Open Access
June 2011 State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing
Christopher J. Long, Patrick L. Purdon, Simona Temereanca, Neil U. Desai, Matti S. Hämäläinen, Emery N. Brown
Ann. Appl. Stat. 5(2B): 1207-1228 (June 2011). DOI: 10.1214/11-AOAS483


Determining the magnitude and location of neural sources within the brain that are responsible for generating magnetoencephalography (MEG) signals measured on the surface of the head is a challenging problem in functional neuroimaging. The number of potential sources within the brain exceeds by an order of magnitude the number of recording sites. As a consequence, the estimates for the magnitude and location of the neural sources will be ill-conditioned because of the underdetermined nature of the problem. One well-known technique designed to address this imbalance is the minimum norm estimator (MNE). This approach imposes an L2 regularization constraint that serves to stabilize and condition the source parameter estimates. However, these classes of regularizer are static in time and do not consider the temporal constraints inherent to the biophysics of the MEG experiment. In this paper we propose a dynamic state-space model that accounts for both spatial and temporal correlations within and across candidate intracortical sources. In our model, the observation model is derived from the steady-state solution to Maxwell’s equations while the latent model representing neural dynamics is given by a random walk process. We show that the Kalman filter (KF) and the Kalman smoother [also known as the fixed-interval smoother (FIS)] may be used to solve the ensuing high-dimensional state-estimation problem. Using a well-known relationship between Bayesian estimation and Kalman filtering, we show that the MNE estimates carry a significant zero bias. Calculating these high-dimensional state estimates is a computationally challenging task that requires High Performance Computing (HPC) resources. To this end, we employ the NSF Teragrid Supercomputing Network to compute the source estimates. We demonstrate improvement in performance of the state-space algorithm relative to MNE in analyses of simulated and actual somatosensory MEG experiments. Our findings establish the benefits of high-dimensional state-space modeling as an effective means to solve the MEG source localization problem.


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Christopher J. Long. Patrick L. Purdon. Simona Temereanca. Neil U. Desai. Matti S. Hämäläinen. Emery N. Brown. "State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing." Ann. Appl. Stat. 5 (2B) 1207 - 1228, June 2011.


Published: June 2011
First available in Project Euclid: 13 July 2011

zbMATH: 1223.62160
MathSciNet: MR2849772
Digital Object Identifier: 10.1214/11-AOAS483

Keywords: fixed interval smoother , Kalman filter , Magnetoencephalography , source localization

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.5 • No. 2B • June 2011
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