A multi-scale finite element model for investigation of chondrocyte mechanics in normal and medial meniscectomy human knee joint during walking

Two-to-three times increase in natural hip and lumbar non-sagittal plane kinematics can lead to anterior cruciate ligament injury and cartilage failure scenarios during single-leg landings

BACKGROUND

Analyzing sports injuries is essential to mitigate risk for injury, but inherently challenging using in vivo approaches. Computational modeling is a powerful engineering tool used to access biomechanical information on tissue failure that cannot be obtained otherwise using traditional motion capture techniques.

METHODS

We extrapolated high-risk kinematics associated with ACL strain and cartilage load and stress from a previous motion analysis of 14 uninjured participants. Computational simulations were used to induce ACL failure strain and cartilage failure load, stress, and contact pressure in two age- and BMI-matched participants, one of each biological sex, during single-leg cross drop and single-leg drop tasks. The high-risk kinematics were exaggerated in 20% intervals, within their physiological range of motion, to determine if injury occurred in the models. Where injury occurred, we reported the kinematic profiles that led to tissue failure.

FINDINGS

Our findings revealed ACL strains up to 9.99%, consistent with reported failure values in existing literature. Cartilage failure was observed in all eight analyzed conditions when increasing each high-risk kinematic parameter by 2.61 ± 0.67 times the participants' natural landing values. The kinematics associated with tissue failure included peak hip internal rotation of 22.48 ± 19.04°, peak hip abduction of 22.51 ± 9.09°, and peak lumbar rotation away from the stance limb of 11.56 ± 9.78°.

INTERPRETATION

Our results support the ability of previously reported high-risk kinematics in the literature to induce injury and add to the literature by reporting extreme motion limits leading to injurious cases. Therefore, training programs able to modify these motions during single-leg landings may reduce the risk of ACL injury and cartilage trauma.

Multiple regression analysis for competitive performance assessment of professional soccer players

BACKGROUND

Being in peak physical condition and having specific motor abilities are necessity for every top-level soccer player in order to achieve success in competition. In order to correctly assess soccer players' performance, this research uses laboratory and field measurements, as well as results of competitive performance obtained by direct software measurements of players' movement during the actual soccer game.

OBJECTIVE

The main goal of this research is to give insight into the key abilities that soccer players need to have in order to perform in competitive tournaments. Besides training adjustments, this research also gives insight into what variables need to be tracked in order to accurately assess the efficiency and functionality of the players.

METHODS

The collected data need to be analyzed using descriptive statistics. Collected data is also used as input for multiple regression models that can predict certain key measurements: total distance covered, percent of effective movements and high index of effective performance movements.

RESULTS

Most of the calculated regression models have high predictability level with statistically significant variables.

CONCLUSION

Based on the results of regression analysis it can be deduced that motor abilities are important factor in measuring soccer player's competitive performance and team's success in the match.

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.

Effect of Whole Body Parameters on Knee Joint Biomechanics: Implications for ACL Injury Prevention During Single-Leg Landings

BACKGROUND

Previous studies have examined the effect of whole body (WB) parameters on anterior cruciate ligament (ACL) strain and loads, as well as knee joint kinetics and kinematics. However, articular cartilage damage occurs in relation to ACL failure, and the effect of WB parameters on ACL strain and articular cartilage biomechanics during dynamic tasks is unclear.

PURPOSES

(1) To investigate the effect of WB parameters on ACL strain, as well as articular cartilage stress and contact force, during a single-leg cross drop (SLCD) and single-leg drop (SLD). (2) To identify WB parameters predictive of high ACL strain during these tasks.

STUDY DESIGN

Descriptive laboratory study.

METHODS

Three-dimensional motion analysis data from 14 physically active men and women were recorded during an SLCD and SLD. OpenSim was used to obtain their kinematics, kinetics, and muscle forces for the WB model. Using these data in kinetically driven finite element simulations of the knee joint produced outputs of ACL strains and articular cartilage stresses and contact forces. Spearman correlation coefficients were used to assess relationships between WB parameters and ACL strain and cartilage biomechanics. Moreover, receiver operating characteristic curve analyses and multivariate binary logistic regressions were used to find the WB parameters that could discriminate high from low ACL strain trials.

