The role of computational models in the search for the mechanical behavior and damage mechanisms of articular cartilage

Contributions of cell behavior to geometric order in embryonic cartilage

During early development, cartilage provides shape and stability to the embryo while serving as a precursor for the skeleton. Correct formation of embryonic cartilage is hence essential for healthy development. In vertebrate cranial cartilage, it has been observed that a flat and laterally extended macroscopic geometry is linked to regular microscopic structure consisting of tightly packed, short, transversal clonar columns. However, it remains an ongoing challenge to identify how individual cells coordinate to successfully shape the tissue, and more precisely which mechanical interactions and cell behaviors contribute to the generation and maintenance of this columnar cartilage geometry during embryogenesis. Here, we apply a three-dimensional cell-based computational model to investigate mechanical principles contributing to column formation. The model accounts for clonal expansion, anisotropic proliferation and the geometrical arrangement of progenitor cells in space. We confirm that oriented cell divisions and repulsive mechanical interactions between cells are key drivers of column formation. In addition, the model suggests that column formation benefits from the spatial gaps created by the extracellular matrix in the initial configuration, and that column maintenance is facilitated by sequential proliferative phases. Our model thus correctly predicts the dependence of local order on division orientation and tissue thickness. The present study presents the first cell-based simulations of cell mechanics during cranial cartilage formation and we anticipate that it will be useful in future studies on the formation and growth of other cartilage geometries.

Cartilage biomechanics: From the basic facts to the challenges of tissue engineering

Articular cartilage (AC) is the thin tissue that covers the long bone ends in the joints and that ensures the transmission of forces between adjacent bones while allowing nearly frictionless movements between them. AC repair is a technologic and scientific challenge that has been addressed with numerous approaches. A major deadlock is the capacity to take in account its complex mechanical properties in repair strategies. In this review, we first describe the major mechanical behaviors of AC for the non-specialists. Then, we show how researchers have progressively identified specific mechanical parameters using mathematical models. There are still gaps in our understanding of some of the observations concerning AC biomechanical properties, particularly the differences in extracellular matrix stiffness measured at the microscale and at the millimetric scale. Nevertheless, for bioengineering applications, AC repair strategies must take into account what are commonly considered the main mechanical features of cartilage: its ability to withstand high stresses through three main behaviors (elasticity, poroelasticity and swelling). Finally, we emphasize that future studies need to investigate AC mechanical properties at different scales, particularly the gradient of mechanical properties around cells and across the cartilage depth, and the differences in mechanical properties at different scales. This multi-scale approach could greatly enhance the success of AC restorative approaches.

A developed multibody knee model for unloading knee with cartilage penetration depth control

Unloader knee braces could relieve pain by decreasing the medial knee loading. Particularly for knee osteoarthritis (KOA) patients, this study investigates the relevance of the knee model after identifying the most influential parameter. Since KOA causes the cartilage in a joint to lose its elasticity and thickness, the lack of normal bone-to-bone separation can be painful. We believe that cartilage penetration depth control is an impactful strategy in this research. Moreover, the knee contact force in KOA is fewer than in healthy knees, confirming that the contact force control cannot be a straight factor. Therefore, a biomechanical human knee model is developed, and a generic procedure for dynamic analysis of contact problems in combination with the musculoskeletal model is introduced. The developed model includes the geometric expression of collision curves and an algorithm for determining collision points. This presentation addresses cartilage penetration depth and contact force calculation through nonlinear discontinuous contact law. In view of this, femur and tibia’s relative motion is analyzed through the combined collision reactions of cartilage and bone in the knee. In the simulation, maximum penetration depth in a healthy knee is reported to be 0.795 mm, while in a 75% KOA is 0.521 mm, including 0.5 mm cartilage-cartilage contact and 0.021 mm bone-bone contact. The top unloading 852 N is achieved, reducing penetration depth to 0.45 mm, avoiding bone-bone contact. This proposed procedure with low computation gives us a suitable analysis method for designing knee assistive devices.

Multiscale modelling for investigating the long-term time-dependent biphasic behaviour of the articular cartilage in the natural hip joint

A better understanding of the time-dependent biomechanical behaviour of the biphasic hip articular cartilage (AC) under physiological loadings is important to understand the onset of joint pathology and guide the clinical treatment. Current computational studies for the biphasic hip AC were usually limited to short-term duration or using elaborate loading. The present study aimed to develop a multiscale computational modelling to investigate the long-term biphasic behaviour of the hip AC under physiological loadings over multiple gait cycles. Two-scale computational modelling including a musculoskeletal model and a finite element model of the natural hip was created. These two models were then combined and used to investigate the biphasic behaviour of hip AC over 80 gait cycles. The results showed that the interstitial fluid pressure in the AC supported over 89% of the loading during gait. When the contact area was located at the AC centre, the contact pressure and fluid pressure increased over time from the first cycle to the 80th cycle, while when the contact area approached the edge, these pressures decreased first dramatically and then slowly over time. The peak stresses and strains in the solid matrix of the AC remained at a low level and increased over time from the first cycle to the 80th cycle. This study demonstrated that the long-term temporal variations of the biphasic behaviour of hip AC under physiological loadings are significant. The methodology has potentially important implications in the biomechanical studies of human cartilage and supporting the development of cartilage substitution.

Finite Element Modelling of Planus and Rectus Foot Types for the Study of First Metatarsophalangeal and First Metatarsocuneiform Joint Contact Mechanics

Evaluating the contact mechanics of human joints is an important element in understanding the pathomechanics of orthopaedic diseases. Although physical testing is essential in the evaluation process, reliable computational models can augment these experiments by non-invasive predictions of biomechanical or surgical variables. The objective of this study was to perform verification of a framework for developing a medial forefoot finite element. Verification was conducted by comparing computational predictions to experimental measurements of first metatarsophalangeal and first metatarsocuneiform joint contact mechanics. A custom-built force-controlled cadaveric test-rig was used to derive measurements of contact pressure, force, and area. A quasi-static finite element was developed and driven under the same boundary and loading conditions. Calibration of cartilage moduli and mesh sensitivity analyses were performed. Mean errors in contact pressures, forces, and areas were 24%, 4%, and 40% at the first metatarsophalangeal joint and 23%, 12%, and 19% at the first Metatarsocuneiform joint, respectively. Verification of a medial forefoot finite element model development framework was presented and found to be within 30% for contact pressure and contact force of both joints. This study presents a method to verify and simulate realistic physiological loading to investigate orthopaedic diseases of the medial forefoot.

The importance of Böhler's angle in calcaneus geometry: A finite element model study

OBJECTIVES

Calcaneal fractures are the most common tarsal fractures following a foot-ankle trauma. The Böhler's angle is an important measurable angle before, during, and after surgery. In this study, we aimed to investigate correlation between Böhler's angle, calcaneal strength, and subtalar joint stress using a finite element analysis (FEA).

