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Journal of Physiology - Paris 98 (2004) 125–134 www.elsevier.com/locate/jphysparis Evidence for implication of primate area V1 in neural 3-D spatial localization processing Yves Trotter *, Simona Celebrini, Jean Baptiste Durand Faculte de Medecine Rangueil, Centre de Recherche Cerveau & Cognition, CNRS, Universite Paul Sabatier, 133 route de Narbonne, 31062 Toulouse Cedex, France Abstract We investigated the neural mechanisms underlying visual localization in 3-D space in area V1 of behaving monkeys. Three different sources of information, retinal disparity, viewing distance and gaze direction, that participate in these neural mechanisms are being reviewed. The way they interact with each other is studied by combining retinal and extraretinal signals. Interactions between retinal disparity and viewing distance have been shown in foveal V1; we have observed a strong modulation of the spontaneous activity and of the visual response of most V1 cells that was highly correlated with the vergence angle. As a consequence of these gain effects, neural horizontal disparity coding is favoured or refined for particular distances of fixation. Changing the gaze direction in the fronto-parallel plane also produces strong gains in the visual response of half of the cells in foveal V1. Cells tested for horizontal disparity and orientation selectivities show gain effects that occur coherently for the same spatial coordinates of the eyes. Shifts in preferred disparity also occurred in several neurons. Cells tested in calcarine V1 at retinal eccentricities larger than 10°, show that horizontal disparity is encoded at least up to 20° around both the horizontal and vertical meridians. At these large retinal eccentricities we found that vertical disparity is also encoded with tuning profiles similar to those of horizontal disparity coding. Combinations of horizontal and vertical disparity signals show that most cells encode both properties. In fact the expression of horizontal disparity coding depends on the vertical disparity signals that produce strong gain effects and frequent changes in peak selectivities. We conclude that the vertical disparity signal and the eye position signal serve to disambiguate the horizontal disparity signal to provide information on 3-D spatial coordinates in terms of distance, gaze direction and retinal eccentricity. We suggest that the relative weight among these different signals is the determining factor involved in the neural processing that gives information on 3-D spatial localization. Ó 2004 Published by Elsevier Ltd. Keywords: 3-D space localization; Foveal and peripheral V1; Horizontal and vertical disparities; Viewing distance; Gaze direction 1. Introduction The simple motor act of grasping an object viewed in the immediate environment is the result of a series of neural transformations processed by the brain, that are still poorly understood and even difficult to replicate artificially. We will focus on the initial step that consists in localizing the objects in the near space. Three dimensional (3-D) spatial localization includes at least stereopsis, viewing distance and gaze direction. The relative position of the images of an object on both retinae will give information on relative depth of the * Corresponding author. E-mail address: [email protected] (Y. Trotter). 0928-4257/$ - see front matter Ó 2004 Published by Elsevier Ltd. doi:10.1016/j.jphysparis.2004.03.004 object, its shape and volume (stereopsis). Evaluation of the distance between the object and the observer will combine stereoscopic and ocular vergence information. If the eyes fixate straight ahead, they converge symmetrically. If the eyes fixate on other positions in space, on the horizontal meridian or obliquely, they converge asymmetrically. Both symmetrical and asymmetrical convergences define gaze directions for a particular orientation of the head. Therefore, to localize visually objects in space, the brain needs to combine information about the position of their images on the retinae with information about the location of the eyes in the orbits and the position of the head. A major question in neurosciences is to determine the neural processing for 3-D spatial localization. Clinical 126 Y. Trotter et al. / Journal of Physiology - Paris 98 (2004) 125–134 studies in humans have described, among other disorders, the difficulty in locating visual targets in space following lesions of the posterior parietal cortex [2,42]. Electrophysiological studies performed in behaving monkeys showed that this cortical area integrates signals from several modalities, among them visual and oculomotor signals. Depending on where the monkey is looking, light sensitive cells respond with a certain neural gain. This neural modulation by the direction of gaze would be the basis for encoding the position of objects in multiple frames of reference, such as eye- and head-centered [3,4]. An alternative is that this transformation is accomplished by dynamic updating of spatial representation in conjunction with voluntary eye movements [16,25]. For many years the parietal cortex was believed to be the main cortical site for processing space localization following the pioneering work of Andersen and col. [1,3]. Since then other cortical areas, from the pre-striate cortex to the pre-motor cortex [12], were also shown to be involved. We will review and give recent evidence that the so-called primary visual cortex, area V1, also closely participates to the neural 3-D space localization processing. 