Abstract
A compact analytic model is proposed to describe the combined orientation preference (OP) and ocular dominance (OD) features of simple cells and their mutual constraints on the spatial layout of the combined OP-OD map in the primary visual cortex (V1). This model consists of three parts: (i) an anisotropic Laplacian (AL) operator that represents the local neural sensitivity to the orientation of visual inputs; and (ii) obtain a receptive field (RF) operator that models the anisotropic spatial projection from nearby neurons to a given V1 cell over scales of a few tenths of a millimeter and combines with the AL operator to give an overall OP operator; and (iii) a map that describes how the parameters of these operators vary approximately periodically across V1. The parameters of the proposed model maximize the neural response at a given OP with an OP tuning curve fitted to experimental results. It is found that the anisotropy of the AL operator does not significantly affect OP selectivity, which is dominated by the RF anisotropy, consistent with Hubel and Wiesel's original conclusions that orientation tuning width of V1 simple cell is inversely related to the elongation of its RF. A simplified and idealized OP-OD map is then constructed to describe the approximately periodic local OP-OD structure of V1 in a compact form. It is shown explicitly that the OP map can be approximated by retaining its dominant spatial Fourier coefficients, which are shown to suffice to reconstruct its basic spatial structure. Moreover, this representation is a suitable form to analyze observed OP maps compactly and to be used in neural field theory (NFT) for analyzing activity modulated by the OP-OD structure of V1. Application to independently simulated V1 OP structure shows that observed irregularities in the map correspond to a spread of dominant coefficients in a circle in Fourier space. In addition, there is a strong bias toward two perpendicular directions when only a small patch of local map is included. The bias is decreased as the amount of V1 included in the Fourier transform is increased.
Highlights
The aim of this study is to: (i) build a simple and idealized orientation preference (OP)-ocular dominance (OD) map representation of V1 which is based on the local feature detection in OP and OD, and the modeling of the neural interaction between nearby hypercolumns; and (ii) obtain a suitable Fourier domain representation of the local area of OP-OD map with the range of a few hypercolumns, in order to place it in the form required to link it to the neural field theory (NFT) of neural activities and connections in approximately periodic structures such as primary visual cortex (V1)
The hypercolumn is consistent with general observations of visual cortical map formation from experimental studies (LeVay et al, 1985; Bonhoeffer and Grinvald, 1991; Bartfeld and Grinvald, 1992; Obermayer et al, 1992a; Obermayer and Blasdel, 1993; Erwin et al, 1995; Müller et al, 2000; Adams et al, 2007), including that: (i) left-eye and right-eye OD stripes are arranged as alternating stripes in V1 of average width ≈1 mm; (ii) OP angles are arranged as pinwheels; (iii) each pinwheel center coincides with the center of its OD band; (iv) OP is continuous at OD boundaries; and (iv) neighboring pinwheels have opposite signs
(ii) We propose a simple approximate anisotropic Laplacian (AL) operator to detect the orientation of the stimulus for local neuron
Summary
The aim of this study is to: (i) build a simple and idealized OP-OD map representation of V1 which is based on the local feature detection in OP and OD, and the modeling of the neural interaction between nearby hypercolumns; and (ii) obtain a suitable Fourier domain representation of the local area of OP-OD map with the range of a few hypercolumns, in order to place it in the form required to link it to the neural field theory (NFT) of neural activities and connections in approximately periodic structures such as primary visual cortex (V1).Analytic Model for OP-OD MapsV1 is the first cortical area that processes visual inputs from the lateral geniculate nucleus (LGN) of the thalamus before projecting output signals to higher visual areas (Hubel and Wiesel, 1961, 1962a, 1972; Garey and Powell, 1967; Hendrickson et al, 1978; Miikkulainen et al, 2005). The feedforward visual pathway from the eyes to V1 involves two main processing steps: (i) light levels at a given spatial location are detected and converted into neural signals by the retina ganglion cells; and (ii) the neural signals are transmitted to V1 through the lateral geniculate nuclei (LGN) of the thalamus (Schiller and Tehovnik, 2015). LGN neurons have approximately circular receptive fields with either a central ON region (activity enhanced by light incident there) surrounded by an OFF annulus (activity enhanced by darkness there), or vice versa (Hubel and Wiesel, 1961; De Angelis et al, 1995).
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