Recent advances in computational mechanics of the human knee joint

Computational modelling of articular joints with biphasic cartilage: recent advances, challenges and opportunities

Biphasic models have been widely used to simulate the time-dependent biomechanical response of soft tissues. Modelling techniques of joints with biphasic weight-bearing soft tissues have been markedly improved over the last decade, enhancing our understanding of the function, degenerative mechanism and outcomes of interventions of joints. This paper reviews the recent advances, challenges and opportunities in computational models of joints with biphasic weight-bearing soft tissues. The review begins with an introduction of the function and degeneration of joints from a biomechanical aspect. Different constitutive models of articular cartilage, in particular biphasic materials, are illustrated in the context of the study of contact mechanics in joints. Approaches, advances and major findings of biphasic models of the hip and knee are presented, followed by a discussion of the challenges awaiting to be addressed, including the convergence issue, high computational cost and inadequate validation. Finally, opportunities and clinical insights in the areas of subject-specific modeling and tissue engineering are provided and discussed.

Validation and evaluation of subject-specific finite element models of the pediatric knee

Finite element (FE) models have been widely used to investigate knee joint biomechanics. Most of these models have been developed to study adult knees, neglecting pediatric populations. In this study, an atlas-based approach was employed to develop subject-specific FE models of the knee for eight typically developing pediatric individuals. Initially, validation simulations were performed at four passive tibiofemoral joint (TFJ) flexion angles, and the resulting TFJ and patellofemoral joint (PFJ) kinematics were compared to corresponding patient-matched measurements derived from magnetic resonance imaging (MRI). A neuromusculoskeletal-(NMSK)-FE pipeline was then used to simulate knee biomechanics during stance phase of walking gait for each participant to evaluate model simulation of a common motor task. Validation simulations demonstrated minimal error and strong correlations between FE-predicted and MRI-measured TFJ and PFJ kinematics (ensemble average of root mean square errors < 5 mm for translations and < 4.1° for rotations). The FE-predicted kinematics were strongly correlated with published reports (ensemble average of Pearson's correlation coefficients (ρ) > 0.9 for translations and ρ > 0.8 for rotations), except for TFJ mediolateral translation and abduction/adduction rotation. For walking gait, NMSK-FE model-predicted knee kinematics, contact areas, and contact pressures were consistent with experimental reports from literature. The strong agreement between model predictions and experimental reports underscores the capability of sequentially linked NMSK-FE models to accurately predict pediatric knee kinematics, as well as complex contact pressure distributions across the TFJ articulations. These models hold promise as effective tools for parametric analyses, population-based clinical studies, and enhancing our understanding of various pediatric knee injury mechanisms. They also support intervention design and prediction of surgical outcomes in pediatric populations.

Experimental Methods for Studying the Contact Mechanics of Joints

Biomechanics researchers often experimentally measure static or fluctuating dynamic contact forces, areas, and stresses at the interface of natural and artificial joints, including the shoulders, elbows, hips, and knees. This information helps explain joint contact mechanics, as well as mechanisms that may contribute to disease, damage, and degradation. Currently, the most common in vitro experimental technique involves a thin pressure-sensitive film inserted into the joint space; but, the film's finite thickness disturbs the joint's ordinary articulation. Similarly, the most common in vivo experimental technique uses video recording of 3D limb motion combined with dynamic analysis of a 3D link-segment model to calculate joint contact force, but this does not provide joint contact area or stress distribution. Moreover, many researchers may be unaware of older or newer alternative techniques that may be more suitable for their particular research application. Thus, this article surveys over 50 years of English-language scientific literature in order to (a) describe the basic working principles, advantages, and disadvantages of each technique, (b) examine the trends among the studies and methods, and (c) make recommendations for future directions. This article will hopefully inform biomechanics investigators about various in vitro and in vivo experimental methods for studying the contact mechanics of joints.

Computational assessment on the impact of collagen fiber orientation in cartilages on healthy and arthritic knee kinetics/kinematics

BACKGROUND

The inhomogeneous distribution of collagen fiber in cartilage can substantially influence the knee kinematics. This becomes vital for understanding the mechanical response of soft tissues, and cartilage deterioration including osteoarthritis (OA). Though the conventional computational models consider geometrical heterogeneity along with fiber reinforcements in the cartilage model as material heterogeneity, the influence of fiber orientation on knee kinetics and kinematics is not fully explored. This work examines how the collagen fiber orientation in the cartilage affects the healthy (intact knee) and arthritic knee response over multiple gait activities like running and walking.

METHODS

A 3D finite element knee joint model is used to compute the articular cartilage response during the gait cycle. A fiber-reinforced porous hyper elastic (FRPHE) material is used to model the soft tissue. A split-line pattern is used to implement the fiber orientation in femoral and tibial cartilage. Four distinct intact cartilage models and three OA models are simulated to assess the impact of the orientation of collagen fibers in a depth wise direction. The cartilage models with fibers oriented in parallel, perpendicular, and inclined to the articular surface are investigated for multiple knee kinematics and kinetics.

FINDINGS

The comparison of models with fiber orientation parallel to articulating surface for walking and running gait has the highest elastic stress and fluid pressure compared with inclined and perpendicular fiber-oriented models. Also, the maximum contact pressure is observed to be higher in the case of intact models during the walking cycle than for OA models. In contrast, the maximum contact pressure is higher during running in OA models than in intact models. Additionally, parallel-oriented models produce higher maximum stresses and fluid pressure for walking and running gait than proximal-distal-oriented models. Interestingly, during the walking cycle, the maximum contact pressure with intact models is approximately three times higher than on OA models. In contrast, the OA models exhibit higher contact pressure during the running cycle.

INTERPRETATION

Overall, the study indicates that collagen orientation is crucial for tissue responsiveness. This investigation provides insights into the development of tailored implants.

Surrogate modeling of articular cartilage degradation to understand the synergistic role of MMP-1 and MMP-9: a case study

A characteristic feature of arthritic diseases is cartilage extracellular matrix (ECM) degradation, often orchestrated by the overexpression of matrix metalloproteinases (MMPs) and other proteases. The interplay between fibril level degradation and the tissue-level aggregate response to biomechanical loading was explored in this work by a computational multiscale cartilaginous model. We considered the relative abundance of collagenases (MMP-1) and gelatinases (MMP-9) in surrogate models, where the diffusion (spatial distribution) of these enzymes and the subsequent, co-localized fibrillar damage were spatially randomized with Latin Hypercube Sampling. The computational model was constructed by incorporating the results from prior molecular dynamics simulations (tensile test) of microfibril degradation into a hyper-elastoplastic fibril-reinforced cartilage model. Including MMPs-mediated collagen fibril-level degradation in computational models may help understand the ECM pathomechanics at the tissue level. The mechanics of cartilage tissue and fibril show variations in mechanical integrity depending on the different combinations of MMPs-1 and 9 with a concentration ratio of 1:1, 3:1, and 1:3 in simulated indentation tests. The fibril yield (local failure) was initiated at 20.2 ± 3.0 (%) and at 23.0 ± 2.8 (%) of bulk strain for col 1:gel 3 and col 3: gel 1, respectively. The reduction in failure stress (global response) was 39.8% for col 1:gel 3, 37.5% for col 1:gel 1, and 36.7% for col 3:gel 1 compared with the failure stress of the degradation free tissue. These findings indicate that cartilage's global and local mechanisms of failure largely depend on the relative abundance of the two key enzymes-collagenase (MMP-1) and gelatinase (MMP-9) and the spatial characteristics of diffusion across the layers of the cartilage ECM.

