title: Energy-optimal electrical-stimulation pulses shaped by the Least-Action Principle.
abstract: Electrical stimulation (ES) devices interact with excitable neural tissue toward eliciting action potentials (AP's) by specific current patterns. Low-energy ES prevents tissue damage and loss of specificity. Hence to identify optimal stimulation-current waveforms is a relevant problem, whose solution may have significant impact on the related medical (e.g. minimized side-effects) and engineering (e.g. maximized battery-life) efficiency. This has typically been addressed by simulation (of a given excitable-tissue model) and iterative numerical optimization with hard discontinuous constraints--e.g. AP's are all-or-none phenomena. Such approach is computationally expensive, while the solution is uncertain--e.g. may converge to local-only energy-minima and be model-specific. We exploit the Least-Action Principle (LAP). First, we derive in closed form the general template of the membrane-potential's temporal trajectory, which minimizes the ES energy integral over time and over any space-clamp ionic current model. From the given model we then obtain the specific energy-efficient current waveform, which is demonstrated to be globally optimal. The solution is model-independent by construction. We illustrate the approach by a broad set of example situations with some of the most popular ionic current models from the literature. The proposed approach may result in the significant improvement of solution efficiency: cumbersome and uncertain iteration is replaced by a single quadrature of a system of ordinary differential equations. The approach is further validated by enabling a general comparison to the conventional simulation and optimization results from the literature, including one of our own, based on finite-horizon optimal control. Applying the LAP also resulted in a number of general ES optimality principles. One such succinct observation is that ES with long pulse durations is much more sensitive to the pulse's shape whereas a rectangular pulse is most frequently optimal for short pulse durations.
authors.affiliation: Polystim Neurotechnologies, Ecole Polytechnique, Montreal, Quebec, Canada.
authors.forename: Nedialko I
authors.initials: NI
authors.lastname: Krouchev
authors.affiliation: Institute for Analysis and Scientific Computing, University of Technology, Vienna, Austria; Center for Medical Physics and Biomedical Engineering, Medical University, Vienna, Austria.
authors.forename: Simon M
authors.initials: SM
authors.lastname: Danner
authors.affiliation: Institut de Genie Biomedical, Universite de Montreal, Montreal, Quebec, Canada.
authors.forename: Alain
authors.initials: A
authors.lastname: Vinet
authors.affiliation: Institute for Analysis and Scientific Computing, University of Technology, Vienna, Austria.
authors.forename: Frank
authors.initials: F
authors.lastname: Rattay
authors.affiliation: Polystim Neurotechnologies, Ecole Polytechnique, Montreal, Quebec, Canada.
authors.forename: Mohamad
authors.initials: M
authors.lastname: Sawan
mesh_terms: D000465:Algorithms; D000818:Animals; D001369:Axons / Q000502:physiology; D001698:Biomedical Engineering / Q000379:methods*; D003198:Computer Simulation; D004558:Electric Stimulation; D004867:Equipment Design; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical; D009186:Myelin Sheath / Q000737:chemistry; D017933:Peripheral Nervous System / Q000502:physiology; D013696:Temperature