A Theoretical Framework for Generative Modeling of Human Functional Brain Networks

Abstract

One of the key challenges in the analyses of the human connectome is the development of a systematic framework for representing and evaluating generative models. Network generative models go beyond summary statistics and attempt to identify principles which can account for the complex patterns of network interconnections. In this project, a theoretical framework for generative modeling is developed to formally hypothesize and test organizational principles in human functional brain networks using fMRI data. The framework is based on a Hidden Markov Random Field, a probabilistic graphical model with latent variables, which provides a natural structure to make an explicit distinction between the abstract functional brain networks and the observable fMRI BOLD connectivity matrices. The framework conceptualizes whole-brain functional network topology as probabilistic constraint satisfaction, and allows representation of high dimensional connectivity matrices using low dimensional probability models where model parameters are interpretable as brain network topology constraints. To explicitly illustrate the use of the framework, a small number of hypotheses compiled from the theoretical and empirical literature are mathematically instantiated and tested using resting-state fMRI data. The empirical studies provide further evidence to support two hypothesized principles of functional brain organization; a wiring cost rule where the probability of functional connectivity between brain areas decreases with physical distance, and a common neighbors rule where the probability of functional connectivity between brain areas increases with the number of shared neighbors. Overall, the preliminary empirical studies are encouraging and warrant further development and application of the theoretical framework.