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

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

### Synopsis

We describe a new approach for performing channel
compression for pTx in cases where the number of elements in the transmit coil
exceeds the number of exciters. Unlike previous methods for channel
compression, the current approach takes local SAR information into account and
seeks to minimize SAR while obtaining a uniform flip angle distribution. We
demonstrate mitigation of local SAR hotspots with the current approach and show
30% reduction in peak local SAR compared to a SAR unaware approach.

### Introduction

Parallel transmit RF coils are typically built to have the
same number of transmit elements as the number of independently controllable
transmit channels (exciters) available on the scanner. Increasingly, however,
there are reasons to build coils whose number of transmit elements exceeds the
number of exciters. This demands a strategy to drive those transmit elements from
a smaller number of independently controlled excitation waveforms; such
strategies have become known as “transmit array compression”. A compression
strategy, called acpTx, has been recently introduced [1]; this strategy uses a
pulse design optimization algorithm to find both the optimal element-to-exciter
mapping and the waveforms to apply at each exciter, to achieve the desired
excitation pattern. However, acpTx uses a SAR-unaware pTx pulse design
algorithm and may therefore lead to the generation of local SAR hotspots. In
this work, we introduce acIMPULSE, a SAR-aware array compression algorithm,
using a modification of the IMPULSE pTx design algorithm [2].### Theory

The procedure for acpTx described in [1] involves a simple modification of the interleaved greedy and local algorithm [3] for finding
spokes locations and channel weightings for pTx by inserting a singular value
truncation step after updating the RF weights in order to force the rank of the
pulse matrix B to be equal to the
number of exciters, as shown in Figure 1. The matrix B can be written as USV
where U gives the element to exciter
mapping and SV describes the
waveform applied to each exciter during the scan. To integrate the acpTx
concept into the IMPULSE algorithm, we used the published SAR-unaware acpTx
procedure to find the optimal value of the element-exciter mapping U. Then, we transform the system matrix
A relating element weightings to the
flip angle profile into a matrix A_u that
relate the exciter weightings to the flip angle profile. This is done by
multiplying rows of A by the mapping
matrix U found in the previous step.
The IMPULSE optimization can be performed using A_u instead of A and
results in the SAR-optimal waveforms to apply to each exciter in order to meet the
specified flip angle inhomogeneity tolerance while achieving minimum SAR, as
described in [2].### Methods

Flip angle and SAR distributions were
derived from B1+ and E fields, which were simulated using Sim4Life, a commercially available FDTD
electromagnetic modeling package (Zurich MedTech AG, Zurich),
employing an 8-channel transmit array and the Duke head model from the Virtual
Family (IT’IS Foundation, Zurich).
8:2 array compression was performed using both the acpTx method [1] and the
proposed acIMPULSE method. The SAR performance of both these methods was compared
to that achieved by driving all 8 channels independently (i.e. without
compression) with channel weightings optimized by IMPULSE. In all cases, the flip
angle inhomogeneity in the excited slice was constrained to be no worse than 3%.

### Results

Figures 2a and 2b show that the SAR-aware
acIMPULSE pulse design results in a substantial reduction of peak local SAR
(>30%) compared to the SAR-unaware acpTx design. Note, however, that this
reduction is still small compared to the SAR reduction (>80% compared to
acpTx) obtained by using conventional IMPULSE (Figure 2c) to design a pTx pulse
that drives all 8 channels fully independently. A significant reason for higher SAR with compression is that the total number of spokes needed to
achieve the specified FAI increases from 3 spokes without array compression to
6 spokes with array compression. More generally, the SAR penalty incurred by
array compression reflects the reduction in parallel transmit degrees of
freedom. However, it is clear that the acIMPULSE algorithm mitigates this inevitable
penalty.

### Discussion

By using the SAR-aware array-compressed
IMPULSE algorithm, it is possible to reduce SAR substantially compared to the
SAR-unaware acpTx approach. In this current study, this SAR reduction is
limited because only two exciters were used, limiting the number of degrees of
freedom very significantly. This is nonetheless a relevant compression ratio
for many existing high field scanners. Future work will
investigate a much broader range of compression ratios, for example 32:8, which
is a practical ratio for scanners that have 8-channel pTx
capability. With these greater number of transmit degrees of freedom, the benefits
of acIMPULSE are expected to be even more substantial. More importantly,
acIMPULSE provides us with a new tool to explore and optimize a greater range
of transmit coil and exciter architectures, with assurance of minimum SAR pTx
performance in all cases. With this tool, we believe that pTx performance can
be more completely optimized, limited only by the available number of exciters.### Acknowledgements

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

[1]
Cao, Z., Yan, X. and Grissom, W. A. (2016), Array-compressed parallel transmit
pulse design. Magn. Reson. Med., 76: 1158–1169
[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] Grissom, W. A., Khalighi, M.-M., Sacolick, L. I., Rutt,
B. K. and Vogel, M. W. (2012), Small-tip-angle spokes pulse design using
interleaved greedy and local optimization methods. Magn Reson Med, 68:
1553–1562