Universal Coils: Multisubject Optimization of 8-Channel Many-Element Parallel Transmit Arrays
William Allyn Grissom1, Xinqiang Yan1, and Zhipeng Cao1

1Vanderbilt University, Nashville, TN, United States


A large number of coils is desirable in parallel transmission to achieve uniform excitation while controlling SAR in a subject-adaptive manner, but only a small number of transmit channels are available on most ultra-high field scanners. We describe an algorithm that optimally groups a large number of coils into a small number of channels, based on the fact that if two coils are in the same channel, the matrix formed by collecting their slice-by-slice RF shims will have rank one. The algorithm was used to optimize the coil-to-channel mappings of a 30-coil array at 7T, based on 8 representative heads.


Many transmit coils are desirable in parallel transmission to mitigate RF field inhomogeneity in ultra-high field (UHF) MRI, but most UHF scanners have only 8 transmit channels due to cost and siting limitations. Array-compressed parallel transmission [1-3] overcomes this limitation and enables a small number of channels to drive a large number of coils, using hardware networks that split the input channel signals to each output coil while applying optimized relative amplitude and phase shifts (Figure 1a). Here we describe an algorithm to co-optimize coil-to-channel assignments and slice-by-slice RF shims, and in analogy to the Universal Pulses concept [4] we apply it to design a Universal Coil for head imaging with 30 elements driven by 8 channels, to achieve population-optimal RF shimming performance.



Our algorithm is based on the observation that two coils in the same channel receive scaled copies of the same vector of RF shim values, so the two-column matrix formed by their shims will have rank one. That is, if the matrix has a large second singular value σ22 the coils should be in different channels, and vice-versa. We can determine a set of RF shims and σ22 values for making coil-to-channel assignments by solving:


where $$$\mathbf{A}_i$$$ contains B1+ maps for slice $$$i$$$, $$$\mathbf{b}_i$$$ contains the shim values for slice $$$i$$$, $$$\mathbf{S}$$$ is a global SAR matrix, and $$$\sigma_{22}\left(\mathbf{b}_l,\mathbf{b}_m\right)$$$ is the paired σ22 for coils $$$l$$$ and $$$m$$$.

A variable splitting with continuation strategy [5] is used to repeatedly solve Equation 1. After the first solution, the two coils with the largest σ22 are assigned to channels 1 and 2. Thereafter, the coil with the largest minimum σ22 with assigned coils is assigned to a new channel, until eight channels are initialized. After that, coils are assigned to the channel with which they have the smallest maximum σ22. Each time a coil is assigned, its $$$\lambda$$$ with coils in other channels is set to zero, and its $$$\lambda$$$ with coils in its own channel is set to a large value. The final coil amplitudes and phases for each channel are determined by SVD of its RF shims [1].

Electromagnetic Simulations

8- and 30-loop (Figure 1b) coil arrays were modeled at 298 MHz in 10 human head models (Figure 1c). The models represented average male and female dimensions in five countries. The arrays had 28 cm diameters to accommodate a receive coil, and height 16 cm (8 loops) and 17.8 cm (30 loops). Each loop in the 30-element array was 7 cm2. Loops were overlapped 2 cm in different rows, while loops in the same row were gapped 5.5 mm for self-decoupling [6].

Multisubject Design and Comparisons

The algorithm was used to co-optimize slice-by-slice RF shims and coil-to-channel assignments across subjects 1-4 and 7-10, in three slice orientations. The coil design corresponding to the knee of the flip angle coefficient of variation (CoV; standard deviation divided by mean) versus global SAR curve was then used to design 8-channel RF shims for subjects 5 and 6, while varying SAR regularization. This optimized design was compared to a conventional array-compressed coil designed with geometric coil-to-channel assignments, and to the 8-coil array with one and two-spoke pulses [7].


Figure 3 shows that RF shimming with 8 coils achieved the worst flip angle CoV versus SAR tradeoff among coil and pulse configurations, and 30 coils with optimized coil-to-channel assignments achieved the best tradeoff. The 8-coil/2-spoke excitations had similar minimum CoV as the optimized 30 coil shims, but with twice the SAR and RF pulse duration. Figure 4 shows slice-by-slice normalized flip angle maps in subject 5, for a matched global SAR of 0.4 W/kg/slice. At this SAR level, the 30 coil RF shims with optimized coil-to-channel assignments were the only ones with average CoV better than 0.05.

Figure 5 shows the amplitudes and phases of the geometric and optimized coil weights for each of the eight channels. The optimized channels contained coils distributed around the circumference of the array, often in clusters. The presented consecutive geometric coil-to-channel assignments performed better than any other geometric assignments (data not shown).

