Purpose

Parallel transmission (pTX) versatility is exploited in multi-spoke¹ RF pulses to tackle the RF inhomogeneity problem at ultra-high field. Due to its robustness versus gradient delays, monopolar pulses are easier to use but are less robust versus ΔB₀ and can impact the minimum TR in fast acquisitions. For those reasons, bipolar spokes are preferred but their sensitivity to gradient delays can quickly deteriorate performance. The most direct way to correct for those delays is to shift temporally the RF waveform² but this requires a high discretization of the RF shapes to account for µs delays, increasing loading time, and it is not applicable to anisotropic delays when dealing with tilted slices or slabs. Gradient delays can also be corrected by adding a phase shift to every other spoke for slice excitations³ where the slice location center is relatively well-defined in space. As a result, it is neither applicable for slab excitations and nor for anisotropic delays. The new method reported, gradient trim⁴ blips, here consists in adding gradient blips between RF sub-pulses to cancel the phase shift induced by the gradient delays. We demonstrate its applicability for tilted slab-selective pulses on a water phantom at 7T.

Methods

Experiments were carried out on a 7T Siemens (Siemens Healthcare, Erlangen, Germany) Magnetom system equipped with an SC72 gradient (40 mT/m nominal maximum gradient strength and 200 T/m/s max slew rate) and the Nova (Nova Medical, Wilmington, USA) 8Tx-32Rx pTX coil. Gradient delays were first characterized based on the method detailed in Gras el al.³ where a slice location dependent phase shift characterizes the gradient delay. The effect of a gradient delay on RF phase for a z location is shown in Fig.1. The first gradient slope, the refocusing lobe and the last gradient slope do not affect the flip angle. Gradient plateaus where RF pulses are applied are displayed. On the first gradient lobe, the part of the plateau lasting T_p - Δt generates a rotation along z axis whose angle is proportional to the same duration, the second part during the RF pulse generates a rotation R1 , the third part of the plateau generates a rotation along $$$\overrightarrow{z}$$$ whose angle is proportional to Tp + Δt. The first and last parts of the second plateau also produce the same rotations but around $$$-\overrightarrow{z}$$$. Gradient commutations (i.e. the middle gradient slopes) induce a zero-order eddy current that can be modelled as a z-rotation. The total rotation matrix is then:
$$R_{TOT}=R_{-\overrightarrow{z},T_{p}-\triangle t}R2R_{\overrightarrow{z},\phi_{EC}}R_{\overrightarrow{z},2\triangle t}R1R_{\overrightarrow{z},T_{p}-\triangle t}$$
We can see here that gradient delays induce a phase shift on the spins between the two RF pulses, yielding 30° phase shift per µs and for 20 mT/m gradient at 5 cm from the isocenter. The zero-order eddy current rotation can be corrected by a uniform phase shift of the second RF sub-pulse while the spatially dependent rotation with angle 2γG_sszΔt (G_ss is the slice selection gradient amplitude, z the center of the slab) can be compensated for all positions by a gradient blip. For the case of tilted slabs/slices and anisotropic delays, this correction is simply applied separately for each axis employed in the slice or slab selection. Pulse design and acquisitions were performed with 2 spokes bipolar pulses on a gel phantom. An AFI⁵ sequence was used to measure the flip angle for two configurations: axial and tilted orientations (4cm slab thickness). A TBWP of 25 (sub-pulse duration 1.9 ms, gradient strength 7.7 mT/m) and an additional delay up to 16µs were used to enhance gradient delay artefacts. Delays were modelled in simulation by simply shifting the waveform of the gradients. Experimental results were compared to simulations and unipolar acquisitions as a reference since unipolar pulses are immune to gradient delays.

Results

Delays of 3.5 µs on x and 4 µs on y and z were measured. Figure 2 shows flip angle maps of bipolar acquisitions compared with simulations; where a good similarity between the experimental results and the theoretical predictions can be observed. Figure 3 for reference shows the ratio of the bipolar (with and without trim blips) results to the unipolar RF pulse version, a ratio of 1 indicating perfect correction of the gradient delays, provided the ΔB₀ effect can be neglected.

Discussion and conclusion

We have presented a method to correct for gradient delays in pTX bipolar spokes. Since the correction relies on additional gradient (trim) blips, the accuracy of the compensation method depends proportionally on the fidelity of their areas, thereby leading to sub-µs accuracy given standard scanners. It is a general solution as it is applicable for both slice and slab excitations as well as anisotropic gradient delays.

Acknowledgements

ERPT equipment program of the Leducq Foundation.

References

[1] Saekho and al. MRM 2006 Apr;55(4):719-24., [2] Tse and al. MRM 2017 Nov;78(5):1883-1890., [3] Gras and al. MRM. 2017 Dec;78(6):2194-2202. [4] Oelhafenand al. MRM. 2004 Nov;52(5):1136-45. [5] Yarnykh MRM 2007 57:192–200