A biphasic multiscale study of the mechanical microenvironment of chondrocytes within articular cartilage under unconfined compression

Computational analyses have been used to study the biomechanical microenvironment of the chondrocyte that cannot be assessed by in vitro experimental studies; yet all computational studies thus far have focused on the effect of zonal location (superficial, middle, and deep) on the mechanical microenvironment of chondrocytes. The aim of this paper was to study the effect of both zonal and radial locations on the biomechanical microenvironment of chondrocytes in inhomogeneous cartilage under unconfined stress relaxation. A biphasic multiscale approach was employed and nine chondrocytes in different locations were studied. Hyperelastic biphasic theory and depth-dependent aggregate modulus and permeability of articular cartilage were included in the models. It was found that both zonal and radial locations affected the biomechanical stresses and strains of the chondrocytes. Chondrocytes in the mid-radial location had increased volume during the early stage of the loading process. Maximum principal shear stress at the interface between the chondrocyte and the extracellular matrix (ECM) increased with depth, yet that at the ECM–pericellular matrix (PCM) interface had an inverse trend. Fluid pressure decreased with depth, while the fluid pressure difference between the top and bottom boundaries of the microscale model increased with depth. Regardless of location, fluid was exchanged between the chondrocyte, PCM, and ECM. These findings suggested that even under simple compressive loading conditions, the biomechanical microenvironment of the chondrocytes, PCM and ECM was spatially dependent. The current study provides new insight on chondrocyte biomechanics.     

Depletion of glycosphingolipids induces excessive response of chondrocytes under mechanical stress

Glycosphingolipids (GSLs) are ubiquitous membrane components that play an indispensable role in maintaining chondrocyte homeostasis. To gain better insight into roles of GSLs, we studied the effects of GSL-deletion on the physiological responses of chondrocytes to mechanical stress. Mice lacking Ugcg gene (Ugcg^-/-) were genetically generated to obtain GSL-deficient mice, and their chondrocytes from the joints were used for functional analyses in vitro culture experiments. The cells were seeded in a three-dimensional collagen gel and subjected to 5%, 10% or 16% cyclic tensile strain for either 3 or 24 h. The gene expressions of chondrocyte anabolic and catabolic factors, and the induction of Ca²⁺ signaling were analyzed. Our results revealed that chondrocytes derived from GSL-deficient mice exhibited an elevation in the expression of catabolic factors (ADAMTS-5, MMP-13) following the exposure to strain with amplitudes of 10%. Likewise, applying cyclic tensile strain with these amplitudes resulted in an increased Ca²⁺ oscillation ratio in chondrocytes from GSL-deficient as compared to the ratio from control mice. These results demonstrated that deletion of GSL stimulated the catabolic responses of chondrocytes to mechanical stress via the augmentation of the sensitivity to mechanical stress that may lead to the cartilage deterioration. These findings suggest that the regulation of the physiological responses of chondrocytes by GSLs could be a potential target in a therapeutic intervention in osteoarthritis.     

Interleukin-17F affects cartilage matrix turnover by increasing the expression of collagenases and stromelysin-1 and by decreasing the expression of their inhibitors and extracellular matrix components in chondrocytes

