Data-Driven Characterization of Knee Structures Using Non-Negative Matrix Factorization of 3D Multi-Echo UTE MRI

T₂* quantification based on multi-echo ultrashort echo time (UTE) MRI has been widely proposed for knee tissue characterization, yet accurate model-based parameter estimation remains challenging due to ill-conditioning of the corresponding inverse problems. Alternatively, data-driven methods such as non-negative matrix factorization (NMF) can derive tissue features without relying on biophysical model assumptions. This study aimed to investigate the use of an NMF-based framework informed by 3D multi-echo UTE MRI for multi-compartmental analysis of healthy and impaired knee structures. To this end, six asymptomatic adults and 13 patients underwent 3-T MRI, including routine anatomical sequences, and a 3D UTE spiral research sequence with six echo times. Convexity-constrained NMF was used to identify characteristic signal components from UTE T₂*-weighted datasets. Basis functions were determined based on asymptomatic knee data and used to compute subject-specific weight maps. Normalized weight distributions were computed for 13 regions of interest across asymptomatic knees and contrasted with median weights of selected structures in patients. The application of the NMF-based framework yielded four reproducible basis functions associated with fast decay, slow decay, water-fat mixing, and fat-like behavior. Knee structures with known short T₂* showed a dominant fast-decaying component (median weights ≥ 0.68), while structures with long T₂* showed a greater contribution from the slowly-decaying component (median weights ≥ 0.44). The fat-like component was predominant in Hoffa's fat pad, while the water-fat mixture-related component's contribution was overall low. Lesioned menisci and ligaments generally displayed reduced fast-decaying and increased slowly decaying component contributions. These findings suggest that convexity-constrained NMF of 3D multi-echo UTE MRI is feasible for data-driven knee tissue characterization as it extracts biophysically related signal components and describes their relative contribution to the measured signal in various knee tissues. Moreover, the proposed framework shows potential for differentiation between asymptomatic and impaired knee tissues, particularly in the posterior horn of the medial meniscus and the anterior cruciate ligament, and consequently holds promise for more objective diagnosis and monitoring of internal knee derangements.