{"title": "A Model of Spatial Representations in Parietal Cortex Explains Hemineglect", "book": "Advances in Neural Information Processing Systems", "page_first": 10, "page_last": 16, "abstract": null, "full_text": "A Model of Spatial Representations in \nParietal Cortex Explains Hemineglect \n\nAlexandre Pouget \nDept of Neurobiology \n\nUCLA \n\nLos Angeles, CA 90095-1763 \n\nalex@salk.edu \n\nTerrence J. Sejnowski \n\nHoward Hughes Medical Institute \n\nThe Salk Institute \nLa Jolla, CA 92037 \n\nterry@salk.edu \n\nAbstract \n\nWe have recently developed a theory of spatial representations in \nwhich the position of an object is not encoded in a particular frame \nof reference but, instead, involves neurons computing basis func(cid:173)\ntions of their sensory inputs. This type of representation is able \nto perform nonlinear sensorimotor transformations and is consis(cid:173)\ntent with the response properties of parietal neurons. We now ask \nwhether the same theory could account for the behavior of human \npatients with parietal lesions. These lesions induce a deficit known \nas hemineglect that is characterized by a lack of reaction to stimuli \nlocated in the hemispace contralateral to the lesion. A simulated \nlesion in a basis function representation was found to replicate three \nof the most important aspects of hemineglect: i) The models failed \nto cross the leftmost lines in line cancellation experiments, ii) the \ndeficit affected multiple frames of reference and, iii) it could be \nobject centered. These results strongly support the basis function \nhypothesis for spatial representations and provide a computational \ntheory of hemineglect at the single cell level. \n\n1 \n\nIntroduction \n\nAccording to current theories of spatial representations, the positions of objects \nare represented in multiple modules throughout the brain, each module being spe(cid:173)\ncialized for a particular sensorimotor transformation and using its own frame of \nreference. For instance, the lateral intraparietal area (LIP) appears to encode the \nlocation of objects in oculocentric coordinates, presumably for the control of sac(cid:173)\ncadic eye movements. The ventral intraparietal cortex (VIP) and the premotor \ncortex, on the other hand, seem to use head-centered coordinates and might be \n\n\fA Model of Spatial Representations in Parietal Cortex Explains Hemineglect \n\n11 \n\nA \n\nB \n\n..... -----.a... Right \nStimulus \n\n.------\n\n~ Left \nStimulus \n\nCl \n\nC2 \n\nit~ Cl \n! \\~ Cl \n\nTarget Distractors \n\nC2 \n\n+ \u2022 \u2022 \u2022 \" \n+ \n\nC2 \n\u2022 \u2022 \u2022 \" C3 \n\nC3 \n\nFP \n\nFigure 1: A. Retinotopic neglect modulated by egocentric position. B. Stimulus(cid:173)\ncentered neglect \n\ninvolved in the control of hand movements toward the face. \n\nThis modular theory of spatial representations is not fully consistent with the be(cid:173)\nhavior of patients with parietal or frontal lesions. Such lesions causes a syndrome \nknown as hemineglect which is characterized by a lack of response to sensory stim(cid:173)\nuli appearing in the hemispace contralateral to the lesion [3]. According to the \nmodular view, the deficit should be behavior dependent, e.g., oculocentric for eye \nmovements, head-centered for reaching. However, experimental and clinical studies \nshow that this is not the case. Instead, neglect affects multiple frames of reference \nsimultaneously, and to a first approximation, independently of the task. \n\nThis point is particularly clear in an experiment by Karnath et al (1993) (Fig(cid:173)\nure 1A). Subjects were asked to identify a stimulus that can appear on either side \nof the fixation point. In order to test whether the position of the stimuli with \nrespect to the body affects performance, two conditions were tested: a control con(cid:173)\ndition with head straight ahead (C1), and a second condition with head rotated \n20 degrees on the right (or equivalently, with the trunk rotated 20 degrees on the \nleft, see figure) (C2). In C2, both stimuli appeared further to the right ofthe trunk \nwhile being at the same location with respect to the head and retina than in Cl. \nMoreover, the trunk-centered position of the left stimulus in C2 