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

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 Na+ and HCO3- secretion into the basolateral (BL) space between nonpigmented epithelial cells (NPECs). However, connection between HCO3- and Na+ is controversial in the regulation of AH production and difficult to study experimentally. Here we propose a mathematical model to theoretically investigate the effect of HCO3- inhibition on the NPEC membrane potential and on the 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) potassium current density JA entering the NPEC at channel intracellular side (A); 3) sodium current density JB entering the BL space at channel 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 spatial distribution of Vm is close to baseline only if HCO3- is included in the simulation. The negative value of Vm 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 HCO3- 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 the mathematical model as a noninvasive complement of the animal model.