{"doi":"10.1002/nbm.4535","title":"Characterization of anisotropic T2W signals from human knee femoral cartilage: The magic angle effect on a spherical surface","abstract":"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.","journal":"NMR in Biomedicine","year":2021,"id":183355,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":13,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9511,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":536401,"name":"Yuxi Pang","orcid":"0000-0001-5039-0236","position":0,"is_corresponding":true}],"reference_count":47,"raw_metadata":null,"created_at":"2026-07-18T23:48:22.008011Z","pmid":"33963785","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}