Department of Electrical & Computer Engineering, Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, United States of America.
Phys Med Biol. 2024 Aug 28;69(17). doi: 10.1088/1361-6560/ad66a9.
Bioelectric modeling problems, such as electroencephalography, magnetoencephalography, transcranial electrical stimulation, deep brain stimulation, and transcranial magnetic stimulation, among others, can be approached through the formulation and resolution of integral equations of the(BEM). Recently, it has been realized that theof the BEM is naturally well-suited for the application of the(FMM). The FMM is a powerful algorithm for the computation of many-body interactions and is widely applied in electromagnetic modeling problems. With the introduction of BEM-FMM in the context of bioelectromagnetism, the BEM can now compete with the(FEM) in a number of application cases. This survey has two goals: first, to give a modern account of the main BEM formulations in the literature and their integration with FMM, directed to general researchers involved in development of BEM software for bioelectromagnetic applications. Second, to survey different techniques and available software, and to contrast different BEM and FEM approaches. As a new contribution, we showcase that the charge-based formulation is dual to the more common surface potential formulation.
生物电建模问题，如脑电图、脑磁图、经颅电刺激、深部脑刺激和经颅磁刺激等，可以通过对边界元法（BEM）的积分方程的建立和求解来解决。最近，人们已经意识到，BEM 的积分方程理论非常适合应用快速多极子算法（FMM）。FMM 是一种用于计算多体相互作用的强大算法，在电磁建模问题中得到了广泛应用。随着 BEM-FMM 在生物电磁学中的应用，BEM 现在可以在许多应用案例中与有限元法（FEM）竞争。本调查有两个目的：首先，为一般研究人员提供文献中主要 BEM 公式及其与 FMM 的集成的现代描述，这些研究人员涉及开发用于生物电磁应用的 BEM 软件。其次，调查不同的技术和可用的软件，并对比不同的 BEM 和 FEM 方法。作为一项新的贡献，我们展示了基于电荷的公式与更常见的表面电位公式是对偶的。
