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. Author manuscript; available in PMC: 2021 Aug 1.
Published in final edited form as: Biomech Model Mechanobiol. 2020 Feb 4;19(4):1309–1317. doi: 10.1007/s10237-020-01295-7

Computational Framework for Population-Based Evaluation of TKR-Implanted Patellofemoral Joint Mechanics

Azhar A Ali 1, Chadd W Clary 1, Lowell M Smoger 1, Douglas A Dennis 1,2, Clare K Fitzpatrick 1,3, Paul J Rullkoetter 1, Peter J Laz 1
PMCID: PMC7398844  NIHMSID: NIHMS1556847  PMID: 32020408

Abstract

Differences in patient anatomy are known to influence joint mechanics. Accordingly, intersubject anatomical variation is an important consideration when assessing the design of joint replacement implants. The objective of this study was to develop a computational workflow to perform population-based evaluations of total knee replacement (TKR) implant mechanics considering variation in patient anatomy and to assess the potential for an efficient sampling strategy to support design phase screening analyses. The approach generated virtual subject anatomies using a statistical shape model of the knee and performed virtual implantation to size and align the implants. A finite element analysis simulated a deep knee bend activity and predicted patellofemoral (PF) mechanics. The study predicted bounds of performance for kinematics and contact mechanics, and investigated relationships between patient factors and outputs. For example, the patella was less flexed throughout the deep knee bend activity for patients with an alta patellar alignment. The results also showed the PF range of motions in AP and ML were generally larger with increasing femoral component size. Comparison of the 10% to 90% bounds between sampling strategies agreed reasonably, suggesting that Latin Hypercube sampling can be used for initial screening evaluations and followed up by more intensive Monte Carlo simulation for refined designs. The platform demonstrated a functional workflow to consider variation in joint anatomy to support robust implant design.

Keywords: population-based evaluation, statistical shape modeling, total knee replacement, patellofemoral joint mechanics, Monte Carlo simulation

1. Introduction

Joint replacement remains the primary treatment for patients with osteoarthritis (OA), which affects one of every two people by the age of 85 (Murphy et al. 2008) and is the leading cause of disability in the elderly (Lawrence et al. 2008). Based on growth in the aging population, the annual rate of total knee arthroplasty in the US is expected to rise from the current 700,000 surgeries per year to more than 3.5 million by 2030 (Kurtz et al. 2007). Patellar complications, which include patellar fracture, dislocation, clunk syndrome, crepitus and anterior knee pain, still account for 10% of TKR complications (Putman et al. 2019, Dennis et al. 2011). Considering the affected population, strategies are needed to understand intersubject variability and its impact on implant performance.

Intersubject variation, including anatomical differences, influence natural knee mechanics and joint loading (Amis et al. 2006, Fitzpatrick et al. 2011, Smoger et al. 2015) and the performance of total knee replacement implants (Bull et al. 2008, Dennis et al. 2011, Fitzpatrick et al. 2012a). However, most evaluations of total knee replacement (TKR) implant performance, which span cadaveric experiments, subject-specific computational models, and measurements of kinematics for implanted patients using bi-plane fluoroscopy, are based on cohorts that are small relative to the potential population (Taylor et al. 2013).

Assessing the performance of an implant in a subject is complex and influenced by many factors, including anatomy, implant sizing and alignment, soft tissue constraint, and joint loading. Probabilistic approaches, leveraging computational models, are well suited to consider variability from multiple sources to evaluate implants for populations. Prior studies have typically focused on one or two sources of variation. For example, investigations varying implant alignment identified key degrees of freedom affecting TKR mechanics (Fitzpatrick et al. 2012b). Variation in joint loading was quantified and integrated into implant evaluations (Kutzner et al. 2010, Fitzpatrick et al. 2012a). In the hip, studies assessed robustness of hip replacement implants subject to surgical alignment and patient variation (Al-Dirini et al. 2018, 2019, Bah et al. 2015a,b). Evaluations were often based on anatomy for a single representative subject, but have recently been expanded to consider cohorts (Al-Dirini et al. 2019, Bah et al. 2015a,b). Workflows, which consider variation in anatomy and virtual implantation, are particularly challenging; changes in the mesh and geometric representation are more difficult to implement in a model than changes to a material property or loading condition. At the same time, these workflows have potential to identify important interactions between implant design, alignment and patient factors, including potential worst-case scenarios for an implant.

