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.

Unconfined Compression of Articular Cartilage: Nonlinear Behavior and Comparison With a Fibril-Reinforced Biphasic Model

1999 ◽  
Vol 122 (2) ◽  
pp. 189-195 ◽  
Author(s):  
M. Fortin ◽  
J. Soulhat ◽  
A. Shirazi-Adl ◽  
E. B. Hunziker ◽  
M. D. Buschmann
Keyword(s):  
Articular Cartilage ◽  
Mechanical Behavior ◽  
Small Amplitude ◽  
Dynamic Stiffness ◽  
Scaling Law ◽  
Nonlinear Behavior ◽  
Hydraulic Permeability ◽  
Unconfined Compression ◽  
Biphasic Model ◽  
Strain Dependent

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. Disks of full-thickness adult articular cartilage from bovine humeral heads were subjected to successive applications of small-amplitude ramp compressions cumulating to a 10 percent compression offset where a series of sinusoidal and ramp compression and ramp release displacements were superposed. We found all equilibrium behavior (up to 10 percent axial compression offset) to be linear, while most nonequilibrium behavior was nonlinear, with the exception of small-amplitude ramp compressions applied from the same compression offset. Observed nonlinear behavior included compression-offset-dependent stiffening of the transient response to ramp compression, nonlinear maintenance of compressive stress during release from a prescribed offset, and a nonlinear reduction in dynamic stiffness with increasing amplitudes of sinusoidal compression. The fibril-reinforced biphasic model was able to describe stress relaxation response to ramp compression, including the high ratio of peak to equilibrium load. However, compression offset-dependent stiffening appeared to suggest strain-dependent parameters involving strain-dependent fibril network stiffness and strain-dependent hydraulic permeability. Finally, testing of disks of different diameters and rescaling of the frequency according to the rule prescribed by current biphasic and poroelastic models (rescaling with respect to the sample’s radius squared) reasonably confirmed the validity of that scaling rule. The overall results of this study support several aspects of current theoretical models of articular cartilage mechanical behavior, motivate further experimental characterization, and suggest the inclusion of specific nonlinear behaviors to models. [S0148-0731(00)00702-0]

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.

Effects of Refrigeration and Freezing on the Electromechanical and Biomechanical Properties of Articular Cartilage

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Adele Changoor ◽  
Liah Fereydoonzad ◽  
Alex Yaroshinsky ◽  
Michael D. Buschmann
Keyword(s):  
Articular Cartilage ◽  
Experimental Testing ◽  
Biomechanical Testing ◽  
Biomechanical Properties ◽  
Fresh Tissue ◽  
Testing Procedures ◽  
Freeze Thaw ◽  
Thaw Cycle ◽  
Freeze Thaw Cycle

In vitro electromechanical and biomechanical testing of articular cartilage provide critical information about the structure and function of this tissue. Difficulties obtaining fresh tissue and lengthy experimental testing procedures often necessitate a storage protocol, which may adversely affect the functional properties of cartilage. The effects of storage at either 4°C for periods of 6 days and 12 days, or during a single freeze-thaw cycle at −20°C were examined in young bovine cartilage. Non-destructive electromechanical measurements and unconfined compression testing on 3 mm diameter disks were used to assess cartilage properties, including the streaming potential integral (SPI), fibril modulus (Ef), matrix modulus (Em), and permeability (k). Cartilage disks were also examined histologically. Compared with controls, significant decreases in SPI (to 32.3±5.5% of control values, p<0.001), Ef (to 3.1±41.3% of control values, p=0.046), Em (to 6.4±8.5% of control values, p<0.0001), and an increase in k (to 2676.7±2562.0% of control values, p=0.004) were observed at day 12 of refrigeration at 4°C, but no significant changes were detected at day 6. A trend toward detecting a decrease in SPI (to 94.2±6.2% of control values, p=0.083) was identified following a single freeze-thaw cycle, but no detectable changes were observed for any biomechanical parameters. All numbers are mean±95% confidence interval. These results indicate that fresh cartilage can be stored in a humid chamber at 4°C for a maximum of 6 days with no detrimental effects to cartilage electromechanical and biomechanical properties, while one freeze-thaw cycle produces minimal deterioration of biomechanical and electromechanical properties. A comparison to literature suggested that particular attention should be paid to the manner in which specimens are thawed after freezing, specifically by minimizing thawing time at higher temperatures.