Interleukin (IL)-17, a proinflammatory cytokine, is produced primarily by activated Th17 cells. IL-17 consists of six ligands that signal through five receptors (IL-17Rs); IL-17A and IL-17F share the highest homology in the family. Matrix metalloproteinases (MMPs) degrade the extracellular matrix during cartilage remodeling whereas tissue inhibitor of metalloproteinases (TIMPs) inhibit the action of MMPs. In the present study, we examined the effect of IL-17F on the degradation and synthesis of the extracellular matrix in cartilage using human articular chondrocytes. We examined the effect of IL-17F on the expression of IL-17Rs, MMPs, TIMPs, type II collagen, aggrecan, link protein, and cyclooxygenases (COXs), as well as on prostaglandin E₂ (PGE₂) production. We also examined the indirect effect of PGE₂ on the above IL-17F-induced/reduced components using NS-398, a specific inhibitor of COX-2. Cells were cultured with or without IL-17F in the presence or absence of either an IL-17R antibody or NS-398 for up to 28 days. Expression of IL-17Rs, MMPs, TIMPs, type II collagen, aggrecan, link protein, and COXs at mRNA and protein levels was determined using real-time polymerase chain reaction and enzyme-linked immunosorbent assay (ELISA), respectively. PGE₂ production was determined by ELISA. The expression of all types of IL-17Rs was detected in chondrocytes. However, IL-17RE expression was extremely low, compared with other IL-17Rs. The expression of MMP-1, MMP-3, MMP-13, and COX-2 as well as PGE₂ production were increased by addition of IL-17F, whereas the expression of IL-17RD, TIMP-2, TIMP-4, type II collagen, aggrecan, link protein, and COX-1 was decreased. The expression of IL-17RA, IL-17RB, IL-17RC, MMP-2, MMP-14, TIMP-1, and TIMP-3 was unaffected by addition of IL-17F. The IL-17R antibody blocked the stimulating/reducing effect of IL-17F on the expression of MMP-1, MMP-3, MMP-13, TIMP-2, TIMP-4, type II collagen, aggrecan, and link protein. NS-398 blocked the reducing effect of IL-17F on aggrecan expression, whereas it did not completely block the stimulating/reducing effects of IL-17F on the expression of MMP-1, MMP-3, MMP-13, TIMP-2, TIMP-4, type II collagen, and link protein. Our results suggest that IL-17F stimulates cartilage degradation by increasing the expression of collagenases (MMP-1 and -13) and stromelysin-1 (MMP-3) and by decreasing expression of their inhibitors (TIMP-2 and -4), type II collagen, aggrecan, and link protein in chondrocytes. Furthermore, our results suggest that the expression of aggrecan, link protein, and TIMP-4 decrease through the autocrine action of PGE₂ in chondrocytes.     

Measurement of the circumferential mechanical properties of the umbilical vein: experimental and numerical analyses

Coronary artery disease is responsible for almost 30% of all deaths worldwide. The saphenous vein and umbilical vein (UV) are the most common veins using for treatment as a coronary artery bypass graft (CABG). The mechanical properties of UV belonging to its long-term patency for CABG are very important. However, there is a lack of knowledge on the linear elastic and nonlinear hyperelastic mechanical properties of the UV. In this study, three stress definitions (second Piola–Kichhoff stress, engineering stress and true stress) and four strain definitions (Almansi–Hamel strain, Green–St Venant strain, engineering strain and true strain) are used to determine the elastic modulus, maximum stress and strain of eight human UVs under circumferential loading. The nonlinear mechanical behaviour of the UV is computationally investigated using Mooney–Rivlin hyperelastic model. A numerical finite element analysis is also carried out to simulate the constitutive modelling versus its numerical results. The results show that the Almansi–Hamel strain definition overestimates the elastic modulus while Green–St Venant strain definition underestimates the elastic modulus at different stress definitions. The true stress–true strain definition, which gives more accurate measurements of the tissue's response using the instantaneous values, reveals the Young's modulus and maximum stress of 2.18 and 6.01 MPa, respectively. The Mooney–Rivlin material model is well represented by the nonlinear mechanical behaviour of the UV. The findings of this study could have implications not only for understanding the extension and rupture mechanism of UV but also for interventions and surgeries, including balloon angioplasty, bypass and stenting.     

Pharmacological treatment with diacerein combined with mechanical stimulation affects the expression of growth factors in human chondrocytes

BackgroundOsteoarthritis (OA) as the main chronic joint disease arises from a disturbed balance between anabolic and catabolic processes leading to destructions of articular cartilage of the joints. While mechanical stress can be disastrous for the metabolism of chondrocytes, mechanical stimulation at the physiological level is known to improve cell function. The disease modifying OA drug (DMOAD) diacerein functions as a slowly-acting drug in OA by exhibiting anti-inflammatory, anti-catabolic, and pro-anabolic properties on cartilage. Combining these two treatment options revealed positive effects on OA-chondrocytes.MethodsCells were grown on flexible silicone membranes and mechanically stimulated by cyclic tensile loading. After seven days in the presence or absence of diacerein, inflammation markers and growth factors were analyzed using quantitative real-time PCR and enzyme linked immune assays. The influence of conditioned medium was tested on cell proliferation and cell migration.ResultsTensile strain and diacerein treatment reduced interleukin-6 (IL-6) expression, whereas cyclooxygenase-2 (COX2) expression was increased only by mechanical stimulation. The basic fibroblast growth factor (bFGF) was down regulated by the combined treatment modalities, whereas prostaglandin E2 (PGE2) synthesis was reduced only under OA conditions. The expression of platelet-derived growth factor (PDGF) and vascular endothelial growth factor A (VEGF-A) was down-regulated by both.ConclusionsFrom our study we conclude that moderate mechanical stimulation appears beneficial for the fate of the cell and improves the pharmacological effect of diacerein based on cross-talks between different initiated pathways.General significanceCombining two different treatment options broadens the perspective to treat OA and improves chondrocytes metabolism.     

