Nonlinear Coherence for Vector Time Series: Defining Region-to-Region Functional Brain Connectivity

TL;DR

This paper introduces nonlinear vector coherence (NVC), a new spectral dependence measure for EEG data, to better characterize brain connectivity alterations in neurodegenerative diseases like Alzheimer's and FTD, enabling improved diagnosis.

Contribution

The paper proposes NVC as a novel, beyond-linear spectral dependence measure for region-to-region brain connectivity analysis in EEG, with a nonparametric inference procedure.

Findings

NVC uncovers distinct connectivity patterns in EEG data.

NVC effectively discriminates healthy individuals from AD and FTD patients.

The inference method is fast, distribution-free, and reliable.

Abstract

Alterations in functional brain connectivity characterize neurodegenerative disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD). As a non-invasive and cost-effective technique, electroencephalography (EEG) is gaining increasing attention for its potential to identify reliable biomarkers for early detection and differential diagnosis of AD and FTD. Considering the behavioral similarities of signals from adjacent EEG channels, we propose a new spectral dependence measure, the nonlinear vector coherence (NVC), to capture beyond-linear interactions between oscillations of two multivariate time series observed from distinct brain regions. This addresses the limitations of conventional channel-to-channel approaches and defines a more natural region-to-region connectivity framework in the frequency domain. As a result, the NVC measure offers a new approach to investigate dependence between brain regions, which then enables to identify altered functional connectivity dynamics associated with AD and FTD. We further introduce a rank-based inference procedure that enables fast and distribution-free estimation of the proposed measure, as well as a fully nonparametric test for spectral independence. The empirical performance of our proposed inference methodology is demonstrated through extensive numerical experiments. An application to resting-state EEG data reveals that our novel NVC measure uncovers distinct and diagnostically meaningful connectivity patterns which effectively discriminate healthy individuals from those with AD and FTD.