Image evaluation

Quantitative measurements were undertaken on a PACS workstation (Greenland, version 6.0) with a dedicated monitor (Jusha, M11 M21 C21). Two senior musculoskeletal radiologists (with 20 and 16 years of experience, respectively) independently measured all parameters in the participants. The reliability between the measurements of the two reviewers was defined as the inter-observer reliability. After a minimum interval of 6 weeks, each MRI assessment was re-evaluated by the one of these two reviewers. The reliability between two measurements of the same reviewer was defined as the intra-observer reliability. The reliability of values of the most senior radiologist among two reviewers between two MRI scans was defined as the inter-scan reliability.

The parameters that were measured by superimposing image slices in the present study included the: (1) angle of Fulkerson [9], angle of Grelsamer [9], angle of Laurin [9], patellar tilt angle (PTA) [9, 10, 14], lateral patellar displacement (LPD) [15], bisect offset ratio (BSO) [10], and congruence angle (CA) [9] for patellar position; (2) sulcus angle (SA) [9, 14], lateral trochlear inclination (LTI) [14], and trochlear facet asymmetry (TFA) [14], and trochlear groove depth (TGD) [14, 16] for trochlear dysplasia; and (3) Insall–Salvati index (ISI) [9, 10, 14], modified Insall–Salvati index (MISI) [9], Caton–Deschamps index (CDI), Blackburne–Peel index (BPI) [13], and patellar trochlear index (PTI) [10, 14] for patellar height (Additional file 1, Figs. ​Figs.1,1, ​,22 and ​and3).3). The angle between the femoral shaft and the tibial shaft in MR images was defined as the flexion angle [11].

Measurements of patellar position: a the angle of Fulkerson is the angle between C and A; b the angle of Grelsamer is the angle between D and the horizontal axis; c the angle of Laurin is the angle between C and B; d patellar tilt angle (PTA) is the angle between D and A; e lateral patellar displacement (LPD) is the shortest distance between E and F; f bisect offset ratio (BSO) = L/P; and (g) congruence angle (CA) is the angle between G and H

Measurements for trochlear dysplasia: a sulcus angle (SA) is the angle between M and L; b lateral trochlear inclination (LTI) is the angle between I and A; c trochlear facet asymmetry (TFA) = M/L; and (d) trochlear groove depth (TGD) = (M + L)/2 − J

Measurements for patellar height: a Insall–Salvati index (ISI) = C/A; b modified Insall–Salvati index (MISI) = E/B; c Caton–Deschamps index (CDI) = D/B; d Blackburne–Peel index (BPI) = F/B; and (e) patellar trochlear index (PTI) = G/B