PATIENTS AND METHODS

Between January 2016 and December 2016, computed tomography (CT) scans were used with MIMICS® software for FEA. The ankle and foot of a 23-year-old male person with a height of 180 cm and weighing 80 kg was modeled as reference. Raw coronal CT images were obtained in Digital Imaging and Communications in Medicine format with the resolution of 512X512 pixels and 0.3-mm slice intervals in 135 kV. The structures including tibia, fibula and 26 other bones (talus, calcaneus, cuboid, navicular, three cuneiforms, five metatarsals, and 14 components of phalanges), cartilage and ligamentous tissues were modeled to form ankle joint. After determining Böhler's angle as 35 degrees for the reference model, a fracture line was created on calcaneus. Calcaneus was remodeled with the Böhler's angle of 45, 40, 30, 25, 20, 10, and 0 degrees respectively. All models were transferred to ANSYS software for FEA and the loads on the lower extremities with normal posture were applied on models.

RESULTS

Analysis of all models based in the reference model revealed that maximum tension values on calcaneus increased, while the Böhler's angle decreased, indicating a statistically significant difference. The decreased Böhler's angle indicated statistically significantly higher maximum tension values (p=0.04). Action force in subtalar joint was evaluated by comparing with the forces in reference model. The increased Böhler's angle was found to be associated with statistically significantly decreased amount of load on subtalar joint. The decreased Böhler's angle was related to the statistically significantly increased amount of load on subtalar joint.

CONCLUSION

Our study results suggest that decreased Böhler's angle increases the possibility of subtalar arthrosis, although overcorrection of the Böhler's angle seems not to increase the risk of subtalar arthrosis.

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

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

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.

Changes in viscoelastic properties of articular cartilage in early stage of osteoarthritis, as determined by optical coherence tomography-based strain rate tomography

BACKGROUND

Biomechanical changes in articular cartilage are associated with the onset of osteoarthritis. We developed an optical coherence tomography-based strain rate tomography method: stress relaxation optical coherence straingraphy (SR-OCSA). The purpose of this study was to establish an approach for measuring mechanical properties of articular cartilage using SR-OCSA, and to investigate the distribution of viscoelastic properties of articular cartilage in early osteoarthritis.

METHODS

Anterior cruciate ligament transection surgery was performed on the left knees of 8-9-month-old New Zealand white rabbits. SR-OCSA was used to visualize and measure the viscoelastic properties of articular cartilage via attenuation coefficient of strain rate (ACSR). Using the same conditions as in the SR-OCSA test, an indentation test was conducted, and relaxation time was measured to evaluate the relationship between ACSR and relaxation time.

RESULTS

SR-OCSA could nondestructively detect and visualize changes in the distribution of viscoelastic properties of articular cartilage in early osteoarthritis. SR-OCSA captured significant increases in ACSR in cartilage at 2 weeks after surgery, when a histologically slight osteoarthritis sign was present. As cartilage degeneration progressed, ACSR increased, whereas relaxation time decreased in a time-dependent manner. Moreover, ACSR negatively correlated with relaxation time. In particular, ACSR was elevated around the tidemark and the elevation tended to move as cartilage degeneration progressed.

CONCLUSIONS

SR-OCSA could tomographically and nondestructively detect and visualize changes in the distribution of viscoelastic properties of articular cartilage in early osteoarthritis. The mechanical properties around the tidemark were degraded as cartilage degeneration progressed. Thus, SR-OCSA provides important data needed to understand the biomechanics of early osteoarthritis.

Numerical Study on Electromechanics in Cartilage Tissue with Respect to Its Electrical Properties

Hyaline cartilage undergoes many substantial age-related physiochemical and biomechanical changes that reduce its ability to overcome the effects of mechanical stress and injury. In quest of therapeutic options, magnetic stimulation and electrical stimulation (ES) have been proposed for improving tissue engineering approaches for the repair of articular cartilage. The aim of this study is to summarize in silico investigations involving induced electrical properties of cartilage tissue due to various biophysical stimuli along their respective mathematical descriptions. Based on these, a preliminary numerical study involving electromechanical transduction in bovine cartilage tissue has been carried out using an open source finite element computational software. The simulation results have been compared to experimental results from the literature. This study serves as a basis for further in silico studies to better understand the behavior of hyaline cartilage tissue due to ES and to find an optimal stimulation protocol for the cartilage regeneration. Moreover, it provides an overview of the basic models along with mathematical description and scope for future research regarding electrical behavior of the cartilage tissue using open source software.

Imaging of nuclear magnetic resonance spin-lattice relaxation activation energy in cartilage

Samples of human and bovine cartilage have been examined using magnetic resonance imaging to determine the proton nuclear magnetic resonance spin-lattice relaxation time, T₁, as a function of depth within through the cartilage tissue. T₁ was measured at five to seven temperatures between 8 and 38°C. From this, it is shown that the T₁ relaxation time is well described by Arrhenius-type behaviour and the activation energy of the relaxation process is quantified. The activation energy within the cartilage is approximately 11 ± 2 kJ mol^-1 with this notably being less than that for both pure water (16.6 ± 0.4 kJ mol^-1) and the phosphate-buffered solution in which the cartilage was immersed (14.7 ± 1.0 kJ mol^-1). It is shown that this activation energy increases as a function of depth in the cartilage. It is known that cartilage composition varies with depth, and hence, these results have been interpreted in terms of the structure within the cartilage tissue and the association of the water with the macromolecular constituents of the cartilage.

Comparison of Compressive Stress-Relaxation Behavior in Osteoarthritic (ICRS Graded) Human Articular Cartilage

Osteoarthritis (OA) is a common joint disorder found mostly in elderly people. The role of mechanical behavior in the progression of OA is complex and remains unclear. The stress-relaxation behavior of human articular cartilage in clinically defined osteoarthritic stages may have importance in diagnosis and prognosis of OA. In this study we investigated differences in the biomechanical responses among human cartilage of ICRS grades I, II and III using polymer dynamics theory. We collected 24 explants of human articular cartilage (eight each of ICRS grade I, II and III) and acquired stress-relaxation data applying a continuous load on the articular surface of each cartilage explant for 1180 s. We observed a significant decrease in Young’s modulus, stress-relaxation time, and stretching exponent in advanced stages of OA (ICRS grade III). The stretch exponential model speculated that significant loss in hyaluronic acid polymer might be the reason for the loss of proteoglycan in advanced OA. This work encourages further biomechanical modelling of osteoarthritic cartilage utilizing these data as input parameters to enhance the fidelity of computational models aimed at revealing how mechanical behaviors play a role in pathogenesis of OA.

