A poroelastic finite element model of the bone–cartilage unit to determine the effects of changes in permeability with osteoarthritis

Controlled Mechanical Property Gradients Within a Digital Light Processing Printed Hydrogel-Composite Osteochondral Scaffold

Tissue engineered scaffolds are needed to support physiological loads and emulate the micrometer-scale strain gradients within tissues that guide cell mechanobiological responses. We designed and fabricated micro-truss structures to possess spatially varying geometry and controlled stiffness gradients. Using a custom projection microstereolithography (μSLA) system, using digital light projection (DLP), and photopolymerizable poly(ethylene glycol) diacrylate (PEGDA) hydrogel monomers, three designs with feature sizes < 200 μm were formed: (1) uniform structure with 1 MPa structural modulus ( E ) designed to match equilibrium modulus of healthy articular cartilage, (2) E  = 1 MPa gradient structure designed to vary strain with depth, and (3) osteochondral bilayer with distinct cartilage ( E  = 1 MPa) and bone ( E  = 7 MPa) layers. Finite element models (FEM) guided design and predicted the local mechanical environment. Empty trusses and poly(ethylene glycol) norbornene hydrogel-infilled composite trusses were compressed during X-ray microscopy (XRM) imaging to evaluate regional stiffnesses. Our designs achieved target moduli for cartilage and bone while maintaining 68-81% porosity. Combined XRM imaging and compression of empty and hydrogel-infilled micro-truss structures revealed regional stiffnesses that were accurately predicted by FEM. In the infilling hydrogel, FEM demonstrated the stress-shielding effect of reinforcing structures while predicting strain distributions. Composite scaffolds made from stiff μSLA-printed polymers support physiological load levels and enable controlled mechanical property gradients which may improve in vivo outcomes for osteochondral defect tissue regeneration. Advanced 3D imaging and FE analysis provide insights into the local mechanical environment surrounding cells in composite scaffolds.

Study on the poroelastic behaviors of the defected osteochondral unit

Osteoarthritis has become a major disease threatening human health. The mechanism of injury under fluid involvement can be studied by finite element method. However, most models only model the articular cartilage to study the subchondral bone structure, which is too simplistic. In this study, a complete osteochondral unit was modeled and provided with a poroelastic material, and as osteoarthritis develops and the size, thickness, and shape of the osteochondral unit defect varies, the fluid flow behavior is altered, which may have functional consequences that feed back into the progression of the injury. The results of the study showed that interstitial fluid pressure and velocity decreased in defective osteochondral units. This trend was exacerbated as the size and thickness of the defect in the osteochondral unit increased. When the defect reached the trabeculae, pressure around the cartilage defect in the osteochondral unit was greatest, flow velocity in the subchondral cortical bone was greatest, and pressure and flow velocity around the trabecular defect were lowest. As osteoarthritis develops, the osteochondral unit becomes more permeable, and the pressure of the interstitial fluid decreases while the flow rate increases, resulting in severe nutrient loss. This may be the fluid flow mechanism behind osteochondral defects and osteoarthritis.

Using a poroelastodynamic model to investigate the dynamic behaviour of articular cartilage

BACKGROUND AND OBJECTIVE

There is still a few studies about the poroelastic model that performed dynamic behaviour, especially for the case of the poroelastic cartilage model. Therefore, this study is aimed to use the poroelastodynamic model to simulate the dynamic behaviour of cartilage.

METHODS

The governing equations of the poroelastodynamic model is firstly established. The validation of the model is initialised by modifying the equations into the static poroelastic model. The modified equations are then discretised using the finite element method. Mandel's problem is used to validate the discretised equations. The numerical solution calculated using FreeFEM++ is validated with the analytical solution for the quasi-static state and compared with the results generated using COMSOL Multiphysics software. Finally, the quasi-static solution is compared with the dynamic solution to discuss the difference in pore pressure and displacement variations of the poroelastic cartilage model.

RESULTS

The dynamic solution showed transient behaviour at the beginning of the excitation. When the compressive force acts on the cartilage, there are obvious fluctuations during the initial stage and then the dynamic numerical solution gradually approaches the quasi-static value over a period of time. The deduced results of the analytical solution were approximately the same as the numerical simulation results.

CONCLUSION

This study was able to use the poroelastodynamics equation to simulate the dynamic behaviour of the poroelastic cartilage model. The comparison between the result coming from poroelastodynamics equation with that of the validated numerical solution was satisfactorily compared. The approximate similarity between the results of quasi-static and dynamic solutions underscored the importance of performing the dynamic solution for a more realistic simulation. This dynamic solution can be further used for the analysis of vibration or stress waves in future research.