Open Knee(s): A Free and Open Source Library of Specimen-Specific Models and Related Digital Assets for Finite Element Analysis of the Knee Joint

There is a growing interest in the use of virtual representations of the knee for musculoskeletal research and clinical decision making, and to generate digital evidence for design and regulation of implants. Accessibility to previously developed models and related digital assets can dramatically reduce barriers to entry to conduct simulation-based studies of the knee joint and therefore help accelerate scientific discovery and clinical innovations. Development of models for finite element analysis is a demanding process that is both time consuming and resource intensive. It necessitates expertise to transform raw data to reliable virtual representations. Modeling and simulation workflow has many processes such as image segmentation, surface geometry generation, mesh generation and finally, creation of a finite element representation with relevant loading and boundary conditions. The outcome of the workflow is not only the end-point knee model but also many other digital by-products. When all of these data, derivate assets, and tools are freely and openly accessible, researchers can bypass some or all the steps required to build models and focus on using them to address their research goals. With provenance to specimen-specific anatomical and mechanical data and traceability of digital assets throughout the whole lifecycle of the model, reproducibility and credibility of the modeling practice can be established. The objective of this study is to disseminate Open Knee(s), a cohort of eight knee models (and relevant digital assets) for finite element analysis, that are based on comprehensive specimen-specific imaging data. In addition, the models and by-products of modeling workflows are described along with model development strategies and tools. Passive flexion served as a test simulation case, demonstrating an end-user application. Potential roadmaps for reuse of Open Knee(s) are also discussed.

Influence of walking on knee ligament response in car-to-pedestrian collisions

Pedestrians are likely to experience walking before accidents. The walking process imposes cyclic loading on knee ligaments and increases knee joint temperature. Both cyclic loading and temperature affect the material properties of ligaments, which further influence the risk of ligament injury. However, the effect of such walking-induced material property changes on pedestrian ligament response has not been considered. Therefore, in this study, we investigated the influence of walking on ligament response in car-to-pedestrian collisions. Using Total Human Model for Safety (THUMS) model, knee ligament responses (i.e., cross-sectional force and local strain) were evaluated under several crash scenarios (i.e., two impact speeds, two knee contact heights, and three pedestrian postures). In worst case scenarios, walking-induced changes in ligament material properties led to a 10% difference in maximum local strain and a 6% difference in maximum cross-sectional force. Further considering the material uncertainty caused by experimental dispersion, the ligament material property changes due to walking resulted in a 28% difference in maximum local strain and a 26% difference in maximum cross-sectional force. This study demonstrates the importance of accounting for walking-induced material property changes for the reliability of safety assessments and injury analysis.

Influence of material heterogeneity on the mechanical response of articulated cartilages in a knee joint

Structurally, the articular cartilages are heterogeneous owing to nonuniform distribution and orientation of its constituents. The oversimplification of this soft tissue as a homogeneous material is generally considered in the simulation domain to estimate contact pressure along with other physical responses. Hence, there is a need for investigating knee cartilages for their actual response to external stimuli. In this article, impact of material and geometrical heterogeneity of the cartilage is resolved using well known material models. The findings are compared with conventional homogeneous models. The results indicate vital differences in contact pressure distribution and tissue deformation. Further, this study paves way for standardizing material models to extract maximum information possible for investigating knee mechanics with variable geometry and case specific parameters.

Evaluation of anterior cruciate ligament surgical reconstruction through finite element analysis

Anterior cruciate ligament (ACL) tear is one of the most common knee injuries. The ACL reconstruction surgery aims to restore healthy knee function by replacing the injured ligament with a graft. Proper selection of the optimal surgery parameters is a complex task. To this end, we developed an automated modeling framework that accepts subject-specific geometries and produces finite element knee models incorporating different surgical techniques. Initially, we developed a reference model of the intact knee, validated with data provided by the Open Knee(s) project. This helped us evaluate the effectiveness of estimating ligament stiffness directly from MRI. Next, we performed a plethora of “what-if” simulations, comparing responses with the reference model. We found that (a) increasing graft pretension and radius reduces relative knee displacement, (b) the correlation of graft radius and tension should not be neglected, (c) graft fixation angle of 20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}∘ can reduce knee laxity, and (d) single-versus double-bundle techniques demonstrate comparable performance in restraining knee translation. In most cases, these findings confirm reported values from comparative clinical studies. The numerical models are made publicly available, allowing for experimental reuse and lowering the barriers for meta-studies. The modeling approach proposed here can complement orthopedic surgeons in their decision-making.

Mechanical properties of meniscal circumferential fibers using an inverse finite element analysis approach

The extracellular matrix (ECM) of the meniscus is a gel-like water solution of proteoglycans embedding bundles of collagen fibers mainly oriented circumferentially. Collagen fibers significantly contribute to meniscal mechanics, however little is known about their mechanical properties. The objective of this study was to propose a constitutive model for collagen fibers embedded in the ECM of the meniscus and to characterize the tissue's pertinent mechanical properties. It was hypothesized that a linear fiber reinforced viscoelastic constitutive model is suitable to describe meniscal mechanical behavior in shear. It was further hypothesized that the mechanical properties governing the model depend on the tissue's composition. Frequency sweep tests were conducted on eight porcine meniscal specimens. A first cohort of experimental data resulted from tissue specimens where collagen fibers oriented parallel with respect to the shear plane were used. This was done to eliminate the contribution of collagen fibers from the mechanical response and characterize the mechanical properties of the ECM. A second cohort with fibers orthogonally oriented with respect to the shear plane that were used to determine the elastic properties of the collagen fibers via inverse finite element analysis. Our testing protocol revealed that tissue ECM mechanical behavior could be described by a generalized Maxwell model with 3 relaxation times. The inverse finite element analysis suggested that collagen fibers can be modeled as linear elastic elements having an average elastic modulus of 287.5 ± 62.6 MPa. Magnitudes of the mechanical parameters governing the ECM and fibers were negatively related to tissue water content.

Patellar Height after High Tibial Osteotomy of the Distal Tibial Tuberosity: A Retrospective Study of Age Stratification

Objective

To explore the effect of age stratification on patellar height after single-plane high tibial osteotomy of the distal tibial tuberosity (DTT-HTO).

Methods

A retrospective analysis was performed on 110 knee joints undergoing DTT-HTO. Patients were divided into three groups according to age: under 60 years old, 28 cases; 60 to 70 years old, 61 cases; and over 70 years old, 21 cases. All patients were followed up for no less than 12 months, and at each follow-up, short-leg radiographs and whole-leg radiographs were taken. The values of the Caton-Deschamps index (CDI) and Blackburne-Peel index (BPI) of single-short-leg radiographs and the femoral-tibial angle (FTA) and weight-bearing line ratio (WBLR) of whole-leg radiographs were measured before and at the last follow-up. The Lysholm score before and at the last follow-up and the visual analogue scale (VAS) score before and 3 days after surgery and at the last follow-up were calculated. The frequency of classification of the normal-height patella, patella alta, and patella baja before and after surgery was recorded.

Results

There were no significant differences in CDI and BPI preoperatively or postoperatively among the three groups (P > 0.05), and there were no statistically significant differences in FTA and WBLR. There were no significant differences in CDI, BPI, FTA, or WBLR between the three groups before and after the operation (P > 0.05). The Lysholm score increased from 48.84 ± 10.10 before surgery to 91.96 ± 3.082 after surgery (P < 0.05); the VAS score decreased from 8.23 ± 0.99 before surgery to 1.93 ± 0.953 at 3 days after surgery and 1.07 ± 0.53 at the last follow-up (P < 0.01). No significant difference was observed in the incidence of each patellar height classification between the three groups preoperatively and postoperatively.

Conclusion

Patellar height is not influenced by DTT-HTO. The age of patients is not a limiting factor for the selection of this surgical procedure. Without affecting the height of the patella, DTT-HTO can effectively reduce pain in the knee joint, restore the function of the knee joint, and delay the progression of patellar arthritis.

