Department of Radiology, University of Michigan, Ann Arbor, Michigan, USA.
NMR Biomed. 2021 Jul;34(7):e4535. doi: 10.1002/nbm.4535. Epub 2021 May 8.
The aim of the current study was to propose a generalized magic angle effect (gMAE) function for characterizing anisotropic T2W signals of human knee femoral cartilage with a spherical surface in clinical studies. A gMAE model function f(α, ε) was formulated for an orientation-dependent (ε) transverse T (i.e., 1/R ) relaxation in cartilage assuming an axially symmetric distribution (α) of collagen fibers. T2W sagittal images were acquired on an adult volunteer's healthy knee at 3 T, and ROI-based average signals S(ε) were extracted from angularly and radially segmented femoral cartilage. Compared with the standard MAE (sMAE) functions in the deep (DZ, α = 0°) and in the superficial (SZ, α = 90°) zones, a general form of R orientation-dependent function f(α, ε) was fitted to S(ε), including an isotropic R contribution (internal reference [REF]). Goodness of fit was evaluated by root-mean-square deviations (RMSDs). An F-test and a paired t-test were respectively used to assess significant differences between the observed variances and means, with statistical significance set to p less than .05. As a symmetric orientation-dependence function with a varying dynamic range, the proposed gMAE model outperformed the previous sMAE functions manifested by significantly reduced RMSDs in the DZ (0.239 ± 0.122 vs. 0.267 ± 0.097, p = .014) and in the SZ (0.183 ± 0.081 vs. 0.254 ± 0.085, p < .001). The fitted average angle α (38.5 ± 34.6° vs. 45.1 ± 30.1°, p < .43) and REF (5.092 ± 0.369 vs. 5.305 ± 0.440, p < .001) were smaller in the DZ than those in SZ, in good agreement with the reported collagen fibril microstructural configurations and the nonbound water contribution to R in articular cartilage. In conclusion, a general form of the magic angle effect function was proposed and demonstrated for better characterizing anisotropic T2W signals from human knee femoral cartilage at 3 T in clinical studies.
本研究旨在提出一种广义魔角效应（gMAE）函数，用于描述具有球面的人体膝关节股骨软骨各向异性 T2W 信号。假设胶原纤维呈轴对称分布（α），建立了一个各向异性（ε）横向 T 弛豫（即 1/R）的 gMAE 模型函数 f(α, ε)。在 3T 下对一名成年志愿者健康膝关节进行矢状 T2W 图像采集，并从角度和径向分割的股骨软骨中提取基于 ROI 的平均信号 S(ε)。与深部（DZ，α=0°）和浅层（SZ，α=90°）的标准 MAE（sMAE）函数相比，拟合了包括各向同性 R 贡献（内部参考[REF]）在内的一般形式的 R 取向依赖函数 f(α, ε)。通过均方根偏差（RMSD）评估拟合优度。分别使用 F 检验和配对 t 检验评估观测方差和均值之间的显著差异，统计学意义设置为 p<.05。作为一种具有变化动态范围的对称取向依赖性函数，所提出的 gMAE 模型优于先前的 sMAE 函数，表现为 DZ（0.239±0.122 比 0.267±0.097，p=.014）和 SZ（0.183±0.081 比 0.254±0.085，p<.001）的 RMSD 显著降低。拟合平均角度 α（38.5±34.6°比 45.1±30.1°，p<.43）和 REF（5.092±0.369 比 5.305±0.440，p<.001）在 DZ 中小于 SZ，与报道的胶原纤维微观结构构型和关节软骨中 R 的非结合水贡献一致。总之，提出并验证了一种通用形式的魔角效应函数，用于更好地描述 3T 下人体膝关节股骨软骨各向异性 T2W 信号在临床研究中的特征。