Statistical shape models (SSMs) have been developed to quantify variation in patient anatomy for larger populations. Using magnetic resonance (MR) or computed tomography (CT) scan data for a population, anatomical representations are segmented, aligned and registered to establish nodal correspondence and then principal component analysis (PCA) is employed to define modes of variation. SSMs have described bone morphology, providing insight into the shape and sizing lines of implants (Fitzpatrick et al. 2007, Dai and Bischoff 2013, Clary et al. 2014). Models developed from an SSM have been used in investigations of fracture risk in the femur (Bryan et al. 2010) and in evaluations of bone-implant interface mechanics for implanted tibial trays considering loading variability in combination with anatomic variation (Galloway et al. 2012, 2013).

Prior studies have primarily employed SSMs to isolate variation for a specific bone, with fewer studies applying joint-level SSMs which enable investigations into kinematics and joint mechanics. Joint-level SSMs have considered coordinated shape changes in multiple structures spanning a joint (Yang et al. 2008, Fitzpatrick et al. 2011), including the femur, tibia, patella and associated cartilages (Rao et al. 2013, Smoger et al. 2015). Using SSM-derived anatomies, interdependencies between morphology and joint mechanics in the natural knee have been assessed, providing insights into the conformity of natural anatomy (Fitzpatrick et al. 2011) and etiology of pathology, e.g. patellar maltracking or dislocation. With characterization of anatomic variation and recent advances in the ability of finite-element models to predict joint mechanics and differentiate implant designs (Ali et al. 2016, 2017, Fitzpatrick et al. 2012b), there is an opportunity to develop a computational framework to perform population-based evaluations of TKR implants and assess robustness to variation. While the TKR components replace the articular surfaces, the mechanics of the implanted knee are influenced by the native anatomy as the articular geometry, limb alignment, and anatomical landmarks are used to size and align implants, and the majority of the surrounding soft tissue structures are retained.

Accordingly, the objective of the current study was to develop a platform to perform population-based evaluation of implant designs for joint mechanics. Specifically, the approach created a virtual cohort of TKR patients where anatomical representations of subjects were derived from an SSM with bone, cartilage and soft tissue structures, a TKR device was appropriately sized, aligned and virtually implanted, and patellofemoral (PF) joint mechanics were evaluated with a finite element analysis for a deep knee bend activity. In the design phase, performing large-scale evaluations with many subjects can be particularly time consuming and expensive, even computationally (Taylor et al. 2013, Bah et al.2015b, O’Rourke et al. 2019). The ability to perform timely screening evaluations using a small number of average and targeted anatomical representations can be valuable to consider the impact of intersubject variation early in the design process. To additionally assess efficiency for design screening evaluations, joint mechanics were predicted with an efficient Latin Hypercube sampling and compared to results from the Monte Carlo simulation.

2. Methods

Leveraging prior work developed in Rao et al. (2013), an SSM of the knee was developed from magnetic resonance (MR) images of 40 subjects (20M/20F, age: 64.6±9.1 years, mass: 72.7±13.5 kg, BMI: 25.3±3.8) and included bone, cartilage and soft tissue attachments for the major ligaments and extensor mechanism. Using scan data from cadaveric testing (Baldwin et al. 2009a, 2012) and the Osteoarthritis Initiative (OAI), the structures of the knee for each subject were segmented from CT and MRI images (in-plane resolution of 0.35 mm) using Simpleware (Synopsys, Exeter, UK). Bone geometries were represented using linear (3-noded) triangular meshes, and cartilage was represented using linear (8-noded) hexahedral meshes. Subject-specific cartilage meshes were automatically morphed from a template hexahedral mesh using a surface-set of handles in Altair Hyperworks; the morphing approach enabled nodal correspondence across subject geometry, optimized mesh quality for finite element analyses, and improved efficiency of the SSM by reducing the overall size.

