Deciphering the "Art" in Modeling and Simulation of the Knee Joint: Assessing Model Calibration Workflows and Outcomes.

Model reproducibility is a point of emphasis for the National Institutes of Health (NIH) and in science, broadly. As the use of computational modeling in biomechanics and orthopedics grows, so does the need to assess the reproducibility of modeling workflows and simulation predictions. The long-term goal of the KneeHub project is to understand the influence of potentially subjective decisions, thus the modeler's "art", on the reproducibility and predictive uncertainty of computational knee joint models. In this paper, we report on the model calibration phase of this project, during which five teams calibrated computational knee joint models of the same specimens from the same specimen-specific joint mechanics dataset. We investigated model calibration approaches and decisions, and compared calibration workflows and model outcomes among the teams. The selection of the calibration targets used in the calibration workflow differed greatly between the teams and was influenced by modeling decisions related to the representation of structures, and considerations for computational cost and implementation of optimization. While calibration improved model performance, differences in the postcalibration ligament properties and predicted kinematics were quantified and discussed in the context of modeling decisions. Even for teams with demonstrated expertise, model calibration is difficult to foresee and plan in detail, and the results of this study underscore the importance of identification and standardization of best practices for data sharing and calibration.

A Method to Compare Heterogeneous Types of Bone and Cartilage Meshes.

Accurately capturing the bone and cartilage morphology and generating a mesh remains a critical step in the workflow of computational knee joint modeling. Currently, there is no standardized method to compare meshes of different element types and nodal densities, making comparisons across research teams a significant challenge. The aim of this paper is to describe a method to quantify differences in knee joint bone and cartilages meshes, independent of bone and cartilage mesh topology. Bone mesh-to-mesh distances, subchondral bone boundaries, and cartilage thicknesses from meshes of any type of mesh are obtained using a series of steps involving registration, resampling, and radial basis function fitting after which the comparisons are performed. Subchondral bone boundaries and cartilage thicknesses are calculated and visualized in a common frame of reference for comparison. The established method is applied to models developed by five modeling teams. Our approach to obtain bone mesh-to-mesh distances decreased the divergence seen in selecting a reference mesh (i.e., comparing mesh A-to-B versus mesh B-to-A). In general, the bone morphology was similar across teams. The cartilage thicknesses for all models were calculated and the mean absolute cartilage thickness difference was presented, the articulating areas had the best agreement across teams. The teams showed disagreement on the subchondral bone boundaries. The method presented in this paper allows for objective comparisons of bone and cartilage geometry that is agnostic to mesh type and nodal density.

Deciphering the "Art" in Modeling and Simulation of the Knee Joint: Variations in Model Development.

The use of computational modeling to investigate knee joint biomechanics has increased exponentially over the last few decades. Developing computational models is a creative process where decisions have to be made, subject to the modelers' knowledge and previous experiences, resulting in the "art" of modeling. The long-term goal of the KneeHub project is to understand the influence of subjective decisions on the final outcomes and the reproducibility of computational knee joint models. In this paper, we report on the model development phase of this project, investigating model development decisions and deviations from initial modeling plans. Five teams developed computational knee joint models from the same dataset, and we compared each teams' initial uncalibrated models and their model development workflows. Variations in the software tools and modeling approaches were found, resulting in differences such as the representation of the anatomical knee joint structures in the model. The teams consistently defined the boundary conditions and used the same anatomical coordinate system convention. However, deviations in the anatomical landmarks used to define the coordinate systems were present, resulting in a large spread in the kinematic outputs of the uncalibrated models. The reported differences and similarities in model development and simulation presented here illustrate the importance of the "art" of modeling and how subjective decision-making can lead to variation in model outputs. All teams deviated from their initial modeling plans, indicating that model development is a flexible process and difficult to plan in advance, even for experienced teams.

Deciphering the "Art" in Modeling and Simulation of the Knee Joint: Overall Strategy.

