Estimation of nonlinear neural source interactions via sliced bicoherence

Neural oscillations and their spatiotemporal interactions are of interest for the description of brain mechanisms. This study offers a novel third order spectral coupling measure named “sliced bicoherence”. It is the diagonal slice of cross-bicoherence allowing an efficient quantification of the nonlinear interactions between neural sources. Our methodology comprises an indirect estimation method, a parametric confidence level formula and a subtracted version for robustness to volume conduction. The methodology provides an efficient estimation of third-order nonlinear cross relations reducing the complexity to the same order of second-order coherence computation. Unlike other bispectral measures, the suggested measure solely holds terms related to cross relations between channel sources and omits the possible strong autobispectral relations. Feasibility and robustness of the methodology are demonstrated both on simulated and publicly available MEG data. The latter were collected for a motor task and an eyes-open resting state. Analytical confidence level marked the non-significant couplings. Simulations confirmed that the subtracted bicoherence enabled robustness to volume conduction by avoiding the spurious nearby channel couplings. Central regions were shown to be coupled with muscular activity by sliced bicoherence. Couplings for spontaneous data occurred particularly at theta and alpha bands. Volume-conduction related bicoherence values originated especially from the low frequencies below 5 Hz. The suggested nonlinear measure is promising to be a part of the rich collection of the multichannel electrophysiological brain connectivity metrics.