scholarly journals An Axisymmetric Boundary Element Model for Determination of Articular Cartilage Pericellular Matrix Properties In Situ via Inverse Analysis of Chondron Deformation

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Eunjung Kim ◽  
Farshid Guilak ◽  
Mansoor A. Haider
Keyword(s):  
Experimental Data ◽  
Articular Cartilage ◽  
Boundary Element ◽  
Elastic Properties ◽  
Inverse Analysis ◽  
Three Dimensional ◽  
Pericellular Matrix ◽  
Unconfined Compression ◽  
Linear Elastic

The pericellular matrix (PCM) is the narrow tissue region surrounding all chondrocytes in articular cartilage and, together, the chondrocyte(s) and surrounding PCM have been termed the chondron. Previous theoretical and experimental studies suggest that the structure and properties of the PCM significantly influence the biomechanical environment at the microscopic scale of the chondrocytes within cartilage. In the present study, an axisymmetric boundary element method (BEM) was developed for linear elastic domains with internal interfaces. The new BEM was employed in a multiscale continuum model to determine linear elastic properties of the PCM in situ, via inverse analysis of previously reported experimental data for the three-dimensional morphological changes of chondrons within a cartilage explant in equilibrium unconfined compression (Choi, et al., 2007, “Zonal Changes in the Three-Dimensional Morphology of the Chondron Under Compression: The Relationship Among Cellular, Pericellular, and Extracellular Deformation in Articular Cartilage,” J. Biomech., 40, pp. 2596–2603). The microscale geometry of the chondron (cell and PCM) within the cartilage extracellular matrix (ECM) was represented as a three-zone equilibrated biphasic region comprised of an ellipsoidal chondrocyte with encapsulating PCM that was embedded within a spherical ECM subjected to boundary conditions for unconfined compression at its outer boundary. Accuracy of the three-zone BEM model was evaluated and compared with analytical finite element solutions. The model was then integrated with a nonlinear optimization technique (Nelder–Mead) to determine PCM elastic properties within the cartilage explant by solving an inverse problem associated with the in situ experimental data for chondron deformation. Depending on the assumed material properties of the ECM and the choice of cost function in the optimization, estimates of the PCM Young's modulus ranged from ∼24 kPa to 59 kPa, consistent with previous measurements of PCM properties on extracted chondrons using micropipette aspiration. Taken together with previous experimental and theoretical studies of cell-matrix interactions in cartilage, these findings suggest an important role for the PCM in modulating the mechanical environment of the chondrocyte.

Zonal Poisson Effect on the Chondron Deformation in Articular Cartilage under Compression

2007 ◽  
Vol 342-343 ◽  
pp. 133-136
Author(s):  
Jae Bong Choi
Keyword(s):  
Extracellular Matrix ◽  
Articular Cartilage ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Pericellular Matrix ◽  
Poisson Effect ◽  
Type Vi Collagen ◽  
Confocal Images ◽  
Three Dimensional Models

The objective of this study was to quantify the zonal difference of the in situ chondron’s Poisson effect under different magnitudes of compression. Fluorescence immunolabeling for type VI collagen was used to identify the pericellular matrix (PCM) and chondron, and a series of fluorescent confocal images were recorded and reconstructed to form quantitative three-dimensional models. The zonal variations in the mechanical response of the chondron do not appear to be due to zonal differences in PCM properties, but rather seem to result from significant inhomogeneities in relative stiffnesses of the extracellular matrix (ECM) and PCM with depth.

Determination of In Situ Articular Cartilage Pericellular Matrix Properties via Inverse BEM Analysis of Chondron Deformation

2010 ◽  
Author(s):  
Eunjung Kim ◽  
Farshid Guilak ◽  
Mansoor A. Haider
Keyword(s):  
Articular Cartilage ◽  
Compressive Strain ◽  
Critical Role ◽  
Three Dimensional ◽  
Cartilage Explants ◽  
Pericellular Matrix ◽  
Type Vi Collagen ◽  
Microscopy Technique

The pericellular matrix (PCM) of articular cartilage is the narrow tissue region surrounding all chondrocytes. Together, the chondrocyte and its surrounding PCM have been termed the chondron. In normal cartilage, the presence of type VI collagen is exclusive to the PCM, and the PCM is believed to play a critical role in regulating biomechanical cell-matrix interactions. Since the PCM is stiffer than the chondrocyte, it has been hypothesized to play a critical role in protecting the cell while, simultaneously, facilitating the transmission of mechanical signals to the cell. Previous studies that represent the cell, PCM and extracellular matrix (ECM) as linear biphasic materials have supported this hypothesized role for the PCM [1–4]. Previous in vitro micropipette studies of isolated chondrons [5–7] have shown that the PCM Young’s modulus ranges between 25–70kPa in middle and deep zone cartilage, separating it by an order of magnitude from both the chondrocyte stiffness (∼1kPa) and ECM stiffness (∼1MPa). In recent years, Choi et al. [8] measured changes in the three-dimensional morphology of the chondron, in situ within the ECM, under equilibrium unconfined compression of porcine cartilage explants subjected to 10–50% compressive strain (Fig. 1). Their study employed a novel 3D confocal microscopy technique, based on immunolabeling of type VI collagen, that yielded ellipsoidal approximations of undeformed and deformed chondron shapes in the superficial, middle and deep zones of the explant. In this study, an efficient computational model, based on the boundary element method (BEM), was developed and used to estimate cartilage PCM linear elastic properties based on the data reported in Choi et al. [8] for the case of middle zone cartilage under 10% compressive strain.

