This study was approved by the institutional review board. The study was carried out in accordance with the ethical standards described by the Local Ethics Committee of the National Health Commission and was approved by the Ethics Committee of Tianjin Hospital (Ethics No.: 2024 Medical Ethics 174).

This study was a diagnostic accuracy design, and it was retrospective. From June 2020 to May 2023, we retrospectively analyzed patients who made appointments for knee specialist outpatient department in Tianjin Hospital, the patients were consecutive over this period. Patients were screened based on inclusion and exclusion criteria. Inclusion criteria: (1) history of anterior knee pain, (2) clear axial patellar radiographs and MRI images of patellofemoral joint, and (3) complete medical records. Exclusion criteria: (1) unavailable imaging modalities, (2) history of knee surgery, (3) history of knee trauma, (4) knee joint bone tumors, and (5) other conditions that may affect the recognition of the knee bone morphology, such as a severe osteoproliferation. After screening by inclusion and exclusion criteria, a total of 212 patients remained.

Patients were reviewed with electronic charts and imaging examinations by a senior knee specialist surgeon (16 years of clinical experience). At present, the definition of LPCS diagnosis is still obscure. As reported by Chen et al. [14]. and Migliorini et al. [5]. , the following were the main clinical manifestations of LPCS patients [15], which can be used as the definition of LPCS in this study: (1) history of anterior knee pain, (2) axial radiographs of the patella showed lateral patellar tilt (in the axial radiograph, the angle formed by the line through the longest axis of the patella and a horizontal line represented patellar tilt, and when the angle was greater than 5°, it was defined as lateral patellar tilt [8]) and/or displacement (in the axial radiograph, the distance between the perpendicular lines passing through the ridge of the patella and the deepest point of the trochlear groove to the horizontal line represented the patellar displacement, when the distance was greater than 5 mm, it was defined as patellar displacement [16]), resulting in narrowing of the lateral patellofemoral joint space, and (3) MRI showed the lateral patellofemoral joint cartilage injury (in T2-weighted fat-suppressed axial sequence, the Recht cartilage injury grading was used as the reference, the cartilage injury in this study referred to Recht grade III and IV [17]).

The (2) and (3) definitions of LPCS used as reference standards to distinguish between two groups of cases. Those meeting the reference standards were included in the LPCS group, other patients were included in the Control group.

All patients underwent axial radiographs of the patella and knee MRI. All examinations were performed using DR (DuraDiagnost, Philips, Amsterdam, Netherlands), 3.0-T MRI (MAGNETOM Skyra, Siemens, Erlangen, Germany). All patients used the same medical equipment and parameters. The imaging parameters used in this study were axial MRI (T2-weighted fat-suppressed axial sequence; TR 1613ms; TE 65ms; FOV 16 cm; matrix 320 × 224; slice thickness 5.5 mm) and axial radiograph (FOV 12 × 4 cm; 80 kV; 160 mA). For both groups, the following angles of axial radiographs of the patella were measured: PCA, TA, CA, AG, and LPA (Fig. 1). TA, CA, AG, and LPA were used to compare with PCA, as these four angles were commonly used to test patellar tilt and displacement in the patellar axial radiographs [6,7,8,9].

Radiographic technique: We referred to the Merchant´s view. The patient was in a supine position, the patient’s lower leg was placed on a brace at a pre-defined 30° flexion [8]. The radiology technician moved the X-ray tube and cassette, the X-ray tube was usually on the upper side of the head, tilted down 30° along the horizontal line and directed in the foot direction. The cassette was placed under the patient’s feet, parallel to their feet. The X-rays were parallel to the patellofemoral interspace, and the Cassette should be at 90° to the beam and to the patellofemoral interspace.

Our measurements were carried out using the image processing software (GCRIS, Carestream, Rochester, America) with an accuracy of 0.01°.

Fig. 2 shows the axial radiographs of the patella of patients in the LPCS group, and Fig. 3 shows the radiographs of patients in the Control group. The patellar ridge, lateral patellar facet of the patella, and lateral trochlear facet can be clearly identified in Figs. 2 and 3. The tangent line of the lateral patellar facet and the tangent line of the lateral trochlear facet were made from the lowest point of the patellar ridge. The angle formed by the two tangent lines is called the patellar compression angle, and the lines open laterally. The results of five imaging examinations used to detect LPCS, including the PCA, TA, AG, LPA, and CA were retrospectively evaluated.

Measurement of PCA angles in LPCS group patients on axial radiographs of the patella. a, d Axial radiographs of the patella at the Merchant position; b, e The red point represents the lowest point of the patellar ridge, the green point represents the inflection point of the tangent line of the lateral patellar facet, and the yellow point represents the highest point of the lateral trochlea. The line connecting the red and green points represents the tangent line of the lateral patellar facet, and the line connecting the red and yellow points represents the tangent line to the lateral trochlear facet through the lowest point of the patellar ridge. PCA angle consists of the angle between both lines. c, f PCA were 4.96° and 9.06°, respectively. (a, b, and c show LPCS caused by patellar tilt, and d, e, and f show LPCS caused by patellar displacement). PCA: Patellar compression angle

Measurement of PCA angles in Control group patients on axial radiographs of the patella. a, d Axial radiographs of the patella at the Merchant position; b, e The red point represents the lowest point of the patellar ridge, the green point represents the inflection point of the tangent line of the lateral patellar facet, and the yellow point represents the highest point of the lateral trochlea. The line connecting the red and green points represents the tangent line of the lateral patellar facet, and the line connecting the red and yellow points represents the tangent line to the lateral trochlear facet through the lowest point of the patellar ridge. PCA angle consists of the angle between both lines. c, f PCA were 16.26° and 18.76°, respectively. PCA: Patellar compression angle

All the angle measurements were independently conducted by two authors, both authors were specialized knee surgeons, they were blinded to any clinical information of all cases. All patients were examined twice at different times. The interval between measurements was at least 4 weeks. All participants were examined twice at different times to determine the intraobserver reliability. The tests were independently performed by the senior author (25 years of clinical experience), and another trained author (4 years of clinical experience). Two authors independently read the radiographic measurements to determine the interobserver reliability.

Statistical significance was set at p < 0.05. All continuous variable data were performed by Kolmogorov–Smirnov test. The independent-samples T test was used for comparison of all continuous variables, including Age, Height, Weight, and BMI. The chi-square test was used for categorical variables, including Laterality and Gender. The accuracy of the angles was assessed by using sensitivity, specificity, accuracy, positive predictive value (PPV), negative predictive value (NPV), positive likelihood ratio (PLR), and negative likelihood ratio (NLR). The reproducibility of the PCA was assessed with the intraclass correlation coefficients (ICCs), which determined the interobserver and intraobserver variation. Receiver operating characteristic (ROC) curve was plotted, and the area under the curve (AUC) was calculated. The cut-off value was derived from the point with the maximal Youden index, which corresponds to the highest sum of sensitivity and specificity, it was exploratory rather than prespecified. The closer the AUC is to 1, the better the diagnostic value. 95% CI of 5 angles for sensitivity, specificity, accuracy, PPV, and NPV were also calculated. The statistical analyses were performed with the SPSS 21.0 software package (SPSS Inc., Chicago, Illinois, USA).