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Bessel function model of corneal topography. (English) Zbl 1329.92058
Summary: 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.

MSC:
92C50 Medical applications (general)
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