Statistical Performance Analysis of Data-Driven Neural Models

Abstract

Data-driven model-based analysis of electrophysiological data is an emerging technique for understanding the mechanisms of seizures. Model-based analysis enables tracking of hidden brain states that are represented by the dynamics of neural mass models. Neural mass models describe the mean firing rates and mean membrane potentials of populations of neurons. Various neural mass models exist with different levels of complexity and realism. An ideal data-driven model-based analysis framework will incorporate the most realistic model possible, enabling accurate imaging of the physiological variables. However, models must be sufficiently parsimonious to enable tracking of important variables using data. This paper provides tools to inform the realism versus parsimony trade-off, the Bayesian Cramer-Rao (lower) Bound (BCRB). We demonstrate how the BCRB can be used to assess the feasibility of using various popular neural mass models to track epilepsy-related dynamics via stochastic filtering methods. A series of simulations show how optimal state estimates relate to measurement noise, model error and initial state uncertainty. We also demonstrate that state estimation accuracy will vary between seizure-like and normal rhythms. The performance of the extended Kalman filter (EKF) is assessed against the BCRB. This work lays a foundation for assessing feasibility of model-based analysis. We discuss how the framework can be used to design experiments to better understand epilepsy.