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

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

A DAMAGE MECHANISM OF MICRO-PARTICLES ON ARTICULAR CARTILAGE OF KNEE BY NANOINDENTATION

Articular cartilage plays an important role in organism due to its excellent shock absorbing and buffering functions. Increasing problems about damages of articular cartilage are making a great deal of trouble to human beings. The damage mechanism of articular cartilage is very complicated and keeps unclear. In this research, the damage mechanism was investigated from the perspective of micro-particle attrition by nanoindentation experiments. The micro-particle was simulated by the indenter in experiments. The experimental results demonstrated that the load from micro-particle could not maintain when water content was adequate. However, the load could maintain and increase after dehydration. It was found that the partial surface of articular cartilage was crushed and adhered to the indenter. The plastic energy was bigger than elastic energy in the nanoindentation process. Therefore, water content was the crucial factor to protect the articular cartilage from damage. And the recurring partial dehydration owing to ongoing compression enhanced the damage of micro-particle to articular cartilage. This research may provide a new understanding to the damage mechanism of articular cartilage.

Real-time observation of fluid flows in tissue during stress relaxation using Raman spectroscopy

This paper outlines a technique to measure fluid levels in articular cartilage tissue during an unconfined stress relaxation test. A time series of Raman spectrum were recorded during relaxation and the changes in the specific Raman spectral bands assigned to water and protein were monitored to determine the fluid content of the tissue. After 1000s unconfined compression the fluid content of the tissue is reduced by an average of 3.9%±1.7%. The reduction in fluid content during compression varies between samples but does not significantly increase with increasing strain. Further development of this technique will allow mapping of fluid distribution and flows during dynamic testing making it a powerful tool to understand the role of interstitial fluid in the functional performance of cartilage.

A Three-Dimensional Finite Element Analysis of Displaced Intra-Articular Calcaneal Fractures

A better understanding of displaced intra-articular calcaneal fractures, their effect on joint mechanics, and the relationship between altered mechanics and osteoarthritis could aid in the development or refinement of treatment methods. Finite element modeling is accepted as the reference standard for evaluating joint contact stresses. The objective of the present study was to analyze the in vivo joint mechanical data from finite element modeling for normal and injured subtalar joints. A 3-dimensional model of the ankle-hindfoot was developed and validated. Both height loss and width increases in the calcaneus were simulated. Next, they were used to investigate the relationship between calcaneal height or width and the contact mechanics of the posterior facet of the subtalar joint. The contact area/joint area ratio increased in the subtalar joint with injury when the calcaneal width increased. Moreover, the peak contact pressure and the proportion of the area under high contact pressure (>6 MPa) increased. The contact area/joint area ratio decreased with reduced calcaneal height, but the peak contact pressure remained almost constant. The width increases of the calcaneus somewhat limited the subtalar joint motion, especially for eversion; however, the height loss mostly resulted in subtalar rotatory instability. The height loss diminished the subtalar joint's stability in eversion, internal rotation, and external rotation. The results of the present study support the advisability of surgery for these complex injuries. Reestablishing the calcaneal height and width could restore the normal kinematics and contact stress distribution in the subtalar joint, improve the tibiotalar position, and diminish long-term degeneration in the ankle.

ANALYSIS OF THE MECHANICAL STATE OF THE HUMAN KNEE JOINT WITH DEFECT CARTILAGE IN STANDING

Knee joint is the hub of human lower limb movement and it is also an important weight-bearing joint, which has the characteristics of load-bearing and heavy physical activities. So the knee joint becomes the predilection site of clinical disease. Once people have the cartilage lesions, their daily life will be affected seriously. The simulation of the knee joint lesions could provide help for clinical knee-joint treatment. Based on the complete model of knee joint, this paper use the finite element method to analyze the biomechanical characteristics of the defective knee joint. The results of simulation show that the stress of cartilages when standing on single leg is approximately doubled than that of standing on two legs. When standing on single leg, the 8-mm diameter osteochondral defect in femur cartilage can generate maximal changes in von-mises stress (by 36.74%), while the von-mises stress on tibia cartilage with 8-mm defect increase by 87%. The stress distribution of cartilages is almost the same, there is no obvious stress concentration when in defect. Increasing the defective diameter, femoral cartilage, meniscus and tibial all present an increasing trend towards stress. When increasing the applied load, the stress of the femoral cartilage, the meniscus and the tibial cartilage all increased.

Hyaluronan-Derived Swelling of Solid Tumors, the Contribution of Collagen and Cancer Cells, and Implications for Cancer Therapy

Despite the important role that mechanical forces play in tumor growth and therapy, the contribution of swelling to tumor mechanopathology remains unexplored. Tumors rich in hyaluronan exhibit a highly negative fixed charge density. Repulsive forces among these negative charges as well as swelling of cancer cells due to regulation of intracellular tonicity can cause tumor swelling and development of stress that might compress blood vessels, compromising tumor perfusion and drug delivery. Here, we designed an experimental strategy, using four orthotopic tumor models, to measure swelling stress and related swelling to extracellular matrix components, hyaluronan and collagen, as well as to tumor perfusion. Subsequently, interventions were performed to measure tumor swelling using matrix-modifying enzymes (hyaluronidase and collagenase) and by repurposing pirfenidone, an approved antifibrotic drug. Finally, in vitro experiments on cancer cell spheroids were performed to identify their contribution to tissue swelling. Swelling stress was measured in the range of 16 to 75 mm Hg, high enough to cause vessel collapse. Interestingly, while depletion of hyaluronan decreased swelling, collagen depletion had the opposite effect, whereas the contribution of cancer cells was negligible. Furthermore, histological analysis revealed the same linear correlation between tumor swelling and the ratio of hyaluronan to collagen content when data from all tumor models were combined. Our data further revealed an inverse relation between tumor perfusion and swelling, suggesting that reduction of swelling decompresses tumor vessels. These results provide guidelines for emerging therapeutic strategies that target the tumor microenvironment to alleviate intratumoral stresses and improve vessel functionality and drug delivery.

Articular Contact Mechanics from an Asymptotic Modeling Perspective: A Review

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

Price A, A. Hulley P, S. Gill H, Doblaré M, Hamdy Doweidar M. Inhomogeneous Response of Articular Cartilage: A Three-Dimensional Multiphasic Heterogeneous Study

Articular cartilage exhibits complex mechano-electrochemical behaviour due to its anisotropy, inhomogeneity and material non-linearity. In this work, the thickness and radial dependence of cartilage properties are incorporated into a 3D mechano-electrochemical model to explore the relevance of heterogeneity in the behaviour of the tissue. The model considers four essential phenomena: (i) osmotic pressure, (ii) convective and diffusive processes, (iii) chemical expansion and (iv) three-dimensional through-the-thickness heterogeneity of the tissue. The need to consider heterogeneity in computational simulations of cartilage behaviour and in manufacturing biomaterials mimicking this tissue is discussed. To this end, healthy tibial plateaus from pigs were mechanically and biochemically tested in-vitro. Heterogeneous properties were included in the mechano-electrochemical computational model to simulate tissue swelling. The simulation results demonstrated that swelling of the heterogeneous samples was significantly lower than swelling under homogeneous and isotropic conditions. Furthermore, there was a significant reduction in the flux of water and ions in the former samples. In conclusion, the computational model presented here can be considered as a valuable tool for predicting how the variation of cartilage properties affects its behaviour, opening up possibilities for exploring the requirements of cartilage-mimicking biomaterials for tissue engineering. Besides, the model also allows the establishment of behavioural patterns of swelling and of water and ion fluxes in articular cartilage.

