Effects of Nonlinear Strain-Dependent Permeability and Rate of Compression on the Stress Behavior of Articular Cartilage

1981 ◽  
Vol 103 (2) ◽  
pp. 61-66 ◽  
Author(s):  
W. M. Lai ◽  
Van C. Mow ◽  
V. Roth
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Compressive Stress ◽  
Articular Surface ◽  
Viscoelastic Behavior ◽  
Elastic Equilibrium ◽  
Nonlinear Flow ◽  
Solid Matrix ◽  
Stress History ◽  
Rate Of Increase

The compressive viscoelastic behavior of articular cartilage, a fiber-reinforced, porous, permeable solid matrix filled with water, is predominately governed by the flow of the interstitial water within the tissue and its exudation across the articular surface. The fluid flow is in turn governed by the permeability of the tissue and the loading imposed upon its surface. But for articular cartilage, the permeability depends nonlinearly on the strain: k = ko exp(Me). Here, M is the nonlinear flow-limiting parameter and e is the dilatation. In this investigation, we studied the influence of M and Ro = koHA / U˙h (where HA is the elastic equilibrium modulus of the solid matrix, h is the tissue’s thickness and U˙ is the rate of compression applied onto the surface via a rigid, porous, free-draining filter) on the stress history of circular plugs of cartilage specimens attached to the bone. It was found that these two parameters have profound effects on the predicted compressive stress history. For very large Ro, the fluid flow effects become negligible. For small Ro and large M, large instantaneous compressive stresses several times larger than those observed at equilibrium are predicted. This amplification of compressive stress is due to the increase of importance of the relative fluid flow effect, i.e., Ro → 0, and nonlinear flow-limit effect, i.e., M > 0. Also, the theoretical curves predict that the rate of increase of stress initially decreases (convex) and finally becomes a constant. The results of our 5 percent offset compression experiments are in good agreement with the theoretical predictions.

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.

An Analysis of the Unconfined Compression of Articular Cartilage

1984 ◽  
Vol 106 (2) ◽  
pp. 165-173 ◽  
Author(s):  
C. G. Armstrong ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Fluid Pressure ◽  
Constant Strain Rate ◽  
Elastic Solid ◽  
Solid Matrix ◽  
Unconfined Compression ◽  
Creep Stress ◽  
Internal Fluid ◽  
Equilibrium Response

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.

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.

Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: II—Effect of Variable Strain Rates

2000 ◽  
Vol 123 (2) ◽  
pp. 198-200 ◽  
Author(s):  
Mark R. DiSilvestro, ◽  
Qiliang Zhu, ◽  
Jun-Kyo Francis Suh
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Strain Rate ◽  
Viscoelastic Behavior ◽  
Viscoelastic Response ◽  
Strain Rates ◽  
Unconfined Compression ◽  
Rate Dependent ◽  
Linear Viscoelastic

This study investigated the abilities of the linear biphasic poroviscoelastic (BPVE) model and the linear biphasic poroelastic (BPE) model to simulate the effect of variable ramp strain rates on the unconfined compression stress relaxation response of articular cartilage. Curve fitting of experimental data showed that the BPVE model was able to successfully account for the ramp strain rate-dependent viscoelastic behavior of articular cartilage under unconfined compression, while the BPE model was able to account for the complete viscoelastic response at a slow strain rate, but only the long-term viscoelastic response at faster strain rates. We concluded that the short-term viscoelastic behavior of articular cartilage, when subjected to a fast ramp strain rate, is primarily governed by a fluid flow-independent (intrinsic) viscoelastic mechanism, whereas the long-term viscoelastic behavior is governed by a fluid flow-dependent (biphasic) viscoelastic mechanism. Furthermore, a linear viscoelastic representation of the solid stress was found to be a valid model assumption for the simulation of ramp strain rate-dependent relaxation behaviors of articular cartilage within the range of ramp strain rates investigated.

scholarly journals A Triphasic Orthotropic Laminate Model for Cartilage Curling Behavior: Fixed Charge Density Versus Mechanical Properties Inhomogeneity

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Leo Q. Wan ◽  
X. Edward Guo ◽  
Van C. Mow
Keyword(s):  
Articular Cartilage ◽  
Osmotic Pressure ◽  
Structural Model ◽  
Articular Surface ◽  
Mixture Theory ◽  
Solid Matrix ◽  
Linear Elastic ◽  
Orthotropic Properties ◽  
First Time

Osmotic pressure and associated residual stresses play important roles in cartilage development and biomechanical function. The curling behavior of articular cartilage was believed to be the combination of results from the osmotic pressure derived from fixed negative charges on proteoglycans and the structural and compositional and material property inhomogeneities within the tissue. In the present study, the in vitro swelling and curling behaviors of thin strips of cartilage were analyzed with a new structural model using the triphasic mixture theory with a collagen-proteoglycan solid matrix composed of a three-layered laminate with each layer possessing a distinct set of orthotropic properties. A conewise linear elastic matrix was also incorporated to account for the well-known tension-compression nonlinearity of the tissue. This model can account, for the first time, for the swelling-induced curvatures found in published experimental results on excised cartilage samples. The results suggest that for a charged-hydrated soft tissue, such as articular cartilage, the balance of proteoglycan swelling and the collagen restraining within the solid matrix is the origin of the in situ residual stress, and that the layered collagen ultrastructure, e.g., relatively dense and with high stiffness at the articular surface, play the dominate role in determining curling behaviors of such tissues.