Local coordinate systems were developed for each bone (Rao et al. 2013); cartilage, ligament and tendon attachments were described in the coordinate system for the associated bone. The coordinate systems for each bone were established using anatomical landmarks; the superior-inferior (SI) axes for the femur and tibia were estimated using the posterior edge of the bone diaphysis; the anterior-posterior (AP) axis for the femur and tibia was defined as the cross product between the SI and ML axes (defined using a cylindrical fit through the condyles for the femur, and lowest points in the medial and lateral dwell for the tibia). The patellar coordinate system was defined using landmarks on the most medial and lateral points and the patellar nose; the ML axis was defined between the most medial and lateral points; the SI axis was defined as the line passing through the midpoint between the medial and lateral points, and the patellar nose; the AP axis was defined as the cross product between the SI and ML axis. The structures for each subject were registered to template meshes derived for the median subject. Nodal correspondence was established across all bone and cartilage geometry using an iterative closest point algorithm accelerated by a k-d tree nearest-neighbor search. The SSM was based on a principal component analysis using nodes for finite element meshes and transformations describing tibiofemoral (TF) and PF alignment for the bones in their as-scanned position.

The population-based evaluation generated virtual subjects (Figure 1) using the SSM with two sampling strategies: 100 instances using Monte Carlo (random) sampling and 12 instances using stratified Latin Hypercube sampling. Both sampling strategies used the first 20 modes from the statistical shape model, which captured 99.5% of the variability in the population, and each mode was sampled between ± 3 standard deviations. The virtual subjects utilized in this work included the bone anatomy, relative alignment between structures, and the soft tissue attachments; the cartilage representations were not used.

Figure 1.

Figure 1.

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Computational workflow for population-based evaluation of TKR joint mechanics.

Using automated scripting, each of the virtual subjects were implanted with a contemporary posterior stabilized TKR using a mechanical alignment approach. Femoral, tibial and medialized dome patellar implants were automatically sized and aligned based on the bony anatomy, landmarks, and established local coordinate systems. The femoral component was aligned to the posterior condyles and sized to avoid anterior notching (Figure 2). Anterior notching was defined as excessive underhang (>2mm) in the AP direction. The femoral resection depth was set to restore the natural height of the femur. Additionally, the femoral component was externally rotated by 3° relative to the neutral axis. The patellar and tibial components were sized to maximize coverage without exceeding 2 mm of overhang; optimizations were performed on the degrees of freedom tangential to the resection surface, e.g. ML and AP for tibial component; ML and SI for patellar component (Clary et al. 2014). The tibial cut depth was set to 8 mm below the higher of the tibial dwell points and a posterior slope of 3°. The thickness of the tibial insert was selected from available implant sizes to restore the native joint line. The internal-external (IE) rotation of the tibial component was aligned to the medial third of the tibial tubercle. Optimization of the patellar component also included the degree of freedom perpendicular to the resection surface (patellar spin); in general, rotations were less than 5°. The patella was resected to a level so that the composite of bone and implant restored the natural thickness (bone and an estimated 2.5 mm for cartilage), while maintaining at least 12 mm of bone. Automatic implantation of each component was performed independently. Monte Carlo instances (100) were automatically implanted in approximately 1.5 hours, and the Latin Hypercube-generated instances (12) were implanted in approximately 10 min. The distribution of selected implant sizes was compared to actual implant size data for 100 consecutive TKR patients from an active clinical practice.

Figure 2.

Figure 2.

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Automatic implantation with SSM-generated virtual subjects (top) and implanted instances (middle). Patellar button implantation algorithm (bottom left) and PF implant occurrences (bottom right).

