Synopsis

Keywords: Quantitative Imaging, Quantitative Imaging

MR-STAT is a framework for simultaneously acquiring multi-parametric quantitative maps from one single short scan. In this work, we design a new 3D MR-STAT sequence and the corresponding two-step reconstruction strategy based on previous work. The framework is improved by designing a faster acquisition framework, and more accurate signal modeling for reconstruction. The proposed sequence takes 7 minutes after retrospectively undersampling, and is validated in a phantom experiment. Furthermore, we apply this 3D MR-STAT sequence the first time for musculoskeletal applications. Knee and lower-leg experiments of healthy volunteers are shown here.

Introduction

MR-STAT is a framework for simultaneously acquiring multi-parametric quantitative maps from one single short scan¹. MR-STAT computes the quantitative tissue parameters, typically T1, T2 and proton density (PD), by solving the following large-scale, nonlinear optimization problem
$$ \alpha^* = \arg \min_\alpha || d - s(\alpha)||_2^2, (1)$$
where $$$s$$$ is the measured k-space data, $$$\alpha$$$ encapsulates all the parameter maps, and $$$s$$$ is the transient-state volumetric signal model. A two-dimensional MR-STAT acquisition uses a gradient-spoiled sequence with a smoothly varying flip-angle train and linear, Cartesian readouts².

Three-dimensional MR-STAT³, compared to 2D acquisitions, allows for an increased SNR and better through-plane resolution. Challenges of the 3D MR-STAT include a prelonged scan time for high-resolution acquisition and the computational burden for accurate 3D model-based reconstruction. To overcome these challenges, we improve our 3D MR-STAT framework based on the previous abstract³, by applying a new acceleration scheme to reduce scan time and optimizing the signal model for accurate and fast quantitative reconstruction.
Currently MR-STAT has primarily been demonstrated in brain⁴, however, quantitative MRI is also relevant for evaluating pathological changes in muscle disorders and degenerative joint diseases^5,6. Therefore we apply the new 3D MR-STAT sequence for musculoskeletal applications in this work. The proposed new 3D sequence takes 7 minutes with retrospective undersampling, and is validated in a phantom experiment. In-vivo feasibility is demonstrated in the knee (0.8x0.8x1.5mm^3 resolution) and lower-leg (1-mm isotropic resolution) of healthy volunteers.

Method

• Sequence design

A 2D MR-STAT acquisition consists of a Cartesian, gradient-spoiled, gradient-echo sequence with smoothly varying flip-angles and linearly increasing phase-encoding (ky) lines sequentially covering five k-spaces. A 3D MR-STAT sequence can be realized by repeating the 2D sequence as short segments for all additional kz phase-encoding lines. In order to reduce the scan time, an undersampling strategy is applied to both phase-encoding directions, leading to a total undersampling factor of 4 [Fig. 1(a)]. A SENSE undersampling factor of 2 is realized in the ky direction, which shortens the length of the 3D segments, and an additional alternating 2-fold undersampling pattern is applied in the kz direction, resulting into an overall under-sampling factor of 4.
The 3D MR-STAT sequence was implemented on a 3T system (Philips, Elition) with prospective ky-undersampling (R=2, dashed and solid bullets in Fig.1(a)). The kz direction undersampling is applied retrospectively (R=4, dashed bullets following the yellow trajectory). The flip-angle train used for the 3D segments is shown in Fig.1(b), which consists of 4 sine-square lobes over 5 undersampled ky phase-encoding lines⁷. To allow for higher T1 sensitivity and SNR, each 3D segment starts with an adiabatic inversion pulse and a 1.75-second waiting time is inserted between segments for longitudinal signal recovery. Note that the 1.75s waiting time is not sufficient for all spins to return to initial equilibrium states, however after the initial 3 to 4 repetitions of the 3D segments, the temporal MR signal responses remain stable for latter repetitions of different kz lines, reaching to a “hyper steady-state”⁸.
The 3D MR-STAT sequence is tested on a Eurospin gel-tube phantom, a knee and a lower-leg (healthy volunteers). All two-fold prospectively under-sampled scans take 14 minutes(R=2) and are virtually shortened to 7 minutes by retrospectively under-sampling(R=4). The sequence parameters are summarized in Table1. A 20-second low-resolution, multi-slice B1 DREAM sequence is run for B1⁺ correction⁹.

• Reconstruction

Reconstructing the large-scale, 3D volumetric MR-STAT data directly using model (1) can be extremely challenging in terms of computer memory and reconstruction time. In order to overcome this problem, we split the 3D reconstruction in two sub-steps: First, a 3D SENSE reconstruction is run for each of the 5 undersampled 3D k-space data to acquire the “fully-sampled” k-space data. Subsequently, the “fully-sampled” k-space data are decoupled along the kz direction such that the 3D problem is decoupled into normal 2D MR-STAT reconstruction¹⁰, which takes approximately 3 to 5 minutes to reconstruct one slice. Note that in the first step, the undersampled transient-state k-space data are in a "hyper steady-state" along the kz direction, and smoothly varying along the ky direction, therefore making the 3D SENSE decoupling possible.

Results

Fig.2 shows the results for the gel phantom experiment. T1 and T2 values computed from both 14-minute(R=2) and 7-minute(R=4) MR-STAT data show high agreements with the gold standard results (computed from inversion- recovery and single spin-echo scans). Noises measured from 7-minute reconstruction results are approximately 20% higher than the 14-minute results.
Fig.3 and Fig.4 show representative reconstructed slices (sagittal and transverse) from the knee and lower-leg experiment. Several ROIs (cartilage, muscle, fat, etc.) are manually drawn on these 2D slices, and corresponding statistics are summarized in Fig.3(c) and Fig.4(c), showing that the reconstructed values are in the range of literature values^11-14.

Conclusion and Discussion

We demonstrated that our 3D MR-STAT sequence can be used for acquiring volumetric quantitative maps with high quality. The 7-minute retrospectively undersampled sequence is demonstrated for knee and lower-leg quantitative imaging. In the future we will prospectively validate the accelerated 3D sequence, and higher acceleration rate and more efficient undersampling strategy will also be investigated. Multi-echo acquisition and multi-compartment reconstruction for water-fat separation will be subject of future work.

Acknowledgements

No acknowledgement found.