Implementation of a gait cycle loading into healthy and meniscectomised knee joint models with fibril-reinforced articular cartilage

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.

Model Properties and Clinical Application in the Finite Element Analysis of Knee Joint: A Review

The knee is the most complex joint in the human body, including bony structures like the femur, tibia, fibula, and patella, and soft tissues like menisci, ligaments, muscles, and tendons. Complex anatomical structures of the knee joint make it difficult to conduct precise biomechanical research and explore the mechanism of movement and injury. The finite element model (FEM), as an important engineering analysis technique, has been widely used in many fields of bioengineering research. The FEM has advantages in the biomechanical analysis of objects with complex structures. Researchers can use this technology to construct a human knee joint model and perform biomechanical analysis on it. At the same time, finite element analysis can effectively evaluate variables such as stress, strain, displacement, and rotation, helping to predict injury mechanisms and optimize surgical techniques, which make up for the shortcomings of traditional biomechanics experimental research. However, few papers introduce what material properties should be selected for each anatomic structure of knee FEM to meet different research purposes. Based on previous finite element studies of the knee joint, this paper summarizes various modeling strategies and applications, serving as a reference for constructing knee joint models and research design.

Biomechanical effects of typical lower limb movements of Chen-style Tai Chi on knee joint

The load and stress distribution on cartilage and meniscus of the knee joint in typical lower limb movements of Chen-style Tai Chi (TC) and deep squat (DS) were analyzed using finite element (FE) analysis. The loadings for this analysis consisted of muscle forces and ground reaction force (GRF), which were calculated through the inverse dynamic approach based on kinematics and force plate measurements obtained from motion capture experiments. Thirteen experienced practitioners performed four typical TC movements, namely, single whip (SW), brush knee and twist step (BKTS), stretch down (SD), and part the wild horse's mane (PWHM), which exhibit lower posture and greater lower limb force compared to other TC styles. The results indicated that TC required greater lower limb muscle strength than DS, resulting in greater knee joint forces. The stress on the medial cartilage in SW and BKTS fell within a range conductive to maintaining the balance between anabolism and catabolism of cartilage matrix. This was due to the fact that SW and BKTS reduce the medial to total tibiofemoral contact force ratios through knee abduction, which may effectively alleviate mild medial knee osteoarthritis (KOA). However, the greater medial contact force ratios observed in SD and PWHM resulted in great contact stresses that may aggravate the pain of patients with KOA. To mitigate these effects, practitioners should consider elevating their postures appropriately to reduce knee flexion angles, especially during the single-leg support phase. This adjustment can decrease the required muscle strength, load and stress on the knee joint.

Comparison of constitutive models for meniscus and their effect on the knee joint biomechanics during gait

Mechanical behavior of meniscus can be modeled using constitutive material models of varying complexity, such as isotropic elastic or fibril reinforced poroelastic (FRPE). However, the FRPE material is complex to implement, computationally demanding in 3D geometries, and simulation is time-consuming. Hence, we aimed to quantify the most suitable and efficient constitutive model of meniscus for simulation of cartilage responses in the knee joint during walking. We showed that simpler constitutive material models can reproduce similar cartilage responses to a knee model with the FRPE meniscus, but only knee models that consider orthotropic elastic meniscus can also reproduce meniscus responses adequately.

A novel knee joint model in FEBio with inhomogeneous fibril-reinforced biphasic cartilage simulating tissue mechanical responses during gait: data from the osteoarthritis initiative

We developed a novel knee joint model in FEBio to simulate walking. Knee cartilage was modeled using a fibril-reinforced biphasic (FRB) formulation with depth-wise collagen architecture and split-lines to account for cartilage structure. Under axial compression, the knee model with FRB cartilage yielded contact pressures, similar to reported experimental data. Furthermore, gait analysis with FRB cartilage simulated spatial and temporal trends in cartilage fluid pressures, stresses, and strains, comparable to those of a fibril-reinforced poroviscoelastic (FRPVE) material in Abaqus. This knee joint model in FEBio could be used for further studies of knee disorders using physiologically relevant loading.

