Finite-Element Simulation in Bioelectromagnetics Without the Need for Modeling and Meshing

Biological data often takes the form of regular grids of samples, e.g., obtained by magnetic resonance imaging (MRI). When the finite-element method is used to predict the electromagnetic fields in volumes specified in this way, the data is first transformed to a geometric model, and then the model is subdivided into finite elements. These steps are expensive and can be unreliable. An alternative is proposed that avoids both steps. A regular mesh of rectangular finite elements is superimposed on the MRI grid. Each element may straddle boundaries between different tissues, but the basis functions are constructed in such a way that they respect the material interfaces. The new method is applied to the forward problem in electroencephalography. A circular head model and a model derived from real MRI data are analyzed with the new method. Sampled potentials at the surface of the scalp compare well with those obtained using the conventional finite-element method.