Cross-bispectral analysis of local field potentials: An application to essential tremor

In this work, bispectral and cross-bispectral analysis was applied to LFP and electromyographic (EMG) signals recorded in a patient with essential tremor, implanted in the subthalamic nucleus (STN) with DBS electrodes. Because the cross-bispectrum has sometimes a not plain interpretation, simulations were conducted to better understand the reliability of the estimation and to obtain a more detailed result interpretation. Both STN LFPs and the EMG had a predominant and highly coherent peak at 5 Hz and a smaller peak at 10 Hz. In addition, a high-beta activity (25-35 Hz) was detected in the STN. Whereas bispectral analysis on STN LFPs disclosed that STN rhythms are independent, cross-bispectral analysis disclosed a significant non-linear synchronizations between LFPs and EMG, suggesting that the 5 Hz subthalamic rhythm and the 5 Hz muscular rhythm were non-linearly interacting and that this interaction produced at least part of the 10 Hz oscillation in the EMG. The results of this work suggest that non-linear synchronizations between subcortical structures and peripheral muscles were found to have a role in the pathophysiology of tremor.