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.

A numerical model for fibril remodeling in articular cartilage

BACKGROUND

Collagen fibrils of articular cartilage have a distinct organization in mature human knee joints. It seems that a mechanobiological process drives the remodeling of newborn collagen fibrils with maturation. Therefore, the goal of the present study was to develop a collagen fibril remodeling algorithm that describes the unique collagen fibril organization in a 3D knee model.

METHOD

A fibril-reinforced, biphasic cartilage model was used with a cuboid and a 3D human knee joint geometries. An isotropic collagen fibril distribution was assigned to the cartilage at the start of the analysis. Each fibril was rotated towards the direction that resulted in a maximum stretch at each time increment of the loading cycle.

RESULTS

The resulting pattern for the collagen fibrils was compared with split line patterns of porcine knee joint cartilage and also data published in the literature. Fibrils on the articular surface had a radial pattern towards the geometrical centroid of the tibial and femoral cartilage. In the tibiofemoral contact regions of superficial zone, fibrils were oriented circumferentially and randomly. In the porcine samples, the split-line patterns were similar to those obtained theoretically. Depth-wise organization of fibril network was characterized by fibrils perpendicular to the subchondral bone in the deeper layers, and fibrils parallel to the surface of cartilage in the superficial zone.

CONCLUSIONS

The maximum stretch criterion, coupled with a biphasic constitutive model, successfully predicted the collagen fibril organization observed in the articular cartilage throughout the depth and on the articular surface.

Finite element modeling with subject-specific mechanical properties to assess knee osteoarthritis initiation and progression

Finite element models of the knee can be used to identify regions at risk of mechanical failure in studies of osteoarthritis. Models of the knee often implement joint geometry obtained from magnetic resonance imaging (MRI) or gait kinematics from motion capture to increase model specificity for a given subject. However, differences exist in cartilage material properties regionally as well as between subjects. This paper presents a method to create subject-specific finite element models of the knee that assigns cartilage material properties from T₂ relaxometry. We compared our T₂ -refined model to identical models with homogeneous material properties. When tested on three subjects from the Osteoarthritis Initiative data set, we found the T₂ -refined models estimated higher principal stresses and shear strains in most cartilage regions and corresponded better to increases in KL grade in follow-ups compared to their corresponding homogeneous material models. Measures of cumulative stress within regions of a T₂ -refined model also correlated better with the region's cartilage morphology MRI Osteoarthritis Knee Score as compared with the homogeneous model. We conclude that spatially heterogeneous T₂ -refined material properties improve the subject-specificity of finite element models compared to homogeneous material properties in osteoarthritis progression studies. Statement of Clinical Significance: T₂ -refined material properties can improve subject-specific finite element model assessments of cartilage degeneration.

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.

T2 Mapping Refined Finite Element Modeling to Predict Knee Osteoarthritis Progression

This paper presents a novel method for informing cartilage material properties in finite element models from T₂ relaxometry. In the developed pipeline, T₂ relaxation values are mapped to elements in subject-specific finite element models of the cartilage and menisci. The Young's modulus for each element within the cartilage is directly calculated from its corresponding T₂ relaxation voxel value. Our model was tested on a single subject (Subject ID 9932809, Kellgren-Lawrence grade 2) from the Osteoarthritis Initiative dataset at baseline imaging. For comparison, an identical finite element model was built with homogeneous material properties. Kinematics of the stance phase of a standard gait cycle were used as model constraints. Simulation results were compared qualitatively to the MRI Osteoarthritis Knee Score (MOAKS) from the same baseline timepoint. Our T₂-refined material model showed higher maximum shear strain in regions with moderate cartilage loss as compared to the homogeneous material model, and the homogeneous model showed higher maximum principal stress and maximum shear strain in regions with no cartilage loss. These results show that a homogeneous material model likely underestimates tissue strains in regions with cartilage damage while overestimating strains in regions with healthy cartilage. This preliminary study demonstrates that T₂-refined material properties are more appropriate than assumptions of homogeneity in predictive models of cartilage damage.Clinical relevance- The proposed pipeline demonstrates a computationally efficient way to improve the subject-specificity of finite element models used for evaluation of osteoarthritis.

