Vol. 14, No. 1, 2019

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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 and Alon Harris

Vol. 14 (2019), No. 1, 65–103
Abstract

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.

Keywords
ion exchangers, eye, ion pumps, aqueous humor, mathematical modeling, simulation, finite element method
Mathematical Subject Classification 2010
Primary: 35K59, 65M60, 76D07, 92C35, 92C37
Secondary: 76Z05
Milestones
Received: 20 December 2017
Revised: 6 December 2018
Accepted: 3 February 2019
Published: 26 April 2019
Authors
Lorenzo Sala
Institut de Recherche Mathématique Avancée
Université de Strasbourg
CNRS
Strasbourg
France
Aurelio Giancarlo Mauri
Dipartimento di Matematica
Politecnico di Milano
Milano
Italy
Riccardo Sacco
Dipartimento di Matematica
Politecnico di Milano
Milano
Italy
Dario Messenio
Eye Clinic
Department of Clinical Science
ASST Fatebenefratelli Sacco
University of Milan
Milan
Italy
Giovanna Guidoboni
Department of Electrical Engineering and Computer Science
University of Missouri
Columbia, MO
United States
Alon Harris
Eugene and Marilyn Glick Eye Institute
Indiana University School of Medicine
Indianapolis, IN
United States