RESULTS

Correlations showed that more lumbar rotation away from the stance limb at peak ACL strain had the strongest overall association (ρ = 0.877) with peak ACL strain. Higher knee anterior shear force (ρ = 0.895) and lower gluteus maximus muscle force (ρ = 0.89) at peak ACL strain demonstrated the strongest associations with peak articular cartilage stress or contact force in ≥1 of the analyzed tasks. The regression model that used muscle forces to predict high ACL strain trials during the dominant limb SLD yielded the highest accuracy (93.5%), sensitivity (0.881), and specificity (0.952) among all regression models.

CONCLUSION

WB parameters that were most consistently associated with and predictive of high ACL strain and poor articular cartilage biomechanics during the SLCD and SLD tasks included greater knee abduction angle at initial contact and higher anterior shear force at peak ACL strain, as well as lower gracilis, gluteus maximus, and medial gastrocnemius muscle forces.

CLINICAL RELEVANCE

Knowledge of which landing postures create a high risk for ACL or cartilage injury may help reduce injuries in athletes by avoiding those postures and practicing the tasks with reduced high-risk motions, as well as by strengthening the muscles that protect the knee during single-leg landings.

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.

Medial meniscus posterior root tears and partial meniscectomy significantly increase stress in the knee joint during dynamic gait

PURPOSE

As a simple and invasive treatment, arthroscopic medial meniscal posterior horn resections (MMPHRs) can relieve the obstructive symptoms of medial meniscus posterior root tears (MMPRTs) but with the risk of aggravating biomechanical changes of the joint. The aim of this study was to analyze dynamic simulation of the knee joint after medial meniscus posterior root tear and posterior horn resection.

METHODS

This study established static and dynamic models of MMPRTs and MMPHRs on the basis of the intact medial meniscus model (IMM). In the finite element analysis, the three models were subjected to 1000 N axial static load and the human walking gait load defined by the ISO14243-1 standard to evaluate the influence of MMPRTs and MMPHRs on knee joint mechanics during static standing and dynamic walking.

RESULTS

In the static state, the load ratio of the medial and lateral compartments remained nearly constant (2:1), while in the dynamic state, the load ratio varied with the gait cycle. After MMPHRs, at 30% of the gait cycle, compared with the MMPRTs condition, the maximum von Mises stress of the lateral meniscus (LM) and the lateral tibial cartilage (LTC) were increased by 166.0% and 50.0%, respectively, while they changed by less than 5% during static analysis. The maximum von Mises stress of the medial meniscus (MM) decreased by 55.7%, and that of the medial femoral cartilage (MFC) increased by 53.5%.

CONCLUSION

After MMPHRs, compared with MMPRTs, there was no significant stress increase in articular cartilage in static analysis, but there was a stress increase and concentration in both medial and lateral compartments in dynamic analysis, which may aggravate joint degeneration. Therefore, in clinical treatments, restoring the natural structure of MMPRTs is first recommended, especially for physically active patients.

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.

Rapid X-Ray-Based 3-D Finite Element Modeling of Medial Knee Joint Cartilage Biomechanics During Walking

Finite element (FE) modeling is becoming an increasingly popular method for analyzing knee joint mechanics and biomechanical mechanisms leading to osteoarthritis (OA). The most common and widely available imaging method for knee OA diagnostics is planar X-ray imaging, while more sophisticated imaging methods, e.g., magnetic resonance imaging (MRI) and computed tomography (CT), are seldom used. Hence, the capability to produce accurate biomechanical knee joint models directly from X-ray imaging would bring FE modeling closer to clinical use. Here, we extend our atlas-based framework by generating FE knee models from X-ray images (N = 28). Based on measured anatomical landmarks from X-ray and MRI, knee joint templates were selected from the atlas library. The cartilage stresses and strains of the X-ray-based model were then compared with the MRI-based model during the stance phase of the gait. The biomechanical responses were statistically not different between MRI- vs. X-ray-based models when the template obtained from X-ray imaging was the same as the MRI template. However, if this was not the case, the peak values of biomechanical responses were statistically different between X-ray and MRI models. The developed X-ray-based framework may pave the way for a clinically feasible approach for knee joint FE modeling.