The mechanical influence of bone spicules in the osteochondral junction: A finite element modelling study

While much has been done to study how cartilage responds to mechanical loading, as well as modelling such responses, arguably less has been accomplished around the mechanics of the cartilage-bone junction. Previously, it has been reported that the presence of bony spicules invading the zone of calcified cartilage, preceded the formation of new subchondral bone and the advancing of the cement line (Thambyah and Broom in Osteoarthr Cartil 17:456-463, 2009). In this study, the morphology and frequency of bone spicules in the cartilage-bone interface of osteochondral beams subjected to three-point bending were modelled, and the results are discussed within the context of biomechanical theories on bone formation. It was found that the stress and strain magnitudes, and their distribution were sensitive to the presence and number of spicules. Spicule numbers and shape were shown to affect the strain energy density (SED) distribution in the areas of the cement line adjacent to spicules. Stresses, strains and SED analyses thus provided evidence that the mechanical environment with the addition of spicules promotes bone formation in the cartilage-bone junction.

Electromyography activities in patients with lower lumbar disc herniation

BACKGROUND

Lumbar disc herniation (LDH) can affect lower limb muscle function resulting in an abnormal gait. This study aims to use surface electromyography (SEMG) to evaluate patients with L4/L5 and L5/S1 LDH throughout muscle movement.

METHODS

Twenty L4/L5 LDH patients (L5 Group), twenty L5/S1 LDH patients (S1 Group), and twenty healthy controls (Healthy) were recruited for the study. SEMG of bilateral tibialis anterior (TA) and lateral gastrocnemius (LG) muscles of patients were recorded using the DELSYS Wireless EMG System (TrignoTM Wireless Systems, Delsys Inc., USA). Root-mean-square (RMS), mean power frequency (MPF), and median frequency (MF) were compared between bilateral limbs in each participant.

RESULTS

Reduced MPF and MF was found in TA measurements of the L5 Group and LG measurements of the S1 Group. The MPF and MF of the TA of symptomatic limbs of the L5 Group were reduced when compared to asymptomatic limbs (p= 0.006, p= 0.012, p< 0.05), and there were no significant differences in LG measurements (p> 0.05). The LG MPF and MF of the S1 Group in symptomatic limbs were reduced when compared to asymptomatic limbs (p= 0.006, p= 0.017, p< 0.05), and there were no significant differences in TA measurements (p> 0.05). Although there were no significant differences in RMS between bilateral limbs of the L5 and S1 Groups, we found some changes in RMS curves. First, compared to asymptomatic limbs of L4/L5LDH patients, β-peaks in the TA of symptomatic limbs appeared earlier. Second, two peaks in the LG of symptomatic limbs were found in L5/S1 LDH patients.

CONCLUSION

TA is affected in patients with LDH of L4/L5, and LG is affected in patients with LDH of L5/S1. As demonstrated, SEMG can identify LDH-related muscle dysfunction.

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.

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.

The Effect of Articular Cartilage Focal Defect Size and Location in Whole Knee Biomechanics Models

Articular cartilage focal defects are common soft tissue injuries potentially linked to osteoarthritis (OA) development. Although several defect characteristics likely contribute to osteoarthritis, their relationship to local tissue deformation remains unclear. Using finite element models with various femoral cartilage geometries, we explore how defects change cartilage deformation and joint kinematics assuming loading representative of the maximum joint compression during the stance phase of gait. We show how defects, in combination with location-dependent cartilage mechanics, alter deformation in affected and opposing cartilages, as well as joint kinematics. Small and average sized defects increased maximum compressive strains by approximately 50% and 100%, respectively, compared to healthy cartilage. Shifts in the spatial locations of maximum compressive strains of defect containing models were also observed, resulting in loading of cartilage regions with reduced initial stiffnesses supporting the new, elevated loading environments. Simulated osteoarthritis (modeled as a global reduction in mean cartilage stiffness) did not significantly alter joint kinematics, but exacerbated tissue deformation. Femoral defects were also found to affect healthy tibial cartilage deformations. Lateral femoral defects increased tibial cartilage maximum compressive strains by 25%, while small and average sized medial defects exhibited decreases of 6% and 15%, respectively, compared to healthy cartilage. Femoral defects also affected the spatial distributions of deformation across the articular surfaces. These deviations are especially meaningful in the context of cartilage with location-dependent mechanics, leading to increases in peak contact stresses supported by the cartilage of between 11% and 34% over healthy cartilage.

