Worbs Torge, Rumi Bianka, Madsen Kristoffer H, Thielscher Axel
Section for Magnetic Resonance, DTU Health Tech, Technical University of Denmark, Kgs Lyngby, Denmark; Danish Research Centre for Magnetic Resonance, Department of Radiology and Nuclear Medicine, Copenhagen University Hospital Amager and Hvidovre, Copenhagen, Denmark.
Danish Research Centre for Magnetic Resonance, Department of Radiology and Nuclear Medicine, Copenhagen University Hospital Amager and Hvidovre, Copenhagen, Denmark; Section for Visual Computing, Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kgs Lyngby, Denmark; Sino-Danish College, University of Chinese Academy of Sciences, Beijing, 100190, China.
Brain Stimul. 2025 Jul-Aug;18(4):1174-1183. doi: 10.1016/j.brs.2025.05.136. Epub 2025 Jun 5.
Transcranial Magnetic Stimulation (TMS) therapies use both focal and unfocal coil designs. Unfocal designs often employ bendable windings and moveable parts, making realistic simulations of their electric fields in inter-individually varying head sizes and shapes challenging. This hampers comparisons of the various coil designs and prevents systematic evaluations of their dose-response relationships.
Introduce and validate a novel method for optimizing the position and shape of flexible coils taking individual head anatomies into account. Evaluate the impact of realistic modeling of flexible coils on the electric field simulated in the brain.
Accurate models of four coils (Brainsway H1, H4, H7; MagVenture MST-Twin) were derived from computed tomography data and mechanical measurements. A generic representation of coil deformations by concatenated linear transformations was introduced and validated. This served as basis for a principled approach to optimize the coil positions and shapes, and to optionally maximize the electric field strength in a region of interest (ROI).
For all four coil models, the new method achieved configurations that followed the scalp anatomy while robustly preventing coil-scalp intersections on 1100 head models. In contrast, setting only the coil center positions without shape deformation regularly led to physically impossible configurations. This also affected the electric field calculated in the cortex, with a median peak difference of ∼16 %. In addition, the new method outperformed grid search-based optimization for maximizing the electric field of a standard Fig. 8 coil in a ROI with a comparable computational complexity.
Our approach alleviates practical hurdles that so far hampered accurate simulations of bendable coils. This enables systematic comparison of dose-response relationships across the various coil designs employed in therapy.
经颅磁刺激（TMS）疗法使用聚焦和非聚焦线圈设计。非聚焦设计通常采用可弯曲绕组和可移动部件，这使得在个体头部大小和形状各异的情况下对其电场进行逼真模拟具有挑战性。这妨碍了对各种线圈设计的比较，并阻碍了对其剂量反应关系的系统评估。
引入并验证一种考虑个体头部解剖结构来优化柔性线圈位置和形状的新方法。评估柔性线圈的逼真建模对大脑中模拟电场的影响。
从计算机断层扫描数据和机械测量中得出四个线圈（Brainsway H1、H4、H7；MagVenture MST-Twin）的精确模型。引入并验证了通过串联线性变换对线圈变形的通用表示。这为优化线圈位置和形状以及在感兴趣区域（ROI）中选择性地最大化电场强度的原则性方法奠定了基础。
对于所有四个线圈模型，新方法实现了符合头皮解剖结构的配置，同时在1100个头部模型上有力地防止了线圈与头皮相交。相比之下，仅设置线圈中心位置而不进行形状变形通常会导致物理上不可能的配置。这也影响了在皮质中计算的电场，中位数峰值差异约为16%。此外，在计算复杂度相当的情况下，新方法在最大化标准8字形线圈在ROI中的电场方面优于基于网格搜索的优化方法。
我们的方法消除了迄今为止阻碍对可弯曲线圈进行精确模拟的实际障碍。这使得能够对治疗中使用的各种线圈设计的剂量反应关系进行系统比较。
