21.4, p < .005 for CR.As shown by the separate v values in Table 2, thisslowing of processing was seen at all locations oneach side. Though slowed processing was the mostconspicuous aspect of GK’s deficit, by comparisonwith controls his VSTM capacity K was also some-what reduced, F(1, 6) = 4.1, p < .05.

DiscussionIn this experiment we measured two TVAparameters, processing rate C and VSTM capacityK. According to TVA, it is K that would mostnaturally be implicated in a primary inability toprocess more than one object or element in a visualarray. While setting K equal to one would make itimpossible to report more than one displayelement, processing of a single element would beunimpaired. Reductions in C, in contrast, shouldaffect processing at all array sizes, including one.

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Table 2. Experiment 1: Model parameters

Left Right

Participant v1 v2 v3 v4 v5 CL v1 v2 v3 v4 v5 CR K t0 �

PatientGK 0 0 1 0 0 2 0 1 1 0 0 3 2.5 107 364

ControlsCX 1 2 12 2 3 20 4 6 11 1 1 22 3.2 1 118JT 6 3 6 2 3 19 7 3 3 2 3 18 3.3 0 146FS 17 8 3 3 3 34 16 9 5 2 3 35 4.5 0 73PK 9 6 5 3 3 26 9 12 7 2 3 33 3.6 0 80RC 24 13 9 5 14 66 19 21 13 10 17 80 4.8 0 96RK 17 10 3 1 2 33 13 6 3 1 1 24 3.8 5 113RP 25 13 4 1 2 45 25 13 4 1 3 46 4.8 31 158

vi = processing rate for element i (elements/s); CL, CR = total processing rate in left and right fields (elements/s); K = visual short-term memory capacity (number of elements); t0 = minimum effective exposure duration (ms); � = additional effective exposurefor unmasked array (ms). Discrepancies between CL, CR and corresponding summed v values reflect rounding errors (all valuesrounded to nearest integer).

Certainly GK showed a major whole reportdeficit, affecting both masked and unmaskeddisplays. In more detail, however, this deficit wasrather surprising. Indeed, there was a modestreduction in K, significant by comparison with thegroup of seven controls. The estimated K value,however, was certainly not one—reflecting thefinding that, at the longer exposure durations, GKactually reported two letters (occasionally eventhree) on around 15% or more trials. Instead, byfar his most conspicuous deficit was an approxi-mately 10-fold reduction in C, implying not anyselective loss in ability to process multiple elements,but rather a massive overall slowing of visualprocessing.

Another possible account of poor perfor-mance—overwhelming bias towards one arraylocation—is ruled out by these data. GK did notshow a pattern of excellent performance for onelocation, accompanied by little to no identificationof letters elsewhere.

One possible reservation over these conclusionsconcerns a technical detail of C estimation. Asevident from Figure 3, GK’s C estimate waspartially dependent on the fit to data fromunmasked displays. For such displays, the estimateof effective exposure duration depends in turn onthe estimate of �, the additional effective exposureof an unmasked display, and—as shown inTable 2—the � estimate was very much greaterin GK than controls. There is no direct reason todoubt this � estimate. It would imply that theduration of iconic memory is substantiallyenhanced in GK or, complementarily, that hisvisual system is sluggish in responding to displayoffset. Furthermore, even masked data alone arestrongly indicative of very slow processing in thispatient (Figure 3). Still, in Experiment 2 weattempted to replicate a measurement of C deficitusing only masked displays.

A second possible reservation over our conclu-sions concerns interpretation of TVA parameters.Though according to the theory a reduction in Cshould affect even single-element displays, the dataof Experiment 1 obviously do not show thisdirectly. In Experiment 3 we measured identifica-tion of single masked letters presented at fixation.

Experiment 2

In Experiment 2, GK was tested with six-lettermasked displays, presented for variable duration.Letters were arranged in a circle around fixation.

MethodProcedures were as before, except as follows. In thisexperiment, there was no initial digit task toencourage central fixation. Instead, the display wasinitiated when GK was confident that he hadlocated the fixation point. The display consisted ofsix letters, equally spaced around an imaginarycircle of radius 3.2°, centred on fixation. There werefive exposure durations (114, 271, 428, 585, and742 ms), varying randomly across trials; all displayswere immediately followed by a 500-ms maskconsisting of the same mask characters as before ineach display position. In this experiment, heights ofletters and masks were 0.75 and 1.5° respectively.Across a number of sessions, GK completed a totalof 475 trials.

