Butler matrix transmit channel compression in pTx: a SAR-aware study.
Mihir Rajendra Pendse1, Riccardo Stara1,2,3, Gianluigi Tiberi4, Alessandra Retico2, Michela Tosetti5, and Brian Rutt1

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


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.


The use of a Butler matrix as a parallel transmit channel compression device has been explored in the past1-2; 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 SAR3, 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 (IMPULSE4) 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.


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). B1+ 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 algorithm4 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.


Simulated B1+ and E field maps are shown in Figure 1 for the Duke head model. While the B1+ 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 B1+ 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 B1+ 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 al3). 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 pTx5.


No acknowledgement found.


1. P. Yazdanbakhsh 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.


Figure 1: |B1+| and |E| field maps of 8 directly driven transmit channels and 8 Butler mode.

Figure 2: Flip angle error and maximum intensity projection SAR maps for optimized pTx pulse with 5% FAI tolerance for 8 channel direct drive and different combinations of Butler modes.

Figure 3: L-curves of peak local SAR vs FAI for optimized pTx pulse for 8 channel direct drive and three different combinations of Butler modes.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)