Biphasic Poroviscoelastic Simulation of the Unconfined Compression of Articular Cartilage: I—Simultaneous Prediction of Reaction Force and Lateral Displacement

2000 ◽  
Vol 123 (2) ◽  
pp. 191-197 ◽  
Author(s):  
Mark R. DiSilvestro ◽  
Qiliang Zhu ◽  
Marcy Wong ◽  
Jukka S. Jurvelin ◽  
Jun-Kyo Francis Suh
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Solid Phase ◽  
Lateral Displacement ◽  
Transverse Isotropy ◽  
Reaction Force ◽  
Solid Matrix ◽  
Inviscid Fluid ◽  
Unconfined Compression ◽  
Interstitial Fluid Flow

This study investigated the ability of the linear biphasic poroelastic (BPE) model and the linear biphasic poroviscoelastic (BPVE) model to simultaneously predict the reaction force and lateral displacement exhibited by articular cartilage during stress relaxation in unconfined compression. Both models consider articular cartilage as a binary mixture of a porous incompressible solid phase and an incompressible inviscid fluid phase. The BPE model assumes the solid phase is elastic, while the BPVE model assumes the solid phase is viscoelastic. In addition, the efficacy of two additional models was also examined, i.e., the transversely isotropic BPE (TIBPE) model, which considers transverse isotropy of the solid matrix within the framework of the linear BPE model assumptions, and a linear viscoelastic solid (LVE) model, which assumes that the viscoelastic behavior of articular cartilage is solely governed by the intrinsic viscoelastic nature of the solid matrix, independent of the interstitial fluid flow. It was found that the BPE model was able to accurately account for the lateral displacement, but unable to fit the short-term reaction force data of all specimens tested. The TIBPE model was able to account for either the lateral displacement or the reaction force, but not both simultaneously. The LVE model was able to account for the complete reaction force, but unable to fit the lateral displacement measured experimentally. The BPVE model was able to completely account for both lateral displacement and reaction force for all specimens tested. These results suggest that both the fluid flow-dependent and fluid flow-independent viscoelastic mechanisms are essential for a complete simulation of the viscoelastic phenomena of articular cartilage.

The Influence of Depth-Dependent Inhomogeneity on the Contact Response of Human Patellar Cartilage

2001 ◽  
Author(s):  
Ramaswamy Krishnan ◽  
Seonghun Park ◽  
Michael A. Soltz ◽  
Robert J. Pawluk ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Functional Response ◽  
Material Properties ◽  
Articular Surface ◽  
Solid Matrix ◽  
Homogeneous Distribution ◽  
Primary Role ◽  
Homogeneous State ◽  
Compressive Properties ◽  
State Of Stress

Abstract One of the aims of modeling articular cartilage is to determine its ability to sustain its physiological loading environment and the mechanisms by which this functional response might be compromised. It has long been hypothesized that excessive stresses in cartilage might initiate osteoarthritis, thus a determination of the state of stress within the tissue has been an important objective. It has also been hypothesized that the interstitial water of articular cartilage plays a primary role in producing low friction and wear as well as shielding the collagen-proteoglycan solid matrix from a significant portion of the loads applied across joints [1]. Furthermore, cartilage exhibits inhomogeneity through its depth, both in its tensile and compressive properties, though the significance of this inhomogeneity on the functional response of cartilage remains to be elucidated. The specific aims of the current study are to (a) experimentally determine the depth-dependent tensile and compressive properties of human patellar articular cartilage; (b) determine the response of cartilage to loading under a contact configuration using finite element models which employ these experimentally determined material properties; and (c) compare the response of the tissue to a hypothetical homogeneous distribution of material properties through the depth. The first hypothesis is that the inhomogeneity of articular cartilage acts to maximize the interstitial fluid load support at the articular surface. The second hypothesis is that the depth-dependent inhomogeneous distribution of cartilage properties acts to produce a more homogeneous state of stress than would be achieved had the properties been constant through the depth. This study extends our previous contact analyses of homogeneous cartilage layers [2,3].