ResultsResults appear in Figure 4. Fits by TVA wereobtained by similar procedures as before. This time,

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Figure 4. Experiment 2: Data for GK. Conventions as forFigure 3, except upper panel: Data as a function of actual exposureduration rather than estimated effective duration.

there was only a single estimated value of C(summed v values across the six display positions).As all displays were masked, there was no estimateof �; data in Figure 4 are plotted as a function ofactual exposure duration rather than estimatedeffective duration. As shown in the upper panel,processing again was very slow, with a C estimate ofonly two elements/s. Examination of data for thesix different display positions (not shown) showedthat this held true for all positions; even for the bestposition (top right), probability of correct reportrose only slowly across exposure durations, to amaximum of around 0.5. As in Experiment 1, GKcommonly reported two letters but only rarely three(Figure 4, lower panel); the estimate of K was 2.2,again very close to the estimate from Experiment 1.For this experiment, t0 was estimated at 51 ms.

DiscussionIn Experiment 2, GK’s major deficit in processingrate was confirmed using only masked displays.Evidently, the C estimate in Experiment 1 was notstrongly dependent on the fitting procedure used tocombine data from masked and unmasked trials.

Experiment 3

In Experiments 1 and 2, GK’s processing of multi-letter arrays was remarkably slow. According toTVA, such slowing reflects impairment in pro-cessing rate C. A strong prediction is thatprocessing should also be slow for a single letterarray. In Experiment 3, this was tested with singleletters presented directly at fixation.

Certainly, TVA’s account of processing rateimpairments could be incorrect. A commonproposal, for example, is that parietal lesionsproduce a deficit in attentional “disengagement,” orremoval from the current focus (Posner, Walker,Friedrich, & Rafal, 1984). This idea is reminiscentof the concept of “sticky” perception in simul-tanagnosia (Kinsbourne & Warrington, 1962);more generally, the idea is that the first element isprocessed normally in a visual array, but moving onto further elements is impaired. As we said earlier,one possible way to incorporate such proposals intoTVA might be reduction in K. A disengage deficit

could also be manifest, however, as slowedprocessing rate only in multi-element displays, afinding that TVA could not incorporate very easily.

As mentioned above, dorsal simultanagnosia hasalso sometimes been interpreted as a bilateralversion of sensory extinction, i.e., an elimination ofprocessing in the visual periphery due in part tofoveal bias. This account predicts little impairmentin processing of single, foveally presented letters.

Method

Participants. In addition to GK, data wereobtained for six healthy controls, five women andone man, aged between 26 and 73 years (mean 52).

Task and procedure. For this experiment themonitor background was set to pale grey. Againthere was no precise control of viewing distance, soreported visual angles are approximate.

Again, each trial began with an unscored digittask designed to encourage central fixation. At trialonset, a red fixation cross, height 1.7°, was centredon the screen. When the experimenter pressed akey, this cross flashed off for 108 ms, on for 108 ms,off for 108 ms, on for 108 ms, off for 108 ms, on for108 ms, then was replaced by a small (0.6°) reddigit, centred on fixation. This remained for314 ms, after which the fixation cross returnedwhile the participant named the digit. Again, digitresponses were not recorded or scored.

On a second keypress from the experimenter,the main target was immediately presented. Itwas a black letter, 3.7° in height, again centredon fixation, randomly drawn from the setBCDFHJKLNPSTXZ. After a variable exposureduration, it was immediately replaced by a 206-msmask, a dense patch of jumbled black lines coveringthe same area as the preceding letter. The fixationcross then returned while the participant attemptedto name the letter, with omissions permitted. As inprevious experiments, responses were unspeeded,and typed into the computer by the experimenter.

As all events were foveal in this experiment, eyemovements were not carefully assessed. For GK,three trials with evident head movements werediscarded.

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Testing took place in blocks of 40 trials, with 8trials at each of 5 exposure durations per block, inrandom order. Controls were given a total of 6blocks, spread over 3 testing sessions devoted toseveral different tasks. Their exposures were alwaysnominally 20, 40, 70, 100, and 150 ms (in fact .98 ofthese values owing to the monitor refresh rate). GKwas also given 6 blocks, in a single session. For thefirst and last block, nominal exposures were as forcontrols; for remaining blocks, they were 70, 100,150, 200, and 250 ms.

