A Dynamical Clustering Model of Brain Connectivity Inspired by the N -Body Problem

We present a method for studying brain connectivity by simulating a dynamical evolution of the nodes of the network. The nodes are treated as particles, and evolved under a simulated force analogous to gravitational acceleration in the well-known N -body problem. The particle nodes correspond to regions of the cortex. The locations of particles are defined as the centers of the respective regions on the cortex and their masses are proportional to each region's volume. The force of attraction is modeled on the gravitational force, and explicitly made proportional to the elements of a connectivity matrix derived from diffusion imaging data. We present experimental results of the simulation on a population of 110 subjects from the Alzheimer's Disease Neuroimaging Initiative (ADNI), consisting of healthy elderly controls, early mild cognitively impaired (eMCI), late MCI (LMCI), and Alzheimer's disease (AD) patients. Results show significant differences in the dynamic properties of connectivity networks in healthy controls, compared to eMCI as well as AD patients.