The effect of modelling parameters in the development and validation of knee joint models on ligament mechanics: A systematic review

BACKGROUND

The ligaments in the knee are prone to injury especially during dynamic activities. The resulting instability can have a profound impact on a patient's daily activities and functional capacity. Musculoskeletal knee modelling provides a non-invasive tool for investigating ligament force-strain behaviour in various dynamic scenarios, as well as potentially complementing existing pre-planning tools to optimise surgical reconstructions. However, despite the development and validation of many musculoskeletal knee models, the effect of modelling parameters on ligament mechanics has not yet been systematically reviewed.

OBJECTIVES

This systematic review aimed to investigate the results of the most recent studies using musculoskeletal modelling techniques to create models of the native knee joint, focusing on ligament mechanics and modelling parameters in various simulated movements.

DATA SOURCES

PubMed, ScienceDirect, Google Scholar, and IEEE Xplore.

ELIGIBILITY CRITERIA FOR SELECTING STUDIES

Databases were searched for articles containing any numerical ligament strain or force data on the intact, ACL-deficient, PCL-deficient, or lateral extra-articular reconstructed (LER) knee joints. The studies had to derive these results from musculoskeletal modelling methods. The dates of the publications were between 1 January 1995 and 30 November 2021.

METHOD

A customised data extraction form was created to extract each selected study's critical musculoskeletal model development parameters. Specific parameters of the musculoskeletal knee model development used in each eligible study were independently extracted, including the (1) musculoskeletal model definition (i.e., software used for modelling, knee type, source of geometry, the inclusion of cartilage and menisci, and articulating joints and joint boundary conditions (i.e., number of degrees of freedom (DoF), subjects, type of activity, collected data and type of simulation)), (2) specifically ligaments modelling techniques (i.e., ligament bundles, attachment points, pathway, wrapping surfaces and ligament material properties such as stiffness and reference length), (3) sensitivity analysis, (4) validation approaches, (5) predicted ligament mechanics (i.e., force, length or strain) and (6) clinical applications if available. The eligible papers were then discussed quantitatively and qualitatively with respect to the above parameters.

RESULTS AND DISCUSSION

From the 1004 articles retrieved by the initial electronic search, only 25 met all inclusion criteria. The results obtained by aggregating data reported in the eligible studies indicate that considerable variability in the predicted ligament mechanics is caused by differences in geometry, boundary conditions and ligament modelling parameters.

CONCLUSION

This systematic review revealed that there is currently a lack of consensus on knee ligament mechanics. Despite this lack of consensus, some papers highlight the potential of developing translational tools using musculoskeletal modelling. Greater consistency in model design, incorporation of sensitivity assessment of the model outcomes and more rigorous validation methods should lead to better agreement in predictions for ligament mechanics between studies. The resulting confidence in the musculoskeletal model outputs may lead to the development of clinical tools that could be used for patient-specific treatments.

Walking Pole Gait to Reduce Joint Loading post Total Knee Athroplasty: Musculoskeletal modeling Approach

Excessive knee contact loading is precursor to osteoarthritis and related knee ailment leading to knee athroplasty. Reducing contact loading through gait modifications using assisted pole walking offers noninvasive process of medial load offloading at knee joint. In this paper, we evaluate the efficacy of different configuration of pole walking for reducing contact force at the knee joint through musculoskeletal (MSK) modeling. We have developed a musculoskeletal model for a subject with knee athroplasty utilizing in-vivo implant data and computed tibio-femoral contact force for different pole walking conditions to evaluate the best possible configuration for guiding rehabilitation, correlated with different gait phases. Effect of gait speed variation on knee contact force, hip joint dynamics and muscle forces are simulated using the developed MSK model. Results indicate some interesting trend of load reduction, dependent on loading phases pertaining to different pole configuration. Insights gained from the simulation can aid in designing personalized rehabilitation therapy for subjects suffering from Osteoarthritis.

Biomechanical Study of a Tricompartmental Unloader Brace for Patellofemoral or Multicompartment Knee Osteoarthritis

Objective: Off-loader knee braces have traditionally focused on redistributing loads away from either the medial or lateral tibiofemoral (TF) compartments. In this article, we study the potential of a novel "tricompartment unloader" (TCU) knee brace intended to simultaneously unload both the patellofemoral (PF) and TF joints during knee flexion. Three different models of the TCU brace are evaluated for their potential to unload the knee joint. Methods: A sagittal plane model of the knee was used to compute PF and TF contact forces, patellar and quadriceps tendon forces, and forces in the anterior and posterior cruciate ligaments during a deep knee bend (DKB) test using motion analysis data from eight participants. Forces were computed for the observed (no brace) and simulated braced conditions. A sensitivity and validity analysis was conducted to determine the valid output range for the model, and Statistical Parameter Mapping was used to quantify the effectual region of the different TCU brace models. Results: PF and TF joint force calculations were valid between ~0 and 100 degrees of flexion. All three simulated brace models significantly (p < 0.001) reduced predicted knee joint loads (by 30-50%) across all structures, at knee flexion angles >~30 degrees during DKB. Conclusions: The TCU brace is predicted to reduce PF and TF knee joint contact loads during weight-bearing activity requiring knee flexion angles between 30 and 100 degrees; this effect may be clinically beneficial for pain reduction or rehabilitation from common knee injuries or joint disorders. Future work is needed to assess the range of possible clinical and prophylactic benefits of the TCU brace.

Modeling the resistance mechanism of passive knee joint flexion and extension for use in rehabilitation equipment

The purpose of this study was to model the resistance mechanism of Passive Knee Joint Flexion and Extension to create a similar torque mechanism in rehabilitation equipment. In order to better model the behavior of passive knee tissues, it is necessary to exactly calculate the two coefficients of elasticity of time-independent and time-dependent parts. Ten healthy male volunteers (mean height 176.4+/-4.59 cm) participated in this study. Passive knee joint flexion and extension occurred at velocities of 15, 45, and 120 (degree/s), and in five consecutive cycles and within the range of 0 to 100° of knee movement on the sagittal plane on Cybex isokinetic dynamometer. To ensure that the muscles were relaxed, the electrical activity of knee muscles was recorded. The elastic coefficient, (K_S) increased with elevating the passive velocity in flexion and extension. The elastic coefficient, (K_P) was observed to grow with the passive velocity increase. While, the viscous coefficient (C) diminished with passive velocity rise in extension and flexion. The heightened passive velocity of the motion resulted in increased hysteresis (at a rate of 42%). The desired of passive velocity is lower so that there is less energy lost and the viscoelastic resistance of the tissue in the movement decreases. The Coefficient of Determination, R² between the model-responses and experimental curves in the extension was 0.96 < R² < 0.99 and in flexion was 0.95 < R² < 0.99. This modeling is capable of predicting the true performance of the components of passive knee movement and we can create a resistance mechanism in the rehabilitation equipment to perform knee joint movement. Quantitative measurements of two elastic coefficients of Time-independent and Time-dependent parts passive knee joint coefficients should be used for better accurate simulation the behavior of passive tissues in the knee which is not seen in other studies.

