Determination of effective brain connectivity from functional connectivity with application to resting state connectivities

Neural field theory insights are used to derive effective brain connectivity matrices from the functional connectivity matrix defined by activity covariances. The symmetric case is exactly solved for a resting state system driven by white noise, in which strengths of connections, often termed effective connectivities, are inferred from functional data; these include strengths of connections that are underestimated or not detected by anatomical imaging. Proximity to criticality is calculated and found to be consistent with estimates obtainable from other methods. Links between anatomical, effective, and functional connectivity and resting state activity are quantified, with applicability to other complex networks. Proof-of-principle results are illustrated using published experimental data on anatomical connectivity and resting state functional connectivity. In particular, it is shown that functional connection matrices can be used to uncover the existence and strength of connections that are missed from anatomical connection matrices, including interhemispheric connections that are difficult to track with techniques such as diffusion spectrum imaging.

Figure 1

Exemplar connectivity matrices (CMs). Each of 998 nodes into which the cortex is divided corresponds to one row and one column. Entries denote connections between nodes, with largest connections near the main diagonal and two diagonals that correspond to interhemispheric connections between homologous regions. Figures (a) and (d) are adapted from [17]. (a) Experimental aCM from diffusion imaging. (b) fCM derived by assuming the structure in the aCM in (a) is an approximation to that of the corresponding deCM. (c) deCM derived from the fCM in (d). (d) Experimental fCM from fMRI covariances after global signal removal.

Figure 2

CM eigenvalues ${\kappa }_j$ vs mode number $j=1-998$, ordered by size for the fCMs in Fig. 1 (gray) and Fig. 1 (black). Inset shows vertical zoom.