scholarly journals Modeling of Neutral Solute Transport in a Dynamically Loaded Porous Permeable Gel: Implications for Articular Cartilage Biosynthesis and Tissue Engineering

2003 ◽  
Vol 125 (5) ◽  
pp. 602-614 ◽  
Author(s):  
Robert L. Mauck ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Solute Transport ◽  
Dynamic Loading ◽  
Interstitial Fluid ◽  
Articular Surface ◽  
Compressive Strain ◽  
Convective Transport ◽  
Solid Matrix ◽  
Bathing Solution ◽  
Loading Frequency

A primary mechanism of solute transport in articular cartilage is believed to occur through passive diffusion across the articular surface, but cyclical loading has been shown experimentally to enhance the transport of large solutes. The objective of this study is to examine the effect of dynamic loading within a theoretical context, and to investigate the circumstances under which convective transport induced by dynamic loading might supplement diffusive transport. The theory of incompressible mixtures was used to model the tissue (gel) as a mixture of a gel solid matrix (extracellular matrix/scaffold), and two fluid phases (interstitial fluid solvent and neutral solute), to solve the problem of solute transport through the lateral surface of a cylindrical sample loaded dynamically in unconfined compression with frictionless impermeable platens in a bathing solution containing an excess of solute. The resulting equations are governed by nondimensional parameters, the most significant of which are the ratio of the diffusive velocity of the interstitial fluid in the gel to the solute diffusivity in the gel Rg, the ratio of actual to ideal solute diffusive velocities inside the gel Rd, the ratio of loading frequency to the characteristic frequency of the gel f^, and the compressive strain amplitude ε0. Results show that when Rg>1,Rd<1, and f^>1, dynamic loading can significantly enhance solute transport into the gel, and that this effect is enhanced as ε0 increases. Based on representative material properties of cartilage and agarose gels, and diffusivities of various solutes in these gels, it is found that the ranges Rg>1,Rd<1 correspond to large solutes, whereas f^>1 is in the range of physiological loading frequencies. These theoretical predictions are thus in agreement with the limited experimental data available in the literature. The results of this study apply to any porous hydrated tissue or material, and it is therefore plausible to hypothesize that dynamic loading may serve to enhance solute transport in a variety of physiological processes.

Permeability of Human Glenohumeral Joint Cartilage

1999 ◽  
Author(s):  
Anna Stankiewicz ◽  
Gerard A. Ateshian ◽  
Louis U. Bigliani ◽  
Van C. Mow
Keyword(s):  
Mechanical Properties ◽  
Articular Cartilage ◽  
Interstitial Fluid ◽  
Glenohumeral Joint ◽  
Solid Matrix ◽  
Joint Cartilage ◽  
Frictional Drag ◽  
Diarthrodial Joints ◽  
Flow Through ◽  
Fluid Pressurization

Abstract The nearly frictionless lubrication in diarthrodial joints and load support within articular cartilage depends on its mechanical properties. It has been shown that the majority of applied loads on cartilage are supported by interstitial fluid pressurization (Ateshian et al., 1994) which results from the frictional drag of flow through the porous permeable solid matrix. The duration and magnitude of this pressurization are a function of the permeability of cartilage (Lai et al., 1981).

Direct Hydraulic Permeability Measurements of Agarose Hydrogels Used as Cell Scaffolds

1999 ◽  
Author(s):  
Michael A. Soltz ◽  
Anna Stankiewicz ◽  
Gerard Ateshian ◽  
Robert L. Mauck ◽  
Clark T. Hung
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Interstitial Fluid ◽  
Convective Transport ◽  
Hydraulic Permeability ◽  
Interstitial Fluid Flow ◽  
Pass Through ◽  
Fluid Pressurization ◽  
First Time

Abstract The objective of this study was to determine the intrinsic hydraulic permeability of 2% agarose hydrogels. Two-percent agarose was chosen because it is a concentration typically used for encapsulation of chondrocytes in suspension cultures [3–5], Hydraulic permeability is a measure of the relative ease by which fluid can pass through a material. Importantly, it governs the level of interstitial fluid flow as well as the interstitial fluid pressurization that is generated in a material during loading. Fluid pressurization is the source of the unique load-bearing and lubrication properties of articular cartilage [1,17] and represents a major component of the in vivo chondrocyte environment. We have previously reported that 2% agarose hydrogels can support fluid pressurization, albeit to a significantly lesser degree than articular cartilage [18]. Interstitial fluid flow gives rise to convective transport of nutrients and ions [6,7] and matrix compaction [9] which may serve as important stimuli to chondrocytes. We report for the first time the strain-dependent hydraulic permeability of 2% agarose hydrogels.