Estimating Minimal Clinically Important Differences for Knee Range of Motion after Stroke

The importance of knee sagittal kinematic parameters, as a predictor of walking performance in post-stroke gait has been emphasised by numerous researchers. However, no studies so far were designed to determine the minimal clinically important differences (MCID), i.e., the smallest difference in the relevant score for the kinematic gait parameters, which are perceived as beneficial for patients with stroke. Studies focusing on clinically important difference are useful because they can identify the clinical relevance of changes in the scores. The purpose of the study was to estimate the MCID for knee range of motion (ROM) in the sagittal plane for the affected and unaffected side at a chronic stage post-stroke. Fifty individuals were identified in a database of a rehabilitation clinic. We estimated MCID values using: an anchor-based method, distribution-based method, linear regression analysis and specification of the receiver operating characteristic (ROC) curve. In the anchor-based study, the mean change in knee flexion/extension ROM for the affected/unaffected side in the MCID group amounted to 8.48°/6.81° (the first MCID estimate). In the distribution-based study, the standard error of measurement for the no-change group was 1.86°/5.63° (the second MCID estimate). Method 3 analyses showed 7.71°/4.66° change in the ROM corresponding to 1.85-point change in the Barthel Index. The best cut-off point, determined with ROC curve, was the value corresponding to 3.9°/3.8° of change in the knee sagittal ROM for the affected/unaffected side (the fourth MCID estimate). We have determined that, in chronic stroke, MCID estimates of knee sagittal ROM for the affected side amount to 8.48° and for the unaffected side to 6.81°. These findings will assist clinicians and researchers in interpreting the significance of changes observed in kinematic sagittal plane parameters of the knee. The data are part of the following clinical trial: Australian New Zealand Clinical Trials Registry: ACTRN12617000436370

Stress response envelopes of intact tibiofemoral joint and knee osteoarthritis

The purpose of this study was to determine stress envelopes for an intact tibiofemoral joint and to study how they vary with knee loading, external–internal rotation, varus–valgus rotation and cartilage degradation (osteoarthritis) using the finite element method. The envelopes were presented in terms of knee flexion angle. The maximum von Mises stress for all tibiofemoral joint components increased with increasing the axial compressive force magnitude. Menisci exhibited the highest magnitude of maximum von Mises stress as compared to the femoral and tibial cartilages. In a range of flexion angles between 0° and 100°, the medial meniscus exhibited the highest maximum von Mises stress than the lateral meniscus and the stress in medial meniscus tended to increase with increasing the flexion angle. External–internal and varus–valgus rotations changed the stress distribution: higher stress on lateral compartment but lower stress on medial compartment, and conversely. The internal rotation provided more extreme effect than the external rotation. For the knee osteoarthritis, cartilage degradation (early stage) caused maximum von Mises stress to increase on the intact menisci revealing that knee osteoarthritis could also cause meniscal tear. The late osteoarthritis caused the maximum von Mises stress to increase on the calcified cartilage and subchondral bone.

Effect of viscoelastic properties on passive torque variations at different velocities of the knee joint extension and flexion movements

This study aimed to investigate the rate of passive torque variations of human knee joint in the different velocities of knee flexion and extension movements. Ten healthy men were invited to participate in the tests. All passive torque tests were performed for the knee joint extension and flexion on the sagittal plane in three different angular velocities of 15, 45, and 120°/s; in 5 consecutive cycles; and within 0° to 100° range of motion. The electrical activity of knee joint extensor and flexor muscles was recorded until there was no muscle activity signal. A Three-element Solid Model (SLS) was used to obtain the viscose and elastic coefficients. As the velocity increases, the stretch rate in velocity-independent tissues increases, and the stretch rate in velocity-dependent tissues decreases. By increasing the velocity, the resistance of velocity-dependent parts increases, and the velocity-independent parts are not affected by velocity. Since the first torque that resists the joint movement is passive torque, the elastic and viscous torques should be simultaneously used. It is better to perform the movement at a low velocity so that less energy is lost. The viscoelastic resistance of tissues diminishes. Graphical abstract.

A Review on Finite Element Modeling and Simulation of the Anterior Cruciate Ligament Reconstruction

The anterior cruciate ligament (ACL) constitutes one of the most important stabilizing tissues of the knee joint whose rapture is very prevalent. ACL reconstruction (ACLR) from a graft is a surgery which yields the best outcome. Taking into account the complicated nature of this operation and the high cost of experiments, finite element (FE) simulations can become a valuable tool for evaluating the surgery in a pre-clinical setting. The present study summarizes, for the first time, the current advancement in ACLR in both clinical and computational level. It also emphasizes on the material modeling and properties of the most popular grafts as well as modeling of different surgery techniques. It can be concluded that more effort is needed to be put toward more realistic simulation of the surgery, including also the use of two bundles for graft representation, graft pretension and artificial grafts. Furthermore, muscles and synovial fluid need to be included, while patellofemoral joint is an important bone that is rarely used. More realistic models are also required for soft tissues, as most articles used isotropic linear elastic models and springs. In summary, accurate and realistic FE analysis in conjunction with multidisciplinary collaboration could contribute to ACLR improvement provided that several important aspects are carefully considered.

A comprehensive testing protocol for macro-scale mechanical characterization of knee articular cartilage with documented experimental repeatability

Articular cartilage mechanics has been extensively studied with various approaches and mechanical characterization strategies. However testing protocols can be highly varying and difficult to reproduce, particularly for specimen-specific analyses. Detailed knowledge of testing protocols is important for reliable use in concordant finite element analyses. This study presents a detailed, robust procedure for cartilage testing-with multiple regions and per sample repeatability data. Samples were taken from femur, tibia and patella of a human cadaver knee and tested in unconfined compression, confined compression and uniaxial tension. Each test was repeated three times. The testing protocols provide elastic and time dependent characterization data. Results, for example equilibrium modulus of 0.28 (0.0024) MPa for patella under unconfined compression indicate that variability is well controlled and that protocol(s) presented here can generate repeatable specimen-specific data. As per the authors' knowledge this is the first study to report in-depth uncertainty assessment of the experimental procedures for multi-region knee cartilage characterization.

Constitutive modeling of menisci tissue: a critical review of analytical and numerical approaches

Menisci are fibrocartilaginous disks consisting of soft tissue with a complex biomechanical structure. They are critical determinants of the kinematics as well as the stability of the knee joint. Several studies have been carried out to formulate tissue mechanical behavior, leading to the development of a wide spectrum of constitutive laws. In addition to developing analytical tools, extensive numerical studies have been conducted on menisci modeling. This study reviews the developments of the most widely used continuum models of the meniscus mechanical properties in conjunction with emerging analytical and numerical models used to study the meniscus. The review presents relevant approaches and assumptions used to develop the models and includes discussions regarding strengths, weaknesses, and discrepancies involved in the presented models. The study presents a comprehensive coverage of relevant publications included in Compendex, EMBASE, MEDLINE, PubMed, ScienceDirect, Springer, and Scopus databases. This review aims at opening novel avenues for improving menisci modeling within the framework of constitutive modeling through highlighting the needs for further research directed toward determining key factors in gaining insight into the biomechanics of menisci which is crucial for the elaborate design of meniscal replacements.

Development of robust finite element models of porcine tibiofemoral joints loaded under varied flexion angles and tibial freedoms

The successful development of cartilage repair treatments for the knee requires understanding of the biomechanical environment within the joint. Computational finite element models play an important role in non-invasively understanding knee mechanics, but it is important to compare model findings to experimental data. The purpose of this study was to develop a methodology for generating subject-specific finite element models of porcine tibiofemoral joints that was robust and valid over multiple different constraint scenarios. Computational model predictions of two knees were compared to experimental studies on corresponding specimens loaded under several different constraint scenarios using a custom designed experimental rig, with variations made to the femoral flexion angle and level of tibial freedom. For both in vitro specimens, changing the femoral flexion angle had a marked effect on the contact distribution observed experimentally. With the tibia fixed, the majority of the contact region shifted to the medial plateau as flexion was increased. This did not occur when the tibia was free to displace and rotate in response to applied load. These trends in contact distribution across the medial and lateral plateaus were replicated in the computational models. In an additional model with the meniscus removed, contact pressures were elevated by a similar magnitude to the increase seen when the meniscus was removed experimentally. Overall, the models were able to capture specimen-specific trends in contact distribution under a variety of different loads, providing the potential to investigate subject-specific outcomes for knee interventions.