Magnetic Resonance Imaging-based biomechanical simulation of cartilage: A systematic review

MRI-based mathematical and computational modeling studies can contribute to a better understanding of the mechanisms governing cartilage's mechanical performance and cartilage disease. In addition, distinct modeling of cartilage is needed to optimize artificial cartilage production. These studies have opened up the prospect of further deepening our understanding of cartilage function. Furthermore, these studies reveal the initiation of an engineering-level approach to how cartilage disease affects material properties and cartilage function. Aimed at researchers in the field of MRI-based cartilage simulation, research articles pertinent to MRI-based cartilage modeling were identified, reviewed, and summarized systematically. Various MRI applications for cartilage modeling are highlighted, and the limitations of different constitutive models used are addressed. In addition, the clinical application of simulations and studied diseases are discussed. The paper's quality, based on the developed questionnaire, was assessed, and out of 79 reviewed papers, 34 papers were determined as high-quality. Due to the lack of the best constitutive models for various clinical conditions, researchers may consider the effect of constitutive material models on the cartilage disease simulation. In the future, research groups may incorporate various aspects of machine learning into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification, such as gait analysis.

Changes in Knee Joint Mechanics After Medial Meniscectomy Determined With a Poromechanical Model

The menisci play a vital role in the mechanical function of knee joint. Unfortunately, meniscal tears often occur. Meniscectomy is a surgical treatment for meniscal tears; however, mechanical changes in the knee joint after meniscectomy is a risk factor to osteoarthritis (OA). The objective of this study was to investigate the altered cartilage mechanics of different medial meniscectomies using a poromechanical model of the knee joint. The cartilaginous tissues were modeled as nonlinear fibril-reinforced porous materials with full saturation. The ligaments were considered as anisotropic hyperelastic and reinforced by a fibrillar collagen network. A compressive creep load of ¾ body weight was applied in full extension of the right knee during 200 s standing. Four finite element models were developed to simulate different meniscectomies of the joint using the intact model as the reference for comparison. The modeling results showed a higher load support in the lateral than medial compartment in the intact joint, and the difference in the load share between the compartments was augmented with medial meniscectomy. Similarly, the contact and fluid pressures were higher in the lateral compartment. On the other hand, the medial meniscus in the normal joint experienced more loading than the lateral one. Furthermore, the contact pressure distribution changed with creep, resulting in a load transfer between cartilage and meniscus within each compartment while the total load born by the compartment remained unchanged. This study has quantified the altered contact mechanics on the type and size of meniscectomies, which may be used to understand meniscal tear or support surgical decisions.

Finite-Element analysis of a lateral femoro-tibial impact on the total knee arthroplasty

BACKGROUND AND OBJECTIVE

Total knee arthroplasty (TKA) is a routine surgery performed to treat patients with severe knee osteoarthritis. The success of a TKA depends strongly on the initial stability of the prosthetic components and its long-term osseointegration due to the optimal distribution of mechanical stresses in the surrounding bones under the effect of the different biomechanical loads applied to the Femur-TKA-Tibia system. The purpose of this study is to analyze the level and the distribution of the induced stresses in a Femur-TKA-Tibia system subjected to combined triaxial forces, which mimic a femoral mechanical shock.

METHODS

In this study, complex TKA system implanted in both femoral and tibial bones has been analyzed numerically with a three-dimensional finite-element method. A virtual model is designed to examine in silico the effect of the combined triaxial forces acting on this prosthesis in femoral region. Anatomical three-dimensional finite-element models of both femoral and tibial bones were constructed to calculate the interfacial stresses around the TKA components. The 3D finite-element processing program ABAQUS was used to perform the analysis.

RESULTS

The stresses propagated in the bone regions adjacent to the TKA osseointegrated components, and the decreased in their magnitude to the outer region. These stresses reached the highest level in the cortical bone areas that are right next to the proximal upper attachment portions of the TKA osseointegrated components. The magnitude of the stresses in the tibial component is higher than that in the femoral component. Finally, it is very important to emphasize the role of the polyethylene articulating spacer in the shock absorption of bone support sections. Thus, this component should be preserved mechanically from the impact of high shocks in order to maintain healthy TKA systems.

CONCLUSIONS

Optimizing TKA model by controlling the biomechanical stresses distributed within its both components and supporting bones is a valid approach to achieving favorable long-term outcomes. The 3D finite-element analysis provides an effective pre-operative method for planning patient-specific TKA prostheses, and for designing future models that preserves the biomechanical function of the Femur-TKA-Tibia system.

