Numerical Prediction of the Temperature Distribution Within a Human Eye During Laser Surgery

Abstract

In this paper a computational heat transfer model for prediction of the temperature distribution within the human eye during laser surgery is presented. The heat transfer within a tissue is described by the classic Pennes bioheat transfer equation. The intraocular temperature distribution is calculated using finite-difference method. Two types of computational domain have been considered: (i) rectangular parallelepiped and (ii) cylindrical. The eye is modeled as a composite layered structure consisting of four different ocular tissues, namely, cornea, aqueous, lens and vitreous. It is assumed that the eye is symmetrical about the pupillary axis. The absorption probability of ocular tissue is modulated based on the Lambert-Beer’s law to reproduce the exponential attenuation of the laser light with depth within a biomaterial. The heat flow is modeled as transient and three-dimensional for rectangular parallelepiped geometry and two-dimensional (axi-symmetric) for the cylindrical geometry. The results indicate that for the insulation condition imposed on the periphery of the eye the model based on rectangular parallelepiped geometry of the eye at no laser power and at the initial temperature of 25°C predicts temperature closer to in-vitro experimental measurements reported in literature whereas the model based on cylindrical geometry predicts higher temperature. The opposite is true (that is, lower temperature is predicted by the model based on cylindrical geometry) for high laser heat flux (2000 W/m2) and higher initial temperature (37°C). This study also presents changes in eye temperature subjected to intermittent laser source used in laser surgery techniques such as PRK and LASIK. A comparison of the results based on three different boundary conditions such as convection (hb = 10 W/m2K), constant temperature (37°C) and insulation on the eye periphery reveals that the model based on insulation condition predicts results closer to that of in-vitro experiment at no laser power and initial temperature of 25°C whereas at a laser power of 200 W/m2 and at the initial temperature of 37°C insulation boundary condition produces highest temperature followed by that produced by convection and constant temperature conditions. The heat transfer is one-dimensional for the insulated eye periphery whereas multi-dimensional heat flow takes place when the circumferential boundary condition is either convective or isothermal.