ResultsIndividual results for each participant appear inFigure 5. Again, the data are plotted as a function ofactual exposure duration rather than estimatedeffective duration. At least for controls, functionsare approximately exponential in form, as predictedby TVA. For GK, the data show a massive reduc-tion in speed of processing, with a proportioncorrect of only .84 even at 250 ms exposure.

Exponential functions were fit separately to thedata for each participant by least squares (usingnominal exposures as reported above). Best fittingparameters appear in Table 3. For this experimentthere is only a single rate parameter (v value),reflecting processing rate for the single foveal letter.By comparison with Experiments 1 and 2,processing was generally faster here, as expected forlarge foveal letters. Again, however, GK showedclose to a 10-fold reduction in rate by comparisonwith controls, F(1, 5) = 39.6, p < .001 (following logtransformation).

DiscussionIn Experiment 3, GK showed major impairment inprocessing even a single foveally presented letter.Indeed, his deficit seemed at least as marked here asin earlier experiments with multi-letter arrays.Again, this deficit is better described as a generalreduction in processing rate than as selective diffi-culty with multiple array elements.

Experiment 4

Closely related to the concept of “simultanagnosia”is “divided attention decrement,” or reduced per-formance when several array elements must beprocessed at once. At face value, simultanagnosiaimplies unusual decrement, or an unusually largedifference between processing one vs. two or moreelements. As we have seen, GK’s impairmentclearly affects both single- and multi-elementdisplays. In Experiment 4 we asked whether hisdivided attention decrement—specifically, the dif-ference in accuracy with 1- and 2-letter displays—isin fact abnormal.

As we show below, this question may be posedquite exactly within TVA. Assume that K > 2(which we have already confirmed for GK and thecontrol participants in Experiment 1, who servedagain in Experiment 4); now performance dependsonly on the competitive processing defined byEquations 1 and 2. Given single-element accuracy(Equation 1) and weight ratio (Equation 2),TVA predicts the exact performance level in a

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Figure 5. Experiment 3: Proportion correct as a function ofexposure duration for GK (squares) and controls (other symbols).

Table 3. Experiment 3: Model parameters

Participant v t0

PatientGK 8 58

ControlsAB 52 16BP 47 20CW 87 18FB 54 17PC 92 16JB 95 20

v = processing rate for single foveal letter (elements/s);t0 = minimum effective exposure duration (ms).

two-element display. In other words, TVA canmake exact predictions concerning the magnitudeof divided attention decrement. In Experiment 4,we assessed its ability to fit data from both GK andcontrols.

For this purpose, it is useful to consider perfor-mance at just a single exposure duration t. For adisplay consisting of a single element i followed by amask, Equation 1 now simplifies to

Pei

iAi

� �11

(3)

where Ai = si(t – t0). For fixed exposure, Ai is propor-tional to Si and so again can be taken as a measure ofbasic sensory efficiency. For a display consisting oftwo elements i and j, we have

� �P

ei i A w w wi i i j

� �

11

/(4)

� �P

ej i A w w wj j i j

� �

11/

(5)

Thus, given measures of accuracy for both i and j inboth one- and two-element displays, we can askwhether there exist estimates for Ai, Aj, and the twoweight ratios which provide a good fit to the data—with the constraint that weight ratios must sumto 1.

In practice, the design of Experiment 4 wasslightly more complex. Instead of just two displaylocations we used four, arranged in a square centredon fixation. Furthermore, the task was a variant ofpartial report (Bundesen, 1990; Sperling, 1960)—insome blocks the task was to identify red letterswhile ignoring green letters, in other blocks thereverse. There were three types of display. First,targets occurred alone, in each of the four possibledisplay locations. Second, pairs of targets werepresented together, either in the same hemifield(upper left + lower left or upper right + lower right),or in opposite hemifields (upper left + upper right orlower left + lower right; no diagonal displays wereused.) For these displays both targets were to bereported, in either order. Third, a single targetcould be accompanied by a single nontarget, again

either in the same hemifield or in oppositehemifields (again without diagonals). In total thisproduces 16 trial types—4 one-target (upper left,lower left, upper right, lower right), 4 two-target(upper left + lower left, upper right + lower right,upper left + upper right, lower left + lower right),and 8 target + nontarget (the same four pairs oflocations, each with either location containing thetarget). Separately for each participant, fits to TVAwere obtained using straightforward extensions ofEquations 3–5 (see Duncan et al., 1999). For eachlocation i, best-fitting estimates were obtained formeasures of sensory effectiveness Ai, attentionalweight of a target wi(T), and attentional weight of anontarget wi(N), with estimates varying freelybetween locations.