2. Stereopsis and viewing distance 2.1. Stereopsis and horizontal disparity sensitivity Stereoscopic depth perception depends on binocular vision, and because of the interocular distance, the image of the viewed object is projected on both retinae in slightly different angular positions, called horizontal retinal disparity. The brain uses this binocular clue to reconstruct relative depth. The demonstration that stereopsis is mainly due to retinal horizontal disparity was given by Wheatstone [96] when he invented the mirror stereoscope. This device allows the simulation of depth by presenting two photographs, one to each eye, taken with a slightly different angular direction. Subsequently Julesz [47] used psychophysical experiments with random dot stereograms to demonstrate that a difference in the horizontal position of corresponding elements of left and right images is sufficient to reconstruct depth. These stereograms are composed of two identical patterns of random dots, except that some or all of them are slightly shifted horizontally. When perceived through a stereoscope, color filters or stereo glasses, the two monocular images are fused and the angular disparity is then interpreted in terms of relative depth with a vivid 3-D percept of a shape floating in front of or behind the background depending on the sign of angular disparity (positive: behind; 0: the plane; negative: in front) introduced between the two images. From the neurophysiological point of view, area V1 is the first cortical site that integrates retinal inputs from both eyes. Left and right receptive fields of a binocular neuron may be in exact topographic correspondence in the two eyes or may have slightly disparate locations. An alternative model to the positional disparity has been proposed, in which retinal disparity information originates from differences in the internal structure of receptive fields of the left and right eyes, described in terms of phase differences [31]. In fact both position and phase differences between the monocular receptive fields appear to coexist for encoding retinal disparities [5]. In both cases, two identical stimuli falling in the same position in both receptive fields or in slightly different positions will produce binocular interactions such as binocular suppression and/or facilitation as first shown in the primary visual cortex of the anaesthetized paralyzed cat [8,28,46,60]. This property of disparity selectivity is generally considered as being the neural basis for stereopsis [69,73]. Experiments performed in the alert behaving monkey in normal conditions of binocular vision have shown in area V1 of the rhesus macaque, the existence of several categories of cells preferentially activated by stimuli located in front, behind or in the plane of fixation (Fig. 1), that appear to share a continuum in space [70– 72,89]. Recent investigations have challenged the statement that disparity sensitivity of cortical neurons in area V1 is used for depth perception. On one hand, relative disparity signals used in primate depth perception would be constructed outside area V1 [85] since the depth sensation is not reflected in the firing rate of V1 neurons [19]. On the other hand single V1 neurons may outperform the depth discrimination performance of the monkey [75]. Neuroimaging experiments in human reveal clear activations of area V1 with PET [39,40,76] or fMRI [7,90], whereas other sudies do not find such activation of area V1 [30,57,61]. Thus the question of the participation of V1 neurons in depth perception is not yet resolved. The clearest demonstration to date of a role of disparity cells in depth perception per se has been shown in area MT of the monkey, as electrical stimulation of clusters of disparity selective MT neurons can bias the monkey perceptual judgements of depth, and this bias is predictable from the disparity preference of neurons at the stimulation site [21]. There is still the unexplored possibility in primates, using such an approach, that intermediate cortical areas such as V3–V3a could also be directly involved in depth perception, as proposed by brain imaging studies [7, 61]. Disparity sensitive cells of area V1 could also be used as a 3-D signal for eliciting rapid involuntary control of vergence eye movements to bring images of both retinae into register as suggested by the use of anticorrelated patterns [51], and/or to maintain precise binocular alignment during stereoscopic vision. Y. Trotter et al. / Journal of Physiology - Paris 98 (2004) 125–134 127 Fig. 1. Categories of horizontal disparity selective cells in area V1. (A) Raster display of a cell sensitive to negative disparities (Near type) with the corresponding tuning curve in B. In C is displayed a schematic representation of the disparity sensitive cell categories. 