The relationship between structural and functional connectivity: graph theoretical analysis of an EEG neural mass model.

We investigated the relationship between structural network properties and both synchronization strength and functional characteristics in a combined neural mass and graph theoretical model of the electroencephalogram (EEG). Thirty-two neural mass models (NMMs), each representing the lump activity of reasonably large groups of interacting excitatory and inhibitory neurons, were reciprocally and excitatory coupled using random rewiring as described by Watts and Strogatz. Numerical analysis of the network revealed an abrupt transition towards a synchronized state as a function of increasing coupling strength alpha. Synchronization increased with increasing degree and decreasing regularity of the network. Parameters of the functional network showed a diverse dependency on structural connectivity: normalized clustering coefficient gamma and path length lambda increased with increasing alpha. For sufficiently large alpha, however, gamma decreased with increasing rewiring probability p, while lambda increased. Hence, a structured functional network exists despite the randomness of the underlying structural network. That is, patterns of functional connectivity are influenced by patterns of the corresponding structural level but do not necessarily agree with those.