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

TL;DR

This paper introduces a novel boundary element method that models complex multi-compartment volume conductors with junctions, improving bioelectromagnetic field computations in intricate geometries.

Contribution

It presents a general surface integral equation and BEM discretization that handle junctions of multiple compartments, extending previous methods' capabilities.

Findings

Validated against finite element method results.

Demonstrated modeling of skull holes affecting EEG potentials.

Enabled BEM modeling of complex multi-compartment geometries.

Abstract

Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-homogeneous medium. The new integral equation allows positioning of field points at junctioned boundary of more than two compartments, enabling the use of linear collocation BEM in such a complex geometry. A modular BEM implementation is presented for linear collocation and Galerkin approaches, starting from standard formulation. The approach and resulting solver are verified in four ways, including comparisons of volume and surface potentials to those obtained using the finite element method (FEM), and the effect of a hole in skull on electroencephalographic scalp potentials is demonstrated.