Multimodal Integration of M/EEG and f/MRI Data in SPM12

This paper presents a new method for localizing the electric activity in the brain based on multichannel surface EEG recordings. In contrast to the models presented up to now the new method does not assume a limited number of dipolar point sources nor a distribution on a given known surface, but directly computes a current distribution throughout the full brain volume. In order to find a unique solution for the 3-dimensional distribution among the infinite set of different possible solutions, the method assumes that neighboring neurons are simultaneously and synchronously activated. The basic assumption rests on evidence from single cell recordings in the brain that demonstrates strong synchronization of adjacent neurons. In view of this physiological consideration the computational task is to select the smoothest of all possible 3-dimensional current distributions, a task that is a common procedure in generalized signal processing. The result is a true 3-dimensional tomography with the characteristic that localization is preserved with a certain amount of dispersion, i.e., it has a relatively low spatial resolution. The new method, which we call Low Resolution Electromagnetic Tomography (LORETA) is illustrated with two different sets of evoked potential data, the first showing the tomography of the P100 component to checkerboard stimulation of the left, right, upper and lower hemiretina, and the second showing the results for the auditory N100 component and the two cognitive components CNV and P300. A direct comparison of the tomography results with those obtained from fitting one and two dipoles illustrates that the new method provides physiologically meaningful results while dipolar solutions fail in many situations. In the case of the cognitive components, the method offers new hypotheses on the location of higher cognitive functions in the brain.

The equation for the magnetic lead field for a given magnetoencephalography (MEG) channel is well known for arbitrary frequencies omega but is not directly applicable to MEG in the quasi-static approximation. In this paper we derive an equation for omega = 0 starting from the very definition of the lead field instead of using Helmholtz's reciprocity theorems. The results are (a) the transpose of the conductivity times the lead field is divergence-free, and (b) the lead field differs from the one in any other volume conductor by a gradient of a scalar function. Consequently, for a piecewise homogeneous and isotropic volume conductor, the lead field is always tangential at the outermost surface. Based on this theoretical result, we formulated a simple and fast method for the MEG forward calculation for one shell of arbitrary shape: we correct the corresponding lead field for a spherical volume conductor by a superposition of basis functions, gradients of harmonic functions constructed here from spherical harmonics, with coefficients fitted to the boundary conditions. The algorithm was tested for a prolate spheroid of realistic shape for which the analytical solution is known. For high order in the expansion, we found the solutions to be essentially exact and for reasonable accuracies much fewer multiplications are needed than in typical implementations of the boundary element methods. The generalization to more shells is straightforward.

The authors have applied estimation theory to the problem of determining primary current distributions from measured neuromagnetic fields. In this procedure, essentially nothing is assumed about the source currents, except that they are spatially restricted to a certain region. Simulation experiments show that the results can describe the structure of the current flow fairly well. By increasing the number of measurements, the estimate can be made more localised. The current distributions may be also used as an interpolation and an extrapolation for the measured field patterns.