Cartilage Interstitial Fluid Load Support in Unconfined Compression

2002 ◽  
Author(s):  
Seonghun Park ◽  
Ramaswamy Krishnan ◽  
Steven B. Nicoll ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Interstitial Fluid ◽  
Articular Surface ◽  
Surface Zone ◽  
Unconfined Compression ◽  
Tissue Samples ◽  
Fluid Load ◽  
Tension And Compression ◽  
Fluid Pressurization ◽  
Theoretical Analyses

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than compression. Theoretical analyses have suggested that this tension-compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression [1]. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone.

Interaction Between the Interstitial Fluid and the Extracellular Matrix in Confined Indentation

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Yiling Lu ◽  
Wen Wang
Keyword(s):  
Extracellular Matrix ◽  
Interstitial Fluid ◽  
Soft Tissues ◽  
Dynamic Equilibrium ◽  
Fluid Pressure ◽  
Pressure Oscillation ◽  
Solid Matrix ◽  
Loading Frequency ◽  
Waste Products ◽  
Fluid Movement

The Movement of the interstitial fluid in extracellular matrices not only affects the mechanical properties of soft tissues, but also facilitates the transport of nutrients and the removal of waste products. In this study, we aim to quantify interstitial fluid movement and fluid-matrix interaction in a new loading configuration—confined tissue indentation, using a poroelastic theory. The tissue sample sits in a cylindrical chamber and loading is applied on the top central surface of the specimen by a porous indenter that is fixed on the specimen. The interaction between the solid and the fluid is examined using a finite element method under ramp and cyclic loads. Typical compression-relaxation responses of the specimen are observed in a ramp load. Under a cyclic load, the system reaches a dynamic equilibrium after a number of loading cycles. Fluid circulation, with opposite directions in the loading and unloading phases in the extracellular matrix, is observed. The most significant variation in the fluid pressure locates just beneath the indenter. Fluid pressurization arrives at equilibrium much faster than the solid matrix deformation. As the loading frequency increases, the location of the peak pressure oscillation moves closer to the indenter and the magnitude of the pressure oscillation increases. Concomitantly, the axial stress variation of the solid matrix is reduced. It is found that interstitial fluid movement helps to alleviate severe strain of the solid matrix beneath the indenter. This study quantifies the interaction between the interstitial fluid and the extracellular matrix by decomposing the loading response of the specimen into the “transient” and “dynamic equilibrium” phases. Confined indentation in this manuscript gives a better representation of some in vitro and in vivo loading configurations where the indenter covers part of the top surface of the tissue.

Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression: Theory and Experiments

1980 ◽  
Vol 102 (1) ◽  
pp. 73-84 ◽  
Author(s):  
V. C. Mow ◽  
S. C. Kuei ◽  
W. M. Lai ◽  
C. G. Armstrong
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Relative Motion ◽  
Interstitial Fluid ◽  
Fluid Phase ◽  
Solid Content ◽  
Solid Matrix ◽  
Frictional Drag ◽  
Tissue Mass ◽  
Biphasic Model

Articular cartilage is a biphasic material composed of a solid matrix phase (∼ 20 percent of the total tissue mass by weight) and an interstitial fluid phase (∼ 80 percent). The intrinsic mechanical properties of each phase as well as the mechanical interaction between these two phases afford the tissue its interesting rheological behavior. In this investigation, the solid matrix was assumed to be intrinsically incompressible, linearly elastic and nondissipative while the interstitial fluid was assumed to be intrinsically incompressible and nondissipative. Further, it was assumed that the only dissipation comes from the frictional drag of relative motion between the phases. However, more general constitutive equations, including a viscoelastic dissipation of the solid matrix as well as a viscous dissipation of interstitial fluid were also developed. A constant “average” permeability of the tissue was assumed, i.e., independent of deformation, and a solid content function Vs/Vf (the ratio of the volume of each of the phases) was assumed to vary with depth in accordance with the experimentally determined weight ratios. This linear, nonhomogeneous theory was applied to describe the experimentally obtained biphasic creep and biphasic stress relaxation data via a nonlinear regression technique. The determined intrinsic “aggregate” elastic modulus, from ten creep experiments, is 0.70 ± 0.09 MN/m2 and, from six stress relaxation experiments, is 0.76 ± 0.03 MN/m2. The “average” permeability of the tissue is (0.76 ± 0.42) × 10−14 m4 /N•s. We concluded that the large spread in the permeability coefficients is due to the assumption of a constant deformation independent permeability. We also concluded that 1) a nonlinearly permeable biphasic model, where the permeability function is given by an experimentally determined empirical law: k = A(p) exp [α(p)e], can be used to describe more accurately the rheological properties of articular cartilage, and 2) the frictional drag of relative motion is the most important factor governing the fluid/solid viscoelastic properties of the tissue in compression.

