Vaezi Seyed Sina, Gomez Luis J
Elmore Family School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Ave, West Lafayette, 47907, IN, USA.
IEEE Trans Magn. 2024 Dec;60(12). doi: 10.1109/tmag.2024.3486081. Epub 2024 Oct 24.
A new volume integral equation (VIE) approach is introduced to study transcranial magnetic stimulation (TMS) and high-contrast media at low frequencies. This new integral equation offers a simple solution to the high-contrast breakdown observed in low-frequency electric field (E-field) dosimetry of conductive media. Specifically, we employ appropriate approximations that are valid for low frequencies and stabilize the VIE by introducing a basis expansion set that removes solutions associated with high eigenvalues in the equation. The new equation is devoid of high-contrast breakdown and does not require the use of auxiliary surface variables or projectors, providing a straightforward practical solution for the VIE analysis of TMS. Our results indicate that the novel VIE formulation matches boundary element, finite element, and analytical solutions. This new VIE represents a first step towards including anisotropy in integral equation E-field dosimetry for brain stimulation.
引入了一种新的体积积分方程（VIE）方法来研究低频下的经颅磁刺激（TMS）和高对比度介质。这种新的积分方程为在导电介质的低频电场（E场）剂量学中观察到的高对比度失效问题提供了一个简单的解决方案。具体而言，我们采用了适用于低频的近似方法，并通过引入一个基展开集来稳定VIE，该基展开集消除了方程中与高特征值相关的解。新方程不存在高对比度失效问题，并且不需要使用辅助表面变量或投影算子，为TMS的VIE分析提供了一种直接的实用解决方案。我们的结果表明，这种新颖的VIE公式与边界元、有限元和解析解相匹配。这种新的VIE代表了在用于脑刺激的积分方程E场剂量学中纳入各向异性的第一步。
