Mathematical modelling of ocular epithelial transport: a review
MAIO 130 Dvoriashyna PDF

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Dvoriashyna M, Foss A, Gaffney E, Repetto R. Mathematical modelling of ocular epithelial transport: a review. MAIO [Internet]. 2023 Oct. 31 [cited 2023 Dec. 4];5(1):1-17. Available from:

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2023 Mariia Dvoriashyna, Alexander Foss, Eamonn Gaffney, Rodolfo Repetto


epithelial water transport; mathematical modelling; ocular epithelia


Purpose: Ocular epithelial layers are fundamental for the physiology of the eye as they regulate water transport. The purpose of this review is to discuss the existing mathematical models of water transport across these layers.

Methods: We detail the physical mechanisms that can induce water transport across epithelial layers and describe how they can be mathematically modelled.

Results: We consider 3 ocular epithelial layers. The first is the epithelium of the ciliary processes, which is responsible for aqueous humour production. The second is the corneal endothelium (functionally an epithelium), which plays a key role in maintaining the delicate hydration state of the cornea. The third is the retinal pigment epithelium, which actively removes water from the retina by pumping it into the choroid.

Conclusion: Owing to the difficulty of obtaining direct measurements of water fluxes across epithelial layers, mathematical models can significantly improve our understanding of this field. For instance, they can help develop insight and predictive capability concerning the role of different ion channels, transporters, exchangers, and pumps, as well as carbon dioxide hydrolysis, in ocular water transport processes. Likewise, they can elucidate the importance of the various mechanisms and associated parameters that are involved.
MAIO 130 Dvoriashyna PDF


Adler FH. Physiology of the Eye. Academic Medicine, 1965;40(7): 720.

Rehfeld A, Nylander M, Karnov K. Compendium of histology: a theoretical and practical guide. Springer, 2017;

Knight DA, Holgate ST. The airway epithelium: structural and functional properties in health and disease. Respirology, 2003;8(4): 432–446.

Hamann S. Molecular mechanisms of water transport in the eye. International review of cytology. 215. Elsevier, 2002; 395–431.

La Cour M. The Retinal Pigment Epithelium. Adler’s Physiology of the Eye: Clinical Applications, 2003; 348–357.

Candia OA, Alvarez LJ. Fluid transport phenomena in ocular epithelia. Progress in retinal and eye research, 2008;27(2): 197–212.

Fischbarg J. Fluid transport across leaky epithelia: central role of the tight junction and supporting role of aquaporins. Physiological reviews, 2010;90(4): 1271–1290.

Diamond JM. Channels in epithelial cell membranes and junctions. Federation proceedings. 37. (12):1978;2639–2643.

Schneeberger E, Lynch R. Tight junctions. Their structure, composition, and function. Circulation research, 1984;55(6): 723–733.

Probstein RF. Physicochemical hydrodynamics: an introduction. John Wiley & Sons, 2005;

Staverman A. The theory of measurement of osmotic pressure. Recueil des Travaux Chimiques des Pays-Bas, 1951;70(4): 344–352.

Li LY. Transport of multicomponent ionic solutions in membrane systems. en. Philosophical Magazine Letters, Sept. 2004;84(9): 593–599. ISSN: 0950-0839, 1362-3036. Available from: http : / /, visited on 12/04/2022, doi: 10.1080/09500830512331325767.

Cheng X, Pinsky PM. The Balance of Fluid and Osmotic Pressures across Active Biological Membranes with Application to the Corneal Endothelium. en. PLOS ONE, Dec. 2015;10(12): ed. by PJ Atzberger, e0145422. ISSN: 1932-6203. Available from: /10.1371/journal.pone.0145422, visited on 12/04/2022, doi: 10.1371/journal.pone.0145422.

Kedem O, Katchalsky A. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. en. Biochimica et Biophysica Acta, Jan. 1958;27, 229–246. ISSN: 00063002. Available from:, visited on 12/05/2022, doi: 10.1016/0006-3002(58)90330-5.

Schultz SG. The role of paracellular pathways in isotonic fluid transport. The Yale Journal of Biology and Medicine, 1977;50(2): 99.

Diamond JM, Bossert WH. Standing-gradient osmotic flow: A mechanism for coupling of water and solute transport in epithelia. J. Gen. Physiol. 1967;50(8): 2061–2083.

Kirkby BJ. Micro- and nanoscalescale fluid mechanics: transport in microfluidic devices. Cambridge University Press, 2010;

Keener JP, Sneyd J. Mathematical physiology. 1. Springer, 1998;

Dvoriashyna M, Foss AJ, Gaffney EA, Repetto R. Mathematical models ofwater transport across ocular epithelial layers. Modeling of Mass Transport Processes in Biological Media. Elsevier, 2022; 405–433.

Le A, Mukesh BN, McCarty CA, Taylor HR. A Mathematical Model of Aqueous Humor Production and Composition. Invest Ophthalmol Vis Sci. 2003;44, 3783–3789.

Kiel J, Hollingsworth M, Rao R, Chen M, Reitsamer H. Ciliary blood flow and aqueous humor production. Progress in Retinal and Eye Research, 2011;30, 1–17.

