Synopsis

Multiple-element transmit (mTx) phased array technology provides significant improvement of the B₁+-field homogeneity in ultra-high field (B₀≥7T) cardiac MRI (cMRI). We propose time efficient semi-combinatorial approach of finding optimal Tx-elements phases presets. The proposed technique allows for searching the transmitter phases providing absolute optimum for а targeted B1+-field cost functions using high redundancy of optimal phase vector space. The technique was tested for pre-phasing of the in-house-built mTX-arrays in pigs at 7T cMRI. Improvement of the B₁+-field homogeneity of >100% and SNR gain >50% was achieved using 10% of the computation time needed when compared with brute-force optimization.

Introduction

Method

For the equal driving amplitudes in each element the B₁⁺-field of an mTX-array is described as:

B_1s⁺ (r) = |Σ Φ_k s_k(r) | k=1..N (1)

where s_k(r) are complex spatial maps of the B₁⁺ for each of N Tx-elements. "Permanent" B₁⁺-shimming or “pre-phasing” of array is performed by setting phase vector {Φ}={Φ₁..Φ_N} to achieve the targeted spatial homogeneity and mean value of B_1s⁺(r). The problem can be solved by maximizing a cost function introduced as:

F({Φ})=[mean(B_1s⁺)] ² / [std(B_1s+) ·(max(B1s+) - mean(B1s+)) ] (2)

The difficulty of solution of the problem (2) are numerous local extrema of the function F({Φ}). The known work-around is a forced exhaustive search varying all possible combination of phase vector components over a discrete grid defined with precision δφ to localize the absolute maximum of F. In our new approach we use an randomly “undersampled” grid U to find the “sparse” approximation of the cost function F({Φ_u}) over phase space within acceptable CPU/GPU computation times on middle class workstation, and with phase precision δφ=10⁰. By further using solver-based optimization, with the reasonable convergence criteria the final optimal phase vector can be refined to a precision of δφ≈1⁰ using only 10% of time needed for full exhaustive search. The methodology was tested using four different mTX arrays which had been designed and developed for large animal (pig) experiments. They consist of 2 physically independent parts. Both parts allocate 8 elements driven by 4 TX-channels of RFPA to form the 8TX/16RX configuration.

The B₁⁺-profiles were computed by full-wave electromagnetic simulation with CST software (CST, Darmstadt, Germany) and validated by channel-by-channel B₁+-mapping on the MR-scanner. A plexiglass sphere phantom ID=160mm filled with tissue imitation sugar-salt solution (ε=55) was used for a validation of the B₁⁺-field simulation by MR-measurements. All MRI measurements were done using a 7T Magnetom(TM) Terra scanner (Siemens, Erlangen, Germany ) equipped with an 8TX channels RFPA. For the GRE-based double-angle measurements (DAM)[3] of magnetization flip-angle the parameters were: TE/TR=1.8/4000ms, pixel size=2x2mm, slice thickness=3.5mm. The nominal FA=300/600 were used. The actual FA reconstruction was performed using in-house Matlab script. Testing the efficiency of the computed phases for B₁⁺ optimization was done using the same GRE-sequence as for DAM measurements using a smaller FA=10⁰.

Results

Figure 1a,b demonstrates the scheme of 2 tested arrays examples (A and B). Figure 1b shows the computed B₁⁺-fields for each TX-channel presented as maximal intensity projection (MIP) over the marked slabs.

Figure 2a,b demonstrates validation of the CST-computed B₁+ profiles of the individual Tx-channels. Two channels for each of two arrays are shown. The computed cross-correlation coefficients between each profile pair are in the range of R²= [0.97 ... 0.99].

Figure 3 and 4 shows the example of B₁⁺ fields optimized for the A and B array designs. The optimizations were done in two “slab” regions with “transversal” and “coronal” orientation. The computation time (proportional to the optimization volume) was ~20hours for a 1000 voxel (64cm³) slab. The results demonstrate the obvious and significant improvement of both homogeneity and the mean value of the obtained B₁⁺ configuration in comparison to the “default phases” profile.

Figure 5(a,b) shows the low flip-angle GRE image acquired using default and optimized phases for the design B. The improvement of the B₁⁺ profile in the selected region of the spherical phantom was confirmed in practice.

Discussion

Conclusion

Acknowledgements

References

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[3] Cunningham CH, Pauly JM, Nayak KS. Saturated double-angle method for rapid B1+ mapping. Magnetic resonance in medicine 2006;55(6):1326-1333.