While our major goal was to test the adequacy ofTVA fits—and, specifically, TVA’s ability tocapture the overall difference between one-targetand two-target displays—the data are potentiallyrelevant to two further issues. First is lateral atten-tional bias: As noted above, GK shows a tendencyto extinguish the left-sided stimulus under bilateralsimultaneous stimulation. We expected to see thissame tendency here with upper left + upper right orlower left + lower right displays. In TVA, such aresult would be reflected in low estimates ofattentional weight for left-sided letters.

Second, we used partial report with the inten-tion of measuring top-down control, or differentialweighting of target and nontarget letters. In fact,poor performance of some controls (see data forthese same participants in Duncan et al., 1999)prevented useful conclusions about GK. As somecontrols showed essentially zero top-down con-trol—i.e., equal weighting for targets and non-targets—it was impossible for GK’s performance tobe worse. Though data from target + nontargetdisplays were used in estimating TVA parameters(see above and Duncan et al., 1999), they will not beconsidered further.

MethodExperiment 4 was run on the same participants asExperiment 1, in interleaved sessions. Except asnoted, procedures for the two were similar. Asdescribed above, letters in Experiment 4 were

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presented at the corners of an imaginary square,4.7 × 4.7°, centred on fixation. In different blocks,the task was either to identify red letters and ignoregreen letters, or vice versa. Again, participants wereasked to report identities (not locations) for justthose targets they were fairly confident of, and thusreported 0, 1, or 2 on each trial. For displays withtwo targets, e.g., upper left + lower left, proportioncorrect was scored separately for each position. Foreach participant there was only a single exposureduration, selected after an initial practice session toproduce accuracy in the range 60–90% in one-target displays. For GK, this exposure was 500 ms,while for controls it was either 57 (RC) or71 (others) ms. All displays were immediatelyfollowed by a 500-ms backward mask, constructedof four masking characters like those in Experiment1, one in each display location.

The same procedure for encouraging centralfixation was used as in Experiment 1. Again GKhad little trouble fixating, with only nine trialsexcluded for eye movements. Overall, GKcompleted approximately 31 trials for each of the 16trial types (see above), while controls completedbetween 32 and 39.

ResultsResults for each participant appear in Figure 6(solid lines). Proportion correct is shown separatelyfor targets in left (left panels) and right (rightpanels) hemifields, presented alone, with an addi-tional target in the same hemifield, or with anadditional target in the opposite hemifield. In eachcase, data from upper and lower positions have beenaveraged. Predictions from the best-fitting set ofTVA parameters for each participant are alsoshown (dotted lines).

The first noteworthy result concerns the overalldifference between one- and two-target displays. Inall cases but one (CX, right field, additional targetin opposite hemifield), there is the expected dividedattention decrement. For both GK and controls,this decrement is well fit by TVA. In GK, the fitaccounted for 96% of the variance between all datapoints (separate data for all four positions and alldisplay types, including target + nontarget), rootmean squared deviation (RMSD) .06. In controls,

fits accounted for 59–95% of the variance, RMSD.05 to .08.

A second noteworthy result is GK’s expectedleft-sided extinction. When targets were simulta-neously presented to left and right (Figure 6, +oppdata points), performance for the left-sided targetwas particularly poor, while performance for theright-sided target was relatively preserved. InTVA’s fits, attentional weights were separatelyestimated for targets and nontargets in each displayposition. To capture attentional bias, a useful index(Duncan et al., 1999) is wL/(wL+ wR), where wL ismean estimated attentional weight for all items onthe left, and similarly for wR on the right. Values ofthis index are shown for each participant in Table 4.As expected, GK’s value was below that of allcontrols, F(1, 6) = 3.6, p < .06 (1-tailed), indicatinglower attentional weights on the left.

DiscussionIn Experiment 4, roughly comparable performancein one-target displays required much longer expo-sures for GK than for controls. This is the resultexpected from a reduction in C, and from the resultsof Experiment 3. In contrast, GK and controlsshowed comparable decrements from one- to two-target displays, well fit by TVA. Once more, theimpression is not of primary difficulty withprocessing more than one letter, but of simpleoverall reduction in processing speed.

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Table 4. Experiment 4: Weight ratios

Participant wL / (wL + wR)

PatientGK .33

ControlsCX .38JT .44FS .54PK .57RC .45RK .54RP .42

For definition of weight ratio see text.