Finite element modelling of the glenohumeral capsule can help assess the tested region during a clinical exam

The objective of this research was to examine the efficacy of evaluating the region of the glenohumeral capsule being tested by clinical exams for shoulder instability using finite element (FE) models of the glenohumeral joint. Specifically, the regions of high capsule strain produced by glenohumeral joint positions commonly used during a clinical exam were identified. Kinematics that simulated a simple translation test with an anterior load at three external rotation angles were applied to a validated, subject-specific FE model of the glenohumeral joint at 60° of abduction. Maximum principal strains on the glenoid side of the inferior glenohumeral ligament (IGHL) were significantly higher than the maximum principal strains on the humeral side, for all three regions of the IGHL at 30° and 60° of external rotation. These regions of localised strain indicate that these joint positions might be used to test the glenoid side of the IGHL during this clinical exam, but are not useful for assessing the humeral side of the IGHL. The use of FE models will facilitate the search for additional joint positions that isolate high strains to other IGHL regions, including the humeral side of the IGHL.     

The mechanical significance of morphological variation in the macaque mandibular symphysis during mastication

Catarrhine symphyseal morphology displays considerable variation. Although this has been related to dentition, phylogeny, sexual dimorphism, and facial orientation, most emphasis has been given to the functional significance of the symphysis to mechanical loading during mastication. The current state of knowledge regarding the mechanical significance of the symphysis is based on a combination of in vivo experimental and comparative studies on Macaca fascicularis. These approaches have provided considerable insight into the stereotypical patterns of loading in the symphyseal region during chewing and hypotheses related to the associated symphyseal morphologies. Finite element analysis (FEA) was used to assess how in silico manipulation translates into the mechanical loading hypotheses previously proposed experimentally. In particular, this study tests the form-function relationship of the symphysis of an adult M. fascicularis mandible during lateral transverse bending and dorsoventral shear of the mandibular symphysis, and a series of modified hypothetical morphologies including absence/presence of tori and variation in the inclination and depth of the symphysis. FEA results of this study support previous findings that stresses associated with lateral transverse bending and dorsoventral shear of the mandibular symphysis can be minimized via an increased labio-lingual thickness in the superior transverse torus, an oblique symphyseal inclination, and/or an increased symphyseal depth. The finding that reduction of strains related to lateral transverse bending and dorsoventral shear can be achieved through a number of different morphologies contributes to our understanding of the influence of morphological and/or developmental constraints, such as dental development, on symphyseal form.     

A microstructurally informed model for the mechanical response of three-dimensional actin networks

We propose a class of microstructurally informed models for the linear elastic mechanical behaviour of cross-linked polymer networks such as the actin cytoskeleton. Salient features of the models include the possibility to represent anisotropic mechanical behaviour resulting from anisotropic filament distributions, and a power law scaling of the mechanical properties with the filament density. Mechanical models within the class are parameterized by seven different constants. We demonstrate a procedure for determining these constants using finite element models of three-dimensional actin networks. Actin filaments and cross-links were modelled as elastic rods, and the networks were constructed at physiological volume fractions and at the scale of an image voxel. We show the performance of the model in estimating the mechanical behaviour of the networks over a wide range of filament densities and degrees of anisotropy.     

Computational simulation of the early stage of bone healing under different configurations of locking compression plates

Flexible fixation or the so-called ‘biological fixation’ has been shown to encourage the formation of fracture callus, leading to better healing outcomes. However, the nature of the relationship between the degree of mechanical stability provided by a flexible fixation and the optimal healing outcomes has not been fully understood. In this study, we have developed a validated quantitative model to predict how cells in fracture callus might respond to change in their mechanical microenvironment due to different configurations of locking compression plate (LCP) in clinical practice, particularly in the early stage of healing. The model predicts that increasing flexibility of the LCP by changing the bone–plate distance (BPD) or the plate working length (WL) could enhance interfragmentary strain in the presence of a relatively large gap size (>3 mm). Furthermore, conventional LCP normally results in asymmetric tissue development during early stage of callus formation, and the increase of BPD or WL is insufficient to alleviate this problem.     

