Incompressibility of the solid matrix of articular cartilage under high hydrostatic pressures

Effect of dynamic loading on calcium signaling in In-Situ chondrocytes

Chondrocytes respond to mechanical stimuli by increasing their intracellular calcium concentration. The response depends on the cellular environment. Previous studies have investigated chondrocytes under slow strain rates or cells embedded in hydrogels, but the response of chondrocytes in their native environment under physiologically relevant cyclic loads and dynamic hydrostatic pressure has not been studied. This study investigated the calcium signaling response of in-situ chondrocytes under physiological cyclic compressive loads and hydrostatic pressure with varying frequency and load rates. Bovine cartilage explants were stained with a fluorescent calcium indicator dye and subjected to physiologically relevant cyclic loads using a custom-built loading device secured on a confocal/multiphoton microscope. Calcium fluorescence intensities of the cells were tracked and analyzed. Loading groups were compared using one-way ANOVA followed by a post-hoc test with Tukey correction (α = 0.05). The percentage of cells signaling increased in all compressive loading conditions compared to the no-load baseline. The percentage of cells responding under 1 Hz load was significantly greater than the slow ramp and 0.1 Hz group (p < 0.05). The number of compression cycles had no effect on the calcium signaling response (p > 0.05). The width and time between consecutive peaks were not different between different loading conditions (p > 0.05). Calcium signaling of in-situ chondrocytes did not increase under dynamic hydrostatic pressure of magnitudes up to 0.2 MPa at frequencies of 0.5 Hz and 0.05 Hz (p > 0.05). In conclusion, in-situ chondrocytes respond to physiological compressive loads in a strain rate-dependent manner with an increased number of responsive cells and unaltered temporal characteristics.

In vivo human knee varus-valgus loading apparatus for analysis of MRI-based intratissue strain and relaxometry

The diagnosis of early-stage osteoarthritis remains as an unmet challenge in medicine and a roadblock to evaluating the efficacy of disease-modifying treatments. Recent studies demonstrate that unique patterns of intratissue cartilage deformation under cyclic loading can serve as potential biomarkers to detect early disease pathogenesis. However, a workflow to obtain deformation, strain maps, and quantitative MRI metrics due to the loading of articular cartilage in vivo has not been fully developed. In this study, we characterize and demonstrate an apparatus that is capable of applying a varus-valgus load to the human knee in vivo within an MRI environment to enable the measurement of cartilage structure and mechanical function. The apparatus was first tested in a lab environment, then the functionality and utility of the apparatus were examined during varus loading in a clinical 3T MRI system for human imaging. We found that the device enables quantitative MRI metrics for biomechanics and relaxometry data acquisition during joint loading leading to compression of the medial knee compartment. Integration with spiral DENSE MRI during cyclic loading provided time-dependent displacement and strain maps within the tibiofemoral cartilage. The results from these procedures demonstrate that the performance of this loading apparatus meets the design criteria and enables a simple and practical workflow for future studies of clinical cohorts, and the identification and validation of imaging-based biomechanical biomarkers.

The effects of physiological and injurious hydrostatic pressure on murine ex vivo articular and growth plate cartilage explants: an RNAseq study

Introduction

Chondrocytes are continuously exposed to loads placed upon them. Physiological loads are pivotal to the maintenance of articular cartilage health, while abnormal loads contribute to pathological joint degradation. Similarly, the growth plate cartilage is subject to various loads during growth and development. Due to the high-water content of cartilage, hydrostatic pressure is considered one of the main biomechanical influencers on chondrocytes and has been shown to play an important role in the mechano-regulation of cartilage.

Methods

Herein, we conducted RNAseq analysis of ex vivo hip cap (articular), and metatarsal (growth plate) cartilage cultures subjected to physiological (5 MPa) and injurious (50 MPa) hydrostatic pressure, using the Illumina platform (n = 4 replicates).

Results

Several hundreds of genes were shown to be differentially modulated by hydrostatic pressure, with the majority of these changes evidenced in hip cap cartilage cultures (375 significantly upregulated and 322 downregulated in 5 MPa versus control; 1022 upregulated and 724 downregulated in 50 MPa versus control). Conversely, fewer genes were differentially affected by hydrostatic pressure in the metatarsal cultures (5 significantly upregulated and 23 downregulated in 5 MPa versus control; 7 significantly upregulated and 19 downregulated in 50 MPa versus control). Using Gene Ontology annotations for Biological Processes, in the hip cap data we identified a number of pathways that were modulated by both physiological and injurious hydrostatic pressure. Pathways upregulated in response to 50 MPa versus control, included those involved in the generation of precursor metabolites and cellular respiration. Biological processes that were downregulated in this tissue included ossification, connective tissue development, and chondrocyte differentiation.

Discussion

Collectively our data highlights the divergent chondrocyte phenotypes in articular and growth plate cartilage. Further, we show that the magnitude of hydrostatic pressure application has distinct effects on gene expression and biological processes in hip cap cartilage explants. Finally, we identified differential expression of a number of genes that have previously been identified as osteoarthritis risk genes, including Ctsk, and Chadl. Together these data may provide potential genetic targets for future investigations in osteoarthritis research and novel therapeutics.

Human Cartilage Biomechanics: Experimental and Theoretical Approaches towards the Identification of Mechanical Properties in Healthy and Osteoarthritic Conditions

Articular cartilage is a complex connective tissue with the fundamental functions of load bearing, shock absorption and lubrication in joints. However, traumatic events, aging and degenerative pathologies may affect its structural integrity and function, causing pain and long-term disability. Osteoarthritis represents a health issue, which concerns an increasing number of people worldwide. Moreover, it has been observed that this pathology also affects the mechanical behavior of the articular cartilage. To better understand this correlation, the here proposed review analyzes the physiological aspects that influence cartilage microstructure and biomechanics, with a special focus on the pathological changes caused by osteoarthritis. Particularly, the experimental data on human articular cartilage are presented with reference to different techniques adopted for mechanical testing and the related theoretical mechanical models usually applied to articular cartilage are briefly discussed.

Regulation of chondrocyte biosynthetic activity by dynamic hydrostatic pressure: the role of TRP channels

INTRODUCTION

Chondrocytes perceive and respond to mechanical loading as signals that regulate their metabolism. Joint loading exposes chondrocytes to multiple modes of mechanical stress, including hydrostatic pressure; however, the mechanisms by which chondrocytes sense physiologically relevant levels of hydrostatic pressure are not well understood. We hypothesized that hydrostatic pressure is transduced to an intracellular signal through mechanosensitive membrane ion channels of chondrocytes. The goals of this study were to examine the effect of hydrostatic loading on the development of engineered cartilage tissue and the contribution of mechanosensitive ion channels on these hydrostatic loading effects.

METHODS

Using a 3D model of porcine chondrocytes in agarose, we applied specific chemical inhibitors to determine the role of transient receptor potential (TRP) ion channels TRPV1, TRPV4, TRPC3, and TRPC1 in transducing hydrostatic pressure.

RESULTS

Hydrostatic loading caused a frequency and magnitude-dependent decrease in sulfated glycosaminoglycans (S-GAG), without changes in DNA content. Inhibiting TRPC3 and TRPV4 decreased S-GAG content; however, only the inhibition of TRPV1 partially attenuated the hydrostatic loading-induced reduction in S-GAG content.

