September 2016
Volume 57, Issue 12
Open Access
ARVO Annual Meeting Abstract  |   September 2016

The role of HCO-3 and Na/K ATPase in the regulation of aqueous humor production: a mathematical model
Author Affiliations & Notes
  • Riccardo Sacco
    Dipartimento di Matematica, Politecnico di Milano, Italy, Milan, Italy
  • Aurelio Giancarlo Mauri
    Dipartimento di Matematica, Politecnico di Milano, Italy, Milan, Italy
  • Lorenzo Sala
    Dipartimento di Matematica, Politecnico di Milano, Italy, Milan, Italy
  • Simone Cassani
    Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, Indianapolis, Indiana, United States
  • Brent A Siesky
    Department of Ophthalmology Eugene and Marilyn Glick Eye Institute, School of Medicine, Indiana University, Indianapolis, Indiana, United States
  • Giovanna Guidoboni
    Department of Mathematical Sciences, Indiana University - Purdue University Indianapolis, Indianapolis, Indiana, United States
    Department of Ophthalmology Eugene and Marilyn Glick Eye Institute, School of Medicine, Indiana University, Indianapolis, Indiana, United States
  • Alon Harris
    Department of Ophthalmology Eugene and Marilyn Glick Eye Institute, School of Medicine, Indiana University, Indianapolis, Indiana, United States
  • Footnotes
    Commercial Relationships   Riccardo Sacco, None; Aurelio Mauri, None; Lorenzo Sala, None; Simone Cassani, None; Brent Siesky, None; Giovanna Guidoboni, None; Alon Harris, AdOM (C), AdOM (I), Biolight (C), Isama therapeutics (C), Nano Retina (C), Ono (C), Oxymap (I), Science Based Health (C), Stemnion Inc. (C)
  • Footnotes
    Support  Statement of work #4503973173: "Modeling of electro-thermo-mechanical and ferroelectric behavior". Contractors: Micron Semiconductor Italia S.r.l.; Dipartimento di Matematica Politecnico di Milano, Italy
Investigative Ophthalmology & Visual Science September 2016, Vol.57, No Pagination Specified. doi:
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      Riccardo Sacco, Aurelio Giancarlo Mauri, Lorenzo Sala, Simone Cassani, Brent A Siesky, Giovanna Guidoboni, Alon Harris;
      The role of HCO-3 and Na/K ATPase in the regulation of aqueous humor production: a mathematical model. Invest. Ophthalmol. Vis. Sci. 201657(12):.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose :
Elevated intraocular pressure (IOP) is an assessed risk factor for glaucoma. Evidences show that 1) steady-state IOP is determined by aqueous humor (AH) production and drainage and 2) AH production is determined by sodium (Na+) and bicarbonate (HCO-3)secretion into the basolateral (BL) space between nonpigmented epithelial cells (NPECs). However, connection between HCO-3 and Na+ in the regulation of AH production is controversial and difficult to study experimentally. Here we propose a mathematical model to theoretically investigate the effect of HCO-3 inhibition on the NPEC membrane potential and on the sodium/potassium (Na/K) ATPase.

Methods :
Ions are modeled as charged fluids under electrochemical and fluid forces. AH is modeled as an incompressible fluid under: 1) ion electrical pressure in channel volume; 2) K+ current density JA entering the NPEC at the intracellular side (A); 3) Na+ current density JB entering the BL space at the aqueous side (B), with JB:JA=3:2 as in physiological Na/K ATPase. Electrostatic potential V is grounded at side A whereas electric field flux is zero at side B. NPEC membrane potential (Vm) is defined as Vm=VB–VA, the baseline being set equal to experimental measurement (on monkeys) in the range [-2.7, -2.3] mV.

Results :
Fig.1 shows that Vm is close to baseline only if HCO-3 is included in the simulation. The negative value of V at side B indicates local net anion accumulation. Fig.2 shows the spatial distributions of Na+ and K+ current densities. Na+ current is positive while K+ current is negative, indicating that Na+ flows out the NPEC and K+ flows into the cell. The ratio between the two currents is 1.53 in excellent agreement with the theoretical value of 1.5.

Conclusions :
Model simulation results suggest that HCO-3 inhibition may prevent physiologically correct baseline values of Vm and Na/K ATPase function. This may provide useful indication in the design of IOP lowering medications to decrease AH production on an effective patient-specific basis, and supports the advantage of using mathematical modelling as a noninvasive complement of the animal model.

This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.

 


Fig. 1. Spatial distribution of V in the NPEC channel. Black curve: HCO-3 is inhibited. Red curve: HCO-3 is included.


Fig. 1. Spatial distribution of V in the NPEC channel. Black curve: HCO-3 is inhibited. Red curve: HCO-3 is included.

 


Spatial distributions of K+ (black) and Na+ (red) steady-state current densities.


Spatial distributions of K+ (black) and Na+ (red) steady-state current densities.

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