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Hierarchical Bayesian estimation for MEG inverse problem Masa-aki Sato,a,b,* Taku Yoshioka,a Shigeki Kajihara,c Keisuke Toyama,c Naokazu Goda,d Kenji Doya,a,b and Mitsuo Kawatoa a ATR Computational Neuroscience Laboratories, Seika, Soraku, Kyoto 619-0288, Japan b CREST, Japan Science and Technology Corporation, Japan c Technology Research Laboratory, Shimadzu Co.

, Seika, Soraku, Kyoto 619-0237, Japan d National Institute for Physiological Sciences, Myodaiji, Okazaki 444-8585, Japan Received

24 November 2003;

revised

1 March 2004;

accepted

22 June

2004 Source current estimation from MEG measurement is an ill-posed problem that requires prior assumptions about brain activity and an efficient estimation algorithm. 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 by using the Variational Bayesian method. 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. A 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. The proposed method provides a unified theory to deal with the following three situations: (1) MEG with no other data, (2) MEG with structural MRI data on cortical surfaces, and (3) MEG with both structural MRI and fMRI data. We investigated the performance of our method and conventional linear inverse methods under these three conditions. Simulation results indicate that our method has better accuracy and spatial resolution than the conven- tional linear inverse methods under all three conditions. It is also shown that accuracy of our method improves as MRI and fMRI information becomes available. Simulation results demonstrate that our method appropriately resolves the inverse problem even if fMRI data convey inaccurate information, while the Wiener filter method is seriously deteriorated by inaccurate fMRI information. D

2004 Elsevier Inc. All rights reserved. Keywords: MEG/EEG inverse problem;

Hierarchical Bayesian method;

Variational Bayesian method;

Variance estimation;

MRI and fMRI information;

Spatial smoothness constraint Introduction Functional magnetic resonance imaging (fMRI) and magneto- encephalography (MEG) are the major recording means of brain activity. fMRI records brain activity with millimeter-order spatial resolution, but its temporal resolution is on the order of several seconds due to slow hemodynamic responses to neural activity (Bandettini, 2000;

Belliveau et al., 1991;

Churchland and Sejnowski, 1988;

Logothetis et al., 2001;

Ogawa et al., 1990). Conversely, MEG measures brain activity with millisecond-order temporal resolution, but its spatial resolution is poor due to the ill-posed nature of the inverse problem for estimating source currents from the electromagnetic measurement (Nunez, 1981). In addition, the number of MEG sensors is generally insufficient to provide a precise reconstruction of the source current (Grave de Peralta Menendez and Gonzalez Andino, 1998). Therefore, prior information on the source currents is essential to solve the inverse problem. Inverse procedures are commonly classified as dipole and distributed source methods. The dipole method (Aine et al., 2000;