Alberto Sorrentino

Dynamical MEG Source Modeling with Multi-Target Bayesian Filtering

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. Hum Brain Mapp, 2009.

A Rao–Blackwellized particle filter for magnetoencephalography

A Rao-Blackwellized particle filter for the tracking of neural sources from biomagnetic data is described. A comparison with a sampling importance resampling particle filter performed in the case of both simulated and real data shows that the use of Rao-Blackwellization is highly recommended since it produces more accurate reconstructions within a lower computational effort.

Forward simulation and inverse dipole localization with the lowest order Raviart—Thomas elements for electroencephalography

Electroencephalography 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 another 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 present approach is compared to the BEM and indirectly also to the recent FEM-based subtraction approach regarding both accuracy, computation time and accessibility of implementation.

Dynamic filtering of static dipoles in magnetoencephalography

We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model. In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation.

Sequential Monte Carlo samplers for semi-linear inverse problems and application to magnetoencephalography

We discuss the use of a recent class of sequential Monte Carlo methods for solving inverse problems characterized by a semi-linear structure, i.e. where the data depend linearly on a subset of variables and nonlinearly on the remaining ones. In this type of problems, under proper Gaussian assumptions one can marginalize the linear variables. This means that the Monte Carlo procedure needs only to be applied to the nonlinear variables, while the linear ones can be treated analytically; as a result, the Monte Carlo variance and/or the computational cost decrease. We use this approach to solve the inverse problem of magnetoencephalography, with a multi-dipole model for the sources. Here, data depend nonlinearly on the number of sources and their locations, and depend linearly on their current vectors. The semi-analytic approach enables us to estimate the number of dipoles and their location from a whole time-series, rather than a single time point, while keeping a low computational cost.

Highly Automated Dipole EStimation (HADES)

Automatic estimation of current dipoles from biomagnetic data is still a problematic task. This is due not only to the ill-posedness of the inverse problem but also to two intrinsic difficulties introduced by the dipolar model: the unknown number of sources and the nonlinear relationship between the source locations and the data. Recently, we have developed a new Bayesian approach, particle filtering, based on dynamical tracking of the dipole constellation. Contrary to many dipole-based methods, particle filtering does not assume stationarity of the source configuration: the number of dipoles and their positions are estimated and updated dynamically during the course of the MEG sequence. We have now developed a Matlab-based graphical user interface, which allows nonexpert users to do automatic dipole estimation from MEG data with particle filtering. In the present paper, we describe the main features of the software and show the analysis of both a synthetic data set and an experimental dataset.

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

In this 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 analysing data from a real experiment, involving somatosensory evoked fields, and compare them to those provided by three other methods.

Statistical Approaches to the Inverse Problem

Magnetoencephalography (MEG) can be considered as one of the most powerful instruments for non-invasive investigation of the brain functions (Hamalainen et al., 1993). Its good temporal resolution (sampling frequency can reach several thousands of Hertz), only comparable to the sampling frequency of electroencephalography (EEG), allows following the neural dynamics on amillisecond time scale. This implies that, with respect to other functional imaging modalities, MEG provides an enormous amount of information about the brain activity. On the other hand, localization of brain activity from MEG data requires to solve a highly ill-posed inverse problem (Sarvas, 1987): exact reconstruction of the neural current is not possible even with noise-free data, and the debate about the actual spatial resolution of MEG is still open. Despite this drawback, the appeal of MEG data is such that a large number of methods have been developed for localizing brain activity from MEG recordings. Starting from the middle Eighties, when the first MinimumNorm Estimate (Hamalainen & Ilmoniemi, 1984) appeared, to the recent developments in spatio temporal regularization (Ou et al., 2009), state space models (Long et al., 2006; Sorrentino et al., 2009) and Markov Chain Monte Carlo (Jun et al., 2005), the attempts to insert enough a priori information to actually provide stable and reliable solutions have been rising rather than diminishing. The goal and the scope are clear: automatic and reliable source localization can be of practical use in several fields, possibly including clinical applications (pre-surgical evaluation, foci localization in epilepsy), new technology development (e.g. brain computer interfaces), and scientific research (e.g. for analysis of large datasets). Despite having been presented in rather different frameworks and with largely different names and techniques, most methods appeared so far in the MEG inverse literature can be described rather straightforwardly in a statistical setting, which helps unifying and clarifying the assumptions and the limitations of the methods. In this chapter, we attempt a brief review of the most largely known methods, as well as of some of the most recently appeared ones, highlighting the statistical features. We first provide a brief description of the statistical approach to inverse problems in Section 2; then we describe the main features of the MEG inverse problem in Section 3; in Section 4 and 5 we review methods developed by other authors, while in Section 6 we discuss our work on Bayesian filtering for MEG. 5

Expectation maximization and the retrieval of the atmospheric extinction coefficients by inversion of Raman lidar data.

We consider the problem of retrieving the aerosol extinction coefficient from Raman lidar measurements. This is an ill-posed inverse problem that needs regularization, and we propose to use the Expectation-Maximization (EM) algorithm to provide stable solutions. Indeed, EM is an iterative algorithm that imposes a positivity constraint on the solution, and provides regularization if iterations are stopped early enough. We describe the algorithm and propose a stopping criterion inspired by a statistical principle. We then discuss its properties concerning the spatial resolution. Finally, we validate the proposed approach by using both synthetic data and experimental measurements; we compare the reconstructions obtained by EM with those obtained by the Tikhonov method, by the Levenberg-Marquardt method, as well as those obtained by combining data smoothing and numerical derivation.

Bayesian smoothing of dipoles in magneto-/electroencephalography

We describe a novel method for dynamic estimation of multi-dipole states from magneto-/electroencephalography (M/EEG) time series. The new approach builds on the recent development of particle filters for M/EEG; these algorithms approximate, with samples and weights, the posterior distribution of the neural sources at time t given the data up to time t. However, for off-line inference purposes it is preferable to work with the smoothing distribution, i.e. the distribution for the neural sources at time t conditioned on the whole time series. In this study, we use a Monte Carlo algorithm to approximate the smoothing distribution for a time-varying set of current dipoles. We show, using numerical simulations, that the estimates provided by the smoothing distribution are more accurate than those provided by the filtering distribution, particularly at the appearance of the source. We validate the proposed algorithm using an experimental data set recorded from an epileptic patient. Improved localization of the source onset can be particularly relevant in source modeling of epileptic patients, where the source onset brings information on the epileptogenic zone.