The role of HCO^-₃ and Na/K ATPase in the regulation of aqueous humor production: a mathematical model

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 J_A entering the NPEC at the intracellular side (A); 3) Na⁺ current density J_B entering the BL space at the aqueous side (B), with J_B:J_A=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 (V_m) is defined as V_m=V_B–V_A, the baseline being set equal to experimental measurement (on monkeys) in the range [-2.7, -2.3] mV.

Results :
Fig.1 shows that V_m 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 V_m 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.