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.

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.

A Fibril-Network-Reinforced Biphasic Model of Cartilage in Unconfined Compression

1999 ◽  
Vol 121 (3) ◽  
pp. 340-347 ◽  
Author(s):  
J. Soulhat ◽  
M. D. Buschmann ◽  
A. Shirazi-Adl
Keyword(s):  
Stress Relaxation ◽  
Composite Structure ◽  
Solid Phase ◽  
Constitutive Law ◽  
Published Data ◽  
Hydraulic Permeability ◽  
Unconfined Compression ◽  
Model Calculations ◽  
Biphasic Model ◽  
Reinforced Composite

Cartilage mechanical function relies on a composite structure of a collagen fibrillar network entrapping a proteoglycan matrix. Previous biphasic or poroelastic models of this tissue, which have approximated its composite structure using a homogeneous solid phase, have experienced difficulties in describing measured material responses. Progress to date in resolving these difficulties has demonstrated that a constitutive law that is successful for one test geometry (confined compression) is not necessarily successful for another (unconfined compression). In this study, we hypothesize that an alternative fibril-reinforced composite biphasic representation of cartilage can predict measured material responses and explore this hypothesis by developing and solving analytically a fibril-reinforced biphasic model for the case of uniaxial unconfined compression with frictionless compressing platens. The fibrils were considered to provide stiffness in tension only. The lateral stiffening provided by the fibril network dramatically increased the frequency dependence of disk rigidity in dynamic sinusoidal compression and the magnitude of the stress relaxation transient, in qualitative agreement with previously published data. Fitting newly obtained experimental stress relaxation data to the composite model allowed extraction of mechanical parameters from these tests, such as the rigidity of the fibril network, in addition to the elastic constants and the hydraulic permeability of the remaining matrix. Model calculations further highlight a potentially important difference between homogeneous and fibril-reinforced composite models. In the latter type of model, the stresses carried by different constituents can be dissimilar, even in sign (compression versus tension) even though strains can be identical. Such behavior, resulting only from a structurally physiological description, could have consequences in the efforts to understand the mechanical signals that determine cellular and extracellular biological responses to mechanical loads in cartilage.

On Unconfined Compression Response of the Porcine Corneal Stroma

2013 ◽  
Author(s):  
Ebitimi Etebu ◽  
Hamed Hatami-Marbini
Keyword(s):  
Mechanical Properties ◽  
Lattice Structure ◽  
Research Work ◽  
Corneal Stroma ◽  
Swelling Pressure ◽  
Transversely Isotropic ◽  
Collagen Fibrils ◽  
Mechanical Parameters ◽  
Unconfined Compression ◽  
Biphasic Model

The corneal stroma constitutes about 90% of the corneal total thickness and is mainly responsible for its mechanical properties. The stroma is a highly ordered structure composed of mostly parallel to the surface stacks of 2 μm thick collagenous lamellae. The collagen fibrils have an almost uniform diameter and are arranged in a pseudohexagonal lattice structure. Under normal physiological conditions, the collagen fibrils are responsible for carrying the membrane tensile stresses caused by the intraocular pressure. It is believed that the interaction between the collagen fibrils and hydrophilic negatively charged proteoglycans are responsible for the stromal architecture as well as the compressive properties of the tissue. Up to date uniaxial strip testing method and biaxial pressure inflation experiments have widely been used to determine the mechanical parameters of the cornea. These experimental measurements often provide the necessary information for characterizing the tissue behavior in tension [1] [2, 3]. Nevertheless, the mechanical parameters of the cornea in compression have received less attention in the literature. Most of the previous studies are focused on describing the swelling pressure and hydration relations [4]. In this research work, we used unconfined compression experiments along with a biphasic model to measure the corneal parameters in compression. This method has been extensively used to explore the mechanical properties of similar hydrated tissues such as the articular cartilage [5]. Due to specific microstructure of the cornea, a transversely isotropic model was used to curve-fit the experimental data and to derive the in-plane modulus of the cornea. The predicted in-plane modulus was compared to the values reported in literature.

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.

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.

Experimental and Biphasic FEM Determinations of the Material Properties and Hydraulic Permeability of the Meniscus in Tension1

2002 ◽  
Vol 124 (3) ◽  
pp. 315-321 ◽  
Author(s):  
Michelle A. LeRoux ◽  
Lori A. Setton
Keyword(s):  
Finite Element ◽  
Stress Relaxation ◽  
Transversely Isotropic ◽  
Element Model ◽  
Tensile Tests ◽  
Solid Matrix ◽  
Hydraulic Permeability ◽  
Permeability Coefficients ◽  
Matrix Properties ◽  
Biphasic Finite Element

Tensile tests and biphasic finite element modeling were used to determine a set of transversely isotropic properties for the meniscus, including the hydraulic permeability coefficients and solid matrix properties. Stress-relaxation tests were conducted on planar samples of canine meniscus samples of different orientations, and the solid matrix properties were determined from equilibrium data. A 3-D linear biphasic and tranversely isotropic finite element model was developed to model the stress-relaxation behavior of the samples in tension, and optimization was used to determine the permeability coefficients, k1 and k2, governing fluid flow parallel and perpendicular to the collagen fibers, respectively. The collagen fibrillar orientation was observed to have an effect on the Young’s moduli (E1=67.8MPa,E2=11.1MPa) and Poisson’s ratios (ν12=2.13,ν21=1.50,ν23=1.02). However, a significant effect of anisotropy on permeability was not detected (k1=0.09×10−16m4/Ns,k2=0.10×10−16m4/Ns). The low permeability values determined in this study provide insight into the extent of fluid pressurization in the meniscus and will impact modeling predictions of load support in the meniscus.

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.

Automated Estimation of Elastic Material Parameters of a Transversely Isotropic Material Using Asymmetric Indentation and Inverse Finite Element Analysis

2015 ◽  
Author(s):  
Yuan Feng ◽  
Chung-Hao Lee ◽  
Lining Sun ◽  
Ruth J. Okamoto ◽  
Songbai Ji
Keyword(s):  
Finite Element ◽  
Soft Tissues ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Biological Tissues ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Soft Biological Tissues ◽  
Tissue Properties ◽  
Brain White Matter

Anisotropy exists in many soft biological tissues. The most common anisotropy is transverse isotropy, which is typical for fiber-reinforced structures, such as the brain white matter, tendon and muscle. Although many methods have been proposed to determine tissue properties, techniques to characterize transversely isotropic materials remain limited. The goal of this study is to investigate the feasibility of asymmetric indentation coupled with numerical optimization based on inverse finite element (FE) simulation to characterize transversely isotropic soft biological tissues. The proposed approach combining indentation and optimization may provide a useful general framework to characterize a variety of fiber-reinforced soft tissues in the future.

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.

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