A Theoretical Analysis of the Influence of Fixational Instability on the Development of Thalamocortical Connectivity

Abstract

Under natural viev;.ring condition;:;, the physiological inotability of visual fixation keeps the projection of the stimulus on the retina in constant motion. After eye opcning 1 chronic exposure to a constantly moving retinal image might inf-luence the experience-dependent refinement of cell rcoponse characterioties. The rcoultf:i of previous modeling studies have f:iuggcstecl a contribution of fixational instability in the Hcbbian maturation of the noccptivc ficlcb of Vl simple cells (Rucci, Edelman, & \iVray 1 2000; Rucci & Casile 1 2004). Thb paper presentr:> a rnathematieal explanation of our previom.; computational results. Using quasi-linear models of LGN units and Vl sirnple cells 1 \Ve derive analytical expressions for the second-order statistics of thalamocortical activity before and after eye opening. \Ale show tha.t. 1 in the presence of natural stimulation) fixationa.l instability introduces a spatially uncorrelated signal in the retinal input) \vhieh strongly influences the :--;tructure of correlated activity in the model.

A theory of the influence of eye movements on the refinement of direction selectivity in the cat's primary visual cortex

“…As a consequence of this “ whitening ”, levels of correlation in our simulations were only determined by the spatial convolution of cell receptive fields, as during stimulation with spatial white noise. With the typical spatial characteristics of geniculate cells and V1 neurons, this convolution is very similar to the considered V1 kernel (Casile and Rucci, 2006). …”

“…In previous modeling studies, we suggested that fixational eye movements contribute to establishing a regime of neural activity compatible with the maturation of distinct ON and OFF subregions in the receptive fields of simple cells (Rucci, Edelman, and Wray, 2000; Rucci and Casile, 2004; Casile and Rucci, 2006). The results of the present study extend this hypothesis to LGN neurons with different response timings.…”

“…We observed that during fixation, the visual input experienced at time t by a receptor at location x on the retina, I r ( x , t ), can be decomposed as the sum of two input signals: a constant signal I r ( x , 0) given by the initial value of the luminance impinging on retinal position x during the fixation period, and the signal Ĩ r ( x , t ) given by the deviation at time t from this value. Under the assumption of fixational eye movements with small amplitude, the fixational modulations of luminance, Ĩ r , can be approximated by means of a Taylor series on the basis of the spatial derivatives of the stimulus (Casile and Rucci, 2006). As explained in Appendix A, this approximation yields the following estimate of the power spectrum of Ĩ r : $$P_{\tilde{I}\tilde{I}}(\mathit{f},u)\approx {false|\mathrm{bold-italicf}false|}^2{P}_S(\mathit{f})R_{\xi \xi }(u)$$ where f and u represent, respectively, spatial and temporal frequencies, P S is the spectrum of the stimulus, and R ξξ is the spectrum of fixational eye movements.…”

“…This section focuses on the elements of the model that are novel to this study. Components of the model described in previous publications are only briefly summarized here (see Rucci and Casile, 2004; Casile and Rucci, 2006). …”

“…We have previously observed that a single correlation-based mechanism of synaptic plasticity is sufficient to explain the development of orientation selectivity before and after eye opening, as fixational eye movements contribute to establishing a regime of neural activity with statistics similar to those of spontaneous activity (Rucci, Edelman, and Wray, 2000; Rucci and Casile, 2004; Casile and Rucci, 2006). Here, we extend these results to the development of cortical direction selectivity.…”