Loading and kinematic profiles for patellofemoral durability testing

Abstract

Patellar complications after total knee replacement (TKR), such as maltracking, fracture, wear, and loosening, can lead to implant failure and revision surgery. However, few in vitro patellofemoral durability tests for the implanted joint have been developed. Existing standards for patellofemoral loading profiles (ISO 14243–5, draft) are generic (not implant-specific) and do not include patient variability. The goal of this study was to derive implant-specific loading profiles to simulate a motor task that reaches high knee flexion and include patient variability. In vivo data, including motion capture and stereo-radiographic images at the knee, were collected for eleven rotating platform TKR patients performing a single-leg lunge activity. Quadriceps forces during the activity were estimated for each patient from marker data and ground forces with a musculoskeletal model. Patellofemoral contact forces were estimated with patient-specific finite element models of the implanted knees. Stereo-radiography patellofemoral kinematics and estimated contact loads were combined to derive seven loading profiles that span the observed inter-patient variability. The loading profiles were experimentally evaluated in a 6-degree-of-freedom testing machine and worst-case loading profiles were identified. The two profiles that generated the highest stresses in the patellar button (43% and 46% of the volume surpassed yield stress, respectively) included the largest internal (4.4°) and external (13.0°) patellar rotation, and greater medio/lateral contact forces (up to 915 N). The same profiles were also tested in a finite element model of the experimental simulator, which was able to adequately replicate location and magnitude of the peak deformations measured in the prostheses after the experiment. The kinematic and loading profiles developed in this study simulated a high-demand motor task and incorporated inter-patient variability, capturing worst-case patellofemoral configurations, and can be utilized for pre-clinical testing of new patellar designs.

1. Introduction

Dynamic mechanical testing of joint replacement designs is an important part of the pre-clinical validation process (DesJardins et al., 2000). Since polyethylene wear and damage is one of the most prevalent causes of total knee replacement (TKR) revision (Sharkey et al., 2002), a significant number of in vitro studies have been performed on the tibiofemoral (TF) articulation to quantify implant durability (Abdel-Jaber et al., 2015; Grupp et al., 2009). Test boundary conditions (loads and kinematics) can be derived from telemetric TKR or fluoroscopy-based kinematic measurements and computational models to simulate physiological conditions (Walker et al., 2000).

Resurfacing of the patella as part of a TKR is a common procedure. Failure of the patellar implant represents a relevant portion of TKR revision causes (Berry and Rand, 1993; Clayton and Thirupathi, 1982; Hamilton et al., 2017; Jordan et al., 2005; Russell et al., 2014; Schindler, 2012). The most common failure modes of the patellar component reported in the literature are wear-related loosening and fracture in the polyethylene, especially at the base of the fixation pegs, depending on the implant design (Berend et al., 2001).

Although failure of the patellar component is a historical cause of revision, few in vitro studies have investigated durability of the implanted patellofemoral (PF) joint, especially in comparison with the advanced TF wear simulations that have been ongoing for several years. Hsu and Walker (1989) designed a testing machine to compare wear and deformation for different patellar component designs by applying a constant compressive load against the femoral component throughout a flexion range (Hsu and Walker, 1989). Both Ellison et al. (2008) and Vanbiervliet et al. (2011) designed an in vitro test to simulate a gait cycle and quantify wear in the patellar component (Ellison et al., 2008; Vanbiervliet et al., 2011). However, due to the dearth of data available, prior studies generally did not derive experimental boundary conditions from in vivo kinematics of the implanted PF joint, but a combination of data from in vitro experiments, and healthy and implanted patients were included. In addition, the only motor activity that was previously simulated was gait, in which the patella does not undergo significant loads because of the limited range of knee flexion.

A combination of single-plane fluoroscopy images and inverse dynamics has been previously used to measure implanted and natural PF kinematics in the sagittal plane and estimate PF compressive load for a deep-knee-bend activity (Leszko et al., 2010; Sharma et al., 2008). Musculoskeletal models were also used to estimate PF compressive load for a limited number of patients with telemetric TF implants during gait (Lin et al., 2010) and activities with high knee flexion angles (Trepczynski et al., 2012). However, the complex relation between contact loads in multiple degrees of freedom and multi-planar PF kinematics was not characterized, and only compressive load was reported.

