Inverse methods are used to reconstruct current sources in the human brain by means of Electroencephalogra- phy (EEG) and Magnetoencephalography (MEG) measure- ments of event related fields or epileptic seizures. There exists a persistent uncertainty regarding the influence of anisotropy of the white matter compartment on neural source reconstruc- tion. In this paper, we study the sensitivity to anisotropy of the EEG/MEG forward problem for a thalamic source in a high resolution finite element volume conductor. The influence of anisotropy on computed fields will be presented by both high resolution visualization of fields and return current flow and topography and magnitude error measures. We pay particular attention to the influence of local conductivity changes in the neighborhood of the source. The combination of simulation and visualization provides deep insight into the effect of white matter conductivity anisotropy. We found that for both EEG and MEG formulations, the local presence of electrical anisotropy in the tissue surroun- ding the source substantially compromised the forward field computation, and correspondingly, the inverse source recons- truction. The degree of error resulting from the uncompen- sated presence of tissue anisotropy depended strongly on the proximity of the anisotropy to the source; remote anisotropy had a much weaker influence than anisotropic tissue that included the source.
In presurgical epilepsy diagnosis, an accurate reconstruction of cortical sources related to epileptic activity is necessary.When using combined electro-(EEG) and magnetoencephalography (MEG) to accomplish this, a common individually calibrated head volume conductor model is crucial since especially the EEG strongly depends on the conductive properties of the head tissues, mainly on skull resistivity.However, this property varies strongly inter-and intra-individually and is difficult to measure in practice.Here, we present a new pipeline for skull conductivity calibration based on Aydin.et.al. 2014 (doi: 10.1371/journal.pone.0093154),exploiting the different sensitivity profiles of EEG and MEG modalities.A 4-layered sphere model, where the analytical solution is known, is used to test the algorithm and to investigate the effects of noise, orientation and depth of the underlying source and different source models used for the forward solutions.For the numerical calculations of the EEG and MEG forward solutions, we use the finite element method which is implemented in the software toolbox duneuro (http://www.duneuro.org).The results suggest that a superficial source with a high signal-to-noise ratio and a strong tangential component is best suited to reliably reconstruct a given skull conductivity using the presented algorithm, showing comparable results between the St. Venant and partial integration source model.Based on these findings, this method is applied to epilepsy patient data using realistic volume conductor head models.The early P20/N20 component of somatosensory evoked potentials/fields is used to individually estimate the skull conductivity in order to use combined EEG/MEG source reconstruction of interictal spikes.In summary, this method seems a promising new tool to individually estimate skull conductivity using non-invasive techniques and should further be validated using realistic head models and datasets.
The electroencephalogram (EEG) represents potential differences recorded from the scalp as function of time (Niedermayer and Lopes da Silva, 1987). The generators of the EEG consist of time-varying ionic currents generated in the brain by biochemical sources. These current sources also generate a small but measurable magnetic induction field, which can be recorded with magnetoencephalographic (MEG) equipment (Hämäläinen et al., 1993). When EEG and MEG are studied in the time or frequency domain, several rhythms can be discriminated that contain valuable information about the collective behavior of the living human brain as a neural network. In this chapter EEG and MEG are discussed in the spatial domain. We consider that these signals are recorded from multiple sensors with known positions and study the spatial distribution of EEG and MEG (in the sequel abbreviated as MEEG) in relation to the spatial distribution of the underlying sources.
In order to perform electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, which is the so-called EEG forward problem. To solve it accurately, it is necessary to apply numerical methods that are able to take the individual geometry and conductivity distribution of the subject's head into account. In this context, the finite element method (FEM) has shown high numerical accuracy with the possibility to model complex geometries and conductive features, e.g., white matter conductivity anisotropy. In this article, we introduce and analyze the application of a discontinuous Galerkin (DG) method, a finite element method that includes features of the finite volume framework, to the EEG forward problem. The DG-FEM approach fulfills the conservation property of electric charge also in the discrete case, making it attractive for a variety of applications. Furthermore, as we show, this approach can alleviate modeling inaccuracies that might occur in head geometries when using classical FE methods, e.g., so-called "skull leakage effects", which may occur in areas where the thickness of the skull is in the range of the mesh resolution. Therefore, we derive a DG formulation of the FEM subtraction approach for the EEG forward problem and present numerical results that highlight the advantageous features and the potential benefits of the proposed approach.
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