Comparing finite difference forward models using free energy based on multiple sparse priors

Due to the ill-posed nature of the EEG source localization problem, the spatial resolution of the reconstructed activity is limited to several centimeters (Baillet, 2001). Advanced forward modeling of the head can contribute to improve the spatial resolution (Hallez, 2007). The boundary element method or BEM is commonly used due to its computation speed. More advanced volume modeling methods, such as finite difference methods or FDM, are computationally more intensive but allow estimating sources inside gray matter (Vanrumste, 2000). FDM also allows to incorporate tissue anisotropy and skull inhomogeneities (Hallez, 2008). Variational Bayesian approaches are getting more popular to solve the reconstruction problem (Friston, 2008 and Wipf, 2010). They allow incorporating several types of prior information in order to get a unique source distribution. Parametric empirical bayes or PEB implemented into the SPM software package allows also to compare different models, incorporating different prior information, based on their free energy (Henson, 2009). However, using PEB in SPM only BEM forward models can be compared. Based on the fact the uncertainty on the anatomy can be incorporated within the free energy (Lopez, 2012), this work extended the PEB framework to FDM models.