A theoretical study of aqueous humor secretion based on a continuum model coupling electrochemical and fluid-dynamical transmembrane mechanisms

Lorenzo Sala, Aurelio Giancarlo Mauri, Riccardo Sacco, Dario Messenio, Giovanna Guidoboni, Alon Harris

Research output: Contribution to journalArticle

2 Scopus citations


Intraocular pressure, resulting from the balance of aqueous humor (AH) production and drainage, is the only approved treatable risk factor in glaucoma. AH production is determined by the concurrent function of ion pumps and aquaporins in the ciliary processes, but their individual contribution is difficult to characterize experimentally. In this work, we propose a novel unified modeling and computational framework for the finite element simulation of the role of the main ion pumps and exchangers involved in AH secretion, namely, the sodium-potassium pump, the calcium-sodium exchanger, the chloride-bicarbonate exchanger, and the sodium-proton exchanger. The theoretical model is developed at the cellular scale and is based on the coupling between electrochemical and fluid-dynamical transmembrane mechanisms characterized by a novel description of the electric pressure exerted by the ions on the intrapore fluid that includes electrochemical and osmotic corrections. Considering a realistic geometry of the ion pumps, the proposed model is demonstrated to correctly predict their functionality as a function of (1) the permanent electric charge density over the pore surface, (2) the osmotic gradient coefficient, and (3) the stoichiometric ratio between the ion pump currents enforced at the inlet and outlet sections of the pore. In particular, theoretical predictions of the transepithelial membrane potential for each simulated pump/exchanger allow us to perform a first significant model comparison with experimental data for monkeys. This is a significant step for future multidisciplinary studies on the action of molecules on AH production.

Original languageEnglish (US)
Pages (from-to)65-103
Number of pages39
JournalCommunications in Applied Mathematics and Computational Science
Issue number1
StatePublished - Jan 1 2019



  • Aqueous humor
  • Eye
  • Finite element method
  • Ion exchangers
  • Ion pumps
  • Mathematical modeling
  • Simulation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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