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.

Use of Computational Modeling to Study Joint Degeneration: A Review

Osteoarthritis (OA), a degenerative joint disease, is the most common chronic condition of the joints, which cannot be prevented effectively. Computational modeling of joint degradation allows to estimate the patient-specific progression of OA, which can aid clinicians to estimate the most suitable time window for surgical intervention in osteoarthritic patients. This paper gives an overview of the different approaches used to model different aspects of joint degeneration, thereby focusing mostly on the knee joint. The paper starts by discussing how OA affects the different components of the joint and how these are accounted for in the models. Subsequently, it discusses the different modeling approaches that can be used to answer questions related to OA etiology, progression and treatment. These models are ordered based on their underlying assumptions and technologies: musculoskeletal models, Finite Element models, (gene) regulatory models, multiscale models and data-driven models (artificial intelligence/machine learning). Finally, it is concluded that in the future, efforts should be made to integrate the different modeling techniques into a more robust computational framework that should not only be efficient to predict OA progression but also easily allow a patient’s individualized risk assessment as screening tool for use in clinical practice.

Numerical Study of Prosthetic Knee Replacement Using Finite Element Analysis

The knee at times undergoes a surgical process to substitute the weight-bearing surfaces of the knee joint. This procedure relieves the pain and disability around the knee joint. This research paper studied the knee arthroplasty, also referred to as knee replacement. This work was aided with computer vision for visual and accuracy. Autodesk fusion 360 and the stl files were used to generate cemented, posterior stabilised knee prosthesis and imported into the COMSOL Multiphysics software. Then, the three-dimensional models of the total knee arthroplasty (TKA) prosthetic structure are produced. The prosthetic components are modelled as linear isotropic elastic materials. Finite element (FE) simulations using COMSOL Multiphysics on a CAD model of a knee are effectuated to show the effect of several loads and strains on the knee. FE analysis of the model indicates that the orthotropic model depicts a more realistic stress distribution of the knee as it reveals the detailed anatomy of the entire knee structure. The computational results of this work displayed a fair agreement with experimental information from the literature.

Integration of Three-dimensional Technologies in Orthopedics: A Tool for Preoperative Planning of Tibial Plateau Fractures

Background:

There is a growing scientific interest in the use of three-dimensional (3D) technologies in orthopedic surgery. Digitalization makes research in orthopedics more accurate and quantitative. Scientific literature describes an overview of current 3D technologies applications in orthopedics, without any emphasis on integrating available technologies as a clinical workflow.

Objective:

To develop a clinical workflow integrating 3D technologies for patient-specific applications in orthopedics validated in practice by employment of a free 3D software solution with the aim of minimizing the intervention.

Method:

By exploring the applications of 3D technologies in orthopedic surgery, we have created a clinical workflow integrating 3D technologies for patient-specific applications in orthopedics. It is validated in practice for preoperative planning of a 49-year-old male patient who had a tibial plateau fracture of Schatzker type VI in his right leg. The software solution we have used is Democratiz3D, from Embodi3d platform, which allows patient-specific modeling and surgical planning.

Results:

By using the proposed methodology we obtained the model of the tibial plateau fracture Schatzker type VI, as a “solid” representation in stl type files, which represents a numerically defined geometry of the bones fragments. It helps surgeons in planning the surgical approach. The time from the beginning to the end of the analysis was 193 min, which is 15% lower than times reported in similar studies.

Conclusion:

The planning potential of the 3D solution is a valuable instrument for surgeons in exploring the nature of tibial plateau fractures and the formulation of a suitable surgical plan for surface alignment, design and screw fixation guides, strength calculations of bone fragments, and printing surgical objects.

Foundations of modeling in cryobiology-II: Heat and mass transport in bulk and at cell membrane and ice-liquid interfaces

Modeling coupled heat and mass transport in biological systems is critical to the understanding of cryobiology. In Part I of this series we derived the transport equation and presented a general thermodynamic derivation of the critical components needed to use the transport equation in cryobiology. Here we refine to more cryobiologically relevant instances of a double free-boundary problem with multiple species. In particular, we present the derivation of appropriate mass and heat transport constitutive equations for a system consisting of a cell or tissue with a free external boundary, surrounded by liquid media with an encroaching free solidification front. This model consists of two parts-namely, transport in the "bulk phases" away from boundaries, and interfacial transport. Here we derive the bulk and interfacial mass, energy, and momentum balance equations and present a simplification of transport within membranes to jump conditions across them. We establish the governing equations for this cell/liquid/solid system whose solution in the case of a ternary mixture is explored in Part III of this series.

Effects of a valgus unloader brace in the medial meniscectomized knee joint: a biomechanical study

Background

Patients undergoing total or partial arthroscopic meniscectomy for treating traumatic meniscal tears are at greater risk of developing knee osteoarthritis (OA) due to increased mechanical load. The purpose of this study was to evaluate the effects of a valgus unloader brace in the medial meniscectomized knee joint during the gait cycle.

Methods

A three-dimensional finite element model of the knee joint was developed using the substructures segmented from magnetic resonance images. Experimentally measured forces and moments for one complete gait cycle, without brace and with brace at three different alignment angles (0°, 4°, and 8°), were applied to the finite element model, and the changes in the tibiofemoral contact mechanics were estimated.

Results

The brace in 0°/4°/8° valgus alignment modes reduced the total contact force in the medial compartment by 16%/46%/82% at opposite toe off and 18%/17%/29% at opposite initial contact events, while it increased the total contact force in the lateral compartment by 31%/81%/110% at opposite toe off and 30%/38%/45% at opposite initial contact events, respectively, when compared to the unbraced meniscectomized knee.

Conclusions

Increasing the valgus alignment from 0° to 4° and 8° resulted in a greater reduction of contact conditions (total contact force, total contact area, peak contact pressure) in the medial compartment and vice versa in the lateral compartment. This decrease in contact conditions in the medial compartment infers enhanced knee joint function due to a valgus unloader brace, which translates to increased knee-related confidence. Results suggest choosing a higher valgus alignment angle could potentially increase the risk for the onset of osteoarthritis in the lateral compartment, and this computational model could be used in validating the effectiveness of braces on joint health.

Electronic supplementary material

The online version of this article (10.1186/s13018-019-1085-1) contains supplementary material, which is available to authorized users.

Functional assessment of strains around a full-thickness and critical sized articular cartilage defect under compressive loading using MRI

OBJECTIVE

The objective of this study was to evaluate the effect of full-thickness chondral defects on intratissue deformation patterns and matrix constituents in an experimental model mimicking in vivo cartilage-on-cartilage contact conditions.

DESIGN

Pairs of bovine osteochondral explants, in a unique cartilage-on-cartilage model system, were compressed uniaxially by 350 N during 2 s loading and 1.4 s unloading cycles (≈1700 repetitions). Tissue deformations under quasi-steady state load deformation response were measured with displacement encoded imaging with stimulated echoes (DENSE) in a 9.4 T magnetic resonance imaging (MRI) scanner. Pre- and post-loading, T₁, T₂ and T_1ρ relaxation time maps were measured. We analyzed differences in strain patterns and relaxation times between intact cartilage (n = 8) and cartilage in which a full-thickness and critical sized defect was created (n = 8).

RESULTS

Under compressive loading, strain magnitudes were elevated at the defect rim, with elevated tensile and compressive principal strains (Δϵ_max = 4.2%, P = 0.02; Δϵ_min = -4.3%, P = 0.02) and maximum shear strain at the defect rim (Δγ_max = 4.4%, P = 0.007). The opposing cartilage showed minimal increase in strain patterns at contact with the defect rim but decreased strains opposing the defect. After defect creation, T₁, T₂ and T_1ρ relaxation times were elevated at the defect rim only. Following loading, the overall relaxations times of the defect tissue and especially at the rim, increased compared to intact cartilage.

