Identification of networks of Wilson-Cowan neuronal oscillators by inverse sigmoidal transformation

摘要

Network neuroscience is an expanding interdisciplinary field at the intersection of engineering, math, physics, and neuroscience dedicated to understanding connectivity in the brain in health and disease. A critical challenge in network neuroscience is inferring brain connectivity from statistical relationships in the functional dynamics of individual brain regions. The ability to map brain connectivity and retain neurophysiologic interpretation of those connections is crucial in the study of cognition and in the diagnosis and treatment of brain network disorders. In this work, we propose a method for estimating structural brain connections from excitatory and inhibitory neuron populations using a neuronal network model of Wilson-Cowan oscillators. Our technique estimates the weights of a neuronal network comprised of Wilson-Cowan oscillators based on the observation of times series data and on the knowledge of individual oscillator parameters. Specifically, we employ a derivative estimation technique and develop an inverse nonlinear transformation, which leads to an estimation problem that is linear on the target network weights. To solve the associated large-scale optimization problem we apply a proximal-type optimization algorithm. Finally, to demonstrate the effectiveness of our method, we perform computational experiments using simulations based on neuroimaging connectivity data, showing that network weights are recovered with high accuracy. Our method contributes to integrating brain connectivity with dynamical models of brain function, and may have an impact in diagnosing and understanding pathophysiology in brain disorders such as Parkinson's, epilepsy, or schizophrenia, in which imbalances in excitation and inhibition affect functional connectivity.