Reconstructing parameters of the FitzHugh-Nagumo system from boundary potential measurements

Yuan He; David E. Keyes

doi:10.1007/s10827-007-0035-9

Reconstructing parameters of the FitzHugh-Nagumo system from boundary potential measurements

Yuan He^*, David E. Keyes

^*Corresponding author for this work

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

21 Scopus citations

Abstract

We consider distributed parameter identification problems for the FitzHugh-Nagumo model of electrocardiology. The model describes the evolution of electrical potentials in heart tissues. The mathematical problem is to reconstruct physical parameters of the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton-Krylov type that combines Newton's method for numerical optimization with Krylov subspace solvers for the resulting Karush-Kuhn-Tucker system. We show by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We discuss the effects of various model parameters on the quality of reconstructions.

Original language	English (US)
Pages (from-to)	251-264
Number of pages	14
Journal	Journal of Computational Neuroscience
Volume	23
Issue number	2
DOIs	https://doi.org/10.1007/s10827-007-0035-9
State	Published - Oct 2007
Externally published	Yes

Bibliographical note

Funding Information:
Fig. 12 Reconstructions with varying excitability contrast; (a)the new objective α is given by α↼x↽ = 0.6 ↼x ∈ D1↽↪ 0.4 ↼x ∈ D2↽↪ 0.1 (otherwise); (b) the new objective α is given by α↼x↽ = 0.05 ↼x ∈ D1↽↪ 0.1 ↼x ∈ D2↽↪ 0.2 (otherwise) Acknowledgements The authors would like to thank Professor George Biros of the University of Pennsylvania for stimulating discussions. Our algorithm is implemented using PETSc citePETSc-web. The simulations were performed on cluster System X at the Virginia Polytechnic Institute and State University. We are very grateful for the technical support of Professor Calvin J. Ribbens in using System X. This work was supported in p art by the National Science Foundation under NSF CCF-03-52334 and by Columbia University under an AQF grant for cluster computing.

Keywords

Electrocardiology
FitzHugh-Nagumo model
Inverse problems
KKTsystem
Newton-Krylov method
PDE-constrained optimization
Parameter identification

ASJC Scopus subject areas

Sensory Systems
Cognitive Neuroscience
Cellular and Molecular Neuroscience

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10.1007/s10827-007-0035-9

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title = "Reconstructing parameters of the FitzHugh-Nagumo system from boundary potential measurements",

abstract = "We consider distributed parameter identification problems for the FitzHugh-Nagumo model of electrocardiology. The model describes the evolution of electrical potentials in heart tissues. The mathematical problem is to reconstruct physical parameters of the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton-Krylov type that combines Newton's method for numerical optimization with Krylov subspace solvers for the resulting Karush-Kuhn-Tucker system. We show by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We discuss the effects of various model parameters on the quality of reconstructions.",

keywords = "Electrocardiology, FitzHugh-Nagumo model, Inverse problems, KKTsystem, Newton-Krylov method, PDE-constrained optimization, Parameter identification",

author = "Yuan He and Keyes, {David E.}",

note = "Funding Information: Fig. 12 Reconstructions with varying excitability contrast; (a)the new objective α is given by α↼x↽ = 0.6 ↼x ∈ D1↽↪ 0.4 ↼x ∈ D2↽↪ 0.1 (otherwise); (b) the new objective α is given by α↼x↽ = 0.05 ↼x ∈ D1↽↪ 0.1 ↼x ∈ D2↽↪ 0.2 (otherwise) Acknowledgements The authors would like to thank Professor George Biros of the University of Pennsylvania for stimulating discussions. Our algorithm is implemented using PETSc citePETSc-web. The simulations were performed on cluster System X at the Virginia Polytechnic Institute and State University. We are very grateful for the technical support of Professor Calvin J. Ribbens in using System X. This work was supported in p art by the National Science Foundation under NSF CCF-03-52334 and by Columbia University under an AQF grant for cluster computing.",

year = "2007",

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doi = "10.1007/s10827-007-0035-9",

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volume = "23",

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AU - Keyes, David E.

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PY - 2007/10

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N2 - We consider distributed parameter identification problems for the FitzHugh-Nagumo model of electrocardiology. The model describes the evolution of electrical potentials in heart tissues. The mathematical problem is to reconstruct physical parameters of the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton-Krylov type that combines Newton's method for numerical optimization with Krylov subspace solvers for the resulting Karush-Kuhn-Tucker system. We show by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We discuss the effects of various model parameters on the quality of reconstructions.

AB - We consider distributed parameter identification problems for the FitzHugh-Nagumo model of electrocardiology. The model describes the evolution of electrical potentials in heart tissues. The mathematical problem is to reconstruct physical parameters of the system through partial knowledge of its solutions on the boundary of the domain. We present a parallel algorithm of Newton-Krylov type that combines Newton's method for numerical optimization with Krylov subspace solvers for the resulting Karush-Kuhn-Tucker system. We show by numerical simulations that parameter reconstruction can be performed from measurements taken on the boundary of the domain only. We discuss the effects of various model parameters on the quality of reconstructions.

KW - Electrocardiology

KW - FitzHugh-Nagumo model

KW - Inverse problems

KW - KKTsystem

KW - Newton-Krylov method

KW - PDE-constrained optimization

KW - Parameter identification

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EP - 264

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JF - Journal of Computational Neuroscience

IS - 2

ER -

Reconstructing parameters of the FitzHugh-Nagumo system from boundary potential measurements

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