CONCLUSIONS

This study demonstrates that the local biomechanical changes occurring after defect creation may induce tissue damage by increasing shear strains and depletion of cartilage constituents at the defect rim under compressive loading.

Cancellous bone and theropod dinosaur locomotion. Part II-a new approach to inferring posture and locomotor biomechanics in extinct tetrapod vertebrates

This paper is the second of a three-part series that investigates the architecture of cancellous bone in the main hindlimb bones of theropod dinosaurs, and uses cancellous bone architectural patterns to infer locomotor biomechanics in extinct non-avian species. Cancellous bone is widely known to be highly sensitive to its mechanical environment, and therefore has the potential to provide insight into locomotor biomechanics in extinct tetrapod vertebrates such as dinosaurs. Here in Part II, a new biomechanical modelling approach is outlined, one which mechanistically links cancellous bone architectural patterns with three-dimensional musculoskeletal and finite element modelling of the hindlimb. In particular, the architecture of cancellous bone is used to derive a single 'characteristic posture' for a given species-one in which bone continuum-level principal stresses best align with cancellous bone fabric-and thereby clarify hindlimb locomotor biomechanics. The quasi-static approach was validated for an extant theropod, the chicken, and is shown to provide a good estimate of limb posture at around mid-stance. It also provides reasonable predictions of bone loading mechanics, especially for the proximal hindlimb, and also provides a broadly accurate assessment of muscle recruitment insofar as limb stabilization is concerned. In addition to being useful for better understanding locomotor biomechanics in extant species, the approach hence provides a new avenue by which to analyse, test and refine palaeobiomechanical hypotheses, not just for extinct theropods, but potentially many other extinct tetrapod groups as well.

Mechanical Metrics of the Proximal Tibia are Precise and Differentiate Osteoarthritic and Normal Knees: A Finite Element Study

Our objective was to identify precise mechanical metrics of the proximal tibia which differentiated OA and normal knees. We developed subject-specific FE models for 14 participants (7 OA, 7 normal) who were imaged three times each for assessing precision (repeatability). We assessed various mechanical metrics (minimum principal and von Mises stress and strain as well as structural stiffness) across the proximal tibia for each subject. In vivo precision of these mechanical metrics was assessed using CV%RMS. We performed parametric and non-parametric statistical analyses and determined Cohen's d effect sizes to explore differences between OA and normal knees. For all FE-based mechanical metrics, average CV%RMS was less than 6%. Minimum principal stress was, on average, 75% higher in OA versus normal knees while minimum principal strain values did not differ. No difference was observed in structural stiffness. FE modeling could precisely quantify and differentiate mechanical metrics variations in normal and OA knees, in vivo. This study suggests that bone stress patterns may be important for understanding OA pathogenesis at the knee.

The peripheral soft tissues should not be ignored in the finite element models of the human knee joint

In finite element models of the either implanted or intact human knee joint, soft tissue structures like tendons and ligaments are being incorporated, but usually skin, peripheral knee soft tissues, and the posterior capsule are ignored and assumed to be of minor influence on knee joint biomechanics. It is, however, unknown how these peripheral structures influence the biomechanical response of the knee. In this study, the aim was to assess the significance of the peripheral soft tissues and posterior capsule on the kinematics and laxities of human knee joint, based on experimental tests on three human cadaveric specimens. Despite the high inter-subject variability of the results, it was demonstrated that the target tissues have a considerable influence on posterior translational and internal and valgus rotational laxities of lax knees under flexion. Consequently, ignoring these tissues from computational models may alter the knee joint biomechanics.

Sensitivity analysis of the material properties of different soft-tissues: implications for a subject-specific knee arthroplasty

Introduction

While developing a subject-specific knee model, different kinds of data-inputs are required. If information about geometries can be definitely obtained from images, more effort is necessary for the in vivo properties. Consequently, such information are recruited from the literature as common habit. However, the effects of the combined sources still need to be evaluated.

Methods

This work aims at developing an intact native subject-specific knee model for performing a sensitivity analysis on soft-tissues. The impacts on the biomechanical outputs were analysed during a daily activity for which articular knee kinetics and kinematics were compared among the different configurations. Prior to the sensitivity analysis, experimental and literature data were checked for the model reliability.

Results

Average values of mixed sources allowed the agreement with experimental data for personalized outputs. From the sensitivity analysis, knee kinematics did not significantly change in the selected ranges of properties for the soft-tissues (in rotation less than 0.5°), while contact stresses were greatly affected, especially for the articular cartilage (with differences in the results more than 100%).

Conclusion

In conclusion, during the development of a personalized knee model, the selection of the correct material properties is fundamental because wrong values could highly affect the numerical results.

Level of evidence

III a.

The influence of a change in the meniscus cross-sectional shape on the medio-lateral translation of the knee joint and meniscal extrusion

OBJECTIVE

The purpose of this study was to evaluate the influence of a change in the meniscus cross sectional shape on its position and on the biomechanics of a knee joint.

METHODS

One main finite element model of a left knee joint was created on the basis of MRI images. The model consisted of bones, articular cartilages, menisci and ligaments. Eight variants of this model with an increased or decreased meniscus height were then prepared. Nonlinear static analyses with a fixed flexion/extension movement for a compressive load of 1000 N were performed. The additional analyses for those models with a constrained medio-lateral relative bone translation allowed for an evaluation of the influence of this translation on a meniscus external shift.

RESULTS

It was observed that a decrease in the meniscus height caused a decrease in the contact area, together with a decrease in the contact force between the flattened meniscus and the cartilage. For the models with an increased meniscus height, a maximal value of force acting on the meniscus in a medio-lateral direction was obtained. The results have shown that the meniscus external shift was approximately proportional to the meniscus slope angle, but that relationship was modified by a medio-lateral relative bone translation. It was found that the translation of the femur relative to the tibia may be dependent on the geometry of the menisci.

CONCLUSIONS

The results have suggested that a change in the meniscus geometry in the cross sectional plane can considerably affect not only the meniscal external shift, but also the medio-lateral translation of the knee joint as well as the congruency of the knee joint.

Estimation of the Effect of Body Weight on the Development of Osteoarthritis Based on Cumulative Stresses in Cartilage: Data from the Osteoarthritis Initiative

Evaluation of the subject-specific biomechanical effects of obesity on the progression of OA is challenging. The aim of this study was to create 3D MRI-based finite element models of the knee joints of seven obese subjects, who had developed OA at 4-year follow-up, and of seven normal weight subjects, who had not developed OA at 4-year follow-up, to test the sensitivity of cumulative maximum principal stresses in cartilage in quantitative risk evaluation of the initiation and progression of knee OA. Volumes of elements with cumulative stresses over 5 MPa in tibial cartilage were significantly (p < 0.05) larger in obese subjects as compared to normal weight subjects. Locations of high peak cumulative stresses at the baseline in most of the obese subjects showed a good agreement with the locations of the cartilage loss and MRI scoring at follow-up. Simulated weight loss (to body mass index 24 kg/m2) in obese subjects led to significant reduction of the highest cumulative stresses in tibial and femoral cartilages. The modeling results suggest that an analysis of cumulative stresses could be used to evaluate subject-specific effects of obesity and weight loss on cartilage responses and potential risks for the progression of knee OA.

