Optimal stimulus current waveshape for a hodgkin-huxley model neuron

Traditionally, rectangular Lilly-type current pulses have been employed to electrically stimulate a neuron. In this paper, we utilize a least squares optimisation approach to assess the optimality of rectangular pulses in the context of electrical current stimulation. To this end, an appropriate cost function to minimise the total charge delivered to a neuron while keeping the waveshape sufficiently smooth, is developed and applied to a Hodgkin-Huxley ionic model of the neural action potential. Cubic spline parameters were utilized to find the optimal stimulation profile for a fixed peak current. Simulation results demonstrate that the optimal stimulation profile for a specified single neuron is a non-rectangular pulse whose shape depends upon the maximum allowable current as well as the stimulus duration.