Evaluation of numerical techniques for solving the current injection problem in biological tissues

Accurate computational modeling of electric fields in the human head has become important in clinical research to study or influence brain functionality. While existing numerical approaches have been evaluated against simple geometries with known closed form solutions, the relationship between these approaches in more complex geometries has not been studied. Here, we compare the three most commonly used approaches for bioelectric modeling: the finite element method (FEM), the finite difference method (FDM), and the boundary element method (BEM). Using both isotropic and anisotropic conductivity distributions, we construct and compare bioelectric models for a realistic head geometry. Our results suggest that both FEM and FDM are capable of accurately model voltages in the brain, while computations from BEM result in significantly larger errors, due to the increased simplicity and implicit model assumptions.