Finite element modeling of finite deformable, biphasic biological tissues with transversely isotropic statistically distributed fibers: toward a practical solution

The distribution of collagen fibers across articular cartilage layers is statistical in nature. Based on the concepts proposed in previous models, we developed a methodology to include the statistically distributed fibers across the cartilage thickness in the commercial FE software COMSOL which avoids extensive routine programming. The model includes many properties that are observed in real cartilage: finite hyperelastic deformation, depth-dependent collagen fiber concentration, depth- and deformation-dependent permeability, and statistically distributed collagen fiber orientation distribution across the cartilage thickness. Numerical tests were performed using confined and unconfined compressions. The model predictions on the depth-dependent strain distributions across the cartilage layer are consistent with the experimental data in the literature.

A nuclear magnetic resonance study of water in aggrecan solutions

Aggrecan, a highly charged macromolecule found in articular cartilage, was investigated in aqueous salt solutions with proton nuclear magnetic resonance. The longitudinal and transverse relaxation rates were determined at two different field strengths, 9.4 T and 0.5 T, for a range of temperatures and aggrecan concentrations. The diffusion coefficients of the water molecules were also measured as a function of temperature and aggrecan concentration, using a pulsed field gradient technique at 9.4 T. Assuming an Arrhenius relationship, the activation energies for the various relaxation processes and the translational motion of the water molecules were determined from temperature dependencies as a function of aggrecan concentration in the range 0-5.3% w/w. The longitudinal relaxation rate and inverse diffusion coefficient were approximately equally dependent on concentration and only increased by upto 20% from that of the salt solution. The transverse relaxation rate at high field demonstrated greatest concentration dependence, changing by an order of magnitude across the concentration range examined. We attribute this primarily to chemical exchange. Activation energies appeared to be approximately independent of aggrecan concentration, except for that of the low-field transverse relaxation rate, which decreased with concentration.

Parameter-dependent behavior of articular cartilage: 3D mechano-electrochemical computational model

BACKGROUND AND OBJECTIVE

Changes in mechano-electrochemical properties of articular cartilage play an essential role in the majority of cartilage diseases. Despite of this importance, the specific effect of each parameter into tissue behavior remains still obscure. Parametric computational modeling of cartilage can provide some insights into this matter, specifically the study of mechano-electrochemical properties variation and their correlation with tissue swelling, water and ion fluxes. Thus, the aim of this study is to evaluate the influence of the main mechanical and electrochemical parameters on the determination of articular cartilage behavior by a parametric analysis through a 3D finite element model.

METHODS

For this purpose, a previous 3D mechano-electrochemical model, developed by the same authors, of articular cartilage behavior has been used. Young's modulus, Poisson coefficient, ion diffusivities and ion activity coefficients variations have been analyzed and quantified through monitoring tissue simulated response.

RESULTS

Simulation results show how Young's modulus and Poisson coefficient control tissue behavior rather than electrochemical properties. Meanwhile, ion diffusivity and ion activity coefficients appear to be vital in controlling velocity of incoming and outgoing fluxes.

CONCLUSIONS

This parametric study establishes a basic guide when defining the main properties that are essential to be included into computational modeling of articular cartilage providing a helpful tool in tissue simulations.

Extremity cone-beam CT for evaluation of medial tibiofemoral osteoarthritis: Initial experience in imaging of the weight-bearing and non-weight-bearing knee

PURPOSE

To investigate differences in joint space width (JSW) and meniscal extrusion (ME) between non-weight bearing (NWB) and weight bearing (WB) examinations of knee joints with medial compartment osteoarthritis (OA) using a cone-beam CT (CBCT) extremity imaging system.

MATERIALS AND METHODS

In this IRB approved prospective study, informed consent was obtained for 17 patients symptomatic for OA (11 F,6 M; 31-78 years, mean 56 years) and 18 asymptomatic controls (0 F,18 M; 29-48 years, mean 38.5 years) enrolled for CBCT exams in NWB and WB positions. Three independent observers measured medial tibiofemoral JSW and ME. Measurements were compared between NWB and WB images using paired Wilcoxon signed-rank sum test.

RESULTS

OA subjects exhibited a statistically significant reduction in JSW between NWB and WB scans (average JSW(NWB)(OA)=2.1 mm and JSW(WB)(OA)=1.5 mm, p=0.016) and increase in ME (average ME(NWB)(OA)=6.9 mm and ME(WB)(OA)=8.2 mm, p=0.018)). For non-OA subjects, the change in JSW and ME between NWB and WB exams was reduced (average JSW(NWB)(nonOA)=3.7 mm and JSW(WB)(nonOA)=3.4 mm; average ME(NWB)(nonOA)=2.6 mm and ME(WB)(nonOA)=2.7 mm) and was not statistically significant. Inter-observer agreement was evaluated using Bland-Altman limits of agreement, with good agreement for all measurements (correlation coefficient 0.89-0.98).

CONCLUSION

The ability to conduct NWB and WB exams in CBCT with a dose profile that is favorable in comparison to multidetector CT (MDCT) and with image quality sufficient for morphological analysis of joint space narrowing and meniscal extrusion could provide a valuable tool for OA diagnosis and treatment assessment.

Physical, Spatial, and Molecular Aspects of Extracellular Matrix of In Vivo Niches and Artificial Scaffolds Relevant to Stem Cells Research

Extracellular matrix can influence stem cell choices, such as self-renewal, quiescence, migration, proliferation, phenotype maintenance, differentiation, or apoptosis. Three aspects of extracellular matrix were extensively studied during the last decade: physical properties, spatial presentation of adhesive epitopes, and molecular complexity. Over 15 different parameters have been shown to influence stem cell choices. Physical aspects include stiffness (or elasticity), viscoelasticity, pore size, porosity, amplitude and frequency of static and dynamic deformations applied to the matrix. Spatial aspects include scaffold dimensionality (2D or 3D) and thickness; cell polarity; area, shape, and microscale topography of cell adhesion surface; epitope concentration, epitope clustering characteristics (number of epitopes per cluster, spacing between epitopes within cluster, spacing between separate clusters, cluster patterns, and level of disorder in epitope arrangement), and nanotopography. Biochemical characteristics of natural extracellular matrix molecules regard diversity and structural complexity of matrix molecules, affinity and specificity of epitope interaction with cell receptors, role of non-affinity domains, complexity of supramolecular organization, and co-signaling by growth factors or matrix epitopes. Synergy between several matrix aspects enables stem cells to retain their function in vivo and may be a key to generation of long-term, robust, and effective in vitro stem cell culture systems.

