Nonlinear Causality in Brain Networks: With Application to Motor Imagery vs Execution

Abstract

One fundamental challenge of data-driven analysis in neuroscience is modeling causal interactions and exploring the connectivity of nodes in a brain network. Various statistical methods, relying on various perspectives and employing different data modalities, are being developed to examine and comprehend the underlying causal structures inherent to brain dynamics. This study introduces a novel statistical approach, TAR4C, to dissect causal interactions in multichannel EEG recordings. TAR4C uses the threshold autoregressive model to describe the causal interaction between nodes or clusters of nodes in a brain network. The perspective involves testing whether one node, which may represent a brain region, can control the dynamics of the other. The node that has such an impact on the other is called a threshold variable and can be classified as a causative because its functionality is the leading source operating as an instantaneous switching mechanism that regulates the time-varying autoregressive structure of the other. This statistical concept is commonly referred to as threshold non-linearity. Once threshold non-linearity has been verified between a pair of nodes, the subsequent essential facet of TAR modeling is to assess the predictive ability of the causal node for the current activity on the other and represent causal interactions in autoregressive terms. This predictive ability is what underlies Granger causality. The TAR4C approach can discover non-linear and time-dependent causal interactions without negating the G-causality perspective. The efficacy of the proposed approach is exemplified by analyzing the EEG signals recorded during the motor movement/imagery experiment. The similarities and differences between the causal interactions manifesting during the execution and the imagery of a given motor movement are demonstrated by analyzing EEG recordings from multiple subjects.