2.2. Viewing distance and horizontal disparity sensitivity Relative disparity provides information about relative distance between objects, independently of where the eyes are looking. It does not give any information on the spatial localization of the objects in terms of distance or retinal eccentricity. Evaluation of distances of objects can be directly calculated by the angle formed by the lines of sight or angle of convergence in the fixation plane. For an object lying outside the fixation plane, it requires a calculation that combines the angle of convergence with the retinal disparity (absolute disparity) of the object. Both types of disparity, relative and absolute, must interact to yield the impression of real depth. A simple way for understanding the interaction between relative and absolute clues is to look at a stereogram in a book, at a close distance. While looking at the stereogram with a fixed relative disparity, if we move the book away from the eyes, it follows that the perceived relative depth of the anaglyph increases rapidly as the absolute distance increases. This is done according to a certain law since retinal disparities are proportional to relative stimulus depth and inversely proportional to the square of the viewing distance [64,66, for reviews]. According to that law any object that is moved away should appear to flatten very rapidly. However this is not the case. A cup for example appears as having the same shape and volume when perceived at 20 or 80 cm despite the fact that disparities are smaller by a factor of 16. This capacity to judge accurately relative depth at various viewing distances refers to depth constancy. This implies that the decrease in retinal disparity as a function of the viewing distance has to be internally compensated. Several candidates have been proposed to explain this transformation process such as ocular vergence, accommodation [29,35,67,79,94] and/or vertical disparity [11,45]. The idea that disparity selective cells in area V1 may have a link with oculomotor signals has been strengthened by experiments in which neural activity has been shown to be dependent on the viewing distance [88,89]. These studies investigated how relative and absolute cues interact in the visual pathway, in area V1 of behaving monkeys. Experiments were conducted to test disparity sensitivity using static random dot stereograms (RDS) at different viewing distances set at 20, 40 or 80 128 Y. Trotter et al. / Journal of Physiology - Paris 98 (2004) 125–134 cm. It was found that more than 75% of recorded cells drastically changed their visual response when the distance of fixation changed, with the consequence that disparity selectivity could be present at a given distance but absent at another one. This is illustrated by the example of Fig. 2A in which the visual response drops close to the spontaneous activity level for a distance of 40 cm. For other cells disparity selectivity was present at all distances but better expressed at one particular distance with higher response amplitude and sharper tuning curves as shown in the example of Fig. 2B for a distance of 40 cm. These modifications of the visual response were independent of the retinal pattern. Another consequence concerned the level of spontaneous activity level that was also modified for half the recorded cells. Because there was no retinal pattern during the time that the spontaneous activity was collected, the source of the modifications could only be extraretinal. Since modulations of both the visual response and the spontaneous activity level appeared nonretinal in origin and possibly related to the ocular convergence, we tested this possibility by using prisms, base out, that produce a change in the vergence angle without changing the distance of fixation, therefore involving the accommodation to a lesser degree [89]. Since then, other studies have been devoted to investigating the effects of manipulating the ocular convergence on disparity coding in area V1. Gonzalez and Perez [36] observed similar modulations of the visual responses for half of the cells of area V1 sensitive to horizontal disparity. On the other hand Cumming and Parker [18] could not reproduce the results of changing the ocular vergence angle. The range of vergence angles