Akram Md Shahadat Hossain, Terada Yasuhiko, Keiichiro Ishi, Kose Katsumi
Institute of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki, Japan.
Institute of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki, Japan.
J Magn Reson. 2014 Aug;245:1-11. doi: 10.1016/j.jmr.2014.05.001. Epub 2014 May 21.
We performed a new coupled circuit numerical simulation of eddy currents in an open compact magnetic resonance imaging (MRI) system. Following the coupled circuit approach, the conducting structures were divided into subdomains along the length (or width) and the thickness, and by implementing coupled circuit concepts we have simulated transient responses of eddy currents for subdomains in different locations. We implemented the Eigen matrix technique to solve the network of coupled differential equations to speed up our simulation program. On the other hand, to compute the coupling relations between the biplanar gradient coil and any other conducting structure, we implemented the solid angle form of Ampere's law. We have also calculated the solid angle for three dimensions to compute inductive couplings in any subdomain of the conducting structures. Details of the temporal and spatial distribution of the eddy currents were then implemented in the secondary magnetic field calculation by the Biot-Savart law. In a desktop computer (Programming platform: Wolfram Mathematica 8.0®, Processor: Intel(R) Core(TM)2 Duo E7500 @ 2.93GHz; OS: Windows 7 Professional; Memory (RAM): 4.00GB), it took less than 3min to simulate the entire calculation of eddy currents and fields, and approximately 6min for X-gradient coil. The results are given in the time-space domain for both the direct and the cross-terms of the eddy current magnetic fields generated by the Z-gradient coil. We have also conducted free induction decay (FID) experiments of eddy fields using a nuclear magnetic resonance (NMR) probe to verify our simulation results. The simulation results were found to be in good agreement with the experimental results. In this study we have also conducted simulations for transient and spatial responses of secondary magnetic field induced by X-gradient coil. Our approach is fast and has much less computational complexity than the conventional electromagnetic numerical simulation methods.
我们对开放式紧凑型磁共振成像（MRI）系统中的涡电流进行了一种新的耦合电路数值模拟。按照耦合电路方法，将导电结构沿长度（或宽度）和厚度划分为子域，并通过应用耦合电路概念，我们模拟了不同位置子域中涡电流的瞬态响应。我们采用特征矩阵技术来求解耦合微分方程组网络，以加速我们的模拟程序。另一方面，为了计算双平面梯度线圈与任何其他导电结构之间的耦合关系，我们应用了安培定律的立体角形式。我们还计算了三维立体角，以计算导电结构任何子域中的感应耦合。然后，通过毕奥 - 萨伐尔定律在二次磁场计算中实现了涡电流时间和空间分布的细节。在一台台式计算机（编程平台：Wolfram Mathematica 8.0®，处理器：英特尔®酷睿™2双核E7500 @ 2.93GHz；操作系统：Windows 7专业版；内存（RAM）：4.00GB）上，模拟涡电流和磁场的整个计算耗时不到3分钟，对于X梯度线圈则约为6分钟。给出了Z梯度线圈产生的涡电流磁场的直接项和交叉项在时空域中的结果。我们还使用核磁共振（NMR）探头进行了涡场的自由感应衰减（FID）实验，以验证我们的模拟结果。发现模拟结果与实验结果吻合良好。在本研究中，我们还对X梯度线圈感应的二次磁场的瞬态和空间响应进行了模拟。我们的方法速度快，与传统电磁数值模拟方法相比计算复杂度低得多。
