Stress–relaxation of human patellar articular cartilage in unconfined compression: Prediction of mechanical response by tissue composition and structure

2008 ◽  
Vol 41 (9) ◽  
pp. 1978-1986 ◽  
Author(s):  
Petro Julkunen ◽  
Wouter Wilson ◽  
Jukka S. Jurvelin ◽  
Jarno Rieppo ◽  
Cheng-Juan Qu ◽  
...  
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Mechanical Response ◽  
Tissue Composition ◽  
Unconfined Compression ◽  
Composition And Structure

An in Situ Dual Indentation and Optimization Method to Determine Mechanical Properties of Articular Cartilage

2007 ◽  
Author(s):  
Jonathan E. Pottle ◽  
J.-K. Francis Suh
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Structural Integrity ◽  
Reaction Force ◽  
Model Parameters ◽  
Unconfined Compression ◽  
Confined Compression ◽  
Practical Applications

The efficacy of the biphasic poroviscoelastic (BPVE) theory [1] in constitutive modeling of articular cartilage biomechanics is well-established [2–4]. Indeed, this model has been used to simultaneously predict stress relaxation force across confined compression, unconfined compression, and indentation protocols [2,3]. Previous works have also demonstrated success in simultaneously curve-fitting the BPVE model to reaction force and lateral deformation data gathered from stress relaxation tests of articular cartilage in unconfined compression [4]. However, a potential limitation of practical applications of such a successful model is seen in some commonly-employed mechanical testing methods for articular cartilage, such as confined compression and unconfined compression. These methods require the excision of a disk of cartilage from its underlying subchondral base, which likely would compromise the structural integrity of the tissue, causing swelling and curling artifacts of the sample [5]. Indentation represents a testing protocol that can be used with an intact cartilage layer. This results in a specimen more closely resembling cartilage in vivo. Using an agarose gel construct, our previous study [6] has demonstrated that a unique set of the six BPVE model parameters of a soft tissue can be determined readily from in situ dual indentation method using stress relaxation and creep viscoelastic protocols. The objective of the current study is to validate the efficacy of this technique as a means to determine the BPVE material parameters of articular cartilage.

scholarly journals Dynamic Response of Immature Bovine Articular Cartilage in Tension and Compression, and Nonlinear Viscoelastic Modeling of the Tensile Response

2006 ◽  
Vol 128 (4) ◽  
pp. 623-630 ◽  
Author(s):  
Seonghun Park ◽  
Gerard A. Ateshian
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Tensile Stress ◽  
Dynamic Modulus ◽  
Relaxation Function ◽  
Tensile Modulus ◽  
Relaxation Response ◽  
Unconfined Compression ◽  
Tensile Response ◽  
Cyclical Loading

Very limited information is currently available on the constitutive modeling of the tensile response of articular cartilage and its dynamic modulus at various loading frequencies. The objectives of this study were to (1) formulate and experimentally validate a constitutive model for the intrinsic viscoelasticity of cartilage in tension, (2) confirm the hypothesis that energy dissipation in tension is less than in compression at various loading frequencies, and (3) test the hypothesis that the dynamic modulus of cartilage in unconfined compression is dependent upon the dynamic tensile modulus. Experiment 1: Immature bovine articular cartilage samples were tested in tensile stress relaxation and cyclical loading. A proposed reduced relaxation function was fitted to the stress-relaxation response and the resulting material coefficients were used to predict the response to cyclical loading. Adjoining tissue samples were tested in unconfined compression stress relaxation and cyclical loading. Experiment 2: Tensile stress relaxation experiments were performed at varying strains to explore the strain-dependence of the viscoelastic response. The proposed relaxation function successfully fit the experimental tensile stress-relaxation response, with R2=0.970±0.019 at 1% strain and R2=0.992±0.007 at 2% strain. The predicted cyclical response agreed well with experimental measurements, particularly for the dynamic modulus at various frequencies. The relaxation function, measured from 2% to 10% strain, was found to be strain dependent, indicating that cartilage is nonlinearly viscoelastic in tension. Under dynamic loading, the tensile modulus at 10Hz was ∼2.3 times the value of the equilibrium modulus. In contrast, the dynamic stiffening ratio in unconfined compression was ∼24. The energy dissipation in tension was found to be significantly smaller than in compression (dynamic phase angle of 16.7±7.4deg versus 53.5±12.8deg at 10−3Hz). A very strong linear correlation was observed between the dynamic tensile and dynamic compressive moduli at various frequencies (R2=0.908±0.100). The tensile response of cartilage is nonlinearly viscoelastic, with the relaxation response varying with strain. A proposed constitutive relation for the tensile response was successfully validated. The frequency response of the tensile modulus of cartilage was reported for the first time. Results emphasize that fluid-flow dependent viscoelasticity dominates the compressive response of cartilage, whereas intrinsic solid matrix viscoelasticity dominates the tensile response. Yet the dynamic compressive modulus of cartilage is critically dependent upon elevated values of the dynamic tensile modulus.

