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

Abstract

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.

Functional brain connectivity is predictable from anatomic network's Laplacian eigen-structure

“…Importantly, the authors incorporate delays between the time series in the model using propagator theory. In particular, Robinson et al (2014) develop a function-structure relationship where matrices C s and C f are assumed to share the eigenvectors, similar to (Galan, 2008). Additionally, function and structure eigenvalues are assumed to be related via an inverse square relationship.…”

Brain imaging of locomotion in neurological conditions

“…Determining this relationship would lead to a more complete characterization of the pathology and its stage, and, thus, to the definition of more robust and reliable biomarkers. Several approaches have been proposed to map functional connectivity from anatomical features extracted directly from white matter streamlines or enforced from graph-theoretical properties [11,38,169,170]. Brain-graphs can be constructed associating nodes to anatomically defined parcels or recording sensors and edges to structural or functional connections.…”

Neural field theory of nonlinear wave-wave and wave-neuron processes

“…Fluctuations in connectivity occur due to modulation of strength of synapses by effects such as potentiation, depression, and neuromodulation (Kandel et al, 2000;Rubenstein and Merzenich, 2003;Sakkalis, 2011;Robinson, 2014), and can be resolved spatially and temporally via brain imaging modalities such as electroencephalography (EEG), magnetoencephalography (MEG), and functional magnetic resonance imaging (fMRI) that measure quantities associated with the resulting neuronal activities (Uddin et al, 2009;Hansen et al, 2015).…”