Parametric identification of flat stochastic systems for effective connectivity characterization

Abstract

Some of the mechanisms that generate neuronal signals are known at the cellular level and rest on a balance of excitatory and inhibitory interactions within and between populations of neurons. Neural mass models assume that a neuronal population can be approximated using very few state variables, generally limited to mean membrane currents, potentials, and firing rates. This article deals with nonlinear parametric identification problems in neurophysiologically based models simulating brain effective connectivity. We propose a novel approach which utilizes optimal control theory for partially flat stochastic differential systems. The optimization-based approach to effective connectivity characterization has been tested through simulation experiments and compared with the extended and unscented Kalman filters. A variety of case studies have been successfully used for connectivity parameter identification: constant functions, step functions, periodic functions and random functions.