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

Abstract

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 intra-cortical 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.

Altered Resting State Brain Dynamics in Temporal Lobe Epilepsy Can Be Observed in Spectral Power, Functional Connectivity and Graph Theory Metrics

“…Despite this progress, many current methodologies are limited by various biases [81], [82], [83] making it difficult to evaluate functional connectivity in source space, particularly in the context of spatial filtering techniques such as beamformers, minimum norm and (s)LORETA [83], [84]. More promising techniques have been recently developed based on Baysian models [82], Kalman filters [85], [86] and particle filters [87]. While fMRI provides high spatial resolution, the slow hemodynamic response acts as a low pass filter obscuring the rich neural dynamics unfolding in the temporal domain.…”

The Virtual Brain Integrates Computational Modeling and Multimodal Neuroimaging

“…As a consequence, the EEG and MEG backward solution is underdetermined. Hence, while the forward problem of EEG has a unique solution, the inverse problem of EEG, that is, the estimation of a tomography of neural sources from EEG channel data, is an ill-conditioned problem lacking a unique solution (Helmholtz, 1853;Long et al, 2011). We address this ill-posedness by the introduction of the aforementioned constraints, namely, realistic, subject-specific head models segmented from anatomical MR images, physiological priors, and source space-based regularization schemes and constraints.…”

A Subspace Pursuit-based Iterative Greedy Hierarchical solution to the neuromagnetic inverse problem

“…Later on, inverse solutions in the framework of Bayesian estimation were introduced, with the underlying assumption of temporal independence (Sato et al, 2004; Phillips et al, 2005; Mattout et al, 2006; Nummenmaa et al, 2007; Wipf and Nagarajan, 2009). In order to impose spatio-temporal smoothness on the inverse solution, subsequent algorithms in the Bayesian framework considered the design of spatio-temporal priors (Baillet and Garnero, 1997; Bolstad et al, 2009; Daunizeau et al, 2006; Daunizeau and Friston, 2007; Friston et al, 2008; Greensite, 2003; Limpiti et al, 2009; Trujillo-Barreto et al, 2008; Zumer et al, 2008) or employed linear state-space models (Galka et al, 2004; Yamashita et al, 2004; Long et al, 2011; Lamus et al, 2007). Despite their improved accuracy in source localization, many of these more recent solutions suffer from unwieldy computational complexity.…”