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Figure 6. Experiment 4: Proportion correct for patient (GK) and controls (remainder), separately for targets in left (left panels) and right(right panels) visual fields. Targets are presented alone, with a second target in the same visual field (+same), or with a second target in theopposite visual field (+opp). Solid lines—data; dotted lines—predictions.

GK: General discussion

Together, Experiments 1 to 4 assessed three dif-ferent accounts of GK’s dorsal simultanagnosia. InTVA, these would be distinguished by impairmentin different processing parameters.

Most obviously, simultanagnosia might bereflected in reduced VSTM capacity, and specifi-cally in a K value of 1. With a brief display, such adeficit would leave processing of a single displayelement unimpaired, but make it impossible toreport more than one. Indeed, GK showed a reduc-tion in K by comparison with controls. His esti-mated value, however, was greater than 2, reflectinghis report of two and occasionally even three letterson some whole report trials. These data do notimply a primary deficit in processing multipledisplay elements.

A second possibility is disordered attentionalweighting. If some positions received much higherattentional weights than others, the result could begood performance for just the favoured position in amulti-element display, but little or no identificationof elements elsewhere. Indeed, GK showed a milddisorder of attentional weighting, with strongerweights on the right. But this was not relevant to hisprimary disorder, reflected in poor performance evenwith vertical whole report arrays (Experiment 1), andwith just a single letter at fixation (Experiment 3).

Instead, the data tell a fairly clear story ofimpaired processing speed, at all display sizes,revealed by a massive reduction in C. As anticipatedby Bálint (1909/1995), Luria (1959), and others,the suggestion is of a general weakening in visualprocessing. Though failures will, of course, bemost conspicuous in demanding, multi-elementdisplays, there is already a major impairment withjust a single display element. Indeed, Experiment 4shows directly that the decrement from one- totwo-target identification in itself is not abnormal.

VENTRAL SIMULTANAGNOSIA

The patient

MP, an English teacher, suffered a stroke at age 56.A CT scan 2 weeks later showed a large lesion of

the left occipital lobe, extending forward into theposterior temporal lobe (Figure 2).

A highly educated man, MP continued toperform in the high average to superior range intests of intellectual function, even in the periodimmediately post-stroke. In identification of singleletters he scored 38/40 correct. His reading, how-ever, was strikingly slow, with the characteristicletter-by-letter pattern of ventral simultanagnosia.For single irregular words, reading times were 20 sor more. He was also blind in the upper right visualquadrant.

Over the succeeding months, MP’s readinggradually improved, though not to the premorbidlevel. The current experiments were run approxi-mately 1.5 years after his stroke. He thus representsthe usual partial recovery from an early ventralsimultanagnosia/pure alexia (see, e.g., Behrmann& Shallice, 1995).

Experiment 5

Experiment 5 used the same whole report methodas Experiment 1. Again, it addresses processing rateC, VSTM capacity K, and positional bias, all forcolumns of letters in left or right hemifield.

MethodProcedures were similar to Experiment 1. Like GK,MP had no trouble maintaining central fixation;one trial was excluded for eye movement. MP’sexposure durations were 29, 100, and 171 ms, againused with and without masks. In total he completed768 trials.

ResultsMP’s results are shown in Figure 7. By comparisonwith the controls from Experiment 1 (Figure 3), hisprocessing was again somewhat slowed (upperpanels). For the left field, he often reported threeletters, and once four (middle left). For the rightfield he never reported more than two (middleright), being blind for the upper three positions(bottom right). Otherwise, his positional prefer-ences (bottom panels) were not unusual.

Fits to TVA were obtained after removing theone trial with four letters reported as an outlier (for

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DORSAL AND VENTRAL SIMULTANAGNOSIA

outlier definition see Duncan et al., 1999; outlierswere not found in controls). Best-fitting parame-ters appear in Table 5. As for GK, comparison withcontrols showed significant impairments in both

CL, F(1, 6) = 5.4, p < .05, and CR, F(1, 6) = 8.5, p <.02 (both tests 1-tailed, following log transforma-tion). The modest K reduction was of borderlinesignificance, F(1, 6) = 3.4, p < .06. Inclusion of theoutlier trial produced very similar results, exceptthat the K estimate increased to 3.2.

DiscussionThough less severe, MP’s whole report impairmentwas essentially similar to that shown by GK. Again,there was a reduction in K, but not so severe as toproduce general inability to report more than oneletter from a display. Instead, the most conspicuousfeature of the deficit was a reduction in processingrate.

