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Mathematical Models of Aqueous Production, Flow and Drainage

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Ocular Fluid Dynamics

Abstract

The aqueous humour (AH) is a transparent fluid with water-like properties that fills the anterior chamber (AC, the region between the cornea and the iris) and the posterior chamber (PC, the region between the iris and the lens) of the eye, which are connected at the pupil. AH is produced at ciliary processes, and it flows from the PC to the AC, where it is drained in the trabecular meshwork. AH flow is important physiologically, as it governs intraocular pressure and delivers nutrients to avascular ocular tissues. Disruption of AH flow may lead to multiple pathological conditions, such as glaucoma and nutrient depletion. Studying aqueous production, flow and drainage is thus relevant to understand eye physiology and pathophysiology.

Mathematical modelling has proven to be a very useful tool for studying AH, as it allows one to understand the mechanisms of the flow by studying them separately. In this chapter we outline the mathematical models of AH production, different AH flow mechanisms and drainage, subsequently. We focus on analytical works and briefly mention the main conclusions of numerical ones.

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Acknowledgements

The authors thank Prof. Federica Grillo, University of Genoa (Italy), for drawing Figs. 1 and 2. Mariia Dvoriashyna acknowledges the Department of Civil, Chemical and Environmental Engineering of the University of Genoa (Italy), where she worked as a PhD student when the original version of this chapter was written.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Mariia Dvoriashyna

  2. Department of Civil, Chemical and Environment Engineering, University of Genoa, Genova, Italy

    Mariia Dvoriashyna & Rodolfo Repetto

  3. Department of Bioengineering, Imperial College London, London, UK

    Jan O. Pralits

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  1. Mariia Dvoriashyna
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  2. Jan O. Pralits
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  3. Jennifer H. Tweedy
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  4. Rodolfo Repetto
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Correspondence to Rodolfo Repetto .

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Editors and Affiliations

  1. Department of Math Sciences, Indiana University – Purdue University I, Indianapolis, IN, USA

    Giovanna Guidoboni

  2. Icahn School of Medicine at Mount Sinai, New York, NY, USA

    Alon Harris

  3. Department of Mathematics, Polytechnic University of Milan, Milan, Italy

    Riccardo Sacco

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Dvoriashyna, M., Pralits, J.O., Tweedy, J.H., Repetto, R. (2019). Mathematical Models of Aqueous Production, Flow and Drainage. In: Guidoboni, G., Harris, A., Sacco, R. (eds) Ocular Fluid Dynamics. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25886-3_9

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