Clinical Contrast-Enhanced Computed Tomography With Semi-Automatic Segmentation Provides Feasible Input for Computational Models of the Knee Joint

Computational models can provide information on joint function and risk of tissue failure related to progression of osteoarthritis (OA). Currently, the joint geometries utilized in modeling are primarily obtained via manual segmentation, which is time-consuming and hence impractical for direct clinical application. The aim of this study was to evaluate the applicability of a previously developed semi-automatic method for segmenting tibial and femoral cartilage to serve as input geometry for finite element (FE) models. Knee joints from seven volunteers were first imaged using a clinical computed tomography (CT) with contrast enhancement and then segmented with semi-automatic and manual methods. In both segmentations, knee joint models with fibril-reinforced poroviscoelastic (FRPVE) properties were generated and the mechanical responses of articular cartilage were computed during physiologically relevant loading. The mean differences in the absolute values of maximum principal stress, maximum principal strain, and fibril strain between the models generated from semi-automatic and manual segmentations were <1 MPa, <0.72% and <0.40%, respectively. Furthermore, contact areas, contact forces, average pore pressures, and average maximum principal strains were not statistically different between the models (p >0.05). This semi-automatic method speeded up the segmentation process by over 90% and there were only negligible differences in the results provided by the models utilizing either manual or semi-automatic segmentations. Thus, the presented CT imaging-based segmentation method represents a novel tool for application in FE modeling in the clinic when a physician needs to evaluate knee joint function.

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.

EMG-Assisted Muscle Force Driven Finite Element Model of the Knee Joint with Fibril-Reinforced Poroelastic Cartilages and Menisci

Abnormal mechanical loading is essential in the onset and progression of knee osteoarthritis. Combined musculoskeletal (MS) and finite element (FE) modeling is a typical method to estimate load distribution and tissue responses in the knee joint. However, earlier combined models mostly utilize static-optimization based MS models and muscle force driven FE models typically use elastic materials for soft tissues or analyze specific time points of gait. Therefore, here we develop an electromyography-assisted muscle force driven FE model with fibril-reinforced poro(visco)elastic cartilages and menisci to analyze knee joint loading during the stance phase of gait. Moreover, since ligament pre-strains are one of the important uncertainties in joint modeling, we conducted a sensitivity analysis on the pre-strains of anterior and posterior cruciate ligaments (ACL and PCL) as well as medial and lateral collateral ligaments (MCL and LCL). The model produced kinematics and kinetics consistent with previous experimental data. Joint contact forces and contact areas were highly sensitive to ACL and PCL pre-strains, while those changed less cartilage stresses, fibril strains, and fluid pressures. The presented workflow could be used in a wide range of applications related to the aetiology of cartilage degeneration, optimization of rehabilitation exercises, and simulation of knee surgeries.

EMG-Assisted Muscle Force Driven Finite Element Model of the Knee Joint with Fibril-Reinforced Poroelastic Cartilages and Menisci

Abnormal mechanical loading is essential in the onset and progression of knee osteoarthritis. Combined musculoskeletal (MS) and finite element (FE) modeling is a typical method to estimate load distribution and tissue responses in the knee joint. However, earlier combined models mostly utilize static-optimization based MS models and muscle force driven FE models typically use elastic materials for soft tissues or analyze specific time points of gait. Therefore, here we develop an electromyography-assisted muscle force driven FE model with fibril-reinforced poro(visco)elastic cartilages and menisci to analyze knee joint loading during the stance phase of gait. Moreover, since ligament pre-strains are one of the important uncertainties in joint modeling, we conducted a sensitivity analysis on the pre-strains of anterior and posterior cruciate ligaments (ACL and PCL) as well as medial and lateral collateral ligaments (MCL and LCL). The model produced kinematics and kinetics consistent with previous experimental data. Joint contact forces and contact areas were highly sensitive to ACL and PCL pre-strains, while those changed less cartilage stresses, fibril strains, and fluid pressures. The presented workflow could be used in a wide range of applications related to the aetiology of cartilage degeneration, optimization of rehabilitation exercises, and simulation of knee surgeries.

Biomechanical role of posterior cruciate ligament in total knee arthroplasty: A finite element analysis

BACKGROUND AND OBJECTIVE

The knee joint is a complex structure which is vulnerable to injury due to various types of loadings as a consequence of walking, running, stair climbing, etc. Total knee arthroplasty (TKA) is a widely used and successful orthopedic procedure which during that the posterior cruciate ligament (PCL) can either be retained or substituted. Different surgical techniques suggest retention or sacrifice of the PCL in TKA for the treatment of osteoarthritis which may alter the post-op outcomes. The objective of this study was to evaluate the biomechanical role of PCL after TKA surgery using finite element (FE) modeling.