Discussion & Conclusion

An algorithm was described that co-optimizes coil-to-channel assignments and slice-by-slice RF shims for many-element coil arrays driven by a small number of transmit channels. It was applied to produce a population-optimal 8-channel/30-element coil with a better flip angle uniformity-to-SAR tradeoff than a conventional 8-element coil, even when two-spoke pulses were used. The algorithm could be extended to optimize a coil for other types of pulses or for all the pulses in an imaging protocol, simultaneously. It could also be extended to prune unnecessary coils from an array.


NIH R01 EB 016695 and U01 EB 025162.


  1. Z. Cao, X. Yan, and W. A. Grissom. Array-compressed parallel transmit pulse design. Magn Reson Med, 76(4):1158–1169, 2016.
  2. X. Yan, Z. Cao, and W. A. Grissom. Experimental implementation of array-compressed parallel transmission at 7 Tesla. Magn Reson Med, 75(6):2545–2552, 2016.
  3. X. Yan, Z. Cao, and W. A. Grissom. Ratio-adjustable power splitters for array-compressed parallel transmission. Magn Reson Med, 79(4):2422–2431, 2018.
  4. V. Gras, A. Vignaud, A. Amadon, D. Le Bihan, and N. Boulant. Universal pulses: A new concept for calibration-free parallel transmission. Magn Reson Med, 77(2):635–643, 2017.
  5. S. G. Lingala, Y. Hu, E. V. R. DiBella, and M. Jacob. Accelerated dynamic MRI exploiting sparsity and low-rank structure: k-t SLR. IEEE Trans Med Imag, 30(5):1042–1054, 2011.
  6. X Yan, J C Gore, and W A Grissom. Self-decoupled radiofrequency coils for magnetic resonance imaging. Nature Communications, 9(1):3481, 2018.
  7. W. A. Grissom, M. M. Khalighi, L. I. Sacolick, B. K. Rutt, and M. W. Vogel. Small-tip-angle spokes pulse design using interleaved greedy and local optimization methods. Magn Reson Med, 68:1553–62, 2012.


Figure 1: (A) The coil optimization problem is to determine which coils should be connected to which transmit channels, and with what relative amplitudes and phase shifts, based on slice-by-slice RF shimming performance in multiple subjects and slice orientations. The optimized channels may have different numbers of coils. (B) The simulated three row/30-element coil array, with visible elements labeled. (C) Illustration of simulated head sizes. Moving left to right, the heads become relatively shorter in the A/P direction and wider in the R/L direction, and the male heads are generally larger than the female heads.

Figure 2: Illustration of how the algorithm assigns coils to channels based on the second singular values (σ22's) of the two-column matrices formed from the collected RF shims of each pair of coils in the array. The middle image shows matrices of regularized σ22 values after each solution of Equation 1. Initially, all coils are unassigned (AssignedChannel = -1) and all σ22's are regularized. When a coil is assigned, the σ22 penalties between that coil and coils in different channels are removed. The final optimized pair map contains non-zero entries only between coils in the same channels.

Figure 3: Flip angle coefficient of variation (CoV) versus global SAR over two heads (male subject 5 and female subject 6), for an 8-loop coil array and RF shimming with one or two spokes, and for the 30-loop/8-channel coil array using one-spoke RF shimming and geometric or optimized coil-to-channel assignments. The dashed vertical line indicates the global SAR level at which the comparison in Figure 4 is made. SAR was calculated assuming a 1 ms RF pulse with average flip angle 1 degree and 1 second TR. The 8-channel/30-element coil with optimized coil-to-channel assignments achieved the best CoV-SAR tradeoff.

Figure 4: Global SAR-matched normalized flip angle maps in subject 5 for the 8-loop coil array using one- or two-spoke excitation, and for the 30-loop/8-channel coil array using one-spoke RF shimming and geometric or optimized coil-to-channel assignments. For the same SAR, the 8-channel/30-element coils achieve improved flip angle homogeneity, and the 8-channel/30-element coil with optimized coil-to-channel assignments was the only array to achieve better than 0.05 flip angle CoV.

Figure 5: Coil-to-channel groupings for the geometric and optimized 8 channel-to-30 coil arrays. Referring to Figure 1b, Coil 1 is in the top left corner and Coil 30 is in the bottom right corner of each 3x10 matrix. The geometric channels were determined manually and contained 3 or 4 consecutive coils. The optimized channels contained between 1 and 8 coils, which were in most cases distributed around the circumference of the array and across its rows.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)