INB-Lunch-Seminar

Simulation and Analysis of Neuronal Pattern Formation in the Visual Cortex

Ghazaleh Afshar

The orientation preference map is characterized by so called pinwheels, singular points in the visual cortex around which neurons preferring all possible orientations are organized in a radial fashion. In 2005, Kaschube et al. developed a novel pinwheel density analysis method and calculated the density and the spatial variation of pinwheels in galagos, ferrets and tree shrews. They found that their statistics is universal in all three species. The average pinwheel density in all three species is <p> = 3.14 +/- 0.03. In 2005, Wolf proposed a model to describe the development of an orientation preference map (OPM).
This model quantitatively reproduces the observed universal properties of orientation maps in the regime of suciently wide and strong long-range interactions.
In this model, the observed pinwheel density is robustly selected shortly after the emergence of the orientation map, and the average pinwheel density converges to the fixed number <p> = PI . However, pinwheel densities in this model fill a band of values between 1.5 and 3.5 with the majority of values between 2 and 3.5, which has a large standard deviation compared to the experimental result.
Optical imaging data of the primary visual cortex (V1) of some species like the cat reveals that the power spectrum of orientation preference maps occupies an annulus in the two dimensional k-plane with a typical wave number k_c , which reflects the fact that orientation preference maps are arranged in
repetitive hypercolumns of typical spacing lambda = 2 PI/k_c . Therefore, the power spectrum of orientation preference maps do not consist of a discrete set of modes. Moreover, the power spectrum has a finite width, which may vary from animal to animal and within different species. In addition, data analysis shows that in some species, for instance the cat, the local spacing of columns varies strongly
within a visual cortical area. Though it has been shown that the local column spacing lambda(x) in some species is heterogeneous, there is no model for orientation preference map that has this feature.
Since there is no analytical approach to study the influence of the heterogeneous column spacing on pinwheel density statistics, I studied this feature numerically. In order to do that, I generalized the Wolf model so as to have a map of local column spacing instead of only a fixed value of column spacing.
In the new proposed model with heterogeneous local column spacing, not only are the pinwheel density variations suppressed compared to the Wolf model, but also the power spectrum of the asymptotically stable solutions shows a continuous band of modes around the mean critical circle which resembles more
closely the experimental data.