Effect of Anisotropic Permeability of the Superficial Layer on the Frictional Property in Articular Cartilage

2013 ◽  
Author(s):  
Kyuichiro Imade ◽  
Hiromichi Fujie
Keyword(s):  
Articular Cartilage ◽  
Hydrodynamic Lubrication ◽  
Articular Surface ◽  
Compressive Strain ◽  
Electron Microscopic Observation ◽  
Superficial Layer ◽  
Frictional Property ◽  
Hydraulic Permeability ◽  
Electron Microscopic ◽  
Biphasic Model

Articular cartilage has a significant lubrication property that has been explained in previous studies by many theories including mixed lubrication, hydrodynamic lubrication, surface gel hydration lubrication, biphasic theory, and so on. However the mechanism of continuously low friction in articular cartilage still remains unclear. Reynaud and Quinn indicated that the hydraulic permeability was significantly anisotropic under compressive strain; the tangential permeability becomes lower than the normal permeability under compression [1]. Meanwhile scanning electron microscopic observation indicated that the superficial layer of articular surface was consisted of close-packed collagen fibers aligning parallel with articular surface and tangling each other in normal cartilage (Fig. 1). It is, therefore, suggested that the permeability is extremely low in the tangential direction when subjected to compressive strain. We have a hypothesis that the unique structure and properties in the articular cartilage superficial layer may improve the lubrication properties [2]. Therefore, we performed an analytical study using a fiber-reinforced poroelastic biphasic model to determine the effect of lateral permeability reduction in the superficial layer on the frictional property of articular cartilage.

Determination of Poisson’s Ratios of Bovine Articular Cartilage in Tension and Compression Using Osmotic and Mechanical Loading

2002 ◽  
Author(s):  
Nadeen O. Chahine ◽  
Christopher C.-B. Wang ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Strain Softening ◽  
Articular Surface ◽  
Swelling Pressure ◽  
Solid Matrix ◽  
Concentration Effects ◽  
Bovine Articular Cartilage ◽  
Free Swelling ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The existence of osmotic pressure inside cartilage gives the tissue a propensity to swell. This swelling pressure is balanced by the tensile stresses generated within the solid matrix at free-swelling [1, 2]. Recent studies have shown that cartilage exhibits significant strain-softening when compressed relative to its free-swelling state [3–5]. Such strain-softening behavior has been physically interpreted within the context of osmotic swelling pressure and tension-compression nonlinearity [4, 9]. This has provided the rationale for extracting both the tensile and compressive Young’s moduli from uniaxial compression tests on the same specimen [4, 5]. The goal of the current study is to optically determine another important elastic property, i.e. the equilibrium Poisson’s ratio of young bovine articular cartilage when uniaxially compressed along its three characteristic directions: parallel and perpendicular to the split-line direction (1- and 2-direction, respectively), and in a direction normal to the articular surface (3-direction). Furthermore, the external bath concentration effects on the Poisson’s ratios will be explored at various strain levels.

Transmission of Rapidly Applied Loads Through Articular Cartilage Part 1: Uncracked Cartilage

1996 ◽  
Vol 210 (1) ◽  
pp. 27-37 ◽  
Author(s):  
P A Kelly ◽  
J J O'Connor
Keyword(s):  
Articular Cartilage ◽  
Interstitial Fluid ◽  
Articular Surface ◽  
Surface Friction ◽  
Integral Representations ◽  
Equilibrium Analysis ◽  
Stress Distributions ◽  
Interstitial Fluid Flow ◽  
Volumetric Change ◽  
Qualitative Similarity

An elastostatic model of rapidly loaded articular cartilage is presented. It is assumed that the cartilage experiences little volumetric change or interstitial fluid flow while loaded instantaneously. Subchondral bone compliance and articular surface friction are incorporated. Integral representations of the stress distributions within cartilage are derived using Fourier transform techniques and the integrals are solved numerically. Localized tensile stresses are found and occur in regions close to the cartilage-bone interface as well as at the articular surface, outside the embrace of the load. The qualitative similarity between the results and those of previous investigations is explained by an elementary equilibrium analysis. The stress distributions suggest that the splits and cracks observed in diseased cartilage may be initiated, or propagated, by tensile stress.