Recent explorations of knee biomechanics have benefited from computational modeling, specifically leveraging advancements in finite element analysis and rigid body dynamics of joint and tissue mechanics. A large number of models have emerged with different levels of fidelity in anatomical and mechanical representation. Adapted modeling and simulation processes vary widely, based on justifiable choices in relation to anticipated use of the model. However, there are situations where modelers' decisions seem to be subjective, arbitrary, and difficult to rationalize. Regardless of the basis, these decisions form the "art" of modeling, which impact the conclusions of simulation-based studies on knee function. These decisions may also hinder the reproducibility of models and simulations, impeding their broader use in areas such as clinical decision making and personalized medicine. This document summarizes an ongoing project that aims to capture the modeling and simulation workflow in its entirety-operation procedures, deviations, models, by-products of modeling, simulation results, and comparative evaluations of case studies and applications. The ultimate goal of the project is to delineate the art of a cohort of knee modeling teams through a publicly accessible, transparent approach and begin to unravel the complex array of factors that may lead to a lack of reproducibility. This manuscript outlines our approach along with progress made so far. Potential implications on reproducibility, on science, engineering, and training of modeling and simulation, on modeling standards, and on regulatory affairs are also noted.

Accuracy tradeoffs between individual bone and joint-level statistical shape models of knee morphology.

Statistical shape models (SSMs) are useful tools in evaluating variation in bony anatomy to assess pathology, plan surgical interventions, and inform the design of orthopaedic implants and instrumentation. Recently, by considering multiple bones spanning a joint or the whole lower extremity, SSMs can support studies investigating articular conformity and joint mechanics. The objective of this study was to assess tradeoffs in accuracy between SSMs of the femur or tibia individually versus a combined joint-level model. Three statistical shape models were developed (femur-only, tibia-only, and joint-level) for a training set of 179 total knee arthroplasty (TKA) patients with osteoarthritis representing both genders and several ethnicities. Bone geometries were segmented from preoperative CT scans, meshed with triangular elements, and registered to a template for each SSM. Principal component analysis was performed to determine modes of variation. The statistical shape models were compared using measures of compactness, accuracy, generalization, and specificity. The generalization evaluation, assessing the ability to describe an unseen instance in a leave-one-out analysis, showed that errors were consistently smaller for the individual femur and tibia SSMs than for the joint-level model. However, when additional modes were included in the joint-level model, the errors were comparable to the individual bone results, with minimal additional computational expense. When developing more complex SSMs at the joint, lower limb, or whole-body level, the use of an error threshold to inform the number of included modes, instead of 95 % of the variation explained, can help to ensure accurate representations of anatomy.

Computational framework for population-based evaluation of TKR-implanted patellofemoral joint mechanics.

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 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 10-90% 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.

Development and calibration of a probabilistic finite element hip capsule representation.

The objective of this study was to develop a probabilistic representation of the hip capsule, which is calibrated to experimental capsular torque-rotation behavior and captures the observed variability for use in population-based studies. A finite element model of the hip capsule was developed with structures composed of a fiber-reinforced membrane, represented by 2D quadrilateral elements embedded with tension-only non-linear spring. An average capsule representation was developed by calibrating ligament properties (linear stiffness, reference strain) so that torque-rotation behavior matched mean cadaveric data. A probabilistic capsule was produced by determining the ligament property variability which represented ±2 SD measured in the experiment. Differences between experimental and model kinematics across all positions had RMS error of 4.7°. Output bounds from the optimized probabilistic capsule representation were consistent with ±2 SD of experimental data; the overall RMS error was 5.1°. This model can be employed in population-based finite element studies of THA to assess mechanics in realistic scenarios considering implant design, as well as surgical and patient factors.

Computer-assisted versus manual alignment in THA: a probabilistic approach to range of motion.

Dislocation remains a major complication after THA, and range of motion before impingement is important in joint stability. Variability in implant alignment affects resultant range of motion. We used a probabilistic modeling approach to assess the effects of implant alignment variability based on manual and computer-assisted surgical (CAS) techniques on resultant range of motion after THA. We implemented a contact detection algorithm within a probabilistic analysis framework. The normally distributed alignment variables (mean +/- 1 standard deviation) were cup abduction (manual = 45 degrees +/- 7.6 degrees , CAS = 45 degrees +/- 5.7 degrees ), cup anteversion (manual = 20 degrees +/- 9.6 degrees , CAS = 20 degrees +/- 4.5 degrees ), and stem anteversion (manual and CAS = 10 degrees +/- 1.5 degrees ). The outcomes of the probabilistic analysis were range of motion distributions with 1% and 99% bounds. The upper bounds of motion for manual and CAS alignment were similar because bony impingement was the limiting factor. The lower bounds of range of motion were substantially different depending on the type of surgical alignment; manual alignment produced a smaller range of motion in 3% to 5% of cases. CAS implant alignment produced range of motion values above minimum acceptable levels in all cases simulated.

