Radiofrequency (RF) modelling offers an efficient means to characterize the design and performance of RF coils. Simulations are particularly important for establishing MRI scan parameters to ensure safety compliance. This talk provides an overview of several numerical methods that may be employed to model the electrodynamics of RF coils; emphasis is placed on the finite-difference time-domain (FDTD) method and considerations for achieving accurate simulation and validation.
Electromagnetic (EM) modelling of RF coils has long been employed by MRI researchers to simulate B1 and E fields, gain insight into field behavior within the body, and evaluate potential interactions with medical implants. The simulation of RF transmit coils and arrays has become particularly important for establishing operational parameters to ensure MRI safety. IEC 60601-2-33 and FDA guidelines on maximum power deposition, quantified as specific absorption rate (SAR, with units W/kg), provide the basis for calculating safety limits, e.g., maximum input power to each RF coil.
Historically, several numerical techniques have been employed effectively to model RF fields; these techniques include closed-form analytical formulations, the method of moments (MoM), the finite element method (FEM), finite-difference time-domain (FDTD), and hybrid combinations thereof. Among the MRI research community, FDTD is often preferred owing to its straightforward full-wave approach to solving Maxwell’s equations, its scalability to large problem sizes, the availability of commercial software solvers, and the ease of subsequently calculating SAR within heterogeneous body models. Moreover, sustained advances in GPU hardware capabilities have had a profound effect on FDTD’s practicability, as parallel computing implementations of FDTD can now simulate large volumes with fine spatial resolution in a matter of minutes. As such, many of the historical limitations and disadvantages of FDTD, e.g., lengthy simulation time and unsuitability to model fine or curved features, are now readily alleviated.
Human body voxel models incorporating detailed anatomical features are essential tools for the computational evaluation of EM fields within the body. Fortunately, numerous adult and youth body models are now available to the research community. The assignment of frequency-dependent dielectric properties to various tissue types has implications on resulting E fields and SAR, given surface eddy currents (arising from σ) and displacement currents (arising from ε). The FDTD method facilitates subsequent calculation of raw SAR throughout heterogeneous tissue regions.
The simplicity of the FDTD method can be misleading to the novice user; commercial software packages may be misconstrued as turnkey solutions, and inaccurate results can easily be generated if fundamental model setup conditions are overlooked. Many features of an RF coil model should be carefully examined within the FDTD mesh, particularly the grid symmetry and alignment with conductor edges; also, conductor meshing on cell surfaces should not impose inaccurate skin depth limitations. Consideration should be given to the type of excitation feed and its source impedance, and the representation of impedance matching circuitry may have significant consequences. For example, the match capacitor may produce a sizable E field, so placing it across the coil feed is inappropriate if it is actually remotely mounted on a mechanical former. Lumped element components, their tolerances, and losses, e.g., capacitor equivalent series resistance and solder resistivity, should also be considered. The inclusion of a separate, albeit detuned, receive array coil has been shown to alter simulated fields. Grid resolution plays an important role in accurately representing fine features and curved conductors. Notably, specifying an accurate condition for the FDTD simulation to terminate, i.e., the convergence criteria, is vital to generating reasonable results. Finally, the stability of an FDTD model may be evaluated by simulating one case with excessively conservative model parameters: grid resolution (e.g., 0.5 mm), termination criteria (< -50 dB), free-space padding cells (> λ/4), etc. One simulation run over a long weekend or holiday can facilitate the establishment of less conservative model parameters while maintaining confidence in subsequent results.
Modelling results must be validated. First, plots of results should be viewed, in both the time and frequency domains, if available. Oscillating frequency-domain curves are an indicator of early termination. Second, the model can be validated against other code; e.g., FDTD results of a coil with a uniform phantom can be compared to results using a high-confidence MoM implementation or analytical formulation. Third, the modelling results should be validated by bench or scan data. B1 fields can be validated against probe measurements or B1 maps. Coupling between coil elements can be compared to S or Z parameter measurements or noise correlation matrices. Coil circuit properties can be referenced against bench measurements of input impedance and Q-factor. For all validation methods suggested above, a simulation case with a uniform phantom may simplify these comparisons.
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