Compressed sensing in quantitative determination of GAG concentration in cartilage by microscopic MRI

Abstract

Purpose: To evaluate the potentials of compressed sensing (CS) in MRI quantification of glycosaminoglycan (GAG) concentration in articular cartilage at microscopic resolution.

Methods: T₁ -weighted 2D experiments of cartilage were fully sampled in k-space with five inversion times at 17.6 μm resolution. These fully sampled k-space data were re-processed, by undersampling at various 1D and 2D CS undersampling factors (UFs). The undersampled data were reconstructed individually into 2D images using nonlinear reconstruction, which were used to calculate 2D maps of T₁ and GAG concentration. The values of T₁ and GAG in cartilage were evaluated at different UFs (up to 16, which used 6.25% of the data). K-space sampling pattern and zonal variations were also investigated.

Results: Using 2D variable density sampling pattern, the T₁ images at UFs up to eight preserved major visual information and produced negligible artifacts. The GAG concentration remained accurate for different sub-tissue zones at various UFs. The variation of the mean GAG concentration through the whole tissue depth was 1.20%, compared to the fully sampled results. The maximum variation was 2.24% in the deep zone of cartilage. Using 1D variable density sampling pattern, the quantitative T₁ mapping and GAG concentration at UFs up to 4 showed negligible variations.

Conclusion: This study demonstrates that CS could be beneficial in microscopic MRI (µMRI) studies of cartilage by acquiring less data, without losing significant accuracy in the quantification of GAG concentration. Magn Reson Med 79:3163-3171, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Keywords: GAG; MRI; T1; anisotropy; cartilage; compressed sensing.

Figure 1

The reconstructed 2D T1-weighted images using three different 2D sampling patterns at an under-sampling factor of 4, at two different inversion times, (i–p: the inversion time of 0.0 s; q–x: the inversion time of 1.1s, which had lower SNR). The fully sampled images were also shown as the ground truth in a. The point spread function (PSF) images for different sampling patterns were shown in Fig 1e–1h. The quality of the reconstructed T1-weighted images was sensitive to the sampling patterns. The optimized sampling pattern was illustrated in Fig 1b with p_a = 1.8, and p_b = 3.6. SZ: superficial zone; TZ: transitional zone; RZ: radial zone. “10X” in the figure label means that the display scale (the up limit) has been reduced to 1/10 to show more clearly the differences between the ground truth and CS reconstructed images.

Figure 2

The optimized k-space sampling patterns at different under-sampling factors (UF), T1b maps, and the corresponding error maps from the fully sampled k-space data (a–c: 1D k-space sampling patterns; d–f 2D k-space sampling patterns). The reconstructed T1b maps are found to be visually comparable with the references at UF up to 4 (1D patterns) and 8 (2D patterns), with major information qualitatively preserved and negligible artifacts, while the reconstructed relaxation maps have worse quality at UF of 8 and 16 (1D patterns) and 16 (2D patterns). (T1b: T1 mapping before Gd administration; T1a: T1 mapping after Gd administration).

Figure 3

Quantitative T_1b and T_1a profiles (a, b), GAG concentration profiles (c, d), and the mean GAG concentration values (e, f) at different under-sampling factors (1, 2, 4, 8, 16) from articular surface (0 μm) to cartilage-bone interface (~ 640 μm). The left half and the right half of the figure used 2D and 1D under-sampling patterns, respectively. T1b, T1a, and the GAG concentration profiles using compressed sensing were very consistent with the fully sampled data using 2D under-sampling pattern, while the profiles varied significantly at 1D under-sampling factors of 8 and 16 (arrows). Little variation of the mean GAG concentration value was found even at a 2D under-sampling factor of 16 (e), while bigger variations were noticeable at 1D under-sampling factors of 8 and 16.

Figure 4

Minimum variations in the T1b, T1a, and GAG concentration in the three histological zones of articular cartilage at various 1D (right) and 2D (left) under-sampling factors (1, 2, 4, 8, 16). Little variation of T1a, T1b, and GAG concentration at any sub-tissue zones was found even at a 2D under-sampling of 16. (SZ: superficial zone; TZ: transitional zone; URZ: upper radial zone; LRZ: lower radial zone.)