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Mathematical Medicine and Biology Advance Access originally published online on April 7, 2009
Mathematical Medicine and Biology 2009 26(2):165-185; doi:10.1093/imammb/dqp008
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

Stephen L. Keeling{dagger} and Georg Propst{ddagger}

Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstraße 36, 8010 Graz, Austria

Georg Stadler§

Institute for Computational Engineering and Sciences, University of Texas at Austin, 1 University Station, C0200 Austin, TX 78712, USA

Werner Wackernagel

Universitäts-Augenklinik, Medizinische Universität Graz, Auenbruggerplatz 4, 8036 Graz, Austria

{dagger} Email: stephen.keeling{at}uni-graz.at

{ddagger} Corresponding author. Email: georg.propst{at}uni-graz.at

§ Email: georgst{at}ices.utexas.edu

Email: werner.wackernagel{at}meduni-graz.at

Received on May 30, 2008. Revised on December 16, 2008. Accepted on March 3, 2009.

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


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