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

TL;DR

This paper introduces a new mathematical framework for detecting genuine high-order neural interactions in brain signals, overcoming limitations of existing methods and validated through simulations and EEG data.

Contribution

It presents a generalized family of antisymmetric cross-polyspectral indices that robustly identify multi-frequency neural couplings, including higher-order interactions.

Findings

Validated indices detect significant higher-order dependencies in EEG data.

Indices are theoretically robust to instantaneous mixing artifacts.

Application suggests potential for personalized brain stimulation protocols.

Abstract

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 $f_N$ arises from the combination of $N-1$ components such that $f_N = \sum_{i=1}^{N-1} f_i$. We introduce a general family of antisymmetric cross-polyspectral indices designed to quantify these harmonic dependencies while being intrinsically robust to instantaneous mixing. We derive the theoretical properties of these quantities and validate them through simulations of cubic nonlinearities. As a proof of concept, we apply the indices to empirical EEG recordings; the results reveal significant higher-order dependencies that elude standard analytical approaches. We further discuss how these indices can inform novel, personalized multi-site transcranial magnetic stimulation (mTMS) protocols by enabling the selective monitoring and modulation of specific multi-frequency network interactions.