On the mechanics of a detaching retina

William J. Bottega, Peter L. Bishay, Jonathan L. Prenner, Howard F. Fine

Research output: Contribution to journalArticle

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Abstract

A mechanics-based mathematical model for retinal detachment is developed, incorporating an energybased criterion for propagation. Retinas with and without central tears are considered and contraction of the vitreous and extension of its fibrils, along with a pressure difference across the retina, are taken as the stimuli for detachment propagation. In addition to the equations of motion, boundary and matching conditions, the variational formulation yields the self-consistent energy release rate that governs detachment, and formulae for critical stress and critical deflections that provide a rational basis for measuring critical parameters. Exact analytical solutions are established for axisymmetric detachment of retinas with and without tears, and numerical simulations are performed based on these solutions. The results yield characteristic behaviour, including threshold levels and stability of detachment, 'dimpling' of the detaching retina, the effects of changes in material and geometric parameters, and the influence of the presence and size of the retinal tear on detachment propagation. The model predicts that once detachment ensues it does so in an unstable manner and is extensive in scope. This is in agreement with clinical observation. Results also suggest that, under appropriate conditions, the presence and size of a retinal tear or hole can have a 'stabilizing' effect with regard to detachment propagation.

Original languageEnglish (US)
Pages (from-to)287-310
Number of pages24
JournalMathematical Medicine and Biology
Volume30
Issue number4
DOIs
StatePublished - Dec 1 2013

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All Science Journal Classification (ASJC) codes

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

Keywords

  • Elastic foundation
  • Retina
  • Retinal detachment
  • Retinal tear
  • Spherical shell
  • Subretinal pressure
  • Vitreous contraction
  • Vitreous fibril tension

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