As wear and fracture are dependent on the complex 3D motion and loading, it is crucial that durability tests replicate in vivo mechanics, and account for the significant surgical and patient variability (implant design and size, femoral component alignment, quadriceps force, PF ligaments, and patellar tendon angle). This is particularly challenging because PF contact loads have not been directly measured in vivo, as instrumented patellar implants are not currently available.

Accordingly, the goal of the present study was to derive realistic boundary conditions for an experimental durability test of TKR patellar components that would (i) account for patient variability, (ii) simulate a motor activity that reaches deep flexion angles, and (iii) capture worst-case conditions for the implant. Stereo-radiography images, motion capture data and ground reaction forces collected for eleven rotating platform TKR patients performing a single-leg lunge were combined in a computational modeling approach to estimate patient-specific PF kinematics and contact loads. Worst-case kinematics and loads in terms of stress in the patellar component were selected and tested in an AMTI VIVO™ (AMTI, Watertown, MA) testing machine.

2. Methods

2.1. Experimental data

Dynamic stereo-radiographic images were collected for eleven patients (age 64 ± 5, 169.5 ± 8.4 cm, 75.4 ± 13.7 kg) with rotating platform TF implants and resurfaced patellae performing a single-leg lunge, using two matching custom radiography systems at 50 frames/s (Ivester et al., 2015) (Fig. 1). The single-leg lunge was chosen because the motion of the knee joint center is limited during this activity, allowing the simultaneous visibility of the joint in both radiographic images throughout most of the flexion range. This study was approved by the University of Denver Institutional Review Board and all participants provided informed consent. Whole body, marker-based motion capture and ground reaction data were simultaneously collected with an eight-camera video photogrammetric system (Vicon, Centennial, CO) and four force plates (Bertec, Columbus, OH). Femoral component and tibial tray CAD geometries from the manufacturer (rotating platform posterior stabilized ATTUNE®, DePuy Synthes, Warsaw, IN) were registered to the 2D stereo-radiographs to measure the six degree-of-freedom (DoF) TF kinematics. Patient-specific patellar bone geometries were reconstructed using a validated statistical shape modeling approach (Smoger et al., 2017), and were used to track PF kinematics. The registration technique was previously described and validated with a human knee phantom (Ivester et al., 2015). Translational and rotational tracking errors of 0.15 mm and 0.3° were assessed. Local coordinate systems were established on the patellar and femoral implant geometry (Fig. 2a). The origin of the femoral coordinate system was located directly superior to the lowest point on the femoral articulating surface at the height of the most posterior point on the articulating surface and at the mid-point of the most medial and lateral aspects of the femur, with three orthogonal axes aligned to the femoral geometry. Likewise, the patella origin was located at the geometric center of the elliptical patella profile on the anterior face of the implant. Relative kinematics between the femur and patella were described using a three-cylindrical open chain kinematic description (Grood and Suntay, 1983). Three and eight patients were implanted with all-polyethylene ATTUNE^® medialized dome and anatomic patellar components (Fig. 2b), respectively (Ali et al., 2018). Femoral component sizes ranged between 4 and 8, and button sizes ranged between 32 and 41 mm. TF and PF kinematics were trimmed to the portion of the task common to all the patients, which was 15–90° of TF flexion.

Fig. 1.

Bi-plane stereo-radiography images were collected at the implanted knee for eleven TKR patients performing a single-leg lunge activity. Motion capture data and ground forces were simultaneously collected and, together with TF and PF kinematics, were used as inputs to eleven patient-specific musculoskeletal models to estimate quadriceps forces exerted during the activity. Quadriceps forces and TF kinematics were inputs to eleven patient-specific FE models of the implanted knees, which were calibrated to match PF kinematics and estimated PF contact forces. PF kinematics and contact loads for the eleven patients were inputs to a PCA to derive loading profiles for durability tests that account for patient variability. The seven loading and kinematic profiles derived from the PCA were applied to a FE model of an AMTI VIVO™ simulator to identify worst-case boundary conditions in terms of stress in the patellar prosthesis.

Fig. 2.

(a) Local coordinate systems established on the patella and femoral implant geometries. (b) Medialized dome and anatomic designs.

