scholarly journals Effects of Collagen Heterogeneity on Myocardial Infarct Mechanics in a Multiscale Fiber Network Model

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Christopher E. Korenczuk ◽  
Victor H. Barocas ◽  
William J. Richardson
Keyword(s):  
Myocardial Infarction ◽  
Finite Element ◽  
Homogeneous Model ◽  
Mechanical Anisotropy ◽  
Local Alignment ◽  
Fiber Density ◽  
Heterogeneous Model ◽  
Fiber Alignment ◽  
Sample Shape ◽  
Homogeneous Models

The scar that forms after a myocardial infarction is often characterized by a highly disordered architecture but generally exhibits some degree of collagen fiber orientation, with a resulting mechanical anisotropy. When viewed in finer detail, however, the heterogeneity of the sample is clear, with different subregions exhibiting different fiber orientations. In this work, we used a multiscale finite element model to explore the consequences of the heterogeneity in terms of mechanical behavior. To do so, we used previously obtained fiber alignment maps of rat myocardial scar slices (n = 15) to generate scar-specific finite element meshes that were populated with fiber models based on the local alignment state. These models were then compared to isotropic models with the same sample shape and fiber density, and to homogeneous models with the same sample shape, fiber density, and average fiber alignment as the scar-specific models. All simulations involved equibiaxial extension of the sample with free motion in the third dimension. We found that heterogeneity led to a lower degree of mechanical anisotropy and a higher level of local stress concentration than the corresponding homogeneous model, and also that fibers failed in the heterogeneous model at much lower macroscopic strains than in the isotropic and homogeneous models. Taken together, these results suggest that scar heterogeneity may impair myocardial mechanical function both in terms of anisotropy and strength, and that individual variations in scar heterogeneity could be an important consideration for understanding scar remodeling and designing therapeutic interventions for patients after myocardial infarction.

scholarly journals Effects of Age and Diabetes on Scleral Stiffness

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Baptiste Coudrillier ◽  
Jacek Pijanka ◽  
Joan Jefferys ◽  
Thomas Sorensen ◽  
Harry A. Quigley ◽  
...  
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Collagen Fiber ◽  
Older Age ◽  
Image Correlation ◽  
Mechanical Anisotropy ◽  
Matrix Stiffness ◽  
Fiber Alignment ◽  
Age Related ◽  
Related Increase

The effects of diabetes on the collagen structure and material properties of the sclera are unknown but may be important to elucidate whether diabetes is a risk factor for major ocular diseases such as glaucoma. This study provides a quantitative assessment of the changes in scleral stiffness and collagen fiber alignment associated with diabetes. Posterior scleral shells from five diabetic donors and seven non-diabetic donors were pressurized to 30 mm Hg. Three-dimensional surface displacements were calculated during inflation testing using digital image correlation (DIC). After testing, each specimen was subjected to wide-angle X-ray scattering (WAXS) measurements of its collagen organization. Specimen-specific finite element models of the posterior scleras were generated from the experimentally measured geometry. An inverse finite element analysis was developed to determine the material properties of the specimens, i.e., matrix and fiber stiffness, by matching DIC-measured and finite element predicted displacement fields. Effects of age and diabetes on the degree of fiber alignment, matrix and collagen fiber stiffness, and mechanical anisotropy were estimated using mixed effects models accounting for spatial autocorrelation. Older age was associated with a lower degree of fiber alignment and larger matrix stiffness for both diabetic and non-diabetic scleras. However, the age-related increase in matrix stiffness was 87% larger in diabetic specimens compared to non-diabetic controls and diabetic scleras had a significantly larger matrix stiffness (p = 0.01). Older age was associated with a nearly significant increase in collagen fiber stiffness for diabetic specimens only (p = 0.06), as well as a decrease in mechanical anisotropy for non-diabetic scleras only (p = 0.04). The interaction between age and diabetes was not significant for all outcomes. This study suggests that the age-related increase in scleral stiffness is accelerated in eyes with diabetes, which may have important implications in glaucoma.