Experimental Verification of the Roles of Intrinsic Matrix Viscoelasticity and Tension-Compression Nonlinearity in the Biphasic Response of Cartilage

2003 ◽  
Vol 125 (1) ◽  
pp. 84-93 ◽  
Author(s):  
Chun-Yuh Huang ◽  
Michael A. Soltz ◽  
Monika Kopacz ◽  
Van C. Mow ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Strain Rate ◽  
Dynamic Loading ◽  
Dynamic Compression ◽  
Solid Matrix ◽  
Supporting Evidence ◽  
Compression Stress ◽  
Unconfined Compression ◽  
Support Mechanism

A biphasic-CLE-QLV model proposed in our recent study [2001, J. Biomech. Eng., 123, pp. 410–417] extended the biphasic theory of Mow et al. [1980, J. Biomech. Eng., 102, pp. 73–84] to include both tension-compression nonlinearity and intrinsic viscoelasticity of the cartilage solid matrix by incorporating it with the conewise linear elasticity (CLE) model [1995, J. Elasticity, 37, pp. 1–38] and the quasi-linear viscoelasticity (QLV) model [Biomechanics: Its foundations and objectives, Prentice Hall, Englewood Cliffs, 1972]. This model demonstrates 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 viscoelastic effects, as well as tension-compression nonlinearity. The objective of this study is to directly test this biphasic-CLE-QLV model against experimental data from unconfined compression stress-relaxation tests at slow and fast strain rates as well as dynamic loading. Twelve full-thickness cartilage cylindrical plugs were harvested from six bovine glenohumeral joints and multiple confined and unconfined compression stress-relaxation tests were performed on each specimen. The material properties of specimens were determined by curve-fitting the experimental results from the confined and unconfined compression stress relaxation tests. The findings of this study demonstrate that the biphasic-CLE-QLV model is able to describe the strain-rate-dependent mechanical behaviors of articular cartilage in unconfined compression as attested by good agreements between experimental and theoretical curvefits (r2=0.966±0.032 for testing at slow strain rate; r2=0.998±0.002 for testing at fast strain rate) and predictions of the dynamic response r2=0.91±0.06. This experimental study also provides supporting evidence for the hypothesis that both tension-compression nonlinearity and intrinsic viscoelasticity of the solid matrix of cartilage are necessary for modeling the transient and equilibrium responses of this tissue in tension and compression. Furthermore, the biphasic-CLE-QLV model can produce better predictions of the dynamic modulus of cartilage in unconfined dynamic compression than the biphasic-CLE and biphasic poroviscoelastic models, indicating that intrinsic viscoelasticity and tension-compression nonlinearity of articular cartilage may play important roles in the load-support mechanism of cartilage under physiologic loading.

SOLUTE TRANSPORT IN CYCLIC DEFORMED HETEROGENEOUS ARTICULAR CARTILAGE

2011 ◽  
Vol 03 (03) ◽  
pp. 507-524 ◽  
Author(s):  
LIHAI ZHANG
Keyword(s):  
Mechanical Properties ◽  
Articular Cartilage ◽  
Solute Transport ◽  
Dynamic Loading ◽  
Biological Effects ◽  
Fluid Velocity ◽  
Biological Tissues ◽  
Hydraulic Permeability ◽  
Material Inhomogeneity ◽  
Transport Behavior

Solute transport in biological tissues is a fundamental process of supplying nutrients to tissue cells. Due to the avascular nature of cartilage, nutrients have to diffuse into the tissue to exert their biological effects. Whilst significant research efforts have been made over last decade towards understanding the solute transport behavior within the cartilage, the effect of dynamic loading on the transport process is still not fully understood. By treating cartilage as a homogeneous tissue, recent theoretical studies generally indicate that physiologically relevant mechanical loading could potentially enhance solute uptake in cartilage. However, like most biological tissues, articular cartilage is actually an inhomogeneous tissue with direction-dependent mechanical properties (such as aggregate modulus and hydraulic permeability). The inhomogeneity of tissue mechanical properties may have considerable influence on solute transport, and thereby need critical investigation. Using an engineering approach, a quantitative theoretical model has been developed in this study to investigate the solute transport behavior in cartilage in consideration of its material inhomogeneity. Using a cylindrical cartilage disk undergoing unconfined cyclic deformation as a case study, the model results demonstrate that inhomogeneous cartilage properties could potentially influence the magnitude and profile of interstitial fluid velocity and pressure throughout the cartilage. Furthermore, the enhancement of solute transport by dynamic loading is depth-dependent due to the inhomogeneous distribution of material properties.

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