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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Implant Design and Effects on Patellofemoral Crepitus.

Background Patellofemoral crepitus is a known complication of posterior stabilized (PS) total knee arthroplasty (TKA). This study compared the incidence of patellofemoral crepitus between two femoral components designs. Materials and Methods Between January 2005 and August 2010, 1,120 patients with complete 2-year follow-up had a PS TKA with two different prosthetic designs (group A, 553 patients; group B, 567 patients). Records were reviewed to identify the incidence of total, symptomatic, and operative patellofemoral crepitus. Results No statistical differences were observed in the incidence of total patellofemoral crepitus (group A 14.1%, group B 14.5%; p = 0.932) or symptomatic patellofemoral crepitus (group A 5.6%, group B 4.2%; p = 0.334). The incidence of operative crepitus was greater in group A (3.3%) than in group B (1.3%; p = 0.026). Analysis of mobile versus fixed bearing designs showed a higher incidence of total patellofemoral crepitus in mobile bearing TKA (16.04 vs. 4.93%; p = 0.006) within group B only. Conclusion Femoral component design with a smoother intercondylar box transition zone resulted in a lower incidence of operative patellofemoral crepitus. No statistical differences were noted regarding the incidence of total and symptomatic patellofemoral crepitus. Mobile bearing TKA exhibited greater total crepitus within group B. Level of Evidence Level III.

The Effects of Prosthesis Inertial Parameters on Inverse Dynamics: A Probabilistic Analysis.

Joint kinetic measurement is a fundamental tool used to quantify compensatory movement patterns in participants with transtibial amputation (TTA). Joint kinetics are calculated through inverse dynamics (ID) and depend on segment kinematics, external forces, and both segment and prosthetic inertial parameters (PIPS); yet the individual influence of PIPs on ID is unknown. The objective of this investigation was to assess the importance of parameterizing PIPs when calculating ID using a probabilistic analysis. A series of Monte Carlo simulations were performed to assess the influence of uncertainty in PIPs on ID. Multivariate input distributions were generated from experimentally measured PIPs (foot/shank: mass, center of mass (COM), moment of inertia) of ten prostheses and output distributions were hip and knee joint kinetics. Confidence bounds (2.5-97.5%) and sensitivity of outputs to model input parameters were calculated throughout one gait cycle. Results demonstrated that PIPs had a larger influence on joint kinetics during the swing period than the stance period (e.g., maximum hip flexion/extension moment confidence bound size: stance = 5.6 N·m, swing: 11.4 N·m). Joint kinetics were most sensitive to shank mass during both the stance and swing periods. Accurate measurement of prosthesis shank mass is necessary to calculate joint kinetics with ID in participants with TTA with passive prostheses consisting of total contact carbon fiber sockets and dynamic elastic response feet during walking.

Patellar component design influences size selection and coverage.

BACKGROUND: Patellofemoral (PF) complications following total knee arthroplasty continue to occur. Outcomes are influenced by implant design, size and alignment in addition to patient factors. The objective of this study was to assess the effect of implant design, specifically round versus oval dome patellar components, on size selected and bony coverage in a population of 100 patients. METHODS: Intraoperative assessments of patella component size were performed using surgical guides for round and oval designs. Digital images of the resected patellae with and without guides were calibrated and analyzed to measure bony coverage. Lastly, the medial-lateral location of the median ridge was assessed in the native patella and compared to the positioning of the apex of the patellar implants. RESULTS: In 82% of subjects, a larger oval implant was selected compared to a round. Modest, but statistically significant, differences were observed in selected component coverage of the resected patella: 82.7% for oval versus 80.9% for round. Further, positioning of the apex of oval patellar components reproduced the median ridge of the native patella more consistently than for round components. CONCLUSIONS: These findings characterized how implant design influenced size selection and coverage in a population of patients. The ability to "upsize" with oval dome components led to increases in bony coverage and better replication of the median ridge compared to round components. Quantifying the interactions between implant design, sizing and coverage for a current implant system in a population of patients supports surgical decision-making and informs the design of future implants.

Patient-Specific Templating of Lumbar Total Disk Replacement to Restore Normal Anatomy and Function.