Finite element analyses were performed on each virtually-implanted model in Abaqus (Dassault Systemes, Providence, RI) under a simulated deep knee bend loading condition (Baldwin et al. 2009a).Models included SSM-predicted bone, aligned implant components, and an extensor mechanism. With the focus on joint mechanics, implants were fixed to their corresponding bones. The bones and implants were modeled as rigid bodies with contact between structures described by a pressure overclosure relationship (Halloran et al. 2010). The extensor mechanism modeled quadriceps tendons (vastus-medialis, vastus-intermedius, vastus-lateralis, and rectus-femoris), patellar tendon, and medial and lateral patellofemoral ligaments using 2D fiber-enforced membrane elements (M3D4R) (Baldwin et al. 2009a). The extensor mechanism was aligned based on SSM-predicted soft tissue attachment locations on the femur and patella. The tibia and insert were initially distracted inferiorly and then loaded to allow for settling in the ML and AP directions. Similarly, the patella and medialized dome button were initially translated anteriorly to avoid initial contact overclosures, and then loaded by the quadriceps to allow for settling within the trochlear groove. During this initial settling step, a 300 N quadriceps load was applied through the extensor mechanism. The quadriceps load was subsequently ramped to 1000 N as the knee was flexed to 100° flexion while TF AP and IE motions were prescribed (Baldwin et al. 2009a, Shaloub et al. 2013). The tibiofemoral translational DOF (ML, SI) and varus-valgus (VV), and all patellofemoral DOF were unconstrained, allowing the implant conformity and relative alignment to drive the motion. The model predicted six-degree-of-freedom PF kinematics and contact mechanics, and by having all models formulated with the same underlying structure, relationships between patient (e.g. alta-baja position) or implant size measures and model outputs were interrogated. Model-predicted kinematics were compared to representative experimental data from cadaveric testing (Baldwin et al. 2009a, 2012).

3. Results

Models of the virtual subjects from both Monte Carlo and Latin Hypercube sampling strategies represented anatomic variability that compared well to a larger anthropometric study (Mahfouz et al. 20 (Figure 3). The automated algorithms successfully generated instances using the SSM, performed virtual implantation to create analysis-ready models, executed the analysis and extracted results. Automated model setup required less than 5 minutes for all instances, and computational analyses were approximately 10 min for each instance with implants and bones modeled as rigid bodies with a pressure overclosure contact definition. For benchmarking, implant size distributions between the virtual population and actual patients were similar (Figure 4). For the tibial component, the model predicted smaller and larger sizes than observed in the patient population.

Figure 3.

Figure 3.

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Cumulative distribution function comparison of SSM training set and sampled analysis groups (Monte Carlo, Latin Hypercube) to prior population study on 1000 subjects with varying ethnicity (Mahfouz et al. 2012).

Figure 4.

Figure 4.

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Comparison of implant sizes from Monte Carlo sampling (100 instances) using the virtual implantation algorithm to clinical data on 100 consecutive TKR patients.

Considering the anatomic and implant size variability, range of motion for the PF kinematics was 53–69° for flexion-extension (sagittal tilt), 2–14° for IE rotation, and 3–7 mm for ML translation during the deep knee bend activity (Figure 5). PF IE rotation exhibited variability in initial alignment, but narrowed with flexion as the patella engaged the femoral trochlear groove (Figure 5). Latin Hypercube sampling with 12 trials generally captured the range of kinematics of the Monte Carlo simulation with 100 trials in a fraction of the computation time. Between sampling strategies, the 10–90% bounds over the cycle were within 6% for flexion-extension and 13% for other degrees of freedom. The kinematics from Monte Carlo and Latin Hypercube sampling largely captured the trends and spread in the representative experimental data (Baldwin et al. 2009a, 2012) for flexion-extension and IE rotations (Figure 5). Some differences in the kinematic profiles were observed between specimens and between model and experiment in ML translation. Experimental variability is likely greater as it includes contributions from anatomy, soft tissue properties and joint loading, while only anatomic variation is included in the model. Peak contact pressure and contact area were also evaluated, but did not show significant variation, which is likely a result of the dome implant, neutral positioning and common loading condition.

Figure 5.

Figure 5.

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Comparison of PF kinematics for flexion-extension (FE), internal-external (IE) and medial-lateral (ML) degrees of freedom between model-predicted Monte Carlo (gray), model-predicted Latin Hypercube (red), and in-vitro experimental data (black).

