TWO PROBABILISTIC ALGORITHMS FOR MEG/EEG SOURCE RECONSTRUCTION Johanna M. Zumer 1,2 , Hagai T. Attias 3 , Kensuke Sekihara 4 , Srikantan S. Nagarajan 1,2 1 Biomagnetic Imaging Lab, Dept. of Radiology, UCSF, San Francisco, CA, 94143-0628 USA 2 Joint Graduate Group in Bioengineering, UCSF/UC Berkeley, San Francisco, CA, 94143-0628 USA 3 Golden Metallic, Inc., San Francisco, CA, 94147, USA 4 Dept. of Systems Design and Engineering, Tokyo Metropolitan University, Tokyo, 191-0065 Japan ABSTRACT We have developed two algorithms for source imaging from MEG/EEG data. Contribution to sensor data from a source at a particular voxel is expressed as the product of a known lead field and temporal basis functions with unknown coefficients. Temporal basis functions are in turn estimated from data. The first algorithm models activity outside the voxel of interest by a full-rank covariance matrix and estimates unknowns by maximizing the likelihood. The second algorithm parameter- izes activity outside the voxel of interest as a linear mixture of a set of unknown Gaussian factors plus Gaussian sensor noise and estimates all unknown quantities using an Expectation- Maximization (EM) algorithm. In both cases, the source im- age map is the likelihood of a dipole source at each voxel. Performance in simulations and real data demonstrate signifi- cant improvement over existing source localization methods. 1. INTRODUCTION Magnetoencephalography (MEG) and electroencephalography (EEG) are popular methods of noninvasively measuring the spatiotemporal characteristics of human neural activity. Both techniques record the effects of neural activity at the scalp with millisecond precision. Arrays of MEG sensors detect femtoTesla changes in the magnetic field outside the head; arrays of EEG sensors measure the corresponding voltage po- tential changes on the scalp. The increasing availability of whole-head MEG/EEG sensor arrays allows for higher-res- olution spatiotemporal reconstruction of neural activity, thus increasing the demand for improved methods for source re- construction. All source localization techniques, which can be broadly classified as parametric or tomographic, make assumptions to overcome the ill-posed inverse problem. Parametric methods, including equivalent current dipole (ECD) fitting techniques, assume knowledge about the number of sources and their ap- proximate locations. A single dipolar source can be localized well, but ECD techniques poorly describe multiple sources or The authors would like to thank Kenneth Hild and Sarang Dalal for help- ful discussions, and NIH R01NS44590 and NIH R01DC004855 for support. sources with large spatial extent. Alternatively, tomographic methods reconstruct an estimate of source activity at every grid point across the whole brain. Specifically, the adaptive beamformer has been shown to have the best spatial resolu- tion and zero localization bias [1]. However, beamformers are very sensitive to highly temporally-correlated sources [2]. This paper presents a probabilistic modeling framework for dipole source localization. Two techniques based on this framework are described and demonstrated. Each technique uses a probabilistic hidden variable model that describes the observed sensor data in terms of activity from unobserved brain and interference sources. The unobserved source ac- tivities and model parameters are inferred from the data by an Expectation-Maximization algorithm. These techniques cre- ate an image of brain activity by scanning the brain, inferring the models from sensor data, and using them to compute the likelihood of a dipole at each voxel. 2. METHODS The probabilistic models in this paper are based on a physi- cal description of neural activity, in which brain sources are modeled by current dipoles. For a given volume conductor model, the K × 3 forward lead field matrix F (r) represents the physical relationship between a dipole at voxel r and its influence on sensor k =1: K [3]. In both models, we as- sume the source activity is a linear combination of J ×N tem- poral basis functions φ computed from the data as described in Section 2.3, spatially weighted at each voxel by a 3 × J dipole mixing matrix G(r). We compute the maximum like- lihood at each voxel; the spatial peaks of this likelihood map correspond to the most likely source locations. 2.1. Model 1 In Model 1, we describe a generative model for the K × 1 sensor data y n : y n = F (r)G(r)φ n + w n (r) (1) The noise w n (r) is modeled by zero-mean Gaussian with