Time optimal control for a reaction diffusion system arising in cardiac electrophysiology - A monolithic approach

Karl Kunisch; Konstantin Pieper; Armin Rund

doi:10.1051/m2an/2015048

Time optimal control for a reaction diffusion system arising in cardiac electrophysiology - A monolithic approach

Karl Kunisch, Konstantin Pieper, Armin Rund

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

Motivated by the termination of undesirable arrhythmia, a time optimal control formulation for the monodomain equations is proposed. It is shown that, under certain conditions, the optimal solutions of this problem steer the system into an appropriate stable neighborhood of the resting state. Towards this goal, some new regularity results and asymptotic properties for the monodomain equations with the Rogers-McCulloch ionic model are obtained. For the numerical realization, a monolithic approach, which simultaneously optimizes for the optimal times and optimal controls, is presented and analyzed. Its practical realization is based on a semismooth Newton method. Numerical examples and comparisons are included.

Original language	English
Pages (from-to)	381-414
Number of pages	34
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Volume	50
Issue number	2
DOIs	https://doi.org/10.1051/m2an/2015048
State	Published - Mar 1 2016
Externally published	Yes

Funding

The third author gratefully acknowledges the Austrian Science Fund (FWF) for financial support under SFB F32, “Mathematical Optimization and Applications in Biomedical Sciences”. Kunisch Karl 1 2 Pieper Konstantin 3 Rund Armin 1 The first and second author gratefully acknowledge support from the International Research Training Group IGDK 1754, funded by the German Science Foundation (DFG) and the Austrian Science Fund (FWF).

Funders	Funder number
German Science Foundation
Deutsche Forschungsgemeinschaft
Austrian Science Fund	SFB F32

Keywords

Asymptotic behavior
Monodomain equations
Reaction diffusion system
Semismooth Newton method
Time optimal control

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title = "Time optimal control for a reaction diffusion system arising in cardiac electrophysiology - A monolithic approach",

abstract = "Motivated by the termination of undesirable arrhythmia, a time optimal control formulation for the monodomain equations is proposed. It is shown that, under certain conditions, the optimal solutions of this problem steer the system into an appropriate stable neighborhood of the resting state. Towards this goal, some new regularity results and asymptotic properties for the monodomain equations with the Rogers-McCulloch ionic model are obtained. For the numerical realization, a monolithic approach, which simultaneously optimizes for the optimal times and optimal controls, is presented and analyzed. Its practical realization is based on a semismooth Newton method. Numerical examples and comparisons are included.",

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AU - Pieper, Konstantin

AU - Rund, Armin

N1 - Publisher Copyright: © EDP Sciences, SMAI 2016.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - Motivated by the termination of undesirable arrhythmia, a time optimal control formulation for the monodomain equations is proposed. It is shown that, under certain conditions, the optimal solutions of this problem steer the system into an appropriate stable neighborhood of the resting state. Towards this goal, some new regularity results and asymptotic properties for the monodomain equations with the Rogers-McCulloch ionic model are obtained. For the numerical realization, a monolithic approach, which simultaneously optimizes for the optimal times and optimal controls, is presented and analyzed. Its practical realization is based on a semismooth Newton method. Numerical examples and comparisons are included.

AB - Motivated by the termination of undesirable arrhythmia, a time optimal control formulation for the monodomain equations is proposed. It is shown that, under certain conditions, the optimal solutions of this problem steer the system into an appropriate stable neighborhood of the resting state. Towards this goal, some new regularity results and asymptotic properties for the monodomain equations with the Rogers-McCulloch ionic model are obtained. For the numerical realization, a monolithic approach, which simultaneously optimizes for the optimal times and optimal controls, is presented and analyzed. Its practical realization is based on a semismooth Newton method. Numerical examples and comparisons are included.

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KW - Monodomain equations

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KW - Semismooth Newton method

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Time optimal control for a reaction diffusion system arising in cardiac electrophysiology - A monolithic approach

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