Bayesian multi-dipole modelling of a single topography in MEG by adaptive sequential Monte Carlo samplers

Abstract

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.

Bayesian multi-dipole modelling in the frequency domain

“…Such method adopts a Bayesian perspective on the problem of estimating the parameters of an unknown number of current dipoles from a set of spatial distributions of complex electromagnetic field. For a detailed description, the reader is referred to [15,30].…”

“…The pair (r, q) can also be seen as a point in a corresponding single-dipole space D. A couple of dipoles can therefore be seen as a point in the corresponding doubledipole space D 2 = D × D, × denoting the Cartesian product; more generally, a n D -tuple of dipoles is a point in D n D . Since in our approach the number of dipoles is among the unknowns, the state-space of the unknown primary current j is eventually defined as the disjoint union of spaces [30], [32, p. 488]:…”

“…In particular, the SASMC sampler described in [15] and used in this study exploits the semi-linear structure of the model (7) by approximating the posterior p(j|y) = p(q 1:n D | y, n D , r 1:n D ) p(n D , r 1:n D | y) (12) through a two-step algorithm: first, an Adaptive Sequential Monte Carlo sampler (ASMC), described in [30] and summarized below, is used to approximate the marginal posterior p(n D , r 1:n D | y) of the number of dipoles and of their location; then, the mean and covariance matrix of the conditional posterior p(q 1:n D | y, n D , r 1:n D ) of the dipole moments are analytically computed through formulas (11 a,b).…”

Inverse Modeling for MEG/EEG Data

“…In [19] the authors assume a uniform prior for the number of dipoles, and use reversible-jump Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. In [39,37], the authors assume a Poisson prior for the number of dipoles, and use sequential Monte Carlo (SMC) samplers [11] to approximate the posterior distribution; as SMC samplers employ multiple Markov Chains running in parallel, they are less likely to remain trapped in local maxima.…”

Identification of Multiple Hard X-Ray Sources in Solar Flares: A Bayesian Analysis of the 2002 February 20 Event

“…We therefore use a Sequential Monte Carlo (SMC) algorithm that produces a sample set which is approximately distributed according to the posterior, and can thus be used to make inference on the values of the various parameters. A brief description of the SMC algorithm is given in the Appendix below; for more details, we refer to Del Moral et al (2006) for the original article in which the SMC method is introduced, and to Sorrentino et al (2014) for an example of its application to a mathematically similar inverse problem.…”