Correlation between Local Stress and Strain and Lamina Cribrosa Connective Tissue Volume Fraction in Normal Monkey Eyes

The lamina cribrosa (LC) is a tissue in the posterior eye with a complex trabecular microstructure. This tissue is of great research interest, as it is likely the initial site of retinal ganglion cell axonal damage in glaucoma. Unfortunately, the LC is difficult to access experimentally, and thus imaging techniques in tandem with image processing have emerged as powerful tools to study the microstructure and biomechanics of this tissue. Here, we present a staining approach to enhance the contrast of the microstructure in micro-computed tomography (micro-CT) imaging as well as a comparison between tissues imaged with micro-CT and second harmonic generation (SHG) microscopy. We then apply a modified version of Frangi's vesselness filter to automatically segment the connective tissue beams of the LC and determine the orientation of each beam. This approach successfully segmented the beams of a porcine optic nerve head from micro-CT in three dimensions and SHG microscopy in two dimensions. As an application of this filter, we present finite-element modelling of the posterior eye that suggests that connective tissue volume fraction is the major driving factor of LC biomechanics. We conclude that segmentation with Frangi's filter is a powerful tool for future image-driven studies of LC biomechanics.

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Large Scale Voxel-Based Finite Element Modeling of Normal and Early Glaucomatous Monkey Lamina Cribrosa

ASME 2008 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2008-192984 ◽

2008 ◽

Author(s):

Sanjay Kodiyalam ◽

Michael D. Roberts ◽

Ian A. Sigal ◽

Richard T. Hart ◽

Claude F. Burgoyne ◽

...

Keyword(s):

Finite Element ◽

Intraocular Pressure ◽

Connective Tissue ◽

Large Scale ◽

Lamina Cribrosa ◽

Posterior Pole ◽

Stress And Strain ◽

Structural Support ◽

Elevated Intraocular Pressure ◽

Related Stress

Glaucoma is a leading cause of blindness worldwide. Some of the chief clinical hallmarks of glaucoma are the permanent posterior cupping of the optic nerve head, in the posterior pole of the eye, and the accompanying damage to the lamina cribrosa — the fenestrated structure of connective tissue spanning the scleral canal that provides structural support to the axon bundles passing through it. While elevated intraocular pressure (IOP) is associated with this disease, its role remains unclear. It has been hypothesized that IOP-related stress and strain within the laminar connective tissue (LCT) underlie the onset and progression of glaucoma [1] and that they may be used to predict the location of axonal insult and the pattern of damage within the LCT.

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Accuracy of the generalized self-consistent method in modelling the elastic behaviour of periodic composites

Philosophical Transactions of the Royal Society of London Series A Physical and Engineering Sciences ◽

10.1098/rsta.1993.0144 ◽

1993 ◽

Vol 345 (1677) ◽

pp. 545-576 ◽

Cited By ~ 16

Keyword(s):

Integral Equation ◽

Volume Fraction ◽

Fibrous Composite ◽

Local Stress ◽

Unit Cell ◽

Elastic Behaviour ◽

Stress And Strain ◽

Two Dimensional ◽

Self Consistent ◽

Consistent Method

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young’s modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

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Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

Tire Science and Technology ◽

10.2346/1.3519536 ◽

2010 ◽

Vol 38 (4) ◽

pp. 286-307

Author(s):

Carey F. Childers

Keyword(s):

Mathematical Model ◽

Transition Zone ◽

Effective Properties ◽

Local Stress ◽

Stress And Strain ◽

Fiber Reinforced ◽

Strain Fields ◽

Shear Moduli ◽

Fiber Reinforced Composite ◽

Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

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Reliability Simulation and Forecast Based on Virtual Prototype for the Running System of Complicated Equipments

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.543-547.195 ◽

2014 ◽

Vol 543-547 ◽

pp. 195-198

Author(s):

Li Jun Cao ◽

Hui Bin Hu ◽

Gui Bo Yu ◽

Shu Hai Wang

Keyword(s):