A multi-subject evaluation of uncertainty in anatomical landmark location on shoulder kinematic description.

An accurate assessment of shoulder kinematics is useful for understanding healthy normal and pathological mechanics. Small variability in identifying and locating anatomical landmarks (ALs) has potential to affect reported shoulder kinematics. The objectives of this study were to quantify the effect of landmark location variability on scapular and humeral kinematic descriptions for multiple subjects using probabilistic analysis methods, and to evaluate the consistency in results across multiple subjects. Data from 11 healthy subjects performing humeral elevation in the scapular plane were used to calculate Euler angles describing humeral and scapular kinematics. Probabilistic analyses were performed for each subject to simulate uncertainty in the locations of 13 upper-extremity ALs. For standard deviations of 4 mm in landmark location, the analysis predicted Euler angle envelopes between the 1 and 99 percentile bounds of up to 16.6 degrees . While absolute kinematics varied with the subject, the average 1-99% kinematic ranges for the motion were consistent across subjects and sensitivity factors showed no statistically significant differences between subjects. The description of humeral kinematics was most sensitive to the location of landmarks on the thorax, while landmarks on the scapula had the greatest effect on the description of scapular elevation. The findings of this study can provide a better understanding of kinematic variability, which can aid in making accurate clinical diagnoses and refining kinematic measurement techniques.

Assessment of scapular morphology and bone quality with statistical models.

The design of total shoulder arthroplasty implants are guided by anatomy. The objective of this study was to develop statistical models to quantify shape and material property variation in the scapula. Material-mapped models were reconstructed from CT scans for a training set of subjects. Statistical shape (SSM) and intensity (SIM) models were created; SSM modes described scaling, changes in the medial border and acromial process, and elongation of the scapular blade. SIM modes captured bone quality changes in the anterior and inferior glenoid. Bone quality was independent of scapular morphology. Variation described by the statistical representations can inform implant design and sizing.

Simulated hip abductor strengthening reduces peak joint contact forces in patients with total hip arthroplasty.

Lower extremity muscle strength training is a focus of rehabilitation following total hip arthroplasty (THA). Strength of the hip abductor muscle group is a predictor of overall function following THA. The purpose of this study was to investigate the effects of hip abductor strengthening following rehabilitation on joint contact forces (JCFs) in the lower extremity and low back during a high demand step down task. Five THA patients performed lower extremity maximum isometric strength tests and a stair descent task. Patient-specific musculoskeletal models were created in OpenSim and maximum isometric strength parameters were scaled to reproduce measured pre-operative joint torques. A pre-operative forward dynamic simulation of each patient performing the stair descent was constructed using their corresponding patient-specific model to predict JCFs at the ankle, knee, hip, and low back. The hip abductor muscles were strengthened with clinically supported increases (0-30%) above pre-operative values in a probabilistic framework to predict the effects on peak JCFs (99% confidence bounds). Simulated hip abductor strengthening resulted in lower peak JCFs relative to pre-operative for all five patients at the hip (18.9-23.8 ±â€¯16.5%) and knee (20.5-23.8 ±â€¯11.2%). Four of the five patients had reductions at the ankle (7.1-8.5 ±â€¯11.3%) and low back (3.5-7.0 ±â€¯5.3%) with one patient demonstrating no change. The reduction in JCF at the hip joint and at joints other than the hip with hip abductor strengthening demonstrates the dynamic and mechanical interdependencies of the knee, hip and spine that can be targeted in early THA rehabilitation to improve overall patient function.

Investigating gender and ethnicity differences in proximal humeral morphology using a statistical shape model.

