Characterising the complexity of neuronal interactions

This work addresses the complexity of neuronal interactions, the nature of this complexity and how it can be characterised in real neurophysiological processes. A measure of complexity has been introduced recently (Tononi et al. [1994]: Proc Natl Acad Sci USA 91:5033-5037) that is sensitive to the joint constraints imposed by two principles of brain organisation: functional segregation and functional integration. Functional segregation implies that the dynamics of a cortical area should reflect the multidimensional attributes for which that area is specialised (in other words, regional dynamics should show a relatively high entropy). Conversely, functional integration implies a distributed and divergent influence of every cortical area on the remaining areas (i.e., the overall dynamics should show a low entropy). Our measure is based on the profile of entropies of different sized regions of the brain. Complexity is high when smaller regions have (on average) a relatively high entropy with respect to the entropy of the whole system. This measure is equivalent to the (average) mutual information between all small regions and the rest of the system in question. We have applied this measure to nonlinear simulations and to neurophysiological data obtained with fMRI during photic stimulation. Because patterns of activity in the brain are intermediate between a state of incoherence, with regionally specific dynamics and a state of global coherence, we predicted that simulated nonlinear processes with similar characteristics would have a high complexity. In the language of nonlinear dynamics we hypothesised that the greatest complexity would be found somewhere between high-dimensional, chaotic behaviour and low-dimensional, orderly behaviour. Equivalently, using the metaphor of loosely coupled oscillators, we predicted that complexity would be highest in the domain between asynchronous oscillations and global synchrony. This hypothesis was confirmed using nonlinear neuronal simulations. In addition, we demonstrate that the complexity of neurophysiological data is easily measured and can show a significant complexity when compared to suitable control processes. (C) 1996 Wiley-Liss, Inc.