Participants

This prospective study was approved by the Committee for Human Research of our institution (No. 2023-139). Participants were recruited consecutively from January 2023 to September 2023. Two senior orthopedic surgeons took a history and conducted the physical examinations to include and exclude all the patients and controls. The RPD group included patients who have experienced at least two dislocations. The exclusion criteria were as follows: (1) prior knee surgery; (2) osteoarthritis (≥ Kellgren-Lawrence grade 3). For ethical reasons, the control group included patients requiring lower limb CT scans, such as those with lower limb injuries, benign tumors, etc. The healthy sides were included in the control group, and the affected sides were also included when there was no involvement of the patellofemoral joint. The exclusion criteria were the same as those used to exclude RPD patients.

WBCT protocol

The WBCT device (DTP580B-3 Angell Technology, Shenzhen, China) has a motorized standing platform between the X-ray tube and flat panel detector. During the scanning, the subject stood with the lower limbs fully extended and was uniformly rotated by the motorized platform for 3D data acquisition. The imaging protocol was as follows: display field of view 300 × 300 × 300 mm, reconstruction thickness 1 mm, reconstruction slice spacing 1 mm, tube output 110 kV and 5 mA, source to image distance 120 cm, scan time 29 s (Fig. 1a).

Fig. 1

a Examination of weight-bearing CT. b Examination of non-weight-bearing CT

NWBCT protocol

The NWBCT images were acquired using conventional CT (Aquilion ONE, Canon Medical Systems, Otawara, Japan). The subject was in supine position with the lower limbs fully extended and relaxed. Imaging protocol was as follows: display field of view 250 × 250 × 160 mm, slice thickness 0.5 mm, slice spacing 0.5 mm, tube rotation 0.5 s, and tube output 100 kV and 70 mA (Fig. 1b).

3D measurement

Two fellowship-trained musculoskeletal radiologists (A and B, with 2 and 9 years of clinical experience, respectively) independently performed the 3D measurements after all the data of the two groups had been mixed blindly and randomly distributed. Furthermore, all measurements were repeated by one of the radiologists (B), with an interval between the first and second measurements of at least 4 weeks.

Generation of 3D bone models

Images in DICOM format were imported into Mimics software (21.0, Materialise, Haasrode, Belgium) to create 3D bone models of knees.

Definition of bony landmarks and lines

Landmarks were defined in Mimics and both 3D models and CT images were used to increase precision of landmark location.

Medial femoral condyle (MFC), lateral femoral condyle (LFC), Roman arch (RA) [24], patellar superior point (PSP), patellar inferior point (PIP), patellar medial point (PMP), patellar lateral point (PLP), patellar central ridge (PCR), patellar oblique diameter (POD) and patellar transverse diameter (PTD) were defined (Fig. 2).

Fig. 2

Definition of bony landmarks and lines. Medial femoral condyle (MFC): the most prominent point on the medial facet of the femoral condyle; lateral femoral condyle (LFC): the most prominent point on the lateral facet of the femoral condyle; Roman arch (RA): the deepest point of the classic Roman arch; patellar superior point (PSP): the most superior point of the patella; patellar inferior point (PIP): the most inferior point of the patella; patellar medial point (PMP): the most medial point of the patella; patellar lateral point (PLP): the most lateral point of the patella; patellar central ridge (PCR): the central ridge of the patella; patellar oblique diameter (POD): the line between PSP and PIP; patellar transverse diameter (PTD): the line between PMP and PLP

Establishment of coordinate system

The midpoint of MFC and LFC was defined as the origin. The line between MFC and LFC from the medial to lateral direction was defined as the X-axis. MFC, LFC and RA made up the X0Y plane. The normal vector of the X0Y plane over the origin from the inferior to superior direction was set as the Z-axis. The Y-axis from the posterior to anterior direction was set to fit the rule of a Cartesian coordinate system of 3D space (Fig. 3).

Fig. 3

Establishment of coordinate system

3D measurement of patellar position

The 3D models, landmarks, and lines were imported into a 3-matic module of Mimics. All the measurements were performed based on user-defined coordinate system.

The spatial displacement of the patella relative to the femur was simplified to shift of the center of the patellar ridge relative to the origin on three axes (Xshift, Yshift, Zshift). Lateral, anterior and superior displacement were designated as positive, while medial, posterior and inferior as negative.

Tilt of the patella around the X-axis (Xtilt) was defined as the angle between POD and X0Z plane, and posterior tilt was designated as positive. Tilt around the Y-axis (Ytilt) was defined as the angle between PTD and X0Y plane, and lateral tilt was designated as positive. Tilt around the Z-axis (Ztilt) was defined as the angle between PTD and X0Z plane, and lateral tilt was designated as positive (Fig. 4).

Fig. 4

Spatial shift and tilt of the patella on three orthogonal axes

Statistical analysis

SPSS Version 26.0 (IBM Corp., Armonk, NY, USA) was used for data analysis. Demographic data were analyzed using descriptive statistics. The single-measure intraclass correlation coefficient (ICC) was used to evaluate the inter-observer and intra-observer reliability (> 0.75, excellent; 0.4–0.75, fair to good; < 0.4, poor). Continuous variables with a normal distribution are expressed as mean ± standard deviations, or medians and percentiles were given if they are not normally distributed. Comparison between the RPD group and control group was evaluated with the Student’s t-test or Mann-Whitney U test, whichever was applicable. Comparison between the WB and NWB conditions was evaluated with the paired t-test or Wilcoxon signed-rank test, whichever was applicable. Receiver operating characteristic (ROC) curve presenting sensitivity and specificity was calculated for measurements, and the area under the ROC curve (AUC) was produced to assess the diagnostic accuracy of measurements for RPD. The reference ranges for non-normally distributed data are delimited by the 2.5th percentile and 97.5th percentile, and for normally distributed data by mean + 1.96 × standard deviation and mean − 1.96 × standard deviation. The level of significance was set at p < 0.05. Post hoc sample size calculation was performed using GPower software (version 3.1.9.6), and power of > 0.8 for all measurements was calculated.