A spatiotemporal dynamic distributed solution to the MEG inverse problem

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-conditioned 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.

MEG source reconstruction constrained by diffusion MRI based whole brain dynamical model

“…Despite such limitations of network specificity, all of the forward and backward connections were reasonably estimated as positive and negative entries, respectively, in the MAR matrix. In both SNR cases, the entries [1][2][3][4][5][6][7][8][9][10][11][12][13] correspond to the connections between the five active sources (1-5: self-connection, 6-8: forward between-connection, 9-11: backward between-connection, 12, 13: no-connection; see the right-hand graph) and the remaining indices are sorted in descending order. Small circles indicate the MAR values for the five active sources, which were computed from the original simulated sources.…”

“…Recent research in MEG source reconstruction has focused on the use of temporal constraints [2][3][4]. While the application of simple temporal smoothness constraints seems to be largely equivalent to filtering the measurements before or the source time courses after source reconstruction [2], it has been shown that imposing more complex spatiotemporal constraints on the current sources improves the inverse solutions substantially [3,4].…”

“…While the application of simple temporal smoothness constraints seems to be largely equivalent to filtering the measurements before or the source time courses after source reconstruction [2], it has been shown that imposing more complex spatiotemporal constraints on the current sources improves the inverse solutions substantially [3,4]. The methods in [3,4] utilize the state-space model to account for spatially local temporal dynamics of the current sources. The idea of incorporating the local dynamics into source reconstruction can be extended to a whole brain dynamical model incorporating long-range neural connections.…”

“…The index numbers 1-3 are the source subscripts in equation(3) and the remaining indices are sorted in descending order. (b) Estimated MAR matrix entries.…”

Bayesian EEG source localization using a structured sparsity prior

“…This can be done by considering sparse Bayesian learning using multiple measurement vectors (Zhang and Rao, 2011) or by using the STOUT (Castaño-Candamil et al, 2015) and dMAP-EM (Lamus et al, 2012) methods that apply physiological considerations to the source representation. It is also possible to model the time evolution of the dipole activity and estimate it using Kalman filtering (Galka et al, 2004;Long et al, 2011), particle filters (Somersalo et al, 2003;Sorrentino et al, 2013;Chen and Godsill, 2013) or by encouraging spatio-temporal structures by promoting structured sparsity (Huang and Zhang, 2010).…”