Characterization of anisotropic T2W signals from human knee femoral cartilage: The magic angle effect on a spherical surface

Abstract

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 T2 (i.e., 1/R2) 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 R2 orientation‐dependent function f(α, ε) was fitted to S(ε), including an isotropic R2 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 R2 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.A generalized magic angle effect (gMAE) function was formulated based on an axially symmetric collagen fibril distribution to better characterize anisotropic T2W signals of cartilage on a curved surface. Compared with the standard MAE models, the proposed function provided significantly improved fitting of segmented T2W signals from an adult healthy knee femoral cartilage at 3 T. The potential applications of the proposed model function could be extended to other highly organized biological tissues beyond human knee articular cartilage.