Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

Erika Camacho, Anca Radulescu, Stephen Wirkus

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.

Original languageEnglish (US)
Pages (from-to)267-276
Number of pages10
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume38
DOIs
StatePublished - Sep 1 2016

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Bifurcation Analysis
Cones
Cone
Interaction
Retina
Equilibrium Solution
Model
Mathematical Model
Mathematical models
Term
Range of data

Keywords

  • Bifurcation
  • Photoreceptor degeneration

ASJC Scopus subject areas

  • Modeling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

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abstract = "Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.",
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AU - Camacho, Erika

AU - Radulescu, Anca

AU - Wirkus, Stephen

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N2 - Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.

AB - Retinitis Pigmentosa (RP) is the term used to describe a diverse set of degenerative eye diseases affecting the photoreceptors (rods and cones) in the retina. This work builds on an existing mathematical model of RP that focused on the interaction of the rods and cones. We non-dimensionalize the model and examine the stability of the equilibria. We then numerically investigate other stable modes that are present in the system for various parameter values and relate these modes to the original problem. Our results show that stable modes exist for a wider range of parameter values than the stability of the equilibrium solutions alone, suggesting that additional approaches to preventing cone death may exist.

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