For the population of virtual subjects, the influence of alta-baja, described with the Insall-Salvati index (Insall and Salvati 1971), was evaluated on patellofemoral kinematics; a baja patella started in a more flexed initial position and exhibited less medial translation through the deep knee bend cycle (Figure 6). The influence of alta-baja was more strongly correlated with FE than other degrees of freedom. Implant size was also found to influence the range of motion. PF range of motion in AP and ML degrees of freedom were, in general, larger with increasing femoral component size (Figure 6), although there was a slight decrease in ML range of motion for size 8.

Figure 6.

Figure 6.

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Joint motion with flexion for a representative instance (top). Influence of implant size on PF ML and AP range of motion (middle), and influence of patellar alta-baja on PF FE and ML (bottom). Error bars represent one standard deviation.

4. Discussion

This study demonstrated a computational platform to perform population-based evaluations of TKR implant mechanics and assessed the potential to use an efficient sampling strategy to capture the range of anatomic variability for the population. The current study focused on patellofemoral mechanics, where PF issues continue to comprise approximately 10% of TKR complications (Putman et al. 2019, Dennis et al. 2011). The workflow automatedly generated a virtual subject from the SSM, sized and placed implants, generated an analysis-ready model, performed the finite element analysis and extracted joint mechanics results. An understanding of the variation in the anatomy and the implications on joint mechanics provides important information to support surgical decision-making and implant design, in particular, establishing links between patient factors (e.g. alta-baja), implant sizing, and kinematics.

A novel aspect of the current study is that population-based analyses were performed for implanted conditions considering anatomic variation at the joint level. Other studies have performed virtual implantation of specific subjects (Al-Dirini et al. 2019, O’Rourke et al. 2019, Bah et al. 2015a,b), but these evaluations have focused on an implant in a single bone (femur or pelvis) to assess primary fixation. The current study captured multiple structures of the joint, thus enabling joint mechanics evaluations. While the current work considered the implant in the optimal or neutral alignment and a consistent deep knee bend loading condition, the framework could be expanded in the future to also consider variation in surgical approaches and/or loading conditions.

Population-based models which use virtually-generated subjects are difficult to validate directly. Comparisons were made at multiple levels for benchmarking. Distributions for anatomic measures and implant sizes were comparable to their associated populations. The Monte Carlo and Latin Hypercube sampling created populations that were similar to the 1000 subjects of varying ethnicity measured by Mahfouz et al. (2012) (Figure 3). The distribution of implant sizes compared well with actual implant sizes for 100 consecutive TKA patients (Figure 4); while not a direct evaluation and not corrected for patient size measurements, the general agreement in the comparison gives confidence in the automated algorithm used to perform the virtual implantations. Lastly, good agreement was observed between the population-based kinematic predictions and the representative experimental data (Baldwin et al. 2009a, 2012). Some differences were noted, that are likely due to greater intersubject variation in the experiment than in the model. The model captures anatomic variation, but does not consider variation in the soft tissue constraint and utilizes a simplified loading condition.

As the emphasis of the current work was on developing the framework to consider the effects of anatomic variability, the approach applied average properties to represent the ligament constraint and a consistent loading condition where tibiofemoral kinematics were prescribed and not varied between subjects. The realism of the model could be improved by considering a probabilistic representation for soft tissue constraint (Baldwin et al. 2009b). The loading conditions could also be improved to assess TF and PF mechanics simultaneously (Baldwin et al. 2012) and implemented for activities of daily living beyond the deep knee bend. Further development could leverage interactions between shape and joint loading, using techniques similar to Galloway et al. (2012) for kinetics and Zhang et al. (2016) for morphing of musculoskeletal models. While peak contact pressures and areas were evaluated in the current study, they would be more meaningful when loading variation is considered. Since the MR scans were performed in an unloaded state, the initial tension in the extensor mechanism and related position of the patella were not known and required an initial pre-tensioning step. Future models could utilize personalized data or probabilistic methods to capture bounds representing soft tissue constraint and loading conditions.

