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FAST MRI IMPLANT SIMULATION USING FDTD AND HUYGENS EXCITATION

I. Introduction

Currently, one of the most challenging problems in medical device simulation is the research and design of active medical implants which do cause heating when exposed to the RF fields of an MRI scanner. Both patients and industry would largely benefit from MRI safe implants. But simulation of a complex implant, embedded in an inhomogeneous body and surrounded by a large electrical resonator, with micrometer resolution is a challenging task.

Many different numerical approaches have been developed to solve Maxwell's equations, each having its own advantages and limitations. For example, Method of Moments (MoM) is fast and accurate for solving metallic structures and electrically large problems. While the Finite Difference Time Domain (FDTD) method is well suited to solving inhomogeneous structures (dielectric and metal), partially due to its straightforward approach. Current trends in GPU based hardware acceleration solutions [1] offering up to 100x faster simulation in desktop form-factors, are still mostly restricted to FDTD solvers. For these reasons, the FDTD method is often chosen as the preferred method for many RF simulations of medical applications where transmitters and patient must be considered. These range from Magnetic Resonance Imaging (MRI) systems to implanted devices with active telemetry like pacemakers. Here FDTD is used to study a number of issues including coil design and field homogeneity, SAR, EMC, worker safety, etc

II. Time Stepping in FDTD

Although FDTD is generally very robust at solving this kind of problem, it is not without its own limitations. One limitation arises because the method is conditionally stable. To guarantee stability the time step used in the simulation must be chosen based on the mesh size used in the FDTD grid. If non-uniform meshing is supported, the time step is chosen based on the minimum mesh size in the grid.

From a practical point of view, this implies that resolving electrically small detail in the structure can have a compound effect on the simulation time. Firstly, refining the mesh increases the overall mesh size Secondly, by decreasing the minimum mesh size, the time step must also be decreased. Since the FDTD simulation time is more-or-less proportional to mesh size and the number of time steps, both effects increases the overall simulation time.

III. Method

SEMCAD X [2], a state-of-the-art commercial simulation platform, offers high performance EM and Thermal FDTD solvers, finite element (FEM) based low frequency static solvers, interface to hardware acceleration provided by Acceleware [1]. Furthermore, a Huygens box [3] excitation is available for the EM FDTD solver, which is proposed to overcome the limitations highlighted in the previous section. The Huygens box is a generalized Total-Field Scattered-Field (TFSF) plane wave excitation. Instead of defining a plane wave incident field, the field distribution from a previous simulation can be used to excite the Huygens box. Unidirectional subgridding is applied under the assumption that the scattered field does not significantly interfere with the source.

Practically speaking, this approach breaks down the simulation into two stages:

1. Primary simulation of incident field: a simulation of source region to determine the incident field distribution on the Huygens box region. Typically characterized by coarse mesh and a large time step and therefore short simulations times.
2. Secondary simulation of Huygens box region: unidirectional subgrid of Huygens box with incident field as the excitation. Typically characterized by fine mesh resolution and small time step, but small overall mesh size result in average simulation times.

The advantage of this approach is two fold. Firstly, the limitation of a very long FDTD simulation with many time steps is overcome by running a faster, coarser simulation followed by a smaller, finer simulation. The immediate benefit being tremendous saving in computation time and memory consumption compared to overall simulation. Secondly, it is actually not necessary to run the simulation of the incident field using FDTD; any method that is able to calculate the field distribution on the Huygens box can be used. The Huygens box can therefore act as a hybridization platform linking other methods (e.g. MoM, FEM, etc.) to FDTD. This implies the additional benefit of being able to apply different methods to solve the parts of the simulations that they are able to address most effectively.

IV. Case Study: Generic Implant with Lead Pass in MRI System

SEMCAD X is used in this case study to highlight the benefit of applying the Huygens box approach to simulate an RF MRI birdcage including a patient with generic implant and lead pass (Figure 2).

Model
The simulations in this study are based on a CAD model of an experimental 1.5 Tesla birdcage developed by Zurich MedTech. The .IGES CAD data has been imported directly into SEMCAD X, where a leg feed excitation is achieved by introducing edge sources at the center of each rung. Matching components are introduced in the rings between the rungs. A high resolution adult male phantom [4] is positioned in the birdcage. A generic pacemaker implant with lead pass is included. The leads are modeled as PEC cylinders covered with dielectric insulation, the tips of the leads are exposed.

Simulation
The goal of the simulation is to study the localized SAR in the vicinity of lead tips. The operational frequency of the birdcage is 64 MHz. In order to resolve the high field gradients at the tips of the leads a very high grid resolution must be used across the diameter (minimum mesh step of 0.3 mm). The resulting FDTD time step is extremely small and causes very long simulation times even when hardware acceleration is used.

Results and Computational Requirements
Figure 3 shows the results from the Huygens box simulation: SAR distribution around the lead tips. The simulation also shows that the implanted device can result in much higher peak and averaged SAR when compared to the simulation without the implant. This effect can be explained by the induced surface currents that flow on the metallic parts of the implant. Furthermore, very good agreement between the high resolution FDTD simulation and the Huygens box simulation highlights the accuracy of this approach.

Table 1: Computational requirements (all simulations are run on a CIB1500 hardware acceleration system)

Table 1 shows the substantial benefit in computational requirements that the Huygens box offers with respect to both RAM memory and overall simulation time: a factor of almost five times reduction in simulation time is achieved and almost five times less RAM is needed. In some cases the benefit may be much more.

V. Conclusions

SEMCAD X is a powerful platform, which can accurately and efficiently simulate highly complex medical system while resolving micrometer range detail. When used together with the latest in hardware acceleration solutions, very large simulation can be reduced from weeks to a single day. The simulation time can be further reduced to several hours by utilizing the Huygens box source as presented in this case study.

VI. References

[1] www.acceleware.com
[2] www.semcad.com
[3] A. Taflove, S. Hagness; “Computational Electrodynamics: The Finite Difference Time Domain Method “, 3rd edition, pg 186-212
[4] www.itis.ethz.ch/index/index_humanmodels.html