Canonical coherence for the estimation of within- and cross-frequency cortico-kinematic interactions

Cortico-kinematic coherence (CKC) quantifies coupling between cortical activity and movement kinematics, serving as a non-invasive marker of sensorimotor integration and motor control. Conventional CKC approaches primarily assess within (linear) frequency coupling and overlook cross-frequency interactions, which are increasingly recognized as central to corticomuscular communication. We present a novel multivariate framework that extends the canonical coherence (caCOH) method by applying a non-linear warping of peripheral measures, enabling detection of cross-frequency CKC. The method jointly analyzes multichannel EEG and acceleration signals, maximizing sensitivity to spatially distributed neural sources while accounting for frequency-specific structure. Simulations with realistic head modeling show that the approach robustly recovers underlying patterns even at very low signal-to-noise ratios, closely matching the ground truth. Application to empirical EEG and acceleration data demonstrates that cross-frequency CKC is statistically significant in most participants and interaction pairs, indicating consistent non-random coupling. We further introduce an analysis strategy to determine whether observed interactions arise from shared (e.g. due to the signal shape) or distinct cortical sources. This framework provides a multivariate tool for characterizing the neural mechanisms of motor control and offers future opportunities for investigating their disruption in neurological disorders.