scholarly journals On the Fluctuation Induced Excess Conductivity in Stainless Steel Sheathed MgB2 Tapes

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Suchitra Rajput ◽  
Sujeet Chaudhary
Keyword(s):  
Magnetic Field ◽  
Experimental Data ◽  
Stainless Steel ◽  
Coherence Length ◽  
Three Dimensional ◽  
Excess Conductivity ◽  
Scaling Functions ◽  
Critical Fluctuations ◽  
Scaling Models

We report on the analyses of fluctuation induced excess conductivity in the - behavior in the in situ prepared MgB2 tapes. The scaling functions for critical fluctuations are employed to investigate the excess conductivity of these tapes around transition. Two scaling models for excess conductivity in the absence of magnetic field, namely, first, Aslamazov and Larkin model, second, Lawrence and Doniach model, have been employed for the study. Fitting the experimental - data with these models indicates the three-dimensional nature of conduction of the carriers as opposed to the 2D character exhibited by the HTSCs. The estimated amplitude of coherence length from the fitted model is ~21 Å.

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 Development of 3D boundary element method for the simulation of acoustic metamaterials/metasurfaces in mean flow for aerospace applications

2020 ◽  
Vol 19 (6-8) ◽  
pp. 324-346
Author(s):  
Imran Bashir ◽  
Michael Carley
Keyword(s):  
Experimental Data ◽  
Mach Number ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Sound Propagation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Mean Flow ◽  
Low Mach Number ◽  
Element Method

Low-cost airlines have significantly increased air transport, thus an increase in aviation noise. Therefore, predicting aircraft noise is an important component for designing an aircraft to reduce its impact on environmental noise along with the cost of testing and certification. The aim of this work is to develop a three-dimensional Boundary Element Method (BEM), which can predict the sound propagation and scattering over metamaterials and metasurfaces in mean flow. A methodology for the implementation of metamaterials and metasurfaces in BEM as an impedance patch is presented here. A three-dimensional BEM named as BEM3D has been developed to solve the aero-acoustics problems, which incorporates the Fast Multipole Method to solve large scale acoustics problems, Taylor’s transformation to account for uniform and non-uniform mean flow, impedance and non-local boundary conditions for the implementation of metamaterials. To validate BEM3D, the predictions have been benchmarked against the Finite Element Method (FEM) simulations and experimental data. It has been concluded that for no flow case BEM3D gives identical acoustics potential values against benchmarked FEM (COMSOL) predictions. For Mach number of 0.1, the BEM3D and FEM (COMSOL) predictions show small differences. The difference between BEM3D and FEM (COMSOL) predictions increases further for higher Mach number of 0.2 and 0.3. The increase in difference with Mach number is because Taylor’s Transformation gives an approximate solution for the boundary integral equation. Nevertheless, it has been concluded that Taylor’s transformation gives reasonable predictions for low Mach number of up to 0.3. BEM3D predictions have been validated against experimental data on a flat plate and a duct. Very good agreement has been found between the measured data and BEM3D predictions for sound propagation without and with the mean flow at low Mach number.

The Elastic Properties of a Dense Glacial Till Deposit

1965 ◽  
Vol 2 (2) ◽  
pp. 116-128 ◽  
Author(s):  
Earle J Klohn
Keyword(s):  
Elastic Properties ◽  
Modulus Of Elasticity ◽  
Elastic Solid ◽  
Strength Properties ◽  
Glacial Till ◽  
Triaxial Tests ◽  
Compression Tests ◽  
Unconfined Compression ◽  
Sample Disturbance

Dense, heavily preconsolidated glacial till is a relatively incompressible soil that occurs throughout most of Canada. When loaded, it undergoes very small settlement, most of which is elastic. For the average structure, these elastic compressions are too small to be of concern and are usually ignored. However, for some structures they can be critical and their magnitude must be estimated prior to construction. To make the necessary analyses requires knowledge of the elastic properties of the in situ glacial till.This paper presents the results of field and laboratory tests that were made on a dense glacial till deposit to determine its modulus of elasticity, in connection with the design and construction of a 100 ft. high combined earth and concrete dam. In the field, in situ loading tests were made against the walls of a 50 ft. deep test shaft. The modulus of elasticity was computed, using elastic equations applicable to the case of a rigid circular plate pressed against a semi-infinite elastic solid. Moreover, during construction of the project, measurements were made of the elastic rebounds and settlements that occurred under known conditions of unloading and loading. Steinbrenner’s approximate solution for computing settlement due to loads acting on the surface of an elastic layer was then used to compute the apparent modulus of elasticity. In the laboratory, unconfined compression tests and repetitive triaxial tests were made on undisturbed samples. The modulus of elasticity was estimated from the stress-strain relationships obtained.The data presented in the paper indicate that the apparent, in situ modulus of elasticity of the glacial till deposit is very high, being in the order of 150,000 lb./sq. in. Reasonable agreement exists between modulus of elasticity values computed from the in situ plate bearing tests and those computed from observed rebounds and settlements. However, modulus of elasticity values computed from unconfined compression and repetitive triaxial tests in the laboratory are apparently too small, being only a fraction of those values obtained by the field procedures. Sample disturbance is thought to be a major factor affecting laboratory test results.Grain size characteristics, density, natural water content, and strength properties of the glacial till deposit are presented in the paper. These data provide a comprehensive description of the material and permit comparison with glacial till deposits encountered at other areas.

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