Parameter Estimation and Dynamic Source Localization for the Magnetoencephalography (Meg) Inverse Problem

Lamus, Camilo; Long, Christopher J.; Hämäläinen, Matti S.; Brown, Emery N.; Purdon, Patrick L.

doi:10.1109/isbi.2007.357046

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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Magnetoencephalography (MEG) is an important non-invasive method for studying activity within the human brain. Source localization methods can be used to estimate spatiotemporal activity from MEG measurements with high temporal resolution, but the spatial resolution of these estimates is poor due to the ill-posed nature of the MEG inverse problem. Recent developments in source localization methodology have emphasized temporal as well as spatial constraints to improve source localization accuracy, but these methods can be computationally intense. Solutions emphasizing spatial sparsity hold tremendous promise, since the underlying neurophysiological processes generating MEG signals are often sparse in nature, whether in the form of focal sources, or distributed sources representing large-scale functional networks. Recent developments in the theory of compressed sensing (CS) provide a rigorous framework to estimate signals with sparse structure. In particular, a class of CS algorithms referred to as greedy pursuit algorithms can provide both high recovery accuracy and low computational complexity. Greedy pursuit algorithms are difficult to apply directly to the MEG inverse problem because of the high-dimensional structure of the MEG source space and the high spatial correlation in MEG measurements. In this paper, we develop a novel greedy pursuit algorithm for sparse MEG source localization that overcomes these fundamental problems. This algorithm, which we refer to as the Subspace Pursuit-based Iterative Greedy Hierarchical (SPIGH) inverse solution, exhibits very low computational complexity while achieving very high localization accuracy. We evaluate the performance of the proposed algorithm using comprehensive simulations, as well as the analysis of human MEG data during spontaneous brain activity and somatosensory stimuli. These studies reveal substantial performance gains provided by the SPIGH algorithm in terms of computational complexity, localization accuracy, and robustness.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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“…Specifically, (1) we describe a model of the spatiotemporal dynamics based on nearest-neighbors multivariate autoregression along the cortical surface; (2) We develop an algorithm for dynamic estimation of cortical current sources and model parameters from MEG/EEG data based on the Kalman Filter, the Fixed Interval Smoother, and the Expectation-Maximization (EM) algorithms; (3) We derive expressions to relate our dynamic estimation formulas to those of standard static algorithms; (4) We apply our spatiotemporal dynamic method to simulated experiments of focal and distributed cortical activation as well as experimental data from a human subject. Portions of this work have been previously presented in Lamus et al (2007).…”

Section: Introductionmentioning

confidence: 99%

A spatiotemporal dynamic distributed solution to the MEG inverse problem

et al. 2012

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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.

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“…In our analysis we computed the KF and FIS estimates by testing different values of the regularization parameter. This parameter can be estimated in an empirical Bayesian [Lamus et al (2007)] or a fully Bayesian framework. The spatial component of the model can be improved by using the structure of the particular experimental design to proposed specific forms of the F state-transition matrix.…”

Section: Somatosensory Meg Experimentmentioning

confidence: 99%

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

Long¹,

Purdon²,

Temereanca³

et al. 2011

Ann. Appl. Stat.

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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.

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Parameter Estimation and Dynamic Source Localization for the Magnetoencephalography (Meg) Inverse Problem

Cited by 9 publications

References 10 publications

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

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

A spatiotemporal dynamic distributed solution to the MEG inverse problem

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

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