Mihir Pendse^{1} and Brian K Rutt^{1}

^{1}Stanford University, Stanford, CA, United States

### Synopsis

We analyze the performance of the IMPULSE pTx optimization
algorithm, which allows SAR-aware pulse design without virtual observation
points (VOP) compression. We compare performance of IMPULSE with conventional optimization methods using VOPs and compare
different values of the overestimation parameter. We show that IMPULSE results in elimination of the time-intensive compression step without significantly increasing the time for real-time optimization. Additionally by eliminating the overestimation error from the VOP compression, IMPULSE is able to achieve better mitigation of local SAR hotspots after optimization than VOP-based methods.

### Introduction

Controlling
local SAR in parallel transmission (pTx) is an important safety concern. When designing pTx pulses to counteract B1+
inhomogeneity, local SAR must be
incorporated into the optimization to limit the generation of hotspots. The pulse design must also be done rapidly while the patient is on
the table, using B1+ maps measured from the patient. Since local SAR must be
evaluated over the entire patient volume, in the form of SAR matrices at each
of possibly more than 100000 voxels, incorporating SAR into the pTx
pulse optimization can result in impractically long optimization times. For
this reason, the Virtual Observation Points (VOP) [1] concept was developed as
a way of compressing the large number of SAR matrices into a smaller set of VOP
matrices, and thereby speeding up the pulse optimization step. The first
drawback of this approach is that the VOP compression step itself is computationally
demanding, requiring several minutes of computation time, and therefore must be
done prior to the patient scan; this is typically accomplished by calculating
SAR matrices using electromagnetic simulation software and a realistic body
model, followed by VOP compression. In addition to requiring substantial
computation time, making “on-the-table” patient-specific SAR-aware pTx
impractical to date, the use of VOPs introduces an error into the SAR
estimation which can result in a suboptimal pTx pulse. Here we show the quantitative
benefits of the IMPULSE pTx optimization algorithm [2] which operates on
uncompressed SAR matrices, thereby not requiring VOPs . We demonstrate that IMPULSE
enables pTx optimization on patient-specific
uncompressed SAR estimates and achieves better elimination of SAR hotspots.### Methods

IMPULSE
finds the pTx channel weightings and spokes locations that minimize SAR subject
to a specified tolerance on flip angle inhomogeneity (FAI) [1]. Here, we
compared this highly efficient SAR-aware pTx optimization algorithm against a
conventional VOP-based algorithm [3]. A key feature of IMPULSE is that it
scales favorably with number of SAR matrices and therefore enables optimization
without the VOP compression step. Two sets of VOP matrices were generated, with overestimation parameter values of 0.025 and 0.15,
respectively. The benefits
of IMPULSE over the VOP-based designs were assessed based on both computation
time and resulting SAR performance. B1+ and electric field distributions were generated
using Sim4Life FDTD simulation package (Zurich
MedTech AG, Zurich) employing the Duke body model from the Virtual Family (IT’IS Foundation, Zurich) and an 8
channel coil model. Pulses were designed to excite an axial slice, and L-curves
of SAR vs FAI were generated for each method using
MATLAB (MathWorks, Natick, MA) by varying the FAI tolerance.### Results

Figure 1 shows the L-curves for the two
algorithms, with two overestimation parameters for the VOP-based algorithm, demonstrating
that there is a SAR penalty associated with the use of VOPs. With a strict overestimation parameter (0.025), there is a penalty of approximately 6% compared to using uncompressed
matrices. Although this SAR penalty is small, the computation
time for VOP compression is significant in this case (620 s). For more relaxed overestimation parameter (0.15) , the compression time is decreased
to 40s, making on-the-table patient-specific pTx pulse design feasible;
however, the SAR penalty compared to IMPULSE increases to approximately 27%. Figure
2 shows representative SAR maps (maximum intensity projection through the whole
head/neck), which indicate that a significantly increased hotspot results with this relaxed parameter. The table in Figure 2
shows that IMPULSE achieves the fastest total computation time while achieving
the lowest peak local SAR.### Discussion

IMPULSE has a clear advantage over the
use of VOP-based methods in terms of both total computation time and the SAR
performance of the optimized pulse. For VOP-based methods, there is a tradeoff
that can be controlled with the overestimation parameter. Low values improve SAR performance at the expense
of longer compression time whereas high values allow for rapid compression but
with poorer SAR performance; however, in both cases performance is worse than
using IMPULSE. Additonally, IMPULSE enables
patient-specific SAR estimation, which ultimately will be more accurate than
using body models with pre-computed E-fields and VOPs. There are several
possible methods to generate the necessary tissue electrical properties for the
patient on the table. With modern-day GPU parallelization of the
electromagnetic simulation step, it is conceivable that the total time needed
for tissue model generation, EM field simulation, and pTx pulse design could be
reduced to a few seconds, i.e. fast enough to enable SAR-aware pTx
while the patient is in the scanner. The elimination of the time-consuming VOP
step using IMPULSE makes “real-time” patient-specific SAR-aware pTx a realistic
possibility.

### Acknowledgements

Research support from the NIH (P41 EB015891, 1 S10 RR026351-01A1), GE Healthcare, and Zurich MedTech AG (Sim4Science program).### References

[1] Eichfelder, MRM 2011;66:1468–1476
[2] M. Pendse and B. Rutt. IMPULSE: A
generalized and scalable algorithm for joint design of minimum SAR parallel
transmit RF pulses. Proceedings ISMRM 23:5008, 2015
[3] Hoyos-Idrobo, Andres, et al.
"On variant strategies to solve the magnitude least squares optimization
problem in parallel transmission pulse design and under strict SAR and power
constraints." IEEE transactions on medical imaging 33.3 (2014):
739-748.