Stenroos Matti
Department of Neuroscience and Biomedical Engineering, Aalto University, PO Box 12200, FI-00076 Aalto, Finland.
Phys Med Biol. 2016 Nov 21;61(22):N606-N617. doi: 10.1088/0031-9155/61/22/N606. Epub 2016 Oct 25.
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 the 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.
边界元方法（BEM）用于多隔室容积导体模型中生物电磁场的正向计算。大多数BEM方法假定每个隔室最多与一个外部隔室接触。在这项工作中，我提出了一个通用的表面积分方程和BEM离散化方法，该方法消除了这一限制，并允许对一般的分段均匀介质进行BEM建模。新的积分方程允许将场点定位在两个以上隔室的交界边界处，从而能够在这种复杂几何结构中使用线性配置BEM。从标准公式出发，针对线性配置和伽辽金方法给出了模块化BEM实现。该方法及由此得到的求解器通过四种方式进行了验证，包括将体积和表面电位与使用有限元方法（FEM）获得的结果进行比较，并展示了颅骨上的一个洞对脑电图头皮电位的影响。
