The patients analysed in this investigation have been described in previous studies utilizing the CAMS-Knee Dataset (https://cams-knee.orthoload.com/) (Taylor et al., 2017; Trepczynski et al., 2019; Trepczynski et al., 2021; Heyland et al., 2023) and are also summarized in Table 1. The inclusion criteria for the instrumented TKA were: patients about to receive a TKA, at least 50 years of age, not more than 100 kg body mass, no other electronic implants (e.g., cardiac pacemakers), and sufficient fitness to participate in subsequent gait analyses. Six out of the nine patients originally implanted with the instrumented TKA, were able to participate in the CAMS-Knee measurements involving mobile fluoroscopy, that were performed 5–7 years postoperatively (Taylor et al., 2017). Due to the rarity of patients with instrumented knee implants, no additional selection criteria were imposed in the current study, and all six patients from the CAMS-Knee dataset were included. In this study, we focus on two activities known to produce large EFMs, sit-stand-sit and squat, of which each patient preformed 5–6 repetitions. Additionally to previously reported parameters such as the hip-knee-ankle (HKA) angle, we have now also quantified the patella height for the CAMS-Patients in terms of the Insall-Salvati-Index (ISI) (Insall and Salvati, 1971). We based the ISI on the patellar position reconstructed from fluoroscopy during the investigated activities, where we took the mean ISI value of all data points within 20°–70° knee flexion range for each patient (Phillips et al., 2010).

The CAMS-Knee dataset contains the reconstructed tibio-femoral (TF) kinematics based on the metal TKA components, which are clearly visible in the fluoroscopic images (Taylor et al., 2017). However, the dataset does not contain any reconstruction of the patellar kinematics, which was a key prerequisite for this study.

Since the focus of the CAMS-Knee study was the accurate capture of the TF kinematics, the visibility of the patella and its characteristic radiographic features was limited in parts of the image data due to occlusions or overexposure. This limitation made it infeasible to reconstruct the patellar kinematics using the same approach that was used for the TF components (List et al., 2017). Instead, we developed a semi-automatic method based on patellar points identified manually on the 2D fluoroscopy images (in-plane kinematics), which were automatically combined with the 3D location of the femoral component (out-of-plane kinematics) using a pin-hole-camera projection model (Hartley and Zisserman, 2004), to yield the 3D location of the patella. For the alignment of the in-plane position, the usually clearly visible metallic marker ball at the centre of the retro-patellar polyethylene implant was used (Figure 1). The out-of-plane position was then adjusted by aligning the centre of the patella implant with the centre of the patellar groove of the femoral component, while preserving the location of the metal ball projected onto the image plane. The patellar tilt was adjusted to align the relatively congruent retro-patellar and femoral implant geometries. For the alignment of the in-plane rotation (patella flexion), one of the following two approaches was used, depending on the visibility of the patella. If the interface between the patellar bone and the retro-patellar implant was clearly visible, its most proximal and distal points were marked (Figure 1A), otherwise 5 points were placed on the anterior patellar bone boundary (Figure 1B). In both approaches, the patella flexion was adjusted to align the patellar bone boundaries projected onto the image plane with the corresponding points marked on the image. The placement of the retro-patellar points was performed by one person, while the anterior patellar points were placed by a separate investigator who also checked the retro-patellar points. The resulting PF kinematic degrees of freedom were plotted for each trial and checked visually for outliers and discontinuities, which were then corrected as necessary. The combined TF and PF implant kinematics were also rendered as 3D animations from different perspectives (sagittal, frontal), and checked visually.

During phases at which the metallic marker ball was not visible in the fluoroscopic images the patellar kinematics were interpolated by fitting curves into the reconstructed time points of a given patient and activity. The curve fitting was based on the relative patello-femoral position (in polar coordinates) and patella rotation in the sagittal plane of the femoral component (patella flexion), into which quadratic functions with respect to knee flexion were fitted. The fitted curves matched the reconstructed kinematic parameters with R ² values of at least 0.98 and root mean square errors (RMSE) of 0.17–0.38 mm for the location’s radial coordinate, 0.33°–0.72° for the location’s angular coordinate, and 0.65°–1.66° for the patella flexion.

Of the 6569 fluoroscopic frames for which patella kinematics was reconstructed, 3740 were registered using the proximal/distal implant interface method (Figure 1A), and 1603 using the anterior boundary method (Figure 1B), while the remaining 1226 were interpolated using quadratic curve fitting.

The musculoskeletal model employed in this study was based on the previously described approach (Trepczynski et al., 2012), which was modified to incorporate the in vivo measured TF loads, as well as TF and PF kinematics from fluoroscopy. The model was constrained to track the measured TF force within 5% error as described in an earlier study (Trepczynski et al., 2018).

