Analysis of Transcranial Magnetic Stimulation Based on the Surface Integral Equation Formulation
Analysis of Transcranial Magnetic Stimulation Based on the Surface Integral Equation Formulation
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DOI：
10.1109/tbme.2015.2393557
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发表时间：
2015-06-01
影响因子：
4.6
通讯作者：
Haueisen, Jens
中科院分区：
文献类型：
--
作者：
Cvetkovic, Mario;Poljak, Dragan;Haueisen, Jens
目标：本文的目的是提供一个严格的模型，因此，更准确地描述经颅磁刺激（TMS）感应场和电流，分别考虑到电感和电容效应，以及传播效应，往往被忽略时，使用准静态近似。方法：该公式是基于表面积分方程（SIE）的方法。从等效定理出发，采用适当的电场边界条件，导出了有耗均匀脑的模型。采用矩量法对SIE进行了数值求解。结果如下：三个典型的TMS线圈的感应电场，电流密度和磁通密度分布在人脑内的数值结果，提出了一个很好的协议与以前的一些分析，以及通过解析方法得到的结果。结论：未来的工作应该与开发更详细的人脑几何模型有关，该模型将考虑复杂的皮质柱状结构以及一些额外的脑组织。重要性：据作者所知，类似的方法在建模TMS还没有以前的报道，虽然积分方程方法正在看到一个复兴的计算电磁学社区。
Goal: The aim of this paper is to provide a rigorous model and, hence, a more accurate description of the transcranial magnetic stimulation (TMS) induced fields and currents, respectively, by taking into account the inductive and capacitive effects, as well as the propagation effects, often being neglected when using quasi-static approximation. Methods: The formulation is based on the surface integral equation (SIE) approach. The model of a lossy homogeneous brain has been derived from the equivalence theorem and using the appropriate boundary conditions for the electric field. The numerical solution of the SIE has been carried out using the method of moments. Results: Numerical results for the induced electric field, electric current density, and the magnetic flux density distribution inside the human brain, presented for three typical TMS coils, are in a good agreement with some previous analysis as well as to the results obtained by analytical approach. Conclusion: The future work should be related to the development of a more detailed geometrical model of the human brain that will take into account complex cortical columnar structures, as well as some additional brain tissues. Significance: To the best of authors knowledge, similar approach in modeling TMS has not been previously reported, albeit integral equation methods are seeing a revival in computational electromagnetics community.