Bessel function model of corneal topography

摘要

In this paper we propose a new nonlinear mathematical model of corneal topography. This model is stated as a two-point boundary value problem. We derive the governing equation from the first physical principles and provide a mathematical analysis concerning its solution. The existence and uniqueness theorems are proved and various estimates are shown. At the end, we fit the simplified model based on a modified Bessel function of the First Kind with the corneal data. The fitting error is of order of 1%, which is sufficiently accurate for this type of data and biomedical applications.