2.2. Musculoskeletal models

Patient-specific musculoskeletal models were created in OpenSim to estimate quadriceps forces exerted during the lunge activity (Delp et al., 2007). A previously-validated average model based on the model developed by Delp et al. was scaled to the segment lengths of each patient (Delp et al., 1990; Navacchia et al., 2016a). Patient-specific TF kinematics (all 6 DoFs) and PF kinematics (flexion/extension, anterior/posterior translation, and superior/inferior translation) from radiography images were implemented in the knee joint to inform muscle moment arms as described by Navacchia et al. (Navacchia et al., 2017). The remaining PF DoFs were not included because their contribution to quadriceps moment arm is limited. An inverse kinematics approach was used to derive joint angles from marker trajectories (Delp et al., 2007). A static optimization that minimized the sum of muscle activations squared at each time frame was performed to estimate muscle forces that produced the net joint moments consistent with patient kinematics and measured ground forces (Anderson and Pandy, 2001; Navacchia et al., 2016b) (Fig. 1).

2.3. Finite element knee models

Eleven patient-specific finite element (FE) models that included TKR geometries and patellar bone were developed in Abaqus/Explicit (SIMULIA, Providence, RI) to estimate PF contact loads (Fig. 1). Bones and TKR components were modeled as rigid bodies with 1-mm triangular elements (R3D3). Penalty-based rigid-body contact was defined between the patellar button and femoral component using a calibrated surface pressure-overclosure relationship and a hard pressure-overclosure relationship (zero surface penetration) was defined between bone and soft tissue (Halloran et al., 2005a, 2005b). PF ligaments and quadriceps extensor geometries were also included in the model. The extensor mechanism was represented with two-dimensional fiber-reinforced membrane elements (Baldwin et al., 2009), whereas the PF medial and lateral ligaments (MPFL and LPFL, respectively) were each modeled with five unidimensional connectors (Ali et al., 2018). The quadriceps tendon was separated into four sections, one for each quadriceps muscle. Patellar ligament and quadriceps tendon membrane elements were represented with a hyperelastic material model calibrated to stress-strain experimental data (Baldwin et al., 2009; Staubli et al., 1999). MPFL and LPFL were modeled as non-linear springs with elastic properties matching previously reported tensile data (Ali et al., 2018; Atkinson et al., 2000). A baseline simulation was developed for each patient positioning the attachments of the PF ligaments and extensor mechanism approximately on the mid points of each side of the patella (PF ligaments on medial/lateral sides, extensor mechanism on superior/inferior sides). Each node in the attachment site was rigidly attached to its closest ligament fiber in order to physiologically transmit the ligament or muscle force to the patellar bone. The tibial tray was driven with 6-DoF experimental TF kinematics and quadriceps forces from the musculoskeletal models were applied to the four quadriceps tendons, leaving the PF joint unconstrained. Attachment locations and orientations of the patellar tendon were calibrated for each model to match PF kinematics from stereo-radiography images. Specifically, a design of experiment (DoE) approach was used to modify the baseline models, based on results from the sensitivity analysis performed in a previous study (Ali et al., 2016), and calibrated to the patient-specific kinematics. The outputs of interest from the FE joint models were the PF contact loads measured at the backside of the patellar button.

2.4. Principal component analysis

PF kinematics and contact loading from the FE knee model for each patient were included in a principal component analysis (PCA). Specifically, flexion/extension, internal/external, and varus/valgus rotations, superior/inferior translation, and PF contact loads in anterior/posterior and medio/lateral directions were combined in the PCA to derive realistic loading conditions to simulate a single-leg lunge in an AMTI VIVO™ testing machine (AMTI, Watertown, MA) (Fig. 3). Seven combinations of loads and kinematics were isolated: average (μ) and μ ± 2 standard deviations (σ) of modes of variation 1–3. Two standard deviations were used to capture the extremes of each mode and identify worst-case conditions. The only DoF that was not changed across the seven combinations was the anterior/posterior force, in order to isolate the effect of kinematics and secondary loads on implant durability.

Fig. 3.

A previously validate FE model of the AMTI VIVO™ testing machine (Fitzpatrick et al., 2016) was adjusted to simulate PF kinematics and contact loads. Seven loading profiles from the PCA were tested in the simulator model on a size 6 femoral component (Attune®, DePuy Synthes, Warsaw, IN) and two 32-mm patellar components (medialized dome and anatomic designs). Specifically, flexion/extension, internal/external, varus/valgus rotations, and superior/inferior translation were driven in displacement control, whereas contact loads were applied in the anterior/posterior and medial/lateral DoFs. The same loading conditions were also tested experimentally on the simulator on the same implant combination (only the medialized dome design was tested).

