A model for the economical encoding of the visual image in cerebral cortex

We propose a model for the first stage of the cortical transformation of the visual image based on the principle that the cortex encodes the information with the minimum number of channels mathematically needed. We restrict our model to be consistent with the data on size adaptation, the known relationships of acuity and the inverse of magnification factor with eccentricity, and the electrophysiological findings on the physiological uniformity of the striate cortex. Assuming that each hypercolumn analyzes a limited spatial domain, we apply the sampling theorem to show that only 16 channels, composed of 4 sizes, are needed for one dimension. The extension to 2 dimensions leads to a possible scheme for the number, spacing, and orientational disposition of the elements, together with predictions about the number of inputs from the eyes and the total number of hypercolumns. Since all these predictions are consistent with physical and neural estimates, we conclude that the cortex may analyze the image along the lines we suggest.Supported by NIH grants EY 03412 and EY 02621     

A ring model for spatiotemporal properties of simple cells in the visual cortex

 A neural model is proposed for the spatiotemporal properties of simple cells in the visual cortex. In the model, several cortical cells are arranged on a ring, with mutual excitatory or inhibitory connections. The cells also receive excitatory inputs either from lagged and nonlagged cells of the lateral geniculate nucleus in one setting or from nonlagged cells in the other. Computer simulation shows that the cortical cells have spatiotemporally inseparable receptive fields in the former setting and separable fields in the latter; spatial profiles at a given time in the spatiotemporal fields are described with a Gabor function whose phase parameter varies regularly from 0 to 2π with rotation along the ring; the inseparable cells have directional selectivity as observed physiologically. Received: 13 November 1995 / Accepted in revised form: 1 July 1997     

Mathematical model of the simple cells in the visual cortex

A mathematical model for the spatial computations performed by simple cells in the mammalian visual cortex is derived. The construction uses as organizing principles the experimentally observed simple cell linearity and rotational symmetry breaking, together with the constraint that simple cell inputs must effectively be ganglion cell outputs. This leads to a closed form expression for the simple cellkernel in terms of Jacobi-functions. Using a-function identity, it is also shown how Gabor sampling arises as an approximation to this exact kernel for most cells. In addition, the model provides a natural mechanism for introducing the type of nonlinearity observed in some simple cells. The cell's responses to a variety of visual stimuli are calculated using the exact kernel and compared to single cell recordings. In all cases, the model's predictions are in agreement with available experimental data.Work supported by the National Science Foundation, grant PHYS86-20266Work supported by the Department of Energy, contract DE-AC02-76ERO2220     

A functional model of the wiring of the simple cells of visual cortex

A computer model of the simple cells in the mammalian visual cortex was constructed. The model cells received inputs from a great number of isopolar centre/surround cells assumed to be located in the lateral geniculate nucleus (LGN). The distribution of input to the model simple cells was either inhibitory/excitatory or inhibitory/excitatory/inhibitory. Such arrangements produced receptive fields containing four or five consecutively antagonistic subfields. Responses produced by the model cells to different types of stimuli (periodical as well as nonperiodical) were obtained and compared to responses of living cells reported from various laboratories under comparable stimulus conditions. In all the situations tested, the responses of the model cells corresponded qualitatively very well to those of living cells. It was seen that the same wiring mechanism was able to account for orientation selectivity, spatial frequency filtering, various phase relationships between stimulus and response, subfield orientational selectivity, and slight end-inhibition. Furthermore, the receptive fields of the model simple cells closely resemble Gabor functions.     

A theory for the development of feature detecting cells in visual cortex

Passive modification of the strength of synaptic junctions that results in the construction of internal mappings with some of the properties of memory is shown to lead to the development of Hubel-Wiesel type feature detectors in visual cortex. With such synaptic modification a cortical cell can become committed to an arbitrary but repeated external pattern, and thus fire every time the pattern is presented even if that cell has no genetic pre-disposition to respond to the particular pattern. The additional assumption of lateral inhibition between cortical cells severely limits the number of cells which respond to one pattern as well as the number of patterns that are picked up by a cell. The introduction of a simple neural mapping from the visual field to the lateral geniculate leads to an interaction between patterns which, combined with our assumptions above, seems to lead to a progression of patterns from column to column of the type observed by Hubel and Wiesel in monkey.     

