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

[1] Application of structural analysis to the mechanical behaviour of the cornea
Anderson, K
El-Sheikh, A
Newson, T
[J]. JOURNAL OF THE ROYAL SOCIETY INTERFACE, 2004, 1 (01) : 3 - 15
[2] [Anonymous], 1948, Handbook of Mathematical Functions withFormulas, Graphs, and Mathematical Tables, DOI DOI 10.1119/1.15378
[3] Physical human model eye and methods of its use to analyse optical performance of soft contact lenses
Bakaraju, Ravi C.
Ehrmann, Klaus
Falk, Darrin
Ho, Arthur
Papas, Eric
[J]. OPTICS EXPRESS, 2010, 18 (16): : 16868 - 16882
[4] Thin film dynamics on a prolate spheroid with application to the cornea
Braun, R. J.
Usha, R.
McFadden, G. B.
Driscoll, T. A.
Cook, L. P.
King-Smith, P. E.
[J]. JOURNAL OF ENGINEERING MATHEMATICS, 2012, 73 (01) : 121 - 138
[5] Braun RJ, 2003, MATH MED BIOL, V20, P1
[6] Canning CR, 2002, IMA J MATH APPL MED, V19, P31
[7] Finite Element Modeling of Corneal Biomechanical Behavior
Elsheikh, Ahmed
[J]. JOURNAL OF REFRACTIVE SURGERY, 2010, 26 (04) : 289 - 300
[8] REVIEW OF PAST AND PRESENT TECHNIQUES OF MEASURING CORNEAL TOPOGRAPHY
FOWLER, CW
DAVE, TN
[J]. OPHTHALMIC AND PHYSIOLOGICAL OPTICS, 1994, 14 (01) : 49 - 58
[9] A remark on "A nonlinear mathematical model of the corneal shape"
He, Ji-Huan
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (06) : 2863 - 2865
[10] Approximating ocular surfaces by generalised conic curves
Kasprzak, Henryk T.
Iskander, D. Robert
[J]. OPHTHALMIC AND PHYSIOLOGICAL OPTICS, 2006, 26 (06) : 602 - 609

← 1 2 3 →