Boundary conditions at the cartilage-synovial fluid interface for joint lubrication and theoretical verifications

The objective of this study is to establish and verify the set of boundary conditions at the interface between a biphasic mixture (articular cartilage) and a Newtonian or non-Newtonian fluid (synovial fluid) such that a set of well-posed mathematical problems may be formulated to investigate joint lubrication problems. A "pseudo-no-slip" kinematic boundary condition is proposed based upon the principle that the conditions at the interface between mixtures or mixtures and fluids must reduce to those boundary conditions in single phase continuum mechanics. From this proposed kinematic boundary condition, and balances of mass, momentum and energy, the boundary conditions at the interface between a biphasic mixture and a Newtonian or non-Newtonian fluid are mathematically derived. Based upon these general results, the appropriate boundary conditions needed in modeling the cartilage-synovial fluid-cartilage lubrication problem are deduced. For two simple cases where a Newtonian viscous fluid is forced to flow (with imposed Couette or Poiseuille flow conditions) over a porous-permeable biphasic material of relatively low permeability, the well known empirical Taylor slip condition may be derived using matched asymptotic analysis of the boundary layer at the interface.     

Fluid transport and mechanical properties of articular cartilage: a review

This review is aimed at unifying our understanding of cartilage viscoelastic properties in compression, in particular the role of compression-dependent permeability in controlling interstitial fluid flow and its contribution to the observed viscoelastic effects. During the previous decade, it was shown that compression causes the permeability of cartilage to drop in a functional manner described by k = ko exp (epsilon M) where ko and M were defined as intrinsic permeability parameters and epsilon is the dilatation of the solid matrix (epsilon = tr delta u). Since permeability is inversely related to the diffusive drag coefficient of relative fluid motion with respect to the porous solid matrix, the measured load-deformation response of the tissue must therefore also depend on the non-linearly permeable nature of the tissue. We have summarized in this review our understanding of this non-linear phenomenon. This understanding of these flow-dependent viscoelastic effects are put into the historical perspective of a comprehensive literature review of earlier attempts to model the compressive viscoelastic properties of articular cartilage.     

The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration

A one-dimensional ultrafiltration problem of fluid flow through a soft permeable tissue or gel under high pressure and compressive strain is solved. A finite deformation biphasic theory is used to model the behavior of the soft porous permeable solid matrix. This theory includes a Helmholtz free energy function which depends on the three principal invariants (I, II, III) of the right Cauchy-Green tensor and which satisfies the Baker-Ericksen inequalities on the principal stresses and strains. The dependence of the porosity phi f and the solidity phi s on deformation is deduced and a generalization of the exponential strain-dependent functional form for the permeability, k = k0 exp (M epsilon), of Lai and Mow (Biorheology 103, 111-123, 1980) is proposed. In this one-dimensional problem, we show that the dependence of the permeability on phi f, phi s, and III is equivalent to its dependence on hydration as proposed by Fatt and Goldstick (J. Colloid Sci. 20, 962-988, 1965). The exact solution of the ultrafiltration problem is derived and asymptotic and numerical methods are used to evaluate it. For high pressures and finite strains, the solution provides some surprising effects. The theory predicts that a material starting with a homogeneous porosity will have a strongly non-homogeneous porosity throughout the column during ultrafiltration. The resulting change in pore size through the filtration column may be very important in understanding its filtration characteristics. It is also found that there is a long delay time, up to 10 to 15 min, before the filtration velocity reaches an equilibrium. In filtration experiments where the rate of mass transport across the tissue or column of gel is important, sufficient time must be allowed for the steady state to be reached.     

Changes in proteoglycan synthesis of chondrocytes in articular cartilage are associated with the time-dependent changes in their mechanical environment

Explant loading experiments were conducted to investigate the effect of load duration on proteoglycan synthesis. A compressive load of 0.1 MPa applied for 10 min was found to stimulate proteoglycan synthesis, while the same load applied for 20 h suppressed synthesis. This bimodal response suggests that the cells are responding to different mechanical stimuli as time progresses. A theoretical model has therefore been developed to describe the mechanical environment perceived by cells within soft hydrated tissues (e.g. articular cartilage) while the tissue is being loaded. The cells are modeled, using the biphasic theory, as fluid-solid inclusions embedded in and attached to a biphasic extracellular matrix of distinct material properties. A method of solution is developed which is valid for any axisymmetric loading configuration, provided that the cell radius, a, is small relative to the tissue height, h (i.e. h/a 1). A closed-form analytical solution for this inclusion problem is then presented for the confined compression configuration. Results from this model show that the mechanical environment in and around the cells is time dependent and inhomogeneous, and can be significantly influenced by differences in properties between the cell and the extracellular matrix.     

