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.

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).

Contact Creep of Biphasic Cartilage Layers

1999 ◽  
Vol 66 (1) ◽  
pp. 137-145 ◽  
Author(s):  
R. Kelkar ◽  
G. A. Ateshian
Keyword(s):  
Material Properties ◽  
Applied Load ◽  
Interstitial Fluid ◽  
Integral Transform ◽  
Solid Phase ◽  
Fluid Phase ◽  
Biphasic Model ◽  
Physiological Loading ◽  
Fluid Pressurization ◽  
Creep Problem

Integral transform methods are used to solve the contact creep problem between two identical cylindrical biphasic cartilage layers bonded to rigid impermeable subchondral bone substrates. The biphasic model employed for cartilage consists of a binary mixture of an incompressible porous-permeable solid phase and an incompressible fluid phase. Solutions are obtained as a function of time, from the instantaneous to the equilibrium responses of the tissue. A significant result of this analysis is that under application of a step load, fluid pressurization may support upward of 96 percent of the total applied load for more congruent joints, shielding the solid collagen-proteoglycan matrix of the tissue from excessive stresses during physiological loading durations. The protection imparted by interstitial fluid pressurization to the solid collagen-proteoglycan matrix of cartilage is investigated, and the influence of material properties and osteoarthritic changes on the potential loss of this protective effect is discussed.

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.

A Linear Viscoelastic Biphasic Model for Soft Tissues Based on the Theory of Porous Media

2001 ◽  
Vol 123 (5) ◽  
pp. 418-424 ◽  
Author(s):  
Wolfgang Ehlers ◽  
Bernd Markert
Keyword(s):  
Porous Media ◽  
Articular Cartilage ◽  
Soft Tissues ◽  
Differential Algebraic Equations ◽  
Solid Matrix ◽  
Numerical Treatment ◽  
Algebraic Equations ◽  
Theory Of Porous Media ◽  
Biphasic Model ◽  
Linear Viscoelastic

Based on the Theory of Porous Media (mixture theories extended by the concept of volume fractions), a model describing the mechanical behavior of hydrated soft tissues such as articular cartilage is presented. As usual, the tissue will be modeled as a materially incompressible binary medium of one linear viscoelastic porous solid skeleton saturated by a single viscous pore-fluid. The contribution of this paper is to combine a descriptive representation of the linear viscoelasticity law for the organic solid matrix with an efficient numerical treatment of the strongly coupled solid-fluid problem. Furthermore, deformation-dependent permeability effects are considered. Within the finite element method (FEM), the weak forms of the governing model equations are set up in a system of differential algebraic equations (DAE) in time. Thus, appropriate embedded error-controlled time integration methods can be applied that allow for a reliable and efficient numerical treatment of complex initial boundary-value problems. The applicability and the efficiency of the presented model are demonstrated within canonical, numerical examples, which reveal the influence of the intrinsic dissipation on the general behavior of hydrated soft tissues, exemplarily on articular cartilage.

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.

Biphasic Viscoelastic Properties of Human TMJ Disc

2008 ◽  
Author(s):  
Jonathan Y. Kuo ◽  
Thierry Bacro ◽  
Hai Yao
Keyword(s):  
Temporomandibular Joint ◽  
Temporal Bone ◽  
Viscoelastic Material ◽  
Viscoelastic Properties ◽  
Interstitial Fluid ◽  
Fluid Phase ◽  
Solid Matrix ◽  
Mandibular Bone ◽  
Articular Surfaces ◽  
Tmj Disc

The temporomandibular joint (TMJ) is a load-bearing joint consisting of the condyle of the mandibular bone, the fossa eminence of the temporal bone, and a fibrocartilaginous disc wedged in between the bone surfaces (Figure 1A). The TMJ disc serves to distribute stress, lubricate movement, and protect the articular surfaces of the joint. The TMJ disc is a viscoelastic material consisting of two principle phases: a solid matrix composed mainly of collagen and proteoglycan, and a fluid phase primarily comprised of interstitial fluid.

Articular Cartilage Biomechanics Modeled via an Intrinsically Compressible Biphasic Model: Implications and Deviations From an Incompressible Biphasic Approach

2013 ◽  
Author(s):  
Francesco Travascio ◽  
Roberto Serpieri ◽  
Shihab Asfour
Keyword(s):  
Articular Cartilage ◽  
Experimental Testing ◽  
Solid Matrix ◽  
Hydraulic Permeability ◽  
Theoretical Frameworks ◽  
Theoretical Formulation ◽  
New Model ◽  
Biphasic Model ◽  
Testing Procedures ◽  
Cartilage Biomechanics

