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.

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 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.

scholarly journals Development and validation of a method for the simultaneous analysis of fatty acid ethyl esters, ethyl sulfate and ethyl glucuronide in neonatal meconium: application in two cases of alcohol consumption during pregnancy

2021 ◽  
Vol 413 (11) ◽  
pp. 3093-3105
Author(s):  
Mateusz Kacper Woźniak ◽  
Laura Banaszkiewicz ◽  
Justyna Aszyk ◽  
Marek Wiergowski ◽  
Iwona Jańczewska ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Fatty Acid ◽  
Alcohol Consumption ◽  
Solid Phase ◽  
Fatty Acid Ethyl Esters ◽  
Ethyl Esters ◽  
Ethyl Glucuronide ◽  
Published Data ◽  
Ethyl Sulfate ◽  
Analytical Approaches

AbstractAlcohol consumption during pregnancy constitutes one of the leading preventable causes of birth defects and neurodevelopmental disorders in the exposed children. Fatty acid ethyl esters (FAEEs), ethyl glucuronide (EtG) and ethyl sulfate (EtS) have been studied as potential biomarkers of alcohol consumption. However, most analytical approaches proposed for their analysis in meconium samples consist of separated extraction procedures requiring the use of two meconium aliquots, which is costly in terms of both time and materials. Therefore, the aim of this study was to develop and validate a method for the simultaneous extraction of 9 FAEEs, EtG and EtS from one meconium aliquot. The sample was homogenized using methanol, and then FAEEs were extracted with hexane while EtG and EtS were isolated using acetonitrile. Then, extracts were applied to solid-phase extraction columns and analysed by gas chromatography mass spectrometry (FAEEs) and liquid chromatography tandem mass spectrometry (EtG and EtS). Calibration curves were linear with r values greater than 0.99. The LODs ranged from 0.8 to 7.5 ng/g for FAEEs and were 0.2 ng/g and 0.8 ng/g for EtS and EtG, respectively. LOQs ranged from 5 to 25 ng/g for FAEEs and were 1 ng/g and 2.5 ng/g for EtS and EtG, respectively. Accuracies and precisions were between 93.8 and 107% and between 3.5 and 9.7%, respectively. The recovery values ranged from 89.1 to 109%. The method proved to be sensitive, specific, simple and fast and allowed for the reduction of the amount of organic solvent used for extraction compared to other published data while higher recoveries were obtained. The method was used for analysis of meconium samples in two cases of mothers who were consuming alcohol during pregnancy.

scholarly journals Numerical modeling of reinforced concrete structures: static and dynamic analysis

2013 ◽  
Vol 66 (4) ◽  
pp. 425-430 ◽  
Author(s):  
Jorge Luis Palomino Tamayo ◽  
Armando Miguel Awruch ◽  
Inácio Benvegnu Morsch
Keyword(s):  
Reinforced Concrete ◽  
Numerical Model ◽  
Finite Elements ◽  
Dynamic Analysis ◽  
Time Integration ◽  
Great Accuracy ◽  
Constitutive Law ◽  
Published Data ◽  
Static And Dynamic Analysis ◽  
Plates And Shells

A numerical model using the Finite Element Method (FEM) for the nonlinear static and dynamic analysis of reinforced concrete (RC) beams, plates and shells is presented in this work. For this purpose, computer programs based on plasticity theory and with crack monitoring capabilities are developed. The static analysis of RC shells up to failure load is carried out using 9-node degenerated shell finite elements while 20-node brick finite elements are used for dynamic applications. The elasto-plastic constitutive law for concrete is coupled with a strain-rate sensitive model in order to take into account high loading rate effect when transient loading is intended. The implicit Newmark scheme with predictor and corrector phases is used for time integration of the nonlinear system of equations. In both cases, the steel reinforcement is considered to be smeared and represented by membrane finite elements. Various benchmark examples are solved with the present numerical model and comparisons with other published data are performed. For all examples, the path failure, collapse loads and failure mechanism is reproduced with great accuracy.

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.