2.5. VIVO simulator model

The seven loading combinations were used to drive a validated FE model of the VIVO™ simulator (Fitzpatrick et al., 2016) adapted to test the PF joint in place of the TF joint (Fig. 3). The patellar prosthesis was positioned on the lower stage of the simulator with its articulating surface facing upward (Fig. 3). The femoral component was mounted onto the upper arm of the simulator with the trochlear groove of the component facing downward to articulate with the patellar prosthesis. Patellofemoral anterior/posterior (compression) and medial/lateral loads were applied to the lower stage together with superior/inferior translation and varus/valgus rotation, whereas flexion/extension and internal/external rotations were applied to the femoral component through the upper stage. The simulations were run with a size 6 femoral component and a 32-mm patellar prosthesis, since this combination represents the worst-case in terms of contact area for the analyzed implant design. The femoral component was meshed with 1-mm triangular elements (R3D3) and modeled as rigid, while the patella prosthesis was meshed with ~7000 hexahedral elements (C3D8) and modeled with an elastic-plastic hardening material model calibrated to experimental data from the manufacturer. The nodes on the bottom surface of the patellar prosthesis were fixed to the lower stage of the simulator. Loading profiles derived from PCA were described as a function of the TF flexion angle. A sequence composed of a first flexion profile (TF flexion: 15–90°), an extension profile (90–15°), and a second flexion profile (15–90°) was simulated to allow the polyethylene hardening properties to affect the patellar prosthesis geometry. Worst-case loading scenarios in terms of volume above yield stress in the patellar button were identified. Both medialized dome and anatomic designs were evaluated.

2.6. VIVO simulator experiment

To validate the model predictions, the seven loading profiles were performed experimentally in the VIVO™ simulator with the same combination of implant component sizes. For each loading profile, ten thousand cycles were applied at a rate of 1 Hz to a new medialized dome patella prosthesis. Ten thousand cycles were chosen to enable accumulation of plastic deformation of the patellar prostheses, but minimizing component wear or creep. The three-dimensional geometry of each patellar prosthesis was scanned with a Wide-Area 3D Measurement System (VR-3100, Keyence, Osaka, Japan) before and at least two days after the test to allow polyethylene recovery, using a custom fixture that indexed the patella position based on the fixation pegs. Geometric differences between the pre- and post-test scans along the anterior-posterior axis were calculated over the surface of the patellar prosthesis, representing permanent deformation of the polyethylene, and compared to model predictions.

3. Results

Stereo-radiography PF kinematics presented patellar internal/external rotations that ranged from − 4.6° to 20.3° (negative values being internal rotations), with a mean trend that decreased linearly with increased TF flexion angle. Medial/lateral translation also decreased linearly with increased flexion, and ranged from 0.2 mm to 10.3 mm. PF flexion increased linearly with TF flexion, reaching a peak of 87.5° (Fig. 4b).

Fig. 4.

(a) Quadriceps forces (mean ± 1 standard deviation across the eleven patients) exerted during single-leg lunge estimated by the patient-specific musculoskeletal models, described in body weights (BW) and as a function of TF flexion angle. (b) PF kinematics (mean ± 1 standard deviation across the eleven patients) estimated by the FE knee models (error bars), compared to experimental measures from stereo-radiography images (shaded regions, mean ± 1 standard deviation). Flexion/extension (F-E), varus/valgus (Var-Val), and internal/external (I-E) rotations are shown on the left, while medial/lateral (M-L), anterior/posterior (A-P), and superior/inferior (S-I) translations are shown on the right. (c) Root mean square errors (RMSE) and Pearson-product correlations (mean ± 1 standard deviation across the eleven patients) between model-predicted and measured PF kinematics.

Average quadriceps forces predicted by the musculoskeletal simulations peaked at 3456 N (4.6 body weights (BW)) when TF flexion was 86° (Fig. 4a).

