A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis,computational aspects and applications

Cartilage is a multi-phase material composed of fluid and electrolytes (68–85% by wet weight), proteoglycans (5–10% by wet weight), chondrocytes, collagen fibres and other glycoproteins. The solid phase constitutes an isotropic proteoglycan gel and a fibre network of predominantly type II collagen, which provides tensile strength and mechanical stiffness. The same two components control diffusion of the fluid phase, e.g. as visualised by diffusion tensor MRI: (i) the proteoglycan gel (giving a baseline isotropic diffusivity) and (ii) the highly anisotropic collagenous fibre network. We propose a new constitutive model and finite element implementation that focus on the essential load-bearing morphology: an incompressible, poroelastic solid matrix reinforced by an inhomogeneous, dispersed fibre fabric, which is saturated with an incompressible fluid residing in strain-dependent pores of the collagen–proteoglycan solid matrix. The inhomogeneous, dispersed fibre fabric of the solid further influences the fluid permeability, as well as an intrafibrillar portion that cannot be ‘squeezed out’ from the tissue. Using representative numerical examples on the mechanical response of cartilage, we reproduce several features that have been demonstrated experimentally in the cartilage mechanics literature.     

Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus

Nonlinear, linear and failure properties of articular cartilage and meniscus in opposing contact surfaces are poorly known in tension. Relationships between the tensile properties of articular cartilage and meniscus in contact with each other within knee joints are also not known. In the present study, rectangular samples were prepared from the superficial lateral femoral condyle cartilage and lateral meniscus of bovine knee joints. Tensile tests were carried out with a loading rate of 5 mm/min until the tissue rupture. Nonlinear properties of the toe region, linear properties in larger strains, and failure properties of both tissues were analysed. The strain-dependent tensile modulus of the toe region, Young's modulus of the linear region, ultimate tensile stress and toughness were on average 98.2, 8.3, 4.0 and 1.9 times greater (p<0.05) for meniscus than for articular cartilage. In contrast, the toe region strain, yield strain and failure strain were on average 9.4, 3.1 and 2.3 times greater (p<0.05) for cartilage than for meniscus. There was a significant negative correlation between the strain-dependent tensile moduli of meniscus and articular cartilage samples within the same joints (r=−0.690, p=0.014). In conclusion, the meniscus possesses higher nonlinear and linear elastic stiffness and energy absorption capability before rupture than contacting articular cartilage, while cartilage has longer nonlinear region and can withstand greater strains before failure. These findings point out different load carrying demands that both articular cartilage and meniscus have to fulfil during normal physiological loading activities of knee joints.     

An augmented Lagrangian finite element formulation for 3D contact of biphasic tissues

Biphasic contact analysis is essential to obtain a complete understanding of soft tissue biomechanics, and the importance of physiological structure on the joint biomechanics has long been recognised; however, up to date, there are no successful developments of biphasic finite element contact analysis for three-dimensional (3D) geometries of physiological joints. The aim of this study was to develop a finite element formulation for biphasic contact of 3D physiological joints. The augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The biphasic contact method was implemented in the commercial software COMSOL Multiphysics 4.2^® (COMSOL, Inc., Burlington, MA). The accuracy of the implementation was verified using 3D biphasic contact problems, including indentation with a flat-ended indenter and contact of glenohumeral cartilage layers. The ability of the method to model multibody biphasic contact of physiological joints was proved by a 3D knee model. The 3D biphasic finite element contact method developed in this study can be used to study the biphasic behaviours of the physiological joints.     

A numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage

A method for numerical solution of the continuous spectrum linear biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. The method is based on an alternate formulation of the continuous spectrum stress-strain law that is implemented using Gaussian quadrature integration combined with quadratic interpolation of the strain history. For N time steps, the cost of the method is O(N). The method is applied to a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. For a range of relaxation times that are representative of articular cartilage, accuracy of the method is demonstrated by direct comparison to a theoretical Laplace transform solution.     