that these last authors used (from 1° to 3.5° in monkeys equivalent to about 2–7° in humans taking the interocular distance into account) was probably too small to sufficiently activate vergence signals, in contrast to the Gonzalez and Perez [36] (3–6.5° range equivalent to about 6–13° in humans) and Trotter et al. [88,89] (2–10° range equivalent to about 4–20° in human) studies. It should be noticed that about 90% of the vergence angle is used within this last range [92]. Finally Dobbins et al. [23] studied the effects of the Fig. 2. Effects of changing the viewing distance (A, B) or the gaze direction (C–F) on visual activity in V1. In A the cell is clearly a Near type cell at a distance of 80 cm but is nonvisually responsive at 40 cm. In B this cell shows a sharper tuning curve (Tuned Far type) and a higher visual amplitude response at 40 cm than at 20 or 80 cm viewing distances. Dashed curves are gabor fittings. In C the cell is a Tuned Excitatory type (TE) for a gaze oriented to the left at )10° or in the center (0°) of a video monitor screen but its visual activity almost disappears for a gaze to the right at +10°. Dashed curves are gabor fittings. In D the cell shows a higher visual response (orientation selective) for a gaze at the center of the screen than for the other directions. The dashed curves are gaussian fittings. In E (recorded in calcarine V1, retinal eccentricity )22.5° the cell is a Near type cell. Its activity increases and the peak of disparity selectivity changes progressively with the deviation of the gaze. In F (calcarine V1, eccentricity )12.5°) this cell shows progressive changes in peak selectivities as the gaze turns from 10° on the right (Tuned Near), to 15° (TE type) and becomes Tuned Far at 18°. Dashed curves are gabor fittings. Y. Trotter et al. / Journal of Physiology - Paris 98 (2004) 125–134 viewing distance in area V1 on another retinal feature, i.e. the size of an image, using similar angular vergence angles to those of Trotter et al. [88,89]. They observed strong modulations of the visual response and of the spontaneous activity, and extended their observations to the cortical area V4. Strong modulations of cell activities in cortical areas V1, V2 and V4 of the behaving monkey were reported recently by changing the viewing distances in similar conditions [82]. 129 gaze and to a lesser extent for a leftward position of the eyes than for a rightward position. For cells that were tested for both horizontal disparity and orientation selectivities the gain effect was congruent for a common gaze direction. Other studies also reported influences of the gaze direction on the visual excitability of foveal V1 neurons in primates [41,82] and in cat area 17 [95]. 3.2. Gaze angle and horizontal disparity in peripheral V1 3. Stereopsis and gaze angle 3.1. Gaze angle and horizontal disparity in foveal V1 Gaze direction has been shown to modulate the neural activity of most cortical areas in the dorsal pathway [12] and has been interpreted as being a neural process involved in spatial localization [1]. Similar modulations also appear to occur in the ventral pathway [14,62]. The question still debated [18] is whether the primary visual cortex (area V1) is involved in the neural process of spatial localization or not. The demonstration of the effects of changing the viewing distance (see above) on the neural activity of V1 cells strongly suggest that area V1 also participates to the neural process of spatial localization. To test this possibility, a series of experiments [87] was performed on behaving monkeys trained to fixate a small target located in the frontoparallel plane at three positions on a video monitor screen (center 0°, left )10°, right +10°). Stimuli such as dynamic RDSs generated through ferro-electric stereo glasses at 60 Hz per eye were projected in the visual field, centered on the receptive field. Static square wave gratings of the same size were also used to test orientation selectivity for evaluating whether the eventual gaze effects could be extended to other cortical properties in a coherent way or not. Neurons were recorded extracellularly in area V1 in the central representation of the visual field. Responses to horizontal disparity and grating orientation as well in about half of the tested cells were strongly modulated in that these properties were present at a given gaze direction, but absent or poorly expressed at another direction. This gain effect was present for 72% of cells studied for disparity and 85% of cells studied for orientation. The cell illustrated in Fig. 2C detects the presence of the stimulus RDS in the plane of fixation (0° disparity angle, i.e. Tuned Excitatory cell) when the monkey fixates straight ahead or on the left ()10°) but very poorly for a fixation on the right (+10°). Shifts in peak selectivity occurred for 17% of disparity selective cells. Similar