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 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.

Orientation dependent proton transverse relaxation in the human brain white matter: The magic angle effect on a cylindrical helix

“…To our knowledge, this is the first time to combine the most relevant degrees of molecular motions for characterizing highly organized microstructures in WM. 26, 28 Second, this proposed model is a generalized MAE model, 24, 25 applied to not only ordered “liquid-like” water on the surface but also dynamic “solid-like” CH2 protons in the interior of bilayers. Further, it can be also used in peripheral nervous system, not to mention other tissues, 25 where ordered water seemed uniformly ( α ≈ 0 ° ) aligned in elongated collagenous tissues as shown in Supplementary Figure S2.…”

“…26, 28 Second, this proposed model is a generalized MAE model, 24, 25 applied to not only ordered “liquid-like” water on the surface but also dynamic “solid-like” CH2 protons in the interior of bilayers. Further, it can be also used in peripheral nervous system, not to mention other tissues, 25 where ordered water seemed uniformly ( α ≈ 0 ° ) aligned in elongated collagenous tissues as shown in Supplementary Figure S2. 58 Third, this generalized model is built upon residual dipolar interactions, 24, 25 fundamentally different from those based on tensorial magnetic susceptibility.…”

“…Further, it can be also used in peripheral nervous system, not to mention other tissues, 25 where ordered water seemed uniformly ( α ≈ 0 ° ) aligned in elongated collagenous tissues as shown in Supplementary Figure S2. 58 Third, this generalized model is built upon residual dipolar interactions, 24, 25 fundamentally different from those based on tensorial magnetic susceptibility. Theoretically, 14 the susceptibility-induced proton transverse relaxation rate is quadratically scaled with the strength of B 0 ; as a result, this relaxation pathway will become more relevant only at a higher B 0 .…”

“…38, 39 A general function of orientation-dependent R 2 has been obtained by averaging ( 3 cos 2 θ − 1) 2 in an axially symmetric system. 24, 25 Equations 1 and 2 provide respectively the reformatted 25 and the original 24 functions with pertinent angles defined as before and depicted in Figure 2C. The angle θ , formed between <H-H> and B 0 , can be expressed by three different angles α, ε and φ denoting respectively between <H-H> and the symmetry axis , between and B 0 , and the azimuthal angle of <H-H>.…”

“…23 A general form of MAE function has long been available 24 and lately reformatted to gain further insight into proton transverse relaxation orientation dependences. 25…”