Hierarchical Bayesian estimation for MEG inverse problem

Abstract

Source current estimation from MEG measurement is an ill-posed problem that requires prior assumptions about brain activity and an efficient estimation algorithm. In this article, we propose a new hierarchical Bayesian method introducing a hierarchical prior that can effectively incorporate both structural and functional MRI data. In our method, the variance of the source current at each source location is considered an unknown parameter and estimated from the observed MEG data and prior information by using the Variational Bayesian method. The fMRI information can be imposed as prior information on the variance distribution rather than the variance itself so that it gives a soft constraint on the variance. A spatial smoothness constraint, that the neural activity within a few millimeter radius tends to be similar due to the neural connections, can also be implemented as a hierarchical prior. The proposed method provides a unified theory to deal with the following three situations: (1) MEG with no other data, (2) MEG with structural MRI data on cortical surfaces, and (3) MEG with both structural MRI and fMRI data. We investigated the performance of our method and conventional linear inverse methods under these three conditions. Simulation results indicate that our method has better accuracy and spatial resolution than the conventional linear inverse methods under all three conditions. It is also shown that accuracy of our method improves as MRI and fMRI information becomes available. Simulation results demonstrate that our method appropriately resolves the inverse problem even if fMRI data convey inaccurate information, while the Wiener filter method is seriously deteriorated by inaccurate fMRI information.