Journal Article

A mathematical model for the deformation of the eyeball by an elastic band

Stephen L. Keeling, Georg Propst, Georg Stadler and Werner Wackernagel

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 26, issue 2, pages 165-185
Published in print June 2009 | ISSN: 1477-8599
Published online April 2009 | e-ISSN: 1477-8602 | DOI:
A mathematical model for the deformation of the eyeball by an elastic band

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  • Applied Mathematics
  • Biomathematics and Statistics


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In a certain kind of eye surgery, the human eyeball is deformed sustainably by the application of an elastic band. This article presents a mathematical model for the mechanics of the combined eye/band structure along with an algorithm to compute the model solutions. These predict the immediate and the lasting indentation of the eyeball. The model is derived from basic physical principles by minimizing a potential energy subject to a volume constraint. Assuming spherical symmetry, this leads to a two-point boundary-value problem for a non-linear second-order ordinary differential equation that describes the minimizing static equilibrium. By comparison with laboratory data, a preliminary validation of the model is given.

Keywords: mathematical model; eyeball; cerclage

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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