The appropriate number of subjects to use in the virtual population also warrants further discussion. The population consisted of 100 virtual subjects, which was selected to be large enough to capture variation in the population, yet computationally tractable. A larger population of virtual subjects and including more outliers by sampling in the tails of the distribution is possible, but some of the emphasis of this study was on balancing variation and efficiency. An additional consideration is the balance between the population of virtual subjects and the number of subjects in the training set used to develop the SSM. The segmentation and processing of the training set subjects was manual and time-consuming given the number of structures (bones, cartilage and soft tissue attachment sites) in the joint-level representation and ensuring compatibility with FE analysis. A larger training set could capture more of the variability in the anatomy of the population and is a goal of our ongoing work. However, anatomical measures for the current training set agreed well with larger population studies (Mahfouz et al. 2012). As a result, the use of a larger training set would likely have a modest impact on the results, particularly for Latin Hypercube given the stratified sampling approach and the limited number of virtual subjects.

When performing population-based evaluations, there are tradeoffs between using instances from an SSM versus a set of subject geometries directly. The SSM registers all of the subjects to a common mesh which facilitates characterization/assessment of the population, automated identification of landmarks and anatomical measures, and streamlined workflows to virtually implant, build finite element models and extract results. The SSM is derived from the training set, so ensuring the training set instances are representative of the target population is an important consideration. Performing analyses on subject geometries instead of virtual instances has a more direct tie to reality and may be preferred when additional data, e.g. outcomes, kinematics, joint loading, etc., is available. The SSM platform has the unique ability to create instances that target specific attributes related to size, bone shape or alignment, which can be useful for considering implants in best or worst-case scenarios.

The Latin Hypercube sampling strategy with 12 subjects reasonably captured the 10–90% bounds of kinematics compared to the Monte Carlo simulation. The ability of Latin Hypercube sampling to efficiently capture much of the variability highlights the potential to perform screening evaluations of TKR designs; however, we also recognize the need in some scenarios to consider larger populations to assess the overall performance or risk, including the tails of the distribution. More broadly, by characterizing how kinematics vary with implant size and patient anatomy, the population-based approach can assess implant robustness, the effectiveness of sizing lines, and also investigate surgical technique, e.g. maximizing coverage versus restoring the median ridge of the patella (Yang et al. 2017) or mechanical versus anatomic alignment.

In closing, the study effectively demonstrated an automated computational workflow for population-based evaluation of TKR mechanics, which enables intersubject variability to be considered when assessing implant designs and informing surgical decision-making. The improved efficiency and tractable runtimes with the Latin Hypercube approach are well suited for early design cycle evaluation of design concepts, while larger Monte Carlo-based simulations, which can incorporate variation in anatomy, alignment and loading conditions, can more rigorously assess robustness of an implant design later in the design cycle.

5. Acknowledgement

This research was supported in part by the National Science Foundation (CBET-1034251), National Institutes of Health (Grant number: 1R01EB015497-01) and DePuy Synthes, a Johnson & Johnson Company.

Disclosures for the authors are as follows: A.A. Ali, L.M. Smoger and C.K. Fitzpatrick have no conflicts of interest to report. P.J. Laz, C.W. Clary and P.J. Rullkoetter have received institutional support from DePuy Synthes. C.W. Clary and P.J. Rullkoetter have served as consultants for DePuy Synthes. D.A. Dennis has received royalties from DePuy Synthes and Innomed, and received honorariums and served as a consultant for DePuy Synthes and Corin. He reports owning stock or stock options in Joint Vue and receiving research or institutional support from DePuy Synthes and Porter Adventist Hospital.

Footnotes

6.

Compliance with Ethical Standards

For the population model, the study used cadaveric data, publically-available data from the Osteoarthritis Initiative, and deidentified data, and was categorized as exempt by the University of Denver Institutional Review Board. With regard to the implant size data for the clinical subjects, the study (ID: 1480194-1) was reviewed and approved by the Catholic Health Initiatives Institute for Research and Innovation Institutional Review Board (CHIRB) Institutional Review Board. The implant size data was deidentified and no patient information was transferred.

Publisher's Disclaimer: This Author Accepted Manuscript is a PDF file of an unedited peer-reviewed manuscript that has been accepted for publication but has not been copyedited or corrected. The official version of record that is published in the journal is kept up to date and so may therefore differ from this version.

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