Bessel function model of corneal topography

被引：16

作者：

Okrasinski, Wojciech ^{[1
]}

Plociniczak, Lukasz ^{[1
]}

机构：

[1] Wroclaw Univ Technol, Inst Math & Comp Sci, PL-50372 Wroclaw, Poland

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 223卷

关键词：

Corneal topography; Mathematical model; Boundary value problem; Bessel function; FILM;

D O I：

10.1016/j.amc.2013.07.097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：436 / 443

页数：8

共 21 条

[11] Axial curvature and the skew ray error in corneal topography
Klein, SA
[J]. OPTOMETRY AND VISION SCIENCE, 1997, 74 (11) : 931 - 944
[12] An alternative mathematical algorithm for the photo- and videokeratoscope
Mahavier, W. Ted
Hunt, J.
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2006, 7 (05) : 1223 - 1232
[13] A review of methods for measuring corneal topography
Mejía-Barbosa, Y
Malacara-Hernández, D
[J]. OPTOMETRY AND VISION SCIENCE, 2001, 78 (04) : 240 - 253
[14] A nonlinear mathematical model of the corneal shape
Okrasinski, Wojciech
Plociniczak, Lukasz
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (03) : 1498 - 1505
[15] Regularization of an ill-posed problem in corneal topography
Plociniczak, L.
Okrasinski, W.
[J]. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2013, 21 (06) : 1090 - 1097
[16] Robert Iskander D., 2001, IEEE T BIOMEDICAL EN, V48
[17] Anterior corneal profile with variable asphericity
Rosales, Marco A.
Juarez-Aubry, Montserrat
Lopez-Olazagasti, Estela
Ibarra, Jorge
Tepichin, Eduardo
[J]. APPLIED OPTICS, 2009, 48 (35) : 6594 - 6599
[18] Modeling Corneal Surfaces With Rational Functions for High-Speed Videokeratoscopy Data Compression
Schneider, Martin
Iskander, D. Robert
Collins, Michael J.
[J]. IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 2009, 56 (02) : 493 - 499
[19] Tikhonov A.N., 1963, Equations of mathematical physics
[20] Trattler W., 2010, CORNEA

← 1 2 3 →