To reconstruct the skeletal kinematics of the lower limb, the 3D patient-specific anatomy from CT data, and skin marker-based kinematics were used as previously described (Trepczynski et al., 2012). However, in this study the skin marker-based kinematics were modified based on the in-plane TF kinematics from fluoroscopy. Unlike our previous studies, where the PF kinematics were based purely on geometric estimations, this study used in vivo PF kinematics directly reconstructed from fluoroscopy, as described in the previous section.

The effective lever arm of the knee extensor mechanism was derived from the fluoroscopic data, based on the functional knee flexion axis computed from TF kinematics (Taylor et al., 2010; Ehrig et al., 2011), and the patellar tendon force line of action computed from patello-tibial kinematics, which was applied to individual attachment sites identified from the image data (Kneifel et al., 2023).

The ratio of the patellar tendon force to quadriceps force (TQR) was determined based on an equilibrium condition for moments acting at the patella in the sagittal plane around the effective PF contact point. The effective PF contact point was estimated based on the fluoroscopic patella location relative to the femur, which was used to identify the approximate PF contact area: all nodes of the patellar implant surface that were closer than 1 mm to the femoral component were considered to be in physical contact, and their positions were averaged to yield the effective PF contact point (Figure 2). Subsequently, the PF contact force was computed from the patellar tendon and quadriceps forces, based on the assumption of equilibrium for these three forces acting on the patella.

To make the loading comparable across patients, the forces were normalized to multiples of each individual’s body weight (BW), while the moments were normalized to body weight times body height (BWHt). In order to plot averaged loading profiles for all trials of each patient with respect to knee flexion, the data was transformed from the time domain to the flexion domain and sampled in 5° knee flexion steps, which was found to provide sufficient resolution to correctly represent the curves. The linear regression analyses were performed using the original data points. Since this study focuses on the loading of the knee extensor mechanism, only time points with clearly positive external flexion moments (EFM >0.001 BWHt) were considered in the linear regression analyses between the EFM and the contact force in the TF and PF joints.

The manual localization of patellar points in the fluoroscopic image data was performed in the ImageJ software (PointPicker-Plugin), while the automatic out-of-plane patella registration, PF contact point estimation, result processing, plotting and statistical analyses were performed using custom code written in R (R-Core-Team, 2022).

The mean peak knee flexion ranged from 77° for patient K1L during squat to 93° for K5R during both activities (Table 2). The effective lever arm of the patella tendon generally decreased with knee flexion, with mean peak values in extension ranging from 51 mm to 58 mm, and mean lowest values in flexion ranging from 42 mm to 47 mm (Table 2; Figure 3). The TQR was also highest in extension, with mean peak values ranging from 0.84 to 1.06 (Table 2). With increasing flexion the TQR decreased, with mean trial minima ranging from 0.61 to 0.83 (Table 2; Figure 4).

The external and internal loading increased with flexion. The in vivo measured TF force was substantial even in extension, with mean minimal values ranging from 0.75 BW to 1.27 BW, rising with increasing flexion to mean peak values of 1.97 BW to 3.24 BW (Table 2). The highest absolute TF-force of 3220 N was observed in patient K1L during sit-stand-sit at 84° knee flexion. In extension, the external flexion moment (EFM) was close to zero or negative and reached mean peak values of 3.2 BWHt to 5.9 BWHt in flexion. The highest absolute EFM of 104 Nm was observed in patient K5R during a squat at 84° knee flexion (Table 2). The PF-force was near zero in extension and followed a similar profile with increasing flexion as the EFM, rising to mean peak values of 1.75 BW to 3.29 BW. The highest normalized PF-force of 3.40 BW was observed in patient K5R during a squat at 90° knee flexion, and was about 5% higher than the TF-force at the same instant. The highest absolute PF-force of 3302 N was observed in patient K1L during a squat at 84° knee flexion, and was about 8% higher than the concurrent TF-force (Table 2; Figure 5).

Linear regression of the EFM and the in vivo measured TF-force showed a good correlation for sit-stand-sit with an R ² of 0.78, but a weaker one for squat with an R ² of 0.43. For both activities, but especially for squat, patient K8L had exceptionally high TF-forces for a given EFM, reducing the overall correlation (Table 3; Figure 6). The correlation between the EFM and the PF-force was strong for both activities, with R ² of 0.95 for sit-stand-sit and R ² of 0.88 for squat. The intercept of the PF-force regressions was close to zero, allowing the regression coefficients to be interpreted as fixed ratios between PF and EFM (Table 3; Figure 7).