PIERS ONLINE, VOL. 6, NO. 4, 2010
395
A Comparison of Ansoft HFSS and CST Microwave Studio
Simulation Software for Multi-channel Coil Design and SAR
Estimation at 7 T MRI
M. Kozlov and R. Turner
Max Planck Institute for Human Cognitive and Brain Sciences
Stephanstrasse 1A, D-04103, Leipzig, Germany
Abstract— We present a comparison of RF simulations with Ansoft HFSS and CST Microwave
studio software, for a commercially available 7 T multi-channel coil. We investigated the conditions influencing precision and simulation time. When simulation parameters (such as mesh size)
are appropriately selected and full coverage of the results is ensured, there is agreement between
simulated and experimentally determined S parameters, between simulated and actual capacitor
values, and between simulated and measured RF field. At this point, both simulation methods
then provide comparable results, to within 15%. In their current implementations, the Ansoft
HFSS frequency domain solver converges much faster than the CST time domain solver. HFSS
based RF circuit and 3-D EM fields co-simulation significantly speeds up MRI coil design, because the simulation time no longer depends strongly on simulated port numbers and the length
of the smallest mesh cell.
1. INTRODUCTION
Human magnetic resonance imaging (MRI) studies conducted at high magnetic fields (7 T and
above) operate in the regime where the wavelength of radio frequency (RF) fields inside an object
is less than the object dimensions. In this regime electrical (E) and magnetic (B1 ) components of
RF fields, as well as the specific absorption ratio (SAR) profiles in the object imaged (e.g., human
head or body) are highly complex and spatially non-uniform.
Reliable estimation of SAR values has become a very important concern since lack of full knowledge is the reason for the typically conservative vendor-provided RF power limits. It is impossible
to measure SAR in-vivo, but reliable SAR values can be easily obtained from E field data. Therefore numerical simulation is a very important component of MRI coil design/analysis and SAR
estimation.
Despite the current rapid development of novel 3-D EM tools, as well as the significant improvement of those already available, there is limited information regarding the suitability of the
commercially-available simulation tools for high-field MRI coil design and validation, and which
setup parameters are important for reliable simulation. Selection of the tools can be made on
the basis of simulation data uncertainties, simulation time, model design limitation, and hardware
requirements. Our goal was to compare simulation results obtained for a commercially-available
Rapid BioMed 7 T multi-channel coil using Ansoft HFSS frequency-domain and CST Microwave
Studio time-domain solvers with the results from actual measurement, and to investigate the conditions that influence the simulation time and the precision of simulated results.
2. METHOD
The realistic coil 3-D EM model includes all construction details for 8 resonance elements, modelled
with precise dimensions (inner Ø = 235 mm, outer Ø = 310 mm) and material electrical properties.
The scanner gradient shield was defined as a copper cylinder with Ø = 683 mm and 0.045 mm
thickness. A perfect absorbing boundary (PAB) was offset to 40 mm from gradient shield in X/Y
directions, the axial distance from coil to the PAB was more than 500 mm (λ/2 in air for 300 MHz).
We employed co-simulation of the RF circuit and 3-D EM fields [1]. For each coil element, the RF
feed network and trim capacitor, which is on the opposite side to the element’s feed point, were
substituted with 50 Ohm ports. This gave a total number of ports as high as 16. For tuning the coil
for each simulation setup, the vendor-provided procedure was used — a Siemens 7 liter water-based
phantom was placed inside the coil. As a result one 3-D EM simulation of the given setup was
enough to tune/match the coil. The simulation values obtained for tune/match capacitors were
compared with the actual values.
PIERS ONLINE, VOL. 6, NO. 4, 2010
Figure 1: Simulation setup.
396
Figure 2: Lumped element mesh. Left: wrong mesh, right: correct
mesh.
Because this coil cannot be re-tuned once installed in the MRI scanner, we kept variable capacitor
values and mesh definition fixed for each simulation setup when conducting an investigation of
SAR. In this case, changing the simulation object from the phantom to a head model corresponds
to experimental substitution of the phantom by an in-vivo subject inside the tuned and matched
MRI coil. SAR was evaluated using an in-vivo load consisting of the head and part of the shoulders
of the Ansoft surface-based human body model (Fig. 1), with different spatial scaling factors.
