IEEE Trans Biomed Eng. 2018 Dec;65(12):2675-2683. doi: 10.1109/TBME.2018.2813261. Epub 2018 Mar 7.
We develop a new accurate version of the boundary element fast multipole method for transcranial magnetic stimulation (TMS) related problems. This method is based on the surface-charge formulation and is using the highly efficient fast multipole accelerator along with analytical computations of neighbor surface integrals.
The method accuracy is demonstrated by comparison with the proven commercial finite-element method (FEM) software ANSYS Maxwell 18.2 2017 operating on unstructured grids and with adaptive mesh refinement. Five realistic high-definition head models from the Population Head Repository (IT'IS Foundation, Switzerland) have been acquired and augmented with a commercial TMS coil model (MRi-B91, MagVenture, Denmark). For each head model, simulations with our method and simulations with the FEM software ANSYS Maxwell 18.2 2017 have been performed. These simulations have been compared with each other and an excellent agreement was established in every case.
At the same time, our new method runs approximately 500 times faster than the ANSYS FEM, finishes in about 200 s on a standard server, and naturally provides a submillimeter field resolution, which is justified using mesh refinement.
Our method can be applied to modeling of brain stimulation and recording technologies such as TMS and magnetoencephalography, and has the potential to become a real-time high-resolution simulation tool.
我们开发了一种新的准确的用于经颅磁刺激（TMS）相关问题的边界元快速多极方法。该方法基于面电荷公式，并结合高效的快速多极加速器以及邻域面积分的解析计算。
通过与经过验证的商用有限元方法（FEM）软件 ANSYS Maxwell 18.2 2017 在非结构网格上运行的比较，并与自适应网格细化进行比较，证明了该方法的准确性。从人口头部存储库（瑞士 IT'IS 基金会）获得了五个现实的高清晰度头部模型，并增加了一个商用 TMS 线圈模型（MRi-B91，MagVenture，丹麦）。针对每个头部模型，使用我们的方法和 ANSYS Maxwell 18.2 2017 的 FEM 软件进行了模拟。将这些模拟进行了相互比较，在每种情况下都建立了极好的一致性。
同时，我们的新方法的运行速度大约比 ANSYS FEM 快 500 倍，在标准服务器上大约 200 秒即可完成，并且自然提供亚毫米级的场分辨率，这可以通过网格细化来证明。
我们的方法可应用于 TMS 和脑磁图等脑刺激和记录技术的建模，并有潜力成为实时高分辨率模拟工具。