Morphological variability in the shoulder influences the joint biomechanics and is an important consideration in arthroplasty and implant design. The objectives of this study were to quantify cortical and cancellous proximal humeral morphology and to assess whether shape variation was influenced by gender and ethnicity, with the overarching goal of informing implant design and treatment. A statistical shape model of the proximal humeral cortical and cancellous regions was developed for a training set of 84 subjects of both genders and different ethnicities. Cortical and cancellous bone geometries were reconstructed from CT scans, meshed with triangular elements, and registered to a template. Principal component analysis was applied to quantify modes of variation. Anatomical measurements were computed on the registered geometries to assess correlation with modes of variation. Parallel analysis identified six significant modes of variation, which accounted for 93% of variation in the training set and described scaling (Mode 1), inclination of the head (Modes 2 and 5), and shape of the greater tuberosity and neck region (Modes 3, 4, and 6). Size differences as described by Mode 1 were statistically significant for gender and ethnicity, where female and Asian subjects were smaller than male and Caucasian subjects, respectively; however, differences in other modes were not significant. Cortical thickness of the shaft after normalization by outer diameter was significantly larger for Asian subjects compared to Caucasian subjects. The statistical shape model quantified cortical and cancellous humeral morphology considering gender and ethnicity, providing descriptive data to support surgical planning, and implant design. © 2018 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:3043-3052, 2018.

Statistical shape modeling characterizes three-dimensional shape and alignment variability in the lumbar spine.

The mechanics of the lumbar spine are heavily dependent on the underlying anatomy. Anatomical measures are used to assess the progression of pathologies related to low back pain and to screen patients for surgical treatment options. To describe anatomical norms and pathological differences for the population, statistical shape modeling, which uses full three-dimensional representations of bone morphology and relative alignment, can capture intersubject variability and enable comparative evaluations of subject to population. Accordingly, the objective of this study was to develop a comprehensive set of three-dimensional statistical models to characterize anatomical variability in the lumbar spine, by specifically describing the shape of individual vertebrae, and shape and alignment of the entire lumbar spine (L1-S1), with a focus on the L4-L5 and L5-S1 functional spinal units (FSU). Using CT scans for a cohort of 52 patients, lumbar spine geometries were registered to a template to establish correspondence and a principal component analysis identified the primary modes of variation. Scaling was the most prevalent mode of variation for all models. Subsequent modes of the statistical shape models of the individual bones characterized shape variation within the processes. Subsequent modes of variation for the FSU and entire spine models described alignment changes associated with disc height and lordosis. Quantification of anatomical variation in the spine with statistical models can inform implant design and sizing, assist clinicians in diagnosing pathologies, screen patients for treatment options, and support pre-operative planning.

The impact of hip implant alignment on muscle and joint loading during dynamic activities.

BACKGROUND: Component alignment is an important consideration in total hip arthroplasty. The impact of changes in alignment on muscle forces and joint contact forces during dynamic tasks are not well understood, and have the potential to influence surgical decision making. The objectives of this study were to assess the impact of femoral head/stem and cup component placement on hip muscle and joint contact forces during tasks of daily living and to identify which alignment parameters have the greatest impact on joint loading. METHODS: Using a series of strength-calibrated, subject-specific musculoskeletal models of patients performing gait, sit-to-stand and step down tasks, component alignments were perturbed and joint contact and muscle forces evaluated. FINDINGS: Based on the range of alignments reported clinically, variation in head/stem anteversion-retroversion had the largest impact of any degree of freedom throughout all three tasks; average contact forces 413.5 (319.1) N during gait, 262.7 (256.4) N during sit to stand, and 572.7 (228.1) N during the step down task. The sensitivity of contact force to anteversion-retroversion of the head/stem was 31.5 N/° for gait, which was similar in magnitude to anterior-posterior position of the cup (34.6 N/m for gait). Additionally, superior-inferior cup alignment resulted in 16.4 (4.9)° of variation in the direction of the hip joint contact force across the three tasks, with the most inferior cup placements moving the force vector towards the cup equator at the point of peak joint contact force. INTERPRETATION: A quantitative understanding of the impact and potential tradeoffs when altering component alignment is valuable in supporting surgical decision making.

