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.

The Strain-Softening of Bovine Articular Cartilage Under Infinitesimal Deformation in Unconfined Compression

2001 ◽  
Author(s):  
Christopher C.-B. Wang ◽  
Nadeen O. Chahine ◽  
Terri-Ann N. Kelly ◽  
W. Michael Lai ◽  
Clark T. Hung ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Strain Softening ◽  
Articular Surface ◽  
Osmotic Swelling ◽  
Bovine Articular Cartilage ◽  
Softening Mechanism ◽  
Softening Behavior ◽  
Depth Direction ◽  
Swelling Equilibrium ◽  
Triphasic Theory

Abstract Significant strain-softening of articular cartilage along its depth direction has been observed in several studies [1,2], where the free-swelling equilibrium state of the tissue was taken to be the reference configuration for subsequent deformation. Microstructural models have been proposed to interpret this softening as buckling of pre-stressed collagen fibers [3,4]. In this study, we propose that a constitutive model which accounts for the disparity in tensile and compressive moduli of cartilage as well as the osmotic swelling response, can explain this experimentally observed strain-softening mechanism. The strain-softening behavior of the tissue is investigated experimentally and theoretically along three mutually perpendicular directions: directions parallel and perpendicular to the split line direction (1- and 2-direction), and normal to the articular surface (3-direction). A conewise nonlinear elasticity model is incorporated into the triphasic theory [5] to interpret this strain-softening in the context of Donnan osmotic swelling [6].

scholarly journals In vitro Articular Cartilage Growth with Sequential Application of IGF-1 and TGF-β1 Enhances Volumetric Growth and Maintains Compressive Properties

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Nathan T. Balcom ◽  
Britta Berg-Johansen ◽  
Kristin J. Dills ◽  
Jennifer R. Van Donk ◽  
Gregory M. Williams ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Articular Cartilage ◽  
Growth Factor ◽  
Extreme Values ◽  
Volumetric Growth ◽  
Bovine Articular Cartilage ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Tgf Β1

In vitro cultures with insulin-like growth factor-1 (IGF-1) and transforming growth factor-β1 (TGF-β1) have previously been shown to differentially modulate the growth of immature bovine articular cartilage. IGF-1 stimulates expansive growth yet decreases compressive moduli and increases compressive Poisson’s ratios, whereas TGF-β1 maintains tissue size, increases compressive moduli, and decreases compressive Poisson’s ratios. The current study’s hypothesis was that sequential application of IGF-1 and TGF-β1 during in vitro culture produces geometric and compressive mechanical properties that lie between extreme values produced when using either growth factor alone. Immature bovine articular cartilage specimens were harvested and either untreated (D0, i.e., day zero) or cultured in vitro for either 6 days with IGF-1 (D6 IGF), 12 days with IGF-1 (D12 IGF), or 6 days with IGF-1 followed by 6 days with TGF-β1 (D12 SEQ, i.e., sequential). Following treatment, all specimens were tested for geometric, biochemical, and compressive mechanical properties. Relative to D0, D12 SEQ treatment enhanced volumetric growth, but to a lower value than that for D12 IGF. Furthermore, D12 SEQ treatment maintained compressive moduli and Poisson’s ratios at values higher and lower, respectively, than those for D12 IGF. Considering the previously described effects of 12 days of treatment with TGF-β1 alone, D12 SEQ induced both growth and mechanical property changes between those produced with either IGF-1 or TGF-β1 alone. The results suggest that it may be possible to vary the durations of select growth factors, including IGF-1 and TGF-β1, to more precisely modulate the geometric, biochemical, and mechanical properties of immature cartilage graft tissue in clinical repair strategies.

A Continuum Theory and an Experiment for the Ion-Induced Swelling Behavior of Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 151-158 ◽  
Author(s):  
E. R. Myers ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Tensile Force ◽  
Continuum Theory ◽  
Swelling Behavior ◽  
Bovine Articular Cartilage ◽  
Free Swelling ◽  
Transient Force

Swelling of normal bovine articular cartilage equilibrated in NaCl solutions was dimensionally measured in thin strips of tissue. The ion-induced strains show that free swelling of articular cartilage is anisotropic and inhomogeneous. For the molar concentrations used, contraction increased linearly with concentration, defining a “coefficient of chemical contraction” (αc). Isometrically constrained specimens registered a rise in tensile force followed by stress relaxation. An extension of the biphasic theory incorporating this ion-induced strain is proposed. This theory can describe the equilibrium anisotropic swelling behavior of cartilage and explain the transient force history observed in the isometric experiment.