Multi-fidelity surrogate modeling through hybrid machine learning for biomechanical and finite element analysis of soft tissues

Biomechanical simulation enables medical researchers to study complex mechano-biological conditions, although for soft tissue modeling, it may apply highly nonlinear multi-physics theories commonly implemented by expensive finite element (FE) solvers. This is a significantly time-consuming process on a regular computer and completely inefficient in urgent situations. One remedy is to first generate a dataset of the possible inputs and outputs of the solver in order to then train an efficient machine learning (ML) model, i.e., the supervised ML-based surrogate, replacing the expensive solver to speed up the simulation. But it still requires a large number of expensive numerical samples. In this regard, we propose a hybrid ML (HML) method that uses a reduced-order model defined by the simplification of the complex multi-physics equations to produce a dataset of the low-fidelity (LF) results. The surrogate then has this efficient numerical model and an ML model that should increase the fidelity of its outputs to the level of high-fidelity (HF) results. Based on our empirical tests via a group of diverse training and numerical modeling conditions, the proposed method can improve training convergence for very limited training samples. In particular, while considerable time gains comparing to the HF numerical models are observed, training of the HML models is also significantly more efficient than the purely ML-based surrogates. From this, we conclude that this non-destructive HML implementation may increase the accuracy and efficiency of surrogate modeling of soft tissues with complex multi-physics properties in small data regimes.

Properties of Cartilage-Subchondral Bone Junctions: A Narrative Review with Specific Focus on the Growth Plate

OBJECTIVE

The purpose of this narrative review is to summarize what is currently known about the structural, chemical, and mechanical properties of cartilage-bone interfaces, which provide tissue integrity across a bimaterial interface of 2 very different structural materials. Maintaining these mechanical interfaces is a key factor for normal bone growth and articular cartilage function and maintenance.

MATERIALS AND METHODS

A comprehensive search was conducted using Google Scholar and PubMed/Medline with a specific focus on the growth plate cartilage-subchondral bone interface. All original articles, reviews in journals, and book chapters were considered. Following a review of the overall structural and functional characteristics of the physis, the literature on histological studies of both articular and growth plate chondro-osseous junctions is briefly reviewed. Next the literature on biochemical properties of these interfaces is reviewed, specifically the literature on elemental analyses across the cartilage-subchondral bone junctions. The literature on biomechanical studies of these junctions at the articular and physeal interfaces is also reviewed and compared.

RESULTS

Unlike the interface between articular cartilage and bone, growth plate cartilage has 2 chondro-osseous junctions. The reserve zone of the mature growth plate is intimately connected to a plate of subchondral bone on the epiphyseal side. This interface resembles that between the subchondral bone and articular cartilage, although much less is known about its makeup and formation.

CONCLUSION

There is a notably paucity of information available on the structural and mechanical properties of reserve zone-subchondral epiphyseal bone interface. This review reveals that further studies are needed on the microstructural and mechanical properties of chondro-osseous junction with the reserve zone.

Development and analytical validation of a finite element model of fluid transport through osteochondral tissue

Fluid transport is critical to joint health. In this study we evaluate an unexplored component of joint fluid transport -fluid transport between cartilage and bone. Such transport across the cartilage-bone interface could potentially provide chondrocytes with an additional source of nutrients and signaling molecules. A biphasic viscoelastic model using an ellipsoidal fiber distribution was created with three distinct layers of cartilage (superficial zone, middle zone, and deep zone) along with a layer of subchondral bone. For stress-relaxation in unconfined compression, our results for compressive stress, radial stress, and effective fluid pressure were compared with established biphasic analytical solutions. Our model also shows the development of fluid pressure gradients at the cartilage-bone interface during loading. Fluid pressure gradients that develop at the cartilage-bone interface show consistently higher pressures in cartilage following the initial loading to 10% stain, followed by convergence of the pressures in cartilage and bone during the 400 s relaxation period. These results provide additional evidence that fluid is transported between cartilage and bone during loading and improves upon estimates of the magnitude of this effect through incorporating a realistic distribution and estimate of the collagen ultrastructure. Understanding fluid transport between cartilage and bone may be key to new insights about the mechanical and biological environment of both tissues in health and disease.

