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.

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.

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.

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.

Isolation, Loading and Estimating the Poroelastic Properties of a Single Osteon

2009 ◽  
Author(s):  
Gaffar Gailani ◽  
Mohammed Benalla ◽  
Rashal Mahamud ◽  
Stephen Cowin ◽  
Luis Cardoso
Keyword(s):  
Mechanical Properties ◽  
Fluid Flow ◽  
Stress Relaxation ◽  
Reasonable Agreement ◽  
Transverse Isotropy ◽  
Bone Mechanics ◽  
Unconfined Compression ◽  
Stress Relaxation Test ◽  
Tools And Methods

Determining the poroelastic properties of osteons is critical to better understand the role of fluid flow in the nutrition, mechanotransduction, remodeling, homeostasis and loss of bone. The permeability of single osteons is among the key properties that may influence these phenomena. The measurement of permeability of a single osteon remains one of the most demanding tasks in bone mechanics to be developed. Two associated challenges are the size of the osteon and the absence of appropriate tools and methods to perform such measurement. In this communication, we present the development of a new procedure to isolate osteons, the design of a mechanism for loading an osteon and the comparison of the stress relaxation test in unconfined compression experiment with the analytical results for a compressible transverse isotropy model that we previously reported in Gailani and Cowin [1]. These experimentally determined values of permeability and mechanical properties have shown reasonable agreement with the previously reported experimentally and theoretically estimated values.

Use of Indentation Test to Determine the Proteoglycan Content of Articular Cartilage

2002 ◽  
Author(s):  
Xin Lu ◽  
Daniel D. Sun ◽  
X. Edward Guo ◽  
Hui Chen ◽  
W. Michael Lai ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Articular Cartilage ◽  
Indentation Test ◽  
Solid Matrix ◽  
Interstitial Fluid Flow ◽  
Fibrous Network ◽  
Indentation Experiment ◽  
Proteoglycan Content ◽  
Creep And Stress Relaxation ◽  
First Time

The indentation experiment has been widely used to determine mechanical properties of articular cartilage [e.g., 1–3]. This method does not disrupt the fibrous network of the tissue nor does it require removing the tissue from the underlying bone. The biphasic indentation theory has been successfully used to determine the effect of interstitial fluid flow and pressurization (load support) on the creep and stress-relaxation behaviors of articular cartilage, and to determine its apparent mechanical properties (i.e., the elastic moduli of the extracellular solid matrix and its permeability) [1, 3]. However, due to its proteoglycan content, articular cartilage is a charged tissue with a high fixed charge density (FCD) [4]. Proteoglycan and collagen contents, water, etc, vary with age or with orthteoarthritis [4, 5]. The FCD plays important physicochemical roles in load support and mechano-electrochemial behaviors of the tissue and also regulates chondrocyte biosynthetic activities [4–7]. It is therefore important to develop an effective technique to determine not only the mechanical properties but also the electrochemical property (e.g., FCD) of the tissue, simultaneously and at the same location. The purpose of the current study is to determine, for the first time, both the mechanical properties and FCD of the extracellular matrix using an indentation test.

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.

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.

Rolling resistance of articular cartilage due to interstitial fluid flow

1997 ◽  
Vol 211 (5) ◽  
pp. 419-424 ◽  
Author(s):  
G A Ateshian ◽  
H Wang
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Friction Coefficient ◽  
Interstitial Fluid ◽  
Frictional Coefficient ◽  
Rolling Resistance ◽  
Rolling Contact ◽  
Interstitial Fluid Flow ◽  
Tissue Properties ◽  
Theoretical Predictions

A mechanism which may contribute to the frictional coefficient of diarthrodial joints is the rolling resistance due to hysteretic energy loss of viscoelastic cartilage resulting from interstitial fluid flow. The hypothesis of this study is that rolling resistance contributes significantly to the measured friction coefficient of articular cartilage. Due to the difficulty of testing this hypothesis experimentally, theoretical predictions of the rolling resistance are obtained using the solution for rolling contact of biphasic cylindrical cartilage layers [Ateshian and Wang (1)]. Over a range of rolling velocities, tissue properties and dimensions, it is found that the coefficient of rolling resistance μR varies in magnitude from 10−6 to 10−2; thus, it is generally negligible in comparison with experimental measurements of the cartilage friction coefficient (10−3-10−1) except, possibly, when the tissue is arthritic. Hence, the hypothesis of this study is rejected on the basis of these results.