CONCLUSIONS

Our findings indicate that TRPV1 may serve as a transducer of hydrostatic pressure in chondrocytes, and provide further support for the role of TRPV4 in regulating chondrocyte anabolism, as well as initial evidence implicating TRPC3 in chondrogenesis. These findings add to our further understanding of the chondrocyte "channelome" and suggest that a range of ion channels mediate the transduction of different biophysical stimuli such as hydrostatic pressure, membrane stretch, or osmotic stress.

Hydrostatic pressure prevents chondrocyte differentiation through heterochromatin remodeling

Articular cartilage protects and lubricates joints for smooth motion and transmission of loads. Owing to its high water content, chondrocytes within the cartilage are exposed to high levels of hydrostatic pressure, which has been shown to promote chondrocyte identity through unknown mechanisms. Here, we investigate the effects of hydrostatic pressure on chondrocyte state and behavior, and discover that application of hydrostatic pressure promotes chondrocyte quiescence and prevents maturation towards the hypertrophic state. Mechanistically, hydrostatic pressure reduces the amount of trimethylated H3K9 (K3K9me3)-marked constitutive heterochromatin and concomitantly increases H3K27me3-marked facultative heterochromatin. Reduced levels of H3K9me3 attenuates expression of pre-hypertrophic genes, replication and transcription, thereby reducing replicative stress. Conversely, promoting replicative stress by inhibition of topoisomerase II decreases Sox9 expression, suggesting that it enhances chondrocyte maturation. Our results reveal how hydrostatic pressure triggers chromatin remodeling to impact cell fate and function.

This article has an associated First Person interview with the first author of the paper.

Highlighted Article: Hydrostatic pressure promotes chondrocyte quiescence and immature chondrocyte state through reducing the amount of H3K9me3-marked heterochromatin.

Transient stiffening of cartilage during joint articulation: A microindentation study

As a mechanoactive tissue, articular cartilage undergoes compression and shear on a daily basis. With the advent of high resolution and sensitive mechanical testing methods, such as micro- and nanoindentation, it has become possible to assess changes in small-scale mechanical properties due to compression and shear of the tissue. However, investigations on the changes of these properties before and after joint articulation have been limited. To simulate articular loading of cartilage in the context of human gait, a previously developed bioreactor system was used. Immediately after bioreactor testing, the stiffness was measured using microindentation. Specifically, we investigated whether the mechanical response of the tissue was transient or permanent, dependent on counterface material, and an effect limited to the superficial zone of cartilage. We found that cartilage surface stiffness increases immediately after articular loading and returns to baseline values within 3 hr. Cartilage-on-cartilage stiffening was found to be higher compared to both alumina- and cobalt chromium-on-cartilage stiffening, which were not significantly different from each other. This stiffening response was found to be unique to the superficial zone, as articular loading on cartilage with the superficial zone removed showed no changes in stiffness. The findings of this study suggest that the cartilage superficial zone may adapt its stiffness as a response to articular loading. As the superficial zone is often compromised during the course of osteoarthritic disease, this finding is of clinical relevance, suggesting that the load-bearing function deteriorates over time.

Modelling the inclusion of swelling pressure in a tissue level poroviscoelastic model of cartilage deformation

Swelling pressure in the interstitial fluid within the pores of cartilage tissue is known to have a significant effect on the rheology of cartilage tissue. The swelling pressure varies rapidly within thin regions inside pores known as Debye layers, caused by the presence of fixed charge, as observed in cartilage. Tissue level calculation of cartilage deformation therefore requires resolution of three distinct spatial scales: the Debye lengthscale within individual pores; the lengthscale of an individual pore; and the tissue lengthscale. We use asymptotics to construct a leading order approximation to the swelling pressure within pores, allowing the swelling pressure to be systematically included within a fluid-solid interaction model at the level of pores in cartilage. We then use homogenization to derive tissue level equations for cartilage deformation that are very similar to those governing the finite deformation of a poroviscoelastic body. The equations derived permit the spatial variations in porosity and electric charge that occur in cartilage tissue. Example solutions are then used to confirm the plausibility of the model derived and to consider the impact of fixed charge heterogeneity, illustrating that local fixed charge loss is predicted to increase deformation gradients under confined compression away from, rather than at, the site of loss.

Validation of an In Vivo Medical Image-Based Young Human Lumbar Spine Finite Element Model

Mathematical models of the human spine can be used to investigate spinal biomechanics without the difficulties, limitations, and ethical concerns associated with physical experimentation. Validation of such models is necessary to ensure that the modeled system behavior accurately represents the physics of the actual system. The goal of this work was to validate a medical image-based nonlinear lumbosacral spine finite element model of a healthy 20-yr-old female subject under physiological moments. Range of motion (ROM), facet joint forces (FJF), and intradiscal pressure (IDP) were compared with experimental values and validated finite element models from the literature. The finite element model presented in this work was in good agreement with published experimental studies and finite element models under pure moments. For applied moments of 7.5 N·m, the ROM in flexion–extension, axial rotation, and lateral bending were 39 deg, 16 deg, and 28 deg, respectively. Excellent agreement was observed between the finite element model and experimental data for IDP under pure compressive loading. The predicted FJFs were lower than those of the experimental results and validated finite element models for extension and torsion, likely due to the nondegenerate properties chosen for the intervertebral disks and morphology of the young female spine. This work is the first to validate a computational lumbar spine model of a young female subject. This model will serve as a valuable tool for predicting orthopedic spinal injuries, studying the effect of intervertebral disk replacements using advanced biomaterials, and investigating soft tissue degeneration.

Hip chondrolabral mechanics during activities of daily living: Role of the labrum and interstitial fluid pressurization

Osteoarthritis of the hip can result from mechanical factors, which can be studied using finite element (FE) analysis. FE studies of the hip often assume there is no significant loss of fluid pressurization in the articular cartilage during simulated activities and approximate the material as incompressible and elastic. This study examined the conditions under which interstitial fluid load support remains sustained during physiological motions, as well as the role of the labrum in maintaining fluid load support and the effect of its presence on the solid phase of the surrounding cartilage. We found that dynamic motions of gait and squatting maintained consistent fluid load support between cycles, while static single-leg stance experienced slight fluid depressurization with significant reduction of solid phase stress and strain. Presence of the labrum did not significantly influence fluid load support within the articular cartilage, but prevented deformation at the cartilage edge, leading to lower stress and strain conditions in the cartilage. A morphologically accurate representation of collagen fibril orientation through the thickness of the articular cartilage was not necessary to predict fluid load support. However, comparison with simplified fibril reinforcement underscored the physiological importance. The results of this study demonstrate that an elastic incompressible material approximation is reasonable for modeling a limited number of cyclic motions of gait and squatting without significant loss of accuracy, but is not appropriate for static motions or numerous repeated motions. Additionally, effects seen from removal of the labrum motivate evaluation of labral reattachment strategies in the context of labral repair.

