On the Connection Between Geometry and Statically Determined Membrane Stresses in the Human Cornea

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
M. Angelillo ◽  
A. Montanino ◽  
A. Pandolfi
Keyword(s):  
Intraocular Pressure ◽  
Stress State ◽  
Principal Stress ◽  
Collagen Fibrils ◽  
Equilibrium Analysis ◽  
Time Dependent ◽  
Patient Specific ◽  
Shear Stresses ◽  
Human Cornea ◽  
The Matrix

Abstract Under the action of the intraocular pressure (IOP), the human cornea is stressed and deforms acquiring a quasi-spherical configuration. If the stressed configuration is known, and the cornea is regarded as a membrane, disregarding flexural behaviors with an equilibrium analysis only is possible to estimate the distribution of the average stress across the thickness. In the cornea, the action of the intraocular pressure is supported by collagen fibrils, immersed into an elastin-proteoglycan matrix, and organized in a very precise architecture to provide the necessary confinement and transparency to the light. With the goal of understanding the static consequences of shape modifications due to pathological dilatation (ectasia), we present a simplified stress analysis of the human cornea modeled as a membrane. A numerical investigation over 40 patient-specific corneas (20 normal and 20 ectatic) is carried out to establish a relationship between the physiological geometry and the distribution of the membrane stresses, and to assess the possibility to obtain information on the stress state based on topographic images only. Comparative analyses reveal that, with respect to normal corneas, in ectatic corneas the pattern of the principal stress lines is modified markedly showing a deviation from the hypothetical dominant orientation of the collagen fibrils. The rotation of the principal stress with respect to the fibril orientation can be thought as responsible of the transmission of a large amount of shear stresses onto the elastin-proteoglycan matrix. The anomalous loading of the matrix could be correlated to the evolution of time-dependent shape modifications leading to ectasia.

scholarly journals Type III collagen can be present on banded collagen fibrils regardless of fibril diameter.

1987 ◽  
Vol 105 (5) ◽  
pp. 2393-2402 ◽  
Author(s):  
D R Keene ◽  
L Y Sakai ◽  
H P Bächinger ◽  
R E Burgeson
Keyword(s):  
Triple Helix ◽  
Collagen Type ◽  
Collagen Fibrils ◽  
Type Iii Collagen ◽  
Human Cornea ◽  
Donor Age ◽  
Ultrastructural Examination ◽  
Type Iii ◽  
The Matrix ◽  
Fibril Diameter

Monoclonal antibodies that recognize an epitope within the triple helix of type III collagen have been used to examine the distribution of that collagen type in human skin, cornea, amnion, aorta, and tendon. Ultrastructural examination of those tissues indicates antibody binding to collagen fibrils in skin, amnion, aorta, and tendon regardless of the diameter of the fibril. The antibody distribution is unchanged with donor age, site of biopsy, or region of tissue examined. In contrast, antibody applied to adult human cornea localizes to isolated fibrils, which appear randomly throughout the matrix. These studies indicate that type III collagen remains associated with collagen fibrils after removal of the amino and carboxyl propeptides, and suggests that fibrils of skin, tendon, and amnion (and presumably many other tissues that contain both types I and III collagens) are copolymers of at least types I and III collagens.

Effects of EDTA, Hyaluronidase and Collagenase on Epiphyseal Cartilage Matrix

1968 ◽  
Vol 26 ◽  
pp. 56-57
Author(s):  
H. Clarke Anderson ◽  
Priscilla R. Coulter
Keyword(s):  
Light And Electron Microscopy ◽  
Matrix Vesicles ◽  
Cartilage Matrix ◽  
Collagen Fibrils ◽  
Epiphyseal Cartilage ◽  
Dense Matrix ◽  
Type Iv ◽  
Bovine Testicular Hyaluronidase ◽  
The Matrix ◽  
Testicular Hyaluronidase