Development of chondrocyte-laden alginate hydrogels with modulated microstructure and properties for cartilage regeneration

Alginate hydrogel is an attractive biomaterial for cell microencapsulation. The microarchitecture of hydrogels can regulate cellular functions. This study aims to investigate the applicability of sodium citrate buffer (SCB) as a culture medium supplement for modulating the microstructure of alginate microbeads to provide a favorable microenvironment for chondrogenic induction. The chondrocyte-laden microbeads, with and without TGF-β3 incorporation, were produced through an encapsulator. The obtained small-sized microbeads (~300 μm) were exposed to a treatment medium containing SCB, composed of varied concentrations of sodium citrate (1.10–1.57 mM), sodium chloride (3.00–4.29 mM), and ethylenediaminetetraacetic acid (0.60–0.86 mM) to partially degrade their crosslinked structure for 3 days, followed by culture in a normal medium until day 21. Scanning electron microscope micrographs demonstrated a loose hydrogel network with an enhanced pore size in the SCB-treated microbeads. Increasing the concentration of SCB in the treatment medium reduced the calcium content of the microbeads via a Na⁺/Ca²⁺ exchange process and improved the water absorption of the microbeads, resulting in a higher swelling ratio. All the tested SCB concentrations were non-cytotoxic. Increases in aggrecan and type II collagen gene expression and their corresponding extracellular matrix accumulation, glycosaminoglycans, and type II collagen were vividly detected in the TGF-β3-containing microbeads with increasing SCB concentrations in the treatment medium. Our findings highlighted that the combination of SCB treatment and TGF-β3 incorporation in the chondrocyte-laden microbeads is a promising strategy for enhancing cartilage regeneration, which may contribute to a versatile application in cell delivery and tissue engineering.     

Aqueous biphasic system for the partial purification of Bacillus subtilis carboxymethyl cellulase

Carboxymethyl cellulase (CMCase) hydrolyses cellulose into glucose and is useful in various industrial applications. Conventional CMCase purification methods are rather complicated and time-consuming; thus, a cost-effective strategy for CMCase recovery is on demand. Polyethylene-glycol (PEG)/sodium citrate aqueous biphasic system (ABS) was adopted in this study to investigate the effectiveness of the ABS in the recovery of extracellular Bacillus subtilis CMCase from fermentation broth. Comprehensive optimization steps were executed that took into consideration the ABS variables of PEG molecular weight, tie-line length (TLL), volume ratio (V_R), crude loading, pH and the addition of sodium chloride (NaCl). A CMCase recovery yield (Y_B) of 88.82% ± 0.69, a purification fold (P_F) of 4.8 and a partition coefficient (K) of 0.44 ± 0.03 were achieved from the bottom phase of the PEG 6000/citrate ABS with TLL of 42.16% (w/w), V_R of 0.29, 1% of (w/w) NaCl, pH 7.0, and 20% (w/w) crude loading. CMCase was mainly segregated to the salt-rich bottom phase because of the hydrophilicity of the enzyme surface. The highly effective recovery technique was further confirmed by SDS-PAGE analysis. Overall, the present study suggests that the ABS is a potential purification strategy for extracellular CMCase.     

Identification of subpopulations with characteristics of mesenchymal progenitor cells from human osteoarthritic cartilage using triple staining for cell surface markers