Effect of variability in anatomical landmark location on knee kinematic description.

Small variability associated with identifying and locating anatomical landmarks on the knee has the potential to affect the joint coordinate systems and reported kinematic descriptions. The objectives of this study were to develop an approach to quantify the effect of landmark location variability on both tibiofemoral and patellofemoral kinematics and to identify the critical landmarks and associated degrees of freedom that most affected the kinematic measures. The commonly used three-cylindric open-chain kinematic description utilized measured rigid body kinematics from a cadaveric specimen during simulated gait. A probabilistic analysis was performed with 11 anatomical landmarks to predict the variability in each kinematic. The model predicted the absolute kinematic bounds and offset kinematic bounds, emphasizing profile shape, for each kinematic over the gait cycle, as well as the range of motion. Standard deviations of up to 2 mm were assumed for the anatomical landmark locations and resulted in significant variability in clinically relevant absolute kinematic parameters of up to 6.5 degrees and 4.4 mm for tibiofemoral and 7.6 degrees and 6.5 mm for patellofemoral kinematics. The location of the femoral epicondylar prominences had the greatest effect on both the tibiofemoral and patellofemoral kinematic descriptions. A quantitative understanding of the potential changes in kinematic description caused by anatomical landmark variability is important not only to the accuracy of kinematic gait studies and the evaluation of total knee arthroplasty implant performance, but also may impact component placement decision-making in computer-assisted surgery.

Effects of rotator cuff tears on muscle moment arms: a computational study.

Rotator cuff tears cause morphologic changes to cuff tendons and muscles, which can alter muscle architecture and moment arm. The effects of these alterations on shoulder mechanical performance in terms of muscle force and joint strength are not well understood. The purpose of this study was to develop a three-dimensional explicit finite element model for investigating morphological changes to rotator cuff tendons following cuff tear. The subsequent objectives were to validate the model by comparing model-predicted moment arms to empirical data, and to use the model to investigate the hypothesis that rotator cuff muscle moment arms are reduced when tendons are divided along the force-bearing direction of the tendon. The model was constructed by extracting tendon, cartilage, and bone geometry from the male Visible Human data set. Infraspinatus and teres minor muscle and tendon paths were identified relative to the humerus and scapula. Kinetic and kinematic boundary conditions in the model replicated experimental protocols, which rotated the humerus from 45 degrees internal to 45 degrees external rotation with constant loads on the tendons. External rotation moment arms were calculated for two conditions of the cuff tendons: intact normal and divided tendon. Predicted moment arms were within the 1-99% confidence intervals of experimental data for nearly all joint angles and tendon sub-regions. In agreement with the experimental findings, when compared to the intact condition, predicted moment arms were reduced for the divided tendon condition. The results of this study provide evidence that one potential mechanism for the reduction in strength observed with cuff tear is reduction of muscle moment arms. The model provides a platform for future studies addressing mechanisms responsible for reduced muscle force and joint strength including changes to muscle length-tension operating range due to altered muscle and tendon excursions, and the effects of cuff tear size and location on moment arms and muscle forces.

Incorporating uncertainty in mechanical properties for finite element-based evaluation of bone mechanics.

Finite element (FE) models of bone, developed from computed tomography (CT) scan data, are used to evaluate stresses and strains, load transfer and fixation of implants, and potential for fracture. The experimentally derived relationships used to transform CT scan data in Hounsfield unit to modulus and strength contain substantial scatter. The scatter in these relationships has potential to impact the results and conclusions of bone studies. The objectives of this study were to develop a computationally efficient probabilistic FE-based platform capable of incorporating uncertainty in bone property relationships, and to apply the model to a representative analysis; variability in stresses and fracture risk was predicted in five proximal femurs under stance loading conditions. Based on published variability in strength and modulus relationships derived in the proximal femur, the probabilistic analysis predicted the distributions of stress and risk. For the five femurs analyzed, the 1 and 99 percentile bounds varied by an average of 17.3 MPa for stress and by 0.28 for risk. In each femur, the predicted variability in risk was greater than 50% of the mean risk calculated, with obvious implications for clinical assessment. Results using the advanced mean value (AMV) method required only seven analysis trials (1h) and differed by less than 2% when compared to a 1000-trial Monte-Carlo simulation (400 h). The probabilistic modeling platform developed has broad applicability to bone studies and can be similarly implemented to investigate other loading conditions, structures, sources of uncertainty, or output measures of interest.

