Estimation of complete mutual information exploiting nonlinear magnitude-phase dependence: Application to spatial FNC for complex-valued fMRI data.

Background: Real-valued mutual information (MI) has been used in spatial functional network connectivity (FNC) to measure high-order and nonlinear dependence between spatial maps extracted from magnitude-only functional magnetic resonance imaging (fMRI). However, real-valued MI cannot fully capture the group differences in spatial FNC from complex-valued fMRI data with magnitude and phase dependence.
Methods: We propose a complete complex-valued MI method according to the chain rule of MI. We fully exploit the dependence among magnitudes and phases of two complex-valued signals using second and fourth-order joint entropies, and propose to use a Gaussian copula transformation with a lower bound property to avoid inaccurate estimation of joint probability density function when computing the joint entropies.
Results: The proposed method achieves more accurate MI estimates than the two histogram-based (normal and symbolic approaches) and kernel density estimation methods for simulated signals, and enhances group differences in spatial functional network connectivity for experimental complex-valued fMRI data.
Comparison With Existing Methods: Compared with the simplified complex-valued MI and real-valued MI, the proposed method yields higher MI estimation accuracy, leading to 17.4 % and 145.5 % wider MI ranges, and more significant connectivity differences between healthy controls and schizophrenia patients. A unique connection between executive control network (EC) and right frontal parietal areas, and three additional connections mainly related to EC are detected than the simplified complex-valued MI.
Conclusions: With capability in quantifying MI fully and accurately, the proposed complex-valued MI is promising in providing qualified FNC biomarkers for identifying mental disorders such as schizophrenia.
Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
(Copyright © 2024 Elsevier B.V. All rights reserved.)