METHODS

A three-dimensional (3D) FE model of the prosthetic knee was developed and its validity was compared to available studies in literature. Further, the effect of the retention or removing of the PCL as well as its degradation (i.e. variation in mechanical properties) and angle on knee biomechanics were evaluated during a weight-bearing squatting movement.

RESULTS

The validity of the intact model were confirmed. The results revealed higher stresses in the PCL and tibial insert at higher femoral flexion angles. In addition, the effect of variations in the stiffness of the PCL was found to be negligible at lower while considerable at higher femoral flexion angles. The variations in the elevation angle of the PCL from 89° to 83° at the critical femoral angles of 60° and 120° showed the highest von Mises stresses in the tibial insert.

CONCLUSIONS

The results have implications not only for understanding the stresses in the prosthetic knee model under squat movement but also for providing comprehensive information about the effects of variations in the PCL stiffness and balancing on the induced stresses of the PCL and tibial insert.

Chondrocyte viability is lost during high-rate impact loading by transfer of amplified strain, but not stress, to pericellular and cellular regions

OBJECTIVE

Deleterious impact loading to cartilage initiates post-traumatic osteoarthritis (OA). While cytokine and enzyme levels regulate disease progression, specific mechanical cues that elucidate cellular OA origins merit further investigation. We defined the dominant pericellular and cellular strain/stress transfer mechanisms following bulk-tissue injury associated with cell death.

METHOD

Using an in vitro model, we investigated rate-dependent loading and spatial localization of cell viability in acute indentation and time-course studies. Atomic force microscopy (AFM) and magnetic resonance imaging (MRI) confirmed depth-wise changes in cartilage micro-/macro-mechanics and structure post-indentation. To understand the transfer of loading to cartilage domains, we computationally modeled full-field strain and stress measures in interstitial matrix, pericellular and cellular regions.

RESULTS

Chondrocyte viability decreased following rapid impact (80%/s) vs slow loading (0.1%/s) or unloaded controls. Viability was lost immediately during impact within regions near the indenter-tissue contact but did not change over 7 days of tissue culture. AFM studies revealed a loss of stiffness following 80%/s loading, and MRI studies confirmed an increased tensile and shear strain, but not relaxometry. Image-based patterns of chondrocyte viability closely matched computational estimates of amplified maximum principal and shear strain in interstitial matrix, pericellular and cellular regions.

CONCLUSION

Rapid indentation worsens chondrocyte death and degrades cartilage matrix stiffness in indentation regions. Cell death at high strain rates may be driven by elevated tensile strains, but not matrix stress. Strain amplification beyond critical thresholds in the pericellular matrix and cells may define a point of origin for early damage in post-traumatic OA.

Evaluation of the Effect of Bariatric Surgery-Induced Weight Loss on Knee Gait and Cartilage Degeneration

The objective of the study was to investigate the effects of bariatric surgery-induced weight loss on knee gait and cartilage degeneration in osteoarthritis (OA) by combining magnetic resonance imaging (MRI), gait analysis, finite element (FE) modeling, and cartilage degeneration algorithm. Gait analyses were performed for obese subjects before and one-year after the bariatric surgery. FE models were created before and after weight loss for those subjects who did not have severe tibio-femoral knee cartilage loss. Knee cartilage degenerations were predicted using an adaptive cartilage degeneration algorithm which is based on cumulative overloading of cartilage, leading to iteratively altered cartilage properties during OA. The average weight loss was 25.7±11.0 kg corresponding to a 9.2±3.9 kg/m2 decrease in body mass index (BMI). External knee rotation moment increased, and minimum knee flexion angle decreased significantly (p < 0.05) after weight loss. Moreover, weight loss decreased maximum cartilage degeneration by 5±23% and 13±11% on the medial and lateral tibial cartilage surfaces, respectively. Average degenerated volumes in the medial and lateral tibial cartilage decreased by 3±31% and 7±32%, respectively, after weight loss. However, increased degeneration levels could also be observed due to altered knee kinetics. The present results suggest that moderate weight loss changes knee kinetics and kinematics and can slow-down cartilage degeneration for certain patients. Simulation results also suggest that prediction of cartilage degeneration is subject-specific and highly depend on the altered gait loading, not just the patient's weight.

Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio

With the recent implementation of multiphasic materials in the open-source finite element (FE) software FEBio (febio.org), 3D models of cells embedded within the tissue may now be analyzed, accounting for porous solid matrix deformation, transport of interstitial fluid and solutes, membrane potential, and reactions. The cell membrane is a critical component in cell models, which selectively regulates the transport of fluid and solutes in the presence of large concentration and electric potential gradients, while also facilitating the transport of various proteins. The cell membrane is much thinner than the cell; therefore, in an FE environment, shell elements formulated as 2D surfaces in 3D space would be preferred for modeling the cell membrane, for the convenience of mesh generation from image-based data, especially for convoluted membranes. However, multiphasic shell elements are yet to be developed in the FE literature and commercial FE software. This study presents a novel formulation of multiphasic shell elements and its implementation in FEBio. The shell model includes front- and back-face nodal degrees of freedom for the solid displacement, effective fluid pressure and effective solute concentrations, and a linear interpolation of these variables across the shell thickness. This formulation was verified against classical models of cell physiology and validated against reported experimental measurements in chondrocytes. This implementation of passive transport of fluid and solutes across multiphasic membranes makes it possible to model the biomechanics of isolated cells or cells embedded in their extracellular matrix, accounting for solvent and solute transport.

The effect of constitutive representations and structural constituents of ligaments on knee joint mechanics

Ligaments provide stability to the human knee joint and play an essential role in restraining motion during daily activities. Compression-tension nonlinearity is a well-known characteristic of ligaments. Moreover, simpler material representations without this feature might give reasonable results because ligaments are primarily in tension during loading. However, the biomechanical role of different constitutive representations and their fibril-reinforced poroelastic properties is unknown. A numerical knee model which considers geometric and material nonlinearities of meniscus and cartilages was applied. Five different constitutive models for the ligaments (spring, elastic, hyperelastic, porohyperelastic, and fibril-reinforced porohyperelastic (FRPHE)) were implemented. Knee joint forces for the models with elastic, hyperelastic and porohyperelastic properties showed similar behavior throughout the stance, while the model with FRPHE properties exhibited lower joint forces during the last 50% of the stance phase. The model with ligaments as springs produced the lowest joint forces at this same stance phase. The results also showed that the fibril network contributed substantially to the knee joint forces, while the nonfibrillar matrix and fluid had small effects. Our results indicate that simpler material models of ligaments with similar properties in compression and tension can be used when the loading is directed primarily along the ligament axis in tension.

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.

Workflow assessing the effect of gait alterations on stresses in the medial tibial cartilage - combined musculoskeletal modelling and finite element analysis

Knee osteoarthritis (KOA) is most common in the medial tibial compartment. We present a novel method to study the effect of gait modifications and lateral wedge insoles (LWIs) on the stresses in the medial tibial cartilage by combining musculoskeletal (MS) modelling with finite element (FE) analysis. Subject's gait was recorded in a gait laboratory, walking normally, with 5° and 10° LWIs, toes inward ('Toe in'), and toes outward ('Toe out wide'). A full lower extremity MRI and a detailed knee MRI were taken. Bones and most soft tissues were segmented from images, and the generic bone architecture of the MS model was morphed into the segmented bones. The output forces from the MS model were then used as an input in the FE model of the subject's knee. During stance, LWIs failed to reduce medial peak pressures apart from Insole 10° during the second peak. Toe in reduced peak pressures by -11% during the first peak but increased them by 12% during the second. Toe out wide reduced peak pressures by -15% during the first and increased them by 7% during the second. The results show that the work flow can assess the effect of interventions on an individual level. In the future, this method can be applied to patients with KOA.

A computational algorithm to simulate disorganization of collagen network in injured articular cartilage

Cartilage defects are a known risk factor for osteoarthritis. Estimation of structural changes in these defects could help us to identify high risk defects and thus to identify patients that are susceptible for the onset and progression of osteoarthritis. Here, we present an algorithm combined with computational modeling to simulate the disorganization of collagen fibril network in injured cartilage. Several potential triggers for collagen disorganization were tested in the algorithm following the assumption that disorganization is dependent on the mechanical stimulus of the tissue. We found that tensile tissue stimulus alone was unable to preserve collagen architecture in intact cartilage as collagen network reoriented throughout the cartilage thickness. However, when collagen reorientation was based on both tensile tissue stimulus and tensile collagen fibril strains or stresses, the collagen network architecture was preserved in intact cartilage. Using the same approach, substantial collagen reorientation was predicted locally near the cartilage defect and particularly at the cartilage-bone interface. The developed algorithm was able to predict similar structural findings reported in the literature that are associated with experimentally observed remodeling in articular cartilage. The proposed algorithm, if further validated, could help to predict structural changes in articular cartilage following post-traumatic injury potentially advancing to impaired cartilage function.