An analysis of the unconfined compression of articular cartilage

Analytical solutions have been obtained for the internal deformation and fluid-flow fields and the externally observable creep, stress relaxation, and constant strain-rate behaviors which occur during the unconfined compression of a cylindrical specimen of a fluid-filled, porous, elastic solid, such as articular cartilage, between smooth, impermeable plates. Instantaneously, the "biphasic" continuum deforms without change in volume and behaves like an incompressible elastic solid of the same shear modulus. Radial fluid flow then allows the internal fluid pressure to equilibrate with the external environment. The equilibrium response is controlled by the Young's modulus and Poisson's ratio of the solid matrix.     

Analysis of the dynamic permeation experiment with implication to cartilaginous tissue engineering

In the present study, a I-D dynamic permeation of a monovalent electrolyte solution through a negatively charged-hydrated cartilaginous tissue is analyzed using the mechano-electrochemical theory developed by Lai et al. (1991) as the constitutive model for the tissue. The spatial distributions of stress, strain, fluid pressure, ion concentrations, electrical potential, ion and fluid fluxes within and across the tissue have been calculated. The dependencies of these mechanical, electrical and physicochemical responses on the tissue fixed charge density, with specified modulus, permeability, diffusion coefficients, and frequency and magnitude of pressure differential are determined. The results demonstrate that these mechanical, electrical and physicochemical fields within the tissue are intrinsically and nonlinearly coupled, and they all vary with time and depth within the tissue.     

The role of flow-independent viscoelasticity in the biphasic tensile and compressive responses of articular cartilage

A long-standing challenge in the biomechanics of connective tissues (e.g., articular cartilage, ligament, tendon) has been the reported disparities between their tensile and compressive properties. In general, the intrinsic tensile properties of the solid matrices of these tissues are dictated by the collagen content and microstructural architecture, and the intrinsic compressive properties are dictated by their proteoglycan content and molecular organization as well as water content. These distinct materials give rise to a pronounced and experimentally well-documented nonlinear tension-compression stress-strain responses, as well as biphasic or intrinsic extracellular matrix viscoelastic responses. While many constitutive models of articular cartilage have captured one or more of these experimental responses, no single constitutive law has successfully described the uniaxial tensile and compressive responses of cartilage within the same framework. The objective of this study was to combine two previously proposed extensions of the biphasic theory of Mow et al. [1980, ASME J. Biomech. Eng., 102, pp. 73-84] to incorporate tension-compression nonlinearity as well as intrinsic viscoelasticity of the solid matrix of cartilage. The biphasic-conewise linear elastic model proposed by Soltz and Ateshian [2000, ASME J. Biomech. Eng., 122, pp. 576-586] and based on the bimodular stress-strain constitutive law introduced by Curnier et al. [1995, J. Elasticity, 37, pp. 1-38], as well as the biphasic poroviscoelastic model of Mak [1986, ASME J. Biomech. Eng., 108, pp. 123-130], which employs the quasi-linear viscoelastic model of Fung [1981, Biomechanics: Mechanical Properties of Living Tissues, Springer-Verlag, New York], were combined in a single model to analyze the response of cartilage to standard testing configurations. Results were compared to experimental data from the literature and it was found that a simultaneous prediction of compression and tension experiments of articular cartilage, under stress-relaxation and dynamic loading, can be achieved when properly taking into account both flow-dependent and flow-independent viscoelasticity effects, as well as tension-compression nonlinearity.     

On the electric potentials inside a charged soft hydrated biological tissue: streaming potential versus diffusion potential

