State-space solutions to the dynamic magnetoencephalography inverse problem using high performance computing

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 $L^2$ 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.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS483 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Numerical modeling in electro- and magnetoencephalography

This Thesis concerns the application of two numerical methods, Boundary Element Method (BEM) and Finite Element Method (FEM) to forward problem solution of bioelectromagnetic source localization in the brain. The aim is to improve the accuracy of the forward problem solution in estimating the electrical activity of the human brain from electric and magnetic field measurements outside the head. Electro- and magnetoencephalography (EEG, MEG) are the most important tools enabling us to gather knowledge about the human brain non-invasively. This task is alternatively named brain mapping. An important step in brain mapping is determining from where the brain signals originate. Using appropriate mathematical models, a localization of the sources of measured signals can be performed. A general motivation of this work was the fact that source localization accuracy can be improved by solving the forward problem with higher accuracy. In BEM studies, accurate representation of model geometry using higher order elements improves the solution of the forward problem. In FEM, complex conductivity information can be incorporated into numerical model. Using Whitney-type finite elements instead of using singular sources such as point dipoles, primary and volume currents are represented as continuous sources. With comparison to analytical solutions available in simple geometries such as sphere, the studied numerical methods show improvements in the forward problem solution of bioelectromagnetic source imaging.reviewe