Finite Element Modelling Simulated Meniscus Translocation and Deformation during Locomotion of the Equine Stifle

Simple Summary

Meniscal tears are one of the most common soft tissue injuries in the equine stifle joint. To date no optimal treatment strategy to heal meniscal tissue is available. Accordingly, there is a need to improve treatment for meniscal injuries and thus to identify appropriate translational animal models. A possible alternative to animal experimentation is the use of finite element modelling (FEMg). FEMg allows simulation of time dependent changes in tissues resulting from biomechanical strains. We developed a finite element model (FEM) of the equine stifle joint to identify pressure peaks and simulate translocation and deformation of the menisci at different joint angles under loading conditions. The FEM model was tested across a range of motion of approximately 30°. Pressure load was higher overall in the lateral meniscus than in the medial meniscus. Accordingly, the simulation showed higher translocation and deformation throughout the whole range of motion in the lateral compared to the medial meniscus. The results encourage further refinement of this FEM model for studying loading patterns on menisci and articular cartilages as well as the resulting mechanical stress in the subchondral bone. A functional FEM model can not only help identify segments in the femoro–tibial joint which are predisposed to injury, but also provide better understanding of the progression of certain stifle disorders, simulate treatment/surgery effects and to optimize implant/transplant properties in order to most closely resemble natural tissue.

Abstract

We developed a finite element model (FEM) of the equine stifle joint to identify pressure peaks and simulate translocation and deformation of the menisci. A series of sectional magnetic resonance images (1.5 T) of the stifle joint of a 23 year old Shetland pony gelding served as basis for image segmentation. Based on the 3D polygon models of femur, tibia, articular cartilages, menisci, collateral ligaments and the meniscotibial ligaments, an FEM model was generated. Tissue material properties were assigned based on data from human (Open knee(s) project) and bovine femoro-tibial joint available in the literature. The FEM model was tested across a range of motion of approximately 30°. Pressure load was overall higher in the lateral meniscus than in the medial. Accordingly, the simulation showed higher translocation and deformation in the lateral compared to the medial meniscus. The results encourage further refinement of this model for studying loading patterns on menisci and articular cartilages as well as the resulting mechanical stress in the subchondral bone (femur and tibia). A functional FEM model can not only help identify segments in the stifle which are predisposed to injury, but also to better understand the progression of certain stifle disorders, simulate treatment/surgery effects and to optimize implant/transplant properties.

Computational evaluation of altered biomechanics related to articular cartilage lesions observed in vivo

Chondral lesions provide a potential risk factor for development of osteoarthritis. Despite the variety of in vitro studies on lesion degeneration, in vivo studies that evaluate relation between lesion characteristics and the risk for the possible progression of OA are lacking. Here, we aimed to characterize different lesions and quantify biomechanical responses experienced by surrounding cartilage tissue. We generated computational knee joint models with nine chondral injuries based on clinical in vivo arthrographic computed tomography images. Finite element models with fibril-reinforced poro(visco)elastic cartilage and menisci were constructed to simulate physiological loading. Systematically, the lesions experienced increased peak values of maximum principal strain, maximum shear strain, and minimum principal strain in the surrounding chondral tissue (p < 0.01) compared with intact tissue. Depth, volume, and area of the lesion correlated with the maximum shear strain (p < 0.05, Spearman rank correlation coefficient ρ = 0.733-0.917). Depth and volume of the lesion correlated also with the maximum principal strain (p < 0.05, ρ = 0.767, and ρ = 0.717, respectively). However, the lesion area had non-significant correlation with this strain parameter (p = 0.06, ρ = 0.65). Potentially, the introduced approach could be developed for clinical evaluation of biomechanical risks of a chondral lesion and planning an intervention. Statement of Clinical Relevance: In this study, we computationally characterized different in vivo chondral lesions and evaluated their risk of cartilage degeneration. This information is vital in decision-making for intervention in order to prevent post-traumatic osteoarthritis. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res.