Tissue material properties and computational modelling of the human tibiofemoral joint: a critical review

Understanding how structural and functional alterations of individual tissues impact on whole-joint function is challenging, particularly in humans where direct invasive experimentation is difficult. Finite element (FE) computational models produce quantitative predictions of the mechanical and physiological behaviour of multiple tissues simultaneously, thereby providing a means to study changes that occur through healthy ageing and disease such as osteoarthritis (OA). As a result, significant research investment has been placed in developing such models of the human knee. Previous work has highlighted that model predictions are highly sensitive to the various inputs used to build them, particularly the mathematical definition of material properties of biological tissues. The goal of this systematic review is two-fold. First, we provide a comprehensive summation and evaluation of existing linear elastic material property data for human tibiofemoral joint tissues, tabulating numerical values as a reference resource for future studies. Second, we review efforts to model tibiofemoral joint mechanical behaviour through FE modelling with particular focus on how studies have sourced tissue material properties. The last decade has seen a renaissance in material testing fuelled by development of a variety of new engineering techniques that allow the mechanical behaviour of both soft and hard tissues to be characterised at a spectrum of scales from nano- to bulk tissue level. As a result, there now exists an extremely broad range of published values for human tibiofemoral joint tissues. However, our systematic review highlights gaps and ambiguities that mean quantitative understanding of how tissue material properties alter with age and OA is limited. It is therefore currently challenging to construct FE models of the knee that are truly representative of a specific age or disease-state. Consequently, recent tibiofemoral joint FE models have been highly generic in terms of material properties even relying on non-human data from multiple species. We highlight this by critically evaluating current ability to quantitatively compare and model (1) young and old and (2) healthy and OA human tibiofemoral joints. We suggest that future research into both healthy and diseased knee function will benefit greatly from a subject- or cohort-specific approach in which FE models are constructed using material properties, medical imagery and loading data from cohorts with consistent demographics and/or disease states.

Ulna-humerus contact mechanics: Finite element analysis and experimental measurements using a tactile pressure sensor

Elbow articular cartilage withstands high compressive and shear forces while protecting the bone from excessive loading. Better understanding of elbow cartilage contact mechanics can provide insight into cartilage degeneration. In this study a tactile pressure sensor was used to measure the contact pressure distribution within the ulno-humeral joint of two cadaver specimens at 20° flexion angle across three different axial loads of 80 N, 110 N, and 140 N. Corresponding 3D finite element (FE) models were constructed from magnetic resonance imaging (MRI) and contact analysis was performed for each specimen with boundary and loading conditions identical to the experiment. Direct comparison between FE results and experimental measurements was conducted for the validation of the FE models and a sensitivity analysis was employed for assessing the effect of cartilage parameters on the model's outputs. The results showed a good agreement between the FE models and the experiments in terms of contact characteristics. The sensitivity analysis demonstrated that outcomes of the model, particularly peak contact pressure is more sensitive to the Poisson's ratio rather than to Young's modulus under static conditions. This result suggests that selection of Poisson's ratio is very critical for accurate prediction of contact mechanics within the ulno-humeral joint.

Simulation of Subject-Specific Progression of Knee Osteoarthritis and Comparison to Experimental Follow-up Data: Data from the Osteoarthritis Initiative

Economic costs of osteoarthritis (OA) are considerable. However, there are no clinical tools to predict the progression of OA or guide patients to a correct treatment for preventing OA. We tested the ability of our cartilage degeneration algorithm to predict the subject-specific development of OA and separate groups with different OA levels. The algorithm was able to predict OA progression similarly with the experimental follow-up data and separate subjects with radiographical OA (Kellgren-Lawrence (KL) grade 2 and 3) from healthy subjects (KL0). Maximum degeneration and degenerated volumes within cartilage were significantly higher (p < 0.05) in OA compared to healthy subjects, KL3 group showing the highest degeneration values. Presented algorithm shows a great potential to predict subject-specific progression of knee OA and has a clinical potential by simulating the effect of interventions on the progression of OA, thus helping decision making in an attempt to delay or prevent further OA symptoms.

Evaluating the effects of material properties of artificial meniscal implant in the human knee joint using finite element analysis

Artificial meniscal implants may replace severely injured meniscus and restore the normal functionality of the knee joint. Implant material stiffness and shape influence the longevity of implantations. This study, using 3D finite element analysis, aimed to evaluate the effects of material stiffness variations of anatomically shaped artificial meniscal implant in the knee joint. Finite element simulations were conducted on five different cases including intact knee, medial meniscectomized knee, and the knee joint with the meniscal implant with three distinct material stiffness. Cartilage contact pressures, compression stresses, shear stresses, and implant kinematics (medial-lateral and posterior-anterior displacement) were evaluated for an axial compressive load of 1150 N at full extension. Compared to the meniscectomized knee, the knee joint with the meniscal implant induced lower peak cartilage contact pressure and reduced the cartilage regions loaded with contact pressures greater than the peak cartilage contact pressure induced by the intact knee. Results of the current study also demonstrate that cartilage contact pressures and implant displacement are sensitive to the implant material stiffness. The meniscal implant with a stiffness of 11 MPa restores the intact knee contact mechanics, thereby reducing the risk of physiological damage to the articular cartilage.

Use of pre-clinical surgically induced models to understand biomechanical and biological consequences of PTOA development

Post-traumatic osteoarthritis (PTOA) development is often observed following traumatic knee injuries involving key stabilising structures such as the cruciate ligaments or the menisci. Both biomechanical and biological alterations that follow knee injuries have been implicated in PTOA development, although it has not been possible to differentiate clearly between the two causal factors. This review critically examines the outcomes from pre-clinical lapine and ovine injury models arising in the authors' laboratories and differing in severity of PTOA development and progression. Specifically, we focus on how varying severity of knee injuries influence the subsequent alterations in kinematics, kinetics, and biological outcomes. The immediate impact of injury on the lubrication capacity of the joint is examined in the context of its influence on biomechanical alterations, thus linking the biological changes to abnormal kinematics, leading to a focus on the potential areas for interventions to inhibit or prevent development of the disease. We believe that PTOA results from altered cartilage surface interactions where biological and biomechanical factors intersect, and mitigating acute joint inflammation may be critical to prolonging PTOA development. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:454-465, 2017.

The influence of muscle-tendon forces on ACL loading during jump landing: a systematic review

BACKGROUND

The goal of this review is to summarise and discuss the reported influence of muscle-tendon forces on anterior cruciate ligament (ACL) loading during the jump-landing task by means of biomechanical analyses of the healthy knee.

METHODS

A systematic review of the literature was conducted using different combinations of the terms "knee", "ligament", "load", "tension ", "length", "strain", "elongation" and "lengthening". 26 original articles (n=16 in vitro studies; n=10 in situ studies) were identified which complied with all inclusion/exclusion criteria.

RESULTS

No apparent trend was found between ACL loading and the ratio between hamstrings and quadriceps muscle-tendon forces prior to or during landing. Four in vitro studies reported reduced peak ACL strain if the quadriceps force was increased; while one in vitro study and one in situ study reported reduced ACL loading if the hamstrings force was increased. A meta-analysis of the reported results was not possible because of the heterogeneity of the confounding factors.

CONCLUSION

The reported results suggest that increased hip flexion during landing may help in reducing ACL strain by lengthening the hamstrings, and thus increasing its passive resistance to stretch. Furthermore, it appears that increased tensile stiffness of the quadriceps may help in stabilising the knee joint during landing, and thus protecting the passive soft-tissue structures from overloading.

LEVEL OF EVIDENCE

Ib.

