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 - 2009

Fingerprint

Theoretical Models
Mathematical Model
Mathematical models
Mechanics
Spherical Symmetry
Indentation
Second-order Ordinary Differential Equations
Band Structure
Two-point Boundary Value Problem
Potential energy
Ordinary differential equations
Band structure
Surgery
Boundary value problems
indentation
potential energy
Model
mechanics
symmetry
Predict

Keywords

  • Cerclage
  • Eyeball
  • Mathematical model

ASJC Scopus subject areas

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

Cite this

A mathematical model for the deformation of the eyeball by an elastic band. / Keeling, Stephen L.; Propst, Georg; Stadler, Georg; Wackernagel, Werner.

In: Mathematical Medicine and Biology, Vol. 26, No. 2, 2009, p. 165-185.

Research output: Contribution to journalArticle

Keeling, Stephen L. ; Propst, Georg ; Stadler, Georg ; Wackernagel, Werner. / A mathematical model for the deformation of the eyeball by an elastic band. In: Mathematical Medicine and Biology. 2009 ; Vol. 26, No. 2. pp. 165-185.
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