Comparison between kinetic and kinetic-kinematic driven knee joint finite element models

Use of knee joint finite element models for diagnostic purposes is challenging due to their complexity. Therefore, simpler models are needed for studies where a high number of patients need to be analyzed, without compromising the results of the model. In this study, more complex, kinetic (forces and moments) and simpler, kinetic-kinematic (forces and angles) driven finite element models were compared during the stance phase of gait. Patella and tendons were included in the most complex model, while they were absent in the simplest model. The greatest difference between the most complex and simplest models was observed in the internal-external rotation and axial joint reaction force, while all other rotations, translations and joint reaction forces were similar to one another. In terms of cartilage stresses and strains, the simpler models behaved similarly with the more complex models in the lateral joint compartment, while minor differences were observed in the medial compartment at the beginning of the stance phase. We suggest that it is feasible to use kinetic-kinematic driven knee joint models with a simpler geometry in studies with a large cohort size, particularly when analyzing cartilage responses and failures related to potential overloads.

3D laser scanning in conjunction with surface texturing to evaluate shift and reduction of the tibiofemoral contact area after meniscectomy

Meniscectomy significantly change the kinematics of the knee joint by reducing the contact area between femoral condyles and the tibial plateau, but the shift in the contact area has been poorly described. The aim of our investigation was to measure the shift of the tibiofemoral contact area occurring after meniscectomy. We used laser scans combined to surface texturing for measuring the 3D position and area of the femoral and tibial surfaces involved in the joint. In particular, natural condyles (porcine model) were analysed and the reverse engineering approach was used for the interpretation of the results from compression tests and local force measurements in conjunction with staining techniques. The results suggested that laser scans combined to surface texturing may be considered as a powerful tool to investigate the stained contours of the contact area. Beside the largely documented reduction of contact area and local pressure increase, a shift of the centroid of the contact area toward the intercondylar notch was measured after meniscectomy. As a consequence of the contact area shift and pressure increase, cartilage degeneration close to the intercondylar notch may occur.

Structure-Function relationships of equine menisci

Meniscal pathologies are among the most common injuries of the femorotibial joint in both human and equine patients. Pathological forces and ensuing injuries of the cranial horn of the equine medial meniscus are considered analogous to those observed in the human posterior medial horn. Biomechanical properties of human menisci are site- and depth- specific. However, the influence of equine meniscus topography and composition on its biomechanical properties is yet unknown. A better understanding of equine meniscus composition and biomechanics could advance not only veterinary therapies for meniscus degeneration or injuries, but also further substantiate the horse as suitable translational animal model for (human) meniscus tissue engineering. Therefore, the aim of this study was to investigate the composition and structure of the equine knee meniscus in a site- and age-specific manner and their relationship with potential site-specific biomechanical properties. The meniscus architecture was investigated histologically. Biomechanical testing included evaluation of the shore hardness (SH), stiffness and energy loss of the menisci. The SH was found to be subjected to both age and site-specific changes, with an overall higher SH of the tibial meniscus surface and increase in SH with age. Stiffness and energy loss showed neither site nor age related significant differences. The macroscopic and histologic similarities between equine and human menisci described in this study, support continued research in this field.

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.

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.