Comparison of the Trueness of Fits of the Biphasic Transverse Isotropic and Kelvin Models to the Tensile Behavior of Temporomandibular Joint Disc

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Wuyang Li ◽  
Sara Trbojevic ◽  
Alejandro J. Almarza
Keyword(s):  
Experimental Data ◽  
Stress Relaxation ◽  
Temporomandibular Joint ◽  
Second Order ◽  
Relaxation Test ◽  
Stress Relaxation Test ◽  
Kelvin Model ◽  
Biphasic Model ◽  
Tmj Disc ◽  
Transverse Isotropic

Abstract This technical brief explores the validity and trueness of fit for using the transverse isotropic biphasic and Kelvin models (first and second order generalized) for characterization of the viscoelastic tensile properties of the temporomandibular joint (TMJ) discs from pigs and goats at a strain rate of 10 mm/min. We performed incremental stress-relaxation tests from 0 to 12% strain, in 4% strain steps on pig TMJ disc samples. In addition, to compare the outcomes of these models between species, we also performed a single-step stress-relaxation test of 10% strain. The transverse isotropic biphasic model yielded reliable fits in reference to the least root mean squared error method only at low strain, while the Kelvin models yielded good fits at both low and high strain, with the second order generalized Kelvin model yielding the best fit. When comparing pig to goat TMJ disc in 10% strain stress-relaxation test, unlike the other two Kelvin models, the transverse isotropic model did not fit well for this larger step. In conclusion, the second order Kelvin model showed the best fits to the experimental data of both species. The transverse isotropic biphasic model did not fit well with the experimental data, although better at low strain, suggesting that the assumption of water flow only applies while uncrimping the collagen fibers. Thus, it is likely that the permeability from the biphasic model is not truly representative, and other biphasic models, such as the poroviscoelastic model, would likely yield more meaningful outputs and should be explored in future works.

A Nonlinear Biphasic Model for Fluid Transport and Tissue Deformation During Constant Flow Rate Infusion Into Brain Tissue

2009 ◽  
Author(s):  
Joshua H. Smith ◽  
Jose Jaime García
Keyword(s):  
Brain Tissue ◽  
Fluid Transport ◽  
Solid Phase ◽  
Phase 1 ◽  
Therapeutic Agents ◽  
Tissue Deformation ◽  
Convection Enhanced Delivery ◽  
Adequate Treatment ◽  
Biphasic Model ◽  
Constant Flow Rate

The delivery of therapeutic agents into the brain is impeded by the blood-brain barrier, preventing adequate treatment of diseases of the central nervous system. Convection enhanced delivery was developed as a means to deliver therapeutic agents directly into brain tissue and to transport the drugs in the extracellular space using convective flow. Poroelastic or biphasic models have been used to study the concomitant fluid transport and tissue deformation that occurs during infusion, however previous studies have been limited by the assumption of linear elasticity of the solid phase [1].

scholarly journals Computation of Opacities for Diatomic Molecules

1994 ◽  
Vol 146 ◽  
pp. 282-295 ◽  
Author(s):  
Robert L. Kurucz
Keyword(s):  
Distribution Function ◽  
Least Squares ◽  
Diatomic Molecules ◽  
Energy Levels ◽  
Published Data ◽  
Molecular Line ◽  
Model Calculations ◽  
Line List ◽  
Thomas Fermi ◽  
Atomic Lines

In this section I briefly describe my efforts to improve the atomic and molecular line data. This work is described in more detail in Kurucz (1992a). In subsequent sections I briefly describe three methods for computing opacity and the models and spectra that result from using them.My model calculations in the 1970s used the distribution-function line opacity computed by Kurucz (1979a,b) from the line data of Kurucz & Peytremann (1975). We had computedgfvalues for 1.7 million atomic lines for sequences up through nickel using scaled-Thomas-Fermi-Dirac wavefunctions and eigenvectors determined from least squares Slater parameter fits to the observed energy levels. We also collected all published data ong fvalues and included them in the line list whenever they appeared to be more reliable than the computed data (that work is ongoing, but I am running behind).

Sign in / Sign up

Export Citation Format

Share Document