Tool Wear Prediction in Machining Process Using a Microstructure-Based Finite Element Model

2015 ◽  
Vol 651-653 ◽  
pp. 1229-1234
Author(s):  
Mikel Sáez-de-Buruaga ◽  
Ibon Poveda ◽  
Pedro José Arrazola
Keyword(s):  
Finite Element ◽  
Wear Rate ◽  
Tool Wear ◽  
Finite Element Model ◽  
Orthogonal Cutting ◽  
Homogeneous Model ◽  
Element Model ◽  
Machining Process ◽  
Heterogeneous Model ◽  
Tool Wear Prediction

The microstructure of materials has a significant influence on tool life, however most of the research in modelling to date considers the material as homogeneous. This research aims to develop a microstructure-based Finite Element Model in order to qualitatively analyze the influence of the scale of the microstructure on the generated tool wear. In particular, this paper is focused on the orthogonal cutting process of a ferrite-pearlite dual-phase steel using uncoated carbide tools. Based on individual mechanical properties of these phases, a 3D coupled Eulerian Lagrangian heterogeneous model was developed. An empirical tool wear rate prediction model was implemented by a user subroutine in both models (heterogeneous and homogeneous) to predict wear and wear rate values. A comparison between the microstructure-base model (heterogeneous) and the homogeneous model considering wear and wear rate values was made. The results demonstrate the validity of microstructure-based Finite Element Model for an improved prediction of the wear phenomena.

Capillary network structure does not affect theoretical analysis of glomerular size selectivity

1995 ◽  
Vol 268 (5) ◽  
pp. F972-F979
Author(s):  
A. Remuzzi ◽  
B. Ene-Iordache
Keyword(s):  
Pressure Drop ◽  
Homogeneous Model ◽  
Wistar Rat ◽  
Size Selectivity ◽  
Membrane Pore ◽  
Heterogeneous Model ◽  
Glomerular Size ◽  
The Difference ◽  
Membrane Pore Size ◽  
Log Normal

Anatomical studies have demonstrated that the glomerular capillaries are complex and heterogeneous networks. Conventional models of glomerular size selectivity, however, are based on the assumption of simplified geometries. We developed a theoretical model of glomerular size-selective function based on the geometric data obtained in a previous reconstruction of a glomerular network from a normal Munich-Wistar rat. This heterogeneous model was compared with the homogeneous model conventionally used to calculate membrane selective parameters from the fractional clearance of two test solutes, neutral dextran and Ficoll. For both models we assumed a hypothetical log-normal distribution of pore sizes and calculated optimal membrane pore-size parameters using previously published values of fractional clearances. The difference between the sieving coefficients calculated with the two models was negligible, never exceeding 5.5%. Since the homogeneous model does not consider the pressure drop along the glomerular capillary, we also computed fractional clearances with the homogeneous model, assuming the same pressure drop as in the heterogeneous one. The differences in computed fractional clearances using the homogeneous model with and without a pressure drop were less than 1.2%. We concluded that models based on identical capillary networks can therefore be used for interpreting sieving coefficients for macromolecules.

scholarly journals Intima heterogeneity in stress assessment of atherosclerotic plaques

2017 ◽  
Vol 8 (1) ◽  
pp. 20170008 ◽  
Author(s):  
Ali C. Akyildiz ◽  
Lambert Speelman ◽  
Bas van Velzen ◽  
Raoul R. F. Stevens ◽  
Antonius F. W. van der Steen ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Plaque Rupture ◽  
Homogeneous Model ◽  
Sensitivity Analyses ◽  
Homogeneous Material ◽  
Sensitivity Index ◽  
Stress Assessment ◽  
Heterogeneous Models ◽  
Homogeneous Models ◽  
Accuracy Stress

