Surrogate articular contact models for computationally efficient multibody dynamic simulations

Assessing the behavior of a hybrid model of the knee with contact surrogate under parameter uncertainties

Modeling the knee is an important factor in increasing the quality of life of both healthy individuals and patients. Nevertheless, the intricate nature of the knee makes this problem complicated. In this study, an extension to an established planar knee joint model with Hertzian contact pairs is proposed with contact mechanics based on polynomial chaos expansion surrogate. Firstly, the finite element (FE) model is made representing a contact pair of sphere-to-plane type with two layers on both bodies, corresponding to the cartilage and the bone. Five variables corresponding to both geometry and material parameters are used to parametrize this model. Then, 128 distinct variants of the FE model are created based on a quasi-Monte Carlo sequence. This dataset is used to train and validate the surrogate. The trained surrogate is proven to have predictive capabilities with an average nRMSE of 0.2% in randomized test/train splits. When included in a model of the knee and tested under parameter uncertainties in Monte Carlo simulations, it results in nRMSE of 58% for angular coordinate compared to the original model with Hertzian pair. This signifies the high influence of contact formulation on the model output and the need for more physically based models in knee contact modeling.

A novel method to accurately recreate in vivo loads and kinematics in computational models of the knee

Despite availability of in vivo knee loads and kinematics data, conventional load- and displacement-controlled configurations still can't accurately predict tibiofemoral loads from kinematics or vice versa. We propose a combined load- and displacement-control method for joint-level simulations of the knee to reliably reproduce in vivo contact mechanics. Prediction errors of the new approach were compared to those of conventional purely load- or displacement-controlled models using in vivo implant loads and kinematics for multiple subjects and activities (CAMS-Knee dataset). Our method reproduced both loads and kinematics more closely than conventional models and thus demonstrates clear advantages for investigating tibiofemoral contact or wear.

Optimal Conformity Design of Tibial Insert Component Based on ISO Standard Wear Test Using Finite Element Analysis and Surrogate Model

Total knee replacement is a standard surgical treatment used to treat osteoarthritis in the knee. The implant is complicated, requiring expensive designs and testing as well as a surgical intervention. This research proposes a technique concerning the optimal conformity design of the symmetric polyethylene tibial insert component for fixed-bearing total knee arthroplasty. The Latin Hypercube Sampling (LHS) design of the experiment was used to create 30 cases of the varied tibial insert conformity that influenced the total knee replacement wear volume. The combination of finite element analysis and a surrogate model was performed to predict wear volume according to the standard of ISO-14243:2014 wear test and to determine the optimal conformity. In the first step, the results could predict wear volume between 5.50 to 72.92 mm3/106 cycle. The Kriging method of a surrogate model has then created the increased design based on the efficient global optimization (EGO) method with improving data 10 design points. The result revealed that the optimum design of tibial insert conformity in a coronal and sagittal plane was 0.70 and 0.59, respectively, with a minimizing wear volume of 3.07 mm3/106 cycle. The verification results revealed that the area surface scrape and wear volume are similar to those predicted by the experiment. The wear behavior on the tibial insert surface was asymmetry of both sides. From this study it can be concluded that the optimal conformity design of the tibial insert component can be by using a finite element and surrogate model combined with the design of conformity to the minimized wear volume.

Spatial Algorithms for Geometric Contact Detection in Multibody System Dynamics

In the present work, different algorithms for contact detection in multibody systems based on smooth contact modelling approaches are presented. Beginning with the simplest ones, some difficult interactions are subsequently introduced. In addition, a brief overview on the different kinds of contact/impact modelling is provided and an underlining of the advantages and the drawbacks of each of them is determined. Finally, some practical examples of each interaction are presented and analyzed and an outline of the issues arisen during the design process and how they have been solved in order to obtain stable and accurate results is given. The main goal of this paper is to provide a resource for the early-stage researchers in the field that serves as an introduction to the modelling of simple contact/impact events in the context of multibody system dynamics.

