Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials

TL;DR

This study develops copula-based tools to characterize non-linear spectral dependence in brain signals, detecting changepoints and effects of stroke on connectivity in rat local field potentials.

Contribution

It introduces a novel copula modeling approach applied to Fourier coefficient magnitudes for analyzing brain signal dependence, including an iterative changepoint detection algorithm.

Findings

Detects changepoints in brain signal dependence regimes.

Shows stroke can alter dependence structures in brain signals.

Demonstrates effectiveness on rat local field potential data.

Abstract

This paper intends to develop tools for characterizing non-linear spectral dependence between spontaneous brain signals. We use parametric copula models (both bivariate and vine models) applied on the magnitude of Fourier coefficients rather than using coherence. The motivation behind this work is an experiment on rats that studied the impact of stroke on the connectivity structure (dependence) between local field potentials recorded at various channels. We address the following major questions. First, we ask whether one can detect any changepoint in the regime of a brain channel for a given frequency band based on a difference between the cumulative distribution functions modeled for each epoch (small window of time). Our proposed approach is an iterative algorithm which compares each successive bivariate copulas on all the epochs range, using a bivariate Kolmogorov-Smirnov statistic. Second, we ask whether stroke can alter the dependence structure of brain signals; and examine whether changes in dependence are present only in some channels or generalized across channels. These questions are addressed by comparing Vine-copulas models fitted for each epoch. We provide the necessary framework and show the effectiveness of our methods through the results for the local field potential data analysis of a rat.