was the same than \nthe trunk-centered position of the right stimulus in C1. \n\nAs expected, subjects with right parietal lesions performed better on the right \nstimulus in the control condition, a result consistent with both, retinotopic and \ntrunk-centered neglect. To distinguish between the two frames of reference, one \nneeds to compare performance across conditions. \nIf the deficit is purely retinocentric, the results should be identical in both condi(cid:173)\ntions, since the retinotopic location of the stimuli does not vary. If, on the other \nhand, the deficit is purely trunk-centered, the performance on the left stimulus \nshould improve when the head is turned right since the stimulus now appears fur(cid:173)\nther toward the right of the trunk-centered hemispace. Furthermore, performance \non the right stimulus in the control condition should be the same as performance on \nthe left stimulus in the rotated condition, since they share the same trunk-centered \nposition in both cases. \n\n\f12 \n\nA. POUGET, T. J. SEJNOWSKI \n\nN either of these hypotheses can fully account for the data. As expected from a \nretinotopic neglect, subjects always performed better on the right stimulus in both \nconditions. However, performance on the left stimulus improved when the head \nwas turned right (C2), though not sufficiently to match the level of performance on \nthe right stimulus in the control condition (C1). Therefore, these results suggest a \nretinotopic neglect modulated by trunk-centered factors. \n\nIn addition, Karnath et al (1991) tested patients on a similar experiment in which \nsubjects were asked to generate a saccade toward the target. The analysis of reaction \ntime revealed the same type of results than the one found in the identification \ntask, thereby demonstrating that the spatial deficit is, to a first approximation, \nindependent of the task. \n\nAn experiment by Arguin and Bub (1993) suggests that neglect can be object(cid:173)\ncentered as well. As shown in figure 1B, they found that reaction times were faster \nwhen the target appeared on the right of a set of distractors (C2), as opposed \nto the left (C1), even though the target is at the same retinotopic location in \nboth conditions. Interestingly, moving the target further to the right leads to even \nfaster reaction times (C3), showing that hemineglect is not only object-centered but \nretinotopic as well in this task. \n\nThese results strongly support the existence of spatial representations using multiple \nframes of reference simultaneously shared by several behaviors. We have recently \ndeveloped a theory [6] which has precisely these properties and we ask here whether \na simulated lesion would lead to a deficit similar to hemineglect. Our theory posits \nthat parietal neurons computes basis function (BF) of sensory signals, such as vi(cid:173)\nsual, or auditory inputs, and posture signals, such as eye or head position. The \nresulting representation, which we called a basis function map, can be used for per(cid:173)\nforming nonlinear transformations of the sensory inputs, the type of transformations \nrequired for sensorimotor coordination. \n\n2 Model Organization \n\nThe model contains two distinct parts: a network for performing sensorimotor trans(cid:173)\nformations and a selection mechanism. \n\n2.1 Network Architecture \n\nWe implemented a network using basis function units in the intermediate layer \nto perform a transformation from a visual retinotopic map to two motor maps \nin, respectively, head-centered and oculocentric coordinates (Figure 2). The input \ncontains a retinotopic visual map analog to the one found in the early stages of \nvisual processing, and a set of units encoding eye position, similar to the neurons \nfound in the intralaminar nucleus of the thalamus. These input units project to a \nset of intermediate units shared by both transformations. Each intermediate unit \ncomputes a gaussian of the retinal location of object, rx , multiplied by a sigmoid of \neye position, ex: \n\nO i= - - - - -\n\n1 + e- e:Z:-/;rj \n\n(1) \n\nThese units are organized in a map covering all possible combinations of retinal \nand eye position selectivities. As we have shown elsewhere [6], this type of response \nfunction is consistent with the response of single parietal neurons found in area 7a. \n\n\fA Model of Spatial Representations in Parietal Cortex Explains Hemineglect \n\n13 \n\nA \n\nSaccadic Eye Movements \n\nt \n\n(00000000000000) \n\nRetinotopic map \n\n(Superior CollicuJus) \n\nReaching t \n\n(0000000000009) \nHead-centered map \n(Premotor Cortex) \n\nB \nt&:-6 .. t .,', J0,\\~ \n\nRetinal position (0) Head-centered position (0) \n\n,. 