Purchase this article with an account.
W. A. Drohan, S. K. Kelly, J. F. Rizzo III, J. Wyatt; Electrode and Axon Models. Invest. Ophthalmol. Vis. Sci. 2009;50(13):4574.
Download citation file:
© ARVO (1962-2015); The Authors (2016-present)
This work is related to the efforts of the Boston Retinal Implant Project to develop a sub-retinal prosthesis to restore vision to the blind. The specific purpose of this effort is to develop accurate mathematical models for stimulating electrodes and for axonal responses to external stimuli. Analytical models based on electrochemical theory have been developed and have been numerically simulated.
Stimulating electrodes embedded in tissue act like capacitors with parallel faradaic currents connected to a resistive tissue path. Electric circuit models have been constructed which accurately reproduce actual waveforms from the biphasic stimulating electrodes. The resultant electric fields in tissue act in an especially sensitive way on ganglion cell axons. Accurate theoretical models have been built to analyze the resultant ionic motion and its effect on membrane depolarization. These models take into account the intra-cytoplasmic ionic motion, in particular, the formation of a Debye layer on the inside of the membrane. The layer thickness and its effect on ionic concentration has been analyzed using the Gouy-Chapman-Stern model, which balance thermodynamic forces and electric forces. The relative importance of transverse vs. axial effects is analyzed. The axial "space-charging" effect is analyzed in terms of equivalent capacitance of the Debye layer in the axial direction. The effect of the Debye charge layer on relative species concentrations is analyzed. Methods of integrating the electric field models and membrane models of voltage gated channels are investigated.
At this time the main components of all models have been mathematically derived and checked for consistency. Numerical simulations have been completed to the point of demonstrating the sufficiency of the numerical algorithms. Plots have been produced showing the spatial distribution of potential and electric fields along the axon. Plots have been produced showing the potential distributions in the Debye layer.
At this time it appears that the axial fields produced by external simulations appear to be much less effective than the transverse fields, due to the thinness of the Debye layer.
This PDF is available to Subscribers Only