Stress Relaxation of Articular Cartilage in Unconfined Compression

2012 ◽  
Author(s):  
Patrick Smyth ◽  
Itzhak Green ◽  
Robert Jackson ◽  
R. Reid Hanson
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Osteoarthritic Cartilage ◽  
Healthy Cartilage ◽  
Storage And Loss Moduli ◽  
Relaxation Experiments ◽  
Insight Into

The articular cartilage function is to allow the bones in a joint to move without causing excess friction and damage. When this cartilage becomes damaged, the supportive and lubricating mechanisms break down, leading to injuries which can be permanent or take extended periods of time for recovery. Because of its importance in general health and body mobility, the unique lubricating properties of cartilage have been studied for many decades. Many current theories exist to characterize the biphasic and triphasic nature of cartilage; however, an important reason that cartilage is so effective is its viscoelastic nature, which allows elastic and dissipative mechanisms to exist simultaneously. It is desired to derive the material properties of cartilage in order to better understand its mechanical effectiveness. Utilizing a CETR-UMT-3 Tribometer, stress relaxation experiments will be performed on freshly harvested equine cartilage plugs that remain hydrated in a fluid bath. Viscoelastic models, such as the Prony series and fractional derivative, are applied to the experimental data to determine the storage and loss moduli of the sample explants. The storage and loss information characterizes the mechanical response of cartilage, and provides insight into the effectiveness and longevity of biological joints. A comparison will be made between joints that experience similar loads, but undergo different relative motions, to determine if the mechanical properties of cartilage are tailored to joint function. Osteoarthritic cartilage will also be explored for deviations in viscoelastic behavior compared to healthy cartilage. Ultimately, it is hoped that a viscoelastic characterization of articular cartilage will lead to insight into the precursors of osteoarthritis, more advanced prosthetics, and biomimetric applications such as the integration of flexible surfaces in mechanical systems.

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 Poroviscoelastic Model Simultaneously Predicts Axial Reaction Force and Lateral Displacement of Articular Cartilage During an Unconfined Compression-Stress Relaxation Experiment

1999 ◽  
Author(s):  
Mark R. DiSilvestro ◽  
Qiliang Zhu ◽  
Marcy Wong ◽  
Jukka Jurvelin ◽  
Jun-Kyo Suh
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Stress Relaxation ◽  
Mechanical Behavior ◽  
Lateral Displacement ◽  
Reaction Force ◽  
Simple Extension ◽  
Unconfined Compression ◽  
Relaxation Experiment ◽  
Diarthrodial Joints

Abstract Articular cartilage lining the articulating surfaces in diarthrodial joints is composed of an extracellular matrix and interstitial fluid. The complex mechanical behavior of this tissue has been successfully modeled by the linear biphasic poroviscoelastic (BPVE) model first introduced by Mak (1986). This model, a simple extension of the well-known biphasic theory first proposed by Mow et al. (1980), accounts for both fluid flow-dependent and fluid flow-independent viscoelastic mechanisms which contribute to the overall mechanical behavior exhibited by the tissue. Despite the success of the linear BPVE model for indentation (Suh and Bai, 1997), as well as that described for unconfined compression (Suh and DiSilvestro, 1997, 1998), the model’s ability to account for more than one measurable variable with a single parameter set has not been established. Therefore, the objective, of this study was to assess the ability of the linear BPVE model to account for both the axial reaction force and lateral deformation of a cylindrical plug of articular cartilage subjected to unconfined compression under a stress relaxation protocol.

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.

Volumetric changes of articular cartilage during stress relaxation in unconfined compression

2000 ◽  
Vol 33 (9) ◽  
pp. 1049-1054 ◽  
Author(s):  
M Wong ◽  
M Ponticiello ◽  
V Kovanen ◽  
J.S Jurvelin
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Unconfined Compression
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