The purpose of this study was to develop a tool to determine optimal placement and size for total disk replacements (TDRs) to improve patient outcomes of pain and function. The authors developed a statistical shape model to determine the anatomical variables that influence the placement, function, and outcome of lumbar TDR. A patient-specific finite element analysis model has been developed that is now used prospectively to identify patients suitable for TDR and to create a surgical template to facilitate implant placement to optimize range of motion and clinical outcomes. Patient factors and surgical techniques that determine success regarding function and pain are discussed in this article.

Statistical modeling to characterize relationships between knee anatomy and kinematics.

The mechanics of the knee are complex and dependent on the shape of the articular surfaces and their relative alignment. Insight into how anatomy relates to kinematics can establish biomechanical norms, support the diagnosis and treatment of various pathologies (e.g., patellar maltracking) and inform implant design. Prior studies have used correlations to identify anatomical measures related to specific motions. The objective of this study was to describe relationships between knee anatomy and tibiofemoral (TF) and patellofemoral (PF) kinematics using a statistical shape and function modeling approach. A principal component (PC) analysis was performed on a 20-specimen dataset consisting of shape of the bone and cartilage for the femur, tibia and patella derived from imaging and six-degree-of-freedom TF and PF kinematics from cadaveric testing during a simulated squat. The PC modes characterized links between anatomy and kinematics; the first mode captured scaling and shape changes in the condylar radii and their influence on TF anterior-posterior translation, internal-external rotation, and the location of the femoral lowest point. Subsequent modes described relations in patella shape and alta/baja alignment impacting PF kinematics. The complex interactions described with the data-driven statistical approach provide insight into knee mechanics that is useful clinically and in implant design.

A probabilistic approach to quantify the impact of uncertainty propagation in musculoskeletal simulations.

Uncertainty that arises from measurement error and parameter estimation can significantly affect the interpretation of musculoskeletal simulations; however, these effects are rarely addressed. The objective of this study was to develop an open-source probabilistic musculoskeletal modeling framework to assess how measurement error and parameter uncertainty propagate through a gait simulation. A baseline gait simulation was performed for a male subject using OpenSim for three stages: inverse kinematics, inverse dynamics, and muscle force prediction. A series of Monte Carlo simulations were performed that considered intrarater variability in marker placement, movement artifacts in each phase of gait, variability in body segment parameters, and variability in muscle parameters calculated from cadaveric investigations. Propagation of uncertainty was performed by also using the output distributions from one stage as input distributions to subsequent stages. Confidence bounds (5-95%) and sensitivity of outputs to model input parameters were calculated throughout the gait cycle. The combined impact of uncertainty resulted in mean bounds that ranged from 2.7° to 6.4° in joint kinematics, 2.7 to 8.1 N m in joint moments, and 35.8 to 130.8 N in muscle forces. The impact of movement artifact was 1.8 times larger than any other propagated source. Sensitivity to specific body segment parameters and muscle parameters were linked to where in the gait cycle they were calculated. We anticipate that through the increased use of probabilistic tools, researchers will better understand the strengths and limitations of their musculoskeletal simulations and more effectively use simulations to evaluate hypotheses and inform clinical decisions.

Patellar mechanics during simulated kneeling in the natural and implanted knee.

Kneeling is required during daily living for many patients after total knee replacement (TKR), yet many patients have reported that they cannot kneel due to pain, or avoid kneeling due to discomfort, which critically impacts quality of life and perceived success of the TKR procedure. The objective of this study was to evaluate the effect of component design on patellofemoral (PF) mechanics during a kneeling activity. A computational model to predict natural and implanted PF kinematics and bone strains after kneeling was developed and kinematics were validated with experimental cadaveric studies. PF joint kinematics and patellar bone strains were compared for implants with dome, medialized dome, and anatomic components. Due to the less conforming nature of the designs, change in sagittal plane tilt as a result of kneeling at 90° knee flexion was approximately twice as large for the medialized-dome and dome implants as the natural case or anatomic implant, which may result in additional stretching of the quadriceps. All implanted cases resulted in substantial increases in bone strains compared with the natural knee, but increased strains in different regions. The anatomic patella demonstrated increased strains inferiorly, while the dome and medialized dome showed increases centrally. An understanding of the effect of implant design on patellar mechanics during kneeling may ultimately provide guidance to component designs that reduces the likelihood of knee pain and patellar fracture during kneeling.