Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 468189, 14 pages
http://dx.doi.org/10.1155/2012/468189
Research Article

The Effects of Control Domain Position on Optimal Control of Cardiac Arrhythmia

Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Johor Bahru, Malaysia

Received 2 October 2012; Accepted 4 November 2012

Academic Editor: Jinyun Yuan

Copyright © 2012 Kin Wei Ng and Ahmad Rohanin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Amann, R. Tratnig, and K. Unterkofler, “A new ventricular fibrillation detection algorithm for automated external defibrillators,” Computers in Cardiology, vol. 32, pp. 559–562, 2005. View at Publisher · View at Google Scholar · View at Scopus
  2. D. J. Dosdall, V. G. Fast, and R. E. Ideker, “Mechanisms of defibrillation,” Annual Review of Biomedical Engineering, vol. 12, pp. 233–258, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. R. C. Klein, M. H. Raitt, B. L. Wilkoff et al., “Analysis of implantable cardioverter defibrillator therapy in the antiarrhythmics versus implantable defibrillators (AVID) trial,” Journal of Cardiovascular Electrophysiology, vol. 14, no. 9, pp. 940–948, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Nagaiah, K. Kunisch, and G. Plank, “Numerical solution for optimal control of the reaction-diffusion equations in cardiac electrophysiology,” Computational Optimization and Applications, vol. 49, no. 1, pp. 149–178, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. S. M. Shuaiby, M. A. Hassan, and M. El-Melegy, “Modeling and simulation of the action potential in human cardiac tissues using finite element method,” Journal of Communications and Computer Engineering, vol. 2, no. 3, pp. 21–27, 2012. View at Google Scholar
  6. Y. Belhamadia, A. Fortin, and Y. Bourgault, “Towards accurate numerical method for monodomain models using a realistic heart geometry,” Mathematical Biosciences, vol. 220, no. 2, pp. 89–101, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. R. H. Clayton and A. V. Panfilov, “A guide to modelling cardiac electrical activity in anatomically detailed ventricles,” Progress in Biophysics and Molecular Biology, vol. 96, no. 1–3, pp. 19–43, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. Y. H. Dai and Y. Yuan, “A nonlinear conjugate gradient method with a strong global convergence property,” SIAM Journal on Optimization, vol. 10, no. 1, pp. 177–182, 1999. View at Google Scholar · View at Scopus
  9. W. W. Hager and H. Zhang, “A new conjugate gradient method with guaranteed descent and an efficient line search,” SIAM Journal on Optimization, vol. 16, no. 1, pp. 170–192, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. E. Polak and G. Ribière, “Note sur la convergence de méthodes de directions conjuguées,” Revue Française d'Informatique et de Recherche Opérationnelle, vol. 16, pp. 35–43, 1969. View at Google Scholar · View at Zentralblatt MATH
  11. B. T. Polyak, “The conjugate gradient method in extremal problems,” USSR Computational Mathematics and Mathematical Physics, vol. 9, no. 4, pp. 94–112, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. C. Nagaiah and K. Kunisch, “Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology,” Applied Numerical Mathematics, vol. 61, no. 1, pp. 53–65, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  13. K. W. Ng and A. Rohanin, “Numerical solution for PDE-constrained optimization problem in cardiac electrophysiology,” International Journal of Computer Applications, vol. 44, no. 12, pp. 11–15, 2012. View at Google Scholar
  14. K. W. Ng and A. Rohanin, “Modified Fletcher-Reeves and Dai-Yuan conjugate gradient methods for solving optimal control problem of monodomain model,” Applied Mathematics, vol. 3, no. 8, pp. 864–872, 2012. View at Publisher · View at Google Scholar
  15. K. W. Ng and A. Rohanin, “The effects of control domain size on optimal control problem of monodomain model,” International Journal of Computer Applications, vol. 47, no. 10, pp. 6–11, 2012. View at Google Scholar
  16. J. M. Rogers and A. D. McCulloch, “A collocation-Galerkin finite element model of cardiac action potential propagation,” IEEE Transactions on Biomedical Engineering, vol. 41, no. 8, pp. 743–757, 1994. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Kunisch and M. Wagner, “Optimal control of the bidomain system (I): the monodomain approximation with the Rogers-McCulloch model,” Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1525–1550, 2012. View at Publisher · View at Google Scholar
  18. Z. Qu and A. Garfinkel, “An advanced algorithm for solving partial differential equation in cardiac conduction,” IEEE Transactions on Biomedical Engineering, vol. 46, no. 9, pp. 1166–1168, 1999. View at Publisher · View at Google Scholar · View at Scopus
  19. L. Zhang, “Two modified Dai-Yuan nonlinear conjugate gradient methods,” Numerical Algorithms, vol. 50, no. 1, pp. 1–16, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. P. C. Franzone, P. Deuflhard, B. Erdmann, J. Lang, and L. F. Pavarino, “Adaptivity in space and time for reaction-diffusion systems in electrocardiology,” SIAM Journal on Scientific Computing, vol. 28, no. 3, pp. 942–962, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus