SEEG dipole source localization based on an empirical Bayesian approach taking into account forward model uncertainties

Abstract

Electromagnetic brain source localization consists in the inversion of a forward model based on a limited number of potential measurements. A wide range of methods has been developed to regularize this severely ill-posed problem and to reduce the solution space, imposing spatial smoothness, anatomical constraint or sparsity of the activated source map. This last criteria, based on physiological assumptions stating that in some particular events (e.g., epileptic spikes, evoked potential) few focal area of the brain are simultaneously actives, has gained more and more interest. Bayesian approaches have the ability to provide sparse solutions under adequate parametrization, and bring a convenient framework for the introduction of priors in the form of probabilistic density functions. However the quality of the forward model is rarely questioned while this parameter has undoubtedly a great influence on the solution. Its construction suffers from numerous approximation and uncertainties, even when using realistic numerical models. In addition, it often encodes a coarse sampling of the continuous solution space due to the computational burden its inversion implies. In this work we propose an empirical Bayesian approach to take into account the uncertainties of the forward model by allowing constrained variations around a prior physical model, in the particular context of SEEG measurements. We demonstrate on simulations that the method enhance the accuracy of the source time-course estimation as well as the sparsity of the resulting source map. Results on real signals prove the applicability of the method in real contexts.