We present a Bayesian filtering approach for automatic estimation of dynamical source models from magnetoencephalographic data. We apply multi-target Bayesian filtering and the theory of Random Finite Sets in an algorithm that recovers the life times, locations and strengths of a set of dipolar sources. The reconstructed dipoles are clustered in time and space to associate them with sources. We applied this new method to synthetic data sets and show here that it is able to automatically estimate the source structure in most cases more accurately than either traditional multi-dipole modeling or minimum current estimation performed by uninformed human operators. We also show that from real somatosensory evoked fields the method reconstructs a source constellation comparable to that obtained by multi-dipole modeling.
Electroencephalography (EEG) is a non-invasive imaging modality in which a primary current density generated by the neural activity in the brain is to be reconstructed based on external electric potential measurements. This paper focuses on the finite element method (FEM) from both forward and inverse aspects. The goal is to establish a clear correspondence between the lowest order Raviart-Thomas basis functions and dipole sources as well as to show that the adopted FEM approach is computationally effective. Each basis function is associated with a dipole moment and a location. Four candidate locations are tested. Numerical experiments cover two different spherical multilayer head models, four mesh resolutions and two different forward simulation approaches, one based on FEM and one based on the boundary element method (BEM) with standard dipoles as sources. The forward simulation accuracy is examined through column-and matrix-wise relative errors as well as through performance in inverse dipole localization. A closed-form approximation of dipole potential was used as the reference forward simulation. The results suggest that the present approach is comparable or superior to BEM and to the recent FEM based subtraction approach regarding both accuracy, computation time and accessibility of implementation.
Abstract:In the present paper, we develop a novel Bayesian approach to the problem of estimating neural currents in the brain from a fixed distribution of magnetic field (called topography), measured by magnetoencephalography. Differently from recent studies that describe inversion techniques, such as spatio-temporal regularization/filtering, in which neural dynamics always plays a role, we face here a purely static inverse problem. Neural currents are modelled as an unknown number of current dipoles, whose state space is described in terms of a variable-dimension model. Within the resulting Bayesian framework, we set up a sequential Monte Carlo sampler to explore the posterior distribution. An adaptation technique is employed in order to effectively balance the computational cost and the quality of the sample approximation. Then, both the number and the parameters of the unknown current dipoles are simultaneously estimated. The performance of the method is assessed by means of synthetic data, generated by source configurations containing up to four dipoles. Eventually, we describe the results obtained by analyzing data from a real experiment, involving somatosensory evoked fields, and compare them to those provided by three other methods.
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