Atherosclerotic plaque rupture is recognized as the primary cause of cardiac and cerebral ischaemic events. High structural plaque stresses have been shown to strongly correlate with plaque rupture. Plaque stresses can be computed with finite-element (FE) models. Current FE models employ homogeneous material properties for the heterogeneous atherosclerotic intima. This study aimed to evaluate the influence of intima heterogeneity on plaque stress computations. Two-dimensional FE models with homogeneous and heterogeneous intima were constructed from histological images of atherosclerotic human coronaries ( n = 12). For homogeneous models, a single stiffness value was employed for the entire intima. For heterogeneous models, the intima was subdivided into four clusters based on the histological information and different stiffness values were assigned to the clusters. To cover the reported local intima stiffness range, 100 cluster stiffness combinations were simulated. Peak cap stresses (PCSs) from the homogeneous and heterogeneous models were analysed and compared. By using a global variance-based sensitivity analysis, the influence of the cluster stiffnesses on the PCS variation in the heterogeneous intima models was determined. Per plaque, the median PCS values of the heterogeneous models ranged from 27 to 160 kPa, and the PCS range varied between 43 and 218 kPa. On average, the homogeneous model PCS values differed from the median PCS values of heterogeneous models by 14%. A positive correlation ( R 2 = 0.72) was found between the homogeneous model PCS and the PCS range of the heterogeneous models. Sensitivity analysis showed that the highest main sensitivity index per plaque ranged from 0.26 to 0.83, and the average was 0.47. Intima heterogeneity resulted in substantial changes in PCS, warranting stress analyses with heterogeneous intima properties for plaque-specific, high accuracy stress assessment. Yet, computations with homogeneous intima assumption are still valuable to perform sensitivity analyses or parametric studies for testing the effect of plaque geometry on PCS. Moreover, homogeneous intima models can help identify low PCS, stable type plaques with thick caps. Yet, for thin cap plaques, accurate stiffness measurements of the clusters in the cap and stress analysis with heterogeneous cap properties are required to characterize the plaque stability.

A Numerical Model for Studying the Effect of Plasma Layer on the Process of Blood Oxygenation in the Pulmonary Capillaries

1990 ◽  
Vol 112 (4) ◽  
pp. 457-463 ◽  
Author(s):  
Maithili Sharan ◽  
M. P. Singh ◽  
A. Aminataei
Keyword(s):  
Molecular Diffusion ◽  
Plasma Layer ◽  
Nonlinear Partial Differential Equations ◽  
Homogeneous Model ◽  
Blood Oxygenation ◽  
Facilitated Diffusion ◽  
Heterogeneous Model ◽  
The Core ◽  
Pulmonary Capillaries ◽  
Diffusion Convection

A two layer model for the blood oxygenation in pulmonary capillaries is proposed. The model consists of a core of erythrocytes surrounded by a symmetrically placed plasma layer. The governing equations in the core describe the free molecular diffusion, convection, and facilitated diffusion due to the presence of haemoglobin. The corresponding equations in the plasma layer are based on the free molecular diffusion and the convective effect of the blood. According to the axial train model for the blood flow proposed by Whitmore (1967), the core will move with a uniform velocity whereas flow in the plasma layer will be fully developed. The resulting system of nonlinear partial differential equations is solved numerically. A fixed point iterative technique is used to deal with the nonlinearities. The distance traversed by the blood before getting fully oxygenated is computed. It is shown that the concentration of O2 increases continuously along the length of the capillary for a given ratio of core radius to capillary radius. It is found that the rate of oxygenation increases as the core to capillary ratio decreases. The equilibration length increases with a heterogeneous model in comparison to that in a homogeneous model. The effect of capillary diameters and core radii on the rate of oxygenation has also been examined.

scholarly journals Homogeneous models and almost decidability

1989 ◽  
Vol 46 (3) ◽  
pp. 343-355 ◽  
Author(s):  
Terry Millar
Keyword(s):  
Elementary Theory ◽  
Homogeneous Model ◽  
Point Of View ◽  
Type Spectrum ◽  
Homogeneous Models ◽  
Theoretic Point

AbstractCountable homogeneous models are ‘simple’ objects from a model theoretic point of view. From a recursion theoretic point of view they can be complex. For instance the elementary theory of such a model might be undecidable, or the set of complete types might be recursively complex. Unfortunately even if neither of these conditions holds, such a model still can be undecidable. This paper investigates countable homogeneous models with respect to a weaker notion of decidability called almost decidable. It is shown that for theories that have only countably many type spectra, any countable homogeneous model of such a theory that has a Σ2 type spectrum is almost decidable.