Reactive Constrained Mixtures for Modeling the Solid Matrix of Biological Tissues

This article illustrates our approach for modeling the solid matrix of biological tissues using reactive constrained mixtures. Several examples are presented to highlight the potential benefits of this approach, showing that seemingly disparate fields of mechanics and chemical kinetics are actually closely interrelated and may be elegantly expressed in a unified framework. Thus, constrained mixture models recover classical theories for fibrous materials with bundles oriented in different directions or having different reference configurations, that produce characteristic fiber recruitment patterns under loading. Reactions that exchange mass among various constituents of a mixture may be used to describe tissue growth and remodeling, which may also alter the material's anisotropy. Similarly, reactions that describe the breaking and reforming of bonds may be used to model free energy dissipation in a viscoelastic material. Therefore, this framework is particularly well suited for modeling biological tissues.

An overview of multiphase cartilage mechanical modelling and its role in understanding function and pathology

There is a long history of mathematical and computational modelling with the objective of understanding the mechanisms governing cartilage׳s remarkable mechanical performance. Nonetheless, despite sophisticated modelling development, simulations of cartilage have consistently lagged behind structural knowledge and thus the relationship between structure and function in cartilage is not fully understood. However, in the most recent generation of studies, there is an emerging confluence between our structural knowledge and the structure represented in cartilage modelling. This raises the prospect of further refinement in our understanding of cartilage function and also the initiation of an engineering-level understanding for how structural degradation and ageing relates to cartilage dysfunction and pathology, as well as informing the potential design of prospective interventions. Aimed at researchers entering the field of cartilage modelling, we thus review the basic principles of cartilage models, discussing the underlying physics and assumptions in relatively simple settings, whilst presenting the derivation of relatively parsimonious multiphase cartilage models consistent with our discussions. We proceed to consider modern developments that start aligning the structure captured in the models with observed complexities. This emphasises the challenges associated with constitutive relations, boundary conditions, parameter estimation and validation in cartilage modelling programmes. Consequently, we further detail how both experimental interrogations and modelling developments can be utilised to investigate and reduce such difficulties before summarising how cartilage modelling initiatives may improve our understanding of cartilage ageing, pathology and intervention.

Mechanical properties of normal and osteoarthritic human articular cartilage

Isotropic hyperelastic models have been used to determine the material properties of normal human cartilage, but there remains an incomplete understanding of how these properties may be altered by osteoarthritis. The aims of this study were to (1) measure the material constants of normal and osteoarthritic human knee cartilage using isotropic hyperelastic models; (2) determine whether the material constants correlate with histological measures of structure and/or cartilage tissue damage; and (3) quantify the abilities of two common isotropic hyperelastic material models, the neo-Hookean and Yeoh models, to describe articular cartilage contact force, area, and pressure. Small osteochondral specimens of normal and osteoarthritic condition were retrieved from human cadaveric knees and from the knees of patients undergoing total knee arthroplasty and tested in unconfined compression at loading rates and large strains representative of weight-bearing activity. Articular surface contact area and lateral deformation were measured concurrently and specimen-specific finite element models then were used to determine the hyperelastic material constants. Structural parameters were measured using histological techniques while the severity of cartilage damage was quantified using the OARSI grading scale. The hyperelastic material constants correlated significantly with OARSI grade, indicating that the mechanical properties of cartilage for large strains change with tissue damage. The measurements of contact area described anisotropy of the tissue constituting the superficial zone. The Yeoh model described contact force and pressure more accurately than the neo-Hookean model, whereas both models under-predicted contact area and poorly described the anisotropy of cartilage within the superficial zone. These results identify the limits by which isotropic hyperelastic material models may be used to describe cartilage contact variables. This study provides novel data for the mechanical properties of normal and osteoarthritic human articular cartilage and enhances our ability to model this tissue using simple isotropic hyperelastic materials.

Use of micro-computed tomography to evaluate the effects of exercise on preventing the degeneration of articular cartilage in tail-suspended rats

Space flight has been shown to induce bone loss and muscle atrophy, which could initiate the degeneration of articular cartilage. Countermeasures to prevent bone loss and muscle atrophy have been explored, but few spaceflight or ground-based studies have focused on the effects on cartilage degeneration. In this study, we investigated the effects of exercise on articular cartilage deterioration in tail-suspended rats. Thirty-two female Sprague-Dawley rats were randomly divided into four groups (n=8 in each): tail suspension (TS), tail suspension plus passive motion (TSP), tail suspension plus active exercise (TSA), and control (CON) groups. In the TS, TSP, and TSA groups, the rat hindlimbs were unloaded for 21 days by tail suspension. Next, the cartilage thickness and volume, and the attenuation coefficient of the distal femur were evaluated by micro-computed tomography (μCT). Histological analysis was used to assess the surface integrity of the cartilage, cartilage thickness, and chondrocytes. The results showed that: (1) the cartilage thickness on the distal femur was significantly lower in the TS and TSP groups compared with the CON and TSA groups; (2) the cartilage volume in the TS group was significantly lower compared with the CON, TSA, and TSP groups; and (3) histomorphology showed that the chondrocytes formed clusters where the degree of matrix staining was lower in the TS and TSP groups. There were no significant differences between any of these parameters in the CON and TSA groups. The cartilage thickness measurements obtained by μCT and histomorphology correlated well. In general, tail suspension could induce articular cartilage degeneration, but active exercise was effective in preventing this degeneration in tail-suspended rats.

What quantitative mechanical loading stimulates in vitro cultivation best?

Articular cartilage has limited regeneration capacities. One of the factors that appear to affect the in vitro cultivation of articular cartilage is mechanical stimulation. So far, no combination of parameters has been identified that offers the best results. The goal is to review the literature in search of the best available set of quantitative mechanical stimuli that lead to optimal in vitro cultivation.The databases Scopus and PubMed were used to survey the literature, and strict in- and exclusion criteria were applied regarding the presence of quantitative data. The review was performed by studying the type of loading (hydrostatic compression or direct compression), the loading magnitude, the frequency and the loading regime (duration of the loading) in comparison to quantitative evidence of cartilage quality response (cellular, signaling and mechanical).Thirty-three studies met all criteria of which 8 studied human, 20 bovine, 2 equine, 1 ovine, 1 porcine and 1 canine cells using four different types of cultivated constructs. Six studies investigated loading magnitude within the same setup, three studies the frequency, and seven the loading regime. Nine studies presented mechanical tissue response. The studies suggest that a certain threshold exits for enhanced cartilage in vitro cultivation of explants (>20 % strain and 0.5 Hz), and that chondrocyte-seeded cultivated constructs show best results when loaded with physiological mechanical stimuli. That is a loading pressure between 5-10 MPa and a loading frequency of 1 Hz exerted at intermittent intervals for a period of a week or longer. Critical aspects remain to be answered for translation into in vivo therapies.

