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

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 crossfrequency 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 Cramér'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-infrequency 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.

Precise measurement of correlations between frequency coupling and visual task performance

“…This highlights the power of MIF to quantify nonlinear relationships across frequencies, which is fundamentally different from the restriction of coherence to samefrequency interactions as made clear by the single frequency indexing in (1). Finally, we mention that coherence (1) has a direct relationship to MIF for linear GPs 5 :…”

“…In order to estimate MI in the frequency domain between two random processes X(t) and Y(t), we augmented the procedure described in 5 with the multitaper approach 9 . One begins by taking non-overlapping windows of sample paths of both processes, and independence between windows is assumed.…”

“…For comparing the variance of the proposed multitaper MIF estimators and determination of how well their estimates would correlate with task-relevant phenomena, we utilized a random sinusoid model similar to what was used in prior work 5 :…”

“…In particular, we analyzed theta (4)(5)(6)(7)(8) coupling between V4 LFPs in the time window starting at 1.6 s and ending at 2 s from the first stimulus onset. This window takes place approximately during the latter part of image two presentation continuing into the beginning of the decision period.…”

Novel EM based ML Kalman estimation framework for superresolution of stochastic three-states microtubule signal

“…Mutual information (MI) is a well-known information extraction criterion that measures the similarity of information content or mutual dependence between two random variables. It was first conceptualized by Shannon [ 28 ], since then it been widely adopted in a variety of applications, especially in the area of biology [ 29 , 30 ]. The mutual information I between two discrete random variables X and Y can be described as in [ 29 ]: …”