Depth and strain rate-dependent mechanical response of chondrocytes in reserve zone cartilage subjected to compressive loading

The role of the growth plate reserve zone is not well understood. It has been proposed to serve as a source of stem cells and to produce morphogens that control the alignment of clones in preparation for the transition into the proliferative zone. We hypothesized that if such a role exists, there are likely to be mechanoregulatory stimuli in cellular response through the depth of the reserve zone. A poroelastic multiscale finite element model of bone/growth-plate/bone was developed for examining the reserve zone cell transient response when compressed to 5% of the cartilage thickness at strain rates of 0.18%/s, 5%/s, 50%/s, and 200%/s. Chondrocyte maximum principal strains, height-, width-, and membrane-strains were found to be highly dependent on reserve zone tissue depth and strain rate. Cell-level strains and fluid transmembrane outflow from the cell were influenced by the permeability of the calcified cartilage between subchondral bone plate and reserve zone and by the applied strain rate. Cell strain levels in the lower reserve zone were less sensitive to epiphyseal permeability than in the upper reserve zone. In contrast, the intracellular fluid pressures were relatively uniform with reserve zone tissue depth and less sensitive to epiphyseal permeability. Fluid shear stress, induced by fluid flow over the cell surface, provided mechanoregulatory signals potentially sufficient to stimulate reserve zone chondrocytes near the subchondral bone plate interface. These results suggest that the strain rate and tissue depth dependence of cell-level strains and cell surface fluid shear stress may provide mechanoregulatory cues in the reserve zone.

Development of Subject Specific Finite Element Models of the Mouse Knee Joint for Preclinical Applications

Osteoarthritis is the most common musculoskeletal disabling disease worldwide. Preclinical studies on mice are commonly performed to test new interventions. Finite element (FE) models can be used to study joint mechanics, but usually simplified geometries are used. The aim of this project was to create a realistic subject specific FE model of the mouse knee joint for the assessment of joint mechanical properties. Four different FE models of a C57Bl/6 female mouse knee joint were created based on micro-computed tomography images of specimens stained with phosphotungstic acid in order to include different features: individual cartilage layers with meniscus, individual cartilage layers without meniscus, homogeneous cartilage layers with two different thickness values, and homogeneous cartilage with same thickness for both condyles. They were all analyzed under compressive displacement and the cartilage contact pressure was compared at 0.3 N reaction force. Peak contact pressure in the femur cartilage was 25% lower in the model with subject specific cartilage compared to the simpler model with homogeneous cartilage. A much more homogeneous pressure distribution across the joint was observed in the model with meniscus, with cartilage peak pressure 5–34% lower in the two condyles compared to that with individual cartilage layers. In conclusion, modeling the meniscus and individual cartilage was found to affect the pressure distribution in the mouse knee joint under compressive load and should be included in realistic models for assessing the effect of interventions preclinically.

A 3D, Dynamically Loaded Hydrogel Model of the Osteochondral Unit to Study Osteocyte Mechanobiology

Osteocytes are mechanosensitive cells that orchestrate signaling in bone and cartilage across the osteochondral unit. The mechanisms by which osteocytes regulate osteochondral homeostasis and degeneration in response to mechanical cues remain unclear. This study introduces a novel 3D hydrogel bilayer composite designed to support osteocyte differentiation and bone matrix deposition in a bone-like layer and to recapitulate key aspects of the osteochondral unit's complex loading environment. The bilayer hydrogel is fabricated with a soft cartilage-like layer overlaying a stiff bone-like layer. The bone-like layer contains a stiff 3D-printed hydrogel structure infilled with a soft, degradable, cellular hydrogel. The IDG-SW3 cells embedded within the soft hydrogel mature into osteocytes and produce a mineralized collagen matrix. Under dynamic compressive strains, near-physiological levels of strain are achieved in the bone layer (≤ 0.08%), while the cartilage layer bears the majority of the strains (>99%). Under loading, the model induces an osteocyte response, measured by prostaglandin E2, that is frequency, but not strain, dependent: a finding attributed to altered fluid flow within the composite. Overall, this new hydrogel platform provides a novel approach to study osteocyte mechanobiology in vitro in an osteochondral tissue-mimetic environment.

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.

Osteochondral Tissue Chip Derived From iPSCs: Modeling OA Pathologies and Testing Drugs

Osteoarthritis (OA) is a chronic disease mainly characterized by degenerative changes in cartilage, but other joint elements such as bone are also affected. To date, there are no disease-modifying OA drugs (DMOADs), owing in part to a deficiency of current models in simulating OA pathologies and etiologies in humans. In this study, we aimed to develop microphysiological osteochondral (OC) tissue chips derived from human induced pluripotent stem cells (iPSCs) to model the pathologies of OA. We first induced iPSCs into mesenchymal progenitor cells (iMPCs) and optimized the chondro- and osteo-inductive conditions for iMPCs. Then iMPCs were encapsulated into photocrosslinked gelatin scaffolds and cultured within a dual-flow bioreactor, in which the top stream was chondrogenic medium and the bottom stream was osteogenic medium. After 28 days of differentiation, OC tissue chips were successfully generated and phenotypes were confirmed by real time RT-PCR and histology. To create an OA model, interleukin-1β (IL-1β) was used to challenge the cartilage component for 7 days. While under control conditions, the bone tissue promoted chondrogenesis and suppressed chondrocyte terminal differentiation of the overlying chondral tissue. Under conditions modeling OA, the bone tissue accelerated the degradation of chondral tissue which is likely via the production of catabolic and inflammatory cytokines. These findings suggest active functional crosstalk between the bone and cartilage tissue components in the OC tissue chip under both normal and pathologic conditions. Finally, a selective COX-2 inhibitor commonly prescribed drug for OA, Celecoxib, was shown to downregulate the expression of catabolic and proinflammatory cytokines in the OA model, demonstrating the utility of the OC tissue chip model for drug screening. In summary, the iPSC-derived OC tissue chip developed in this study represents a high-throughput platform applicable for modeling OA and for the screening and testing of candidate DMOADs.