Galbert BT, Kaufman PL. Production and Flow of Aqueous Humor. Adler’s Physiology of the Eye, 11th Edition (e-version). Ed. by L Levin, S Nilsson, J ver Hoeve, S Wu, P Kaufman, A Alm. Elsevier Inc, Amsterdam, 2011; 715–806.

Sacco R, Guidoboni G, Jerome JW, Bonifazi G, Marazzi NM, Verticchio Vercellin AC, et al. A Theoretical Approach for the Electrochemical Characterization of Ciliary Epithelium. Life, 2020;10, 8,doi:10.3390/life10020008.

Dvoriashyna M, Foss AJ, Gaffney EA, Repetto R. A Mathematical Model of Aqueous Humor Production and Composition. Invest Ophthalmol Vis Sci. 2022;63(9): 1–11.

Goel M, Picciani RG, Lee RK, Bhattacharya SK. Aqueous Humor Dynamics: A Review. The Open Ophthalmology Journal, 2010;4, 52–59.

To CH, Do CW, Zamudio AC, Candia OA. Model of ionic transport for bovine ciliary epithelium: effects of acetazolamide and HCO−3 . American Journal of Physiology-Cell Physiology, 2001;280(6): C1521–C1530.

Edelhauser HF, Ubels JL, Hejny C. The Cornea and the Sclera. Adler’s Physiology of the Eye: Clinical Applications, 2003; pp. 47–114.

Maurice DM. The structure andtransparency of the cornea. The Journal of physiology, 1957;136(2): 263–286.

Benedek G. Theory of transparency of the eye. Applied optics, 1971;10(3): 459–473.

Klyce SD. Endothelial pump and barrier function. Experimental eye research, 2020;198, 108068.

Maurice D. The location of the fluid pump in the cornea. The Journal of physiology, 1972;221(1): 43–54.

Bonanno JA. Molecular mechanisms underlying the corneal endothelial pump. Experimental eye research, 2012;95(1): 2–7.

Leung B, Bonanno J, Radke C. Oxygen-deficient metabolism and corneal edema. en. Progress in Retinal and Eye Research, Nov. 2011;30(6): 471–492. ISSN: 13509462. Available from:, visited on 12/02/2022, doi: 10.1016/j.preteyeres.2011.07.001.

Cheng X, Pinsky PM. A numerical model for metabolism, metabolite transport and edema in the human cornea. en. Computer Methods in Applied Mechanics and Engineering, Feb. 2017;314, 323–344. ISSN: 00457825. Available from:, visited on 12/02/2022, doi: 10.1016/j.cma.2016.09.014.

Sanchez J, Li Y, Rubashkin A, Iserovich P, Wen Q, Ruberti J, et al. Evidence for a central role for electroosmosis in fluid transport by corneal endothelium. Journal of Membrane Biology, 2002;187(1): 37–50.

Rubashkin A, Iserovich P, Hernandez J, Fischbarg J. Epithelial fluid transport: protruding macromolecules and space charges can bring about electro-osmotic coupling at the tight junctions. The Journal of membrane biology, 2006;208(3): 251–263.

Sharma RK, Ehinger B. Development and structure of the retina. Adler’s Physiology of the Eye: Clinical Applications, 2003;10, 319–347.

Hughes BA, Miller SS, Machen TE. Effects of cyclic AMP on fluid absorption and ion transport across frog retinal pigment epithelium.Measurements in the open-circuit state. The Journal of general physiology, 1984;83(6): 875–899.

Shi G, Maminishkis A, Banzon T, Jalickee S, Li R, Hammer J, et al. Control of chemokine gradients by the retinal pigment epithelium. Investigative ophthalmology & visual science, 2008;49(10): 4620–4630. doi: 10.1167/iovs.08-1816.

Gallemore R, Hughes B, Miller S. Transport mechanisms in the retinal pigment epithelium. The Retinal Pigment Epithelium. Ed. byMMarmor, T Wolfensberger.Oxford University Press NewYork, 1998; 103–134.

Spring KR. Mechanism of fluid transport by epithelia. Comprehensive physiology, 2010; doi: 10.1002/cphy.cp060405.

Dvoriashyna M, Foss AJ, Gaffney EA, Jensen OE, Repetto R. Osmotic and electroosmotic fluid transport across the retinal pigment epithelium: a mathematical model. Journal of Theoretical Biology, 2018;456, 233–248.

Dvoriashyna M, Foss AJ, Gaffney EA, Repetto R. Fluid and solute transport across the retinal pigment epithelium: a theoretical model. Journal of the Royal Society Interface, 2020;17(163): 20190735.

Cour M Dornonville de la. Ion transport in the retinal pigment epithelium. A study with double barrelled ion-selective microelectrodes. Acta Ophthalmologica supplements, 1993;(209): 1.

Reichhart N, Strauß O. Ion channels and transporters of the retinal pigment epithelium. Experimental Eye Research, 2014;126, 27–37. doi: 10.1016/j.exer.2014.05.005..

Hamann S, Kiilgaard JF, Cour M la, Prause JU, Zeuthen T. Cotransport of H+, lactate, and H2O in porcine retinal pigment epithelial cells. Experimental eye research, 2003;76(4): 493–504.

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