Singular Perturbation Analysis of the Nonlinear, Flow-Dependent Compressive Stress Relaxation Behavior of Articular Cartilage

1985 ◽  
Vol 107 (3) ◽  
pp. 206-218 ◽  
Author(s):  
M. H. Holmes ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Articular Surface ◽  
Uniaxial Stress ◽  
Biological Tissues ◽  
Nonlinear Flow ◽  
Stress Fields ◽  
Singular Perturbation Analysis ◽  
Strain Dependent

The dominant mechanism giving rise to the viscoelastic response of articular cartilage during compression is the nonlinear diffusive interaction of the fluid and solid phases of the tissue as they flow relative to one another. The present study is concerned with the role of this interaction under uniaxial stress relaxation in compression. The model is a biphasic mixture of fluid and solid which incorporates the strain-dependent permeability found earlier from permeation experiments. When a ramp-displacement is imposed on the articular surface, simple, but accurate, asymptotic approximations are derived for the deformation and stress fields in the tissue for slow and moderately fast rates of compression. They are shown to agree very well with experiment and they provide a simple means for determining the material parameters. Moreover, they lead to important insights into the role of the flow-dependent viscoelastic nature of articular cartilage and other hydrated biological tissues.

scholarly journals Anatomy of the Intermetatarsal Facets of the Fourth and Fifth Metatarsals

2021 ◽  
Vol 6 (1) ◽  
pp. 247301142097570
Author(s):  
Mossub Qatu ◽  
George Borrelli ◽  
Christopher Traynor ◽  
Joseph Weistroffer ◽  
James Jastifer
Keyword(s):  
Articular Cartilage ◽  
Digital Imaging ◽  
Articular Surface ◽  
Implant Design ◽  
Joint Surface ◽  
Fracture Classification ◽  
Articular Damage ◽  
Metatarsal Fracture ◽  
Metatarsal Fractures ◽  
The Mean

Background: The intermetatarsal joint between the fourth and fifth metatarsals (4-5 IM) is important in defining fifth metatarsal fractures. The purpose of the current study was to quantify this joint in order to determine the mean cartilage area, the percentage of the articulation that is cartilage, and to give the clinician data to help understand the joint anatomy as it relates to fifth metatarsal fracture classification. Methods: Twenty cadaver 4-5 IM joints were dissected. Digital images were taken and the articular cartilage was quantified by calibrated digital imaging software. Results: For the lateral fourth proximal intermetatarsal articulation, the mean area of articulation was 188 ± 49 mm2, with 49% of the area composed of articular cartilage. The shape of the articular cartilage had 3 variations: triangular, oval, and square. A triangular variant was the most common (80%, 16 of 20 specimens). For the medial fifth proximal intermetatarsal articulation, the mean area of articulation was 143 ± 30 mm2, with 48% of the joint surface being composed of articular cartilage. The shape of the articular surface was oval or triangular. An oval variant was the most common (75%, 15 of 20 specimens). Conclusion: This study supports the notion that the 4-5 IM joint is not completely articular and has both fibrous and cartilaginous components. Clinical Relevance: The clinical significance of this study is that it quantifies the articular surface area and shape. This information may be useful in understanding fifth metatarsal fracture extension into the articular surface and to inform implant design and also help guide surgeons intraoperatively in order to minimize articular damage.

A Review of the Collagen Orientation in the Articular Cartilage

Cartilage ◽  
2021 ◽  
pp. 194760352098877
Author(s):  
Roy D. Bloebaum ◽  
Andrew S. Wilson ◽  
William N. Martin
Keyword(s):  
Surface Layer ◽  
Articular Cartilage ◽  
Fiber Orientation ◽  
Collagen Fiber ◽  
Articular Surface ◽  
Imaging Techniques ◽  
Collagen Fibers ◽  
Deep Zone ◽  
Collagen Fiber Orientation ◽  
Critical Point Drying

Objective There has been a debate as to the alignment of the collagen fibers. Using a hand lens, Sir William Hunter demonstrated that the collagen fibers ran perpendicular and later aspects were supported by Benninghoff. Despite these 2 historical studies, modern technology has conflicting data on the collagen alignment. Design Ten mature New Zealand rabbits were used to obtain 40 condyle specimens. The specimens were passed through ascending grades of alcohol, subjected to critical point drying (CPD), and viewed in the scanning electron microscope. Specimens revealed splits from the dehydration process. When observing the fibers exposed within the opening of the splits, parallel fibers were observed to run in a radial direction, normal to the surface of the articular cartilage, radiating from the deep zone and arcading as they approach the surface layer. After these observations, the same samples were mechanically fractured and damaged by scalpel. Results The splits in the articular surface created deep fissures, exposing parallel bundles of collagen fibers, radiating from the deep zone and arcading as they approach the surface layer. On higher magnification, individual fibers were observed to run parallel to one another, traversing radially toward the surface of the articular cartilage and arcading. Mechanical fracturing and scalpel damage induced on the same specimens with the splits showed randomly oriented fibers. Conclusion Collagen fiber orientation corroborates aspects of Hunter’s findings and compliments Benninghoff. Investigators must be aware of the limits of their processing and imaging techniques in order to interpret collagen fiber orientation in cartilage.

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