We first identified and isolated cellular subpopulations with characteristics of mesenchymal progenitor cells (MPCs) in osteoarthritic cartilage using fluorescence-activated cell sorting (FACS). Cells from osteoarthritic cartilage were enzymatically isolated and analyzed directly or after culture expansion over several passages by FACS using various combinations of surface markers that have been identified on human MPCs (CD9, CD44, CD54, CD90, CD166). Culture expanded cells combined and the subpopulation derived from initially sorted CD9+, CD90+, CD166+ cells were tested for their osteogenic, adipogenic and chondrogenic potential using established differentiation protocols. The differentiation was analyzed by immunohistochemistry and by RT-PCR for the expression of lineage related marker genes. Using FACS analysis we found that various triple combinations of CD9, CD44, CD54, CD90 and CD166 positive cells within osteoarthritic cartilage account for 2-12% of the total population. After adhesion and cultivation their relative amount was markedly higher, with levels between 24% and 48%. Culture expanded cells combined and the initially sorted CD9/CD90/CD166 triple positive subpopulation had multipotency for chondrogenic, osteogenic and adipogenic differentiation. In conclusion, human osteoarthritic cartilage contains cells with characteristics of MPCs. Their relative enrichment during in vitro cultivation and the ability of cell sorting to obtain more homogeneous populations offer interesting perspectives for future studies on the activation of regenerative processes within osteoarthritic joints.     

Replica immunoelectron microscopic study of the upper surface layer in rat mandibular condylar cartilage by a quick-freezing method

A quick-freezing and deep-etching method in combination with replica immunoelectron microscopy was applied for examining localization of hyaluronic acid and fibronectin on the upper surface layer of rat mandibular condylar cartilage. Rat temporomandibular joints were dissected with articular disks in order to leave the articular cartilage surface intact. The disks were slightly cut with razor blades for exposing the condylar articular cartilage surface. They were quickly frozen with the isopentane-propane cryogen (–193°C) and prepared for freeze-fracturing and deep-etching replica membranes. They were additionally treated with 5% SDS and 0.5% collagenase to keep some antigens attached on the replica membranes. After such a treatment, a routine immunogold method was applied for clarifying the localization of hyaluronic acid and fibronectin in the upper surface layer. Small immunogold particles for hyaluronic acid were mainly localized around upper filamentous networks covered with amorphous materials, but large immunogold ones for fibronectin were localized on deep thicker fibrils. We have revealed the native architecture of the upper surface layer of mandibular condylar cartilage on the replica membranes and also three-dimensional localization of hyaluronic acid and fibronectin by the immunogold method.     

A simple cryopreservation method for the maintenance of cell viability and mechanical integrity of a cultured cartilage analog

A method for cryopreserving a 100-microm-thick sheet of tissue produced by cultured rabbit chondrocytes has been developed. The method maintains cell viability and avoids tissue fracture and degradation of mechanical properties. A slow-freeze, fast-thaw procedure with 2 M Me(2)SO as the cryoprotectant resulted in no tissue fracture and approximately 90% viable cells after storage in culture flasks at -80 degrees C. The cells in the retrieved tissue remained responsive to IL-1beta, and tensile and fracture toughness properties of the tissue were not degraded by cryopreservation.     

A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage

A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss–Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage.     

Theoretical investigation of an artificial joint with micro-pocket-covered component and biphasic cartilage on the opposite articulating surface

This paper presents a theoretical investigation of a geometrically idealized artificial joint with micro-pocket-covered component and biphasic cartilage on the opposite articulating surface. The fluid that exudes from the biphasic cartilage fills and pressurizes the micro-pockets. In this way, a poro-elasto-hydrodynamic regime of lubrication is developed. Assuming that lower friction would result in lower adhesive wear, and neglecting the fatigue as well as the abrasive wear, the proposed bearing system hypothetically could reduce the amount of wear debris. Equations of the linear biphasic theory are applied for the confined and unconfined compression of the cartilage. The fluid pressure and the elastic deformation of the biphasic cartilage are explicitly presented. The effective and equilibrium friction coefficients are obtained for the particular configuration of this bearing system. The micro-pockets geometrical parameters (depth, radius, surface distribution and edge radius) must be established to reduce the local contact stresses, to assure low friction forces and to minimize the biphasic cartilage damage. The influence of the applied pressure, porosity of the micro-pocket-covered component, filling time, cartilage elasticity, permeability and porosity upon the micro-pockets depth is illustrated. Our results are based upon the previously published data for a biphasic cartilage.     