Average RMSE and Pearson-Product correlations between PF kinematics predicted by the calibrated FE knee models and experimental data were 4.4°/1.0 (flexion/extension), 3.4°/0.49 (varus/valgus rotation), 4.3°/0.31 (internal/external rotation), 2.0 mm/0.78 (medial/lateral translation), 1.6 mm/0.99 (anterior/posterior translation), and 2.8 mm/0.98 (superior/inferior translation) (Fig. 4c). Varus/valgus rotation, internal/external rotation, and medial/lateral translation presented limited ranges of motion in comparison to the other DoF, which degraded the corresponding Pearson-Product correlations.

Differences in PF kinematics, quadriceps forces, and PF contact loads between patients with domed (n = 3) and anatomic (n = 8) buttons were tested for statistical significance with unpaired t-tests performed at intervals of 1° throughout the common flexion range (15–90°). No statistically significant difference was observed, except for a more inferior position of the patella exhibited by domed implants between 35° and 90° of flexion.

Full 6 DoF loading and kinematic boundary conditions were developed combining anterior/posterior and medial/lateral loads with kinematics for the remaining 4 DoFs. PF compressive loads estimated with the calibrated knee models increased linearly with flexion angle, with an average peak of 3478 N (4.6 BW), while mean medial/lateral loading reached a maximum of 386 N (0.6 BW) (Fig. 5).

Fig. 5.

Kinematic and load profiles generated by the PCA. Mean profiles are shown in black, while red, orange and yellow lines represent mean ± 2 standard deviations of the first three modes of variation, which explained 89% of the inter-patient variability. The grey shaded regions on the back represent mean kinematics and loads ± 1 standard deviation across the eleven patients. Kinematics profiles are defined as the relative motion between the local coordinate systems of the implant components, and according to the Grood and Suntay notation (Grood and Suntay, 1983). Contact loads represent the load generated by the femoral component onto the patellar button. Therefore, a medial force (e.g. solid orange line) represents the contact force on the lateral side of the button, which pushes the patella medially. Conversely, a lateral force (e.g. dashed orange line) represents a force that pushes the patellar button laterally (for interpretation of the references to color in this figure legend, the reader is referred to the web version of this article).

The first three modes of the PCA explained 89% of the total variability. Mode 1 (71%) described changes in PF flexion/extension, internal/external rotation and superior/inferior translation. Mode 2 (11%) captured the variability in internal/external rotation and medial/lateral loads. Mode 3 (8%) described changes in flexion/extension and varus/valgus rotation. The seven kinematic and load profiles generated from the PCA are shown in Fig. 5 and are described according to the Grood and Suntay notation applied to the PF joint (Grood and Suntay, 1983).

Seven kinematic and loading profiles were generated from the PCA. The profiles that presented a more externally rotated position (e.g. Mode 2: μ + 2σ) throughout the cycle also had larger PF medial contact (forces that push the button medially), which caused large stress on the lateral side (Figs. 5 and 6). On the contrary, profiles with a more internal rotation (e.g. Mode 2: μ − 2σ) presented larger lateral contact forces. Larger deformations were observed on the superior part of the button for kinematic profiles that presented a more inferior position of the patella (e.g. Mode 1: μ + 2σ), in comparison to profiles with a more superior position (e.g. Mode 1: μ − 2σ).

Fig. 6.

The regions of the patellar prostheses that surpassed the polyethylene yield point are shown for each loading profile. Medialized dome prostheses are shown at the top, anatomic prostheses are shown at the bottom.

The kinematics and load combinations that produced the largest volume with Von Mises stresses higher than the polyethylene yield point were Mode 2: μ + 2σ for the medialized dome design, and Mode 2: μ − 2σ for the anatomic design. Specifically, 43% (25%/18% on the medial/lateral side) and 46% (27%/19% on the medial/lateral side) of the total volume surpassed yield in the two cases, respectively (Figs. 6 and 7).

Fig. 7.

The volume of the buttons that surpassed yield stress was quantified as a percentage of the total volume and divided into medial and lateral. The loading profiles that presented largest yield volume were Mode 2: μ + 2σ for the medialized dome design, and Mode 2: μ − 2σ for the anatomic design. Largest yield volume on the lateral side (where the thinner region is) was observed for Mode 1: μ + 2σ.

The worst-case loading profile for the medialized dome presented a more externally rotated position throughout the cycle, and highest contact force on the medial side of the button (peak: – 915 N). The worst-case loading scenario for the anatomic design presented a more internally rotated position, reaching a peak of −4.4° at deepest flexion, and highest contact force on the lateral side of the button (peak: 164 N).

