Electro-fluid dynamics of aqueous humor production: simulations and new directions

Aurelio Giancarlo Mauri, Lorenzo Sala, Paolo Airoldi, Giovanni Novielli, Riccardo Sacco, Simone Cassani, Giovanna Guidoboni, Brent Siesky, Alon Harris

Abstract


Purpose: to theoretically investigate the role of bicarbonate ion (HCO−3 ) on the nonpigmented transepithelial potential dierence Vm, the sodium potassium pump (Na/K) and the active secretion of aqueous humor.

Methods: a three-dimensional mathematical model is proposed to isolate the roles of HCO−3 and Na+, which are diicult to investigate experimentally. The model combines the velocity-extended Poisson-Nernst-Planck equations to describe ion electrodiusion and the Stokes equations to describe aqueous humor flow into the basolateral space adjacent to the nonpigmented ephitelial cells.

Results: Computations showthat Vm is close to baseline experimental measurements (on monkeys) in the range [−2.7,−2.3]mVonly if HCO−3 is included in the simulation. The model is also capable of reproducing the flow of Na+ exiting the cell and the flow of K+ entering the cell, in accordance with the physiology of the Na/K pump. The simulated Na/K ratio is 1.53, which is in very good agreement with the theoretical value of 1.5.

Conclusion: Model simulations suggest that HCO−3 inhibition may prevent physiologically correct baseline values of the nonpigmented transepithelial potential difference and Na/K ATPase function. This may provide useful indication in the design of medications that decrease the active secretion of aqueous humor, and supports the advantage of using mathematical models as a noninvasive complement of animal models.


Keywords


aqueous humor production, electrochemical transport, mathematical modeling, numerical simulation, sodium-potassium pump

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