Strikingly, overall processing rate was almostequally affected in the two hemifields. Though thelesion effectively produced complete blindness forthe top three positions in the right visual field, thiswas compensated for by relatively strong perfor-mance in the remaining two. This is the result weshould expect if overall processing rate is similar onthe two sides, but with the upper right letters elimi-nated as competitors (cf. Equation 2). Thus themost striking result of a left occipital lesion issubstantial bilateral impairment in overall rate ofuptake of visual input—very similar, indeed, to theeffect of GK’s extensive bilateral lesions.

Experiment 6

Experiment 6 used the partial report task of Experi-ment 4. Again, the data presented here concernjust one- and two-target displays, bearing on theabsolute size of divided attention decrement and

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696 COGNITIVE NEUROPSYCHOLOGY, 2003, 20 (8)

Figure 7. Experiment 5: Data for MP. Conventions as forFigure 3.

Table 5. Experiment 5: Model parameters

Left Right———————————— ————————————

Participant v1 v2 v3 v4 v5 CL v1 v2 v3 v4 v5 CR K t0 �

PatientMP 1 0 6 2 2 11 0 0 0 3 4 7 2.7 36 316

vi = processing rate for element i (elements/s); CL, CR = total processing rate in left and right fields (elements/s); K = visual short-term memory capacity (number of elements); t0 = minimum effective exposure duration (ms); � = additional effective exposurefor unmasked array (ms).

(when two targets appear in opposite hemifields)on lateral attentional bias.

MethodProcedures were similar to Experiment 4. Again,MP completed 768 trials, with just 1 excluded foreye movement. Exposure duration was 128 ms withmasking.

ResultsResults appear in Figure 8. As MP was blind in theupper right quadrant, only data for targets in thelower visual field (left and right) are presented.Thus the figure shows proportion correct for thesetargets presented alone, accompanied by a secondtarget on the same side (hence in the upper field), oraccompanied by a second target on the oppositeside (hence also in the lower field).

In three cases out of four, two-target displaysshowed the usual divided attention decrement. Theexception concerns targets in the (lower) right fieldaccompanied by a second target on the same side; asthis second target fell in the blind (upper) quadrant,it had no effect on lower-field accuracy. Apart fromthis, the overall performance difference betweenone- and two-target displays was not unusual, andwas well fitted by TVA. The fit accounted for 99%of the variance between all data points (separatedata for all four positions and all display types, againincluding target + nontarget), RMSD .03.

Displays with one target in each hemifieldshowed a strong pattern of contralesional extinc-tion. For the left field target, the decrement from

one-target accuracy was very small (Figure 8, leftpanel, +opp vs. alone); for the right field target, itwas substantial (Figure 8, right panel, +opp vs.alone). To capture this bias away from thecontralesional field, we used the index wR/(wL+wR), calculated as previously decribed from TVA’sestimated attentional weights for lower-fielddisplay items. The index of .26 differed sig-nificantly from that of the seven controls fromExperiment 4, F(1, 6) = 11.6, p < .01.

DiscussionIn milder form, MP’s overall impairment inExperiment 6 resembled that shown by GK inExperiment 4. As compared to the Experiment 4controls, MP required a somewhat longer exposureduration for equivalent one-target performance.Given this, however, the two-target decrementwas quite normal. Again, the data do not suggestprimary difficulty with processing of multipledisplay elements.

The second result concerns attentional bias. Inline with other studies of ventral simultanagnosia(e.g., Behrmann & Shallice, 1995; Kinsbourne &Warrington, 1962; Levine & Calvanio, 1978; Rapp& Caramazza, 1991), the data showed bias to theleft ipsilesional field.

MP: General discussion

Overall, MP’s results were strikingly similar tothose of GK. By comparison with controls, therewas a modest impairment in K, a marked reductionin C, a normal overall divided attention decrement,and a lateral attentional bias, here favouring the left.For the basic visual functions measured in TVA,the data suggest rather similar impairments indorsal and ventral simultanagnosia.