Measurement of cartilage sub-component distributions through the surface by Raman spectroscopy-based multivariate analysis

Articular cartilage posesses unique material properties due to a complex depth-dependent composition of sub-components. Raman spectroscopy has proven valuable in quantifying this composition through cartilage cross-sections. However, cross-sectioning requires tissue destruction and is not practical in situ. In this work, Raman spectroscopy-based multivariate curve resolution (MCR) was employed in porcine cartilage samples (n = 12) to measure collagen, glycosaminoglycan, and water distributions through the surface for the first time; these were compared against cross-section standards. Through the surface Raman measurements proved reliable in predicting composition distribution up to a depth of approximately 0.5 mm. A fructose-based optical clearing agent (OCA) was also used in an attempt to further improve depth of resolution of this measurement method. However, it did not; mainly due to a high-spectral overlap with the Raman spectra of main cartilage sub-components. This measurement technique potentially could be used in situ, to better understand the etiology of joint diseases such as osteoarthritis (OA).     

A quantitative and qualitative method for direct 2-DE analysis of murine cartilage

Direct 2-DE analysis of cartilage is difficult due to the high proteoglycan content. Proteoglycan removal before IEF may however cause the partial or total loss of specific proteins making this approach ineffective when quantitative data are required to investigate protein expression differences. Thus, we have developed a 2-DE method including passive rehydration loading that does not require sample pretreatment and allows direct protein expression studies in cartilage samples.     

Decreased collagen thermal stability as a response to the loss of structural integrity of thyroid cartilage

The amino acid composition, thermal behavior and birefringence properties of thyroid cartilage tissues have been studied. A collagen component in perichondrium consists of type-I and type-II collagens whose fibers form a highly ordered anisotropic structure with a birefringence of 4.75 × 10^?3 and a melting (denaturation) temperature of 65°C. The hyaline constituent, which is visualized as a quasi-anisotropic medium, contains of only type-II collagen, which does not denature in intact tissues at temperatures up to 100°C. However, in tissues whose proteoglycane subsystem is damaged by trypsin, the denaturation of collagen takes place at 60°C. In the integral perichondrium-hyaline system, the temperature of collagen denaturation in the perichondrium reaches 75°C, which indicates the immobilization of collagen in this tissue by the extracellular matrix of the hyaline constituent.     

Recovery efficiency of a hydrophilic ionic-liquid aqueous biphasic system for the primary purification of cytochrome c from simulated Saccharomyces cerevisiae fermentation broth

Ionic liquid-based aqueous biphasic system (ILABS) has emerged as an attractive green approach for the extraction and separation of various biomolecules. The growing market demands of cytochrome c (cyt c) due to its vast uses in medical applications have urged the search for cost-efficient approaches for the production and purification of cyt c. In this study, the feasibility of ILABS to recover cyt c from simulated Saccharomyces cerevisiae cell cultures was investigated by evaluating the effects of phase composition, pH, and additives concentration on the recovery efficiency of cyt c. The ILABS was developed using the hydrophilic ionic liquids, 1-hexyl-3-methylimidazolium bromide ((C6mim)Br) and potassium citrate. The optimal separation conditions for recovery of cyt c from simulated cells cultures were attained with ILABS of pH 9 comprising of 28% (w/w) of (C6mim)Br and 24% (w/w) of potassium citrate and the addition of 0.2% (w/w) NaCl at room temperature (25 °C). Cyt c was recovered in the IL-rich phase with partition coefficient (Kc) of 364.00 ± 1.09, recovery yield (Y) of 99.76% ± 0.03 and selectivity (S) of 223.31 ± 0.56. The results suggest that ILABS can efficiently recover cyt c from microbial fermentation broth with high recovery yields and separation efficiency.     

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

Abstract

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