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D. E. Henry, C. J. Roberts, A. S. Litsky, P. A. Weber; Computational Model of the Elastic and Viscous Properties of the Cornea. Invest. Ophthalmol. Vis. Sci. 2007;48(13):1854.
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© ARVO (1962-2015); The Authors (2016-present)
To develop a method for evaluating viscosity and elasticity of the cornea using the hysteresis measurement gathered with the Reichert Ocular Response Analyzer (ORA) and to examine the effect both behaviors have on hysteresis.
A standard three-element spring and dashpot model was used to represent the viscoelastic behavior of the cornea during an ORA measurement. The model was used to drive a computer simulation using Matlab 7.3.0 with Simulink. Values for elasticity and viscosity were assigned and a step function stress was applied to the model. Values for elasticity and viscosity were varied while a sinusoidal stress was applied to the model.
The model reproduced the expected viscoelastic responses to step and sinusoidal loadings. Ophthalmologically relevant findings included a direct relationship between the viscosity of the dashpot element and hysteresis. An inverse relationship was found between the stiffness of the spring in parallel with the dashpot and the hysteresis. The behavior was opposite in the purely elastic element in that as spring constant was increased, hysteresis increased. If both elastic elements are varied together, hysteresis peaks as a function of viscosity. Below the peak value, lower values of elasticity are associated with higher levels of hysteresis. Above the peak value, higher values of elasticity are associated with higher levels of hysteresis
Clinically, hysteresis has been shown to be an independent, but weak, risk factor for glaucomatous damage. In addition, hysteresis has been shown to be low in keratoconus and to increase after stiffening the cornea via cross-linking techniques. This model illustrates how changing viscosity and elasticity effects the hysteresis measurement in various ways. It also allows viscosity and elasticity measurements to be calculated from hysteresis, using clinical data of position, time, and stress from ORA signal analysis. Our next steps will be to use the ORA and our simulation to calculate the viscous and elastic properties of a phantom to validate accuracy of our measurements, followed by clinical data. Ultimately this model might be used to explore how changes in viscosity and elasticity affect hysteresis and if either component is stronger predictor of glaucomatous damage or corneal behavior in pathologic conditions.
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