Finite element-based probabilistic analysis tool for orthopaedic applications.

Orthopaedic implants, as well as other physical systems, contain inherent variability in geometry, material properties, component alignment, and loading conditions. While complex, deterministic finite element (FE) models do not account for the potential impact of variability on performance, probabilistic studies have typically predicted behavior from simplified FE models to achieve practical solution times. The objective of this research was to develop an efficient and versatile probabilistic FE tool to quantify the effect of uncertainty in the design variables on the performance of orthopaedic components under relevant conditions. Key aspects of the computational tool developed include parametric and automated FE model creation for changes in dimensional variables, efficient solution using the advanced mean-value (AMV) reliability method, and identification of the most significant design variables. Two orthopaedic applications are presented to demonstrate the ability of the computational tool to efficiently and accurately represent component performance.

Efficient probabilistic finite element analysis of a lumbar motion segment.

Finite element models of the lumbar spine are useful in assessing biomechanics and performance of implants. Models are often developed using the anatomy of an individual subject. Average mechanical property values for the annulus and other soft tissue structures are typically utilized from the literature, as data for the same subject are not available. However, these properties can have significant variability. While probabilistic methods enable the impact of soft tissue property variability on spine mechanics to be assessed, they often require lengthy computation times. Accordingly, the objective of this study was to develop efficient methods to perform Monte Carlo simulations of a finite element model of the L4 L5 functional spinal unit considering variability in the properties of the soft tissue structures. Distributions for the soft tissue properties included the stiffness of spinal ligaments and parameters of a Holzapfel-Gasser-Ogden constitutive material model of the disc. Variance reduction sampling methods, including the Sobol and Descriptive sampling techniques, were assessed for efficiency and accuracy in comparison to traditional random Monte Carlo sampling. Comparisons were based on output torque-rotation curves at the 10th and 90th percentile for flexion, extension, axial rotation, and lateral bending. The Descriptive sampling technique best matched the random sampling technique, at the extremes of rotation, with a 3.6% mean difference. This was achieved with a 10× reduction in the number of iterations and computation time. Improvements in efficiency and maintained accuracy enable intersubject variability to be considered in a variety of biomechanical evaluations, including design-phase screening of orthopedic implants.

Statistical shape modeling predicts patellar bone geometry to enable stereo-radiographic kinematic tracking.

Complications in the patellofemoral (PF) joint of patients with total knee replacements include patellar subluxation and dislocation, and remain a cause for revision. Kinematic measurements to assess these complications and evaluate implant designs require the accuracy of dynamic stereo-radiographic systems with 3D-2D registration techniques. While tibiofemoral kinematics are typically derived by tracking metallic implants, PF kinematic measurements are difficult as the patellar implant is radiotransparent and a representation of the resected patella bone requires either pre-surgical imaging and precise implant placement or post-surgical imaging. Statistical shape models (SSMs), used to characterize anatomic variation, provide an alternative means to obtain the representation of the resected patella for use in kinematic tracking. Using a virtual platform of a stereo-radiographic system, the objectives of this study were to evaluate the ability of an SSM to predict subject-specific 3D implanted patellar geometries from simulated 2D image profiles, and to formulate an effective data collection methodology for PF kinematics by considering accuracy for a variety of patient pose scenarios. An SSM of the patella was developed for 50 subjects and a leave-one-out approach compared SSM-predicted and actual geometries; average 3D errors were 0.45±0.07mm (mean±standard deviation), which is comparable to the accuracy of traditional segmentation. Further, initial imaging of the patella in five unique stereo radiographic perspectives yielded the most accurate representation. The ability to predict the remaining patellar geometry of the implanted PF joint with radiographic images and SSM, instead of CT, can reduce radiation exposure and streamline in vivo kinematic evaluations.