Heat Transfer in Fixed Bed Elliptic Cylindrical Reactor via Two-Phase Model

2020 ◽  
Vol 400 ◽  
pp. 45-50
Author(s):  
Antonildo Santos Pereira ◽  
Rodrigo Moura da Silva ◽  
Maria Conceição Nóbrega Machado ◽  
Luan Pedro Melo Azerêdo ◽  
Anderson Ferreira Vilela ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Solid Phase ◽  
Homogeneous Model ◽  
Fixed Bed ◽  
Fluid Phase ◽  
Packed Bed ◽  
Two Phase ◽  
Heterogeneous Model ◽  
Fully Implicit ◽  
Cylindrical Reactor

The study of heat transfer in fixed bed tubular reactors of heated or cooled walls has presented great interest by the academy and industry. The adequate and safe design of such equipment requires the use of reliable and realistic mathematical. Unfortunately several studies are restrict to homogeneous model applied to circular and elliptic cylindrical reactors. Then, the objective of this work was to predict heat transfer in packed-bed elliptic cylindrical reactor, by using a proposed heterogeneous model. The mathematical model is composed for one solid phase and another fluid phase, in which the balance equation for each constituent is applied separately. The finite volume method was utilized to solve the partial differential equations using the WUDS scheme for interpolation of the convective and diffusive terms, and the fully implicit formulation. Results of the temperature distribution of the fluid and solid phases along the reactor are presented and analyzed. It was verified that the highest temperature gradients of the phases are located close to the wall and inlet of the reactor.

On the Use of Conventional Dough Extension Tests in Characterising Flours for Dough Sheetability. II. Simulations

2016 ◽  
Vol 12 (3) ◽  
pp. 231-245 ◽  
Author(s):  
Milan J. Patel ◽  
Sumana Chakrabarti-Bell
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Fe Simulation ◽  
Force Extension ◽  
Product Use ◽  
Sample Shape ◽  
Simulation Based ◽  
Shape Effects ◽  
Selection For

Abstract Dough extension tests are used in industry to rate flours for dough processability. The results impact flour selection for product use. Previously, it was shown that dough extension data correlated poorly with dough sheetability irrespective of whether doughs were tested fresh or rested. It was noted that sample shapes varied between specimens of flours. To understand how sample shape affects extensigraph tests, a finite element (FE) simulation-based approach was taken. Real extensigraph samples were drawn on a computer equipped with the commercial FE package ABAQUS and using the anisotropic Bergstrom Boyce model with Mullins damage (ABBM) constitutive model to describe the dough’s rheology. Results show that the force–extension traces were affected by sample shape, and that thinning occurs more from the sides than the bulk for slumped samples. The FE predictions for sample shape effects on hook force were validated against real tests. Similar dependencies on sample shape are also predicted for the alveograph and Kieffer micro-extensigraph tests.

scholarly journals The Quartic Piecewise-Linear Criterion for the Multiaxial Yield Behavior of Human Trabecular Bone

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Arnav Sanyal ◽  
Joanna Scheffelin ◽  
Tony M. Keaveny
Keyword(s):  
Finite Element ◽  
Trabecular Bone ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Shear Loading ◽  
Bone Volume ◽  
Mechanical Anisotropy ◽  
Bone Volume Fraction ◽  
Human Trabecular Bone ◽  
Strain Space

Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (μCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5 mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36), mechanical anisotropy (range of E3/E1 = 3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension, compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space. The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal boxlike shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized-strain space combined with a piecewise linear yield criterion in two planes for normal-shear loading (mean error ± SD: 4.6 ± 0.8% for the finite element data versus the criterion). This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture.

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