Since the SAR calculation procedure incorporated within CST is very slow (up to 10 hours for
50 million mesh cells) and HFSS does not include IEC-recommended SAR evaluation, we generally
used a home-built fast and reliable SAR calculation procedure, versatile with regard to both 3-D
EM solver strategies, and adapted to multi-core processing [2]. We found negligible difference in
the SAR data evaluated by CST procedure and this in-house method.
3. RESULTS AND DISCUSSION
HFSS offers a reliable mesh adaptation algorithm and several simulation coverage criteria, sufficient
to obtain reliable data in one simulation run. Correct trim capacitor estimation was obtained in an
HFSS simulation, in which initial manual mesh seeding was provided to get at least 3 tetrahedra
within each current-conducting element cross section. The S-parameter coverage criteria were
defined to be better than 0.0025. The project mesh reached ∼2.4 million tetrahedra after 5 mesh
adaptation steps.
CST also includes several coverage criteria but its suitable for multi-channel MRI coil simulation
mesh adaptation procedure is based on increasing the “Lines per wavelength” and “Lower mesh
limit” settings. This refinement over the entire model volume is a less robust approach, compared
with HFSS mesh refinement, which is performed mostly in the volumes containing maximum field
values. For complex MRI coil simulations, CST coverage criteria are used rather seldom, due to the
extremely long computational times. In addition, mesh refinement for a given wavelength makes it
impossible to keep the same mesh of coil elements for phantom and human model simulations. As
it will be shown below the latter is important for reliable SAR prediction.
For CST simulations, mesh definition has a significant influence on representation of areas that
include ports and lumped elements. In the simulated coil, ports and lumped elements are not aligned
parallel to a coordinate axis. In these areas the mesh step was decreased until the relevant mesh
vertexes were accurately positioned as start and end points for integration across ports or lumped
elements (Fig. 2). If too coarse a mesh is used, integration defining a significant dependence of port
impedance and lumped element properties may erroneously include conductor material. This may
result in overestimation or underestimation of SAR by up to 30%.
Keeping correct port and lumped element mesh definition (mesh step size as small as 0.25 mm)
the coil element mesh size was manually decreased, step by step, until the difference between experimental and simulated trim capacitor values vanished (Table 1). Because the current distribution
is maximal on the conductor edges, a relatively small hexahedral mesh step must be used for the
reliable representation of radiative coil elements when these are not aligned parallel to a coordinate axis. This result underlines the importance of keeping the same coil element mesh definition
between phantom and human model simulations.
For CST simulation, increasing the number of mesh cells resulted in nearly the same shape of
B1 + profile within a phantom (Fig. 3), but approximately a 75% variation of peak SAR value
PIERS ONLINE, VOL. 6, NO. 4, 2010
397
for some head models (Table 1). SAR was found to be coupled to two different E field sources
(conservative and non-conservative). The first is the penetration of the E field from the distributed
capacitors commonly used in high field MRI coils, the second is the E field that accompanies the
propagating magnetic field. When the conservative E field has significant influence, care must be
taken to ensure that the mesh definition is smaller than 1.25 mm, whenever a part of the human
body model is close to a capacitor (Fig. 4).
For the mainly non-conservative E field within the body, changes of the SAR value for the coil
investigated are less than +/ − 10%, once the mesh cell size is less than 2 mm isotropic for coil
elements.
There is less than 15% difference between field and SAR (point to point data comparison) for
HFSS and CST simulations, once simulation setup and parameters are correctly chosen. For CST
this means that the steady state monitor must be set below −60 dB, in addition to the precautions
Table 1: CST and HFSS simulation data.
Coil element mesh, isotropic [mm]
Tune capacitor value [pF]
SAR for Head model
SAR for Head 0.8 scaled model
2.25
29.8
2.00
1.73
2
24.9
1.87
1.64
CST
1.5 1.25
17.1 16.1
1.43 1.38
1.68 1.71
1
12.8
1.30
1.74
0.8
11.3
1.28
1.70
HFSS
variable
11.2
1.21
1.76
Figure 3: Transversal B1 + maps for Siemens phantom. Left: CST coil mesh 2.25 mm, center: CST coil
mesh 1 mm, right: HFSS.
