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W. Liu, Z. Yang, M. Sivaprakasam; Modeling and Analysis of Virtual Electrodes in Retinal Prosthesis . Invest. Ophthalmol. Vis. Sci. 2006;47(13):3188.
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We propose a virtual electrode scheme to increase the number of pixels on the retina without increasing the number of the physical electrodes. The feasibility of virtual electrodes is investigated and proven by mathematical model involving the stimulation and geometrical parameters of the electrodes.
E field profile induced by electrodes is generated by a double layer vitreous–retinal model. Varying the timing and magnitude of the stimulation pulse, E field’s distribution in both temporal and spatial domains are controllable. The induced cross membrane voltage distribution is obtained by combining this E field profile with a nonlinear compartmental neuron model. Generally in a conventional approach, the cross membrane voltage is applied to the standard HH model and the action of a neuron depends on a threshold voltage. However, due to channel’s statistical nature, this approach is not accurate. In our analysis, in order to produce a reliable simulation, the cross membrane voltage distribution is applied to a kinetic sodium channel model which allows analyzing the behavior of a single sodium channel and the activation of an action potential. The channel’s kinetic theory shows that the possibility of opening of the sodium channel follows Boltzmann Equation. To make sure that the virtual pixels on retina can be selectively simulated without activating neurons directly under electrodes, we have developed strict requirements on the width and timing of stimulation current pulse which has its theoretical basis in the electrostatic model of the voltage sensors (S4) in sodium channel. To make the virtual electrode function, geometric parameters must be carefully chosen too. Additional depressing pulse is used to reduce the crosstalk from nearby electrodes.
The derived model proves that in order to create virtual electrodes, the stimulation can not be arbitrary but has to meet certain conditions of stimulation parameters. The model also shows the feasibility of virtual electrodes with a ratio of 6:1. In other words, 200 physical electrodes can support 1200 pixels on the surface of the retina. The maximum current amplitude required to support the virtual electrodes is estimated around hundreds of uA at most. Crosstalk from nearby electrodes is controlled below –20dB.
A virtual electrode model to increase the number of stimulation pixels on the retina has been developed. According to the model, a six fold increase in the number of pixels is possible. The feasibility has been verified theoretically. A validation of the model based on an in–vitro setup is on going.
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