Receptive Field

… large-scale integration effects are thought to be generally involved in the generation of stable visual percepts.

A famous example of this kind is the aperture problem (Hildreth and Koch, 1987 ; Wallach, 1935 ). The area where a neuron in the visual system can be excited by a stimulus is constrained by the finite dimensions of its receptive field, the neuronquotidns window or aperture to the outer world. If an elongated stimulus passes over such a receptive field, the neuron will only respond to the motion component orthogonal to the orientation of the stimulus. This effect occurs essentially for all cells at lower visual processing stages where receptive fields are small and the ability of individual neurons to unambiguously encode stimulus properties is hence limited. On the other hand, the activity of a subset of neurons usually provides sufficient information to resolve these ambiguities at higher levels. It has, for instance, been demonstrated that the aperture problem is resolved by integration in the motion sensitive area MT (Pack and Born, 2001 ).

At early stages of visual processing in the cortex, neurons view the visual environment through a window – or receptive field – which affords only a restricted view of the world. Receptive fields are located at every position in the visual field and tuned into different ranges along multiple visual dimensions. For example, the same neuron can signal the tilt, size, color, motion direction and absolute depth of an object at one location in the visual field. The output of this coding scheme is a piecemeal representation of the visual scene which cannot be used to unambiguously guide sensorimotor behavior. Subsequent stages of cortical visual processing almost certainly serve to reconstitute early visual signals into a coherent representation of a visual scene, most likely by striking a delicate, and possibly flexible, balance between the integration and segmentation of early visual signals. Yet we have still not figured out the computational principles governing this fundamentally important combinatorial process.

The origin of spatiotemporal nonlinearities in GCs is still not fully understood. In this paper, we suggest that two visual illusions, caused by fixational eye movements, may be directly related to specific properties of retinal MC ganglion cells (GCs).

Effects of fixational eye movements on retinal ganglion cell responses: A modelling study
Matthias H. Hennig1* and Florentin Wörgötter2
Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh, UK
Bernstein Center for Computational Neuroscience, University of Göttingen, Germany

FIGURE 6

www.frontiersin.orgFigure 6. Examples of stimuli that elicit motion-induced illusions similar to those seen for the star. (A) Purkinje Illusion (Wade, 2003 ). (B) The Responsive Eye from Bridget Riley (Wade, 2003 ). (C) The MacKay Illusion (Pirenne et al., 1958 ). (D) Ouchi Illusion (Spillmann and Werner, 1990 ).

The aperture problem has been discussed previously in conjunction with apparent motion effects that are induced by fixational eye movements. Models have been made to explain the Ouchi illusion (Figure 6 D) and others (Fermüller et al., 1997 ; Fermüller et al., 2000 ; Mather, 2000 ) by means of simulated cortical motion detectors (Zanker, 2004 ; Zanker and Walker, 2004 ). Our study augments these findings by providing arguments for a retinal origin of such apparent motion effects. It is conceivable that the apparent motion elicited by these illusions requires at some point the activation of cortical motion detectors. Our results, however, indicate that this percept may not be the consequence of specific properties of cortical motion detectors.

FIGURE 1


Figure 1. Summary of the model connectivity and behaviour. (A) Schematic diagram of the model retina. Photoreceptors (P) connect by excitatory synapses (⊕) to horizontal cells (H) and by sign-inverting synapses (⊖) to on-centre bipolar cells (BCs). Horizontal cells connect to BCs with sign-conserving synapses. The receptive field of on-centre GCs consists of excitatory input from on-centre BCs (centre) and inhibitory input from wide field amacrine cells (A, surround). For MC-cells, the presynaptic BCs receive inhibition from narrow-field amacrine cells (N) at the axon terminal (forming a subgroup of transient BCs). Narrow-field amacrine cells receive excitatory input from BCs and inhibition from wide-field amacrine cells (W). Wide-field amacrine cells are excited by transient BCs and receive inhibition from narrow-field amacrine cells. Combined, this coupling of amacrine cells forms a nested circuit (shaded region), which leads to transient responses in MC-GCs. (B) Spatial parameters of the simulated network (relative sizes are to scale). Shown are the point spread function (PSF) simulating ocular blurring, the separation of photoreceptors (open circles) and PC- and MC-GCs (filled circles). (C) Responses of a photoreceptor, sustained and transient BC and PC- and MC-GC during contrast reversal of a sinusoidal grating (90 degree phase, 11 cpd, 5Hz). (D) Contrast sensitivity for simulated PC- (grey) and MC-cells (black) as a function of spatial frequency, calculated by estimating the slope of the contrast-response function (inset shows this for a 2 cpd grating). Response amplitudes are the first harmonics (F1) of the membrane potential in response to drifting sinusoidal gratings (8 Hz). (E) Receptive field nonlinearities in simulated MC-cells. The top graph shows the first (F1) and second harmonic (F2) response of a MC-cell during stimulation with a contrast-reversed sine grating (8 Hz; black: 8 cpd; grey: 12 cpd) as a function of the RF location relative to the stimulus. The response amplitudes were multiplied by the sign of the response phase. The bottom graph shows the corresponding nonlinearity indices (F2/F1) as a function of the spatial frequency.

