Cortico-Muscular Coherence with Time Lag with Application to Delay Estimation

Functional coupling between the motor cortex and muscle activity is usually detected and characterized using the spectral method of corticomuscular coherence (CMC). This functional coupling occurs with a time delay, which, if not properly accounted for, may decrease the coherence and make the synchrony difficult to detect. In this paper, we introduce the concept of CMC with time lag (CMCTL), that is the coherence between segments of motor cortex electroencephalogram (EEG) and electromyography (EMG) signals displaced from a central observation point. This concept is motivated by the need to compensate for the unknown delay between coupled cortex and muscle processes. We demonstrate using simulated data that under certain conditions the time lag between EEG and EMG segments at points of local maxima of CMCTL corresponds to the average delay along the involved corticomuscular conduction pathways. Using neurophysiological data, we then show that CMCTL with appropriate time lag enhances the coherence between cortical and muscle signals, and that time lags which correspond to local maxima of CMCTL provide estimates of delays involved in corticomuscular coupling that are consistent with the underlying physiology.