A multi-stage model for fundamental functional properties in primary visual cortex

Many neurons in mammalian primary visual cortex have properties such as sharp tuning for contour orientation, strong selectivity for motion direction, and insensitivity to stimulus polarity, that are not shared with their sub-cortical counterparts. Successful models have been developed for a number of these properties but in one case, direction selectivity, there is no consensus about underlying mechanisms. We here define a model that accounts for many of the empirical observations concerning direction selectivity. The model describes a single column of cat primary visual cortex and comprises a series of processing stages. Each neuron in the first cortical stage receives input from a small number of on-centre and off-centre relay cells in the lateral geniculate nucleus. Consistent with recent physiological evidence, the off-centre inputs to cortex precede the on-centre inputs by a small (～4 ms) interval, and it is this difference that confers direction selectivity on model neurons. We show that the resulting model successfully matches the following empirical data: the proportion of cells that are direction selective; tilted spatiotemporal receptive fields; phase advance in the response to a stationary contrast-reversing grating stepped across the receptive field. The model also accounts for several other fundamental properties. Receptive fields have elongated subregions, orientation selectivity is strong, and the distribution of orientation tuning bandwidth across neurons is similar to that seen in the laboratory. Finally, neurons in the first stage have properties corresponding to simple cells, and more complex-like cells emerge in later stages. The results therefore show that a simple feed-forward model can account for a number of the fundamental properties of primary visual cortex.     

A neural network model for the development of direction selectivity in the visual cortex

A neural network model is proposed to explain the development of direction selectivity of cortical cells. The model is constructed under the following three hypotheses that are very plausible from recent neurophysiological findings. (1) Direction selectivity is developed by modifiable inhibitory synapses. (2) It results not from the direct convergence of many excitatory inputs from LGN cells but from cortical neural networks. (3) Direction-selective mechanism is independent of orientation-selective mechanism.—The model was simulated on a computer for a few kinds of inhibitory connections and initial conditions. The results were consistent with neurophysiological facts not only for normal cats but for cats reared in an abnormal visual environment.     

A model for feature linking via collective oscillations in the primary visual cortex

A neural network model for explaining experimentally observed neuronal responses in cat primary visual cortex is proposed. In our model, the basic functional unit is an orientation column which is represented by a large homogeneous population of neurons modeled as integrate-and-fire type excitable elements. The orientation column exhibits spontaneous collective oscillations in activity in response to suitable visual stimuli. Such oscillations are caused by mutual synchronization among the neurons within the column. Numerical simulation for various stimulus patterns shows that as a result of activity correlations between different columns, the amplitude and the phase of the oscillation in each column depend strongly on the global feature of the stimulus pattern. These results satisfactorily account for experimental observations.     

A mathematical model of the primary visual cortex and hypercolumn

A mathematical model of the primary visual cortex is presented. Basically, the model comprises two features. Firstly, in analogy with the principle of the computerized tomography (CT), it assumes that simple cells in each hypercolumn are not merely detecting line segments in images as features, but rather that they are as a whole representing the local image with a certain representation. Secondly, it assumes that each hypercolumn is performing spatial frequency analyses of local images using that representation, and that the resultant spectra are represented by complex cells. The model is analyzed using numerical simulations and its advantages are discussed from the viewpoint of visual information processing. It is shown that 1) the proposed processing is tolerant to shifts in position of input images, and that 2) spatial frequency filtering operations can be easily performed in the model.     

Propagating waves in visual cortex: a large-scale model of turtle visual cortex

This article describes a large-scale model of turtle visual cortex that simulates the propagating waves of activity seen in real turtle cortex. The cortex model contains 744 multicompartment models of pyramidal cells, stellate cells, and horizontal cells. Input is provided by an array of 201 geniculate neurons modeled as single compartments with spike-generating mechanisms and axons modeled as delay lines. Diffuse retinal flashes or presentation of spots of light to the retina are simulated by activating groups of geniculate neurons. The model is limited in that it does not have a retina to provide realistic input to the geniculate, and the cortex and does not incorporate all of the biophysical details of real cortical neurons. However, the model does reproduce the fundamental features of planar propagating waves. Activation of geniculate neurons produces a wave of activity that originates at the rostrolateral pole of the cortex at the point where a high density of geniculate afferents enter the cortex. Waves propagate across the cortex with velocities of 4 m/ms to 70 m/ms and occasionally reflect from the caudolateral border of the cortex.     

A self-organising neural network model of image velocity encoding

A self-organising neural network has been developed which maps the image velocities of rigid objects, moving in the fronto-parallel plane, topologically over a neural layer. The input is information in the Fourier domain about the spatial components of the image. The computation performed by the network may be viewed as a neural instantiation of the Intersection of Constraints solution to the aperture problem. The model has biological plausibility in that the connectivity develops simply as a result of exposure to inputs derived from rigid translation of textures and its overall organisation is consistent with psychophysical evidence.     

