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Optimal RF-Spoiling for Bias-Free Displacement Field Estimation in Fast 3D MR Elastography Sequences

Christian Guenthner¹ and Sebastian Kozerke¹
¹University and ETH Zurich, Zurich, Switzerland

Synopsis

RF-spoiling is employed in order to reduce transverse coherences. While spoiling angles are typically optimized for contrast, efficacy for bias-free phase-contrast measurements is yet to be proven. Here, we investigate the influence of the RF-spoiling angle on displacement estimates in fast GRE-MR Elastography sequences using Extended Phase Graph simulations. Theoretical findings are validated using a novel RF-spoiling test sequence as well as conventional MRE phantom experiments. An optimal spoiling angle of 158° degrees is identified allowing for bias-free MRE acquisitions at repetition times as low as 5ms.

Introduction

MR Elastography (MRE) utilizes phase-contrast MR imaging to determine the local shear displacement field resulting from external actuation.¹ As customary in gradient-echo (GRE) phase-contrast MRI, RF-spoiling with a quadratic phase increment$$\;\phi_n=\phi_{n-1}+n\cdot\phi\;$$is employed to reduce transverse coherences and thus the influence of spin-history on the overall MR signal.^2–5 RF-spoiling angles have been optimized to produce contrast in agreement to Ernst’s simplified GRE-contrast equation and to produce bias-free$$$\;$$$T₁ and$$$\;$$$B₁$$$\;$$$estimates.^2,6–8 As magnetization in MRE is subject only to minute periodic displacement and hence resides in the imaging volume for the whole scan, spin-history effects can interfere with encoding especially when short repetition times are employed. While current MRE acquisition schemes, relying on multi-slice schemes with long per-slice repetition time, are less prone to spin-history artifacts, accelerated acquisitions using e.g. compressed sensing with undersampling along two phase-encode directions necessitate switching to slab excitation and very short TR. Here, the efficacy of RF-spoiling remains to be investigated.

In the present work, extended phase graph (EPG) simulations are used to study the influence of RF spoiling angles on the phase-contrast signal in 3D GRE-MRE. A test sequence is proposed allowing to directly quantify the effect of spin history on the encoded displacement. The theoretical findings are validated using phantom experiments.^9,10 An optimal spoiling angle of$$$\;\phi=158^\circ\;$$$is identified showing minimal displacement errors.

Methods

An EPG simulation of an RF-spoiled GRE sequence was extended to include periodic phase accrual as found in fast GRE-MRE sequences such as Ristretto or eXpresso MRE (Figure 1A) by adding a phase to the configuration states$$$\;F_k\;$$$in each$$$\;$$$TR^11,12$$F_k\;\to\;F_k\;e^{i\angle_n}.$$Phase encoding from spoiling gradients was neglected as phase-difference measurements were simulated. The simulation was iterated to steady state to allow the extraction of both signal magnitude and phase enabling the comparison between reconstructed and input displacement (EPG Parameters in Figure 3).

An RF-spoiling test sequence was designed replacing the MEG in the Ristretto MRE sequence by a unipolar gradient in readout direction. Sinusoidal stepping of the gradient (Figure 1B) results in equivalent periodic phase accrual as in conventional MRE without the need of actuation. As shown in Figure 1C, the apparent displacement is directly given by the product of the voxel position in readout direction$$$\;x\;$$$and the maximum encoding moment$$$\;k_0\;$$$allowing to exactly quantify the displacement error over a wide range of input displacements.

Ristretto GRE-MRE measurements with Hadamard encoding were performed on a 3T Ingenia system (Philips, Best, The Netherlands) on a QA phantom (CIRS, Norfolk, USA) using electromagnetic actuation (Sequence parameters in Figure 4).^11,13

The test sequence was employed on the same scanner in an agarose phantom. A maximum encoding moment of$$\;k_0=142.5\;\text{rad/m}\;$$was used creating an apparent displacement of ±1.5π over$$$\;\sim$$$70mm. Images were processed as in MRE using 2D unwrapping (SNAPHU),¹⁴temporal unwrapping, directional decoding,¹³ followed by Fourier transformation (Figure 3A).
Both sequences were repeated with different RF spoiling angles, i.e.$$$\;\phi=0^\circ\;$$$(no RF spoiling), 117° and 150° (vendor depending defaults) as well as 158° (proposed optimal spoiling angle). Flip angles were chosen as the Ernst angle with$$$\;$$$T₁=750ms$$$\;$$$(Liver at 3T).