A Conceptual Blueprint for Making Neuromusculoskeletal Models Clinically Useful

The ultimate goal of most neuromusculoskeletal modeling research is to improve the treatment of movement impairments. However, even though neuromusculoskeletal models have become more realistic anatomically, physiologically, and neurologically over the past 25 years, they have yet to make a positive impact on the design of clinical treatments for movement impairments. Such impairments are caused by common conditions such as stroke, osteoarthritis, Parkinson’s disease, spinal cord injury, cerebral palsy, limb amputation, and even cancer. The lack of clinical impact is somewhat surprising given that comparable computational technology has transformed the design of airplanes, automobiles, and other commercial products over the same time period. This paper provides the author’s personal perspective for how neuromusculoskeletal models can become clinically useful. First, the paper motivates the potential value of neuromusculoskeletal models for clinical treatment design. Next, it highlights five challenges to achieving clinical utility and provides suggestions for how to overcome them. After that, it describes clinical, technical, collaboration, and practical needs that must be addressed for neuromusculoskeletal models to fulfill their clinical potential, along with recommendations for meeting them. Finally, it discusses how more complex modeling and experimental methods could enhance neuromusculoskeletal model fidelity, personalization, and utilization. The author hopes that these ideas will provide a conceptual blueprint that will help the neuromusculoskeletal modeling research community work toward clinical utility.

Rigid-body modeling of knee cartilage and meniscus using experimental pressure-strain curves

Rigid-body knee models have gained popularity thanks to computational speed and ease of setup compared to finite element models-showing exciting potential for clinical patient-specific models in the future. However, Rigid-body studies in general have encountered difficulty in modeling cartilage and especially meniscus material properties, often relying on computationally costly optimization techniques. This paper presents two new methods to alleviate the difficulty-one to define model contact pressure and one to define meniscus internal forces-and is the first to our knowledge to use experimental pressure-strain curves from the literature to simulate cartilage and meniscus behavior in a rigid body model. This paper describes the methodology to derive the proof of concept model and preliminary results from a gait simulation based on ISO 14243-1.

Efficacy and efficiency of multivariate linear regression for rapid prediction of femoral strain fields during activity

Multivariate Linear Regression-based (MLR) surrogate models were explored to reduce the computational cost of predicting femoral strains during normal activity in comparison with finite element analysis. The musculoskeletal model of one individual, the finite-element model of the right femur, and experimental force and motion data for normal walking, fast walking, stair ascent, stair descent, and rising from a chair were obtained from a previous study. Equivalent Von Mises strain was calculated for 1000 frames uniformly distributed across activities. MLR surrogate models were generated using training sets of 50, 100, 200 and 300 samples. The finite-element and MLR analyses were compared using linear regression. The Root Mean Square Error (RMSE) and the 95th percentile of the strain error distribution were used as indicators of average and peak error. The MLR model trained using 200 samples (RMSE < 108 µε; peak error < 228 µε) was used as a reference. The finite-element method required 66 s per frame on a standard desktop computer. The MLR model required 0.1 s per frame plus 1848 s of training time. RMSE ranged from 1.2% to 1.3% while peak error ranged from 2.2% to 3.6% of the maximum micro-strain (5020 µε). Performance within an activity was lower during early and late stance, with RMSE of 4.1% and peak error of 8.6% of the maximum computed micro-strain. These results show that MLR surrogate models may be used to rapidly and accurately estimate strain fields in long bones during daily physical activity.