observations were made concerning stimulus orientation except for changes in peak (0%). Fig. 2D shows an example of a cell whose orientation selectivity (oblique) is better expressed for a centered A second series of experiments was performed in the peripheral region of the primary visual cortex called calcarine V1, anatomically located just below foveal V1. Except for the cortical mapping of receptive fields located at retinal eccentricities larger than 10° along either the horizontal meridian (dorsal calcarine V1) or the vertical meridian (ventral calcarine V1) [20,33,91], very little is known concerning their functional properties [9,68]. A Rhesus monkey, with scleral coils implanted in both eyes, was trained to fixate at up to seven directions in the fronto-parallel plane. Visual stimuli were the same as those used in the foveal V1 study. Experimental recordings show that cells in this region are still highly selective to stimulus disparity (36% of cells) and/or stimulus orientation (100% of cells) and also to the direction of gaze (75% of cells). Gaze effects are similar to those reported in foveal V1. The example in Fig. 2E illustrates a cell (Near type) that combines modulation of the visual response and progressive changes in peak positions as the gaze rotates progressively from 8° to 12°. In Fig. 2F the cell shows changes in peak selectivity not associated with the modulations of the visual response. It is a Tuned Near cell for a gaze at 10° on the right, then is Tuned 0° for a gaze at 15° and becomes a Tuned Far cell at 18°. For these changes in the peak of disparity selectivity that appear in the foveal and peripheral V1, one possible explanation is the following. For a gaze directed in the center of the screen, the normal to the binocular axis and the tangent to the Vieth-M€ uller circle, that is used as a reference for stereoscopic judgements, are superimposed. For a gaze directed on the left or on the right (asymmetrical convergence) the normal to the direction of gaze is rotated away from the tangent, that should induce a change in binocular correspondence and therefore errors in stereoscopic judgements. However psychophysical experiments do not find such misjudgements. Therefore for the normal surface to yield correct stereoscopic spatial perception, a compensation process must take place [56,65]. The subset of neurons that change their preferred disparity angle may be a part of the neural substrate that allows the compensation for this shift in depth. Indeed after calculation, taking into account the hemisphere and retinal eccentricity, the shift 130 Y. Trotter et al. / Journal of Physiology - Paris 98 (2004) 125–134 in peaks corresponds exactly to the angular rotation in depth of the normal axis to the tangent. 4. Eye position signals, retinal versus extraretinal Concerning the gain effects in foveal V1 produced by changing the viewing distance, the signal responsible for it, is probably oculomotor in origin related to the eye position. Modulation of the visual response and of the spontaneous activity by ocular vergence indicates that the visual pathway receives an extraretinal source related to ocular motility. If the modulations of the visual response resulted from feedback influences from higher cortical areas, they should occur with some delay in the course of the visual response. But this was not the case as these modulations were present at the beginning of the visual response and remain constant throughout [87]. A probable source of feed-forward interaction between retinal and extraretinal signals may reflect a neural gating that could be mediated from the dorsolateral geniculate nucleus (LGNd). It should be pointed out that spontaneous activity modulation of about onethird of the LGNd cells has been described by manipulating the vergence angle with prisms in the awake monkey [78]. Also eye position signals have been shown to influence visual activity of LGNd neurones in other species such as the cat [24,50] and the rabbit [55]. What are the possible origins of these signals? The two classical possible sources are efference copy and extraocular muscle proprioception (EMP). Both are probably involved to a certain degree in spatial localization [34] and many studies have provided evidence for a functional role of EMP in spatial location, construction of extrapersonal space, eye alignment control, postnatal development of depth perception and of neuronal selectivities including disparity coding [15,83,86, for reviews]. There is another signal that may possibly account for the gaze effects on V1 cells, not in the foveal representation of the visual field where it is negligible, but in the peripheral field where it occurs naturally: this is vertical disparity that has been recently shown to be encoded in area V1 at peripheral eccentricities [26]. 