Epiphyseal cartilage matrix contains fibrils and particles of at least 5 different types: 1. Banded collagen fibrils, present throughout the matrix, but not seen in the lacunae. 2. Non-periodic fine fibrils <100Å in diameter (Fig. 1), which are most notable in the lacunae, and may represent immature collagen. 3. Electron dense matrix granules (Fig. 1) which are often attached to fine fibrils and collagen fibrils, and probably contain protein-polysaccharide although the possibility of a mineral content has not been excluded. 4. Matrix vesicles (Fig. 2) which show a selective distribution throughout the epiphysis, and may play a role in calcification. 5. Needle-like apatite crystals (Fig. 2).Blocks of formalin-fixed epiphysis from weanling mice were digested with the following agents in 0.1M phosphate buffer: a) 5% ethylenediaminetetraacetate (EDTA) at pH 8.3, b) 0.015% bovine testicular hyaluronidase (Sigma, type IV, 750 units/mg) at pH 5.5, and c) 0.1% collagenase (Worthington, chromatograhically pure, 200 units/mg) at pH 7.4. All digestions were carried out at 37°C overnight. Following digestion tissues were examined by light and electron microscopy to determine changes in the various fibrils and particles of the matrix.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

scholarly journals Expression of VEGF-A Signaling Pathway in Cartilage of ACLT-induced Osteoarthritis Mouse Model

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Jia-jia Qian ◽  
Qi Xu ◽  
Wei-min Xu ◽  
Ren Cai ◽  
Gui-cheng Huang
Keyword(s):  
Signaling Pathway ◽  
Cruciate Ligament ◽  
Time Dependent ◽  
Pathological Changes ◽  
The Matrix ◽  
Vegfr2 Signaling ◽  
Cox 2 ◽  
Anterior Cruciate ◽  
A Disintegrin And Metalloproteinase ◽  
Safranin O

Abstract Background Anterior cruciate ligament transection surgery (ACLT)-induced OA model was often used to investigate the molecular mechanism of knee osteoarthritis (KOA). Researches have shown that vascular endothelial growth factor (VEGF) played an important role in OA. The present study aimed to investigate the pathological changes after ACLT surgery and reveal the expression characteristics of the VEGF-A/VEGFR2 signaling pathway in this model. Methods Moderate KOA model was established by ACLT, and 1, 2, 4, 8, and 12 weeks after surgery, hematoxylin-eosin (HE) and Safranin-O(S-O) staining were used to detect the pathological changes in mouse knee cartilage, and the matrix biomarkers A Disintegrin and Metalloproteinase with Thrombospondin Motifs 5(ADAMTS5), Collagen II (COL-II) were detected using immunohistochemistry (IHC), CD31 was detected by immunofluorescence (IF) to show the vascular invasion in cartilage, and proteins expression of VEGF-A pathway were detected by Western blot (WB). Meanwhile, the inflammatory biomarkers cyclooxygenase-2 (COX-2) and inducible nitric oxide synthase (iNOS) in cartilage were detected by WB. Results ACLT surgery can lead to degeneration of cartilage in mice, and the characteristics of the lesion were time-dependent. The ADAMTS5-positive cells increased while COL-II decreased in OA cartilage with time, and new blood vessels labeled by CD31 can be seen from 1 week in OA cartilage, and increased in 8 and 12 weeks. The expression of VEGF-A, VEGFR2, COX-2, and iNOS were higher than control groups, which were basically consistent with the degree of osteoarthritis. Conclusions The degenerative degree of articular cartilage was time-dependent; angiogenesis and inflammation were important pathological changes of cartilage in KOA. The expression of the VEGF-A/VEGFR2 signaling pathway was basically correlated with the degree of KOA.

Spectral analysis of M/G/1 and G/M/1 type Markov chains

1996 ◽  
Vol 28 (01) ◽  
pp. 114-165 ◽  
Author(s):  
H. R. Gail ◽  
S. L. Hantler ◽  
B. A. Taylor
Keyword(s):  
Markov Chains ◽  
Generating Functions ◽  
Complex Analysis ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Equilibrium Analysis ◽  
Transform Method ◽  
Technical Problems ◽  
The Matrix ◽  
Transient Case

