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W. A. Drohan, S. K. Kelly, J. F. Rizzo, J. L. Wyatt; External Field Firing Thresholds for Neurons. Invest. Ophthalmol. Vis. Sci. 2008;49(13):3032.
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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 determine the minimum magnitude of the impressed electric field (i.e. threshold field) external to a target cell which will cause the cell to emit an action potential. In order to define this value, models for cell firing thresholds have been developed and computer simulations have been built to help validate these models.
The basic neuron firing model developed by Hodgkin and Huxley has been reformulated to apply to the prosthetic application. In this case the external field acts like a voltage clamp on the cell membrane for a short time before the emitting of an action potential by the target neuron. During the voltage clamp time the ionic currents are swept away by the applied field and the cell membrane is not charged. Also during this time the voltage gated sodium channels begin to open more than they were during the homeostatic rest state. At the end of the prosthetic pulse the ionic currents resume their normal effect in charging the cell membrane . Sometimes this will cause an action potential and sometimes it will not, depending on the applied field strength and duration. A unique bi-state feedback model is derived which makes clear the exact condition required for action potential generation as a function of ganglion cell type dependency and gate porosity at the membrane patch in question. This potentially illustrates the cell type dependency and the cell surface variability of response. Computer simulations are run to help verify this model under various conditions.
At this time the model has been completed to the point of showing the prosthetic condition as well as its end points and the consequent firing or not firing of action potentials. Particular interesting results are the specific average open state of the sodium gates during rest as well as the more open state at the end of the prosthetic pulse. It appears that the required state at the end of the prosthetic pulse is quite sharply defined in terms of fairly well understood physical constants. It also appears that the required open state of the gates to cause an action potential is quite small.
The cell firing model has been shown to be an excellent tool for exactly quantifying the required electric field energy from a prosthetic device to cause target cells of various types to emit action potentials.
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