Synopsis

Magnetic Resonance Elastography (MRE) is performed by the application of motion-sensitive gradients. In this study, RF pulses are designed with an optimal control algorithm to obtain a desired magnetization phase distribution. Such pulse, in presence of a constant gradient, allows to simultaneously perform spatially selective excitation and motion encoding. This offers some advantages when compared to standard MRE encoding strategy. Simulations, phantom and ex vivo experiments show that phase-to-noise ratios are improved. These results demonstrate that optimal control-based pulses can be used to encode motion in the MRE excitation phase with relevant advantages for further in vivo liver rat studies.

Introduction

MRE has become a valuable technique to quantify mechanical properties of tissues based on the characteristics of shear waves propagation. Conventionally, motion encoding gradients are applied between RF excitation and signal acquisition yielding phase images that depict the propagation of the shear wave¹. The drawback of this technique is a longer echo-time and thus a degraded SNR. For that purpose, we propose to use a single RF excitation pulse that could simultaneously enable the slice selection and the motion encoding in the phase of the MR signal while also maximizing its norm. To this end, we use the optimal control (OC) formalism to design this RF pulse.

Methods

The application of optimal control theory to MRE consists in designing OC RF pulses which manipulate the magnetization ($$$\vec{M}$$$), whose evolution is governed by Bloch equations, towards a target state in which the isochromats phase is directly linked to the phase of the wave motion they are experiencing² while also taking into account the T2 so as to maximize the transverse magnetization. The OC pulse computation is performed with the GRAPE algorithm³.

In the OC MRE strategy, the RF pulse is applied simultaneously with a constant gradient.This imposes slice selectivity⁴ by considering isochromats located at different positions in the slice ($$$z^{(j)}$$$). Consequently to the application of the constant gradient G and sinusoidal shear wave motion at frequency $$$f_e$$$, static field variations experienced by an isochromat in position $$$θ^{(i)}$$$ along the propagating shear wave and $$$z^{(j)}$$$ in the slice direction are given:

$$ΔB_0^{(i,j)}(t)=G(Asin(-2πf_et+θ^{(i)})+z^{(j)})$$

Different target states will be attributed whether an isochromat is located in ($$$Δz_{in}$$$) (the selected slice) or in ($$$Δz_{out}$$$), as illustrated in Fig. 1.

$$ \vec{T}^{(i,j)}=ρ(CosΦ^i,SinΦ^i,0) ~~ if ~~ j\inΔz_{in}$$

$$ \vec{T}^{(i,j)}=(0,0,1) ~~ if ~~ j\inΔz_{out}$$

The defined cost function :

$$ C=\sum_{j=1}^{J}\sum_{i=1}^{N}\parallel\vec{M}^{(i,j)}(t_f)-\vec{T}^{(i,j)}\parallel^2$$

requires minimizing the difference between final magnetization state ($$$\vec{M}^{(i,j)}$$$) and target state ($$$\vec{T}^{(i,j)}$$$) of the $$$(i,j)$$$ spin ensemble.

The OC-MRE strategy was compared to standard MRE, through phantom and ex vivo MRE experiments. MRI measurements were run on a Bruker 4.7 T small-animal MRI-system, with a 70mm inner diameter volume coil. Shear waves were generated using a piezoelectric actuator (CEDRAT Technologies). Phantom experiments were carried out on a 100% plastisol (suspension of polyvinyl chloride particles in a liquid plasticizer) phantom5 whose relaxation times [T1, T2] = [300, 25] ms. Ex-vivo experiments were performed on a piece of bovine liver; relaxation times [T1, T2] = [650, 30] ms. The OC-pulse was optimized for an excitation frequency of 400Hz, a T2=20ms and a duration of 13.8ms. We used a RARE MRI sequence with parameters described in table 1. For the standard MRE, a conventional RARE MRE sequence was used, with an equal number of sinusoidal gradient periods (N_G = 2,4,6,8 for phantom and 2,4 for ex-vivo) before and after the refocusing pulse.

Results

Fig. 2. illustrates the B1 pulse magnitude obtained and the corresponding simulated and experimentally measured slice profiles demonstrating correct in-slice homogeneity and selectivity. Fig. 3. illustrates the phase images obtained on ex-vivo and phantom experiments. Fig. 4. compares phantom and ex vivo, standard and OC-MRE acquisitions. For standard acquisitions, increasing N_G increases the phase encoding (Δ) but decreases SNR. Computing a phase-to-noise ratio; PNR=Δ×SNR, accounts simultaneously for both. For phantom experiments, the OC-MRE produces good values of Δ while yielding the best SNR resulting in higher PNR. Furthermore, despite the difference between liver’s T2 and the optimized T2, ex-vivo OC-MRE results show that OC-MRE still outperforms standard MRE.

Conclusion and Discussion

Acknowledgements

References

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