A Dynamic Directional Model for Effective Brain Connectivity Using Electrocorticographic (ECoG) Time Series

Abstract

We introduce a dynamic directional model (DDM) for studying brain effective connectivity based on intracranial electrocorticographic (ECoG) time series. The DDM consists of two parts: a set of differential equations describing neuronal activity of brain components (state equations), and observation equations linking the underlying neuronal states to observed data. When applied to functional MRI or EEG data, DDMs usually have complex formulations and thus can accommodate only a few regions, due to limitations in spatial resolution and/or temporal resolution of these imaging modalities. In contrast, we formulate our model in the context of ECoG data. The combined high temporal and spatial resolution of ECoG data result in a much simpler DDM, allowing investigation of complex connections between many regions. To identify functionally segregated sub-networks, a form of biologically economical brain networks, we propose the Potts model for the DDM parameters. The neuronal states of brain components are represented by cubic spline bases and the parameters are estimated by minimizing a log-likelihood criterion that combines the state and observation equations. The Potts model is converted to the Potts penalty in the penalized regression approach to achieve sparsity in parameter estimation, for which a fast iterative algorithm is developed. The methods are applied to an auditory ECoG dataset.

Highly adaptive tests for group differences in brain functional connectivity

“…In this way it is straightforward to apply the highly adaptive NBS test to more than two groups. In addition, rather than using the graphical lasso, other methods ( Eavani et al, 2014 ) can be used to estimate the undirected networks, or dynamic/directional networks ( Ou et al, 2014 , Zhang et al, 2014a , Zhang et al, 2015 ), based on which of our proposed tests can be applied. Furthermore, instead of Pearson's correlations or partial correlations as considered here, other association measures ( Lindquist et al, 2014 , Varoquaux and Craddock, 2013 ) may be also used.…”

Multiple Matrix Gaussian Graphs Estimation

“…Third, it is often desirable to encourage the graphs estimated to be similar across groups, under the belief that the differences of graphical structure would usually concentrate on some local areas of the nodes. For instance, in brain connectivity analysis, the brain region connections are usually sparse (Zhang et al, 2015), and the differences in brain connections across different populations usually localize in some subnetworks of the brain (Toussaint et al, 2014).…”

Matrix Graph Hypothesis Testing and Application in Brain Connectivity Alternation Detection

“…Brain connectivity analysis is now in the foreground of neuroscience research (Bullmore and Sporns, 2009;Fornito et al, 2013), and is drawing ever increasing attention in the statistics field as well (Kim et al, 2014;Ahn et al, 2015;Narayan et al, 2015;Zhang et al, 2015;Han et al, 2016;Kang et al, 2016;Qiu et al, 2016;Wang et al, 2016;Xia and Li, 2017, among others). Brain functional connectivity reveals synchronization of brain systems via correlations in neurophysiological measures of brain activity.…”