Simulating contact using the elastic foundation algorithm in OpenSim

Modeling joint contact in OpenSim is not well understood. This study systematically investigated the variables associated with the elastic foundation contact model within OpenSim by performing a series of controlled benchtop experiment and concomitant simulations. Four metal-on-plastic interactions were modeled, including a model of a total knee replacement (TKR). Load-displacement curves were recorded during cyclic loading between 100 and 750 N. Geometries were imported and into OpenSim and contact mechanics were modeled with the on-board elastic foundation algorithm. A hybrid optimization algorithm determined that stiffness and dissipation coefficients for TKR implants were 1.52 × 10¹⁰ N/m and 57.7 Ns/m, respectively. Estimations of contact forces were 10.2% of blinded experimental data (average root mean square error: 76.82 ± 11.47 N). In the second portion of this study, freely available eTibia TKR renderings were used to test the ubiquity of the tuning parameters. They were also used to perform a sensitivity analysis of material stiffness and mesh density with regard to penetration depth and computational time. When a stiffness of 1 × 10¹⁰ was applied to an eTibia model with 5000 faces, a 100 kg load caused 0.259 mm of penetration. Under the same conditions, the tuned model experienced 0.300 mm of penetration. Material stiffnesses between 1 × 10¹³ and 1 × 10¹⁵ N/m increased computation time by factors of 12-23. This study provides much needed clarity regarding the use of the OpenSim EF algorithm. It also demonstrates the utility of OpenSim to model deformable materials and complex geometries, and this approach can be adapted to make reasonable estimations for both natural and surgically modified joints.

Predictive Simulations of Neuromuscular Coordination and Joint-Contact Loading in Human Gait

We implemented direct collocation on a full-body neuromusculoskeletal model to calculate muscle forces, ground reaction forces and knee contact loading simultaneously for one cycle of human gait. A data-tracking collocation problem was solved for walking at the normal speed to establish the practicality of incorporating a 3D model of articular contact and a model of foot-ground interaction explicitly in a dynamic optimization simulation. The data-tracking solution then was used as an initial guess to solve predictive collocation problems, where novel patterns of movement were generated for walking at slow and fast speeds, independent of experimental data. The data-tracking solutions accurately reproduced joint motion, ground forces and knee contact loads measured for two total knee arthroplasty patients walking at their preferred speeds. RMS errors in joint kinematics were < 2.0° for rotations and < 0.3 cm for translations while errors in the model-computed ground-reaction and knee-contact forces were < 0.07 BW and < 0.4 BW, respectively. The predictive solutions were also consistent with joint kinematics, ground forces, knee contact loads and muscle activation patterns measured for slow and fast walking. The results demonstrate the feasibility of performing computationally-efficient, predictive, dynamic optimization simulations of movement using full-body, muscle-actuated models with realistic representations of joint function.

Evaluation of a Surrogate Contact Model in Force-Dependent Kinematic Simulations of Total Knee Replacement

Knowing the forces in the human body is of great clinical interest and musculoskeletal (MS) models are the most commonly used tool to estimate them in vivo. Unfortunately, the process of computing muscle, joint contact, and ligament forces simultaneously is computationally highly demanding. The goal of this study was to develop a fast surrogate model of the tibiofemoral (TF) contact in a total knee replacement (TKR) model and apply it to force-dependent kinematic (FDK) simulations of activities of daily living (ADLs). Multiple domains were populated with sample points from the reference TKR contact model, based on reference simulations and design-of-experiments. Artificial neural networks (ANN) learned the relationship between TF pose and loads from the medial and lateral sides of the TKR implant. Normal and right-turn gait, rising-from-a-chair, and a squat were simulated using both surrogate and reference contact models. Compared to the reference contact model, the surrogate contact model predicted TF forces with a root-mean-square error (RMSE) lower than 10 N and TF moments lower than 0.3 N·m over all simulated activities. Secondary knee kinematics were predicted with RMSE lower than 0.2 mm and 0.2 deg. Simulations that used the surrogate contact model ran on average three times faster than those using the reference model, allowing the simulation of a full gait cycle in 4.5 min. This modeling approach proved fast and accurate enough to perform extensive parametric analyses, such as simulating subject-specific variations and surgical-related factors in TKR.

A Computational Efficient Method to Assess the Sensitivity of Finite-Element Models: An Illustration With the Hemipelvis

Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.

Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review

In the present paper, we review the current state-of-the-art in asymptotic modeling of articular contact. Particular attention has been given to the knee joint contact mechanics with a special emphasis on implications drawn from the asymptotic models, including average characteristics for articular cartilage layer. By listing a number of complicating effects such as transverse anisotropy, non-homogeneity, variable thickness, nonlinear deformations, shear loading, and bone deformation, which may be accounted for by asymptotic modeling, some unsolved problems and directions for future research are also discussed.