Effects of Friction on the Unconfined Compressive Response of Articular Cartilage: A Finite Element Analysis

1990 ◽  
Vol 112 (2) ◽  
pp. 138-146 ◽  
Author(s):  
Robert L. Spilker ◽  
Jun-Kyo Suh ◽  
Van C. Mow
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Articular Cartilage ◽  
Soft Tissues ◽  
Solid Phase ◽  
Mechanical Test ◽  
Fluid Phase ◽  
Element Formulation ◽  
Unconfined Compression ◽  
Element Analysis

A finite element analysis is used to study a previously unresolved issue of the effects of platen-specimen friction on the response of the unconfined compression test; effects of platen permeability are also determined. The finite element formulation is based on the linear KLM biphasic model for articular cartilage and other hydrated soft tissues. A Galerkin weighted residual method is applied to both the solid phase and the fluid phase, and the continuity equation for the intrinsically incompressible binary mixture is introduced via a penalty method. The solid phase displacements and fluid phase velocities are interpolated for each element in terms of unknown nodal values, producing a system of first order differential equations which are solved using a standard numerical finite difference technique. An axisymmetric element of quadrilateral cross-section is developed and applied to the mechanical test problem of a cylindrical specimen of soft tissue in unconfined compression. These studies show that interfacial friction plays a major role in the unconfined compression response of articular cartilage specimens with small thickness to diameter ratios.

On the Electric Potentials Inside a Charged Soft Hydrated Biological Tissue: Streaming Potential Versus Diffusion Potential

2000 ◽  
Vol 122 (4) ◽  
pp. 336-346 ◽  
Author(s):  
W. Michael Lai ◽  
Van C. Mow ◽  
Daniel D. Sun ◽  
Gerard A. Ateshian
Keyword(s):  
Fluid Flow ◽  
Articular Cartilage ◽  
Electric Potential ◽  
Compressive Strain ◽  
Streaming Potential ◽  
Potential Effect ◽  
Diffusion Potential ◽  
Confined Compression ◽  
Interstitial Fluid Flow ◽  
One Dimensional

The main objective of this study is to determine the nature of electric fields inside articular cartilage while accounting for the effects of both streaming potential and diffusion potential. Specifically, we solve two tissue mechano-electrochemical problems using the triphasic theories developed by Lai et al. (1991, ASME J. Biomech Eng., 113, pp. 245–258) and Gu et al. (1998, ASME J. Biomech. Eng., 120, pp. 169–180) (1) the steady one-dimensional permeation problem; and (2) the transient one-dimensional ramped-displacement, confined-compression, stress-relaxation problem (both in an open circuit condition) so as to be able to calculate the compressive strain, the electric potential, and the fixed charged density (FCD) inside cartilage. Our calculations show that in these two technically important problems, the diffusion potential effects compete against the flow-induced kinetic effects (streaming potential) for dominance of the electric potential inside the tissue. For softer tissues of similar FCD (i.e., lower aggregate modulus), the diffusion potential effects are enhanced when the tissue is being compressed (i.e., increasing its FCD in a nonuniform manner) either by direct compression or by drag-induced compaction; indeed, the diffusion potential effect may dominate over the streaming potential effect. The polarity of the electric potential field is in the same direction of interstitial fluid flow when streaming potential dominates, and in the opposite direction of fluid flow when diffusion potential dominates. For physiologically realistic articular cartilage material parameters, the polarity of electric potential across the tissue on the outside (surface to surface) may be opposite to the polarity across the tissue on the inside (surface to surface). Since the electromechanical signals that chodrocytes perceive in situ are the stresses, strains, pressures and the electric field generated inside the extracellular matrix when the tissue is deformed, the results from this study offer new challenges for the understanding of possible mechanisms that control chondrocyte biosyntheses. [S0148-0731(00)00604-X]

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