Mathematical Modelling for Cornea Viscoelastic and Thermal Behavior

Abstract

Corneal biomechanics is of great interest to researchers recently. Clinical findings relate them to corneal diseases and to outcomes of refractive surgery. To have a solid understanding of corneal diseases’ progression, it is important to understand corneal biomechanics. Also, they are essential for better explaining outcomes of refractive surgeries and their undesired consequences. There is a difficulty for studying corneal biomechanics in-vivo and multiple limitations arise for ex-vivo studies. Hence mathematical modelling is considered as a proper solution to overcome such obstacles. Mathematical modelling of cornea in-vivo allows studying corneal viscoelasticity with taking into consideration all boundary conditions existing in real in-vivo situation. In this paper, three mathematical models are used to simulate corneal viscoelasticity and thermal behavior in two different loading situations: constant and transient loading. Two models of the three are used for viscoelasticity simulation which are Kelvin-Voigt and standard linear solid models. Viscoelasticity simulation results show that standard linear solid model is efficient for describing the viscoelastic behavior of human cornea in both loading conditions. Results show also that the deformation amplitude obtained from standard linear solid model is more reasonable for corneal soft-tissue deformation with respect to corresponding clinical findings than that obtained from Kelvin-Voigt model. Also, temperature rise due to the ultrasound pressure push is calculated using bioheat transfer model for both the axial direction and as a 2D spatial map using the third model. Thermal behavior results estimated corneal temperature rise to be about 0.2°C, which conforms with FDA regulations for soft tissue safety.

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