GENERAL DISCUSSION

Primary processing deficits insimultanagnosia

Together, the results of these experiments suggestsomething surprising about “simultanagnosia.”According to TVA, either disordered short-term

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Figure 8. Experiment 6: Data for MP. Conventions as forFigure 6.

memory or disordered attentional weights couldlead to specific impairment in processing more thanone visual display element. A K value of 1 wouldhave no influence on processing a single displayelement, but would make it impossible to identifytwo or more. Strong attentional focus on onedisplay region, e.g., foveal dominance, would alsohave little effect until two or more elements were incompetition. For both of our patients, indeed, thedata showed impairments in both VSTM capacityand attentional weighting. In neither case, how-ever, were these the primary deficits. Instead, themost prominent result was a simple reduction inprocessing speed, which at least in GK affectedeven a single letter presented directly at fixation.

In the literature, as we have seen, there isevidence in different cases that poor single elementprocessing (Bálint, 1909/1995; Kinsbourne &Warrington, 1962; Luria, 1959), spatial bias(Kinsbourne & Warrington, 1962), and K valuesclose to 1 (Coslett & Saffran, 1991; see also Pavese,Coslett, Saffran, & Buxbaum, 2002) can allcontribute to simultanagnosia. The present cases,however, suggest that the dominant factor mayoften be processing speed rather than a specificimpairment in simultaneous perception.

Can such an account deal adequately with theclinical phenomena of simultanagnosia? In a clut-tered visual world, with multiple elements simulta-neously competing to be processed, it is plausiblethat often only the strongest one will survive amassive reduction in processing rate, others failingto complete even with long exposures. Eitherbecause of stronger attentional weights at the fovea,or simply because of better sensory input and thushigher v value, this surviving element might oftenbe the element that is fixated. Bálint (1909/1995),for example, described that “. . . fixating a needlemade it impossible for (the patient) to perceive acandle light placed at a 5 cm distance from him”(p. 269). Any kind of differentiation in attentionalweights, however, could produce similar results.When GK is shown overlapping pictures andwords, for example, he very commonly reports justthe picture (Humphreys et al., 1994), a result thatcould easily follow from impaired processing rateaccompanying greater attentional weight for

pictures. A greater attentional weight for moving ornewly appearing objects (Yantis & Hillstrom,1994) could explain how, for Luria’s (1959) patient,a sheet of paper seemed to disappear when a movingpencil tip approached. In a competitive visualworld, it is easy to see how a primary deficit inprocessing speed might often translate intooutright failure to see any objects but the one or twomost dominant.

Letter-by-letter reading

For ventral simultanagnosia, perhaps the mostconspicuous clinical deficit is letter-by-letter read-ing. Accounts of this phenomenon fall into twobroad classes. In the first type of account, thecentral deficit is specific impairment in wordperception, e.g., impairment in a visual word-formsystem (Warrington & Shallice, 1980). In thesecond, letter-by-letter processing reflects adapta-tion of reading to a broader visual deficit (e.g.,Farah & Wallace,1991).

Evidently, an account in terms of TVA’s rateparameter C falls into the second category. Ifprocessing is slow, one reasonable solution mightbe to minimise competition by top-down selectionof one display location after another. This could beespecially important if attentional weights aresomewhat biased to the left (e.g., Behrmann &Shallice, 1995; Kinsbourne & Warrington, 1962;Levine & Calvanio, 1978; Rapp & Caramazza,1991), tending to focus even what processing thereis on the early letters in a word. Indeed, the basicaccount of letter-by-letter reading as just one mani-festation of a broader “ventral simultanagnosia”presumes a deficit outside word recognition itself.

On its own, however, this account leaves some-thing out. Like other ventral simultanagnosics, ourpatient MP read words letter by letter in the earlyperiod after his stroke. Despite an even more severereduction in C, GK, like other dorsal simul-tanagnosics, does not read in this way. On thecontrary, he has a form of “attentional dyslexia”(Shallice & Warrington, 1977), reading wholewords quite successfully, but having difficultyidentifying the separate letters in their correctpositions (Hall, Humphreys, & Cooper, 2001).