Effect of Anisotropic Permeability of the Superficial Layer on the Frictional Property in Articular Cartilage

2013 ◽  
Author(s):  
Kyuichiro Imade ◽  
Hiromichi Fujie
Keyword(s):  
Articular Cartilage ◽  
Hydrodynamic Lubrication ◽  
Articular Surface ◽  
Compressive Strain ◽  
Electron Microscopic Observation ◽  
Superficial Layer ◽  
Frictional Property ◽  
Hydraulic Permeability ◽  
Electron Microscopic ◽  
Biphasic Model

Articular cartilage has a significant lubrication property that has been explained in previous studies by many theories including mixed lubrication, hydrodynamic lubrication, surface gel hydration lubrication, biphasic theory, and so on. However the mechanism of continuously low friction in articular cartilage still remains unclear. Reynaud and Quinn indicated that the hydraulic permeability was significantly anisotropic under compressive strain; the tangential permeability becomes lower than the normal permeability under compression [1]. Meanwhile scanning electron microscopic observation indicated that the superficial layer of articular surface was consisted of close-packed collagen fibers aligning parallel with articular surface and tangling each other in normal cartilage (Fig. 1). It is, therefore, suggested that the permeability is extremely low in the tangential direction when subjected to compressive strain. We have a hypothesis that the unique structure and properties in the articular cartilage superficial layer may improve the lubrication properties [2]. Therefore, we performed an analytical study using a fiber-reinforced poroelastic biphasic model to determine the effect of lateral permeability reduction in the superficial layer on the frictional property of articular cartilage.

Field Determined Live Load Distribution Factors for Modular Press-Brake-Formed Tub Girders

2021 ◽  
pp. 036119812098375
Author(s):  
Karl E. Barth ◽  
Gregory K. Michaelson ◽  
Adam D. Roh ◽  
Robert M. Tennant
Keyword(s):  
West Virginia ◽  
Experimental Testing ◽  
Field Performance ◽  
Live Load ◽  
Steel Bridge ◽  
Testing Procedures ◽  
Bending Capacity ◽  
Short Span ◽  
And Performance ◽  
Live Load Distribution

This paper is focused on the field performance of a modular press-brake-formed tub girder (PBFTG) system in short span bridge applications. The scope of this project to conduct a live load field test on West Virginia State Project no. S322-37-3.29 00, a bridge utilizing PBFTGs located near Ranger, West Virginia. The modular PBFTG is a shallow trapezoidal box girder cold-formed using press-brakes from standard mill plate widths and thicknesses. A technical working group within the Steel Market Development Institute’s Short Span Steel Bridge Alliance, led by the current authors, was charged with the development of this concept. Research of PBFTGs has included analyzing the flexural bending capacity using experimental testing and analytical methods. This paper presents the experimental testing procedures and performance of a composite PBFTG bridge.

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).

Mechanical anisotropy of the human knee articular cartilage in compression

2003 ◽  
Vol 217 (3) ◽  
pp. 215-219 ◽  
Author(s):  
J S Jurvelin ◽  
M D Buschmann ◽  
E B Hunziker
Keyword(s):  
Articular Cartilage ◽  
Poisson’S Ratio ◽  
Articular Surface ◽  
Mechanical Anisotropy ◽  
Poisson's Ratio ◽  
Hydraulic Permeability ◽  
Compression Tests ◽  
Direction Parallel ◽  
Anisotropic Mechanical Properties ◽  
Femoral Groove

Articular cartilage exhibits anisotropic mechanical properties when subjected to tension. However, mechanical anisotropy of mature cartilage in compression is poorly known. In this study, both confined and unconfined compression tests of cylindrical cartilage discs, taken from the adult human patello-femoral groove and cut either perpendicular (normal disc) or parallel (tangential disc) to the articular surface, were utilized to determine possible anisotropy in Young's modulus, E, aggregate modulus, Ha, Poisson's ratio, v and hydraulic permeability, k, of articular cartilage. The results indicated that Ha was significantly higher in the direction parallel to the articular surface as compared with the direction perpendicular to the surface ( Ha = 1.237 ± 0.486 MPa versus Ha = 0.845 ± 0.383 MPa, p = 0.017, n = 10). The values of Poisson's ratio were similar, 0.158 ± 0.148 for normal discs compared with 0.180 ± 0.046 for tangential discs. Analysis using the linear biphasic model revealed that the decrease of permeability during the offset compression of 0–20 per cent was higher ( p = 0.015, n = 10) in normal (from 25.5 × 10− 15 to 1.8 × 10−15 m4/N s) than in tangential (from 12.3 × 10− 15 to 1.3 × 10− 15 m4/N s) discs. Based on the results, it is concluded that the mechanical characteristics of adult femoral groove articular cartilage are anisotropic also during compression. Anisotropy during compression may be essential for normal cartilage function. This property has to be considered when developing advanced theoretical models for cartilage biomechanics.

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