Topographic shear and the relation of ocular dominance columns to orientation columns in primate and cat visual cortex

Shear has been known to exist for many years in the topographic structure o f the primary visual cortex, but has received little attention in the model ing literature. Although the topographic map of V1 is largely conformal (i. e. zero shear), several groups have observed topographic shear in the regio n of the V1/V2 border. Furthermore, shear has also been revealed by anisotr opy of cortical magnification factor within a single ocular dominance colum n. In the present paper, we make a functional hypothesis: the major axis of the topographic shear tensor provides cortical neurons with a preferred di rection of orientation tuning. We demonstrate that isotropic neuronal summa tion of a sheared topographic map, in the presence of additional random she ar, can provide the major features of cortical functional architecture with the ocular dominance column system acting as the principal source of the s hear tensor. The major principal axis of the shear tensor determines the di rection and its eigenvalues the relative strength of cortical orientation p reference. This hypothesis is then shown to be qualitatively consistent wit h a variety of experimental results on cat and monkey orientation column pr operties obtained from optical recording and from other anatomical and phys iological techniques. In addition, we show that a recent result of Das and Gilbert (Das, A., & Gilbert, C. D., 1997. Distortions of visuotopic map mat ch orientation singularities in primary visual cortex. Nature, 387, 594-598 ) is consistent with an infinite set of parameterized solutions for the cor tical map. We exploit this freedom to choose a particular instance of the D as-Gilbert solution set which is consistent with the full range of local sp atial structure in V1. These results suggest that further relationships bet ween ocular dominance columns, orientation columns, and local topography ma y be revealed by experimental testing. (C) 1999 Elsevier Science Ltd. All r ights reserved.