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

Abstract

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.

Lesion-Constrained Electrical Source Imaging: A Novel Approach in Epilepsy Surgery for Tuberous Sclerosis Complex

“…Anisotropic white matter conductivities were incorporated using the method of Tuch [22], and dipole orientation constraints were identified using a model based approach [6]. We have previously demonstrated that this model attains a similar degree of accuracy as the finite element method [4]. This model was used to construct the leadfield matrix, which models the measurement of EEG data as:…”

Development, validation, and pilot MRI safety study of a high-resolution, open source, whole body pediatric numerical simulation model

“…The areas of computational modeling with human body are wide: fluid dynamics [1], electromagnetics [2], optics [3], ultrasound [4], thermodynamics [5], and mechanics [6,7]. Computational modeling with virtual humans is helpful in studying the interaction of complex biological problems in silico [7], for source localization [8,9], radio-frequency (RF) and specific absorption rate (SAR) exposure [10], and neurostimulation [11][12][13]. The accurate anatomical representation of human numerical models has become an integral part of many state-of-the-art safety studies, such as computed tomography (CT) dosimetry [14] and in MRI RF exposure [15][16][17].…”

Benchmarking transcranial electrical stimulation finite element models: a comparison study

“…Segmented head models are then meshed into desired element sizes and types (hexahedral or tetrahedral elements). Commercial platforms [2, 14–16] or specialized software [5, 16–18] have typically been used to solve FE [19–21], finite difference or boundary element method [22] simulations.…”

“…Hexahedral models were determined in studies by Wagner et al [27] and Vorwerk et al [28] to produce accurate results, but cautioned that the method of generating the hexahedral mesh must be chosen carefully to avoid leakage or artificially closed compartments. Tetrahedral elements have been constructed by compartmentalizing individual voxel-based hexahedral elements into multiple tetrahedral elements [22] or into free meshes using constrained Delaunay tetrahedralization (CDT) approaches [25, 29]. To simulate EEG data, meshed head models and electrodes are typically assigned homogeneous (insulating) Neumann boundary conditions on the head surface, and zero potential at ground electrodes [23].…”

“…Internal sources mimicking an active cortex are approximated as dipolar current sources and voltage differences caused by current dipoles are calculated using the reciprocity principle [30]. These forward problems have often been implemented using in-house or freely available FE software such as NeuroFEM [31], SimBio [13, 23, 24, 32, 33], SCIRun [22, 34].…”