Energy-optimal electrical excitation of nerve fibers.

We derive, based on an analytical nerve membrane model and optimal control theory of dynamical systems, an energy-optimal stimulation current waveform for electrical excitation of nerve fibers. Optimal stimulation waveforms for nonleaky and leaky membranes are calculated. The case with a leaky membrane is a realistic case. Finally, we compare the waveforms and energies necessary for excitation of a leaky membrane in the case where the stimulation waveform is a square-wave current pulse, and in the case of energy-optimal stimulation. The optimal stimulation waveform is an exponentially rising waveform and necessitates considerably less energy to excite the nerve than a square-wave pulse (especially true for larger pulse durations). The described theoretical results can lead to drastically increased battery lifetime and/or decreased energy transmission requirements for implanted biomedical systems.