An Equilibrium Constitutive Model of Anisotropic Cartilage Damage to Elucidate Mechanisms of Damage Initiation and Progression

Traumatic injuries and gradual wear-and-tear of articular cartilage (AC) that can lead to osteoarthritis (OA) have been hypothesized to result from tissue damage to AC. In this study, a previous equilibrium constitutive model of AC was extended to a constitutive damage articular cartilage (CDAC) model. In particular, anisotropic collagen (COL) fibril damage and isotropic glycosaminoglycan (GAG) damage were considered in a 3D formulation. In the CDAC model, time-dependent effects, such as viscoelasticity and poroelasticity, were neglected, and thus all results represent the equilibrium response after all time-dependent effects have dissipated. The resulting CDAC model was implemented in two different finite-element models. The first simulated uniaxial tensile loading to failure, while the second simulated spherical indentation with a rigid indenter displaced into a bilayer AC sample. Uniaxial tension to failure simulations were performed for three COL fibril Lagrangian failure strain (i.e., the maximum elastic COL fibril strain) values of 15%, 30%, and 45%, while spherical indentation simulations were performed with a COL fibril Lagrangian failure strain of 15%. GAG damage parameters were held constant for all simulations. Our results indicated that the equilibrium postyield tensile response of AC and the macroscopic tissue failure strain are highly dependent on COL fibril Lagrangian failure strain. The uniaxial tensile response consisted of an initial nonlinear ramp region due to the recruitment of intact fibrils followed by a rapid decrease in tissue stress at initial COL fibril failure, as a result of COL fibril damage which continued until ultimate tissue failure. In the spherical indentation simulation, damage to both the COL fibril and GAG constituents was located only in the superficial zone (SZ) and near the articular surface with tissue thickening following unloading. Spherical indentation simulation results are in agreement with published experimental observations. Our results indicate that the proposed CDAC model is capable of simulating both initial small magnitude damage as well as complete failure of AC tissue. The results of this study may help to elucidate the mechanisms of AC tissue damage, which initiate and propagate OA.

Altered swelling and ion fluxes in articular cartilage as a biomarker in osteoarthritis and joint immobilization: a computational analysis

In healthy cartilage, mechano-electrochemical phenomena act together to maintain tissue homeostasis. Osteoarthritis (OA) and degenerative diseases disrupt this biological equilibrium by causing structural deterioration and subsequent dysfunction of the tissue. Swelling and ion flux alteration as well as abnormal ion distribution are proposed as primary indicators of tissue degradation. In this paper, we present an extension of a previous three-dimensional computational model of the cartilage behaviour developed by the authors to simulate the contribution of the main tissue components in its behaviour. The model considers the mechano-electrochemical events as concurrent phenomena in a three-dimensional environment. This model has been extended here to include the effect of repulsion of negative charges attached to proteoglycans. Moreover, we have studied the fluctuation of these charges owning to proteoglycan variations in healthy and pathological articular cartilage. In this sense, standard patterns of healthy and degraded tissue behaviour can be obtained which could be a helpful diagnostic tool. By introducing measured properties of unhealthy cartilage into the computational model, the severity of tissue degeneration can be predicted avoiding complex tissue extraction and subsequent in vitro analysis. In this work, the model has been applied to monitor and analyse cartilage behaviour at different stages of OA and in both short (four, six and eight weeks) and long-term (11 weeks) fully immobilized joints. Simulation results showed marked differences in the corresponding swelling phenomena, in outgoing cation fluxes and in cation distributions. Furthermore, long-term immobilized patients display similar swelling as well as fluxes and distribution of cations to patients in the early stages of OA, thus, preventive treatments are highly recommended to avoid tissue deterioration.

Measuring microscale strain fields in articular cartilage during rapid impact reveals thresholds for chondrocyte death and a protective role for the superficial layer

Articular cartilage is a heterogeneous soft tissue that dissipates and distributes loads in mammalian joints. Though robust, cartilage is susceptible to damage from loading at high rates or magnitudes. Such injurious loads have been implicated in degenerative changes, including chronic osteoarthritis (OA), which remains a leading cause of disability in developed nations. Despite decades of research, mechanisms of OA initiation after trauma remain poorly understood. Indeed, although bulk cartilage mechanics are measurable during impact, current techniques cannot access microscale mechanics at those rapid time scales. We aimed to address this knowledge gap by imaging the microscale mechanics and corresponding acute biological changes of cartilage in response to rapid loading. In this study, we utilized fast-camera and confocal microscopy to achieve roughly 85 µm spatial resolution of both the cartilage deformation during a rapid (~3 ms), localized impact and the chondrocyte death following impact. Our results showed that, at these high rates, strain and chondrocyte death were highly correlated (p<0.001) with a threshold of 8% microscale strain norm before any cell death occurred. Additionally, chondrocyte death had developed by two hours after impact, suggesting a time frame for clinical therapeutics. Moreover, when the superficial layer was removed, strain - and subsequently chondrocyte death - penetrated deeper into the samples (p<0.001), suggesting a protective role for the superficial layer of articular cartilage. Combined, these results provide insight regarding the detailed biomechanics that drive early chondrocyte damage after trauma and emphasize the importance of understanding cartilage and its mechanics on the microscale.

Multiscale cartilage biomechanics: technical challenges in realizing a high-throughput modelling and simulation workflow

