Surface-source modeling and estimation using biomagnetic measurements

General bounds for electrode mislocation on the EEG inverse problem

We analyze the effect of electrode mislocation on the electroencephalography (EEG) inverse problem using the Cramér-Rao bound (CRB) for single dipolar source parameters. We adopt a realistic head shape model, and solve the forward problem using the Boundary Element Method; the use of the CRB allows us to obtain general results which do not depend on the algorithm used for solving the inverse problem. We consider two possible causes for the electrode mislocation, errors in the measurement of the electrode positions and an imperfect registration between the electrodes and the scalp surfaces. For 120 electrodes placed in the scalp according to the 10-20 standard, and errors on the electrode location with a standard deviation of 5mm, the lower bound on the standard deviation in the source depth estimation is approximately 1mm in the worst case. Therefore, we conclude that errors in the electrode location may be tolerated since their effect on the EEG inverse problem are negligible from a practical point of view.

On the EEG/MEG forward problem solution for distributed cortical sources

In studies of EEG/MEG problems involving cortical sources, the cortex may be modeled by a 2-D manifold inside the brain. In such cases the primary or impressed current density over this manifold is usually approximated by a set of dipolar sources located at the vertices of the cortical surface tessellation. In this study, we analyze the different errors induced by this approximation on the EEG/MEG forward problem. Our results show that in order to obtain more accurate solutions of the forward problems with the multiple dipoles approximation, the moments of the dipoles should be weighted by the area of the surrounding triangles, or using an alternative approximation of the primary current as a constant or linearly varying current density over plane triangular elements of the cortical surface tessellation. This should be taken into account when computing the lead field matrix for solving the EEG/MEG inverse problem in brain imaging methods.

Size matters: MEG empirical and simulation study on source localization of the earliest visual activity in the occipital cortex

While the relationship between sensory stimulation and tasks and the size of the cortical activations is generally unknown, the visual modality offers a unique possibility of an experimental manipulation of stimulus size-related increases of the spatial extent of cortical activation even during the earliest activity in the retinotopically organized primary visual cortex. We used magnetoecephalography (MEG), visual stimuli of increasing size, and numerical simulations on realistic cortical surfaces to explore the effects of increasing spatial extent of the activated cortical sources on the neuromagnetic fields, location estimation biases, and source resolution. Source localization was performed assuming multiple dipoles in a sphere model using an efficient, automatically restarted multi-start simplex minimizer within the Calibrated Start Spatio-Temporal (CSST) algorithm. We found size-related effects on amplitude and latencies and differences in relative locations of the earliest occipital sources evoked by stimuli of increasing size presented at the same eccentricity. This finding was confirmed by single patch simulations. Additionally, simulations of multiple extended sources demonstrated size-related increase in limits in source resolution for bilaterally simulated sources, biases in location estimates for a given separation of sources, and limits in source resolution due to source multiplicity within a hemisphere.

Practical constraints on estimation of source extent with MEG beamformers

We aimed to determine practical constraints on the estimation of the spatial extent of neuronal activation using MEG beamformers. Correct estimation of spatial extent is a pre-requisite for accurate models of electrical activity, allows one to estimate current density, and enables non-invasive monitoring of functional recovery following stroke. The output of an MEG beamformer is maximum when the correct source model is used, so that the spatial extent of a source can in principal be determined through evaluation of different source models with the beamformer. Here, we simulated 275-channel MEG data using sources of varying spatial extents that followed the cortical geometry. These data were subsequently used to estimate the spatial extent of generic disc elements without knowledge of the underlying surface, and we compared these results to estimates based on cortical surface geometry (with and without error in surface location). We found that disc-shaped source models are too simplistic, particularly for areas with high curvature. For areas with low curvature spatial extent was underestimated, although on average there was a linear relationship between the true and estimated extent. In contrast, cortical surface models gave accurate predictions of spatial extent. However, adding small errors (>2 mm) to the estimated location of the cortical surface abolished this relationship between true and estimated extent, implying that accurate co-registration is needed with such models. Our results show that models exploiting surface information are necessary in order to model spatial extent and in turn current density, but in order to render such models applicable in practical situations, the accuracy of the cortical surface model itself needs to improve.