Characterization of Complex Brain Functions with Sparse Nonlinear Dynamical Modeling

Abstract

Building computational models to explain and mimic complex brain functions is one of the most challenging goals in science and engineering. In this article, we describe a specific form of input-output model of brain functions termed sparse generalized Laguerre-Volterra model. In this approach, input and output signals are spike trains a brain region receives from and sends out to other brain regions. Brain function is defined as its input-output transformational properties that can be represented by a multi-input, multi-output nonlinear dynamical model. Using regularized estimation and basis functions, sparse form of the model can be derived to reduce model complexity and better capture the sparse connectivities in the brain. This approach has been successfully applied to the human hippocampus. The resulting hippocampal CA3-CA1 model accurately predicts the CA1 (output) spike trains based on the ongoing CA3 (input) spike trains and provides a computational basis for developing hippocampal memory prostheses.