Understanding the mechanical environment of articular cartilage and chondrocytes is of the utmost importance in evaluating tissue damage which is often related to failure of the fibre architecture and mechanical injury to the cells. This knowledge also has significant implications for understanding the mechanobiological response in healthy and diseased cartilage and can drive the development of intervention strategies, ranging from the design of tissue-engineered constructs to the establishment of rehabilitation protocols. Spanning multiple spatial scales, a wide range of biomechanical factors dictate this mechanical environment. Computational modelling and simulation provide descriptive and predictive tools to identify multiscale interactions, and can lead towards a greater comprehension of healthy and diseased cartilage function, possibly in an individualized manner. Cartilage and chondrocyte mechanics can be examined in silico, through post-processing or feed-forward approaches. First, joint-tissue level simulations, typically using the finite-element method, solve boundary value problems representing the joint articulation and underlying tissue, which can differentiate the role of compartmental joint loading in cartilage contact mechanics and macroscale cartilage field mechanics. Subsequently, tissue-cell scale simulations, driven by the macroscale cartilage mechanical field information, can predict chondrocyte deformation metrics along with the mechanics of the surrounding pericellular and extracellular matrices. A high-throughput modelling and simulation framework is necessary to develop models representative of regional and population-wide variations in cartilage and chondrocyte anatomy and mechanical properties, and to conduct large-scale analysis accommodating a multitude of loading scenarios. However, realization of such a framework is a daunting task, with technical difficulties hindering the processes of model development, scale coupling, simulation and interpretation of the results. This study aims to summarize various strategies to address the technical challenges of post-processing-based simulations of cartilage and chondrocyte mechanics with the ultimate goal of establishing the foundations of a high-throughput multiscale analysis framework. At the joint-tissue scale, rapid development of regional models of articular contact is possible by automating the process of generating parametric representations of cartilage boundaries and depth-dependent zonal delineation with associated constitutive relationships. At the tissue-cell scale, models descriptive of multicellular and fibrillar architecture of cartilage zones can also be generated in an automated fashion. Through post-processing, scripts can extract biphasic mechanical metrics at a desired point in the cartilage to assign loading and boundary conditions to models at the lower spatial scale of cells. Cell deformation metrics can be extracted from simulation results to provide a simplified description of individual chondrocyte responses. Simulations at the tissue-cell scale can be parallelized owing to the loosely coupled nature of the feed-forward approach. Verification studies illustrated the necessity of a second-order data passing scheme between scales and evaluated the role that the microscale representative volume size plays in appropriately predicting the mechanical response of the chondrocytes. The tools summarized in this study collectively provide a framework for high-throughput exploration of cartilage biomechanics, which includes minimally supervised model generation, and prediction of multiscale biomechanical metrics across a range of spatial scales, from joint regions and cartilage zones, down to that of the chondrocytes.

A depth dependent transversely isotropic micromechanic model of articular cartilage

Articular cartilage owing to the variation of collagen fibers orientation through its zones has been indicated to have depth dependent mechanical properties. The aim of this study was to present an innovative micromechanics model to predict the depth dependent mechanical properties of articular cartilage as a function of collagen fibers and proteoglycan matrix mechanical properties, collagen fibers volume fraction as well as angle toward cartilage surface. The variation of collagen fibers angle toward the cartilage surface as a function of cartilage depth was computed using the micromechanics model. This function showed that the collagen fibers parallel to the cartilage surface in the superficial zone have a nonlinear angle variation in the transition zone and become perpendicular to cartilage surface in the deep zone. Depth dependent elastic modulus in perpendicular to cartilage surface plane direction was calculated using presented micromechanics model and variation function of the collagen fibers' angle. The results revealed a suitable agreement with that of the experimental measurements in different samples at different ages and races (R2=0.944). The results also showed that the elastic and aggregate modules perpendicular to the cartilage surface plane in the deep zone were 25.8 and 26.3 times higher than that of the superficial zone, respectively. These findings have implications not only for computing the depth dependent mechanical properties of any type of articular cartilage at different ages and races, but also of potential ability for developing a depth dependent transversely isotropic biphasic model to predict the accurate mechanical behavior of articular cartilage.

Modeling and simulation of the effects of cyclic loading on articular cartilage lesion formation

We present a model of articular cartilage lesion formation to simulate the effects of cyclic loading. This model extends and modifies the reaction-diffusion-delay model by Graham et al., 2012 for the spread of a lesion formed though a single traumatic event. Our model represents 'implicitly' the effects of loading, meaning through a cyclic sink term in the equations for live cells. Our model forms the basis for in silico studies of cartilage damage relevant to questions in osteoarthritis, for example, that may not be easily answered through in vivo or in vitro studies. Computational results are presented that indicate the impact of differing levels of erythropoietin on articular cartilage lesion abatement.

The effect of collagen crosslinking on the biphasic poroviscoelastic cartilage properties determined from a semi-automated microindentation protocol for stress relaxation

Given the important role of the collagenous structure in cartilage mechanics, there is considerable interest in the relationship between collagen crosslinking and the mechanical behavior of the cartilage matrix. While crosslink-induced alterations to the elastic modulus of cartilage have been described, changes to time-dependent behavior have not yet been determined. The objective of the study was to quantify changes to cartilage material properties, including viscoelastic coefficients, with crosslinking via indentation. To accomplish this, a semi-autonomous microindentation stress relaxation protocol was first developed, validated and then applied to cartilage specimens before and after crosslinking. The change in mechanical properties with crosslinking was analyzed both in the unloading portions of the test via the Oliver-Pharr method and in the holding portion with an inverse iterative finite element model that represented cartilage as a biphasic poroviscoelastic material. Although both techniques suggested a similar increase in equilibrium modulus in the crosslinked specimens as compared to the controls, distinct differences in the control specimens were apparent, suggesting that the two different techniques may be capturing different aspects of the material behavior. No differences in time-dependent properties were observed between the crosslinked and the control specimens. These results give further insight into the effects of crosslinking in cartilage mechanical behavior. Additionally, the microindentation stress relaxation protocol may enable increased automation for high-throughput testing.

In vivo patellofemoral contact mechanics during active extension using a novel dynamic MRI-based methodology

OBJECTIVES

To establish an in vivo, normative patellofemoral (PF) cartilage contact mechanics database acquired during voluntary muscle control using a novel, dynamic, magnetic resonance (MR) imaging-based, computational methodology and validate the contact mechanics sensitivity to the known sub-millimeter methodological accuracies.

DESIGN

Dynamic cine phase-contrast and multi-plane cine (MPC) images were acquired while female subjects (n = 20, sample of convenience) performed an open kinetic chain (knee flexion-extension) exercise inside a 3-T MR scanner. Static cartilage models were created from high resolution three-dimensional static MR data and accurately placed in their dynamic pose at each time frame based on the cine-PC (CPC) data. Cartilage contact parameters were calculated based on the surface overlap. Statistical analysis was performed using paired t-test and a one-sample repeated measures ANOVA. The sensitivity of the contact parameters to the known errors in the PF kinematics was determined.

RESULTS

Peak mean PF contact area was 228.7 ± 173.6 mm(2) at 40° knee angle. During extension, contact centroid and peak strain locations tracked medially on the femoral and patellar cartilage and were not significantly different from each other. At 25°, 30°, 35°, and 40° of knee extension, contact area was significantly different. Contact area and centroid locations were insensitive to rotational and translational perturbations.

CONCLUSION

This study is a first step towards unfolding the biomechanical pathways to anterior PF pain and osteoarthritis (OA) using dynamic, in vivo, and accurate methodologies. The database provides crucial data for future studies and for validation of, or as an input to, computational models.

