Magnetic resonance imaging (MRI) is an indispensable tool in medical applications [1] and will continue to thrive with the development of ultra-high field (UHF) systems [2]. In the UHF MRI apparatus, the static magnetic field B0 is larger or equal to 7 T [1,3], corresponding to an operating frequency of at least 300 MHz or above [1,3]. This will bring radio frequency (RF) problems such as severe wave behaviors and high specific absorption rates (SAR) [[3], [4], [5]]. The wave behavior will distort the B1+ field distribution and cause undesirable imaging results. High SAR is hazardous for the patient and will cause overheating problems in the human tissue [[3], [4], [5]].

The analysis and design of RF coil at UHF usually need numerical methods such as finite-difference time-domain (FDTD) [[6], [7], [8], [9]], finite element method (FEM) [9,10] and method of moments (MoM) [9,11,12]. FDTD suits solving problems involving heterogeneous imaging loads such as human tissue, but it may encounter difficulty when modelling RF coil [9,13]. This is because the grid used in FDTD is usually cubic mesh, which can bring stair-casing errors when modelling RF coils with curved structures [13]. The FEM is a popular method widely used in electromagnetic (EM) applications, but it can be problematic when dealing with radio-frequency field interactions with human tissues [13]. MoM, being an integral method, can solve RF coil current distribution with high accuracy and efficiency. However, it is unsuitable for calculating EM fields in human tissue. Because when solving such problems, a dense matrix function is needed to be solved, and this can downgrade the calculation speed and accuracy [9,13]. To leverage the strengths of each technique, hybrid methods have been developed for MRI RF coil design applications. Hybrid FDTD/MoM is one of the hybrid methods, where the MoM is used for calculating RF coil current distribution, and FDTD is employed to solve the EM field of the imaging load [[13], [14], [15], [16]]. This numerical technique has been improved in the past few years [4,[13], [14], [15], [16]]. However, full 3D FDTD modelling is still computationally expensive and may not always be necessary for certain applications, and a 2D slice in the FDTD space could suffice for modelling some types of EM problems. In this work, we propose to combine the 2D-FDTD method with the 3D-MoM method, using Huygens' equivalent surface to connect the two methods. The hybrid 2D-FDTD/3D-MoM method can realize faster calculations than the 3D hybrid FDTD/MoM method while maintaining the high accuracy of RF coil modelling. In the hybrid 2D-FDTD/3D-MoM method, the number of grids in the FDTD zone is decreased, thus enabling accurate EM calculations in a shortened time frame. This new development represents a promising EM solution for RF coil design and analysis at UHF MRI systems.

The paper is organized as follows: in section two, the hybrid 2D-FDTD/3D-MoM method is described in detail, and an ellipse RF coil is modelling to testify to the correctness of the method; the results are compared to the 3D hybrid FDTD/MoM method. Then in section three, the proposed method is used to analyze the RF coil with a multilayer dielectric pad (DP), and the magnetic field is calculated for three types of DPs. In section four, a human head slice phantom is used for the analysis of the RF coil, and the magnetic field with DP and without DP cases are compared.