Biphasic continuum models have been extensively deployed for modeling macroscopic articular cartilage biomechanics [1,2]. This consolidated theoretical approach schematizes tissue as a mixture of an elastic solid matrix embedded in a fluid phase. In physiological conditions, intrinsic compressibility of each phase is very limited when compared to the whole tissue macroscopic counterpart. Based on such experimental evidence, intrinsic phase compressibility is generally reasonably neglected [3]. Hence, traditionally, cartilage biomechanics models have been developed on the basis of incompressible biphasic formulations [3–5], often referred to as Incompressible Theories of Mixtures (ITM). Alternatively, a more general biphasic model for cartilage biomechanics, accounting for full intrinsic compressibility of phases, may be considered. A consistent theoretical formulation of this type has been recently made available [6,7], hereby referred to as Theory of Microscopically Compressible Porous Media (TMCPM). In the present contribution, a new model for articular cartilage biomechanics, based on TMCPM, was developed. Predictions of this new model, and its deviations from a traditional ITM approach were studied. In particular, deviations between compressible and incompressible theoretical frameworks were investigated with a specific focus on the repercussions on models’ capability of characterizing fundamental tissue properties, such as hydraulic permeability, via established experimental testing procedures.

The Frictional Coefficient of Bovine Articular Cartilage Correlates With Interstitial Fluid Load Support in Creep

2002 ◽  
Author(s):  
Ramaswamy Krishnan ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Friction And Wear ◽  
Interstitial Fluid ◽  
Load Transfer ◽  
Frictional Coefficient ◽  
Fluid Phase ◽  
Constant Load ◽  
Low Friction ◽  
Bovine Articular Cartilage ◽  
Fluid Load

Articular cartilage functions as the bearing material in joints and provides low friction and wear over a lifetime. The cartilage lubrication mechanism has not yet been fully characterized though several theories have been proposed. In previous studies [1–3] it was hypothesized that interstitial fluid load support contributes significantly to the reduction of the frictional coefficient due to load transfer from the solid to the fluid phase of the tissue. This study provides experimental verification for a theoretical model based on this hypothesis [1,4]. The specific aim of this study is to experimentally investigate the correlation between the frictional response of bovine articular cartilage, and its interstitial fluid load support during sliding against glass under a constant load.

A Biphasic Transversely Isotropic Poroviscoelastic Model for the Unconfined Compression of Hydrated Soft Tissue

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
H. Hatami-Marbini ◽  
R. Maulik
Keyword(s):  
Articular Cartilage ◽  
Soft Tissue ◽  
Stress Relaxation ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Viscoelastic Model ◽  
Transversely Isotropic ◽  
Solid Matrix ◽  
Unconfined Compression ◽  
Material Parameters

The unconfined compression experiments are commonly used for characterizing the mechanical behavior of hydrated soft tissues such as articular cartilage. Several analytical constitutive models have been proposed over the years to analyze the unconfined compression experimental data and subsequently estimate the material parameters. Nevertheless, new mathematical models are still required to obtain more accurate numerical estimates. The present study aims at developing a linear transversely isotropic poroviscoelastic theory by combining a viscoelastic material law with the transversely isotropic biphasic model. In particular, an integral type viscoelastic model is used to describe the intrinsic viscoelastic properties of a transversely isotropic solid matrix. The proposed constitutive theory incorporates viscoelastic contributions from both the fluid flow and the intrinsic viscoelasticity to the overall stress-relaxation behavior. Moreover, this new material model allows investigating the biomechanical properties of tissues whose extracellular matrix exhibits transverse isotropy. In the present work, a comprehensive parametric study was conducted to determine the influence of various material parameters on the stress–relaxation history. Furthermore, the efficacy of the proposed theory in representing the unconfined compression experiments was assessed by comparing its theoretical predictions with those obtained from other versions of the biphasic theory such as the isotropic, transversely isotropic, and viscoelastic models. The unconfined compression behavior of articular cartilage as well as corneal stroma was used for this purpose. It is concluded that while the proposed model is capable of accurately representing the viscoelastic behavior of any hydrated soft tissue in unconfined compression, it is particularly useful in modeling the behavior of those with a transversely isotropic skeleton.

A Transversely Isotropic Biphasic Model for Unconfined Compression of Growth Plate and Chondroepiphysis

1998 ◽  
Vol 120 (4) ◽  
pp. 491-496 ◽  
Author(s):  
B. Cohen ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Stress Relaxation ◽  
Growth Plate ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Solid Matrix ◽  
Elastic Model ◽  
Unconfined Compression ◽  
Biphasic Model ◽  
Cylindrical Axis

Using the biphasic theory for hydrated soft tissues (Mow et al., 1980) and a transversely isotropic elastic model for the solid matrix, an analytical solution is presented for the unconfined compression of cylindrical disks of growth plate tissues compressed between two rigid platens with a frictionless interface. The axisymmetric case where the plane of transverse isotropy is perpendicular to the cylindrical axis is studied, and the stress-relaxation response to imposed step and ramp displacements is solved. This solution is then used to analyze experimental data from unconfined compression stress-relaxation tests performed on specimens from bovine distal ulnar growth plate and chondroepiphysis to determine the biphasic material parameters. The transversely isotropic biphasic model provides an excellent agreement between theory and experimental results, better than was previously achieved with an isotropic model, and can explain the observed experimental behavior in unconfined compression of these tissues.

Sign in / Sign up

Export Citation Format

Share Document