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 journalArticlepeer-review

21 Scopus citations


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 languageEnglish (US)
Pages (from-to)251-264
Number of pages14
JournalJournal of Computational Neuroscience
Issue number2
StatePublished - Oct 2007
Externally publishedYes

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.


  • 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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