Statistical Brain Signal Analysis

Researchers: Toni Auranen, Iiro P. Jääskeläinen, Jouko Lampinen, Aapo Nummenmaa, Mikko Sams, Aki Vehtari

Localizing the neural currents indicating brain activity based on noninvasiveMEG and EEG measurements (i.e. solving the electromagnetic inverse problem) is most naturally formulated in probabilistic terms and thus becomes a problem of statistical inference. Because of the illposedness of the inverse problem, reliable inference cannot be made relying on the data only. Some additional a priori information must be provided in order to obtain sensible results, necessitating a Bayesian treatment of the problem.

The overall aim of the research is to apply the methods of Bayesian data-analysis to the study of cognitive brain functions as revealed by MEG, EEG and fMRI. Our focus is especially on the computationally more intensive methods such as Markov chain Monte Carlo (MCMC). By using a state-of-the-art data simulation model, we have studied generalizations of previously proposed MEG/EEG data-analysis methods in collaboration with Massachusetts General Hospital–Harvard Medical School NMR Center (Dr. JohnW. Belliveau and Dr. Matti S. Hämäläinen).

We propose a full Bayesian approach in theMEGinverse problem with -norm priors. This model contains as special cases the minimum norm estimate (MNE) and minimum current estimate (MCE), which are both widely used in practice. The choice between MCE and MNE is completely arbitrary; our method deals with this by introducing a hyperparameter which continuously varies between the limiting cases of MCE and MNE. Instead of fixing the hyperparameter to some value ad hoc, it is integrated over using MCMC methods when performing the final analysis.

Figure 51

Figure 51: Left figure shows a simulated activation plotted on the discretized cortical white-matter gray-matter boundary viewed from the left. In the middle, an inverse estimate obtained by using the MCMC samples (shown on the right) from the posterior distribution of the hierarchical model.

We also proposed an alternative hierarchical extension of the model corresponding to the minimum norm estimate (see Fig. 51). Instead of assuming a single Gaussian prior for the neural currents, we built a hierarchical structure to the model by imposing individual Gaussian priors with a common hyperprior distribution. The outcome of integrating over the hyperparameters was a heavy-tailed prior distribution especially suitable for reconstructing focal brain activations.

Tentative results of the simulation studies were promising and we have started more extensive simulation and real data experiments. Means for reducing the dimensionality (the number of free parameters) of the inverse problem were preliminarily studied. This included spatial correlation models, principal component analysis, and parametric/semiparametric models for brain activation patterns. These issues will be further investigated in the future and applied to real problems of cognitive neuroscience.