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

    Fingerprint

    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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    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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