Finite element prediction of transchondral stress and strain in the human hip

Cartilage fissures, surface fibrillation, and delamination represent early signs of hip osteoarthritis (OA). This damage may be caused by elevated first principal (most tensile) strain and maximum shear stress. The objectives of this study were to use a population of validated finite element (FE) models of normal human hips to evaluate the required mesh for converged predictions of cartilage tensile strain and shear stress, to assess the sensitivity to cartilage constitutive assumptions, and to determine the patterns of transchondral stress and strain that occur during activities of daily living. Five specimen-specific FE models were evaluated using three constitutive models for articular cartilage: quasilinear neo-Hookean, nonlinear Veronda Westmann, and tension-compression nonlinear ellipsoidal fiber distribution (EFD). Transchondral predictions of maximum shear stress and first principal strain were determined. Mesh convergence analysis demonstrated that five trilinear elements were adequate through the depth of the cartilage for precise predictions. The EFD model had the stiffest response with increasing strains, predicting the largest peak stresses and smallest peak strains. Conversely, the neo-Hookean model predicted the smallest peak stresses and largest peak strains. Models with neo-Hookean cartilage predicted smaller transchondral gradients of maximum shear stress than those with Veronda Westmann and EFD models. For FE models with EFD cartilage, the anterolateral region of the acetabulum had larger peak maximum shear stress and first principal strain than all other anatomical regions, consistent with observations of cartilage damage in disease. Results demonstrate that tension-compression nonlinearity of a continuous fiber distribution exhibiting strain induced anisotropy incorporates important features that have large effects on predictions of transchondral stress and strain. This population of normal hips provides baseline data for future comparisons to pathomorphologic hips. This approach can be used to evaluate these and other mechanical variables in the human hip and their potential role in the pathogenesis of osteoarthritis (OA).

Computational modeling of chemical reactions and interstitial growth and remodeling involving charged solutes and solid-bound molecules

Mechanobiological processes are rooted in mechanics and chemistry, and such processes may be modeled in a framework that couples their governing equations starting from fundamental principles. In many biological applications, the reactants and products of chemical reactions may be electrically charged, and these charge effects may produce driving forces and constraints that significantly influence outcomes. In this study, a novel formulation and computational implementation are presented for modeling chemical reactions in biological tissues that involve charged solutes and solid-bound molecules within a deformable porous hydrated solid matrix, coupling mechanics with chemistry while accounting for electric charges. The deposition or removal of solid-bound molecules contributes to the growth and remodeling of the solid matrix; in particular, volumetric growth may be driven by Donnan osmotic swelling, resulting from charged molecular species fixed to the solid matrix. This formulation incorporates the state of strain as a state variable in the production rate of chemical reactions, explicitly tying chemistry with mechanics for the purpose of modeling mechanobiology. To achieve these objectives, this treatment identifies the specific theoretical and computational challenges faced in modeling complex systems of interacting neutral and charged constituents while accommodating any number of simultaneous reactions where reactants and products may be modeled explicitly or implicitly. Several finite element verification problems are shown to agree with closed-form analytical solutions. An illustrative tissue engineering analysis demonstrates tissue growth and swelling resulting from the deposition of chondroitin sulfate, a charged solid-bound molecular species. This implementation is released in the open-source program FEBio ( www.febio.org ). The availability of this framework may be particularly beneficial to optimizing tissue engineering culture systems by examining the influence of nutrient availability on the evolution of inhomogeneous tissue composition and mechanical properties, the evolution of construct dimensions with growth, the influence of solute and solid matrix electric charge on the transport of cytokines, the influence of binding kinetics on transport, the influence of loading on binding kinetics, and the differential growth response to dynamically loaded versus free-swelling culture conditions.

Deciphering mechanical regulation of chondrogenesis in fibrin-polyurethane composite scaffolds enriched with human mesenchymal stem cells: a dual computational and experimental approach

Fibrin-polyurethane composite scaffolds support chondrogenesis of human mesenchymal stem cells (hMSCs) derived from bone marrow and due to their robust mechanical properties allow mechanical loading in dynamic bioreactors, which has been shown to increase the chondrogenic differentiation of MSCs through the transforming growth factor beta pathway. The aim of this study was to use the finite element method, mechanical testing, and dynamic in vitro cell culture experiments on hMSC-enriched fibrin-polyurethane composite scaffolds to quantitatively decipher the mechanoregulation of chondrogenesis within these constructs. The study identified compressive principal strains as the key regulator of chondrogenesis in the constructs. Although dynamic uniaxial compression did not induce chondrogenesis, multiaxial loading by combined application of dynamic compression and interfacial shear induced significant chondrogenesis at locations where all the three principal strains were compressive and had a minimum magnitude of 10%. In contrast, no direct correlation was identified between the level of pore fluid velocity and chondrogenesis. Due to the high permeability of the constructs, the pore fluid pressures could not be increased sufficiently by mechanical loading, and instead, chondrogenesis was induced by triaxial compressive deformations of the matrix with a minimum magnitude of 10%. Thus, it can be concluded that dynamic triaxial compressive deformations of the matrix is sufficient to induce chondrogenesis in a threshold-dependent manner, even where the pore fluid pressure is negligible.

Composite three-dimensional woven scaffolds with interpenetrating network hydrogels to create functional synthetic articular cartilage

The development of synthetic biomaterials that possess mechanical properties that mimic those of native tissues remains an important challenge to the field of materials. In particular, articular cartilage is a complex nonlinear, viscoelastic, and anisotropic material that exhibits a very low coefficient of friction, allowing it to withstand millions of cycles of joint loading over decades of wear. Here we show that a three-dimensionally woven fiber scaffold that is infiltrated with an interpenetrating network hydrogel can provide a functional biomaterial that provides the load-bearing and tribological properties of native cartilage. An interpenetrating dual-network "tough-gel" consisting of alginate and polyacrylamide was infused into a porous three-dimensionally woven poly(ε-caprolactone) fiber scaffold, providing a versatile fiber-reinforced composite structure as a potential acellular or cell-based replacement for cartilage repair.

Cyclic hydrostatic pressure promotes a stable cartilage phenotype and enhances the functional development of cartilaginous grafts engineered using multipotent stromal cells isolated from bone marrow and infrapatellar fat pad

The objective of this study was to investigate how joint specific biomechanical loading influences the functional development and phenotypic stability of cartilage grafts engineered in vitro using stem/progenitor cells isolated from different source tissues. Porcine bone marrow derived multipotent stromal cells (BMSCs) and infrapatellar fat pad derived multipotent stromal cells (FPSCs) were seeded in agarose hydrogels and cultured in chondrogenic medium, while simultaneously subjected to 10MPa of cyclic hydrostatic pressure (HP). To mimic the endochondral phenotype observed in vivo with cartilaginous tissues engineered using BMSCs, the culture media was additionally supplemented with hypertrophic factors, while the loss of phenotype observed in vivo with FPSCs was induced by withdrawing transforming growth factor (TGF)-β3 from the media. The application of HP was found to enhance the functional development of cartilaginous tissues engineered using both BMSCs and FPSCs. In addition, HP was found to suppress calcification of tissues engineered using BMSCs cultured in chondrogenic conditions and acted to maintain a chondrogenic phenotype in cartilaginous grafts engineered using FPSCs. The results of this study point to the importance of in vivo specific mechanical cues for determining the terminal phenotype of chondrogenically primed multipotent stromal cells. Furthermore, demonstrating that stem or progenitor cells will appropriately differentiate in response to such biophysical cues might also be considered as an additional functional assay for evaluating their therapeutic potential.

