The aim of this paper is to show how the Hodgkin-Huxley model of the neuron's membrane potential can be extended to a stochastic one. This extension can be done either by adding fluctuations to the equations of the model or by using Markov kinetic schemes' formalism. We are presenting a new extension of the model. This modification simplifies computational complexity of the neuron model especially when considering a hardware implementation. The hardware implementation of the extended model as a system on a chip using a field-programmable gate array (FPGA) is demonstrated in this paper. The results confirm the reliability of the extended model presented here.

Abstract-The tool was created to support the auxiliary clinical observation of the eyeballs movements in cases of different states of consciousness. It enables performing objective observation of the patient reaction to a given external light stimuli. The tool analyzes the coordination of the eyeballs movement with the position of the light stimuli. Images are obtained by camera equipped with infrared filters blocking all visible light with the cutoff light length 715nm.