A multi-scale mechanobiological model of in-stent restenosis: deciphering the role of matrix metalloproteinase and extracellular matrix changes

Since their first introduction, stents have revolutionised the treatment of atherosclerosis; however, the development of in-stent restenosis still remains the Achilles' heel of stent deployment procedures. Computational modelling can be used as a means to model the biological response of arteries to different stent designs using mechanobiological models, whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells. Changes occurring within the arterial wall due to stent-induced mechanical injury, specifically changes within the extracellular matrix, have been postulated to be a major cause of activation of vascular smooth muscle cells and the subsequent development of in-stent restenosis. In this study, a mechanistic multi-scale mechanobiological model of in-stent restenosis using finite element models and agent-based modelling is presented, which allows quantitative evaluation of the collagen matrix turnover following stent-induced arterial injury and the subsequent development of in-stent restenosis. The model is specifically used to study the influence of stent deployment diameter and stent strut thickness on the level of in-stent restenosis. The model demonstrates that there exists a direct correlation between the stent deployment diameter and the level of in-stent restenosis. In addition, investigating the influence of stent strut thickness using the mechanobiological model reveals that thicker strut stents induce a higher level of in-stent restenosis due to a higher extent of arterial injury. The presented mechanobiological modelling framework provides a robust platform for testing hypotheses on the mechanisms underlying the development of in-stent restenosis and lends itself for use as a tool for optimisation of the mechanical parameters involved in stent design.     

Epigenetic mechanical factors in the evolution of long bone epiphyses

In developing vertebrate long bones in which endochondral ossification occurs, it is preceded or accompanied by perichondral ossification. The speed and extent of perichondral apposition relative to endochondral ossification varies in different taxa. Perichondral ossification dominates early long bone development in extinct basal tetrapods and dinosaurs, extant bony fish, amphibians, and birds. In mammals and lizards, perichondral and endochondral ossification proceed more synchronously. One of the most important epigenetic factors in skeletogenesis is mechanical loading caused by muscle contractions which begin in utero or in ovo . It has been previously shown that the stress distributions created perinatally in the chondroepiphysis during human skeletal development can influence the appearance of secondary ossification centres. Using finite element computer models representing bones near birth or hatching, we demonstrate that in vertebrates in which perichondral ossification significantly precedes endochondral ossification, the distribution of mechanical stresses in the ossifying cartilage anlagen tends to inhibit the appearance of secondary ossification centres in the ends of long bones. In models representing vertebrates in which endochondral ossification keeps pace with perichondral apposition, the appearance of secondary centres is promoted. The appearance of secondary centres leads to the formation of bony epiphyses and growth plates, which are most common in mammals and extant lizards. We postulate that genotypic factors influencing the relative speed and extent of perichondral and endochondral ossification interact with mechanical epigenetic factors early in development to account for many of the morphological differences observed in vertebrate skeletons.     

Multiscale modelling and simulation of the deformation and adhesion of a single gecko seta

A 3D multiscale model is presented which describes the adhesion and deformation of a gecko seta. The multiscale approach combines three models at different length scales: at the top level, on the order of several micrometers, a nonlinear finite element beam model is chosen to capture the branched microstructure of the gecko seta. At the intermediate level, on the order of several nanometers, a second finite element model is used to capture the detailed behaviour of the seta tips, the so-called spatulae. At the lowest level, on the order of a few angstroms, a molecular interaction potential is used to describe the van der Waals adhesion forces between spatulae and substrate. Coarse-graining techiques are used to bridge the scale between the model levels. To illustrate and validate the proposed gecko seta model, numerical pull-off simulations are shown and compared to experimental data from the literature.     