Modeling sample/patient-specific structural and diffusional responses of cartilage using DT-MRI

We propose a new 3D biphasic constitutive model designed to incorporate structural data on the sample/patient-specific collagen fiber network. The finite strain model focuses on the load-bearing morphology, that is, an incompressible, poroelastic solid matrix, reinforced by an inhomogeneous, dispersed fiber fabric, saturated with an incompressible fluid at constant electrolytic conditions residing in strain-dependent pores of the collagen-proteoglycan solid matrix. In addition, the fiber network of the solid influences the fluid permeability and an intrafibrillar portion that cannot be 'squeezed out' from the tissue. We implement the model into a finite element code. To demonstrate the utility of our proposed modeling approach, we test two hypotheses by simulating an indentation experiment for a human tissue sample. The simulations use ultra-high field diffusion tensor magnetic resonance imaging that was performed on the tissue sample. We test the following hypotheses: (i) the through-thickness structural arrangement of the collagen fiber network adjusts fluid permeation to maintain fluid pressure (Biomech. Model. Mechanobiol. 7:367-378, 2008); and (ii) the inhomogeneity of mechanical properties through the cartilage thickness acts to maintain fluid pressure at the articular surface (J. Biomech. Eng. 125:569-577, 2003). For the tissue sample investigated, both through-thickness inhomogeneities of the collagen fiber distribution and of the material properties serve to influence the interstitial fluid pressure distribution and maintain fluid pressure underneath the indenter at the cartilage surface. Tissue inhomogeneity appears to have a larger effect on fluid pressure retention in this tissue sample and on the advantageous pressure distribution.

Strain-dependent oxidant release in articular cartilage originates from mitochondria

Mechanical loading is essential for articular cartilage homeostasis and plays a central role in the cartilage pathology, yet the mechanotransduction processes that underlie these effects remain unclear. Previously, we showed that lethal amounts of reactive oxygen species (ROS) were liberated from the mitochondria in response to mechanical insult and that chondrocyte deformation may be a source of ROS. To this end, we hypothesized that mechanically induced mitochondrial ROS is related to the magnitude of cartilage deformation. To test this, we measured axial tissue strains in cartilage explants subjected to semi-confined compressive stresses of 0, 0.05, 0.1, 0.25, 0.5, or 1.0 MPa. The presence of ROS was then determined by confocal imaging with dihydroethidium, an oxidant sensitive fluorescent probe. Our results indicated that ROS levels increased linearly relative to the magnitude of axial strains (r(2) = 0.87, p < 0.05), and significant cell death was observed at strains >40%. By contrast, hydrostatic stress, which causes minimal tissue strain, had no significant effect. Cell-permeable superoxide dismutase mimetic Mn(III)tetrakis (1-methyl-4-pyridyl) porphyrin pentachloride significantly decreased ROS levels at 0.5 and 0.25 MPa. Electron transport chain inhibitor, rotenone, and cytoskeletal inhibitor, cytochalasin B, significantly decreased ROS levels at 0.25 MPa. Our findings strongly suggest that ROS and mitochondrial oxidants contribute to cartilage mechanobiology.

Mechanical regulation of chondrogenesis

Mechanical factors play a crucial role in the development of articular cartilage in vivo. In this regard, tissue engineers have sought to leverage native mechanotransduction pathways to enhance in vitro stem cell-based cartilage repair strategies. However, a thorough understanding of how individual mechanical factors influence stem cell fate is needed to predictably and effectively utilize this strategy of mechanically-induced chondrogenesis. This article summarizes some of the latest findings on mechanically stimulated chondrogenesis, highlighting several new areas of interest, such as the effects of mechanical stimulation on matrix maintenance and terminal differentiation, as well as the use of multifactorial bioreactors. Additionally, the roles of individual biophysical factors, such as hydrostatic or osmotic pressure, are examined in light of their potential to induce mesenchymal stem cell chondrogenesis. An improved understanding of biomechanically-driven tissue development and maturation of stem cell-based cartilage replacements will hopefully lead to the development of cell-based therapies for cartilage degeneration and disease.

Synovial fluid concentrations and relative potency of interleukin-1 alpha and beta in cartilage and meniscus degradation

Cartilage degeneration with osteoarthritis (OA) is believed to involve the activities of interleukin-1 (IL-1), which exists as alpha and beta isoforms. The goal of this study was to measure the concentrations of both isoforms of IL-1 in the synovial fluid of normal and spontaneously osteoarthritic porcine knees, and to test the hypothesis that physiologic concentrations of IL-1α and IL-1β exhibit different potencies in activating calcium signaling, the production of matrix metalloproteinases and nitric oxide, and the loss of proteoglycans and tissue mechanical properties in cartilage and meniscus. Median concentrations of IL-1α were 0.043 ng/ml with mild OA and 0.288 ng/ml with moderate OA, whereas IL-1β concentrations were 0.109 ng/ml with mild OA and 0.122 ng/ml with moderate OA. Both isoforms induced calcium signaling in chondrocytes and meniscal cells at all concentrations. Overall, cartilage and meniscus catabolism was significantly more sensitive to IL-1α than IL-1β at concentrations of 1 ng/ml or less, while few differences were observed between the two forms at 10 ng/ml. These data provide a range of physiologic IL-1 concentrations that can serve as a framework for the comparison of various in vitro studies, as well as providing further insight for the development of anti-cytokine therapies for OA.

Biomechanical factors in osteoarthritis

Biomechanical factors play an important role in the health of diarthrodial joints. Altered joint loading - associated to obesity, malalignment, trauma or joint instability - is a critical risk factor for joint degeneration, whereas exercise and weight loss have generally been shown to promote beneficial effects for osteoarthritic joints. The mechanisms by which mechanical stress alters the physiology or pathophysiology of articular cartilage or other joint tissues likely involve complex interactions with genetic and molecular influences, particularly local or systemic inflammation secondary to injury or obesity. Chondrocytes perceive physical signals from their environment using a variety of mechanisms, including ion channels, integrin-mediated connections to the extracellular matrix that involve membrane, cytoskeletal and intracellular deformation. An improved understanding of the biophysical and molecular pathways involved in chondrocyte mechanotransduction can provide insight into the development of novel therapeutic approaches for osteoarthritis.

The inhibition by interleukin 1 of MSC chondrogenesis and the development of biomechanical properties in biomimetic 3D woven PCL scaffolds

Tissue-engineered constructs designed to treat large cartilage defects or osteoarthritic lesions may be exposed to significant mechanical loading as well as an inflammatory environment upon implantation in an injured or diseased joint. We hypothesized that a three-dimensionally (3D) woven poly(ε-caprolactone) (PCL) scaffold seeded with bone marrow-derived mesenchymal stem cells (MSCs) would provide biomimetic mechanical properties in early stages of in vitro culture as the MSCs assembled a functional, cartilaginous extracellular matrix (ECM). We also hypothesized that these properties would be maintained even in the presence of the pro-inflammatory cytokine interleukin-1 (IL-1), which is found at high levels in injured or diseased joints. MSC-seeded 3D woven scaffolds cultured in chondrogenic conditions synthesized a functional ECM rich in collagen and proteoglycan content, reaching an aggregate modulus of ~0.75 MPa within 14 days of culture. However, the presence of pathophysiologically relevant levels of IL-1 limited matrix accumulation and inhibited any increase in mechanical properties over baseline values. On the other hand, the mechanical properties of constructs cultured in chondrogenic conditions for 4 weeks prior to IL-1 exposure were protected from deleterious effects of the cytokine. These findings demonstrate that IL-1 significantly inhibits the chondrogenic development and maturation of MSC-seeded constructs; however, the overall mechanical functionality of the engineered tissue can be preserved through the use of a 3D woven scaffold designed to recreate the mechanical properties of native articular cartilage.

