Magnetic resonance imaging (MRI) is a widely used technology for internal human structure studies and diagnosing diseases [1]. MRI is known for nonionizing radiation, multi-parameter imaging, and unparalleled signal-to-noise ratio (SNR) in soft tissue applications [2,3]. Ultra-high field (UHF) MRI unitizes a more powerful static magnetic field (B0 field) ≥ 7 Tesla, which can enable higher imaging resolution for better disease inspection [2]. With the development of superconductor technologies, UHF MRI has become more accessible and feasible [[4], [5], [6], [7]]. However, a high magnetic field brings problems of high specific absorption rate (SAR) and non-uniform B1 field, thus impairing the image quality [8,9]. Improving the radio frequency (RF) coil designs is one of the technical solutions to enhance UHF MRI applications.

The RF coils in UHF MRI usually work at high frequencies (300 MHz and above), causing a serious wavelength effect [8,9]. Several numerical methods, such as finite-difference time-domain (FDTD) [10], method of moments (MoM) [11], and finite element method (FEM) [12], have been used to design appropriate RF coils for high-frequency applications. Furthermore, combining two of these three methods can create a powerful EM tool that can solve high-frequency problems more efficiently and accurately [13]. The hybrid FDTD/MoM method usually interfaces by a Huygens' equivalent surface (HES), which adopts the advantages of FDTD in modeling complex electromagnetic parameters of human tissue and MoM in accurately calculating curved antenna structures, has been previously developed by researchers [[14], [15], [16]]. This hybrid method has been used in modeling MRI RF coils and has applications in other areas, such as modeling vehicle antennas, ground penetration radar, and mobile phone antennas [[17], [18], [19]]. Usually, the HES is a rectangular box that separates the biological tissue and metal antenna [[14], [15], [16]]. In some cases, such as coil-imaged subject being too close to each other, the shape-fixed HES may be unsuitable to accommodate the geometric structures and meet numerical instabilities and thus incapable of providing accurate modeling results for heavily loaded coils.

In this paper, we propose a conformal HES for implementing the FDTD/MoM method for RF modeling at UHF MRI. In the following sections, the concept of construction of conformal HES is described, then introduce two kinds of conformal HES models: a 2-dimensional (2D) and a 3-dimensional (3D) conformal HES model; they are suitable for the analysis of different RF coils. The hybrid FDTD/MoM method is numerically verified against an FDTD-only algorithm, and the normal (non-conformal) HES are compared with the conformal HES calculations.