Introduction

In recent years there has been growing interest in parallel transmit (pTx) RF systems. At high field strengths, pTx can be used to create a more homogenous B₁⁺ over the whole body or a specific region of interest¹. The control over transmit fields provided by pTx can also allow one to better control the interaction of the transmit field with embedded or interventional devices².
The vast majority of pTx systems have a number of identical RF power amplifiers (RFPAs) connected to an equal number of transmit array elements. This is straightforward from a design perspective, but it means that if different amounts of power are required for each array element, the maximum transmit field (B₁⁺) that can be produced is limited by the amplifier supplying the most power-hungry element while other amplifiers operate substantially below their maximum capability. This has the effect of both limiting the maximum achievable B₁⁺ and increasing the expense of the parallel transmit system, as the amplifiers need to be more generously sized. Here we explore an approach to sharing power between channels. We look in detail at a 2-channel exemplar arrangement, but the approach can be generalized to multiple channels.

Theory and Methods

Fortunately, there exist networks of RF components that can be used to share power between parallel transmit channels³. Figure 1 shows an example. The fixed network in figure 1B is efficient when excitations either 0° or 180° apart are required, allowing power to be shared un-evenly (e.g., for two 1W amplifiers, 1.5W for coil 1 and 0.5W for coil 2). However, performance is very dependent on the relative phases required as shown in figure 3A. Performance rapidly drops as the relative phase deviates from the optimal angle for the network.
To overcome this, we have examined inserting a variable phase shifter between the power sharing network and the transmit array elements (fig. 1C). This allows for the relative phase of the power sharing network’s outputs to remain closer to optimal as the relative coil phases are changed, improving the range over which the system performs well.
High-power phase shifters are typically digital devices. Figure 2 shows a 3-bit example. Because each bit requires two RF switches and an additional length of transmission line, it is desirable to use the fewest bits possible to minimize losses.
To explore performance, we calculated the maximum power that can be delivered as functions of the relative phase and power imbalance between channels. The basic power-sharing network in figure 1B and the phase-shifted power-sharing network in figure 1C and figure 2 were compared to the conventional configuration in figure 1A. We also simulated 100,000 random shims and explored what fraction of these would benefit from the proposed network with phase shifters of different bit depths.

Results

Figure 3 shows how adding even a phase shifter with just a few bits dramatically improves the range of angles over which a substantial improvement to flexibility is achieved. Adding 1-2 bits reduces the severity of a worst-case shim and using 3 bits allows for good performance at a wide range of phases and ratios.
Figures 4 and 5 shows the results of the random shim simulations. Figure 4 shows that the majority of shims benefit from the basic (i.e. non-phase-shifted) power sharing networks, but adding a few bits of phase shifting substantially improves the fraction of shims that benefit. In figure 5 we see that in addition to improving the fraction of shims that benefit from power sharing, adding a phase shifter also decreases the performance penalty associated with a poorly-conditioned shim.

Conclusion

Power sharing networks have the potential to expand the capabilities of parallel transmit systems by increasing the maximum B₁⁺ that a parallel transmit system can produce. Conventional power sharing networks, such as those based on 90° hybrid couplers, enable unequal division of RF power between array coil elements, but only perform well over a small range of relative phases. Adding high-power phase shifters between the power sharing network and the coil elements improves the flexibility of the power-sharing system, increasing the fraction of shims over which it provides an advantage over conventional parallel transmit systems. The phase shifter only needs a few bits to provide a dramatic improvement.
Combining simple power-sharing networks with simple high-power phase shifters has the potential to increase the maximum B₁⁺ available from existing pTx systems as well as to reduce the cost of new systems, which may be able to operate with lower-power amplifiers without sacrificing performance. This study focused on a 2-channel example, but the concepts are readily expanded to more channels and the gains in maximum power also scale with the number of channels.
This preliminary analysis has focused on B₁⁺ shimming, but dynamically modulated complex pulses also stand to benefit from power sharing. Either an average phase shift could be chosen to maximize performance, or pulses could be designed to try to take advantage of the power-sharing network by considering the impact of relative phase in an optimization.

Acknowledgements

This work was supported by core funding from the Wellcome/EPSRC Centre for Medical Engineering [WT203148/Z/16/Z] and by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy’s and St Thomas’ NHS Foundation Trust and King’s College London and/or the NIHR Clinical Research Facility. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care.