The main objective of this study is to determine the nature of electric fields inside articular cartilage while accounting for the effects of both streaming potential and diffusion potential. Specifically, we solve two tissue mechano-electrochemical problems using the triphasic theories developed by Lai et al. (1991, ASME J. Biomech Eng., 113, pp. 245-258) and Gu et al. (1998, ASME J. Biomech. Eng., 120, pp. 169-180) (1) the steady one-dimensional permeation problem; and (2) the transient one-dimensional ramped-displacement, confined-compression, stress-relaxation problem (both in an open circuit condition) so as to be able to calculate the compressive strain, the electric potential, and the fixed charged density (FCD) inside cartilage. Our calculations show that in these two technically important problems, the diffusion potential effects compete against the flow-induced kinetic effects (streaming potential) for dominance of the electric potential inside the tissue. For softer tissues of similar FCD (i.e., lower aggregate modulus), the diffusion potential effects are enhanced when the tissue is being compressed (i.e., increasing its FCD in a nonuniform manner) either by direct compression or by drag-induced compaction; indeed, the diffusion potential effect may dominate over the streaming potential effect. The polarity of the electric potential field is in the same direction of interstitial fluid flow when streaming potential dominates, and in the opposite direction of fluid flow when diffusion potential dominates. For physiologically realistic articular cartilage material parameters, the polarity of electric potential across the tissue on the outside (surface to surface) may be opposite to the polarity across the tissue on the inside (surface to surface). Since the electromechanical signals that chondrocytes perceive in situ are the stresses, strains, pressures and the electric field generated inside the extracellular matrix when the tissue is deformed, the results from this study offer new challenges for the understanding of possible mechanisms that control chondrocyte biosyntheses.     

Inhibition of enterovirus 71 (EV-71) infections by a novel antiviral peptide derived from EV-71 capsid protein VP1

Enterovirus 71 (EV-71) is the main causative agent of hand, foot and mouth disease (HFMD). In recent years, EV-71 infections were reported to cause high fatalities and severe neurological complications in Asia. Currently, no effective antiviral or vaccine is available to treat or prevent EV-71 infection. In this study, we have discovered a synthetic peptide which could be developed as a potential antiviral for inhibition of EV-71. Ninety five synthetic peptides (15-mers) overlapping the entire EV-71 capsid protein, VP1, were chemically synthesized and tested for antiviral properties against EV-71 in human Rhabdomyosarcoma (RD) cells. One peptide, SP40, was found to significantly reduce cytopathic effects of all representative EV-71 strains from genotypes A, B and C tested, with IC(50) values ranging from 6-9.3 μM in RD cells. The in vitro inhibitory effect of SP40 exhibited a dose dependent concentration corresponding to a decrease in infectious viral particles, total viral RNA and the levels of VP1 protein. The antiviral activity of SP40 peptide was not restricted to a specific cell line as inhibition of EV-71 was observed in RD, HeLa, HT-29 and Vero cells. Besides inhibition of EV-71, it also had antiviral activities against CV-A16 and poliovirus type 1 in cell culture. Mechanism of action studies suggested that the SP40 peptide was not virucidal but was able to block viral attachment to the RD cells. Substitutions of arginine and lysine residues with alanine in the SP40 peptide at positions R3A, R4A, K5A and R13A were found to significantly decrease antiviral activities, implying the importance of positively charged amino acids for the antiviral activities. The data demonstrated the potential and feasibility of SP40 as a broad spectrum antiviral agent against EV-71.     

Constituents and pH changes in protein rich hyaluronan solution affect the biotribological properties of artificial articular joints.

The relationship between the coefficient of friction and pH value or protein constituents of lubricating fluid, together with viscosity, were studied within a bearing surface model for artificial joint, ultra-high molecular weight polyethylene (UHMWPE) against stainless steel (SUS), using a mechanical spectrometer. Four lubricants were tested in this study: sodium hyaluronate (HA), HA with albumin, HA with gamma-globulin, and HA with (L)alpha-dipalmitoyl phosphatidylcholine ((L)alpha-DPPC). The coefficient of friction between UHMWPE and SUS in HA with albumin or HA with gamma-globulin varied from 0.035 to 0.070 depending on angular velocity and pH. The coefficient of friction in HA or HA with (L)alpha-DPPC varied from 0.023 to 0.045 depending on angular velocity and pH. The variation in pH for HA with albumin had a large effect on the coefficient of friction at low range of angular velocity with viscosity independence. The variation in pH for HA with gamma-globulin had a large effect on the coefficient of friction with viscosity dependence at high angular velocity. The addition of (L)alpha-DPPC showed a small effect on the coefficient of friction at low angular velocity. This study confirms that the presence of albumin in the lubricant promotes pH dependence and viscosity independence of the tribological properties at low speed while the presence of globulin promotes pH and viscosity independence at low speed and promotes pH and viscosity dependence at high speed in the lubrication of UHMWPE against SUS. This study supports the clinical hypothesis that the effect of constituents and pH changes in periprosthetic fluid for the lubrication is a clue toward resolving many complications after total joint replacement.