PDF《www.elsevier.com/locate/ynimg》

Hari, 1991;

Mosher et al., 1992) approximates brain activity by a small number of current dipoles. Although this method gives good estimate when the number of active areas is small, it is difficult to determine the appropriate number of dipole sources for complicated spatio-temporal activity. In addition, neural current distribution over the cortical surface cannot be estimated by the dipole method. The distributed source method assumes distributed currents in the brain (Hamalainen et al., 1993). In a linear approach to resolve the inverse problem, several prior assumptions have been used such as the (weighted) minimum norm method (Hamalainen and Ilmoniemi, 1994;

Hamalainen et al., 1993;

Wang et al., 1992), the maximum smoothness method (Pascual-Marqui, 1999;

Pascual-Marqui et al., 1994), the minimum L1-norm method (Uutela et al., 1999), and others (Huang et al., 1997;

Toyama et al., 1999). Bayesian methods have also been proposed to incorporate nonlinear smoothness constraints (Baillet and Garnero, 1997). Unfortu- nately, the prior assumptions are still insufficient to fully resolve 1053-8119/$ - see front matter D

2004 Elsevier Inc. All rights reserved. doi:10.1016/j.neuroimage.2004.06.037 * Corresponding author. ATR Computational Neuroscience Laborato- ries, 2-2-2 Hikaridai, Seika, Soraku, Kyoto 619-0288, Japan. Fax: +81

774 95 1259. E-mail address: [email protected] (M. Sato). Available online on ScienceDirect (www.sciencedirect.com.) www.elsevier.com/locate/ynimg NeuroImage

23 (2004) 806C826 the ill-posed nature of the inverse problem, and thus the spatial resolution of these methods is still rather low. Attempts have been made to overcome these limitations by supplementing the information of other imaging means (Ahlfors et al., 1999;

Dale and Sereno, 1993;

Dale et al., 2000;

Fujimaki et al., 2002;

Heinze et al., 1994;

Kajihara et al., 2004;

Liu et al., 1998;

Phillips et al., 2002;

Schmidt et al., 1999). The MRI image gives information on the position and orientation of the cortical dipoles, while fMRI provides topographical information on active dipoles. Although fMRI has high spatial resolution, it has been pointed out that the hemodynamic signals of fMRI may not precisely correspond to neural activity due to various factors such as the effects of noise and artifacts. In particular, the fMRI activity corresponds to an average of several thousands of MEG time series data because of the time resolution difference between MEG and fMRI. When higher brain functions are examined, several different processes may occur within several seconds, and these activities are averaged out in the fMRI data. Consequently, the fMRI active areas may include inactive current areas in the MEG time slice data, and the fMRI activity for the active current may be smeared by the temporal averaging. The recent approaches, such as the Wiener filter or the Bayesian method (Dale et al., 2000;

Kajihara et al., 2004;

Phillips et al., 2002;

Schmidt et al., 1999), use the fMRI data as prior information on the source current variance by assuming that the current variances for fMRI active dipoles are large compared with those for fMRI inactive dipoles. Source current estimation based on these methods may fail if the fMRI data contain incorrect information. 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. 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. Therefore, our method is capable of appropriately estimating the source current variance from the MEG data supplemented with the fMRI data, even if fMRI data convey inaccurate information. Accordingly, our method is robust against inaccurate fMRI information. The 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. Because of the hierarchical prior, the estimation problem becomes nonlinear and cannot be solved analytically. Therefore, the approximate posterior distribution is calculated by using the Variational Bayesian (VB) method (Attias, 1999;