Predictive Mathematical Models for the Spread and Treatment of Hyperoxia-induced Photoreceptor Degeneration in Retinitis Pigmentosa

Paul Roberts, Eamonn Gaffney, Jonathan Whiteley, Philip Luthert, Alexander Foss, Helen Byrne

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Purpose: To determine whether the oxygen toxicity hypothesis can explain the distinctive spatio-temporal patterns of retinal degeneration associated with human retinitis pigmentosa (RP) and to predict the effects of antioxidant and trophic factor treatments under this hypothesis.

Methods: Three mathematical models were derived to describe the evolution of the retinal oxygen concentration and photoreceptor density over time. The first model considers only hyperoxia-induced degeneration, while the second and third models include mutation-induced rod and cone loss respectively. The models were formulated as systems of partial differential equations, defined on a two-dimensional domain spanning the region between the foveal center and the ora serrata, and were solved numerically using the finite element method.

Results: The mathematical models recapitulate patterns of retinal degeneration which involve preferential loss of photoreceptors in the parafoveal/perifoveal and far-peripheral retina, while those which involve a preferential loss of midperipheral photoreceptors cannot be reproduced. Treatment with antioxidants or trophic factors is predicted to delay, halt, or partially reverse retinal degeneration, depending upon the strength and timing of treatment and disease severity.

Conclusions: The model simulations indicate that while the oxygen toxicity hypothesis is sufficient to explain some of the patterns of retinal degeneration observed in human RP, additional mechanisms are necessary to explain the full range of behaviors. The models further suggest that antioxidant and trophic factor treatments have the potential to reduce hyperoxia-induced disease severity and that, where possible, these treatments should be targeted at retinal regions with low photoreceptor density to maximize their efficacy.
Original languageEnglish
Pages (from-to)1238-1249
Number of pages12
JournalInvestigative Opthalmology & Visual Science
Issue number3
Publication statusPublished - 1 Mar 2018


  • Retina
  • Oxygen Toxicity
  • Reaction-diffusion Equations
  • Finite Element Method
  • Retinitis Pigmentosa
  • Photoreceptors
  • Mathematical Model

ASJC Scopus subject areas

  • Applied Mathematics
  • Modelling and Simulation
  • Ophthalmology


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