A Generalized Framework of Antisymmetric Polyspectral Indices for Identifying High-Order Neural Interactions

A team led by Alessio Basti (University of Chieti-Pescara, Italy) and including researchers from the Netherlands, Germany, and Italy has published a new theoretical framework in arXiv (q-bio.NC) that tackles a long-standing problem in neuroscience: accurately identifying cross-frequency interactions in brain signals. These interactions are fundamental for information integration across temporal scales, but existing metrics are confounded by complex multi-frequency nonlinearities and spurious zero-lag correlations introduced by volume conduction — the mixing of signals from multiple sources as they travel through the skull and scalp.

The proposed solution is a family of antisymmetric cross-polyspectral indices. Unlike conventional bispectrum or cross-spectrum methods, these indices are designed to detect harmonic dependencies where a frequency f_N emerges from the combination of N-1 lower frequencies (i.e., f_N = Σ f_i). The antisymmetry property makes them intrinsically robust to instantaneous mixing, so they can distinguish genuine coupling from mere measurement artifacts. The authors derived theoretical properties, validated the indices on simulated cubic nonlinearities, and applied them to empirical EEG recordings. The indices revealed higher-order interactions that standard analysis missed. As a concrete application, the paper outlines how these indices could inform personalized multi-site transcranial magnetic stimulation (mTMS) protocols, allowing clinicians to selectively monitor and modulate specific multi-frequency network interactions.