Abstracts

RATIONALE: For spike localization from EEG or MEG data, distributed source models can be used, if the number of sources is unknown a priori. Traditionally, distributed source models assume the simultaneous activity of several thousand point sources j. A data and a model term are minimized: j = arg min ||C(m-Lj)||+l||Wj|| = (WTW)-1LTCT(CL(WTW)-1LTCT+lI)-1Cm. If sources are known to be extended spatially or temporally, this can be modeled by a coupling of neighbored activity via a non-diagonal matrix W. This approach leads to long computation times due to the inversion of WTW. We propose a method that does not compute point sources but extended sources directly. METHODS: A vector u of extended sources is related to j by j=Ku. The matrix K encodes the shape of the extended sources. We get u = arg min ||C(m-LKu)||+l||Wu|| = (WTW)-1KTLTCT(CLK(WTW)-1KTLTCT+lI)-1Cm. Here, W is a diagonal matrix used for depth and location weighting and WTW can be inverted on the fly. The term LKu ensures that the lead field matrix can still be set up for point sources. After u has been computed, j is derived and displayed. The matrix K is stored and applied in a format that is optimized for its sparseness. Possible designs for K include gaussian, linear, or boxcar-shaped falloff. An extension to the temporal domain is straightforward. Then, K can model temporal smoothness or a set of activation functions. In all these cases, the minimum norm constraint is imposed upon the extended sources. RESULTS: The method reconstructs extended sources in little more than the time needed to perform a standard solution. CONCLUSIONS: The extended character of the results obtained with this method is a prior, not an artifact produced by the underlying norm, as with minimum norm least squares (MNLS). When the method is used in an MNLS framework, however, the two effects overlay (smearing due to the MNLS and source extension due to the prior). When the method is used with the L1 norm, which normally produces few point sources, few extended sources are computed.