00000000000000 \n00000000000000 \n~ , 8 00000000000000 \n\n] . :::::::::::::: \n.~ 0 00000000000000 \n& ., :::::::::::::: \nQ) -,0 00000000000000 \n~ .1' :::::::::::::0 \n\nRetinal position (0) \n\nBFmap \n\n(7a) \n\n\u00b0 c:: \n,g \nl \n~ \n'\" \n\nBFmap \n\n(7a) \n\n\" \n\n7~i1i \n\n~ ~ \n\n. . \n\n10 \n\n. \n\ntJ\\,L\\. \n\n_20 \n\n_10 \n\n0 \n\nRetinal position (0) \n\n000000000 \nRetinotopic map \n\n(VI) \n\nEye position cells \n\n(Thalamus) \n\nFigure 2: A. Network architecture B. Typical pattern of activity \n\nThe resulting map forms a basis function map which encodes the location of objects \nin head-centered and retinotopic coordinates simultaneously. \n\nThe activity of the unit in the output maps is computed by a simple linear combi(cid:173)\nnation of the BF unit activities. Appropriate values of the weights were found by \nusing linear regression techniques. \n\nThis architecture mimics the pattern of projections of the parietal area 7a. 7a is \nknown to project to, both, the superior colliculus and the premotor cortex (via the \nventral parietal area, VIP) , in which neurons have, respectively, retinotopic and \nhead-centered visual receptive fields. Figure 2B shows a typical pattern of activity \nin the network when two stimuli are presented simultaneously while the eye fixated \n10 degrees toward the right. \n\n2.2 Hemispheric Biases and Lesion Model \n\nNeurophysiological data indicate that both hemispheres contain neurons with all \npossible combinations of retinal and eye position selectivities, but with a contralat(cid:173)\neral bias. Hence, most neurons in the right parietal cortex (resp. left) have their \nretinal receptive field on the left hemiretina (resp. right) . The bias for eye position \nis much weaker but a trend has been reported in several studies [1] . \n\nTherefore, spatial representations in a patient with a right parietal lesions are biased \ntoward the right side of space. We modeled such a lesion by using a similar bias in \nthe intermediate layer of our network. The BF map simply has more neurons tuned \nto right retinal and eye positions. We found that the exact profile of the neuronal \ngradient across the basis function maps did not matter as long as it was monotonic \nand contralateral for both eye position and retinal location . \n\n2.3 Selection model \n\nWe also developed a selection mechanism to model the behavior of patients when \npresented with several stimuli simultaneously. The simultaneous presentation of \n\n\f14 \n\nA. POUGET, T. J. SEJNOWSKI \n\nstimuli induces multiple hills of activity in the network (see for instance the pattern \nof activity shown in figure IB for two visual stimuli). Our selection mechanism \noperates on the peak values of these hills. \nAt each time step, the most active stimulus is selected according to a winner-take(cid:173)\nall and its corresponding activity is set to zero (inhibition of return). At the next \ntime step, the second highest stimuli is selected while the previously selected item \nis allowed to recover slowly. This procedure ensures that the most active item is \nnot selected twice in a row, but because of the recovery process, stimulus with high \nactivity might be selected again if displayed long enough. \n\nThis mechanism is such that the probability of selecting an item is proportional \nto two factors: the absolute amount of activity associated with the item, and the \nrelative activity with respect to other competing items. \n\n2.4 Evaluating network performance \n\nWe used this model to simulate several experiments in which patient performance \nwas evaluated according to reaction time or percent of correct response. \n\nReaction time in the model was taken to be proportional to the number of time \nsteps required by our