… as at least one study has reported rapid perceptual fading within 80 ms during retinal image stabilisation (Coppola and Purves, 1996 ), matching well the transient time course of MC-cell responses.

FIGURE 3

Figure 3. Population activity of retinal GCs during presentation of a star-shaped stimulus (at half-saturating photoreceptor luminance, 100% contrast, diameter 110′, bar width 2.86″). (A) Schematic drawing of the stimulus. Bars indicate where the single cell activity in panels G (red) and H (blue) was recorded. (B) Simulated horizontal (red) and vertical (blue) eye movements. t1 and t2 indicate where the snapshots in C, D and E, F were taken. The relative two-dimensional motion direction is indicated by arrows. (C–F) Spatial population activity of PC-cells (Cand D) and MC-cells (E and F), taken at t1 and t2, as indicated in B. (G) Activity of single photoreceptors, PC- and MC-cells at a location where axial fading is visible at time t2 (red bar in A). The asterisks indicate where fading occurs in PC- and MC-cells (the location marked by an asterisk in A). (H) as G, but illustrating line-splitting. Responses were taken from the region marked by a blue bar in A. Diamonds indicate where splitting is visible. In G and H, GC responses were clipped below resting potential to enhance visibility of the effects. Calibration bars correspond to 3 mV.

Therefore, it is unlikely that the strength of receptive field nonlinearities and the splitting effect is exaggerated in the simulations.

FIGURE 4

Figure 4. Nonlinear spatial summation in MC-cells causes line-splitting. (A) Simulated responses (150 ms) of photoreceptors; (B) their temporal derivatives calculated numerically and (C) MC-cell responses to two lines of the star-shaped stimulus calculated with the full model. Brackets indicate the central 7′ of the MC-cell receptive field. The response of the differentiated signals (B) summed across the bracket after inversion are shown in D (upper trace: raw data, lower trace: after low-pass filtering with τ = 4 ms). The low-pass filtered trace is also shown in C. All responses were taken from the simulations shown in Figure 3 . Calibration bars indicate 5 mV.
Figure 5. Effect of modifications of the model on the line-splitting effect. Each panel shows a snapshot of the GC population response during stimulation with the star-shaped stimulus (Figure 3 A, at saturating photoreceptor luminance, 100% contrast, diameter 91′, bar width 2.4″). (A, B) responses for the full PC- and MC-cell model, respectively. The circle in B indicates a location where line-splitting occurs. (C) MC-cell responses after replacing the original photoreceptor model with a linear model. (D) MC-cell response with an inactivated nested amacrine circuit. (E) Response for MC-cells, when the receptive field centre consists of a single cone.

Fixational eye movements

It is interesting to note that fixational eye movements, which are normally assumed to improve vision (Ditchburn and Ginsborg, 1953 )are in this case the source of false percepts. These effects are caused by drift movements, as the microtremor, consistent with an analysis by Barlow (1952) , fails to produce strong responses in GCs due to its small amplitude.

Recent work indicates that microsaccades can induce correlations in retinal motion on short time scales (Engbert and Kliegl, 2004 ) and their occurrence is not random, but depends on the history of drift movements (Engbert and Mergenthaler, 2006 ). psychophysical studies of related visual illusions indicate that mainly slow drift movements, not microsaccades, cause the relevant effects (Murakami et al., 2006 ; Zanker, 2004 ; Zanker and Walker, 2004 ). In line with these results, the most likely effect of microsaccades on the effects described here is that they produce strong bursts of activity that would disrupt the fading and splitting effects.

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