Antisymmetric polyspectral indices for high-order neural interactions: general theory and a fourth-order proof of concept

Le résumé fourni par la source

Cross-frequency interactions are fundamental brain mechanisms for integrating information across temporal scales. However, accurate identification of these couplings is hindered by complex multi-frequency nonlinearities and by spurious, zero-lag artifacts caused by volume conduction. To our knowledge, conventional metrics lack a robust framework to characterize genuine interactions among multiple time series where a frequency of interest \(f_m\) arises from the combination of \(m-1\) components such that \(f_m = \sum _{i=1}^{m-1} f_i\) . We introduce a general family of antisymmetric cross-polyspectral indices designed to quantify these higher-order multi-frequency dependencies while being intrinsically robust to instantaneous mixing. We derive the theoretical properties of these quantities and validate the bivariate fourth-order case through simulations of cubic nonlinearities. As an exploratory proof of concept, we apply the corresponding antisymmetric cross-trispectral index to a single-subject EEG recording. The resulting sensor-level maps illustrate putative patterns compatible with higher-order dependencies and differing from those obtained with selected standard measures. We further discuss how these indices may inform future multi-site transcranial magnetic stimulation (mTMS) protocols by enabling the monitoring of specific multi-frequency network interactions.

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