The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding/ngeneral brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of/n(in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by/nderiving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely/npreserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only/na small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the/nphase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked/nthat of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous/ncoupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived/nanalytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct/nrelationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be/nmodified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit/nnot a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical/nconnectivity structure reported by Hagmann and others.

This work was funded by ERC Advanced Grant: DYSTRUCTURE (n. 295129), by the Spanish Research Project SAF2010-16085 and by the CONSOLIDER-/nINGENIO 2010 Program CSD2007-00012, and the FP7-ICT BrainScale