Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

Abstract

This paper considers a problem of estimating brain effective connectivity from EEG signals using a Granger causality (GC) concept characterized on state-space models. We propose a state-space model for explaining coupled dynamics of the source and EEG signals where EEG is a linear combination of sources according to the characteristics of volume conduction. Our formulation has a sparsity prior on the source output matrix that can further classify active and inactive sources. The scheme is comprised of two main steps: model estimation and model inference to estimate brain connectivity. The model estimation consists of performing a subspace identification and the active source selection based on a group-norm regularized least-squares. The model inference relies on the concept of state-space GC that requires solving a discrete-time Riccati equation for the covariance of estimation error. We verify the performance on simulated data sets that represent realistic human brain activities under several conditions including percentages of active sources, a number of EEG electrodes and the location of active sources. The performance of estimating brain networks is compared with a two-stage approach using source reconstruction algorithms and VAR-based Granger analysis. Our method achieved better performances than the two-stage approach under the assumptions that the true source dynamics are sparse and generated from state-space models. The method is applied to a real EEG SSVEP data set and we found that the temporal lobe played a role of a mediator of connections between temporal and occipital areas, which agreed with findings in previous studies.

Brain and brain-heart Granger causality during wakefulness and sleep

“…Hence, when conducting such analyses, the observed connectivity patterns should be interpreted in reference to the EEG electrode locations, which should not be used as a proxy to underlying brain areas (though one can hypothesize based on the physiological mechanisms that characterize the specific states being studied). One way of minimizing volume conduction or extracting some source information from surface EEG is through source decomposition, e.g., using a state-space ( Manomaisaowapak et al, 2022 ) or Independent Component Analysis ( Cohen and Mohammad-Rezazadeh, 2015 ) approach, and subsequent estimation of connectivity from the decomposed signals. However, even such decomposition does not pinpoint the location of the source, thus, the estimated directed connectivity between the reconstructed sources is not always a reflection of the ground truth ( Anzolin et al, 2019 ).…”

NLGC: Network Localized Granger Causality with Application to MEG Directional Functional Connectivity Analysis

“…Existing methods aim at addressing the aforementioned challenges separately. In order to address challenge 1, source localization is used in a two-stage approach, where the cortical sources are first estimated using a source localization method, then followed by GC analysis (Cai et al, 2021(Cai et al, , 2018Owen et al, 2012); in order to address challenge 2, regularized least squares estimation is used to reduce the variance of the estimated VAR parameters (Endemann et al, 2022;Bolstad et al, 2011); and challenge 3 is usually addressed using non-parametric statistical testing, which may have limited power due to the large number of statistical comparisons involved (Cheung et al, 2010;Sekihara et al, 2010;Manomaisaowapak et al, 2021). It is noteworthy that these challenges are highly inter-dependent.…”

“…While these methods are able to notably increase the spatiotemporal resolution of the estimated sources, they come with massive computational requirements, especially when the number of sources and the length of the temporal integration window grows (Long et al, 2011; Cheung et al, 2010; Sekihara et al, 2010). Finally, existing methods that address these challenges lack a precise statistical inference framework to assess the quality of the inferred GC links and control spurious detection (Manomaisaowapak et al, 2021).…”

Directed Functional Coordination Analysis of Swallowing Muscles in Healthy and Dysphagic Subjects by Surface Electromyography

“…They provide information only on the interchannel interaction strength, not on the directionality of the interaction [32], which is a relevant physiological characteristic of swallowing. Granger causality (G-causality) has been widely used to determine brain functional connectivity to identify regional activations and to characterize functional circuits from functional magnetic resonance imaging, electroencephalography, and magnetoencephalography [33][34][35][36]. Based on the hypothesis that causes precede and help to predict effects and that manipulations of the cause change the effects [37], G-causality provides a statistical measurement of functional interaction strength based on the relative prediction improvement to identify linear directional interdependence between multivariate time series [32,36].…”