Surrogate modeling of deformable joint contact using artificial neural networks

Deformable joint contact models can be used to estimate loading conditions for cartilage-cartilage, implant-implant, human-orthotic, and foot-ground interactions. However, contact evaluations are often so expensive computationally that they can be prohibitive for simulations or optimizations requiring thousands or even millions of contact evaluations. To overcome this limitation, we developed a novel surrogate contact modeling method based on artificial neural networks (ANNs). The method uses special sampling techniques to gather input-output data points from an original (slow) contact model in multiple domains of input space, where each domain represents a different physical situation likely to be encountered. For each contact force and torque output by the original contact model, a multi-layer feed-forward ANN is defined, trained, and incorporated into a surrogate contact model. As an evaluation problem, we created an ANN-based surrogate contact model of an artificial tibiofemoral joint using over 75,000 evaluations of a fine-grid elastic foundation (EF) contact model. The surrogate contact model computed contact forces and torques about 1000 times faster than a less accurate coarse grid EF contact model. Furthermore, the surrogate contact model was seven times more accurate than the coarse grid EF contact model within the input domain of a walking motion. For larger input domains, the surrogate contact model showed the expected trend of increasing error with increasing domain size. In addition, the surrogate contact model was able to identify out-of-contact situations with high accuracy. Computational contact models created using our proposed ANN approach may remove an important computational bottleneck from musculoskeletal simulations or optimizations incorporating deformable joint contact models.

An Open-Source Toolbox for Surrogate Modeling of Joint Contact Mechanics

GOAL

Incorporation of elastic joint contact models into simulations of human movement could facilitate studying the interactions between muscles, ligaments, and bones. Unfortunately, elastic joint contact models are often too expensive computationally to be used within iterative simulation frameworks. This limitation can be overcome by using fast and accurate surrogate contact models that fit or interpolate input-output data sampled from existing elastic contact models. However, construction of surrogate contact models remains an arduous task. The aim of this paper is to introduce an open-source program called Surrogate Contact Modeling Toolbox (SCMT) that facilitates surrogate contact model creation, evaluation, and use.

METHODS

SCMT interacts with the third-party software FEBio to perform elastic contact analyses of finite-element models and uses MATLAB to train neural networks that fit the input-output contact data. SCMT features sample point generation for multiple domains, automated sampling, sample point filtering, and surrogate model training and testing.

RESULTS

An overview of the software is presented along with two example applications. The first example demonstrates creation of surrogate contact models of artificial tibiofemoral and patellofemoral joints and evaluates their computational speed and accuracy, while the second demonstrates the use of surrogate contact models in a forward dynamic simulation of an open-chain leg extension-flexion motion.

CONCLUSION

SCMT facilitates the creation of computationally fast and accurate surrogate contact models. Additionally, it serves as a bridge between FEBio and OpenSim musculoskeletal modeling software.

SIGNIFICANCE

Researchers may now create and deploy surrogate models of elastic joint contact with minimal effort.

Prediction of contact mechanics in metal-on-metal Total Hip Replacement for parametrically comprehensive designs and loads

Manufacturers and investigators of Total Hip Replacement (THR) bearings require tools to predict the contact mechanics resulting from diverse design and loading parameters. This study provides contact mechanics solutions for metal-on-metal (MoM) bearings that encompass the current design space and could aid pre-clinical design optimization and evaluation. Stochastic finite element (FE) simulation was used to calculate the head-on-cup contact mechanics for five thousand combinations of design and loading parameters. FE results were used to train a Random Forest (RF) surrogate model to rapidly predict the contact patch dimensions, contact area, pressures and plastic deformations for arbitrary designs and loading. In addition to widely observed polar and edge contact, FE results included ring-polar, asymmetric-polar, and transitional categories which have previously received limited attention. Combinations of design and load parameters associated with each contact category were identified. Polar contact pressures were predicted in the range of 0-200 MPa with no permanent deformation. Edge loading (with subluxation) was associated with pressures greater than 500 MPa and induced permanent deformation in 83% of cases. Transitional-edge contact (with little subluxation) was associated with intermediate pressures and permanent deformation in most cases, indicating that, even with ideal anatomical alignment, bearings may face extreme wear challenges. Surrogate models were able to accurately predict contact mechanics 18,000 times faster than FE analyses. The developed surrogate models enable rapid prediction of MoM bearing contact mechanics across the most comprehensive range of loading and designs to date, and may be useful to those performing bearing design optimization or evaluation.

