A wire length minimization approach to ocular dominance patterns in mammalian visual cortex

The primary visual area (V1) of the mammalian brain is a thin sheet of neurons. Because each neuron is dominated by either right or left eye one can treat V1 as a binary mixture of neurons. The spatial arrangement of neurons dominated by different eyes is known as the ocular dominance (OD) pattern. We propose a theory for OD patterns based on the premise that they are evolutionary adaptations to minimize the length of intra-cortical connections. Thus, the existing OD patterns are obtained by solving a wire length minimization problem. We divide all the neurons into two classes: right- and left-eye dominated. We find that if the number of connections of each neuron with the neurons of the same class differs from that with the other class, the segregation of neurons into monocular regions indeed reduces the wire length. The shape of the regions depends on the relative number of neurons in the two classes. If both classes are equally represented we find that the optimal OD pattern consists of alternating stripes. If one class is less numerous than the other, the optimal OD pattern consists of patches of the underrepresented (ipsilateral) eye dominated neurons surrounded by the neurons of the other class. We predict the transition from stripes to patches when the fraction of neurons dominated by the ipsilateral eye is about 40%. This prediction agrees with the data in macaque and Cebus monkeys. Our theory can be applied to other binary cortical systems.