Morales Leah, Wartman William A, Ferreira Jonathan, Miles Alton, Daneshzand Mohammad, Lu Hanbing, Nummenmaa Aapo R, Deng Zhi-De, Makaroff Sergey N
Electrical and Computer Engineering, Worcester Polytechnic Inst., Worcester, MA 01609 USA.
Analog Devices, Inc., 1 Analog Way, Wilmington, MA 01887 USA.
bioRxiv. 2023 Aug 21:2023.08.20.554037. doi: 10.1101/2023.08.20.554037.
This study aims to describe a MATLAB software package for transcranial magnetic stimulation (TMS) coil analysis and design.
Electric and magnetic fields of the coils as well as their self- and mutual (for coil arrays) inductances are computed, with or without a magnetic core. Solid and stranded (Litz wire) conductors are also taken into consideration. The starting point is the centerline of a coil conductor(s), which is a 3D curve defined by the user. Then, a wire mesh and a computer aided design (CAD) mesh for the volume conductor of a given cross-section (circular, elliptical, or rectangular) are automatically generated. Self- and mutual inductances of the coil(s) are computed. Given the conductor current and its time derivative, electric and magnetic fields of the coil(s) are determined anywhere in space.Computations are performed with the fast multipole method (FMM), which is the most efficient way to evaluate the fields of many elementary current elements (current dipoles) comprising the current carrying conductor at a large number of observation points. This is the major underlying mathematical operation behind both inductance and field calculations.
The wire-based approach enables precise replication of even the most complex physical conductor geometries, while the FMM acceleration quickly evaluates large quantities of elementary current filaments. Agreement to within 0.74% was obtained between the inductances computed by the FMM method and ANSYS Maxwell 3D for the same coil model. Although not provided in this study, it is possible to evaluate non-linear magnetic cores in addition to the linear core exemplified. An experimental comparison was carried out against a physical MagVenture C-B60 coil; the measured and simulated inductances differed by only 1.25%, and nearly perfect correlation was found between the measured and computed E-field values at each observation point.
The developed software package is applicable to any quasistatic inductor design, not necessarily to the TMS coils only.
本研究旨在描述一种用于经颅磁刺激（TMS）线圈分析与设计的MATLAB软件包。
计算线圈的电场和磁场以及它们的自感和互感（对于线圈阵列），有无磁芯均可。还考虑了实心和绞合（利兹线）导体。起点是线圈导体的中心线，它是用户定义的三维曲线。然后，自动生成给定横截面（圆形、椭圆形或矩形）的体积导体的线网和计算机辅助设计（CAD）网格。计算线圈的自感和互感。给定导体电流及其时间导数，可确定空间中任意位置的线圈电场和磁场。使用快速多极子方法（FMM）进行计算，这是在大量观测点评估构成载流导体的许多基本电流元件（电流偶极子）的场的最有效方法。这是电感和场计算背后的主要基础数学运算。
基于导线的方法能够精确复制即使是最复杂的物理导体几何形状，而FMM加速能够快速评估大量基本电流细丝。对于相同的线圈模型，FMM方法计算的电感与ANSYS Maxwell 3D计算的电感之间的一致性在0.74%以内。尽管本研究未提供，但除了示例的线性磁芯外，还可以评估非线性磁芯。针对物理MagVenture C-B60线圈进行了实验比较；测量电感与模拟电感仅相差1.25%，并且在每个观测点的测量电场值与计算电场值之间发现了几乎完美的相关性。
所开发的软件包适用于任何准静态电感器设计，不一定仅适用于TMS线圈。