Figure 4: Head with scaling 1. Left: CST SAR for coil mesh 2.25 mm, center: CST SAR for coil mesh
0.8 mm, right: HFSS SAR data.
PIERS ONLINE, VOL. 6, NO. 4, 2010
398
discussed above that ensure full coverage and agreement between simulated and actual capacitor
values. This monitor guides CST solver accuracy during time domain simulation by comparing
the total energy at each time point within the volume of interest relative to the peak value of
this total energy. The simulation terminates when the defined level is reached. The lower this
level, the more accurate are both the S parameters and the field simulation data obtained by
the Fourier transformation of the time domain values. The simulations of the coil investigated
required several months and about 16 GB RAM memory for CST, and two days and 62 GB RAM
memory for HFSS projects running on the same computer, without simulation parallelization and
hardware acceleration. The memory size disadvantage for HFSS is not severely problematic today,
with commercially available 64 GB memory workstations. The computational time disadvantage
for CST is a consequence of the inverse proportionality of the simulation time to the length of the
smallest mesh cell, which has to be quite small for reliable simulation of a complex MRI coil. In
addition, if the computation is performed in CST, each port is simulated independently. This means
that the simulation time for the entire project is linearly proportional to the number of ports, and
simulation of 8-channel coil with 16 ports, could take several weeks, despite use of several computers
for port simulation parallelization.
Usage of the RF circuit and 3-D EM co-simulation approach is not a reason for the extremely
long CST simulation time (Table 2). In opposite, if the approach is used simulation time is the
shortest for coils, which effective coil-loss resistance (RΣ ) is less than 6.25 Ohm. RΣ is calculated
from the power absorbed by coil and the sum of each element’s feed current. RΣ = 0.52 Ohm for
the coil investigated.
Figure 5: Head with scaling 0.8. Left: CST SAR for coil mesh 1 mm, right: HFSS SAR data.
Table 2: Comparison of CST FDTD simulation time for an 8 channel coil with given coil quality factor Q.
Number of excitations
Simulation time of single
excitation in proportion to
Total simulation time
in proportion to
Simultaneous port
excitation of
tuned/matched coil
1
Individual ports
excitation of
tuned/matched coil
8
Q
Q
Q
8×Q
RF circuit
3-D EM
co-simulation
16
RΣ
Q×
2 × Rport
Q×
16 × RΣ
2 × Rport
PIERS ONLINE, VOL. 6, NO. 4, 2010
399
4. CONCLUSION
When simulation parameters (such as mesh size and coverage criteria) are appropriately selected,
there is agreement between simulated and experimentally determined S parameters, and also between simulated and actual capacitor values. At this point, RF field simulations and measurements
also agree and both simulation methods then provide comparable results. In their current implementations, the Ansoft HFSS frequency domain solver converges much faster than the CST time
domain solver. HFSS based RF circuit and 3-D EM fields co-simulation significantly speeds up MRI
coil design, because the simulation time no longer depends strongly on simulated port numbers and
the length of the smallest mesh cell. To obtain reliable CST data, the CST solver accuracy requires
a steady state monitor setting that is better than −60 dB, and the mesh size must be manually
decreased step-by-step to ensure full coverage of the results. Furthermore, simulation must be
performed using a realistic head model, together with the same mesh definition and tune/match
network as used for simulation with a phantom corresponding to the standard product tuning procedure. For the reliable simulation of distributed capacitance, the CST mesh has to be smaller
than the thinnest dielectric elements of the coil. This is more important for coil tuning (e.g., trim
capacitor) estimation than for SAR.
REFERENCES
1. Kozlov, M. and R. Turner, “Fast MRI coil analysis based on 3-D electromagnetic and RF
circuit co-simulation,” Journal of Magnetic Resonance, Vol. 200 147–152, 2009.
2. Kozlov, M. and R. Turner, “Optimization of SAR calculation for 3-D EM time and frequency
domain data,” Proceedings of International Society for Magnetic Resonance in Medicine, 4779,
Honolulu, USA, April 2009.