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.

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.

Influence of tibiofemoral congruency design on the wear of patient-specific unicompartmental knee arthroplasty using finite element analysis

Objectives

Unicompartmental knee arthroplasty (UKA) is an alternative to total knee arthroplasty for patients who require treatment of single-compartment osteoarthritis, especially for young patients. To satisfy this requirement, new patient-specific prosthetic designs have been introduced. The patient-specific UKA is designed on the basis of data from preoperative medical images. In general, knee implant design with increased conformity has been developed to provide lower contact stress and reduced wear on the tibial insert compared with flat knee designs. The different tibiofemoral conformity may provide designers the opportunity to address both wear and kinematic design goals simultaneously. The aim of this study was to evaluate wear prediction with respect to tibiofemoral conformity design in patient-specific UKA under gait loading conditions by using a previously validated computational wear method.

Methods

Three designs with different conformities were developed with the same femoral component: a flat design normally used in fixed-bearing UKA, a tibia plateau anatomy mimetic (AM) design, and an increased conforming design. We investigated the kinematics, contact stress, contact area, wear rate, and volumetric wear of the three different tibial insert designs.

Results

Conforming increased design showed a lower contact stress and increased contact area. In addition, increased conformity resulted in a reduction of the wear rate and volumetric wear. However, the increased conformity design showed limited kinematics.

Conclusion

Our results indicated that increased conformity provided improvements in wear but resulted in limited kinematics. Therefore, increased conformity should be avoided in fixed-bearing patient-specific UKA design. We recommend a flat or plateau AM tibial insert design in patient-specific UKA.

Cite this article: Y-G. Koh, K-M. Park, H-Y. Lee, K-T. Kang. Influence of tibiofemoral congruency design on the wear of patient-specific unicompartmental knee arthroplasty using finite element analysis. Bone Joint Res 2019;8:156–164. DOI: 10.1302/2046-3758.83.BJR-2018-0193.R1.

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.

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.

Dynamic simulation of knee-joint loading during gait using force-feedback control and surrogate contact modelling

The aim of this study was to perform multi-body, muscle-driven, forward-dynamics simulations of human gait using a 6-degree-of-freedom (6-DOF) model of the knee in tandem with a surrogate model of articular contact and force control. A forward-dynamics simulation incorporating position, velocity and contact force-feedback control (FFC) was used to track full-body motion capture data recorded for multiple trials of level walking and stair descent performed by two individuals with instrumented knee implants. Tibiofemoral contact force errors for FFC were compared against those obtained from a standard computed muscle control algorithm (CMC) with a 6-DOF knee contact model (CMC6); CMC with a 1-DOF translating hinge-knee model (CMC1); and static optimization with a 1-DOF translating hinge-knee model (SO). Tibiofemoral joint loads predicted by FFC and CMC6 were comparable for level walking, however FFC produced more accurate results for stair descent. SO yielded reasonable predictions of joint contact loading for level walking but significant differences between model and experiment were observed for stair descent. CMC1 produced the least accurate predictions of tibiofemoral contact loads for both tasks. Our findings suggest that reliable estimates of knee-joint loading may be obtained by incorporating position, velocity and force-feedback control with a multi-DOF model of joint contact in a forward-dynamics simulation of gait.

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.

Dual-joint modeling for estimation of total knee replacement contact forces during locomotion

Model-based estimation of in vivo contact forces arising between components of a total knee replacement is challenging because such forces depend upon accurate modeling of muscles, tendons, ligaments, contact, and multibody dynamics. Here we describe an approach to solving this problem with results that are tested by comparison to knee loads measured in vivo for a single subject and made available through the Grand Challenge Competition to Predict in vivo Tibiofemoral Loads. The approach makes use of a "dual-joint" paradigm in which the knee joint is alternately represented by (1) a ball-joint knee for inverse dynamic computation of required muscle controls and (2) a 12 degree-of-freedom (DOF) knee with elastic foundation contact at the tibiofemoral and patellofemoral articulations for forward dynamic integration. Measured external forces and kinematics were applied as a feedback controller and static optimization attempted to track measured knee flexion angles and electromyographic (EMG) activity. The resulting simulations showed excellent tracking of knee flexion (average RMS error of 2.53 deg) and EMG (muscle activations within ±10% envelopes of normalized measured EMG signals). Simulated tibiofemoral contact forces agreed qualitatively with measured contact forces, but their RMS errors were approximately 25% of the peak measured values. These results demonstrate the potential of a dual-joint modeling approach to predict joint contact forces from kinesiological data measured in the motion laboratory. It is anticipated that errors in the estimation of contact force will be reduced as more accurate subject-specific models of muscles and other soft tissues are developed.