The effects of geometric uncertainties on computational modelling of knee biomechanics

The geometry of the articular components of the knee is an important factor in predicting joint mechanics in computational models. There are a number of uncertainties in the definition of the geometry of cartilage and meniscus, and evaluating the effects of these uncertainties is fundamental to understanding the level of reliability of the models. In this study, the sensitivity of knee mechanics to geometric uncertainties was investigated by comparing polynomial-based and image-based knee models and varying the size of meniscus. The results suggested that the geometric uncertainties in cartilage and meniscus resulting from the resolution of MRI and the accuracy of segmentation caused considerable effects on the predicted knee mechanics. Moreover, even if the mathematical geometric descriptors can be very close to the imaged-based articular surfaces, the detailed contact pressure distribution produced by the mathematical geometric descriptors was not the same as that of the image-based model. However, the trends predicted by the models based on mathematical geometric descriptors were similar to those of the imaged-based models.

Structure-function relationships of human meniscus

Biomechanical properties of human meniscus have been shown to be site-specific. However, it is not known which meniscus constituents at different depths and locations contribute to biomechanical properties obtained from indentation testing. Therefore, we investigated the composition and structure of human meniscus in a site- and depth-dependent manner and their relationships with tissue site-specific biomechanical properties. Elastic and poroelastic properties were analyzed from experimental stress-relaxation and sinusoidal indentation measurements with fibril reinforced poroelastic finite element modeling. Proteoglycan (PG) and collagen contents, as well as the collagen orientation angle, were determined as a function of tissue depth using microscopic and spectroscopic methods, and they were compared with biomechanical properties. For all the measurement sites (anterior, middle and posterior) of lateral and medial menisci (n=26), PG content and collagen orientation angle increased as a function of tissue depth while the collagen content had an initial sharp increase followed by a decrease across tissue depth. The highest values (p<0.05) of elastic parameters (equilibrium and instantaneous moduli) and strain-dependent biomechanical parameters (strain-dependent fibril network modulus and permeability) were observed in the anterior horn of the medial meniscus. This location had also higher (p<0.05) PG content in the deep meniscus, higher (p<0.05) collagen content in the entire tissue depth, and lower (p<0.05) collagen orientation angle at the superficial tissue, as compared to many other locations. On the other hand, in certain comparisons (such as anterior vs. middle sites of the medial meniscus) significantly higher (p<0.05) collagen content and lower orientation angle, without any difference in the PG content, were consistent with increased meniscus modulus and/or nonlinear permeability. This study suggests that nonlinear biomechanical properties of meniscus, caused by the collagen network and fluid, may be strongly influenced by tissue osmotic swelling from the deep meniscus caused by the increased PG content, leading to increased collagen fibril tension. These nonlinear biomechanical properties are suggested to be further amplified by higher collagen content at all tissue depths and superficial collagen fibril orientation. However, these structure-function relationships are suggested to be highly site-specific.

Quantitative Evaluation of the Mechanical Risks Caused by Focal Cartilage Defects in the Knee

Focal cartilage lesions can proceed to severe osteoarthritis or remain unaltered even for years. A method to identify high risk defects would be of utmost importance to guide clinical decision making and to identify the patients that are at the highest risk for the onset and progression of osteoarthritis. Based on cone beam computed tomography arthrography, we present a novel computational model for evaluating changes in local mechanical responses around cartilage defects. Our model, based on data obtained from a human knee in vivo, demonstrated that the most substantial alterations around the defect, as compared to the intact tissue, were observed in minimum principal (compressive) strains and shear strains. Both strain values experienced up to 3-fold increase, exceeding levels previously associated with chondrocyte apoptosis and failure of collagen crosslinks. Furthermore, defects at the central regions of medial tibial cartilage with direct cartilage-cartilage contact were the most vulnerable to loading. Also locations under the meniscus experienced substantially increased minimum principal strains. We suggest that during knee joint loading particularly minimum principal and shear strains are increased above tissue failure limits around cartilage defects which might lead to osteoarthritis. However, this increase in strains is highly location-specific on the joint surface.

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.