Computational simulation of the multiphasic degeneration of the bone-cartilage unit during osteoarthritis via indentation and unconfined compression tests

It has been experimentally proposed that the discrete regions of articular cartilage, along with different subchondral bone tissues, known as the bone-cartilage unit, are biomechanically altered during osteoarthritis degeneration. However, a computational framework capturing all of the dominant changes in the multiphasic parameters has not yet been developed. This article proposes a new finite element model of the bone-cartilage unit by combining several validated, nonlinear, depth-dependent, fibril-reinforced, and swelling models, which can computationally simulate the variations in the dominant parameters during osteoarthritis degeneration by indentation and unconfined compression tests. The mentioned dominant parameters include the proteoglycan depletion, collagen fibrillar softening, permeability, and fluid fraction increase for approximately non-advanced osteoarthritis. The results depict the importance of subchondral bone tissues in fluid distribution within the bone-cartilage units by decreasing the fluid permeation and pressure (up to a maximum of 100 kPa) during osteoarthritis, supporting the notion that subchondral bones might play a role in the pathogenesis of osteoarthritis. Furthermore, the osteoarthritis composition-based studies shed light on the significant biomechanical role of the calcified cartilage, which experienced a maximum change of 70 kPa in stress, together with relative load contributions of articular cartilage constituents during osteoarthritis, in which the osmotic pressure bore around 70% of the loads after degeneration. To conclude, the new insights provided by the results reveal the significance of the multiphasic osteoarthritis simulation and demonstrate the functionality of the proposed bone-cartilage unit model.

Finite element modelling of the developing infant femur using paired CT and MRI scans

Bone finite element (FE) studies based on infant post-mortem computed tomography (CT) examinations are being developed to provide quantitative information to assist the differentiation between accidental and inflicted injury, and unsuspected underlying disease. As the growing skeleton contains non-ossified cartilaginous regions at the epiphyses, which are not well characterised on CT examinations, it is difficult to evaluate the mechanical behaviour of the developing whole bone. This study made use of paired paediatric post mortem femoral CT and magnetic resonance imaging (MRI) examinations at two different stages of development (4 and 7 months) to provide anatomical and constitutive information for both hard and soft tissues. The work aimed to evaluate the effect of epiphyseal ossification on the propensity to shaft fractures in infants. The outcomes suggest that the failure load of the femoral diaphysis in the models incorporating the non-ossified epiphysis is within the range of bone-only FE models. There may however be an effect on the metaphysis. Confirmation of these findings is required in a larger cohort of children.

Effect of the anisotropic permeability in the frequency dependent properties of the superficial layer of articular cartilage

Articular cartilage is a tissue of fundamental importance for the mechanics of joints, since it provides a smooth and lubricated surface for the proper transfer of loads. From a mechanical point of view, this tissue is an anisotropic poroviscoelastic material: its characteristics at the macroscopic level depend on the complex microscopic architecture. With the ability to probe the local microscopic features, dynamic nanoindentation test is a powerful tool to investigate cartilage mechanics. In this work we focus on a length scale where the time dependent behaviour is regulated by poroelasticity more than viscoelasticity and we aim to understand the effect of the anisotropic permeability on the mechanics of the superficial layer of the articular cartilage. In a previous work, a finite element model for the dynamic nanoindentation test has been presented. In this work, we improve the model by considering the presence of an anisotropic permeability tensor that depends on the collagen fibers distribution. Our sensitivity analysis highlights that the permeability decreases with increasing indentation, thus making the tissue stiffer than the case of isotropic permeability, when solicited at the same frequency. With this improved model, a revised identification of the mechanical and physical parameters for articular cartilage is provided. To this purpose the model was used to simulate experimental data from tests performed on bovine tissue, giving a better estimation of the anisotropy in the elastic properties. A relation between the identified macroscopic anisotropic permeability properties and the microscopic rearrangement of the fiber/matrix structure during indentation is also provided.