5. Vertical disparity Differences in the position of similar binocular images in the vertical dimension are called vertical disparities. In normal use of the eyes, they occur when the eyes converge at a close distance. In that case, the images of all points located above or below the visual plane, except those lying in the median plane, are vertically disparate. Vertical disparities occur in all situations where an object is closer to one eye (eccentric images, oblique gaze. . .). Its image is larger on the retina of this eye resulting in angular disparities that include the vertical dimension. Vertical disparities decrease with distance but increase with retinal size, with horizontal and vertical eccentricities and with gaze directions. Whether vertical disparities affect the binocular perception of depth has been and still is a matter of debate. They affect depth perception if the vertical angular deviations are too important [59] and can be regarded as just a geometrical defect (an error) more or less tolerated by the visual system. As a result, an ocular shift must occur to compensate for the vertical angular deviations in order to recover the binocular matching involved in stereopsis. Vertical disparities may thus act as retinal signals sent to the oculomotor centers for driving vergence movements in the vertical dimension to align the eyes, just as horizontal disparities do for driving horizontal ocular vergence. In other words horizontal vergence occurs when the gaze is shifted from one depth plane to another and vertical vergence occurs when the gaze shifts in oblique directions towards a target in a tertiary position [43]. Gain for vertical vergence increases as the stimulus area increases around the fovea [44]. Vertical disparities occur naturally in stereoscopic vision, the angular range depending on the size of the images and on their retinal eccentricities [66]. The first demonstration of a functional role of vertical disparity in depth perception was given by ‘the induced effect’ [63]. When a meridional lens (one that produces a horizontal size disparity) is placed in front of one eye, the apparent plane appears rotated around the vertical axis in a way predicted by geometry (geometrical effect). If a vertical lens (one that produces a vertical size disparity) is placed in front of one eye, the apparent plane appears rotated in the opposite direction in a way not predictable by geometry, as if a meridional lens was applied in front of the other eye (induced effect). Psychophysical experiments have confirmed the functional role of vertical disparity in stereoscopic vision [6,10,13,48,80, 81,84]. Vertical disparity carries information that theoretically permits the disambiguation of horizontal disparity signals in terms of 3-D localization. Several models have been proposed to explain how horizontal and vertical disparity signals could interact to recover the 3-D space characteristics with or without an extraretinal source of information on the position of the eyes in their orbits [32,49,53]. In contrast to horizontal disparity that has been the object of increasing interest at the neurophysiological level during the past few years, very few studies have been devoted to vertical disparity sensitivity [37,69]. Vertical incongruities of receptive fields of binocular neurons were first shown in the cortical areas 17 and 18 of the anaesthetized cat [8,46,60,93]. In primates, sensitivity of cortical neurons to vertical disparity was shown in the foveal area V1 of the behaving monkey [17,38], in area MT of the anaesthetized monkey [52] and in the Y. Trotter et al. / Journal of Physiology - Paris 98 (2004) 125–134 131 disparity encoding, the percentage of selective cells is lower than what is found in the foveal part of V1 (about half) but half of them are Tuned Near and Tuned Far types. Since stereoscopic vision is low or absent at such retinal eccentricities, these disparity sensitive cells can hardly account for a neural process involved in stereoscopic depth per se but rather in a fine ocular alignment control. 6. Conclusions Fig. 3. Vertical disparity tuning profiles of cells located in the calcarine V1. On top, cells exhibit tuning profiles similar to those of horizontal disparity selective cells. Red curves are gabor fittings. In at the bottom example of a cell tested for 70 combinations of horizontal and vertical disparities. This cell is selective to both dimensions, to horizontal disparity (HD of 0.4–0.6°, Far type) and vertical disparity (VD of 0.4– 0.6°, Far-like). wulst of the awake barn owl [58]. These studies were usually performed in the central part (within 10°) of the representation of the visual field, paying less attention to the peripheral field probably because stereoscopic vision rapidly vanishes outside of the fovea [54,77]. In contrast vertical disparity increases with retinal eccentricity. Therefore it is in the peripheral field that one should expect this signal to