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

Abstract

In this paper, we present a free and open source platform by using the equivalent-circuit finite-difference timedomain (FDTD) method adapted to cylindrical coordinates to efficiently model cylindrically shaped objects. We will address the special characteristics of a cylindrical FDTD mesh such as the mesh singularity at r D 0 and discuss how cylindrical subgrids for small radii can reduce the simulation time considerably. Furthermore, we will demonstrate the applicability and advantages of this cylindrical equivalent-circuit FDTD method to evaluate new types of conformal ring antennas used in the context of high-field (7T) traveling wave magnetic resonance imaging (MRI).:680-696 openEMS-A FREE AND OPEN SOURCE EC FDTD SIMULATION PLATFORM 681 It is worth noting that the EC FDTD formulation has clear benefits such as a reduced numerical effort inside the iteration loop because of a reduced number of multiplications (which is intrinsic to the representation with state variables such as voltages and currents) and the aforementioned intuitive incorporation of (highly) dispersive materials. For example, materials that are represented by multipolar Drude/Lorentz type models [7,8] can be easily implemented along corresponding extensions of the associated EC in the form of small tailored filter sections, which mimics the material dispersion underlying, for example, plasmonic structures [11,12], wide band-conducting sheet models [6], or even more challenging material properties such as biological tissue [13]. An additional virtue of the EC FDTD formulation is its affinity to an energy-based stability criterion [7,8] that tends to be less strict than the usually applied Courant-Friedrich-Levy (CFL) stability criterion. Interestingly, this alternative criterion is in principle also applicable to the conventional FDTD scheme offering thus a promise for potentially larger time steps.In the following, we will show that an adaption of our EC FDTD algorithm to a cylindrical mesh can be realized with only minimal changes to the EC FDTD operator coefficients allowing the use of a generic (and potentially highly optimized) EC FDTD iteration engine while enabling all well-known FDTD features (e.g., perfectly matched layer (PML) boundary conditions, Mur-absorbing boundary conditions, dispersive material models, and conducting sheet models) at virtually unaltered numerical efficiency. Please note that our cylindrical EC FDTD implementation is more general than the body of revolution version of FDTD provided, for example, by other FDTD simulation packages such as MEEP [14] because the body of revolution representation is restricted to rotationally symmetric problems, whereas our proposed method qualifies as a full vectorial three-dimensional (3D) EC FDTD scheme adapted to cylindrical r-coordinates,˛-coordinates, and´-coordinates.Cylindrical FDTD implementations-and in particular for magnetic resonance imaging (MRI) applications-have already been carried out, for example, by Trakic et al. [15] for the analysis of transient eddy currents ...

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