Results & Discussion

Figure 2 shows the EPG simulation results as a function of RF spoiling angle$$$\;\phi\;$$$and$$$\;$$$TR. (A) depicts the magnitude variation as a result of transverse coherences. In (B), the upper limit on input vs. reconstructed displacement is shown, where maximal deviations of 34% are identified, when no RF spoiling is employed. Conventional spoiling angles of$$$\;\phi=117^\circ\;$$$and$$$\;\phi=150^\circ\;$$$reduce displacement errors down to 14%. An optimal spoiling angle of$$$\;\phi=158^\circ\;$$$can be identified minimizing both displacement error and magnitude variations. For the four marked spoiling angles, (C) denotes relative displacement error as a function of the input displacement and$$$\;$$$TR, where (D) shows the dependence on$$$\;$$$T₁ and$$$\;$$$T₂.

In Figure 3C, the absolute error between reconstructed and input displacement is shown for both the test sequence and theoretical predictions. Theory and experiment are in good agreement. Minimal displacement errors are found in the case of$$$\;\phi=158^\circ$$$.

In Figure 4, predicted magnitude variations are compared with MRE phantom experiments for TR=15ms. Pronounced spin-history dependent magnitude variations can be observed for spoiling angles of 0°, 2°, 3°, 90° and 150°.$$$\;$$$117°$$$\;$$$shows reduced artifacts especially in the background gel, whereas artifacts are visible in the right inclusion due to its longer$$$\;$$$T₂$$$\;$$$relaxation time. For$$$\;\phi=158^\circ$$$, no magnitude variation can be observed and overall contrast compares well with the reference image (bottom right).

Figure 5 depicts the displacement field difference to the reference scan (bottom right,$$$\;$$$TR=95ms). Low spoiling angles as well as disabled RF-spoiling show pronounced displacement error, which is spatially varying depending on relaxation properties. Estimates are improved using the standard RF spoiling angles of 117° and 150°, however, minimal error was again found in the case of$$$\;\phi=158^\circ$$$.

Conclusion

The use of RF-spoiling in GRE-MRE, especially when employing short repetition times (e.g. in 3D scans), is necessary to reduce biases in displacement estimates. While default spoiling angles are helping in reducing transverse coherences, an optimal spoiling angle of$$$\;\phi=158^\circ\;$$$could be identified for Ristretto MRE with four wave phase offsets, allowing bias-free displacement field estimation at repetition times as low as 5ms. Due to the strong dependence on the exact phase accrual, further analysis is warranted regarding different number of wave phase offsets and Ristretto phase interleave orderings before 158° can be established as a general optimized spoiling angle.

Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 668039.

References

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Figures

Figure 1: (A) Ristretto GRE-MRE sequence with RF and gradient spoiling. The sequence interleaves wave phase acquisitions allowing for fast multi-slice and 3D Elastography. (B) Proposed test sequence to study the influence of RF spoiling on displacement encoding. The MEG of (A) is replaced by a unipolar gradient in readout direction, which is stepped as a function of time according to a sinusoidal pattern (C) leading to periodic phase accrual as in MRE. The apparent displacement amplitude is directly proportional to the position in readout direction relative to the isocenter.

Figure 2: EPG simulation results depicting the influence of RF spoiling on the MR signal magnitude and the reconstructed displacement for different repetition times and relaxation parameters. Signal magnitude fluctuations of up to 34% are observed without RF spoiling and short TR. Reconstructed displacement errors are dependent on relaxation properties and the choice of spoiling angle, resulting in two orders of magnitude change in relative displacement error. An optimal spoiling angle of Φ=158° could be identified. T₁/T₂ values were chosen for liver tissue at 3T.

Figure 3: (A) pictorial description of the processing steps for the test sequence data showing the unwrapped phase images for each of the four simulated wave-phase offsets. While n=1 & 3 should show no phase accrual (encoding gradient off), phase fluctuations can be observed resulting from spin-history effects.

(B) shows the difference between encoded and reconstructed displacement for three different TR and four spoiling angles comparing theory (circles) with experimental results (lines). Minimal displacement error is found for Φ=158° as predicted in the EPG simualtions.

Figure 4: Comparison of magnitude images of the phantom measurements with TR=15 ms and 3D slab encoding. Magnitude variations are in qualitative agreement with the depicted theoretical signal variation. Pronounced magnitude variations can be observed for no and low RF spoiling angles and 90°. While the typical spoiling angle of 117° leads to artifact reduction, at 150°, magnitude variations remain pronounced. Minimal artifacts were found for 158°, with image contrast comparable to the reference image. Residual signal variations can be attributed to intra-voxel phase dispersion.

Figure 5: Comparison of displacement field differences relative to the reference acquisition (TR=95ms) and predicted maximal relative displacement errors for one exemplary slice and encoding direction. RMSE is calculated over the full FOV. No RF spoiling and low spoiling angles show maximal displacement error. At 33°, a pronounced increase in the displacement error can be observed in the right inclusion due to high T2 (marked). While 117° and 150° show a reduction in the error compared to no RF spoiling, minimal displacement error was again found for the optimal spoiling angle of 158°.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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