A Subject-Specific Musculoskeletal Modeling Framework to Predict In Vivo Mechanics of Total Knee Arthroplasty

Musculoskeletal (MS) models should be able to integrate patient-specific MS architecture and undergo thorough validation prior to their introduction into clinical practice. We present a methodology to develop subject-specific models able to simultaneously predict muscle, ligament, and knee joint contact forces along with secondary knee kinematics. The MS architecture of a generic cadaver-based model was scaled using an advanced morphing technique to the subject-specific morphology of a patient implanted with an instrumented total knee arthroplasty (TKA) available in the fifth “grand challenge competition to predict in vivo knee loads” dataset. We implemented two separate knee models, one employing traditional hinge constraints, which was solved using an inverse dynamics technique, and another one using an 11-degree-of-freedom (DOF) representation of the tibiofemoral (TF) and patellofemoral (PF) joints, which was solved using a combined inverse dynamic and quasi-static analysis, called force-dependent kinematics (FDK). TF joint forces for one gait and one right-turn trial and secondary knee kinematics for one unloaded leg-swing trial were predicted and evaluated using experimental data available in the grand challenge dataset. Total compressive TF contact forces were predicted by both hinge and FDK knee models with a root-mean-square error (RMSE) and a coefficient of determination (R2) smaller than 0.3 body weight (BW) and equal to 0.9 in the gait trial simulation and smaller than 0.4 BW and larger than 0.8 in the right-turn trial simulation, respectively. Total, medial, and lateral TF joint contact force predictions were highly similar, regardless of the type of knee model used. Medial (respectively lateral) TF forces were over- (respectively, under-) predicted with a magnitude error of M < 0.2 (respectively > −0.4) in the gait trial, and under- (respectively, over-) predicted with a magnitude error of M > −0.4 (respectively < 0.3) in the right-turn trial. Secondary knee kinematics from the unloaded leg-swing trial were overall better approximated using the FDK model (average Sprague and Geers' combined error C = 0.06) than when using a hinged knee model (C = 0.34). The proposed modeling approach allows detailed subject-specific scaling and personalization and does not contain any nonphysiological parameters. This modeling framework has potential applications in aiding the clinical decision-making in orthopedics procedures and as a tool for virtual implant design.

Estimating total knee replacement joint load ratios from kinematics

Accurate prediction of loads acting at the joint in total knee replacement (TKR) patients is key to developing experimental or computational simulations which evaluate implant designs under physiological loading conditions. In vivo joint loads have been measured for a small number of telemetric TKR patients, but in order to assess device performance across the entire patient population, a larger patient cohort is necessary. This study investigates the accuracy of predicting joint loads from joint kinematics. Specifically, the objective of the study was to assess the accuracy of internal-external (I-E) and anterior-posterior (A-P) joint load predictions from I-E and A-P motions under a given compressive load, and to evaluate the repeatability of joint load ratios (I-E torque to compressive force (I-E:C), and A-P force to compressive force (A-P:C)) for a range of compressive loading profiles. A tibiofemoral finite element model was developed and used to simulate deep knee bend, chair-rise and step-up activities for five patients. Root-mean-square (RMS) differences in I-E:C and A-P:C load ratios between telemetric measurements and model predictions were less than 1.10e-3 Nm/N and 0.035 N/N for all activities. I-E:C and A-P:C load ratios were consistently reproduced regardless of the compressive force profile applied (RMS differences less than 0.53e-3 Nm/N and 0.010 N/N, respectively). When error in kinematic measurement was introduced to the model, joint load predictions were forgiving to kinematic measurement error when conformity between femoral and tibial components was low. The prevalence of kinematic data, in conjunction with the analysis presented here, facilitates determining the scope of A-P and I-E joint loading ratios experienced by the TKR population.

