Data-driven parceling and entropic inference in MEG.

In Amblard et al. [Amblard, C., Lapalme, E., Lina, J.M. 2004. Biomagnetic source detection by maximum entropy and graphical models. IEEE Trans. Biomed. Eng. 55 (3) 427--442], the authors introduced the maximum entropy on the mean (MEM) as a methodological framework for solving the magnetoencephalography (MEG) inverse problem. The main component of the MEM is a reference probability density that enables one to include all kind of prior information on the source intensity distribution to be estimated. This reference law also encompasses the definition of a model. We consider a distributed source model together with a clustering hypothesis that assumes functionally coherent dipoles. The reference probability distribution is defined as a prior parceling of the cortical surface. In this paper, we present a data-driven approach for parceling out the cortex into regions that are functionally coherent. Based on the recently developed multivariate source pre-localization (MSP) principle [Mattout, J., Pelegrini-Issac, M., Garnero, L., Benali, H. 2005. Multivariate source pre-localization (MSP): Use of functionally informed basis functions for better conditioning the MEG inverse problem. NeuroImage 26 (2) 356--373], the data-driven clustering (DDC) of the dipoles provides an efficient parceling of the sources as well as an estimate of parameters of the initial reference probability distribution. On MEG simulated data, the DDC is shown to further improve the MEM inverse approach, as evaluated considering two different iterative algorithms and using classical error metrics as well as ROC (receiver operating characteristic) curve analysis. The MEM solution is also compared to a LORETA-like inverse approach. The data-driven clustering allows to take most advantage of the MEM formalism. Its main trumps lie in the flexible probabilistic way of introducing priors and in the notion of spatial coherent regions of activation. The latter reduces the dimensionality of the problem. In so doing, it narrows down the gap between the two types of inverse methods, the popular dipolar approaches and the distributed ones.