selection mechanism to select a particular target. Performance \non identification task was assumed to be proportional to the strength of the activity \ngenerated by the stimuli in the BF map. \n\n3 Results \n\n3.1 Line cancellation \n\nWe first tested the network on the line cancellation test, a test in which patients are \nasked to cross out short line segments uniformly spread over a page. To simulate \nthis test, we presented the display shown in figure 3A and we ran the selection \nmechanism to determine which lines get selected by the network. As illustrated in \nfigure 3A, the network crosses out only the lines located in the right half of the \ndisplay, just as left neglect patients do in the same task. The rightward gradient \nintroduced by the lesion biases the selection mechanism in favor of the most active \nlines, i.e., the ones on the right. As a result, the rightmost lines win the competition \nover and over, preventing the network from selecting the left lines. \n\n3.2 Mixture of frames of reference \n\nNext, we sought to determine the frame of reference of neglect in the model. Since \nKarnath et al (1993) manipulated head position, we simulated their experiment \nby using a BF map integrating visual inputs with head position, rather than eye \nposition. We show in figure 3B the pattern of activity obtained in the retinotopic \noutput layer of the network in the various experimental conditions (the other maps \nbehaved in a similar way). In both conditions, head straight ahead (dotted lines) or \nturned on the side (solid lines), the right stimulus is associated with more activity \nthan the left stimulus. This is the consequence of the larger number of cells in \nthe basis function map for rightward position. In addition, the activity for the left \nstimulus increases when the head is turned to the right. This effect is related to the \nlarger number of cells in the basis function maps tuned to right head positions. \n\nSince network performance is proportional to activity strength, the overall pattern \nof performance was found to be similar to what has been reported in human patients \n\n\fA Model of Spatial Representations in Parietal Cortex Explains Hemineglect \n\n15 \n\nA \n\nB \n\nc \n\na1 ___________ _ \n\n., , , \n,., ! , \n\" \n'\\ \n\n, \n\n'\\ \n\n,. \n\n! ',I\u00b7 '_.' \n\nI \n\nI \n\n.1 \n\n+ \n\nFP \n\n)( \u2022 \u2022 \u2022 C1 \n\nTarget Distractors \n\na21-----:--;-~-~ \n\n.\" .... ,. '.' ... ~ \n\n+ \u2022 \u2022 \u2022 )( \n\nC2 \n\nLeft \n\nStimulus \n\nRight \n\nStimulus \n\na3 \n\n+ \n\n-----------------------\n\n,', \n\" . . \n,.. \" \n\n' . / ' \n\n, ... \n\n1\". I\u00b7 \n\n\u2022 \u2022 \u2022 )( C3 \n\nFigure 3: Network behavior in line cancellation task (A). Activity patterns in the \nretinotopic output layer when simulating the experiments by Karnath et al (1993) \n(B) and Arguin et al (1993) (C) \n\n(figure lA), namely: the right stimulus was better processed than the left stimulus \nand performance on the left stimulus increases when the head is rotated toward the \nright. Therefore, just like in human, neglect in the model is neither retinocentric \nnor trunk-centered alone, but both at the same time. \n\n3.3 Object-centered effect \n\nWhen simulating Arguin et al (1993) experiments, the network reaction times were \nfound to follow the same trends than for human patients. Figure 3C illustrates the \npatterns of activity in the retinotopic output layer of the network when simulating \nthe three conditions of Arguin experiments. Notice that the absolute activity asso(cid:173)\nciated with the target (solid lines) in conditions 1 and 2 is the same, but the activity \nof the distractors (dotted lines) differs in the two conditions. In condition 1, they \nhave higher relative activity and thereby strongly delay the detection of the target \nby the selection mechanism. In condition 2, the distractors are now less active than \nthe target and do not delay target processing as much as they do in condition 1. \nThe reaction time decreases even more in condition 3, due to a higher absolute \nactivity associated with the target. Therefore, the network exhibits retinocentric \nand object-centered neglect, just like parietal patients [2]. \n\n4 