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In all likelihood, the issue here turns on whatcounts as a single, competing “display element” forTVA. Like other object-based theories (Duncan,1984), TVA presumes that some visual groupingprocess determines what parts of the visual inputbelong together as parts of a single object, and thatit is the objects so created that serve as the theory’scompeting “display elements” (Bundesen, 1990). Indorsal simultanagnosia, as in normal vision, group-ing strongly determines the nature of attentionalcompetition. Luria’s (1959) patient, for example,could perceive the whole Star of David when it wasdrawn in a single colour, but saw only one compo-nent triangle or the other when one was red and theother blue. In word perception, it is commonlypresumed that learning has bound componentletters into a single familiar object, releasing themfrom the competition that unrelated letters wouldsuffer (Siéroff & Posner, 1988). For GK and otherdorsal simultanagnosics, we would suggest that thisbinding remains intact. No doubt word perceptionis slowed, but as regards competition, words act assingle display elements. For MP and other ventralsimultanagnosics, with their characteristic leftoccipital lesion, we would suggest that reduction inC is complicated by an additional, specific deficitin word recognition itself. Because of this deficit,even letters in familiar words suffer some of thesame processing competition as unrelated displayelements. Hence a basic visual impairment, in itselfsimilar to that in dorsal simultanagnosia, is espe-cially evident in word recognition.

Relationship to neglect

In a previous study, we used similar methods toanalyse attentional impairments associated withleft visual neglect (Duncan et al., 1999). In thesepatients, there were lesions affecting the rightinferior parietal lobule (IPL), often extending intothe posterior frontal lobe and/or superior temporallobe. Two similarities to the present results arenoteworthy.

The first concerns processing rate C. As in thepresent two patients, the IPL group showed a majorC reduction in whole report. Again this was evidenteven with vertically aligned arrays, and though it

was somewhat stronger in the left (contralesional)field, the major effect was bilateral. Though thesewere patients selected for left-field neglect, theirmost obvious impairment was slow processing inboth visual fields.

Because of the bilateral parietal lesions, it hassometimes been supposed that Bálint’s syndrome isa bilateral version of neglect (Harvey & Milner,1995). For GK, indeed, whole report on both sidesresembles the contralesional performance of theworst neglect patients (Duncan et al., 1999), in linewith this interpretation. MP’s data, however, showthat much the same bilateral reduction in C canresult from a quite different lesion, in the left occip-ital lobe. In all probability, overall processing rate isdetermined by several interacting influences. C, ofcourse, reflects the efficiency of pattern recogni-tion, and it is plausible that a left occipital lesionshould have a direct effect on a letter recognitionsystem processing material from both visual fields.This seems less plausible for a right inferior parietallesion; here we may be dealing with some moregeneral contribution to construction of a consciouspercept (Corbetta, Kincade, Ollinger, McAvoy,& Shulman, 2000; Downar, Crawley, Mikulis, &Davis, 2000).

The second similarity with the neglect dataconcerns attentional weighting. In neglect patients,as expected, there was a reduction of attentionalweights on the left, reflecting contralesional extinc-tion. Again, MP’s data show that a similar lateralbias can also follow from a left occipitotemporallesion. As other data confirm (e.g., Vallar et al.,1994), a tendency to extinction—lateral attentionalbias with competing inputs on the two sides—candoubtless be the result of many different lesions, insome cases even those outside the central nervoussystem (Bender, 1952; see also Duncan, 1996).

In recent work, a number of temporal processingdeficits have been associated with parietal lesionsand/or neglect. One example is impaired temporalorder judgment, such that ipsilesional events appearto be seen earlier than similar contralesional events(Rorden, Mattingley, Karnath, & Driver, 1997).Another is lengthened “attentional blink,” orperiod of impairment in identifying a secondtarget stimulus when it follows shortly after a first

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(Husain, Shapiro, Martin, & Kennard, 1997).Though these have some similarities with dataindicating reduced processing speed, we would becautious in proposing any direct correspondence. Innormal subjects, for example, “processing” in thesense defined by TVA—entry of a stimulusdescription into VSTM—typically completes overtens of milliseconds from stimulus onset, while theattentional blink lasts hundreds of milliseconds.Further work is needed to address relationsbetween these different temporal phenomena, inboth normal subjects and parietal and/or neglectpatients.

Conclusion

In this paper, we have tried to show the merit ofanalysing simultanagnosic impairments with awell-specified theory of normal attentional func-tions. In the context of TVA, many previoussuggestions concerning simultanagnosia can beformalised and related, including proposals ofprimary deficit in processing multiple stimuli,attentional “stickiness,” foveal bias, and bilateralneglect. Interestingly, the account fitting our casesis closest to Bálint’s (1909/1995) and Luria’s (1959)ideas of general weakening in visual representa-tions. Rather than a true “simultanagnosia,” there isa general slowing of visual processing, producingperceptual failure for all but the most dominantelements in a complex, cluttered, visual world.

Manuscript received 25 October 2002Revised manuscript received 22 January 2003Revised manuscript accepted 22 January 2003

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