Diurnal variations in articular cartilage thickness and strain in the human knee

Due to the biphasic viscoelastic nature of cartilage, joint loading may result in deformations that require times on the order of hours to fully recover. Thus, cartilaginous tissues may exhibit cumulative strain over the course of each day. The goal of this study was to assess the magnitude and spatial distribution of strain in the articular cartilage of the knee with daily activity. Magnetic resonance (MR) images of 10 asymptomatic subjects (six males and four females) with mean age of 29 years were obtained at 8:00 AM and 4:00 PM on the same day using a 3T magnet. These images were used to create 3D models of the femur, tibia, and patella from which cartilage thickness distributions were quantified. Cartilage thickness generally decreased from AM to PM in all areas except the patellofemoral groove and was associated with significant compressive strains in the medial condyle and tibial plateau. From AM to PM, cartilage of the medial tibial plateau exhibited a compressive strain of -5.1±1.0% (mean±SEM) averaged over all locations, while strains in the lateral plateau were slightly lower (-3.1±0.6%). Femoral cartilage showed an average strain of -1.9±0.6%. The findings of this study show that human knee cartilage undergoes diurnal changes in strain that vary with site in the joint. Since abnormal joint loading can be detrimental to cartilage homeostasis, these data provide a baseline for future studies investigating the effects of altered biomechanics on diurnal cartilage strains and cartilage physiology.

Depth-dependent anisotropy of the micromechanical properties of the extracellular and pericellular matrices of articular cartilage evaluated via atomic force microscopy

The extracellular matrix (ECM) of articular cartilage is structurally and mechanically inhomogeneous and anisotropic, exhibiting variations in composition, collagen fiber architecture, and pericellular matrix (PCM) morphology among the different zones (superficial, middle, and deep). Joint loading exposes chondrocytes to a complex biomechanical environment, as the microscale mechanical environment of the chondrocyte depends on the relative properties of its PCM and local ECM. ECM anisotropy and chondrocyte deformation are influenced by the split-line direction, the preferred collagen fiber orientation parallel to the articular surface. While previous studies have demonstrated that cartilage macroscale properties vary with depth and the direction of loading relative to the split-line direction, the potential anisotropic behavior of the ECM and PCM at the microscale has yet to be examined. The goal of this study was to characterize the depth and directional dependence of the microscale biomechanical properties of porcine cartilage ECM and PCM in situ. Cartilage was cryosectioned to generate samples oriented parallel and perpendicular to the split-line direction and normal to the articular surface. Atomic force microscopy (AFM)-based stiffness mapping was utilized to measure ECM and PCM microscale elastic properties in all three directions within each zone. Distinct anisotropy in ECM elastic moduli was observed in the superficial and deep zones, while the middle zone exhibited subtle anisotropy. PCM elastic moduli exhibited zonal uniformity with depth and directional dependence when pooled across the zones. These findings provide new evidence for mechanical inhomogeneity and anisotropy at the microscale in articular cartilage.

Reconsideration on the use of elastic models to predict the instantaneous load response of the knee joint

Fluid pressurization in articular cartilages and menisci plays an important role in the mechanical function of the knee joint. However, fluid pressure has not been incorporated in previous finite element modelling of the knee, instead elastic models of the knee are widely used. It is believed that an elastic model can be used to predict the instantaneous load response of the knee as long as large effective moduli for the cartilaginous tissues are used. In the present study, the instantaneous response of the knee was obtained from a proposed model including fluid pressure and fibril reinforcement in the cartilaginous tissues. The results were then compared with those obtained from an elastic model using the effective modulus method. It was found that the deformations and contact pressures predicted by the two models were substantially different. An unconfined compression of a tissue disc was used to help understand the issue. It was clear that a full equivalence between the instantaneous and elastic responses could not be established even for this simple case. A partial equivalence in stress could be conditionally established for a given unconfined compression, but it was not valid for a different magnitude of compression. The instantaneous deformation of the intact tissues in the joint was even more difficult to determine using the effective modulus method. The results thus obtained were further compromised because of the uncertainty over the choice of effective modulus. The tissue non-linearity was one of the factors that made it difficult to establish the equivalence in stress. The pressurized tissue behaved differently from a solid material when non-linear fibril reinforcement was presented. The direct prediction of the instantaneous response using the proposed poromechanical model had the advantage of determining the fluid pressure and incompressible deformation.

Engineered cartilage using primary chondrocytes cultured in a porous cartilage-derived matrix

AIM

To investigate the cell growth, matrix accumulation and mechanical properties of neocartilage formed by human or porcine articular chondrocytes on a porous, porcine cartilage-derived matrix (CDM) for use in cartilage tissue engineering.

MATERIALS & METHODS

We examined the physical properties, cell infiltration and matrix accumulation in different formulations of CDM and selected a CDM made of homogenized cartilage slurry as an appropriate scaffold for long-term culture of human and porcine articular chondrocytes.

RESULTS

The CDM scaffold supported growth and proliferation of both human and porcine chondrocytes. Histology and immunohistochemistry showed abundant cartilage-specific macromolecule deposition at day 28. Human chondrocytes migrated throughout the CDM, showing a relatively homogeneous distribution of new tissue accumulation, whereas porcine chondrocytes tended to form a proteoglycan-rich layer primarily on the surfaces of the scaffold. Human chondrocyte-seeded scaffolds had a significantly lower aggregate modulus and hydraulic permeability at day 28.

CONCLUSIONS

These data show that a scaffold derived from native porcine articular cartilage can support neocartilage formation in the absence of exogenous growth factors. The overall characteristics and properties of the constructs depend on factors such as the concentration of CDM used, the porosity of the scaffold, and the species of chondrocytes.

DT-MRI based computation of collagen fiber deformation in human articular cartilage: a feasibility study

Accurate techniques for simulating the deformation of soft biological tissues are an increasingly valuable tool in many areas of biomechanical analysis and medical image computing. To model the complex morphology and response of articular cartilage, a hyperviscoelastic (dispersed) fiber-reinforced constitutive model is employed to complete two specimen-specific finite element (FE) simulations of an indentation experiment, with and without considering fiber dispersion. Ultra-high field Diffusion Tensor Magnetic Resonance Imaging (17.6 T DT-MRI) is performed on a specimen of human articular cartilage before and after indentation to approximately 20% compression. Based on this DT-MRI data, we detail a novel FE approach to determine the geometry (edge detection from first eigenvalue), the meshing (semi-automated smoothing of DTI measurement voxels), and the fiber structural input (estimated principal fiber direction and dispersion). The global and fiber fabric deformations of both the un-dispersed and dispersed fiber models provide a satisfactory match to that estimated experimentally. In both simulations, the fiber fabric in the superficial and middle zones becomes more aligned with the articular surface, although the dispersed model appears more consistent with the literature. In the future, a multi-disciplinary combination of DT-MRI and numerical simulation will allow the functional state of articular cartilage to be determined in vivo.

