Multiscale parcellation of dynamic causal models of the brain

The hierarchical organization of the brain's distributed network has received growing interest from the neuroscientific community, largely because of its potential to enhance our understanding of human cognition and behavior, in health and disease. This interest is motivated by the hypothesis that near-critical brain dynamics enable multiscale integration and segregation of neural dynamics. While most multiscale connectivity analyses focus on structural and functional networks, characterizing the effective connectome across multiple scales has been somewhat overlooked-primarily for computational reasons. The difficulty of estimating large cyclic causal models, together with the scarcity of theoretical frameworks for systematically moving between scales, has hindered progress in this direction. This technical note introduces a top-down multiscale parcellation scheme for dynamic causal models, with application to neuroimaging data. The method is based on Bayesian model comparison, as a generalization of the well-known $\Delta BIC$ method. To facilitate computation, recent developments in linear dynamic causal modeling (DCM) and Bayesian model reduction (BMR) are deployed. Specifically, a naïve version of BMR is introduced, enabling the parcellation scheme to scale to hundreds or thousands of regions. Notably, the derivations reveal an analytical relationship between reduced model evidence and minimum cut problem in graph theory. This duality puts the tools of graph theory at the service of model evidence optimization and significance testing. The proposed method was applied to simulated and empirical causal models to establish face and construct validity. Consequently, the large empirical causal network, inferred from a neuroimaging dataset, exhibited log-log scaling trends, suggestive of scale invariance in multiple dynamical measures. Future generalizations of this technique and its potential applications in systems and clinical neuroscience are discussed.