Determination of effective brain connectivity from functional connectivity using propagator-based interferometry and neural field theory with application to the corticothalamic system

It is shown how to compute both direct and total effective connection matrices (deCMs and teCMs), which embody the strengths of neural connections between regions, from correlation-based functional CMs using propagator-based interferometry, a method that stems from geophysics and acoustics, coupled with the recent identification of deCMs and teCMs with bare and dressed propagators, respectively. The approach incorporates excitatory and inhibitory connections, multiple structures and populations, and measurement effects. The propagator is found for a generalized scalar wave equation derived from neural field theory, and expressed in terms of neural activity correlations and covariances, and wave damping rates. It is then related to correlation matrices that are commonly used to express functional and effective connectivities in the brain. The results are illustrated in analytically tractable test cases.

Figure 1

Schematic of the terms in Eq. (1), showing contributions to activity $Q_a(\mathbf{r},t)$, including the local contribution $N_a(\mathbf{r},t)$ that results from external inputs, and the contribution that results from activity propagating directly from $Q_b({\mathbf{r}}^{\prime },t^{\prime })$ [26].

Figure 2

Schematic of corticothalamic system, showing the excitatory $\left(e\right)$, inhibitory $\left(i\right)$, reticular nucleus $\left(r\right)$, and specific nuclei $\left(s\right)$ populations, inputs $n$ and the fields that travel between them.