An Improved Cylindrical FDTD Algorithm and Its Application to Field-Tissue Interaction Study in MRI

Abstract

This paper presents a three-dimensional finite-difference time-domain (FDTD) scheme in cylindrical coordinates with an improved algorithm for accommodating the numerical singularity associated with the polar axis. The regularization of this singularity problem is realized based on Faraday's law (for updating the -component) and Ampere's law (for updating the -, -components). The proposed algorithm has been detailed and verified against a problem with a known solution obtained from a commercial electromagnetic simulation package. The numerical scheme is also illustrated by modeling high-frequency RF field-human body interactions in magnetic resonance imaging (MRI). The results demonstrate the accuracy and capability of the proposed algorithm.

openEMS – a free and open source equivalent‐circuit (EC) FDTD simulation platform supporting cylindrical coordinates suitable for the analysis of traveling wave MRI applications

“…Comparing the EC FDTD update equations for the Cartesian mesh in equations (11) and (13) to the cylindrical mesh update equations (14) and (16) reveals the identical formulation for the update coefficients. The only difference between the Cartesian and cylindrical formulation emerges in the calculation of the surface areas A d , Q A d (with d 2 r;˛; z) and edge lengths d , Q d needed to evaluate the EC FDTD quantities C d , G d , L d , and R d .…”

“… for the analysis of transient eddy currents stemming from switching magnetic field gradients as well as by Chi et al . for the comprehensive analysis of radio‐frequency (RF) field‐tissue interactions. In addition, Wang et al .…”

“… proposed a parallelization scheme for an earlier FDTD version supporting both Cartesian and cylindrical meshes, which relies on a distributed memory architecture while adapting the message‐passing interface (MPI) library. Chi et al was also offering a numerical regularization scheme for handling the polar‐axis singularity apparent in the cylindrical implementation, using Ampère's and Faraday's laws as an indirect access to the field quantities in the singularity. Alternative measures based on corresponding coordinate transformations are proposed by Kancleris .…”

“…Alternative measures based on corresponding coordinate transformations are proposed by Kancleris . The authors also speculates about the need for subgridding that may possibly become an issue to be considered because of the costly mesh refinement inherent to the morphology of the cylindrical discretization. In our paper, we will demonstrate that subgridding is less an option than an inevitable feature to be included in any cylindrical FDTD implementation because of the severe constraints posed by the CFL limit (or a similar energy‐based criterion ).…”

Electromagnetic Field and Radio Frequency Circuit Co-Simulation for Magnetic Resonance Imaging Dual-Tuned Radio Frequency Coils

“…The conventional EM numerical analysis method is primarily based on the finite element method and finite-difference time-domain algorithms [7]–[9]. In these approaches, the coil structure with tuning and matching circuits are built directly into the model.…”