Synopsis
Appropriate
high-permittivity, low-conductivity materials placed between the RF coil and
the sample can provide performance improvement in both transmission and
reception. We employed a simulation framework based on dyadic Green’s functions
for multi-layered spherical geometries to analyze how HPMs affect the tradeoff
between excitation homogeneity and global Specific Absorption Rate (SAR) for RF
shimming at 7T using an L-curves analysis. Three target excitation profiles
were analyzed, with uniform amplitude and varied phase, to determine the
influence that target phase distribution has on the optimal relative
permittivity results.Purpose
Placing high
permittivity, low conductivity materials (HPM) between the radiofrequency (RF) coil
and the sample has been proposed as a method for reshaping B
1+
fields, independent of RF shimming or parallel transmission
1,2,3. HPMs have also been shown to improve both receive sensitivity
2,4 and
transmit efficiency
2,5,6 of RF coils. L-curves analysis has been employed
to optimize the relative permittivity of an encircling layer of HPM surrounding
the imaging sample
7. Specifically, the optimal tradeoff between
global SAR and profile fidelity was investigated for different HPMs using Ultimate
Intrinsic SAR (UISAR) as a performance reference for a SAR-minimizing RF
shimming algorithm
8. However, the algorithm constrains the target
excitation profile to have flat amplitude and phase throughout the excitation
plane, whereas phase-relaxed RF shimming approaches are much more common, and can
allow for larger SAR reduction. Relaxing the phase constraint in the algorithm
would make SAR minimization a non-convex optimization. Therefore, to investigate
the effects that the phase of the target excitation profile has on the optimal
relative permittivity of the HPM, we generated L-curves for realistic phase
distributions.
Methods
Simulations for a closely-packed
48-coil array geometry
9 were performed with a full-wave simulation tool
based on dyadic Green’s functions
10. The array elements were placed
at a 1 cm distance from a uniform spherical phantom (radius
sphere =
8.4cm) (
Figure 1) with electrical
properties of average brain tissue
11 (ε
R = 63, σ =
0.46S/m) at 7 Tesla. The space between the coil and the phantom was filled with
HPM, for which conductivity was kept to zero and relative permittivity was
varied between 1 and 300. UISAR and global SAR of the array were calculated for
three target excitation profiles with uniform amplitude and: flat phase,
Gaussian phase, and a CP-like phase (
Figure
2). The Gaussian phase distribution was chosen to match a low-field phase
profile, while the CP-like phase distribution was chosen to match
phase-unconstrained excitation profiles
12. All excitations were for a
transverse plane through the center of the sphere. The SAR of the array was normalized
by the UISAR and plotted as a function of the root mean square error (RMSE) of
the achieved excitation profile for various degrees of regularization (i.e.,
L-curve plots). For each case, the optimal relative permittivity for the HPM
layer was chosen based on the proximity of the corresponding L-curve to the
origin, and results were compared to the case without HPM.
Results
UISAR for a near perfect excitation (RMSE < .001)
was constant for the three phase profiles. UISAR values varied for different
phase profiles only for large RMSE (
Figure
3). The phase distribution of the target excitation profile did not affect
the optimal relative permittivity for the HPM layer, which was ε
R =
100 for the cases of Gaussian, CP-like, and flat phase (
Figure 4). L-curves for optimal HPM show similar performance
benefits when compared to the case without HPM for all three phase
distributions (
Figure 5).
Discussion and Conclusions
Similar coil performance was found for the realistic
profile phase distributions and the original flat-phase excitation. Some
performance benefit was seen under a case of poor excitation uniformity for the
Gaussian phase distribution, similar to what may be expected at lower field
strength. However, performance loss was seen under the same conditions for the
CP-like phase distribution, which may be explained by a misalignment of the
CP-like phase profile with the coil geometry. This and previous work
7
suggest that, for a given field strength, the optimal relative permittivity depends
mainly on the array geometry. However, since previous work has shown that lower
global SAR can be achieved by relaxing the phase constraint
13,
another explanation could be that the spatial distribution of the phase in a
target excitation profile has a smaller effect on coil performance than the constraint
of the phase in the RF shimming algorithm. In all cases the target profile
amplitude was uniform to investigate the effect of the phases. Future work will
include combining realistic phase with smoother distributions of the profile
amplitude, which are known to improve coil performance
8, and could
result in different optimal HPM properties. In addition, to confirm that the
choice of the target profile has a minor effect, phase-unconstrained RF
shimming optimization will be explored in future work.
Acknowledgements
The Center for Advanced Imaging Innovation and Research (CAI2R, www.cai2r.net) at New York University School of Medicine is supported by NIH/NIBIB grant number P41 EB017183.References
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