Two of the seven loading profiles (Mode 1: μ − 2σ and Mode 2: μ + 2σ) were not run in the experiment because the medial/lateral contact forces exceeded the load limits of the VIVO™ simulator. The largest deformation in the components was observed for Mode 3: μ − 2σ (0.99 mm) and it was located at the tip of the lateral flange (Fig. 8, Experiment). Deformation patterns on the surface of the button were distinct for each profile, and were adequately predicted by the simulator model, although the deformation peaks resulted in smaller magnitudes, with an overall peak of 0.84 mm for Mode 3: μ − 2σ (Fig. 8, Model). The inter-profile deformation trends were correctly captured by the model, as indicated by a Peason-product correlation coefficient of 0.91 between model and experimental deformation peaks on the medial and lateral facets of the button (shown in Fig. 8, Peaks, and in Fig. 9). Deformation differences up to –48% of the overall peak were observed between model predictions and experimental measurements, but largest differences were not located at the peak (Fig. 8, Delta).

Fig. 8.

Deformation results. Experiment: Deformation in the anterior/posterior direction was measured with a Wide-Area 3D Measurement System after 10,000 cycles of each loading profile. Model: Corresponding deformations predicted by the FE model of the simulator for the same loading profiles. Delta: Difference between model-predicted and experimental deformations, indicated as percentage of the maximum deformation measured experimentally (0.99 mm). Peaks: Locations of the experimental (black circles) and model-predicted (yellow diamonds) deformation peaks on the medial and lateral sides of the button for the five loading profiles. Contact Area predictions are also shown on the left to highlight the similarity between contact patches and experimental deformation areas.

Fig. 9.

Model-predicted vs. experimental deformation peaks on both the medial and lateral facets for the five profiles run in the test machine. A Pearson-Product correlation coefficient of 0.91 was observed between model predictions and experimental measures.

4. Discussion

The present study derived loading and kinematic profiles for durability tests of TKR patellar components from a combination of state-of-the-art in vivo experimental data and a number of patient-specific computational models at the whole-body scale and of the implanted joint. High speed stereo-radiography images were collected at the implanted knee of eleven patients while performing a single-leg lunge activity. An equal number of patient-specific musculoskeletal models estimated quadriceps forces exerted during the activity and calibrated FE models of the TF and PF joints were developed to compute PF contact forces. Derived loads and kinematics accounted for patient variability, simulated a challenging motor task, and were used to identify the worst-case scenario for stress in the patellar button. Five loading profiles were tested in a 6-DoF testing machine and deformation measurements were used to validate model results.

Mode of variation 2 generally described the worst-case conditions in terms of largest volume with plastic deformation in the patellar button. The two profiles (μ + 2σ and μ − 2σ) captured kinematics and contact loads for those patients that presented the largest external and internal rotation, and greatest contact force on the lateral and medial sides, respectively. These results are not surprising since patellar maltracking has been previously indicated as one of the main complications of the resurfaced patella (Dennis, 1992). In addition to pain, patellar maltracking can cause larger contact pressures due to the limited contact area, which result in increased wear (Vanbiervliet et al., 2011), and greater shear contact forces, as indicated by the PCA results for Mode 2, which can lead to failure at the peg-button interface (Huang et al., 1999). Looking more closely at the percentage of deformed volume in the two profiles from Mode 2, it is possible to make distinctions between them. Mode 2: μ + 2σ had the largest medial shear contact load in deep flexion and, consequently, presented most of its plastic deformation on the very edge of the lateral flange. Medialized patellar components are more sensitive to large pressure and wear at this location, since it is the thinnest region. Although Mode 2: μ − 2σ presents volumes past yield stress on the lateral side comparable for the two designs, the location of most of the stress in the thinnest part makes Mode 2: μ + 2σ more critical for potential failure of the implant. Interestingly, the largest volume that surpassed yield stress on the lateral side was observed for Mode 1: μ + 2σ, but, as for Mode 2: μ − 2σ, it was not located on the flange. On the contrary, Mode 1: μ − 2σ showed the second largest medial shear load and presented large yield volume on the flange.

