### 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 language | English (US) |
---|---|

Pages (from-to) | 165-185 |

Number of pages | 21 |

Journal | Mathematical Medicine and Biology |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - 2009 |

### Fingerprint

### 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

*Mathematical Medicine and Biology*,

*26*(2), 165-185. https://doi.org/10.1093/imammb/dqp008

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

Research output: Contribution to journal › Article

*Mathematical Medicine and Biology*, vol. 26, no. 2, pp. 165-185. https://doi.org/10.1093/imammb/dqp008

}

TY - JOUR

T1 - A mathematical model for the deformation of the eyeball by an elastic band

AU - Keeling, Stephen L.

AU - Propst, Georg

AU - Stadler, Georg

AU - Wackernagel, Werner

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Cerclage

KW - Eyeball

KW - Mathematical model

UR - http://www.scopus.com/inward/record.url?scp=67649099210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649099210&partnerID=8YFLogxK

U2 - 10.1093/imammb/dqp008

DO - 10.1093/imammb/dqp008

M3 - Article

C2 - 19351791

AN - SCOPUS:67649099210

VL - 26

SP - 165

EP - 185

JO - Mathematical Medicine and Biology

JF - Mathematical Medicine and Biology

SN - 1477-8599

IS - 2

ER -