A Theoretical Approach for the Electrochemical Characterization of Ciliary Epithelium.

The ciliary epithelium (CE) is the primary site of aqueous humor (AH) production, which results from the combined action of ultrafiltration and ionic secretion. Modulation of ionic secretion is a fundamental target for drug therapy in glaucoma, and therefore it is important to identify the main factors contributing to it. As several ion transporters have been hypothesized as relevant players in CE physiology, we propose a theoretical approach to complement experimental methods in characterizing their role in the electrochemical and fluid-dynamical conditions of CE.

Computational models in nano-bioelectronics: simulation of ionic transport in voltage operated channels.

In this article, a novel mathematical and computational model is proposed for the numerical simulation of Voltage Operated ionic Channels (VOC) in Nano-bioelectronics applications. This is a first step towards a multi-physics description of hybrid bio-electronical devices such as bio-chips. The model consists of a coupled system of nonlinear partial differential equations, comprising a Poisson-Nernst-Planck system to account for electro-chemical phenomena, and a Navier-Stokes system to account for fluid-mechanical phenomena.

Electrodiffusion model simulation of rectangular current pulses in a voltage-biased biological channel.

Numerical methods are presented for simulating stochastic-in-time current pulses for an electrodiffusion model of the biological channel, with a fixed applied voltage across the channel. The electrodiffusion model consists of the parabolic advection-diffusion equation coupled either to Gauss' law or Poisson's equation, depending on the choice of boundary conditions. The TRBDF2 method is employed for the advection-diffusion equation.