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.

scholarly journals Depth-varying Density and Organization of Chondrocytes in Immature and Mature Bovine Articular Cartilage Assessed by 3D Imaging and Analysis

2005 ◽  
Vol 53 (9) ◽  
pp. 1109-1119 ◽  
Author(s):  
Kyle D. Jadin ◽  
Benjamin L. Wong ◽  
Won C. Bae ◽  
Kelvin W. Li ◽  
Amanda K. Williamson ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
3D Imaging ◽  
Articular Surface ◽  
Three Dimensional ◽  
Neighboring Cell ◽  
3D Images ◽  
Bovine Articular Cartilage ◽  
Stages Of Growth ◽  
Cell Organization ◽  
Heterogeneous Tissue

Articular cartilage is a heterogeneous tissue, with cell density and organization varying with depth from the surface. The objectives of the present study were to establish a method for localizing individual cells in three-dimensional (3D) images of cartilage and quantifying depth-associated variation in cellularity and cell organization at different stages of growth. Accuracy of nucleus localization was high, with 99% sensitivity relative to manual localization. Cellularity (million cells per cm3) decreased from 290, 310, and 150 near the articular surface in fetal, calf, and adult samples, respectively, to 120, 110, and 50 at a depth of 1.0 mm. The distance/angle to the nearest neighboring cell was 7.9 μm/31°, 7.1 μm/31°, and 9.1 μm/31° for cells at the articular surface of fetal, calf, and adult samples, respectively, and increased/decreased to 11.6 μm/31°, 12.0 μm/30°, and 19.2 μm/25° at a depth of 0.7 mm. The methodologies described here may be useful for analyzing the 3D cellular organization of cartilage during growth, maturation, aging, degeneration, and regeneration.

A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage

1991 ◽  
Vol 113 (3) ◽  
pp. 245-258 ◽  
Author(s):  
W. M. Lai ◽  
J. S. Hou ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Charge Density ◽  
Fixed Charge ◽  
Solid Matrix ◽  
Confined Compression ◽  
Fixed Charge Density ◽  
Chemical Expansion ◽  
Chemical Potentials ◽  
Free Swelling ◽  
Triphasic Theory

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by μi = μoi + (RT/Mi)ln[γ±2c (c + c F)] and μW = μow + [p − RTφ(2c + cF) + Bwe]/ρTw, where R, T, Mi, γ±, φ, ρTw and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is σ = − pI − TcI + λs(trE)I + 2μsE, where E is the strain tensor and (λs,μs) are the Lame´ constants of the elastic solid matrix. The chemical-expansion stress (− Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the “pre-stress” in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.

Fibre Reinforcement and Mechanical Stability in Articular Cartilage

1984 ◽  
Vol 13 (3) ◽  
pp. 153-156 ◽  
Author(s):  
D W L Hukins ◽  
R M Aspden ◽  
Y E Yarker
Keyword(s):  
Articular Cartilage ◽  
Tensile Stress ◽  
Articular Surface ◽  
Applied Pressure ◽  
Swelling Pressure ◽  
Collagen Fibrils ◽  
Torsional Stiffness ◽  
Surface Zone ◽  
Fibre Reinforcement ◽  
Deep Zone

The gel phase of articular cartilage is reinforced by collagen fibrils. These fibrils have low flexural and torsional stiffness, but are able to provide reinforcement if deformation of the tissue increases their tensile stress. An estimate suggests that the lengths of collagen fibrils in articular cartilage are at least of the same order as their critical length so that tensile stress in the tissue will increase the stress in the fibrils rather than simply pull them out of the gel. In the surface zone the collagen fibrils are oriented so that the efficiency of reinforcement, η, is about 0.6 tangential to the surface; tension in the fibrils is thus able to withstand swelling pressure within the tissue whose condition for stability resembles that of a pressure vessel. Swelling pressure allows the tissue to support applied pressure. An intermediate zone has a roughly isotropic η value of about 0.2, while in the deep zone collagen fibrils appear to tie the cartilage to the subchondral bone; in this deep zone η has a value of about 0.6 perpendicular to the surface direction. There is also some preferred orientation of collagen fibrils in the plane of the articular surface within the surface zone; in patellar cartilage the preferred orientations can be related to the direction of stress which could be generated by movement of the joint.