A computational model of vertical signal propagation in the primary visual cortex

A computational model of the flow of activity in a vertically organized slab of cat primary visual cortex (area 17) has been developed. The membrane potential of each cell in the model, as a function of time, is given by the solution of a system of first order, coupled, non-linear differential equations. When firing threshold is exceeded, an action potential waveform is pasted in. The behavior of the model following a brief simulated stimulus to afferents from the dorsal lateral geniculate nucleus (dLGN) is explored. Excitatory and inhibitory post-synaptic potential (E and IPSP) latencies, as a function of cortical depth, were generated by the model. These data were compared with the experimental literature. In general, good agreement was found for EPSPs. Many disynaptic inhibitory inputs were found to be masked by the firing of action potentials in the model. To our knowledge this phenomenon has not been reported in the experimental literature. The model demonstrates that whether a cell exhibits disynaptic or polysynaptic PSP latencies is not a fixed consequence of anatomical connectivity, but rather, can be influenced by connection strengths, and may be influenced by the ongoing pattern of activity in the cortex.Supported by a grant from Cray Research Inc.     

Neuronal selectivity and local map structure in visual cortex

The organization of primary visual cortex (V1) into functional maps makes individual cells operate in a variety of contexts. For instance, some neurons lie in regions of fairly homogeneous orientation preference (iso-orientation domains), while others lie in regions with a variety of preferences (e.g., pinwheel centers). We asked whether this diversity in local map structure correlates with the degree of selectivity of spike responses. We used a combination of imaging and electrophysiology to reveal that neurons in regions of homogeneous orientation preference have much sharper tuning. Moreover, in both monkeys and cats, a common principle links the structure of the orientation map, on the spatial scale of dendritic integration, to the degree of selectivity of individual cells. We conclude that neural computation is not invariant across the cortical surface. This finding must factor into future theories of receptive field wiring and map development.     

The local and non-local components of the local field potential in awake primate visual cortex

The Local Field Potential (LFP) is the analog signal recorded from a microelectrode inserted into cortex, typically in the frequency band of approximately 1 to 200 Hz. Here visual stimuli were flashed on in the receptive fields of primary visual cortical neurons in awake behaving macaques, and both isolated single units (neurons) and the LFP signal were recorded from the same unipolar microelectrode. The fall-off of single unit activity as a visual stimulus was moved from near the center to near the edge of the receptive field paralleled the fall-off of the stimulus-locked (evoked) LFP response. This suggests that the evoked LFP strongly reflects local neuronal activity. However, the evoked LFP could be significant even when the visual stimulus was completely outside the receptive field and the single unit response had fallen to zero, although this phenomenon was variable. Some of the non-local components of the LFP may be related to the slow distributed, or non-retinotopic, LFP signal previously observed in anesthetized animals. The induced (not time-locked to stimulus onset) component of the LFP showed significant increases only for stimuli within the receptive field of the single units. While the LFP primarily reflects local neuronal activity, it can also reflect neuronal activity at more distant sites, although these non-local components are typically more variable, slower, and weaker than the local components.     

A computational model of the vertical anatomical organization of primary visual cortex

A method for modeling anatomical connectivity for a vertically organized slab of cortical tissue in mammalian primary visual cortex has been developed. The modeled slab covers 500 × 500 m of cortical surface and extends vertically throughout the full depth of the cortex. The model slab was divided into 6 laminae and neuronal somata were distributed in three dimensions through the slab in accordance with experimentally derived cell densities. Axonal and dendritic arborizations were modeled as line segments. A total of 17 morphological types of neurons were included. Connectivity was established based on proximity between axonal and dendritic arbors. There is good general agreement between the vertical distribution of connections generated by the model and the vertical distribution of synapses observed for cat area 17. In all layers, fewer connections were generated in the model than synapses in cat area 17. This is due, at least in part, to the exclusion of long range intracortical projections and sources of afferent input other than the dorsal lateral geniculate nucleus from the model. The connection scheme described here will be used in conjunction with a physiology model to model vertical signal flow, and will be expanded further to model receptive fields of cortical neurons.Supported in part by a grant from Cray Research Inc.     

Developing velocity sensitivity in a model neuron by local synaptic plasticity

Sensor neurons, like those in the visual cortex, display specific functional properties, e.g., tuning for the orientation, direction and velocity of a moving stimulus. It is still unclear how these properties arise from the processing of the inputs which converge at a given cell. Specifically, little is known how such properties can develop by ways of synaptic plasticity. In this study we investigate the hypothesis that velocity sensitivity can develop at a neuron from different types of synaptic plasticity at different dendritic sub-structures. Specifically we are implementing spike-timing dependent plasticity at one dendritic branch and conventional long-term potentiation at another branch, both driven by dendritic spikes triggered by moving inputs. In the first part of the study, we show how velocity sensitivity can arise from such a spatially localized difference in the plasticity. In the second part we show how this scenario is augmented by the interaction between dendritic spikes and back-propagating spikes also at different dendritic branches. Recent theoretical (Saudargiene et al. in Neural Comput 16:595–626, 2004) and experimental (Froemke et al. in Nature 434:221–225, 2005) results on spatially localized plasticity suggest that such processes may play a major role in determining how synapses will change depending on their site. The current study suggests that such mechanisms could be used to develop the functional specificities of a neuron.