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