Magnetic resonance electrical impedance tomography (MREIT) and current density imaging (MRCDI) are emerging as new methods to non-invasively assess the electric conductivity of and current density distributions within biological tissue in vivo. The accurate and fast computation of magnetic fields caused by low frequency electrical currents is a central component of the development, evaluation and application of reconstruction methods that underlie the estimations of the conductivity and current density, respectively, from the measured MR data. However, methods for performing these computations have not been well established in the literature. In the current work, we describe a fast and efficient technique to evaluate the Biot-Savart integral based on the fast Fourier transform (FFT), and evaluate its convergence. We show that the method can calculate magnetic fields in realistic human head models in one minute on a standard computer, while keeping error below 2%.

磁共振电阻抗断层扫描（MREIT）和电流密度成像（MRCDI）新兴成为无创地评估体内生物组织内的电导率和电流密度分布的新方法。由低频电流引起的磁场的准确而快速的计算是重建方法的开发，评估和应用的重要组成部分，这些重建方法分别是根据测得的MR数据估算电导率和电流密度的基础。然而，在文献中尚未很好地建立用于执行这些计算的方法。在当前的工作中，我们描述了一种基于快速傅立叶变换（FFT）评估Biot-Savart积分的快速有效技术，并评估其收敛性。