CFP last date
22 April 2024
Call for Paper
May Edition
IJCA solicits high quality original research papers for the upcoming May edition of the journal. The last date of research paper submission is 22 April 2024

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

The Effects of Control Domain Size on Optimal Control Problem of Monodomain Model

by Kin Wei Ng, Ahmad Rohanin
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 47 - Number 10
Year of Publication: 2012
Authors: Kin Wei Ng, Ahmad Rohanin
10.5120/7222-0046

Kin Wei Ng, Ahmad Rohanin . The Effects of Control Domain Size on Optimal Control Problem of Monodomain Model. International Journal of Computer Applications. 47, 10 ( June 2012), 6-11. DOI=10.5120/7222-0046

@article{ 10.5120/7222-0046,
author = { Kin Wei Ng, Ahmad Rohanin },
title = { The Effects of Control Domain Size on Optimal Control Problem of Monodomain Model },
journal = { International Journal of Computer Applications },
issue_date = { June 2012 },
volume = { 47 },
number = { 10 },
month = { June },
year = { 2012 },
issn = { 0975-8887 },
pages = { 6-11 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume47/number10/7222-0046/ },
doi = { 10.5120/7222-0046 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:41:29.851535+05:30
%A Kin Wei Ng
%A Ahmad Rohanin
%T The Effects of Control Domain Size on Optimal Control Problem of Monodomain Model
%J International Journal of Computer Applications
%@ 0975-8887
%V 47
%N 10
%P 6-11
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, we study the effects of the size of the control domain on the optimal control problem of monodomain model. The optimal control problem of monodomain model is a nonlinear optimization problem that is constrained by the monodomain model that represents the electrical behavior of the cardiac tissue. Two test cases with different sizes of control domain are considered, namely Test Case 1 and Test Case 2. Numerical results show that the excitation wavefront is successfully dampened out by the optimal applied current in both test cases. However, Test Case 2 (with smaller size of the control domain) requires more iteration as well as longer time to dampen the excitation wavefront. Our numerical results also indicate that higher current is required in the dampening process when the size of the control domain changed to a smaller one.

References
  1. Nagaiah, C. , Kunisch, K. , and Plank, G. 2011. Numerical solution for optimal control of the reaction-diffusion equations in cardiac electrophysiology. Comput. Optim. Appl. 49, 149-178.
  2. Nagaiah, C. , Kunisch, K. , and Plank, G. 2009. Second order numerical solution for optimal control of monodomain model in cardiac electrophysiology. In Proceedings of ALGORITMY.
  3. Nagaiah, C. and Kunisch, K. 2011. Higher order optimization and adaptive numerical solution for optimal control of monodomain equations in cardiac electrophysiology. Appl. Numer. Math. 61, 53-65.
  4. Kunisch, K. and Wagner, M. 2011. Optimal control of the bidomain system (I): The monodomain approximation with the Rogers-McCulloch model. Nonlinear Anal. : Real World Appl. 13 (4), 1525-1550.
  5. Ng, K. W. and Rohanin, A. 2012. Numerical solution for PDE-constrained optimization problem in cardiac electrophysiology. Int. J. Comput. Appl. 44 (12), 11-15.
  6. Belhamadia, Y. , Fortin, A. , and Bourgault, Y. 2009. Towards accurate numerical method for monodomain models using a realistic heart geometry. Math. Biosci. 220 (2), 89-101.
  7. Shuaiby, S. M. , Hassan, M. A. , and El-Melegy, M. 2012. Modeling and simulation of the action potential in human cardiac tissues using finite element method. J. Commun. Comput. Eng. 2 (3), 21-27.
  8. Polak, E. and Ribière, G. 1969. Note sur la convergence de méthodes de directions conjuguées. Rev. Francaise Informat. Recherche Opérationnelle. 16, 35-43.
  9. Polyak, B. T. 1969. The conjugate gradient method in extreme problems. USSR Comp. Math. Math. Phys. 9, 94-112.
  10. Dai, Y. H. and Yuan, Y. 1999. A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim. 10 (1), 177-182.
  11. Hager, W. W. and Zhang, H. 2005. A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16, 170-192.
  12. Zhang, L. 2009. Two modified Dai-Yuan nonlinear conjugate gradient methods. Numer. Algor. 50, 1-16.
  13. Li, D. H. and Fukushima, M. 2001. A modified BFGS method and its global convergence in nonconvex minimization. J. Comput. Appl. Math. 129, 15-35.
  14. Rogers, J. M. and McCulloch, A. D. 1994. A collocation-Galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 41, 743-757.
  15. Qu, Z. and Garfinkel, A. 1999. An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Trans. Biomed. Eng. 46 (9), 1166-1168.
  16. Franzone, P. C. , Deuflhard, P. , Ermann, B. , Lang, J. , and Pavarino, L. F. 2006. Adaptivity in space and time for reaction-diffusion systems in electrocardiology. SIAM J. Sci. Comput. 28 (3), 942-962.
Index Terms

Computer Science
Information Sciences

Keywords

Galerkin Finite Element Method Monodomain Model Optimal Control Cardiac Electrophysiology

Powered by PhDFocusTM