Brain Dynamics Through the Lens of Statistical Mechanics by Unifying Structure and Function

This paper introduces a novel method that unifies structural connectivity and functional time series to form a signed coupling interaction network or “signed resting state structural connectome” (signed rs-SC) to describe neural excitation and inhibition. We employ an energy representation of neural activity based on the Ising model from statistical mechanics, hereby bypassing traditional BOLD correlations. The spin model is a function of a coupling interaction (traditionally positive or negative) and spin-states of paired brain regions. Observed functional time series represent brain states over time. A maximum pseudolikelihood with a constraint is used to estimate the coupling interaction. The constraint is introduced as a penalty function such that the learned interactions are scaled relative to structural connectivity; the sign of the interactions may infer inhibition or excitation over an underlying structure. We evaluate our method by comparing a group of otherwise healthy APOE-e4 carriers with a control group of non APOE-e4 subjects. Our results identify a global shift in the excitation-inhibition balance of the APOE e4 signed rs-SC compared to the control group, providing the first connectomics-based support for hyperexcitation related to APOE e4.