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Energy-optimal electrical-stimulation pulses shaped by the Least-Action Principle
Journal article   Open access   Peer reviewed

Energy-optimal electrical-stimulation pulses shaped by the Least-Action Principle

Nedialko I Krouchev, Simon M Danner, Alain Vinet, Frank Rattay and Mohamad Sawan
PloS one, v 9(3), pp e90480-e90480
2014
DOI: https://doi.org/10.1371/journal.pone.0090480
PMID: 24625822
url
https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0090480&type=printableView
Published, Version of Record (VoR) Open
url
https://doi.org/10.1371/journal.pone.0090480View
Published, Version of Record (VoR) Open

Abstract

Algorithms Animals Axons - physiology Biomedical Engineering - methods Computer Simulation Electric Stimulation Equipment Design Humans Mathematics Models, Theoretical Myelin Sheath - chemistry Peripheral Nervous System - physiology Temperature
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.

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Neurosciences
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