BEM for the Pennes Bioheat equation in the human eye

Abstract

Heat transfer inside the human eye is an interesting area of research. Current methods to determine the temperature of the surface of the eye include infrared thermography. However this method is unable to measure the temperature inside. Previous mathematical models for ocular heat transfer have employed the use of the finite and boundary element methods with good results. In particular, the boundary element method has been applied to the main regions in the eye which have their unique thermal conductivities. Following which the results then have to be assembled together to observe the temperature field over the whole eye. To increase the efficiency of the boundary element method, this paper aims to model the thermal conductivity of the 2 dimensional eye as a continuous function of its geometry. The function to be used is a polynomial that is a linear combination of solutions to the Laplace Equation.

The results show that the temperature predicted by the heat transfer model is in good agreement with previous mathematical models if the appropriate function is chosen. Parameter analysis will also be carried out using the model developed to investigate how the temperature in the eyeball changes under varying conditions. Finally, the shortcomings and applications of the results will be discussed with room for future research.