Discussion \n\nThe model of parietal cortex presented here was originally developed by consider(cid:173)\ning the response properties of parietal neurons and the computational constraints \ninherent in sensorimotor transformations. It was not designed to model neglect, so \nits ability to account for a wide range of deficits is additional evidence in favor of \nthe basis function hypothesis. \n\nAs we have shown, our model captures three essential aspects of the neglect syn(cid:173)\ndrome: 1) It reproduces the pattern of line crossing reported in patients in line(cid:173)\ncancellation experiments, 2) the deficit coexists in multiple frames of reference si(cid:173)\nmultaneously, and 3) the model accounts for some of the object-based effects. \n\n\f16 \n\nA. POUGET, T. J. SEJNOWSKI \n\nWe can account for a very large number of studies beyond the ones we have con(cid:173)\nsidered here, using very similar computational principles. We can reproduce, in \nparticular, the behavior of patients in line-bisection experiments and we can ex(cid:173)\nplain why neglect affects multiple cartesian frames of reference such as retinotopic, \nhead-centered, trunk-centered, environment-centered (i.e. with respect to gravity), \nand object-centered. \nIt must be emphasized that these results have been obtained without using ex(cid:173)\nplicit representations of these various cartesian frames of reference (except for the \nretinotopy of the BF map). In fact, this is precisely because the lesion affected \nnoncartesian representations that we have been able to reproduce these results. We \nhave assumed that the lesion affects the functional space in which the basis functions \nare defined. This functional space shares common dimensions with cartesian spaces, \nbut cannot be reduced to the latter. Hence, a basis function map integrating retinal \nlocation and head position is retinotopic, but not solely retinotopic. Consequently, \nany attempts to determine the cartesian space in which hemineglect operates is \nbound to lead to inconclusive results in which cartesian frames of reference appear \nto be mixed. \n\nThis study and previous research [6] suggests that the parietal cortex represents \nthe position of objects by computing basis functions of the sensory and posture \ninputs. It would now be interesting to see if this hypothesis could also account for \nsensorimotor adaptation, such as learning to reach properly when wearing visual \nprisms. We predict that adaptation takes place in several frames of reference simul(cid:173)\ntaneously, a prediction that is testable and would provide further support for the \nbasis function framework. \n\nReferences \n\n[1] R.A. Andersen, C. Asanuma, G. Essick, and R.M. Siegel. Corticocortical connec(cid:173)\n\ntions of anatomically and physiologically defined subdivisions within the inferior \nparietal lobule. Journal of Comparative Neurology, 296(1):65-113,1990. \n\n[2] M. Arguin and D.N. Bub. Evidence for an independent stimulus-centered refer(cid:173)\n\nence frame from a case of visual hemineglect. Cortex, 29:349-357, 1993. \n\n[3] K.M. Heilman, R.T. Watson, and E. Valenstein. Neglect and related disorders. \nIn K.M. Heilman and E. Valenstein, editors, Clinical Neuropsychology, pages \n243-294. Oxford University Press, New York, 1985. \n\n[4] H.O. Karnath, K. Christ, and W. Hartje. Decrease of contralateral neglect by \nneck muscle vibration and spatial orientation of trunk midline. Brain, 116:383-\n396, 1993. \n\n[5] H.O. Karnath, P. Schenkel, and B. Fischer. Trunk orientation as the determin(cid:173)\ning factor of the 'contralateral' deficit in the neglect syndrome and as the phys(cid:173)\nical anchor of the internal representation of body orientation in space. Brain, \n114:1997-2014, 1991. \n\n[6] A. Pouget and T.J. Sejnowski. Spatial representations in the parietal cortex \n\nmay use basis functions. In G. Tesauro, D.S. Touretzky, and T.K. Leen, edi(cid:173)\ntors, Advances in Neural Information Processing Systems, volume 7. MIT Press, \nCambridge, MA, 1995. \n\n\f", "award": [], "sourceid": 1071, "authors": [{"given_name": "Alexandre", "family_name": "Pouget", "institution": null}, {"given_name": "Terrence", "family_name": "Sejnowski", "institution": null}]}