Entropy and cortical activity: information theory and PET findings

Functional segregation requires convergence and divergence of neuroanatomical connections. Furthermore, the nature of functional segregation suggests that (1) signals in convergent afferents are correlated and (2) signals in divergent efferents are uncorrelated. The aim of this article is to show that this arrangement can be predicted mathematically, using information theory and an idealized model of cortical processing. In theory, the existence of bifurcating axons limits the number of independent output channels from any small cortical region, relative to the number of inputs. An information theoretic analysis of this special (high input:output ratio) constraint indicates that the maximal transfer of information between inputs, to a cortical region, and its outputs will occur when (1) extrinsic connectivity to the area is organized such that the entropy of neural activity in afferents is optimally low and (2) connectivity intrinsic to the region is arranged to maximize the entropy measured at the initial segments of projection neurons. Under the constraints of the model, a low entropy is synonymous with high correlations between axonal firing rates (and vice versa). Consequently this antisymmetric arrangement of functional activity in convergent and divergent connections underlying functional segregation is exactly that predicted by the principle of maximum preservation of information, considered in the context of axonal bifurcation. The hypothesis that firing in convergent afferents is correlated (has low entropy) and spatially coherent was tested using positron emission tomographic measurements of cortical synaptic function in man. This hypothesis was confirmed.