Mutual Information in Frequency and its Application to Measure Cross-Frequency Coupling in Epilepsy

TL;DR

This paper introduces a novel mutual information in frequency metric to detect and quantify cross-frequency coupling in brain signals, especially in non-Gaussian data, with applications to epilepsy treatment.

Contribution

It proposes a new MI-in-frequency metric based on Shannon's mutual information, capable of detecting statistical dependence in non-Gaussian brain signals, validated with simulations and applied to epilepsy data.

Findings

MI-in-frequency effectively detects cross-frequency coupling.

The metric outperforms existing methods in non-Gaussian scenarios.

Application to epilepsy data reveals important coupling patterns.

Abstract

We define a metric, mutual information in frequency (MI-in-frequency), to detect and quantify the statistical dependence between different frequency components in the data, referred to as cross-frequency coupling and apply it to electrophysiological recordings from the brain to infer cross-frequency coupling. The current metrics used to quantify the cross-frequency coupling in neuroscience cannot detect if two frequency components in non-Gaussian brain recordings are statistically independent or not. Our MI-in-frequency metric, based on Shannon's mutual information between the Cramer's representation of stochastic processes, overcomes this shortcoming and can detect statistical dependence in frequency between non-Gaussian signals. We then describe two data-driven estimators of MI-in-frequency: one based on kernel density estimation and the other based on the nearest neighbor algorithm and validate their performance on simulated data. We then use MI-in-frequency to estimate mutual information between two data streams that are dependent across time, without making any parametric model assumptions. Finally, we use the MI-in- frequency metric to investigate the cross-frequency coupling in seizure onset zone from electrocorticographic recordings during seizures. The inferred cross-frequency coupling characteristics are essential to optimize the spatial and spectral parameters of electrical stimulation based treatments of epilepsy.