Study of the Mechanical Environment of Chondrocytes in Articular Cartilage Defects Repaired Area under Cyclic Compressive Loading

COMSOL finite element software was used to establish a solid-liquid coupling biphasic model of articular cartilage and a microscopic model of chondrocytes, using modeling to take into account the shape and number of chondrocytes in cartilage lacuna in each layer. The effects of cyclic loading at different frequencies on the micromechanical environment of chondrocytes in different regions of the cartilage were studied. The results showed that low frequency loading can cause stress concentration of superficial chondrocytes. Moreover, along with increased frequency, the maximum value of stress response curve of chondrocytes decreased, while the minimum value increased. When the frequency was greater than 0.2 Hz, the extreme value stress of response curve tended to be constant. Cyclic loading had a large influence on the distribution of liquid pressure in chondrocytes in the middle and deep layers. The concentration of fluid pressure changed alternately from intracellular to peripheral in the middle layer. Both the range of liquid pressure in the upper chondrocytes and the maximum value of liquid pressure in the lower chondrocytes in the same lacunae varied greatly in the deep layer. At the same loading frequency, the elastic modulus of artificial cartilage had little effect on the mechanical environment of chondrocytes.

Systems approaches in osteoarthritis: Identifying routes to novel diagnostic and therapeutic strategies

Systems orientated research offers the possibility of identifying novel therapeutic targets and relevant diagnostic markers for complex diseases such as osteoarthritis. This review demonstrates that the osteoarthritis research community has been slow to incorporate systems orientated approaches into research studies, although a number of key studies reveal novel insights into the regulatory mechanisms that contribute both to joint tissue homeostasis and its dysfunction. The review introduces both top-down and bottom-up approaches employed in the study of osteoarthritis. A holistic and multiscale approach, where clinical measurements may predict dysregulation and progression of joint degeneration, should be a key objective in future research. The review concludes with suggestions for further research and emerging trends not least of which is the coupled development of diagnostic tests and therapeutics as part of a concerted effort by the osteoarthritis research community to meet clinical needs. © 2017 The Authors. Journal of Orthopaedic Research Published by Wiley Periodicals, Inc. on behalf of Orthopaedic Research Society. J Orthop Res 35:1573-1588, 2017.

Combined measurement and modeling of specimen-specific knee mechanics for healthy and ACL-deficient conditions

Quantifying the mechanical environment at the knee is crucial for developing successful rehabilitation and surgical protocols. Computational models have been developed to complement in vitro studies, but are typically created to represent healthy conditions, and may not be useful in modeling pathology and repair. Thus, the objective of this study was to create finite element (FE) models of the natural knee, including specimen-specific tibiofemoral (TF) and patellofemoral (PF) soft tissue structures, and to evaluate joint mechanics in intact and ACL-deficient conditions. Simulated gait in a whole joint knee simulator was performed on two cadaveric specimens in an intact state and subsequently repeated following ACL resection. Simulated gait was performed using motor-actuated quadriceps, and loads at the hip and ankle. Specimen-specific FE models of these experiments were developed in both intact and ACL-deficient states. Model simulations compared kinematics and loading of the experimental TF and PF joints, with average RMS differences [max] of 3.0° [8.2°] and 2.1° [8.4°] in rotations, and 1.7 [3.0] and 2.5 [5.1] mm in translations, for intact and ACL-deficient states, respectively. The timing of peak quadriceps force during stance and swing phase of gait was accurately replicated within 2° of knee flexion and with an average error of 16.7% across specimens and pathology. Ligament recruitment patterns were unique in each specimen; recruitment variability was likely influenced by variations in ligament attachment locations. ACL resections demonstrated contrasting joint mechanics in the two specimens with altered knee motion shown in one specimen (up to 5mm anterior tibial translation) while increased TF joint loading was shown in the other (up to 400N).