Relative contributions of design, alignment, and loading variability in knee replacement mechanics

Substantial variation in total knee replacement (TKR) outcomes exists within the patient population. Some of this variability is due to differences in the design of the implanted components and variation in surgical alignment, while other variability is due to differences in the applied forces and torques due to anatomic and physiological differences within a patient population. We evaluated the relative contributions of implant design, surgical alignment, and patient-specific loading variability to overall tibiofemoral joint mechanics to provide insight into which measures can be influenced through design and surgical decisions, and which are inherently dependent on variation within the patient population and should be considered in the robustness of the implant design and surgical procedure. Design, surgical, and loading parameters were assessed using probabilistic finite element methods during simulated stance-phase gait and squat activities. Patient-specific loading was found to be the primary contributor to joint loading and kinematics during low flexion, particularly under conditions of high external loads (for instance, the gait cycle with high internal-external torque), while design and surgical factors, particularly femoral posterior radius and posterior slope of the tibial insert became increasingly important in TKR performance in deeper flexion.

A methodology to accurately quantify patellofemoral cartilage contact kinematics by combining 3D image shape registration and cine-PC MRI velocity data

Patellofemoral osteoarthritis and its potential precursor patellofemoral pain syndrome (PFPS) are common, costly, and debilitating diseases. PFPS has been shown to be associated with altered patellofemoral joint mechanics; however, an actual variation in joint contact stresses has not been established due to challenges in accurately quantifying in vivo contact kinematics (area and location). This study developed and validated a method for tracking dynamic, in vivo cartilage contact kinematics by combining three magnetic resonance imaging (MRI) techniques, cine-phase contrast (CPC), multi-plane cine (MPC), and 3D high-resolution static imaging. CPC and MPC data were acquired from 12 healthy volunteers while they actively extended/flexed their knee within the MRI scanner. Since no gold standard exists for the quantification of in vivo dynamic cartilage contact kinematics, the accuracy of tracking a single point (patellar origin relative to the femur) represented the accuracy of tracking the kinematics of an entire surface. The accuracy was determined by the average absolute error between the PF kinematics derived through registration of MPC images to a static model and those derived through integration of the CPC velocity data. The accuracy ranged from 0.47 mm to 0.77 mm for the patella and femur and from 0.68 mm to 0.86 mm for the patellofemoral joint. For purely quantifying joint kinematics, CPC remains an analytically simpler and more accurate (accuracy <0.33 mm) technique. However, for application requiring the tracking of an entire surface, such as quantifying cartilage contact kinematics, this combined imaging approach produces accurate results with minimal operator intervention.

Grand challenge competition to predict in vivo knee loads

Impairment of the human neuromusculoskeletal system can lead to significant mobility limitations and decreased quality of life. Computational models that accurately represent the musculoskeletal systems of individual patients could be used to explore different treatment options and optimize clinical outcome. The most significant barrier to model-based treatment design is validation of model-based estimates of in vivo contact and muscle forces. This paper introduces an annual "Grand Challenge Competition to Predict In Vivo Knee Loads" based on a series of comprehensive publicly available in vivo data sets for evaluating musculoskeletal model predictions of contact and muscle forces in the knee. The data sets come from patients implanted with force-measuring tibial prostheses. Following a historical review of musculoskeletal modeling methods used for estimating knee muscle and contact forces, we describe the first two data sets used for the first two competitions and summarize four subsequent data sets to be used for future competitions. These data sets include tibial contact force, video motion, ground reaction, muscle EMG, muscle strength, static and dynamic imaging, and implant geometry data. Competition participants create musculoskeletal models to predict tibial contact forces without having access to the corresponding in vivo measurements. These blinded predictions provide an unbiased evaluation of the capabilities and limitations of musculoskeletal modeling methods. The paper concludes with a discussion of how these unique data sets can be used by the musculoskeletal modeling research community to improve the estimation of in vivo muscle and contact forces and ultimately to help make musculoskeletal models clinically useful.