The effects of osmotic stress on the structure and function of the cell nucleus

Osmotic stress is a potent regulator of the normal function of cells that are exposed to osmotically active environments under physiologic or pathologic conditions. The ability of cells to alter gene expression and metabolic activity in response to changes in the osmotic environment provides an additional regulatory mechanism for a diverse array of tissues and organs in the human body. In addition to the activation of various osmotically- or volume-activated ion channels, osmotic stress may also act on the genome via a direct biophysical pathway. Changes in extracellular osmolality alter cell volume, and therefore, the concentration of intracellular macromolecules. In turn, intracellular macromolecule concentration is a key physical parameter affecting the spatial organization and pressurization of the nucleus. Hyper-osmotic stress shrinks the nucleus and causes it to assume a convoluted shape, whereas hypo-osmotic stress swells the nucleus to a size that is limited by stretch of the nuclear lamina and induces a smooth, round shape of the nucleus. These behaviors are consistent with a model of the nucleus as a charged core/shell structure pressurized by uneven partition of macromolecules between the nucleoplasm and the cytoplasm. These osmotically-induced alterations in the internal structure and arrangement of chromatin, as well as potential changes in the nuclear membrane and pores are hypothesized to influence gene transcription and/or nucleocytoplasmic transport. A further understanding of the biophysical and biochemical mechanisms involved in these processes would have important ramifications for a range of fields including differentiation, migration, mechanotransduction, DNA repair, and tumorigenesis.

A Phenomenological Approach Toward Patient-Specific Computational Modeling of Articular Cartilage Including Collagen Fiber Tracking

To model the cartilage morphology and the material response, a phenomenological and patient-specific simulation approach incorporating the collagen fiber fabric is proposed. Cartilage tissue response is nearly isochoric and time-dependent under physiological pressure levels. Hence, a viscoelastic constitutive model capable of reproducing finite strains is employed, while the time-dependent deformation change is purely isochoric. The model incorporates seven material parameters, which all have a physical interpretation. To calibrate the model and facilitate further analysis, five human cartilage specimens underwent a number of tests. A series of magnetic resonance imaging (MRI) sequences is taken, next the cartilage surface is imaged, then mechanical indentation tests are completed at 2–7 different locations per sample, resulting in force/displacement data over time, and finally, the underlying bone surface is imaged. Imaging and mechanical testing are performed with a custom-built robotics-based testing device. Stereo reconstruction of the cartilage and subchondral bone surface is employed, which, together with the proposed constitutive model, led to specimen-specific finite element simulations of the mechanical indentation tests. The force-time response of 23 such indentation experiment simulations is optimized to estimate the mean material parameters and corresponding standard deviations. The model is capable of reproducing the deformation behavior of human articular cartilage in the physiological loading domain, as demonstrated by the good agreement between the experiment and numerical results (R2=0.95±0.03, mean±standard deviation of force-time response for 23 indentation tests). To address validation, a sevenfold cross-validation experiment is performed on the 21 experiments representing healthy cartilage. To quantify the predictive error, the mean of the absolute force differences and Pearson’s correlation coefficient are both calculated. Deviations in the mean absolute difference, normalized by the peak force, range from 4% to 90%, with 40±25%(M±SD). The correlation coefficients across all predictions have a minimum of 0.939, and a maximum of 0.993 with 0.975±0.013(M±SD), which demonstrates an excellent match of the decay characteristics. A novel feature of the proposed method is 3D sample-specific numerical tracking of the fiber fabric deformation under general loading. This feature is demonstrated by comparing the estimated fiber fabric deformation with recently published experimental data determined by diffusion tensor MRI. The proposed approach is efficient enough to enable large-scale 3D contact simulations of knee joint loading in simulations with accurate joint geometries.

Effects of temporal hydrostatic pressure on tissue-engineered bovine articular cartilage constructs

The objective of this study was to determine the effects of temporal hydrostatic pressure (HP) on the properties of scaffoldless bovine articular cartilage constructs. The study was organized in three phases: First, a suitable control for HP application was identified. Second, 10 MPa static HP was applied at three different timepoints (6-10 days, 10-14 days, and 14-18 days) to identify a window in construct development when HP application would be most beneficial. Third, the temporal effects of 10-14-day static HP application, as determined in phase II, were assessed at 2, 4, and 8 weeks. Compressive and tensile mechanical properties, GAG and collagen content, histology for GAG and collagen, and immunohistochemistry for collagen types I and II were assessed. When a culture control identified in phase I was used in phase II, HP application from 10 to 14 days resulted in a significant 1.4-fold increase in aggregate modulus, accompanied by an increase in GAG content, while HP application at all timepoints enhanced tensile properties and collagen content. In phase III, HP had an immediate effect on GAG content, collagen content, and compressive stiffness, while there was a delayed increase in tensile stiffness. The enhanced tensile stiffness was still present at 8 weeks. For the first time, this study examined the immediate and long-term effects of HP on biomechanical properties, and demonstrated that HP has an optimal application time in construct development. These findings are exciting as HP stimulation allowed for the formation of robust tissue-engineered cartilage; for example, 10 MPa static HP resulted in an aggregate modulus of 273 +/- 123 kPa, a Young's modulus of 1.6 +/- 0.4 MPa, a GAG/wet weight of 6.1 +/- 1.4%, and a collagen/wet weight of 10.6 +/- 2.4% at 4 weeks.

Hydrostatic pressure in articular cartilage tissue engineering: from chondrocytes to tissue regeneration

Cartilage has a poor intrinsic healing response, and neither the innate healing response nor current clinical treatments can restore its function. Therefore, articular cartilage tissue engineering is a promising approach for the regeneration of damaged tissue. Because cartilage is exposed to mechanical forces during joint loading, many tissue engineering strategies use exogenous stimuli to enhance the biochemical or biomechanical properties of the engineered tissue. Hydrostatic pressure (HP) is emerging as arguably one of the most important mechanical stimuli for cartilage, although no optimal treatment has been established across all culture systems. Therefore, this review evaluates prior studies on articular cartilage involving the use of HP, with a particular emphasis on the treatments that appear promising for use in future studies. Additionally, this review addresses HP bioreactor design, chondroprotective effects of HP, the use of HP for chondrogenic differentiation, the effects of high pressures, and HP mechanotransduction.