Probability Density ◽

Local Stress ◽

Virtual Prototype ◽

Probability Density Distribution ◽

Stress And Strain ◽

Load Spectrum ◽

Density Distribution Function ◽

Running System ◽

Maintenance Cycle ◽

Damage Theory

The running system is the key part to finish training or battle tasks of complicated equipments. But formidable working conditions influence the measurement of load spectrums and it is difficult to analyze and forecast the reliability of running system. Actual vehicle experiments and virtual prototype are firstly combined to obtain complete load spectrum of running system. According to the materials S-N curve, stress and strain spectrums can be computed. Nominal stress method and local stress and strain method are combined with probability density accumulation damage theory to compute the probability density distribution function. Then, the reliability of running system can be forecasted, which provide adequate reference for the maintenance cycle confirmation and mission reliability prediction.

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Forming Limit Stress Diagram Prediction of Pure Titanium Sheet Based on GTN Model

Materials ◽

10.3390/ma12111783 ◽

2019 ◽

Vol 12 (11) ◽

pp. 1783 ◽

Cited By ~ 4

Author(s):

Tao Huang ◽

Mei Zhan ◽

Kun Wang ◽

Fuxiao Chen ◽

Junqing Guo ◽

...

Keyword(s):

Volume Fraction ◽

Pure Titanium ◽

Void Volume Fraction ◽

Void Volume ◽

Forming Limit ◽

Stress And Strain ◽

Gtn Model ◽

Stress Diagram ◽

Limit Stress ◽

Hemispherical Punch

In this paper, the initial values of damage parameters in the Gurson–Tvergaard–Needleman (GTN) model are determined by a microscopic test combined with empirical formulas, and the final accurate values are determined by finite element reverse calibration. The original void volume fraction (f0), the volume fraction of potential nucleated voids (fN), the critical void volume fraction (fc), the void volume fraction at the final failure (fF) of material are assigned as 0.006, 0.001, 0.03, 0.06 according to the simulation results, respectively. The hemispherical punch stretching test of commercially pure titanium (TA1) sheet is simulated by a plastic constitutive formula derived from the GTN model. The stress and strain are obtained at the last loading step before crack. The forming limit diagram (FLD) and the forming limit stress diagram (FLSD) of the TA1 sheet under plastic forming conditions are plotted, which are in good agreement with the FLD obtained by the hemispherical punch stretching test and the FLSD obtained by the conversion between stress and strain during the sheet forming process. The results show that the GTN model determined by the finite element reverse calibration method can be used to predict the forming limit of the TA1 sheet metal.

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Influence of Orthotropy on Biomechanics of Peri-Implant Bone in Complete Mandible Model with Full Dentition

BioMed Research International ◽

10.1155/2014/709398 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 4

Author(s):

Xi Ding ◽

Sheng-Hui Liao ◽

Xing-Hao Zhu ◽

Hui-Ming Wang

Keyword(s):

Orthotropic Material ◽

Tooth Enamel ◽

Local Stress ◽

Isotropic Case ◽

Stress And Strain ◽

Isotropic Model ◽

Bone Interface ◽

Multiple Data ◽

Cad Models ◽

The Impact

Objective.The study was to investigate the impact of orthotropic material on the biomechanics of dental implant, based on a detailed mandible with high geometric and mechanical similarity.Materials and Methods.Multiple data sources were used to elaborate detailed biological structures and implant CAD models. In addition, an extended orthotropic material assignment methodology based on harmonic fields was used to handle the alveolar ridge region to generate compatible orthotropic fields. The influence of orthotropic material was compared with the commonly used isotropic model and simplified orthotropic model.Results.The simulation results showed that the values of stress and strain on the implant-bone interface almost increased in the orthotropic model compared to the isotropic case, especially for the cancellous bone. However, the local stress concentration was more obvious in the isotropic case compared to that in orthotropic case. The simple orthotropic model revealed irregular stress and strain distribution, compared to the isotropic model and the real orthotropic model. The influence of orthotropy was little on the implant, periodontal ligament, tooth enamel, and dentin.Conclusion.The orthotropic material has significant effect on stress and strain of implant-bone interface in the mandible, compared with the isotropic simulation. Real orthotropic mechanical properties of mandible should be emphasized in biomechanical studies of dental implants.

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