Introduction

Parallel transmission (pTx) is a popular strategy to solve the B1+ inhomogeneity problem at 7 Tesla, however its widespread acceptance is hampered by 1) expensive hardware (~$100k per transmit channel), 2) complex management of the specific absorption rate (SAR) and 3) complex pulse design. So-called “universal pulses” have been proposed that relax this last constraint^1,2, but the first two problems remain. Recently, we have proposed using the additional degrees-of-freedom provided by B0 shim array coils in order to achieve slice-selective³ and 3D⁴ uniform flip-angle (FA) excitations (INtegrated Shimming and Tip-Angle NormalizaTion, or INSTANT), which bypasses problems 1) and 2). Here, we assess the performance of kT-point and INSTANT pulses for 3D 90° brain excitations in seven volunteers and a realistic head phantom. We design the pulses in a “universal” manner which avoids the need for lengthy pulse optimization and field maps acquisition while the patient is in scanner.

Methods

Volunteers & phantom measurements: We scanned seven healthy volunteers (3 males/4 females, ages: 22-38 yo, height: 158-193 cm, weight: 110-230 lbs) on our 7 Tesla MAGNETOM Terra scanner (Siemens Healthcare, Erlangen, Germany). B1+ maps were acquired using a pre-saturation-based sequence. B0 maps were acquired using double-echo GRE. The kT-point and RF+gradient optimized pulses were evaluated on a Nova Medical with 32 Rx channel and a single birdcage transmit coil. The RF+gradient+shim current optimized pulses (INSTANT) were evaluated on a realistic head phantom in a custom “AC/DC” coil with 32 Rx channels, 32 shim channels (combined with the Rx loops) and one birdcage Tx coil^5,6. The field maps of every channel of the AC/DC coil were mapped using three GRE acquisitions with TEs 2.35/2.85/5.85ms.
INSTANT optimization: We minimize the mean square error (MSE) between the target MZ magnetization and the MZ magnetization achieved by arbitrary RF, gradient and shim current waveforms. For 90° pulses, the target MZ is 0 (magnitude least-squares). The MZ distribution is computed as MZ=|a|² - |b|², where a and b are the Caley-Klein parameters of the pulse obtained using a forward Bloch simulation. The derivatives of the objective function are computed from the derivatives of the Caley-Klein parameters a and b with respect to the unknown, i.e.: da/dReal(RF), da/dImag(RF), da/dG_x, da/dG_y, da/dG_z and da/dSC_i, where RF is the complex RF pulse, G_x, G_y and G_z are the gradient waveforms and SC_i is the shim current waveform for coil i of the shim array (similar derivatives for b). The analytical expressions for these derivatives are complicated, but can be computed analytically in an efficient manner using a forward and a backward Bloch simulation^3,4. We use a C++ implementation accelerated on 20 cores. We do not perform the optimization for the fully sampled field maps, but on a small sets of points in the brain (150-200 points per subject). In order to yield waveforms that are playable in practice, the gradient amplitude, slew-rate and acceleration are constrained to the system maximum. Peak RF is also constrained, as is the shim current maximum amplitude, slew-rate and acceleration. We design “universal” pulses by stacking the field maps of multiple subjects on top of one another.
kT-point pulses: We design kT-point pulses7 with fully optimized RF and gradient blips. Location of the kT-points are optimized by 1) performing a greedy search whereby we add one kT-point at a time (for each new kT location, we test a number of positions placed on an expanding circle in kx-ky) and 2) refinement by joint optimization of the kT-point locations and the RF amplitudes.

Results

Fig. 1 shows the subjects’ field maps used in the universal designs (3 first subjects) as well as for testing of the universal pulses (4 additional subjects). Fig. 2 (2ms, 400V peak RF) and 4 (1ms, 250V peak RF) shows that joint optimization of the RF and gradient waveforms improves the flip-angle quality compared to the kT-point strategy, both in the min-max and RMSE metrics. However, the additional DOFs provided by the shim array (INSTANT) do not further improve the pulse performance. Fig. 3 confirms this finding in-vivo, i.e. the RF + gradient optimization strategy yields slightly more uniform flip-angle maps, although it is noteworthy that the kT-point strategy works well in this “universal” approach and yields a large improvement over the standard RECT excitation pulse. Fig. 5 illustrates our optimized shim array pulses “RF + SC” in a realistic head phantom. The slew-rate and curvature constraints imposed during optimization are critical to keep most of pulse power within the amplifier bandwidth.

Discussion

“Universal” kT-point pulses are efficient at generating uniform FA distribution in the brain at 7 Tesla, even without the use of pTx, as long as the kT-point locations are optimized along with the RF amplitudes. Further FA homogeneity improvement can be obtained by jointly optimizing the RF and gradient waveforms. Finally, the additional DOFs of the shim array coils did not significantly improve the excitation quality, indicating that the gradient coils do the “heavy lifting” of the spatially varying spin dephasing in this application. As we have shown previously, it is likely that the main benefit of the INSTANT technique is for more complex excitation pattern such as slice-selective excitations.

Acknowledgements

NIH R00EB021349, U24EB028984, R00EB019482