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.

Adaptive surrogate modeling for expedited estimation of nonlinear tissue properties through inverse finite element analysis

Simulation-based prediction of specimen-specific biomechanical behavior commonly requires inverse analysis using geometrically consistent finite element (FE) models. Optimization drives such analyses but previous studies have highlighted a large computational cost dictated by iterative use of nonlinear FE models. The goal of this study was to evaluate the performance of a local regression-based adaptive surrogate modeling approach to decrease computational cost for both global and local optimization approaches using an inverse FE application. Nonlinear elastic material parameters for patient-specific heel-pad tissue were found, both with and without the surrogate model. Surrogate prediction replaced a FE simulation using local regression of previous simulations when the corresponding error estimate was less than a given tolerance. Performance depended on optimization type and tolerance value. The surrogate reduced local optimization expense up to 68%, but achieved accurate results for only 1 of 20 initial conditions. Conversely, up to a tolerance value of 20 N(2), global optimization with the surrogate yielded consistent parameter predictions with a concurrent decrease in computational cost (up to 77%). However, the local optimization method without the surrogate, although sensitive to the initial conditions, was still on average seven times faster than the global approach. Our results help establish guidelines for setting acceptable tolerance values while using an adaptive surrogate model for inverse FE analysis. Most important, the study demonstrates the benefits of a surrogate modeling approach for intensive FE-based iterative analysis.

Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading

Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care.

Surrogate articular contact models for computationally efficient multibody dynamic simulations

Contact occurs in a wide variety of multibody dynamic systems, including the human musculoskeletal system. However, sensitivity and optimization studies of such systems have been limited by the high computational cost of repeated contact analyses. This study presents a novel surrogate modeling approach for performing computationally efficient three-dimensional elastic contact analyses within multibody dynamic simulations. The approach fits a computationally cheap surrogate contact model to data points sampled from a computationally expensive elastic contact model (e.g., a finite element or elastic foundation model) and resolves several unique challenges involved in applying surrogate modeling techniques to elastic contact problems. As an example application, we performed multibody dynamic simulations of a Stanmore wear simulator machine using surrogate and elastic foundation (EF) contact models of a total knee replacement. Accuracy was assessed by performing eleven dynamic simulations with both types of contact models utilizing large variations in motion and load inputs to the machine. Wear volumes predicted with the surrogate contact models were within 1.5% of those predicted with the EF contact models. Computational speed was assessed by performing five Monte Carlo analyses (over 1000 dynamic simulations each) with surrogate contact models utilizing realistic variations in motion and load inputs. Computation time was reduced from an estimated 284 h per analysis with the EF contact models to 1.4 h with the surrogate contact models (i.e., 17 min vs. 5 s per simulation), with higher wear sensitivity observed for motion variations than for load variations. The proposed surrogate modeling approach can significantly improve the computational speed of multibody dynamic simulations incorporating three-dimensional elastic contact models with general surface geometry.

Modeling, Simulation, and Optimal Initiation Planning For Needle Insertion Into the Liver

