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Energy-Optimal Electrical-Stimulation Pulses Shaped by the Least-Action Principle

Nedialko I. Krouchev, Simon M. Danner, Alain Vinet, Frank Rattay and Mohamad Sawan

Article (2014)

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Cite this document: Krouchev, N. I., Danner, S. M., Vinet, A., Rattay, F. & Sawan, M. (2014). Energy-Optimal Electrical-Stimulation Pulses Shaped by the Least-Action Principle. PLOS One, 9(3). doi:10.1371/journal.pone.0090480
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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.

Uncontrolled Keywords

Algorithms; Animals; Axons; Biomedical Engineering; Computer Simulation; Electric Stimulation; Equipment Design; Humans; Mathematics; Models, Theoretical; Myelin Sheath; Peripheral Nervous System; Temperature

Open Access document in PolyPublie
Subjects: 2500 Génie électrique et électronique > 2500 Génie électrique et électronique
Department: Département de génie électrique
Research Center: Autre
Funders: Fonds de recherche du Quebec - Nature et technologies and the Natural Sciences, Engineering Research Council of Canada, Vienna Science and Technology Fund
Grant number: LS11-057
Date Deposited: 22 Nov 2018 15:36
Last Modified: 13 Jan 2022 11:22
PolyPublie URL: https://publications.polymtl.ca/3463/
Document issued by the official publisher
Journal Title: PLOS One (vol. 9, no. 3)
Publisher: PLOS
Official URL: https://doi.org/10.1371/journal.pone.0090480


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