Integral equations and boundary-element solution for static potential in a general piece-wise homogeneous volume...

Area of Science:

• Bioelectromagnetics
• Computational modeling
• Biophysics

Background:

• Boundary element methods (BEM) are widely used for bioelectromagnetic field computations in multi-compartment models.
• Existing BEM approaches often limit compartment contact to a single external compartment, restricting model complexity.
• This limitation hinders accurate modeling of intricate biological tissues and systems.

Purpose of the Study:

• To develop a generalized surface integral equation and BEM discretization for modeling piecewise-homogeneous media.
• To overcome the limitations of existing BEM by allowing contact between multiple external compartments.
• To enable accurate bioelectromagnetic field computation in complex geometries, including junctions of more than two compartments.

Main Methods:

• A novel surface integral equation and BEM discretization were formulated.
• The method was implemented using a modular approach for linear collocation and Galerkin methods.
• The solver was validated through comparisons with finite element method (FEM) results and experimental data.

Main Results:

• The generalized BEM successfully models piecewise-homogeneous media with complex compartment interactions.
• The new integral equation allows field point positioning at boundaries involving more than two compartments.
• Validation confirmed the accuracy of the BEM approach, showing good agreement with FEM and demonstrating its utility in analyzing skull defects' effects on EEG.

Conclusions:

• The presented BEM formulation offers a significant advancement for bioelectromagnetic field modeling.
• This method enables the simulation of more realistic and complex biological models.
• The validated solver provides a powerful tool for research in neuroelectrophysiology and other bioelectromagnetic applications.