Validation and Inference of Structural Connectivity and Neural Dynamics with MRI data

Abstract

Diffusion- and functional MRI are promising avenues for revealing functional organization in the living human brain since they provide noninvasive measurements pertaining to the anatomy of cortical connectivity and the physiology of brain activity. Diffusion MRI sheds light on the functional segregation of the cortex, a framework known as connectivity-based cortex parcellation, whereas functional MRI reveals functional integration that describes the physiology of interactions between functionally specialized cortical units, a framework known as dynamic causal models.Since there is so little evidence regarding the true functional segregation of the cortex, we propose a novel model validation method, known as approximation set coding, to identify a parcellation (i.e. “functional fingerprint”) that is informative yet robust against fluctuations in the diffusion measurements. Furthermore, we ultimately rank a pipeline of algorithms for connectivity-based cortex parcellation using a trade-off between informativeness and robustness against diffusion MRI noise.A second contribution is a novel model inversion method for dynamic causal modeling as well as a broad class of dynamical systems. The model inversion method is based upon the gradient matching formulation which matches the slope of the observations with the gradient determined by the ODEs. Our method is called mean-field GM and exploits local linearity properties of nonlinear ODEs where “locally linear” refers to ODEs that are linear in the ODE parameters and/or linear in an individual state. In the context of dynamic causal modeling, we further argue that mean-field GM is more expert-aware because it imposes a prior on the functional form of hidden brain activity as opposed to directly on the ODE parameters.