scholarly journals Localization of proteoglycan monomer and link protein in the matrix of bovine articular cartilage: An immunohistochemical study.

1980 ◽  
Vol 28 (7) ◽  
pp. 621-635 ◽  
Author(s):  
A R Poole ◽  
I Pidoux ◽  
A Reiner ◽  
L H Tang ◽  
H Choi ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Articular Surface ◽  
Guanidine Hydrochloride ◽  
Cartilage Matrix ◽  
Binding Studies ◽  
Superficial Zone ◽  
Surface Culture ◽  
Bovine Articular Cartilage ◽  
Link Protein ◽  
The Matrix

Using monospecific antisera and immunofluorescence microscopy, proteoglycan monomer (PG), and link proteins were demonstrated throughout the extracellular matrix of bovine articular cartilage. A narrow band of strong pericellular staining was usually observed for both molecules, indicating a pericellular concentration of proteoglycan monomer: this conclusion was supported by dye-binding studies. Whereas PG was evenly distributed throughout the remaining matrix, more link protein was detectable in interterritorial sites in middle and deep zones. Well-defined zones of weaker territorial staining for link protein stained strongest for chondroitin sulfate. Trypsin treatment of cartilage resulted in a loss of most of the PG staining, but some selective retention of link protein, particularly around chondrocytes in the superficial zone at and near the articular surface. This residual staining was largely removed if sections were fixed after chondroitinase treatment. After extraction of cartilage with 4M guanidine hydrochloride, only PG remained and this was concentrated in the superficial zone. These observations are shown to support the concept of aggregation of PG and link protein with hyaluronic acid (HA) in cartilage matrix, and the binding of PG and link protein to HA, which is attached to the chondrocyte surface. Culture of cartilage depleted of PG and link protein by trypsin demonstrated that individual chondrocytes can secrete both PG and link proteins and that the organization of cartilage matrix can be regenerated in part over a period of 4 days.

ASSESSMENT OF THREE-DIMENSIONAL ARCHITECTURE OF COLLAGEN FIBERS IN THE SUPERFICIAL ZONE OF BOVINE ARTICULAR CARTILAGE

2004 ◽  
Vol 08 (04) ◽  
pp. 167-179 ◽  
Author(s):  
J. P. Wu ◽  
T. B. Kirk ◽  
M. H. Zheng
Keyword(s):  
Articular Cartilage ◽  
Laser Scanning ◽  
3D Visualization ◽  
Articular Surface ◽  
3D Structure ◽  
Collagen Matrix ◽  
Laser Scanning Confocal Microscopy ◽  
Collagen Fibres ◽  
Superficial Zone ◽  
Bovine Articular Cartilage

The aim of this study is to investigate the structure and the collagen matrix of the superficial zone of articular cartilage using a 3D imaging technique. The split line thought to represent the orientation of the collagen fibres in the superficial zone was found using Hultkrantz's method. A semitransparent membrane was physically peeled off from the most superficial surface of bovine articular cartilage. Using fibre optic laser scanning confocal microscopy, the collagen matrix in normal cartilage, the membrane and the cartilage with the membrane peeled off were studied. The superficial zone was found to contain a more sophisticated 3D collagenous matrix than previously reported. The collagen matrix in the membrane consists of interwoven long collagen bundles, and the collagen fibres immediately subjacent to it align spatially in a predominantly oblique direction to the articular surface. The split line does not represent the orientation of the collagen in the membrane. This study presents a 3D visualization technique for a minimal-invasive examination of the 3D architecture of the collagen fibres in the superficial zone of articular cartilage, and offers a new insight into the 3D structure of the collagen matrix in the superficial zone of native cartilage.

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