A Novel Method to Simulate the Progression of Collagen Degeneration of Cartilage in the Knee: Data from the Osteoarthritis Initiative

We present a novel algorithm combined with computational modeling to simulate the development of knee osteoarthritis. The degeneration algorithm was based on excessive and cumulatively accumulated stresses within knee joint cartilage during physiological gait loading. In the algorithm, the collagen network stiffness of cartilage was reduced iteratively if excessive maximum principal stresses were observed. The developed algorithm was tested and validated against experimental baseline and 4-year follow-up Kellgren-Lawrence grades, indicating different levels of cartilage degeneration at the tibiofemoral contact region. Test groups consisted of normal weight and obese subjects with the same gender and similar age and height without osteoarthritic changes. The algorithm accurately simulated cartilage degeneration as compared to the Kellgren-Lawrence findings in the subject group with excess weight, while the healthy subject group’s joint remained intact. Furthermore, the developed algorithm followed the experimentally found trend of cartilage degeneration in the obese group (R² = 0.95, p < 0.05; experiments vs. model), in which the rapid degeneration immediately after initiation of osteoarthritis (0–2 years, p < 0.001) was followed by a slow or negligible degeneration (2–4 years, p > 0.05). The proposed algorithm revealed a great potential to objectively simulate the progression of knee osteoarthritis.

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.

Three dimensional patient-specific collagen architecture modulates cartilage responses in the knee joint during gait

Site-specific variation of collagen fibril orientations can affect cartilage stresses in knee joints. However, this has not been confirmed by 3-D analyses. Therefore, we present a novel method for evaluation of the effect of patient-specific collagen architecture on time-dependent mechanical responses of knee joint cartilage during gait. 3-D finite element (FE) models of a human knee joint were created with the collagen architectures obtained from T2 mapped MRI (patient-specific model) and from literature (literature model). The effect of accuracy of the implementation of collagen fibril architecture into the model was examined by using a submodel with denser FE mesh. Compared to the literature model, fibril strains and maximum principal stresses were reduced especially in the superficial/middle regions of medial tibial cartilage in the patient-specific model after the loading response of gait (up to -413 and -26%, respectively). Compared to the more coarsely meshed joint model, the patient-specific submodel demonstrated similar strain and stress distributions but increased values particularly in the superficial cartilage regions (especially stresses increased >60%). The results demonstrate that implementation of subject-specific collagen architecture of cartilage in 3-D modulates location- and time-dependent mechanical responses of human knee joint cartilage. Submodeling with more accurate implementation of collagen fibril architecture alters cartilage stresses particularly in the superficial/middle tissue.

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

Mechanical signals experienced by chondrocytes (articular cartilage cells) modulate cell synthesis and cartilage health. Multi-scale modeling can be used to study how forces are transferred from joint surfaces through tissues to chondrocytes. Therefore, estimation of chondrocyte behavior during certain physical activities, such as walking, could provide information about how cells respond to normal and abnormal loading in joints. In this study, a 3D multi-scale model was developed for evaluating chondrocyte and surrounding peri- and extracellular matrix responses during gait loading within healthy and medial meniscectomy knee joints. The knee joint geometry was based on MRI, whereas the input used for gait loading was obtained from the literature. Femoral and tibial cartilages were modeled as fibril-reinforced poroviscoelastic materials, whereas menisci were considered as transversely isotropic. Fluid pressures in the chondrocyte and cartilage tissue increased up to 2MPa (an increase of 30%) in the meniscectomy joint compared to the normal, healthy joint. The elevated level of fluid pressure was observed during the entire stance phase of gait. A medial meniscectomy caused substantially larger (up to 60%) changes in maximum principal strains in the chondrocyte compared to those in the peri- or extracellular matrices. Chondrocyte volume or morphology did not change substantially due to a medial meniscectomy. Current findings suggest that during walking chondrocyte deformations are not substantially altered due to a medial meniscectomy, while abnormal joint loading exposes chondrocytes to elevated levels of fluid pressure and maximum principal strains (compared to strains in the peri- or extracellular matrices). These might contribute to cell viability and the onset of osteoarthritis.