Needle insertion simulation and planning systems (SPSs) will play an important role in diminishing inappropriate insertions into soft tissues and resultant complications. Difficulties in SPS development are due in large part to the computational requirements of the extensive calculations in finite element (FE) models of tissue. For clinical feasibility, the computational speed of SPSs must be improved. At the same time, a realistic model of tissue properties that reflects large and velocity-dependent deformations must be employed. The purpose of this study is to address the aforementioned difficulties by presenting a cost-effective SPS platform for needle insertions into the liver. The study was constrained to planar (2D) cases, but can be extended to 3D insertions. To accommodate large and velocity-dependent deformations, a hyperviscoelastic model was devised to produce an FE model of liver tissue. Material constants were identified by a genetic algorithm applied to the experimental results of unconfined compressions of bovine liver. The approach for SPS involves B-spline interpolations of sample data generated from the FE model of liver. Two interpolation-based models are introduced to approximate puncture times and to approximate the coordinates of FE model nodes interacting with the needle tip as a function of the needle initiation pose; the latter was also a function of postpuncture time. A real-time simulation framework is provided, and its computational benefit is highlighted by comparing its performance with the FE method. A planning algorithm for optimal needle initiation was designed, and its effectiveness was evaluated by analyzing its accuracy in reaching a random set of targets at different resolutions of sampled data using the FE model. The proposed simulation framework can easily surpass haptic rates (>500 Hz), even with a high pose resolution level (∼30). The computational time required to update the coordinates of the node at the needle tip in the provided example was reduced from 177 s to 0.8069 ms. The planning accuracy was acceptable even with moderate resolution levels: root-mean-square and maximum errors were 1 mm and 1.2 mm, respectively, for a pose and PPT resolution levels of 17 and 20, respectively. The proposed interpolation-based models significantly improve the computational speed of needle insertion simulation and planning, based on the discretized (FE) model of the liver and can be utilized to establish a cost-effective planning platform. This modeling approach can also be extended for use in other surgical simulations.

Increased Conformity Offers Diminishing Returns for Reducing Total Knee Replacement Wear

Wear remains a significant problem limiting the lifespan of total knee replacements (TKRs). Though increased conformity between TKR components has the potential to decrease wear, the optimal amount and planes of conformity have not been investigated. Furthermore, differing conformities in the medial and lateral compartments may provide designers the opportunity to address both wear and kinematic design goals simultaneously. This study used a computational model of a Stanmore knee simulator machine and a previously validated wear model to investigate this issue for simulated gait. TKR geometries with different amounts and planes of conformity on the medial and lateral sides were created and tested in two phases. The first phase utilized a wide range of sagittal and coronal conformity combinations to blanket a physically realistic design space. The second phase performed a focused investigation of the conformity conditions from the first phase to which predicted wear volume was sensitive. For the first phase, sagittal but not coronal conformity was found to have a significant effect on predicted wear volume. For the second phase, increased sagittal conformity was found to decrease predicted wear volume in a nonlinear fashion, with reductions gradually diminishing as conformity increased. These results suggest that TKR geometric design efforts aimed at minimizing wear should focus on sagittal rather than coronal conformity and that at least moderate sagittal conformity is desirable in both compartments.

Simultaneous prediction of muscle and contact forces in the knee during gait

Musculoskeletal models are currently the primary means for estimating in vivo muscle and contact forces in the knee during gait. These models typically couple a dynamic skeletal model with individual muscle models but rarely include articular contact models due to their high computational cost. This study evaluates a novel method for predicting muscle and contact forces simultaneously in the knee during gait. The method utilizes a 12 degree-of-freedom knee model (femur, tibia, and patella) combining muscle, articular contact, and dynamic skeletal models. Eight static optimization problems were formulated using two cost functions (one based on muscle activations and one based on contact forces) and four constraints sets (each composed of different combinations of inverse dynamic loads). The estimated muscle and contact forces were evaluated using in vivo tibial contact force data collected from a patient with a force-measuring knee implant. When the eight optimization problems were solved with added constraints to match the in vivo contact force measurements, root-mean-square errors in predicted contact forces were less than 10 N. Furthermore, muscle and patellar contact forces predicted by the two cost functions became more similar as more inverse dynamic loads were used as constraints. When the contact force constraints were removed, estimated medial contact forces were similar and lateral contact forces lower in magnitude compared to measured contact forces, with estimated muscle forces being sensitive and estimated patellar contact forces relatively insensitive to the choice of cost function and constraint set. These results suggest that optimization problem formulation coupled with knee model complexity can significantly affect predicted muscle and contact forces in the knee during gait. Further research using a complete lower limb model is needed to assess the importance of this finding to the muscle and contact force estimation process.

Computational Models for Neuromuscular Function

Computational models of the neuromuscular system hold the potential to allow us to reach a deeper understanding of neuromuscular function and clinical rehabilitation by complementing experimentation. By serving as a means to distill and explore specific hypotheses, computational models emerge from prior experimental data and motivate future experimental work. Here we review computational tools used to understand neuromuscular function including musculoskeletal modeling, machine learning, control theory, and statistical model analysis. We conclude that these tools, when used in combination, have the potential to further our understanding of neuromuscular function by serving as a rigorous means to test scientific hypotheses in ways that complement and leverage experimental data.