A reachable probability approach for the analysis of spatio-temporal dynamics in the human functional network

The dynamic architecture of the human brain has been consistently observed. However, there is still limited modeling work to elucidate how neuronal circuits are hierarchically and flexibly organized in functional systems. Here we proposed a reachable probability approach based on non-homogeneous Markov chains, to characterize all possible connectivity flows and the hierarchical structure of brain functional systems at the dynamic level. We proved at the theoretical level the convergence of the functional brain network system, and demonstrated that this approach is able to detect network steady states across connectivity structure, particularly in areas of the default mode network. We further explored the dynamically hierarchical functional organization centered at the primary sensory cortices. We observed smaller optimal reachable steps to their local functional regions, and differentiated patterns in larger optimal reachable steps for primary perceptual modalities. The reachable paths with the largest and second largest transition probabilities between primary sensory seeds via multisensory integration regions were also tracked to explore the flexibility and plasticity of the multisensory integration. The present work provides a novel approach to depict both the stable and flexible hierarchical connectivity organization of the human brain.