Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

Erika Camacho; Anca Radulescu; Stephen Wirkus

doi:10.1016/j.cnsns.2016.02.030

Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

Erika Camacho, Anca Radulescu, Stephen Wirkus

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English (US)
Pages (from-to)	267-276
Number of pages	10
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	38
DOIs	https://doi.org/10.1016/j.cnsns.2016.02.030
State	Published - Sep 1 2016

Keywords

Bifurcation
Photoreceptor degeneration

ASJC Scopus subject areas

Modeling and Simulation
Numerical Analysis
Applied Mathematics

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10.1016/j.cnsns.2016.02.030

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title = "Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa",

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.",

keywords = "Bifurcation, Photoreceptor degeneration",

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T1 - Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

AU - Camacho, Erika

AU - Radulescu, Anca

AU - Wirkus, Stephen

PY - 2016/9/1

Y1 - 2016/9/1

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.

KW - Bifurcation

KW - Photoreceptor degeneration

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JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

Bifurcation analysis of a photoreceptor interaction model for Retinitis Pigmentosa

Abstract

Keywords

ASJC Scopus subject areas

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