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Generative mathematical modelling to demonstrate virtual simulations of neovascular age related macular degeneration

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  • David Hoyle
  • Tariq Mehmood Aslam

Abstract

Purpose: To develop a generative mathematical model of wet age-related macular degeneration (AMD) and model the impact of injections of anti-vascular endothelial growth factor to virtual patients with the condition. Methods: We isolated key pathophysiological components of macular degeneration in terms of macular edema development and response to anti-vascular endothelial growth factor (VEGF) agents. We developed mathematical models for each of these components using constants determined from published biological experimentation. Consequently, we combined the mathematical models of the separate components to arrive at an end-to-end model of the evolution of macular edema size and its response to treatment. Results: We present a series of simulations based upon our idealised model. Initially, we demonstrate the theoretical change in macular edema height in wet macular degeneration over time without and with anti-VEGF interventions. In our final simulation, we demonstrate the powerful possibilities of virtual clinical trials by simulating a virtual model of a landmark study using our existing mathematical AMD model. Conclusions: Using our mathematical modelling based upon known pathological and pharmacological processes we have been able to model the effect of intravitreal injection of an anti-VEGF agent on macular edema from age related macular degeneration. We were subsequently able to mathematically simulate a major clinical trial with results that mirror many key features of the clinical established study. We anticipate that the generative model presented here can evolve to be a useful supportive tool in the challenge to deliver optimal therapy for patients with wet macular degeneration.

Suggested Citation

  • David Hoyle & Tariq Mehmood Aslam, 2017. "Generative mathematical modelling to demonstrate virtual simulations of neovascular age related macular degeneration," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-12, December.
    • Handle: RePEc:plo:pone00:0189053
    DOI: 10.1371/journal.pone.0189053
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    References listed on IDEAS

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    1. Soetaert, Karline & Petzoldt, Thomas & Setzer, R. Woodrow, 2010. "Solving Differential Equations in R: Package deSolve," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i09).
    2. Alberto Ferreira & Alexandros Sagkriotis & Melvin Olson & Jingsong Lu & Charles Makin & Fran Milnes, 2015. "Treatment Frequency and Dosing Interval of Ranibizumab and Aflibercept for Neovascular Age-Related Macular Degeneration in Routine Clinical Practice in the USA," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-12, July.
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