Comparison of patella bone strain between females with and without patellofemoral pain: a finite element analysis study

Elevated bone principal strain (an indicator of potential bone injury) resulting from reduced cartilage thickness has been suggested to contribute to patellofemoral symptoms. However, research linking patella bone strain, articular cartilage thickness, and patellofemoral pain (PFP) remains limited. The primary purpose was to determine whether females with PFP exhibit elevated patella bone strain when compared to pain-free controls. A secondary objective was to determine the influence of patella cartilage thickness on patella bone strain. Ten females with PFP and 10 gender, age, and activity-matched pain-free controls participated. Patella bone strain fields were quantified utilizing subject-specific finite element (FE) models of the patellofemoral joint (PFJ). Input parameters for the FE model included (1) PFJ geometry, (2) elastic moduli of the patella bone, (3) weight-bearing PFJ kinematics, and (4) quadriceps muscle forces. Using quasi-static simulations, peak and average minimum principal strains as well as peak and average maximum principal strains were quantified. Cartilage thickness was quantified by computing the perpendicular distance between opposing voxels defining the cartilage edges on axial plane magnetic resonance images. Compared to the pain-free controls, individuals with PFP exhibited increased peak and average minimum and maximum principal strain magnitudes in the patella. Additionally, patella cartilage thickness was negatively associated with peak minimum principal patella strain and peak maximum principal patella strain. The elevated bone strain magnitudes resulting from reduced cartilage thickness may contribute to patellofemoral symptoms and bone injury in persons with PFP.

Finite element predictions of cartilage contact mechanics in hips with retroverted acetabula

BACKGROUND

A contributory factor to hip osteoarthritis (OA) is abnormal cartilage mechanics. Acetabular retroversion, a version deformity of the acetabulum, has been postulated to cause OA via decreased posterior contact area and increased posterior contact stress. Although cartilage mechanics cannot be measured directly in vivo to evaluate the causes of OA, they can be predicted using finite element (FE) modeling.

OBJECTIVE

The objective of this study was to compare cartilage contact mechanics between hips with normal and retroverted acetabula using subject-specific FE modeling.

METHODS

Twenty subjects were recruited and imaged: 10 with normal acetabula and 10 with retroverted acetabula. FE models were constructed using a validated protocol. Walking, stair ascent, stair descent and rising from a chair were simulated. Acetabular cartilage contact stress and contact area were compared between groups.

RESULTS

Retroverted acetabula had superomedial cartilage contact patterns, while normal acetabula had widely distributed cartilage contact patterns. In the posterolateral acetabulum, average contact stress and contact area during walking and stair descent were 2.6-7.6 times larger in normal than retroverted acetabula (P ≤ 0.017). Conversely, in the superomedial acetabulum, peak contact stress during walking was 1.2-1.6 times larger in retroverted than normal acetabula (P ≤ 0.044). Further differences varied by region and activity.

CONCLUSIONS

This study demonstrated superomedial contact patterns in retroverted acetabula vs widely distributed contact patterns in normal acetabula. Smaller posterolateral contact stress in retroverted acetabula than in normal acetabula suggests that increased posterior contact stress alone may not be the link between retroversion and OA.

Influences of the depth-dependent material inhomogeneity of articular cartilage on the fluid pressurization in the human knee

The material properties of articular cartilage are depth-dependent, i.e. they differ in the superficial, middle and deep zones. The role of this depth-dependent material inhomogeneity in the poromechanical response of the knee joint has not been investigated with patient-specific joint modeling. In the present study, the depth-dependent and site-specific material properties were incorporated in an anatomically accurate knee model that consisted of the distal femur, femoral cartilage, menisci, tibial cartilage and proximal tibia. The collagen fibers, proteoglycan matrix and fluid in articular cartilage and menisci were considered as distinct constituents. The fluid pressurization in the knee was determined with finite element analysis. The results demonstrated the influences of the depth-dependent inhomogeneity on the fluid pressurization, compressive stress, first principal stress and strain along the tissue depth. The depth-dependent inhomogeneity enhanced the fluid support to loading in the superficial zone by raising the fluid pressure and lowering the compressive effective stress at the same time. The depth-dependence also reduced the tensile stress and strain at the cartilage-bone interface. The present 3D modeling revealed a complex fluid pressurization and 3D stresses that depended on the mechanical contact and relaxation time, which could not be predicted by existing 2D models from the literature. The greatest fluid pressure was observed in the medial condyle, regardless of the depth-dependent inhomogeneity. The results indicated the roles of the tissue inhomogeneity in reducing deep tissue fractures, protecting the superficial tissue from excessive compressive stress and improving the lubrication in the joint.

Specimen-specific predictions of contact stress under physiological loading in the human hip: validation and sensitivity studies

Hip osteoarthritis may be initiated and advanced by abnormal cartilage contact mechanics, and finite element (FE) modeling provides an approach with the potential to allow the study of this process. Previous FE models of the human hip have been limited by single specimen validation and the use of quasi-linear or linear elastic constitutive models of articular cartilage. The effects of the latter assumptions on model predictions are unknown, partially because data for the instantaneous behavior of healthy human hip cartilage are unavailable. The aims of this study were to develop and validate a series of specimen-specific FE models, to characterize the regional instantaneous response of healthy human hip cartilage in compression, and to assess the effects of material nonlinearity, inhomogeneity and specimen-specific material coefficients on FE predictions of cartilage contact stress and contact area. Five cadaveric specimens underwent experimental loading, cartilage material characterization and specimen-specific FE modeling. Cartilage in the FE models was represented by average neo-Hookean, average Veronda Westmann and specimen- and region-specific Veronda Westmann hyperelastic constitutive models. Experimental measurements and FE predictions compared well for all three cartilage representations, which was reflected in average RMS errors in contact stress of less than 25%. The instantaneous material behavior of healthy human hip cartilage varied spatially, with stiffer acetabular cartilage than femoral cartilage and stiffer cartilage in lateral regions than in medial regions. The Veronda Westmann constitutive model with average material coefficients accurately predicted peak contact stress, average contact stress, contact area and contact patterns. The use of subject- and region-specific material coefficients did not increase the accuracy of FE model predictions. The neo-Hookean constitutive model underpredicted peak contact stress in areas of high stress. The results of this study support the use of average cartilage material coefficients in predictions of cartilage contact stress and contact area in the normal hip. The regional characterization of cartilage material behavior provides the necessary inputs for future computational studies, to investigate other mechanical parameters that may be correlated with OA and cartilage damage in the human hip. In the future, the results of this study can be applied to subject-specific models to better understand how abnormal hip contact stress and contact area contribute to OA.

Spontaneous osteoarthritis in Str/ort mice is unlikely due to greater vulnerability to mechanical trauma

OBJECTIVE

Relative contributions of genetic and mechanical factors to osteoarthritis (OA) remain ill-defined. We have used a joint loading model found to produce focal articular cartilage (AC) lesions, to address whether genetic susceptibility to OA in Str/ort mice is related to AC vulnerability to mechanical trauma and whether joint loading influences spontaneous OA development. We also develop finite element (FE) models to examine whether AC thickness may explain any differential vulnerability to load-induced lesions.