Osteoarthritis year in review 2016: mechanics

Inappropriate biomechanics, namely wear-and-tear, has been long believed to be a main cause of osteoarthritis (OA). However, this view is now being re-evaluated, especially when examined alongside mechanobiology and new biomechanical studies. These are multiscale experimental and computational studies focussing on cell- and tissue-level mechanobiology through to organ- and whole-body-level biomechanics, which focuses on the biomechanical and biochemical environment of the joint tissues. This review examined papers from April 2015 to April 2016, with a focus on multiscale experimental and computational biomechanical studies of OA. Assessing the onset or progression of OA at organ- and whole-body-levels, gait analysis, medical imaging and neuromusculoskeletal modelling revealed the extent to which tissue damage changes the view of inappropriate biomechanics. Traditional gait analyses studies reported that conservative treatments can alter joint biomechanics, thereby improving pain and function experienced by those with OA. Results of animal models of OA were consistent with these human studies, showing interactions among bone, cartilage and meniscus biomechanics and the onset and/or progression OA. Going down size scales, experimental and computational studies probed the nanosize biomechanics of molecules, cells and extracellular matrix, and demonstrated how the interactions between biomechanics and morphology affect cartilage dynamic poroelastic behaviour and pathways to OA. Finally, integration of multiscale experimental data and computational models were proposed to predict cartilage extracellular matrix remodelling and the development of OA. Summarising, experimental and computational methods provided a nuanced biomechanical understanding of the sub-cellular, cellular, tissue, organ and whole-body mechanisms involved in OA.

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.

Importance of Patella, Quadriceps Forces, and Depthwise Cartilage Structure on Knee Joint Motion and Cartilage Response During Gait

In finite-element (FE) models of the knee joint, patella is often omitted. We investigated the importance of patella and quadriceps forces on the knee joint motion by creating an FE model of the subject's knee. In addition, depthwise strains and stresses in patellar cartilage with different tissue properties were determined. An FE model was created from subject's magnetic resonance images. Knee rotations, moments, and translational forces during gait were recorded in a motion laboratory and used as an input for the model. Three material models were implemented into the patellar cartilage: (1) homogeneous model, (2) inhomogeneous (arcadelike fibrils), and (3) random fibrils at the superficial zone, mimicking early stages of osteoarthritis (OA). Implementation of patella and quadriceps forces into the model substantially reduced the internal–external femoral rotations (versus without patella). The simulated rotations in the model with the patella matched the measured rotations at its best. In the inhomogeneous model, maximum principal stresses increased substantially in the middle zone of the cartilage. The early OA model showed increased compressive strains in the superficial and middle zones of the cartilage and decreased stresses and fibril strains especially in the middle zone. The results suggest that patella and quadriceps forces should be included in moment- and force-driven FE knee joint models. The results indicate that the middle zone has a major role in resisting shear forces in the patellar cartilage. Also, early degenerative changes in the collagen network substantially affect the cartilage depthwise response in the patella during walking.

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.

Osteoarthritis year in review 2015: mechanics

Motivated by the conceptual framework of multi-scale biomechanics, this narrative review highlights recent major advances with a focus on gait and joint kinematics, then tissue-level mechanics, cell mechanics and mechanotransduction, matrix mechanics, and finally the nanoscale mechanics of matrix macromolecules. A literature review was conducted from January 2014 to April 2015 using PubMed to identify major developments in mechanics related to osteoarthritis (OA). Studies of knee adduction, flexion, rotation, and contact mechanics have extended our understanding of medial compartment loading. In turn, advances in measurement methodologies have shown how injuries to both the meniscus and ligaments, together, can alter joint kinematics. At the tissue scale, novel findings have emerged regarding the mechanics of the meniscus as well as cartilage superficial zone. Moving to the cell level, poroelastic and poro-viscoelastic mechanisms underlying chondrocyte deformation have been reported, along with the response to osmotic stress. Further developments have emerged on the role of calcium signaling in chondrocyte mechanobiology, including exciting findings on the function of mechanically activated cation channels newly found to be expressed in chondrocytes. Finally, AFM-based nano-rheology systems have enabled studies of thin murine tissues and brush layers of matrix molecules over a wide range of loading rates including high rates corresponding to impact injury. With OA acknowledged to be a disease of the joint as an organ, understanding mechanical behavior at each length scale helps to elucidate the connections between cell biology, matrix biochemistry and tissue structure/function that may play a role in the pathomechanics of OA.

WITHDRAWN: Meniscus mechanics and mechanobiology

The Publisher regrets that this article is an accidental duplication of an article that has already been published, http://dx.doi.org/10.1016/j.jbiomech.2015.03.020. The duplicate article has therefore been withdrawn. The full Elsevier Policy on Article Withdrawal can be found at http://www.elsevier.com/locate/withdrawalpolicy.