Development of a computer algorithm for feedback controlled electrical nerve fiber stimulation

The purpose of this research is to develop an algorithm for a feedback controlled local electrical nerve fiber stimulation system which has the purpose to stop the repetitive firing in a particular region of the nervous system. The electrophysiological behavior of the neurons (under electrical currents) is modeled by Hodgkin-Huxley (HH) type nonlinear nerve fiber dynamics. The repetitive firing of in the modeled fiber is due to the deviations in the channel parameters, which is also called as bifurcation in the nonlinear systems theory. A washout filter is augmented to the HH dynamics and then the output of the filter is fed to the external current generator through a linear gain. This gain is computed by linear projective control theory. That is a linear output feedback control technique where the closed loop spectrum of the full state feedback closed loop is partially maintained. By obtaining a spectrum of eigenvalues with completely negative real parts the nerve fibers can be relaxed to the equilibrium point with or without a damped oscillation. The MATLAB script applying the theory of this work is provided at the end of this paper. A MATLAB-Simulink computer simulation is performed in order to verify the algorithm.