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.
Jezernik
Saso
S
wiss Federal Institute of Technology (ETH Zürich), Automatic Control Laboratory, Physikstrasse 3, 8092 Zürich, Switzerland. jezernik@control.ee.ethz.ch
Morari
Manfred
M
D000200:Action Potentials / Q000502:physiology*; D002462:Cell Membrane / Q000502:physiology; D003198:Computer Simulation; D004307:Dose-Response Relationship, Radiation; D004558:Electric Stimulation / Q000379:methods*; D004574:Electromagnetic Fields; D004735:Energy Transfer / Q000502:physiology*; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009412:Nerve Fibers / Q000502:physiology*; D011829:Radiation Dosage; D009435:Synaptic Transmission / Q000502:physiology*