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

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 2 (i.e., 1/ R 2 ) 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 2 orientation‐dependent function f ( α ,  ε ) was fitted to S ( ε ), including an isotropic R 2 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 2 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.