When analyzing the equilibrium behavior of M/G/1 type Markov chains by transform methods, restrictive hypotheses are often made to avoid technical problems that arise in applying results from complex analysis and linear algebra. It is shown that such restrictive assumptions are unnecessary, and an analysis of these chains using generating functions is given under only the natural hypotheses that first moments (or second moments in the null recurrent case) exist. The key to the analysis is the identification of an important subspace of the space of bounded solutions of the system of homogeneous vector-valued Wiener–Hopf equations associated with the chain. In particular, the linear equations in the boundary probabilities obtained from the transform method are shown to correspond to a spectral basis of the shift operator on this subspace. Necessary and sufficient conditions under which the chain is ergodic, null recurrent or transient are derived in terms of properties of the matrix-valued generating functions determined by transitions of the Markov chain. In the transient case, the Martin exit boundary is identified and shown to be associated with certain eigenvalues and vectors of one of these generating functions. An equilibrium analysis of the class of G/M/1 type Markov chains by similar methods is also presented.

scholarly journals A Numerical Approach for Evaluating the Time-Dependent Distribution of a Quasi Birth-Death Process

2021 ◽  
Author(s):  
Michel Mandjes ◽  
Birgit Sollie
Keyword(s):  
Continuous Time ◽  
Real Life ◽  
Numerical Approach ◽  
Time Dependent ◽  
Death Process ◽  
Continuous Time Markov Chain ◽  
Likelihood Estimator ◽  
Real Life Data ◽  
The Matrix ◽  
Birth Death

AbstractThis paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle is proposed and formally justified. Its performance is investigated and compared with two existing approaches: one based on numerical evaluation of the matrix exponential underlying the qbd process, and one based on the uniformization technique. It is shown that in many settings the approach based on Erlangization is faster than the other approaches, while still being highly accurate. In the last part of the paper, we demonstrate the use of the developed technique in the context of the evaluation of the likelihood pertaining to a time series, which can then be optimized over its parameters to obtain the maximum likelihood estimator. More specifically, through a series of examples with simulated and real-life data, we show how it can be deployed in model selection problems that involve the choice between a qbd and its non-modulated counterpart.

Scavenging of Soluble Gaseous Pollutants by Rain Droplets in the Atmosphere With Nocturnal Temperature Profile

2010 ◽  
Author(s):  
Andrew Fominykh ◽  
Tov Elperin ◽  
Boris Krasovitov
Keyword(s):  
Trace Gases ◽  
Vertical Direction ◽  
Temperature Inversion ◽  
Transformation Method ◽  
Time Dependent ◽  
Trace Gas ◽  
Shear Stresses ◽  
Linear Convolution ◽  
Temperature Boundary ◽  
Transfer Equations

We analyze non-isothermal absorption of trace gases by the rain droplets with internal circulation which is caused by interfacial shear stresses. It is assumed that the temperature and concentration of soluble trace gases in the atmosphere varies in a vertical direction. The rate of scavenging of soluble trace gases by falling rain droplets is determined by solving heat and mass transfer equations. In the analysis we accounted for the accumulation of the absorbate in the bulk of the falling rain droplet. The problem is solved in the approximation of a thin concentration and temperature boundary layers in the droplet and in the surrounding air. We assumed that the bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and concentration of the absorbate and temperature are homogeneous and time-dependent in the bulk. By combining the generalized similarity transformation method with Duhamel’s theorem, the system of transient conjugate equations of convective diffusion and energy conservation for absorbate transport in liquid and gaseous phases with time-dependent boundary conditions is reduced to a system of linear convolution Volterra integral equations of the second kind which is solved numerically. Calculations are performed using available experimental data on nocturnal temperature profiles in the atmosphere. It is shown than if concentration of a trace gas in the atmosphere is homogeneous and temperature in the atmosphere increases with altitude, droplet absorbs gas during all the period of its fall. Neglecting temperature inhomogenity in the atmosphere described by nocturnal temperature inversion leads to essential underestimation of the trace gas concentration in a droplet on the ground.