A statistically-augmented computational platform for evaluating meniscal function

Meniscal implants have been developed in an attempt to provide pain relief and prevent pathological degeneration of articular cartilage. However, as yet there has been no systematic and comprehensive analysis of the effects of the meniscal design variables on meniscal function across a wide patient population, and there are no clear design criteria to ensure the functional performance of candidate meniscal implants. Our aim was to develop a statistically-augmented, experimentally-validated, computational platform to assess the effect of meniscal properties and patient variables on knee joint contact mechanics during the activity of walking. Our analysis used Finite Element Models (FEMs) that represented the geometry, kinematics as based on simulated gait and contact mechanics of three laboratory tested human cadaveric knees. The FEMs were subsequently programmed to represent prescribed meniscal variables (circumferential and radial/axial moduli-Ecm, Erm, stiffness of the meniscal attachments-Slpma, Slamp) and patient variables (varus/valgus alignment-VVA, and articular cartilage modulus-Ec). The contact mechanics data generated from the FEM runs were used as training data to a statistical interpolator which estimated joint contact data for untested configurations of input variables. Our data suggested that while Ecm and Erm of a meniscus are critical in determining knee joint mechanics in early and late stance (peak 1 and peak 3 of the gait cycle), for some knees that have greater laxity in the mid-stance phase of gait, the stiffness of the articular cartilage, Ec, can influence force distribution across the tibial plateau. We found that the medial meniscus plays a dominant load-carrying role in the early stance phase and less so in late stance, while the lateral meniscus distributes load throughout gait. Joint contact mechanics in the medial compartment are more sensitive to Ecm than those in the lateral compartment. Finally, throughout stance, varus-valgus alignment can overwhelm these relationships while the stiffness of meniscal attachments in the range studied have minimal effects on the knee joint mechanics. In summary, our statistically-augmented, computational platform allowed us to study how meniscal implant design variables (which can be controlled at the time of manufacture or implantation) interact with patient variables (which can be set in FEMs but cannot be controlled in patient studies) to affect joint contact mechanics during the activity of simulated walking.

A viscoelastic poromechanical model of the knee joint in large compression

The elastic response of the knee joint in various loading and pathological conditions has been investigated using anatomically accurate geometry. However, it is still challenging to predict the poromechanical response of the knee in realistic loading conditions. In the present study, a viscoelastic, poromechanical model of the knee joint was developed for soft tissues undergoing large deformation. Cartilages and menisci were modeled as fibril-reinforced porous materials and ligaments were considered as fibril-reinforced hyperelastic solids. Quasi-linear viscoelasticty was formulated for the collagen network of these tissues and nearly incompressible Neo-Hookean hyperelasticity was used for the non-fibrillar matrix. The constitutive model was coded with a user defined FORTRAN subroutine, in order to use ABAQUS for the finite element analysis. Creep and stress relaxation were investigated with large compression of the knee in full extension. The contact pressure distributions were found similar in creep and stress relaxation. However, the load transfer in the joint was completely different in these two loading scenarios. During creep, the contact pressure between cartilages decreased but the pressure between cartilage and meniscus increased with time. This led to a gradual transfer of some loading from the central part of cartilages to menisci. During stress relaxation, however, both contact pressures decreased monotonically.

Development and validation of a computational model of the knee joint for the evaluation of surgical treatments for osteoarthritis

A three-dimensional (3D) knee joint computational model was developed and validated to predict knee joint contact forces and pressures for different degrees of malalignment. A 3D computational knee model was created from high-resolution radiological images to emulate passive sagittal rotation (full-extension to 65°-flexion) and weight acceptance. A cadaveric knee mounted on a six-degree-of-freedom robot was subjected to matching boundary and loading conditions. A ligament-tuning process minimised kinematic differences between the robotically loaded cadaver specimen and the finite element (FE) model. The model was validated by measured intra-articular force and pressure measurements. Percent full scale error between EE-predicted and in vitro-measured values in the medial and lateral compartments were 6.67% and 5.94%, respectively, for normalised peak pressure values, and 7.56% and 4.48%, respectively, for normalised force values. The knee model can accurately predict normalised intra-articular pressure and forces for different loading conditions and could be further developed for subject-specific surgical planning.