Statistical Brain Signal Analysis

Centre of Excellence in Computational Complex Systems Research

 

Statistical Brain Signal Analysis

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

Statistical brain signal analysis project is multidisciplinary project combining the expertise of both Bayesian Methodology group and Cognitive Science and Technology group.

Localizing the neural currents indicating brain activity based on noninvasive MEG 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 ill-posedness 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 this project 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. John W. Belliveau and Dr. Matti S. Hämäläinen).

We performed a Bayesian analysis to the MEG inverse problem with lp-norm priors. Our model contains as special cases the minimum-norm estimate (MNE; l2) and minimum-current estimate (MCE; l1), which are both widely used in practice. With our method, the joint posterior distribution of all the model parameters can be obtained, making it possible to investigate the uncertainties of almost equally probable solution estimates rather than only a maximum a posteriori (MAP) estimate. Furthermore, the arbitrary choice between the l1- and l2-norm priors is inferred from the data by introducing a continuous parameter p between the limiting cases of MCE and MNE. The method is automatic, yet mathematically very straightforward which enables the addition of almost any kind of feasible prior information to improve the source localization. The results with real somatomotor MEG data look promising (see Figures).

Figure 1 (animation)

Figure 1 (animation) Measured data plotted on the MEG helmet sensor locations with red color denoting positive and blue color negative values (zero-values are green). The brain is visualized inside the transparent skin and the whole model is rotated 360 degrees in an animation.

Figure 2

Figure 2 The solution estimate (red line) is plotted against the original data (blue circles) with one sigma error bars.

Figure 3

Figure 3 Right index finger lifting produces activation contralaterally on the left hemisphere somatomotor hand areas (plotted on inflated brain surface).

Figure 4

Figure 4 Posterior distribution of parameter p defining the lp-norm order.

We also proposed an alternative hierarchical extension of the model corresponding to the minimum norm estimate. 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. This method is also applicable to full spatiotemporal datasets without significant increase in computational burden. We have made tentative comparisons of the approach with a recently proposed similar model treated with the variational Bayesian method.

References

  • Auranen, T., Nummenmaa, A., Hämäläinen, M. S., Jääskeläinen, I. P., Lampinen, J., Vehtari, A., and Sams, M. Bayesian Analysis of the neuromagnetic inverse problem with l p-norm priors. NeuroImage, 26(3): 870-884, 2005. Journal homepage on Elsevier.com. (revised personal version: PDF ~2.6MB)

  • Auranen, T., Nummenmaa, A., Hämäläinen, M. S., Jääskeläinen, I. P., Lampinen, J., Vehtari, A., and Sams, M. Full Bayesian Analysis of the MEG Inverse Problem with l p-norm Priors. Poster presented at 10th Annual Meeting of the Organization for Human Brain Mapping. Budapest, Hungary, June 13-17, 2004. (PDF~1.2MB)

  • Nummenmaa, A., Auranen, T., Hämäläinen, M. S., Jääskeläinen, I. P., Lampinen, J., Sams, M., and Vehtari A. A Hierarchical Bayesian Approach in Distributed MEG Source Modelling. Poster presented at 10th Annual Meeting of the Organization for Human Brain Mapping. Budapest, Hungary, June 13-17, 2004. (PDF~1.2MB)