Introduction

Osteoarthritis (OA) is a multi-systemic degenerative disease characterised by structural and biochemical deterioration of the hyaline articular cartilage ¹. It is also one of the most common and disabling joint diseases ¹. Quantitative MRI techniques such as T₁ and T₂ mapping provide relevant information on macromolecular changes in cartilage and are a promising effective and non-invasive approach to identify early cartilage degeneration ². However, conventional T₁ and T₂ mapping techniques require long acquisition times and are usually performed sequentially in separate 2D scans ³. Furthermore, most approaches are limited to anisotropic resolution to reduce scan time. The aim of this study is to determine the feasibility of a recently proposed free-running T₁- T₂ mapping 3D radial sequence ⁴ to enable multiparametric characterization of articular cartilage with isotropic spatial resolution of 1mm³ in ~4 min scan time.

Methods

The proposed knee joint T₁-T₂ mapping sequence consists of water-selective spoiled gradient echo readout with a 3D golden-angle radial trajectory ⁴. Each shot interval is preceded by an inversion recovery (IR) pulse and a T₂ preparation pulse (T_2-prep) with varying echo times of 0 ms (no T_2-prep), 30 ms and 60 ms, respectively. This acquisition pattern is repeated to provide enough T₁ and T₂ encoding (Figure 1).

The proposed approach was evaluated on a standardized T1MES phantom ⁸ and in-vivo experiments in a healthy subject. Acquisitions were performed on a 3T scanner (Philips, Ingenia) with a 16-channel knee coil. Main acquisition parameters include: FOV= 120 mm, isotropic resolution= 1 mm, flip angle = 6°, TR/TE=10.3 ms/ 4.1ms, acquisition pattern repeated 100 times with 195 readouts in each shot, IR repetition time = 2200 ms, total scan time = 4.5 min.

After the acquisition data was binned into 10 different IR times for eachT₂-prep. The reconstruction of 5 compressed contrasts ⁵ was performed using dictionary based low rank inversion with high-dimensional patch-based low-rank regularization (HD-PROST) ⁶. The dictionary D, which provides the signal evolution for different combinations of T₁ and T₂ values, was generated using Bloch simulations. Values for T₁ were between 200 ms and 3000 ms with increments of 2%, and values for T₂ were between 10 ms and 250 ms with increments of 1%.

Images were recovered by minimizing the following Lagrangian with ADMM:
$$L(x,T, Y)=∥Ex−Wk∥^2_2+λ∑_p∥T_p∥_∗+μ/2∑_p∥T_p−Pp(x)−P_p(Y)∥^2_F$$

Where $$$x∈C^{(Nr×1)}$$$ is the multi-contrast complex image with $$$N$$$ voxels and $$$r$$$ different singular images corresponding to the first $$$r$$$ singular values of the dictionary compression, $$$k∈C^{KN_c×1}$$$ is the k-space acquired data with $$$K$$$ samples and $$$N_c$$$ coils, $$$W$$$ is a k-space density compensation matrix, $$$E=WFU_rS$$$ is the encoding operator with $$$S∈C^{NN_cr×Nr}$$$ the estimated sensitivity maps, $$$F∈C^{KN_c×NN_cL}$$$ the non-uniform Fourier transform operator with $$$L$$$ the total number of contrasts, and $$$U_r∈R^{NN_cL×NN_cr}$$$ the compressed signal-evolution dictionary with the highest $$$r$$$ singular values of the dictionary compression. $$$T_p$$$ is the HD-PROST tensor formed with similar patches centered at voxel $$$p$$$, $$$P_p(∙)$$$ is the patch-selecting operator centred at voxel $$$p$$$, $$$Y$$$ are the augmented Lagrange multipliers, $$$λ$$$ and $$$μ$$$ are regularization parameters, and $$$∥∙∥_*$$$ , $$$∥∙∥_F$$$ are the nuclear and Frobenius norms. Main reconstruction parameters were set to $$$r=5$$$, $$$λ=0.04$$$.

After obtaining $$$x$$$, a phase-sensitive dictionary matching was used to obtain T₁ and T₂ maps. Transverse magnetization sign was recovered for each complex-image ⁷ and a real image $$$x_s$$$ was obtained. Dot-product matching was performed between the previously generated dictionary $$$D$$$ and $$$x_s$$$ to estimate the maps.

Results

Phantom: Proposed joint T₁ and T₂ maps for the standardized phantom are shown in Figure 2. Correlation plots between the T₁ and T₂ values obtained for each vial with the proposed approach and reference values provided by the vendor. T₁ and T₂ values measured with the proposed approach are in very good agreement with reference values for the range of interest, with high values (higher than ~1500 ms for T₁ and higher than ~150 ms for T₂) being over-estimated for T₁ and under-estimated for T₂, because of the choice of echo times for -prep and IR time.
Healthy subject: Proposed joint T₁ and T₂ maps for a representative healthy subject is shown in Figure 3 in all three orthogonal dimensions. The T₁ and T₂ values of the hyaline cartilage of the knee using the proposed simultaneous free-running T₁-T₂ sequence were T₁ = 898.99 ± 83.73 ms and T₂= 22.91 ± 3.79 ms, which are in agreement with clinical values reported in the literature ^2,3 which corresponds to T₁=907.42 ± 140.53 ms and T₂ = 34.74±2.48 ms.

Discussion and conclusion

In this study we demonstrate the feasibility of simultaneous joint T₁-T₂ mapping of the knee with a free-running 3D radial sequence for quantitative evaluation of hyaline articular cartilage with isotropic spatial resolution of 1 mm³ in ~4 min total scan time. The proposed approach achieves T₁ and T₂ values comparable to reference values reported in the literature. Further studies will compare the proposed approach against conventional mapping in healthy subjects and patients with osteoarthritis.

References

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