Two-dimensional strain fields on the cross-section of the bovine humeral head under contact loading

The objective of this study was to provide a detailed experimental assessment of the two-dimensional cartilage strain distribution on the cross-section of immature and mature bovine humeral heads subjected to contact loading at a relatively rapid physiological loading rate. Six immature and six mature humeral head specimens were loaded against glass and strains were measured at the end of a 5s loading ramp on the textured articular cross-section using digital image correlation analysis. The primary findings indicate that elevated tensile and compressive strains occur near the articular surface, around the center of the contact region. Few qualitative or quantitative differences were observed between mature and immature joints. Under an average contact stress of approximately 1.7 MPa, the peak compressive strains averaged -0.131+/-0.048, which was significantly less than the relative change in cartilage thickness, -0.104+/-0.032 (p<0.05). The peak tensile strains were significantly smaller in magnitude, at 0.0325+/-0.013. These experimental findings differ from a previous finite element analysis of articular contact, which predicted peak strains at the cartilage-bone interface even when accounting for the porous-hydrated nature of the tissue, its depth-dependent inhomogeneity, and the disparity between its tensile and compressive properties. These experimental results yield new insights into the local mechanical environment of the tissue and cells, and suggest that further refinements are needed in the modeling of contacting articular layers.

An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

Finite element models for hydrated soft biological tissue are numerous but often exhibit certain essential deficiencies concerning the reproduction of relevant mechanical and electro-chemical responses. As a matter of fact, singlephasic models can never predict the interstitial fluid flow or related effects like osmosis. Quite a few models have more than one constituent, but are often restricted to the small-strain domain, are not capable of capturing the intrinsic viscoelasticity of the solid skeleton, or do not account for a collagen fibre reinforcement. It is the goal of this contribution to overcome these drawbacks and to present a thermodynamically consistent model, which is formulated in a very general way in order to reproduce the behaviour of almost any charged hydrated tissue. Herein, the Theory of Porous Media (TPM) is applied in combination with polyconvex Ogden-type material laws describing the anisotropic and intrinsically viscoelastic behaviour of the solid matrix on the basis of a generalised Maxwell model. Moreover, other features like the deformation-dependent permeability, the possibility to include inhomogeneities like varying fibre alignment and behaviour, or osmotic effects based on the simplifying assumption of Lanir are also included. Finally, the human intervertebral disc is chosen as a representative for complex soft biological tissue behaviour. In this regard, two numerical examples will be presented with focus on the viscoelastic and osmotic capacity of the model.

Synergistic and additive effects of hydrostatic pressure and growth factors on tissue formation

Background

Hydrostatic pressure (HP) is a significant factor in the function of many tissues, including cartilage, knee meniscus, temporomandibular joint disc, intervertebral disc, bone, bladder, and vasculature. Though studies have been performed in assessing the role of HP in tissue biochemistry, to the best of our knowledge, no studies have demonstrated enhanced mechanical properties from HP application in any tissue.

Methodology/Principal Findings

The objective of this study was to determine the effects of hydrostatic pressure (HP), with and without growth factors, on the biomechanical and biochemical properties of engineered articular cartilage constructs, using a two-phased approach. In phase I, a 3×3 full-factorial design of HP magnitude (1, 5, 10 MPa) and frequency (0, 0.1, 1 Hz) was used, and the best two treatments were selected for use in phase II. Static HP at 5 MPa and 10 MPa resulted in significant 95% and 96% increases, respectively, in aggregate modulus (H_A), with corresponding increases in GAG content. These regimens also resulted in significant 101% and 92% increases in Young's modulus (E_Y), with corresponding increases in collagen content. Phase II employed a 3×3 full-factorial design of HP (no HP, 5 MPa static, 10 MPa static) and growth factor application (no GF, BMP-2+IGF-I, TGF-β1). The combination of 10 MPa static HP and TGF-β1 treatment had an additive effect on both H_A and E_Y, as well as a synergistic effect on collagen content. This group demonstrated a 164% increase in H_A, a 231% increase in E_Y, an 85% increase in GAG/wet weight (WW), and a 173% increase in collagen/WW, relative to control.

Conclusions/Significance

To our knowledge, this is the first study to demonstrate increases in the biomechanical properties of tissue from pure HP application, using a cartilage model. Furthermore, it is the only study to demonstrate additive or synergistic effects between HP and growth factors on tissue functional properties. These findings are exciting as coupling HP stimulation with growth factor application has allowed for the formation of tissue engineered constructs with biomechanical and biochemical properties spanning native tissue values.

Equivalence between short-time biphasic and incompressible elastic material responses

Porous-permeable tissues have often been modeled using porous media theories such as the biphasic theory. This study examines the equivalence of the short-time biphasic and incompressible elastic responses for arbitrary deformations and constitutive relations from first principles. This equivalence is illustrated in problems of unconfined compression of a disk, and of articular contact under finite deformation, using two different constitutive relations for the solid matrix of cartilage, one of which accounts for the large disparity observed between the tensile and compressive moduli in this tissue. Demonstrating this equivalence under general conditions provides a rationale for using available finite element codes for incompressible elastic materials as a practical substitute for biphasic analyses, so long as only the short-time biphasic response is sought. In practice, an incompressible elastic analysis is representative of a biphasic analysis over the short-term response deltat<<Delta(2) / //parallelC(4)//K//, where Delta is a characteristic dimension, C(4) is the elasticity tensor, and K is the hydraulic permeability tensor of the solid matrix. Certain notes of caution are provided with regard to implementation issues, particularly when finite element formulations of incompressible elasticity employ an uncoupled strain energy function consisting of additive deviatoric and volumetric components.

On the theory of reactive mixtures for modeling biological growth

Mixture theory, which can combine continuum theories for the motion and deformation of solids and fluids with general principles of chemistry, is well suited for modeling the complex responses of biological tissues, including tissue growth and remodeling, tissue engineering, mechanobiology of cells and a variety of other active processes. A comprehensive presentation of the equations of reactive mixtures of charged solid and fluid constituents is lacking in the biomechanics literature. This study provides the conservation laws and entropy inequality, as well as interface jump conditions, for reactive mixtures consisting of a constrained solid mixture and multiple fluid constituents. The constituents are intrinsically incompressible and may carry an electrical charge. The interface jump condition on the mass flux of individual constituents is shown to define a surface growth equation, which predicts deposition or removal of material points from the solid matrix, complementing the description of volume growth described by the conservation of mass. A formulation is proposed for the reference configuration of a body whose material point set varies with time. State variables are defined which can account for solid matrix volume growth and remodeling. Constitutive constraints are provided on the stresses and momentum supplies of the various constituents, as well as the interface jump conditions for the electrochemical potential of the fluids. Simplifications appropriate for biological tissues are also proposed, which help reduce the governing equations into a more practical format. It is shown that explicit mechanisms of growth-induced residual stresses can be predicted in this framework.

Constitutive Modeling of Cartilaginous Tissues: A Review

An important and longstanding field of research in orthopedic biomechanics is the elucidation and mathematical modeling of the mechanical response of cartilaginous tissues. Traditional approaches have treated such tissues as continua and have described their mechanical response in terms of macroscopic models borrowed from solid mechanics. The most important of such models are the biphasic and single-phase viscoelastic models, and the many variations thereof. These models have reached a high level of maturity and have been successful in describing a wide range of phenomena. An alternative approach that has received considerable recent interest, both in orthopedic biomechanics and in other fields, is the description of mechanical response based on consideration of a tissue's structure—so-called microstructural modeling. Examples of microstructurally based approaches include fibril-reinforced biphasic models and homogenization approaches. A review of both macroscopic and microstructural constitutive models is given in the present work.