A Spatiotemporal Dynamic Solution to the MEG Inverse Problem: An Empirical Bayes Approach

Abstract

MEG/EEG are non-invasive imaging techniques that record brain activity with high temporal resolution. However, estimation of brain source currents from surface recordings requires solving an ill-posed inverse problem. Converging lines of evidence in neuroscience, from neuronal network models to resting-state imaging and neurophysiology, suggest that cortical activation is a distributed spatiotemporal dynamic process, supported by both local and long-distance neuroanatomic connections. Because spatiotemporal dynamics of this kind are central to brain physiology, inverse solutions could be improved by incorporating models of these dynamics. In this article, we present a model for cortical activity based on nearest-neighbor autoregression that incorporates local spatiotemporal interactions between distributed sources in a manner consistent with neurophysiology and neuroanatomy. We develop a dynamic Maximum a Posteriori Expectation-Maximization (dMAP-EM) source localization algorithm for estimation of cortical sources and model parameters based on the Kalman Filter, the Fixed Interval Smoother, and the EM algorithms. We apply the dMAP-EM algorithm to simulated experiments as well as to human experimental data. Furthermore, we derive expressions to relate our dynamic estimation formulas to those of standard static models, and show how dynamic methods optimally assimilate past and future data. Our results establish the feasibility of spatiotemporal dynamic estimation in large-scale distributed source spaces with several thousand source locations and hundreds of sensors, with resulting inverse solutions that provide substantial performance improvements over static methods.