A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure

Schwartz, Nathan Jay; Mackay, R. Stuart; Sackman, Jerome L.

doi:10.1007/bf02476865

Cited by 52 publications

(25 citation statements)

References 8 publications

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“…Unfortunately, reported values of YM for a given tissue can span several orders of magnitude. The human cornea is a good example, with reported modulus values ranging from 2.9 kPa 36 to 19 MPa 37 when measured by atomic force microscopy (AFM) 38 tensile stretching, 39,40 tonometry, [41][42][43] or inflation/bulge testing, 36,37,[44][45][46][47] This wide variation in reported YM values is not limited to the cornea. Part of the variation in reported YM values stems from variation in controllable experimental variables.…”

Section: Introductionmentioning

confidence: 99%

Indentation Versus Tensile Measurements of Young's Modulus for Soft Biological Tissues

McKee

Russell

Murphy³

2011

Tissue Engineering Part B: Reviews

592

402

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Section: Introductionmentioning

confidence: 99%

Indentation Versus Tensile Measurements of Young's Modulus for Soft Biological Tissues

McKee

Russell

Murphy³

2011

Tissue Engineering Part B: Reviews

592

402

View full text Add to dashboard Cite

“…Most of the theoretical mathematical models of the cornea related to applanation tonometry were published (Schwartz et al, 1966;Mow, 1968;Woo et al, 1972) before the experimental papers listed above that demonstrated the effect of corneal dimensions on the applanating pressures were published. As a result, these theoretical studies did not consider the effect of corneal dimensions on applanation tonometry.…”

Section: Introductionmentioning

confidence: 99%

Determination of the True Intraocular Pressure and Modulus of Elasticity of the Human Cornea in vivo

Orssengo

Pye²

1999

Bulletin of Mathematical Biology

285

202

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The purpose of this study was to determine the true intraocular pressure and modulus of elasticity of the human cornea in vivo. The cornea was modeled as a shell, and the equations for the deformations of a shell due to applanating and intraocular pressures were combined to model the behavior of the cornea during applanation tonometry. At certain corneal dimensions called the calibration dimensions, the applanating and intraocular pressures are considered to be equal. This relationship was used to determine the modulus of elasticity of the cornea and the relationship between the applanating and intraocular pressures. The true intraocular pressure (IOPT) was found to be related to Goldmann's applanating pressure (IOPG) as IOPT = IOPG/K, where K is a correction factor. For the calibration corneal thickness of 0.52 mm, the modulus of elasticity E in MPa of the human cornea was found to be related to the true intraocular pressure IOPT in mmHg as E = 0.02291OPT. The generalization of the Imbert-Fick law that takes into account the effect of corneal dimensions and stiffness was found to be given by IOPT = 73.5W/(K A), where W is the applanating weight in gf (gram force) and A is the applanated area in mm2. The calculated true intraocular pressure and modulus of elasticity were found to agree with published experimental results. The mathematical model developed may therefore be used to improve results from applanation tonometry and to estimate the mechanical property of the cornea in vivo.

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“…Updike etal[4] investigated the load behavior of an compressed elastic shell, coming up with an analytical formulation for elastic load-deflection and also buckling phenomena wherein the shell deforms with an axisymmetric dimple at the center. Subsequent studies by Shwarz [5] and Kitching [6] focused on load-interference behavior as a function of shell thickness and radius. Interestingly, they were looking at contrasting shell applications, one concerning cornea and other collision of vehicles.…”

Section: Introductionmentioning

confidence: 99%

Elastic Critical Load Characterization of Ellipsoidal Shells of Revolution: Design Study and Generalized Shell Parameters

Sravanthi¹

2018

IJRASET

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Shells are used for multiple load bearing applications due to their attractive property of high stiffness to weight ratio. Various studies were reported in literature on buckling, free vibration and elastic-plastic transition of hemispherical shells. Few studies dealt with ellipsoidal shells subjected to internal/external pressure. In this paper, we study the elastic critical load characteristics of ellipsoidal shells of revolution subject to compression, targeting a load sensing application. A validated finite element model is built to perform a careful unified study of multiple design configurations and new generalised shell parameters are proposed which represent both hemispherical and elliptical configurations. This helps the designers explore a larger design space in a unified framework and arrive at an optimum configuration. Keywords: Shells, Elastic critical load, Ellipsoidal shells of revolution, Finite Element Analysis I. INTRODUCTION Shells subjected to rigid plate compression have been studied extensively in the literature. Many of the studies analysed the hemispherical cross-section subjected to loads in both elastic and plastic regimes. Over the years, methods of varying fidelity have been used to detail the load-deformation behaviour of these shells under compression. In particular, buckling characteristics were reported for different thickness ratios, height ratios and material properties. A brief overview of the prior literature is detailed below along with motivation for the present study. With regards to hemispherical shells, Reissner[1] investigated the shell-plate contact problem and provided expressions for direct and bending stresses for shallow shells with h/R < 4. Naghdi[2] later extended Reissner's study to include the effect of shear strains. Kalnins[3] devised a multi-segment method for nonlinear analysis of elastic shells. Updike etal[4] investigated the load behavior of an compressed elastic shell, coming up with an analytical formulation for elastic load-deflection and also buckling phenomena wherein the shell deforms with an axisymmetric dimple at the center. Subsequent studies by Shwarz[5] and Kitching[6] focused on load-interference behavior as a function of shell thickness and radius. Interestingly, they were looking at contrasting shell applications, one concerning cornea and other collision of vehicles. Gupta etal [7] focused on buckling of hemispherical shells across a range of thickness ratios (R/t : 15 to 240) and showed good agreement between experimental and theoretical results. Another interesting shell load application to ping pong ball was studied by Pauchard etal[8]. Shariati etal[9] performed experimental and numerical study of buckling behavior of steel shells with flat tops under various loadings. The study of Longqiu Li etal[10] provides a pointer in using FE model to derive useful information on onset of plastic yielding but is limited to the treatment of hemi-spherical shells. Other recent studies on deformation behavior of hemispherical shells are c...

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A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure

Cited by 52 publications

References 8 publications

Indentation Versus Tensile Measurements of Young's Modulus for Soft Biological Tissues

Indentation Versus Tensile Measurements of Young's Modulus for Soft Biological Tissues

Determination of the True Intraocular Pressure and Modulus of Elasticity of the Human Cornea in vivo

Elastic Critical Load Characterization of Ellipsoidal Shells of Revolution: Design Study and Generalized Shell Parameters

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