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 journalArticlepeer-review


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
Issue number2
StatePublished - 2009


  • Cerclage
  • Eyeball
  • Mathematical model

ASJC Scopus subject areas

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


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