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

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

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)165-185
Number of pages21
JournalMathematical Medicine and Biology
Volume26
Issue number2
DOIs
StatePublished - Jan 1 2009

Keywords

  • Cerclage
  • Eyeball
  • Mathematical model

ASJC Scopus subject areas

  • Neuroscience(all)
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Environmental Science(all)
  • Pharmacology
  • Applied Mathematics

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