Introduction

At UHF field strengths it is desirable to maximize the number of transmit channels available to shape and correct RF field (B₁⁺) inhomogeneities caused by wavelength effects. We previously proposed the array compressed parallel transmission method to increase the number of coil elements without increasing the number of amplifiers already available [1,2], by introducing an optimized amplitude and phase splitting network between a small number of transmit channels and a large number of coils. One unanswered question is whether acpTx with a fixed network can outperform a conventional one-channel-to-one-coil 8-channel array [3,4]. We previously described a 7T 30-loop head transmit array as well as low-loss miniaturized ratio-adjustable power splitter circuits which serve as network building blocks [5,6]. In this work, we report a framework to design the weights implemented in the low-loss network to drive the 30-channel coil, where the weights are jointly optimized in multiple human head models for a multislice RF shimming application. The design process includes the weight design and considers feasible coil-to-channel mapping schemes based on cabling considerations, to create a feasible optimized acpTx 8-channel/30-coil transmit system with high performance [7].

Methods

Fig 1. shows the overall transmit system along with the constructed 30-ch pTx coil and examples of the low-loss ratio adjustable power splitter PCBs that make up the optimized network. Given the previously built coil array, we know where each of the coil elements is situated. In simulation, we used 2 head models to calculate the E and H fields and global SAR matrices for the array. The resulting fields are shown in Fig 2. Given cabling constraints, we determined that each amplifier should drive a group of coils physically adjacent to one another. We began with a reference coil-to-channel grouping option and then shifted, flipped horizontally, and vertically to create 40 unique configuration options to exhaustively evaluate, as shown in Fig 3. For each of these 40 possible coil-to-channel configurations, we solved a magnitude least squares joint multislice shim problem that uses a rank constraint to enforce feasible compression weights that connect the channels and coil elements:

\begin{array}{ll} \textrm{minimize}& \frac{1}{2} \sum_{i = 1}^{N_{sl}} \sum_{j = 1}^{N_{x}^i} \left| 1 - \left| \{ {S}_{i} {b}_{i} \}_j \right| \right|^2 + \frac{\lambda}{2} {b}_i {Q} {b}_i \\ \textrm{subject to} & \textrm{rank}({B}_k) = 1, \hspace{0.5cm} k=1, \dots, N_{ch}, \end{array}

Where, S_i is an N_xⁱxN_c matrix of complex-valued B₁⁺ maps for each of the N_sl slices, and N_xⁱ is the number of spatial locations. b_i is a length N_c vector of shims. λ is a SAR regularization parameter and Q is an N_cXN_c global SAR matrix

Importantly, this solution ensured that the shim for each coil element would be a scaled copy of the transmit channel shim. We used the l-curve method to compare the 40 configuration options by plotting the magnitude-squared error term against the SAR term, solving repeatedly across a range of l values to vary the SAR-homogeneity tradeoff. We also completed a range of shim designs using the identified optimal coil-to-channel mapping but setting the network weights to have equal uniform amplitude and CP-mode phase.

Results

The l-curve results are shown for each of the 40 coil-to-channel mapping and the CP mode configuration in Fig 4. The different coil-to-channel mappings have very different l-curves, with one or two clear winning mappings; the mapping with a point closest to the origin (the green curve) was selected as the winner. The CP-mode mapping was among the worst five optimized mappings. Fig. 5 shows shimmed B₁⁺ maps across axial slices in one of the models for both the CP-mode network with optimized shim weights and optimal network with optimized weights. The coefficient of variation (CoV) for the CP-mode network with optimized weights is 0.0802 with SAR cost of approximately 9.28e6 and the CoV for the optimal network with optimized weights is 0.0436 with a SAR cost of approximately 5.47e6.

Discussion & Conclusion

We have described a framework to optimize a full acpTx transmit system given a fixed number of amplifiers, a set number of coil elements with cabling constraints, and a desired imaging application. The optimal network outperformed a CP-mode coil combination with optimized 8-channel shim weights by approximately 2-fold. This improvement in CoV, given the fixed number of configurations, shows the homogeneity in the field that can be gained by optimizing the network in comparison to a CP-mode network with an optimized set of weights, representing a more conventional 8-channel coil. A B₁⁺ homogeneity improvement was seen in every slice. In future work, the optimized weights will be implemented for an imaging-based validation of the design.

Acknowledgements

The authors thank Zhipeng Cao for previous work and thoughtful discussions. This work was supported by NIH grants R01 EB 016695, U01 EB 025162, 2T32 EB 001628-21, and R01 EB 031078.

References

[1] Yan, X., Cao, Z., & Grissom, W. A. (2016). Experimental implementation of array‐compressed parallel transmission at 7 tesla. Magnetic resonance in medicine, 75(6), 2545-2552.[2] Cao, Z., Yan, X., & Grissom, W. A. (2016). Array‐compressed parallel transmit pulse design. MRM, 76(4), 1158-1169. [3] Cao, Z., Yan, X., Gore, J. C., & Grissom, W. A. (2020). Designing parallel transmit head coil arrays based on radiofrequency pulse performance. Magnetic resonance in medicine, 83(6), 2331-2342.[4] Grissom, W. A., Yan, X., & Cao, Z. (2019). Universal Coils: Multisubject Optimization of 8-Channel Many-Element Parallel Transmit Arrays. In Proc 27th Annual Meeting ISMRM, Montreal, QC, Canada.[5] Sappo, C. R., Drake, G., Yan, X., & Grissom, W. A. (2021). A 30-element transmit array for 7 Tesla brain imaging with array compressed parallel transmission. In Proc Annual Meeting ISMRM, Virtual (p. 1426).[6] Sappo, C. R., Gallego, G. L., Grissom, W. A., & Yan, X. (2022). On the design and manufacturing of miniaturized microstripline power splitters for driving multicoil transmit arrays with arbitrary ratios at 7 T. NMR in Biomedicine, 35(11), e4793.[7] Webb, A. G. (Ed.). (2016). Magnetic resonance technology: hardware and system component design. Royal Society of Chemistry.