A UNIFIED FORMALISM OF THERMAL QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (14) ◽  
pp. 2363-2409 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Vacuum Polarization ◽  
Time Dependent ◽  
Quantum Field ◽  
Bogoliubov Transformation ◽  
Transformation Matrices ◽  
Thermo Field Dynamics ◽  
The Matrix ◽  
Recent Developments

We present a comprehensive review of the most fundamental and practical aspects of thermo-field dynamics (TFD), including some of the most recent developments in the field. To make TFD fully consistent, some suitable changes in the structure of the thermal doublets and the Bogoliubov transformation matrices have been made. A close comparison between TFD and the Schwinger-Keldysh closed time path formalism (SKF) is presented. We find that TFD and SKF are in many ways the same in form; in particular, the two approaches are identical in stationary situations. However, TFD and SKF are quite different in time-dependent nonequilibrium situations. The main source of this difference is that the time evolution of the density matrix itself is ignored in SKF while in TFD it is replaced by a time-dependent Bogoliubov transformation. In this sense TFD is a better candidate for time-dependent quantum field theory. Even in equilibrium situations, TFD has some remarkable advantages over the Matsubara approach and SKF, the most notable being the Feynman diagram recipes, which we will present. We will show that the calculations of two-point functions are simplified, instead of being complicated, by the matrix nature of the formalism. We will present some explicit calculations using TFD, including space-time inhomogeneous situations and the vacuum polarization in equilibrium relativistic QED.

Mechanics of the Segmentation of an Embedded Fiber, Part I: Experimental Investigations

1995 ◽  
Vol 62 (1) ◽  
pp. 87-97 ◽  
Author(s):  
A. ten Busschen ◽  
A. P. S. Selvadurai
Keyword(s):  
Structural Parameters ◽  
Matrix Material ◽  
Micromechanical Modeling ◽  
Experimental Investigations ◽  
Shear Stresses ◽  
Research Attention ◽  
Fragmentation Test ◽  
The Matrix ◽  
Matrix Region ◽  
Interface Bond

Micromechanical modeling is an important aspect in the study of fiber-reinforced composites. In such studies, an important class of structural parameters is formed by the interaction between the matrix and the embedded fibers. These interactive processes can be investigated by an appeal to a test which involves the segmentation of an embedded fiber. This test is referred to as a “fragmentation test.” During a fragmentation test, two distinct fracture phenomena are observed. These phenomena are directly related to the integrity of bond between the embedded fiber and the matrix. The first phenomenon involves situations where the interface bond is weaker than the matrix material. In this case the fiber fragment ends will slip and in this region shear stresses are transmitted by friction and/or interlocking mechanical actions. In contrast, when the interface bond has stronger properties than the matrix material, cracking will occur in the matrix region. Here, a crack initiated in the fiber will propagate into the matrix region typically forming conoidal cracks, or combinations of conoidal and flat cracks. This paper describes the background of the fragmentation test and the associated experimental research. Attention is focused on the experimental evaluation of matrix fracture topographies encountered in the fragmentation test.

scholarly journals Force parameters of metal deformation during sheet drawing

2020 ◽  
Vol 16 (6) ◽  
pp. 493-503
Author(s):  
Yury A. Morozov
Keyword(s):  
Stress State ◽  
Strain State ◽  
Sheet Material ◽  
Forming Force ◽  
High Quality ◽  
State Process ◽  
The Matrix ◽  
Metal Deformation ◽  
Volumetric Stress ◽  
Steady State Process

The aim of the work. The effect of the curvature of the rounding of torus surfaces during the formation of a cylindrical product (glass) is investigated, taking into account the plastic thinning of the deformable material at the end edges of the matrix and pressing punch. Methods. The existing scheme for determining the power parameters of sheet drawing is analyzed, based on the assumption of the implementation of some abstract stress state in the material; mainly conditional tensile strength. At the same time, the possibility of forming the product without destruction determines the obvious overestimation of the stress level. A mathematical model of the volumetric stress state of the metal is being developed, which makes it possible to assess the deformation and stress state during the formation of a cold-drawn product, i. e. the folding of the sheet blank along the end radius of the rounding of the pressing punch and the steady-state process of drawing the blank into the deformation zone with successive bending/straightening of the material along the edge of the matrix are considered. The level of radial stresses during folding and stretching of sheet material is estimated, taking into account its strain hardening and thinning, which determine the forming force. The obtained results will make it possible to simulate the stress-strain state of the metal during the development of sheet drawing technology: to establish the amount of thinning, to estimate the level of radial stresses in the formation of rounding of torus surfaces along the end edges of the matrix and the pressing punch, as well as to determine the power parameters of the formation, which will prevent the destruction of the pulled part, guaranteeing obtaining high-quality products and more accurately choosing the deforming equipment.

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