Modeling the Human Tibiofemoral Joint Using Ex Vivo Determined Compliance Matrices

Several approaches have been used to devise a model of the human tibiofemoral joint for embedment in lower limb musculoskeletal models. However, no study has considered the use of cadaveric 6 × 6 compliance (or stiffness) matrices to model the tibiofemoral joint under normal or pathological conditions. The aim of this paper is to present a method to determine the compliance matrix of an ex vivo tibiofemoral joint for any given equilibrium pose. Experiments were carried out on a single ex vivo knee, first intact and, then, with the anterior cruciate ligament (ACL) transected. Controlled linear and angular displacements were imposed in single degree-of-freedom (DoF) tests to the specimen, and the resulting forces and moments were measured using an instrumented robotic arm. This was done starting from seven equilibrium poses characterized by the following flexion angles: 0 deg, 15 deg, 30 deg, 45 deg, 60 deg, 75 deg, and 90 deg. A compliance matrix for each of the selected equilibrium poses and for both the intact and ACL-deficient specimen was calculated. The matrix, embedding the experimental load-displacement relationship of the examined DoFs, was calculated using a linear least squares inversion based on a QR decomposition, assuming symmetric and positive-defined matrices. Single compliance matrix terms were in agreement with the literature. Results showed an overall increase of the compliance matrix terms due to the ACL transection (2.6 ratio for rotational terms at full extension) confirming its role in the joint stabilization. Validation experiments were carried out by performing a Lachman test (the tibia is pulled forward) under load control on both the intact and ACL-deficient knee and assessing the difference (error) between measured linear and angular displacements and those estimated using the appropriate compliance matrix. This error increased nonlinearly with respect to the values of the load. In particular, when an incremental posterior-anterior force up to 6 N was applied to the tibia of the intact specimen, the errors on the estimated linear and angular displacements were up to 0.6 mm and 1.5 deg, while for a force up to 18 N, the errors were 1.5 mm and 10.5 deg, respectively. In conclusion, the method used in this study may be a viable alternative to characterize the tibiofemoral load-dependent behavior in several applications.

Comparison of different material models of articular cartilage in 3D computational modeling of the knee: Data from the Osteoarthritis Initiative (OAI)

The intricate properties of articular cartilage and the complexity of the loading environment are some of the key challenges in developing models for biomechanical analysis of the knee joint. Fibril-reinforced poroelastic (FRPE) material models have been reported to accurately capture characteristic responses of cartilage during dynamic and static loadings. However, high computational and time costs associated with such advanced models limit applicability of FRPE models when multiple subjects need to be analyzed. If choosing simpler material models, it is important to show that they can still produce truthful predictions. Therefore, the aim of this study was to compare depth-dependent maximum principal stresses and strains within articular cartilage in the 3D knee joint between FRPE material models and simpler isotropic elastic (IE), isotropic poroelastic (IPE) and transversely isotropic poroelastic (TIPE) material models during simulated gait cycle. When cartilage-cartilage contact pressures were matched between the models (15% allowed difference), maximum principal stresses in the IE, IPE and TIPE models were substantially lower than those in the FRPE model (by more than 50%, TIPE model being closest to the FRPE model), and stresses occurred only in compression in the IE model. Additional simulations were performed to find material parameters for the TIPE model (due to its anisotropic nature) that would yield maximum principal stresses similar to the FRPE model. The modified homogeneous TIPE model was in a better agreement with the homogeneous FRPE model, and the average and maximum differences in maximum principal stresses throughout the depth of cartilage were 7% and 9%, respectively, in the lateral compartment and 9% and 11% in the medial compartment. This study revealed that it is possible to match simultaneously maximum principal stresses and strains of cartilage between non-fibril-reinforced and fibril-reinforced knee joint models during gait. Depending on the research question (such as analysis of fibril strain necessitates the use of fibril-reinforced material models) or clinical demand (fast simulations with simpler material models), the choice of the material model should be done carefully.

How accurate and reproducible are the identification of cruciate and collateral ligament insertions using MRI?

BACKGROUND

At present, increasing the accuracy of identification of knee ligament insertions is fundamental in developing accurate patient-specific three-dimensional (3D) models for preoperative planning surgeries, designing patient-specific instrumentation or implants, and conducting biomechanical analyses. The accuracy and reproducibility of magnetic resonance imaging (MRI) scans in identifying cruciate and collateral ligament insertions have not been investigated thus far, despite their wide use. This study aimed to define and validate a method for this purpose.

METHODS

First, the femur and tibia bones were oriented. Then, the sites of cruciate and collateral ligament insertions were identified. The inter- and intra-class correlation coefficients (ICCs) were calculated after multiple operators were applied to the images of different patients. The effect of the quality of the available MRI scans on the accuracy of identifying ligament insertions was also investigated. Moreover, non-expert operators were also found to be capable of performing the procedure after a video tutorial, and its efficacy was tested.

RESULTS

The mean intra-observer variability was always <1.5mm for all landmarks, whereas the mean inter-observer variability was always <2.5mm except for the medial collateral ligament localized on the tibia (6.7mm). The ICCs showed good results, up to 0.99. A lower image quality had no noticeable effect on the procedure for identifying cruciate ligaments. Video tutorials were found to improve the ICCs up to 45%.

CONCLUSIONS

This procedure is suitable for the univocal and accurate identification of cruciate and lateral collateral ligaments on MRI scans.

CLINICAL RELEVANCE

This study demonstrates that MRI scans are highly suited to identifying cruciate ligament insertions.

Relative contribution of articular cartilage's constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.

THE EFFECT OF COLLATERAL LIGAMENT INJURY ON CARTILAGE CONTACT IN KNEE JOINTS MODELED WITH SIX DEGREES OF FREEDOM

The purpose of this study was to create a kinematic model of the knee joint with six degrees of freedom (DOF) and evaluate the effect of medial collateral ligament (MCL) and lateral collateral ligament (LCL) rupture on cartilage contact point distribution on the tibia during flexion. We hypothesized that collateral ligament contributions vary over six DOF of knee joint articulation and affect the cartilage contact point distribution during joint articulation. The ligament contributions and distribution of joint cartilage contact points cannot be fully assessed with simplified joint models or invasive experiments. Therefore, we developed a new model in which the tibia and femur centers of mass were determined from their surface geometry, and the displacement of the moving tibia was determined from the displacements of the attached ligaments. Compared to the intact knee, the tibia with the LCL removed had higher medial translation and lower valgus rotation. The tibia with the MCL removed had higher lateral translation and higher valgus rotation than the intact knee. At 0[Formula: see text], 30[Formula: see text], and 60[Formula: see text], the tibia with the LCL removed had more internal rotation than the intact knee. Understanding six DOF knee joint kinematics with integration of ligament contributions and cartilage contact positions is useful for the diagnosis of ligament injuries and the design of articulating surfaces for total arthroplasty.

Open Knee: Open Source Modeling and Simulation in Knee Biomechanics

Virtual representations of the knee joint can provide clinicians, scientists, and engineers the tools to explore mechanical functions of the knee and its tissue structures in health and disease. Modeling and simulation approaches such as finite element analysis also provide the possibility to understand the influence of surgical procedures and implants on joint stresses and tissue deformations. A large number of knee joint models are described in the biomechanics literature. However, freely accessible, customizable, and easy-to-use models are scarce. Availability of such models can accelerate clinical translation of simulations, where labor-intensive reproduction of model development steps can be avoided. Interested parties can immediately utilize readily available models for scientific discovery and clinical care. Motivated by this gap, this study aims to describe an open source and freely available finite element representation of the tibiofemoral joint, namely Open Knee, which includes the detailed anatomical representation of the joint's major tissue structures and their nonlinear mechanical properties and interactions. Three use cases illustrate customization potential of the model, its predictive capacity, and its scientific and clinical utility: prediction of joint movements during passive flexion, examining the role of meniscectomy on contact mechanics and joint movements, and understanding anterior cruciate ligament mechanics. A summary of scientific and clinically directed studies conducted by other investigators are also provided. The utilization of this open source model by groups other than its developers emphasizes the premise of model sharing as an accelerator of simulation-based medicine. Finally, the imminent need to develop next-generation knee models is noted. These are anticipated to incorporate individualized anatomy and tissue properties supported by specimen-specific joint mechanics data for evaluation, all acquired in vitro from varying age groups and pathological states.