Kernel Granger Causality Mapping Effective Connectivity on fMRI Data

Although it is accepted that linear Granger causality can reveal effective connectivity in functional magnetic resonance imaging (fMRI), the issue of detecting nonlinear connectivity has hitherto not been considered. In this paper, we address kernel Granger causality (KGC) to describe effective connectivity in simulation studies and real fMRI data of a motor imagery task. Based on the theory of reproducing kernel Hilbert spaces, KGC performs linear Granger causality in the feature space of suitable kernel functions, assuming an arbitrary degree of nonlinearity. Our results demonstrate that KGC captures effective couplings not revealed by the linear case. In addition, effective connectivity networks between the supplementary motor area (SMA) as the seed and other brain areas are obtained from KGC.