METHODS

Right knees of 8-week-old Str/ort mice were loaded, AC integrity scored and thickness compared to CBA mice. Mechanical forces engendered in this model and the impact of AC thickness were simulated in C57Bl/6 mice using quasi-static FE modelling.

RESULTS

Unlike joints in non-OA prone CBA mice, Str/ort knees did not exhibit lateral femur (LF) lesions in response to applied loading; but exhibited thicker AC. FE modeling showed increased contact pressure and shear on the lateral femoral surface in loaded joints, and these diminished in joints containing thicker AC. Histological analysis of natural lesions in the tibia of Str/ort joints revealed that applied loading increased OA severity, proteoglycan loss and collagen type II degradation.

CONCLUSION

Genetic OA susceptibility in Str/ort mice is not apparently related to greater AC vulnerability to trauma, but joint loading modifies severity of natural OA lesions in the medial tibia. FE modelling suggests that thicker AC in Str/ort mice diminishes tissue stresses and protects against load-induced AC lesions in the LF but that this is unrelated to their genetic susceptibility to OA.

A review of the combination of experimental measurements and fibril-reinforced modeling for investigation of articular cartilage and chondrocyte response to loading

The function of articular cartilage depends on its structure and composition, sensitively impaired in disease (e.g. osteoarthritis, OA). Responses of chondrocytes to tissue loading are modulated by the structure. Altered cell responses as an effect of OA may regulate cartilage mechanotransduction and cell biosynthesis. To be able to evaluate cell responses and factors affecting the onset and progression of OA, local tissue and cell stresses and strains in cartilage need to be characterized. This is extremely challenging with the presently available experimental techniques and therefore computational modeling is required. Modern models of articular cartilage are inhomogeneous and anisotropic, and they include many aspects of the real tissue structure and composition. In this paper, we provide an overview of the computational applications that have been developed for modeling the mechanics of articular cartilage at the tissue and cellular level. We concentrate on the use of fibril-reinforced models of cartilage. Furthermore, we introduce practical considerations for modeling applications, including also experimental tests that can be combined with the modeling approach. At the end, we discuss the prospects for patient-specific models when aiming to use finite element modeling analysis and evaluation of articular cartilage function, cellular responses, failure points, OA progression, and rehabilitation.

Periosteum, bone's "smart" bounding membrane, exhibits direction-dependent permeability

The periosteum serves as bone's bounding membrane, exhibits hallmarks of semipermeable epithelial barrier membranes, and contains mechanically sensitive progenitor cells capable of generating bone. The current paucity of data regarding the periosteum's permeability and bidirectional transport properties provided the impetus for the current study. In ovine femur and tibia samples, the periosteum's hydraulic permeability coefficient, k, was calculated using Darcy's Law and a custom-designed permeability tester to apply controlled, volumetric flow of phosphate-buffered saline through periosteum samples. Based on these data, ovine periosteum demonstrates mechanically responsive and directionally dependent (anisotropic) permeability properties. At baseline flow rates comparable to interstitial fluid flow (0.5 µL/s), permeability is low and does not exhibit anisotropy. In contrast, at high flow rates comparable to those prevailing during traumatic injury, femoral periosteum exhibits an order of magnitude higher permeability compared to baseline flow rates. In addition, at high flow rates permeability exhibits significant directional dependence, with permeability higher in the bone to muscle direction than vice versa. Furthermore, compared to periosteum in which the intrinsic tension (pre-stress) is maintained, free relaxation of the tibial periosteum after resection significantly increases its permeability in both flow directions. Hence, the structure and mechanical stress state of periosteum influences its role as bone's bounding membrane. During periods of homeostasis, periosteum may serve as a barrier membrane on the outer surface of bone, allowing for equal albeit low quiescent molecular communication between tissue compartments including bone and muscle. In contrast, increases in pressure and baseline flow rates within the periosteum resulting from injury, trauma, and/or disease may result in a significant increase in periosteum permeability and consequently in increased molecular communication between tissue compartments. Elucidation of the periosteum's permeability properties is key to understanding periosteal mechanobiology in bone health and healing, as well as to elucidate periosteum structure and function as a smart biomaterial that allows bidirectional and mechanically responsive fluid transport.

Recent advances in computational mechanics of the human knee joint

Computational mechanics has been advanced in every area of orthopedic biomechanics. The objective of this paper is to provide a general review of the computational models used in the analysis of the mechanical function of the knee joint in different loading and pathological conditions. Major review articles published in related areas are summarized first. The constitutive models for soft tissues of the knee are briefly discussed to facilitate understanding the joint modeling. A detailed review of the tibiofemoral joint models is presented thereafter. The geometry reconstruction procedures as well as some critical issues in finite element modeling are also discussed. Computational modeling can be a reliable and effective method for the study of mechanical behavior of the knee joint, if the model is constructed correctly. Single-phase material models have been used to predict the instantaneous load response for the healthy knees and repaired joints, such as total and partial meniscectomies, ACL and PCL reconstructions, and joint replacements. Recently, poromechanical models accounting for fluid pressurization in soft tissues have been proposed to study the viscoelastic response of the healthy and impaired knee joints. While the constitutive modeling has been considerably advanced at the tissue level, many challenges still exist in applying a good material model to three-dimensional joint simulations. A complete model validation at the joint level seems impossible presently, because only simple data can be obtained experimentally. Therefore, model validation may be concentrated on the constitutive laws using multiple mechanical tests of the tissues. Extensive model verifications at the joint level are still crucial for the accuracy of the modeling.

Subject-specific analysis of joint contact mechanics: application to the study of osteoarthritis and surgical planning

Advances in computational mechanics, constitutive modeling, and techniques for subject-specific modeling have opened the door to patient-specific simulation of the relationships between joint mechanics and osteoarthritis (OA), as well as patient-specific preoperative planning. This article reviews the application of computational biomechanics to the simulation of joint contact mechanics as relevant to the study of OA. This review begins with background regarding OA and the mechanical causes of OA in the context of simulations of joint mechanics. The broad range of technical considerations in creating validated subject-specific whole joint models is discussed. The types of computational models available for the study of joint mechanics are reviewed. The types of constitutive models that are available for articular cartilage are reviewed, with special attention to choosing an appropriate constitutive model for the application at hand. Issues related to model generation are discussed, including acquisition of model geometry from volumetric image data and specific considerations for acquisition of computed tomography and magnetic resonance imaging data. Approaches to model validation are reviewed. The areas of parametric analysis, factorial design, and probabilistic analysis are reviewed in the context of simulations of joint contact mechanics. Following the review of technical considerations, the article details insights that have been obtained from computational models of joint mechanics for normal joints; patient populations; the study of specific aspects of joint mechanics relevant to OA, such as congruency and instability; and preoperative planning. Finally, future directions for research and application are summarized.