Interaction among cortical maps

Abstract

Relationships among cortical feature maps may influence the ability of the early visual system to sense the orientation and position of a line stimulus. Several combinations of orientation maps and visuotopic maps were studied. The neurons were characterized by their receptive fields in the space of stimulus parameters and a stochastical response. Fisher information was calculated for each stimulus parameter and the average bound on the variance was used as the measure of error of parameter estimation. We conclude that the distortions of the visuotopic map suggested by the experimentally measured statistics result in decreased accuracy of the parameter estimation.

Introduction

The ability of a neuronal population to extract a particular parameter from a stimulus is determined by the set of receptive fields associated with this population. It is generally accepted, that the estimation of parameters describing the stimulus is performed locally, producing values of parameters derived from the activity of neurons sampled from a small region of cortex. This study investigates the relationship between the mapping from cortex to visual space of a model patch of primary visual cortex, which we call the location map, and the map of preferred orientation. This relationship influences receptive field parameters represented within the population and affects the accuracy in estimating the locations and orientations of lines used as sample stimuli.

Cortical feature maps describe how properties of the receptive fields vary from point to point on the cortex. Several stable cortical maps have been observed experimentally. Optical imaging combined with microelectrode recordings provides means of determining the organization of the map of preferred orientation on the visual cortex. The resolution (tens of microns) and scope (millimeters) of this technique allows assigning the value of the preferred orientation, θ to each cortical minicolumn within the cortical region. Several interesting features, such as singularities and linear zones, of the orientation preference map have been observed experimentally [4]. Orientation preference varies gradually with cortical position in linear zones and saddle regions, while changing rapidly near singularities and fractures.

The mapping from the cortex to the visual space, or location map, is believed to be smooth, and can be characterized by the so-called cortical magnification factor g. Receptive fields of neurons a distance Δz apart on the cortex are separated by Δr=Δz/g in visual space. Although the magnification factor varies with eccentricity and may be anisotropic, we shall assume that g is constant and isotropic over the model patch of cortex. However, there is evidence that the location map becomes discontinuous at scales less than several hundred microns [1], which is on the order of the average inter-singularity distance S. Since the distance between the receptive field centers of nearby neurons is proportional to the difference between their preferred orientations, there is little overlap between receptive fields of neurons with orthogonal preferred orientations. However, there is no experimental method that enables one to determine the location of the receptive field center simultaneously for all neurons in the population to accuracy greater than the receptive field size. In this study we construct a complete mapping of receptive field locations that yields statistical parameters similar to those measured experimentally and investigate the accuracy of stimulus parameter estimation from the response of a model neuronal population.