Energy-Optimal Electrical-Stimulation Pulses Shaped by the Least-Action Principle
| Autor: | Alain Vinet, Mohamad Sawan, Simon M. Danner, Nedialko I. Krouchev, Frank Rattay |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Circuit Models
Medical Physics Biomedical Engineering Biophysics lcsh:Medicine Bioengineering Bioinformatics Biophysics Simulations Ion Channels Principle of least action Engineering Control theory Waveform Control Theory lcsh:Science Biology Mathematics Computational Neuroscience Multidisciplinary Applied Mathematics Physics lcsh:R Computational Biology Optimal control Action (physics) Pulse (physics) Quadrature (mathematics) Single Neuron Function Nonlinear Dynamics Ordinary differential equation Cellular Neuroscience Computer Science lcsh:Q Energy (signal processing) Algorithms Research Article Neuroscience Computer Modeling |
| Zdroj: | PLoS ONE PLoS ONE, Vol 9, Iss 3, p e90480 (2014) |
| ISSN: | 1932-6203 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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