The comparison between model-predicted and experimental deformation demonstrated that load and kinematic profiles were correctly applied in vitro. Deformation peaks predicted by the model were consistently located at the experimental peak (Fig. 8). In addition, a correlation of 0.91 was found between model and experimental deformation peak values, indicating that inter- and intra-profile deformation trends were correctly represented (Fig. 9). Deformation patches from the model and experiment also compared favorably with previously reported data. Specifically, all profiles generated the previously reported ‘papillon’ pattern with two larger deformation areas on the medial and lateral facets and less deformation in the center, observed in previous retrieval and in vitro studies (Ellison et al., 2008; Schwartz et al., 2002; Vanbiervliet et al., 2011). Plastic deformation peaks were also consistent with Ellison et al. (2008) which reported a peak deformation of 0.947 mm. The wear contribution to this maximum penetration (4 million cycles were simulated) was compensated by the smaller compressive force applied (~1400 N), which presumably resulted in smaller plastic deformations than in the present study.

Musculoskeletal models were previously used to estimate PF contact forces (Lin et al., 2010; Trepczynski et al., 2012). In particular, Trepczynski et al. estimated TF and PF contact forces for two patients with telemetric knee implants during walking, stair climbing, sit-to-stand, and squat. Even though the patients they analyzed reached similar peak flexion angles to the ones in our study during sit-to-stand and squatting (~90°), their peak PF contact force predictions were lower (~3.7 BW during squat for one patient vs. 4.6 BW on average in our study). This discrepancy may be motivated by the difference between the activities: while squatting is a symmetric activity involving equally both legs, most of the weight of the body is sustained by the involved leg during single-leg lunge.

Previous studies derived loading conditions for experimental tests from a combination of various sources (Ellison et al., 2008; Hsu and Walker, 1989; Vanbiervliet et al., 2011). Specifically, Hsu and Walker (1989) applied a constant load throughout flexion (55–100°), whereas Ellison et al. (2008) and Vanbiervliet et al. (2011) simulated a gait activity including multi-axis loads and kinematics. A peak anterior/posterior load of 1500 N was applied in this study, which might correctly simulate in vivo wear behavior, but does not replicate extreme loading conditions that contribute to failure mechanisms such as fracture. Vanbiervliet et al. (2011) simulated surgical variability by including a 5° malrotation of the femoral component. However, overall population variability has never been included in PF durability tests. Since it is reasonable to assume that nominal kinematics and loads represent the behavior of a successful implant, it is important to broaden the spectrum of testing boundary conditions to best capture realistic failure mechanisms. The method implemented in this study resulted in design-specific loading conditions derived from high-accuracy experimental data, which simulated a challenging motor task and included patient variability. The extension of the same loading and kinematic profiles to test the contact mechanics and failure modes of different implant designs should be evaluated carefully, since PF motion and loads depend on several factors such as component geometry, positioning and conformity. However, given the large inter-patient variability observed in this study, the adoption of the seven loading profiles to test implant designs that share sufficient similarities in shape and conformity with the ones used here would be reasonable.

The current study has several limitations. First, a limited number of patients was used (n = 11). Data for a larger number of patients were collected (n = 36), but different TF flexion ranges were captured in the radiographs. The 15–90° range was selected to maximize the number of patients while including a relatively large flexion range, which increases sliding distance between the two implant components and, consequently, wear, and relatively deep flexion angles resulting in greater PF contact forces. An additional confounding factor is that patients with both domed and anatomic patellar designs were included in the study. PCA Mode 1, which partially described the variation in flexion/extension and superior/inferior translation, might have been influenced by the inclusion of the two designs. Specifically, Mode 1: μ + 2σ might represent the 3 patients with the domed design, presenting a more flexed and inferior position throughout the flexion cycle. However, the fact that some of the patients with anatomic implants presented similar flexion/extension and superior/inferior ranges as for the domed implants, together with the limited number of overall patients, motivated our choice of not separating the data from the two designs. A second limitation was that only 1.5 activity cycles were tested in the FE model of the simulator, whereas 10,000 cycles were performed experimentally. This limited the comparison of the plastic deformation between model and experiment, which resulted in percent differences up to 48%, because the model did not represent any non-recoverable cold flow occurring over 10,000 cycles.

In conclusion, a combination of in vivo data from patients with rotating platform TKR and computational models were used to derive loading and kinematic profiles for an in vitro PF durability test. The pipeline developed in this study demonstrates how computational modeling can be used in conjunction with high-accuracy experimental data to improve pre-clinical testing and validation of novel medical devices.