The influence of fiber dispersion on the mechanical response of aortic tissues in health and disease: a computational study

Changes in the structural components of aortic tissues have been shown to play a significant role in the pathogenesis of aortic degeneration. Therefore, reliable stress analyses require a suitable and meaningful constitutive model that captures micro-structural changes. As recent data show, in-plane and out-of-plane collagen fiber dispersions vary significantly between healthy and aneurysmatic aortic walls. The aim of this study is to computationally investigate the influence of fiber dispersion on the mechanical response of aortic tissues in health and disease. In particular, the influence of three different fiber dispersions is studied: (i) non-rotationally symmetric dispersion, the most realistic assumption for aortic tissues; (ii) transversely isotropic dispersion, a special case; (iii) perfectly aligned fibers (no dispersion in either plane), another special case. Explicit expressions for the stress and elasticity tensors as needed for the implementation in a finite element code are provided. Three representative numerical examples are studied: planar biaxial extension, inflation of residually stressed and pre-stretched aortic segments and inflation of an idealized abdominal aortic aneurysm (AAA) geometry. For the AAA geometry the case of isotropic dispersion is additionally analyzed. Documented structural and mechanical parameters are taken from human aortas (healthy media/adventitia and AAA). The influence of fiber dispersions upon magnitudes and distributions of stresses and deformations are presented and analyzed. Stresses vary significantly, especially in the AAA case, where material stiffening is significantly influenced by fiber dispersion. The results highlight the need to incorporate the structural differences into finite element simulations to obtain more accurate stress predictions. Additionally, results show the capability of one constitutive model to represent different scenarios of aortic micro-structures allowing future studies of collagen reorientation during disease progression.     

Biomechanical Response of the Root System in Tomato Seedlings under Wind Disturbance

Wind disturbance as a green method can effectively prevent the overgrowth of tomato seedlings, and its mechanism may be related to root system mechanics. This study characterized the biophysical mechanical properties of taproot and lateral roots of tomato seedlings at five seedling ages and seedling substrates with three different moisture content. The corresponding root system-substrate finite element (FE) model was then developed and validated. The study showed that seedling age significantly affected the biomechanical properties of the taproot and lateral roots of the seedlings and that moisture content significantly affected the biomechanical properties of the seedling substrate (p < 0.05). The established FE model was sensitive to wind speed, substrate moisture content, strong seedling index, and seedling age and was robust. The multiple linear regression equations obtained could predict the maximum stress and strain of the root system of tomato seedlings in the wind field. The strong seedling index had the greatest impact on the biomechanical response of the seedling root system during wind disturbance, followed by wind speed. In contrast, seedling age had no significant effect on the biomechanical response of the root system during wind disturbance. In the simulation, no mechanical damage was observed on the tissue of the seedling root system, but there were some strain behaviors. Based on the plant stress resistance, wind disturbance may affect the growth and development of the root system in the later growth stage. In this study, finite element and statistical analysis methods were combined to provide an effective approach for in-depth analysis of the biomechanical mechanisms of wind disturbances that inhibit tomato seedlings’ growth from the root system’s perspective.     

Modelling the mechanical behaviour of pit membranes in bordered pits with respect to cavitation resistance in angiosperms

Background and Aims

Various correlations have been identified between anatomical features of bordered pits in angiosperm xylem and vulnerability to cavitation, suggesting that the mechanical behaviour of the pits may play a role. Theoretical modelling of the membrane behaviour has been undertaken, but it requires input of parameters at the nanoscale level. However, to date, no experimental data have indicated clearly that pit membranes experience strain at high levels during cavitation events.

Methods

Transmission electron microscopy (TEM) was used in order to quantify the pit micromorphology of four tree species that show contrasting differences in vulnerability to cavitation, namely Sorbus aria, Carpinus betulus, Fagus sylvatica and Populus tremula. This allowed anatomical characters to be included in a mechanical model that was based on the Kirchhoff–Love thin plate theory. A mechanistic model was developed that included the geometric features of the pits that could be measured, with the purpose of evaluating the pit membrane strain that results from a pressure difference being applied across the membrane. This approach allowed an assessment to be made of the impact of the geometry of a pit on its mechanical behaviour, and provided an estimate of the impact on air-seeding resistance.

Key Results

The TEM observations showed evidence of residual strains on the pit membranes, thus demonstrating that this membrane may experience a large degree of strain during cavitation. The mechanical modelling revealed the interspecific variability of the strains experienced by the pit membrane, which varied according to the pit geometry and the pressure experienced. The modelling output combined with the TEM observations suggests that cavitation occurs after the pit membrane has been deflected against the pit border. Interspecific variability of the strains experienced was correlated with vulnerability to cavitation. Assuming that air-seeding occurs at a given pit membrane strain, the pressure predicted by the model to achieve this mechanical state corresponds to experimental values of cavitation sensitivity (P₅₀).

Conclusions

The results provide a functional understanding of the importance of pit geometry and pit membrane structure in air-seeding, and thus in vulnerability to cavitation.