Mihir Rajendra Pendse^{1}, Riccardo Stara^{1,2,3}, Gianluigi Tiberi^{4}, Alessandra Retico^{2}, Michela Tosetti^{5}, and Brian Rutt^{1}

^{1}Stanford University, Stanford, CA, United States, ^{2}Istituto Nazionale di Fisica Nucleare (Pisa), Pisa, Italy, ^{3}Universita' di Pisa, Pisa, Italy, ^{4}IMAGO7, Pisa, Italy, ^{5}ISRCC Stella maris, Calambrone (Pisa), Italy

### Synopsis

**The use of
a Butler matrix in pTx is thought to allow transmit channel compression by a
factor of 2 or more compared to direct drive, while maintaining similar flip
angle control. However, the SAR-related consequences of this compression strategy
are relatively unexplored. Using a SAR-aware pTx design method (IMPULSE), we
demonstrate that excellent flip angle uniformity is indeed possible using only
2 or 4 Butler modes compared to 8 direct drive channels; however, this comes at
the expense of increased SAR.
We also present a
generalized strategy for selecting the optimal subset of Butler modes, i.e. the
subset that provides adequate flip angle control at minimum SAR. **### Purpose

The use of
a Butler matrix as a parallel transmit channel compression device has been explored
in the past

^{1-2}; the conclusion has generally been that compared to direct
excitation of N coil channels, similar flip angle control can be achieved using
N/2 or fewer circularly polarized modes of the Butler matrix, thus saving on
hardware cost such as power amplifiers. More recently, the use of “dark modes”
has been described as a method for reducing SAR

^{3}, without examining
the implication in transmit channel compression, since all N Butler matrix
channels were used. In the present work, we study transmit channel compression
using a rigorous SAR-aware pTx algorithm (IMPULSE

^{4}) by assessing the
performance of N/4 or N/2 Butler modes in terms of FAI and SAR. We demonstrate
that while adequate flip angle homogeneity can be achieved with N/4 or N/2 Butler
modes, this comes at the expense of increased SAR. A significantly novel finding is that by choosing N/2 modes intelligently, it is
possible to achieve

*acceptable FAI and comparable SAR to direct drive of all N
channels*, thus providing an effective strategy for SAR-optimal Butler
channel compression.

### Methods

A
head-sized 8-channel transmit loop array with inner diameter 28.5 cm was
simulated using the commercial software SEMCAD (ZMT, Zurich) and body models
selected from the Virtual Family (IT’IS Foundation, Zurich). B

_{1}^{+}
and E field maps, obtained for individually driven coil ports, were combined in
Matlab, allowing for simulation of Butler matrix phase increments and thereby modeling
the resulting field distributions for arbitrary direct drive and Butler
configurations. Three spoke pTx pulses were designed using the IMPULSE algorithm

^{4}
which optimizes RF channel weightings and spokes locations to minimize the peak
local SAR over the exposed mass while constraining the resulting Flip Angle Inhomogeneity
(FAI) to be below a user-specified tolerance. We generated L-curves of peak
local SAR vs. FAI for direct drive of all 8 coil elements (Direct-8) as well as
all combinations of compressed Butler modes. Here we explicitly investigate two
such combinations that have been considered in the past (Butler-2R: 1R,2R and Butler-4R:
1R,2R,3R,4R) as well as one novel combination (Butler-2R2L:1R,2R,1L,2L), and
demonstrate the FAI and SAR consequences of these compressed Butler mode
configurations compared to the direct drive configuration.

### Results

Simulated B

_{1}^{+} and E field maps are shown in Figure 1
for the Duke head model. While the B

_{1}^{+} is concentrated in the
1R and 2R modes, there is significant E-field in the 1L and 2L modes. As shown
in Figures 2 and 3, the Butler-2R and Butler-4R configurations are both able to
achieve good flip angle homogeneity (FAI<5%) but at the expense of
significantly increased SAR compared to the Direct-8 configuration (factors of 4.11
and 2.11 higher for local SAR, 2.5 and 2 higher for global SAR, respectively). Interestingly,
the novel Butler-2R2L configuration is able to achieve the desired 5% FAI at substantially
lower SAR than either of the other two compressed Butler configurations, and at
very similar local and global SAR compared to the Direct-8 configuration.
Indeed, Figure 3 shows how the L-curve for Butler-2R2L follows closely the one
for Direct-8, whereas Butler-4R and Butler-2R experience a drastic increase in
SAR for lower FAI, with the second being unable to achieve FAI below 5%.

### Discussion
and conclusion

For a cylindrical
transmit array, most of the B

_{1}^{+} is generated by the homogeneous (1R) and linear (2R) Butler
modes. These two modes show complementary patterns inside a typical head load
and are therefore the two most useful modes for flip angle homogenization by pTx.
The 1L and 2L Butler modes produce significant E-field with similar shape to
the corresponding R modes, despite negligible B

_{1}^{+} intensity, and are therefore
particularly effective at reducing SAR by destructive interference (this result
confirms and extends the concept of “dark modes” introduced by Setsompop et al

^{3}).
In contrast, the 3R and 4R modes do not generate significant E-field, allowing
little opportunity for SAR reduction. Based on our results, we can provide a
useful recommendation for an optimal Butler compression method. For cases where
local SAR is of significant concern, the optimal transmit channel compression strategy
involves using N/2 modes: 1R,…,(N/4)R and 1L,…,(N/4)L. An IMPULSE-optimized pTx
pulse using these modes is expected to produce similar SAR to a pTx pulse using
all N channels. When local SAR is not a major factor, using N/4 circularly
polarized modes: 1R,…,(N/4)R could be sufficient for achieving acceptable FAI,
as has been demonstrated to be useful, for example, in knee applications of pTx

^{5}.

### Acknowledgements

No acknowledgement found.### References

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and K. Solbach. Microstrip Butler matrix design and realization for 7 T MRI.
Magnetic Resonance in Medicine, 66(1):270–280, 2011.

2. V. Alagappanet
al. Degenerate mode band-pass birdcage coil for accelerated parallel
excitation. Magnetic Resonance in Medicine, 57(6), 1148-1158, 2007.

3. K. Setsompop
and L.L. Wald. SAR Reduction through dark mode excitation. Proceedings ISMRM 19:3890,
2011.

4. 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.

5. R. Stara.
A novel splittable design of degenerate birdcage with integrated Tx/Rx switches
and Butler matrix. PhD thesis, University of Pisa, 2015.