be encoded rather than in the central field. We have conducted a study in a behaving monkey [26] to test vertical disparity selectivities, and horizontal disparity as well, in the calcarine area V1 and area V2, hence beyond 10° of retinal eccentricity. A Rhesus macaque was trained to perform a fixation task, gaze straight ahead, with scleral coils implanted in both eyes. Both horizontal and vertical disparity selectivities were tested using dynamic RDS. A large proportion of the tested cells were selective to both types of disparities (47%), and to a lesser extent to only one type (horizontal: 8%; vertical: 23%). We found a true encoding of vertical disparity, with the same diversity in the tuning profiles as described for horizontal disparity (Fig. 3, top view), that cannot be assimilated with a simple disturbance of the binocular matching process as proposed earlier [69]. Moreover, cells sensitive to vertical disparities cover a finer angular scale than those of horizontal disparities, which is coherent with the smaller range of naturally occurring vertical disparities. The cell in Fig. 3 (bottom) was tested for combined horizontal and vertical disparities (matrix of 70 combinations). This cell shows a clear interdependence between horizontal and vertical disparity codings, which is a Far type cell for horizontal disparity and Far-like type for vertical disparities both centered on 0.4–0.6°. For the horizontal The viewing distance effects on the activity of foveal V1 cells most probably originate from eye position signals since vertical disparity of the receptive fields within 3° of retinal eccentricity is too small, around 1 min of arc at 20 cm and 0.3 min of arc at 80 cm, to account for the strong modulations of visual responsiveness. And vertical disparity obviously cannot account for the modulations of the spontaneous activity in absence of visual stimulation. On the other hand, the gaze direction effects in the cortical area V1 likely originate from various combinations of eye position signals, horizontal and vertical disparity signals. Horizontal disparity by itself is not informative about 3-D characteristics of space in terms of distance or eccentricity. Eye position and vertical disparity signals must contribute at least with a relative weight depending on the 3-D configurations (small image size/large size, foveal/peripheric, close distance/far, gaze direction ahead/oblique. . .) as proposed by psychophysical [13,80] and modelling studies [6,10,27,32]. These different weighted combinations should allow transformations of frame coordinates in Fig. 4. Schematic representation of the activity of a neurone (Far type) that is dependent on 3-D eye coordinates. The activity of this cell is optimally expressed for a gaze of )10° on the left, at 40 cm of viewing distance. The elliptic shape in gradual blue represents this zone in space and can be regarded as a 3-D module defined by eye position coordinates. 132 Y. Trotter et al. / Journal of Physiology - Paris 98 (2004) 125–134 order to reconstruct the 3-D space for reaching the objects accurately, possibly through a basis function representation that predicts that a large majority of cells should encode two or more signals simultaneously and combine these signals nonlinearly [22,74]. However, the way these combinations are processed at the neuronal level remains to be investigated. Preliminary experiments on these combinations in our laboratory show that some neurons in area V1 have gain effects that cannot be explained totally by vertical disparity signal alone or by eye position signal alone, while others can be explained mostly by one or by the other. Further neurophysiological studies will be needed to determine the weight of these respective factors at the cellular level, to better understand sensorimotor transformation processing necessary to navigate in 3-D space. If we bring together the results on the effects of the viewing distance and those of the gaze direction in area V1, we come up with the proposal that cortical properties such as orientation and retinal disparity selectivities, that define shapes and volumes of objects, are optimally expressed in a limited range of 3–D gaze directions so that information about stimuli in the V1 area is conveyed by cell populations only when the object is present within restricted volumes of space. Fig. 4 illustrates for one hypothetical neuron this spatial representation inside a restricted volume of space defined by 3-D eye position and/or vertical disparity signals. These modules should be regarded as 3-D fields, as being a part of the neural substrate that is involved in sensory-motor transformations for 3-D space localization. Acknowledgements We thank E. Galy and S.P. Zhu for their participation in some of the experiments. References [1] R.A. Andersen, G.K. Essick, R.M. 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