A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields

Abstract

Overview

Common modeling approaches, such as the cable equation, have traditionally been used to simulate the effects of electromagnetic fields (EMFs) on excitable cells like neurons. However, these methods involve simplifying assumptions that limit their accuracy and predictive power. To address this issue, more comprehensive bidomain or "whole" finite element methods have been developed. In this study, the authors introduce a novel bidomain integral equation that enables full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.

Methods

• Developed a boundary element formulation to solve an integral equation connecting devices, tissue inhomogeneity, and cell membrane-induced electric fields.
• Utilized first-order nodal elements and a stable Crank-Nicholson time-stepping scheme.
• Validated the method via simulations of cylindrical Hodgkin-Huxley axons and spherical cells under various brain stimulation scenarios.

Findings

• The boundary element approach produced accurate results for both electric and magnetic stimulation of neural cells.
• No need for complex volume meshes with features at different scales, facilitating the modeling of microscale features within macroscale models.
• The approach allows for flexible modeling of device placement and cell populations.

Significance

Device-induced EMFs are widely used for modulating brain activity, both in research and therapeutics. The use of bidomain solvers allows for realistic modeling of cell geometry, external E-fields, and neuron populations. Advanced multi-cell studies would significantly benefit from faster and scalable bidomain solvers, particularly for studying health and safety impacts of EMF exposures.

Conclusion

• Introduced a new bidomain integral equation method for modeling neuron cell responses to device-induced EMFs.
• Canonical tests showed hybrid cable-equation works for most scenarios, but advanced studies need fast-bidomain solvers.
• Findings reinforce the importance of considering the full electromagnetic environment when predicting cellular and health responses to EMFs, underlining that electromagnetic fields can influence cellular activity, which is a crucial consideration for EMF safety and exposure guidelines.
• Future work aims to further develop these computational tools for more realistic and scalable neural simulations.