Abstract
We study the electrical field in the human body, generated by the ventricular muscle, by means of numerical simulations. The involved mathematical model consists of two partial differential equations (PDEs) that are also coupled with a system of ordinary differential equations (ODEs). Following the strategy of operator-splitting, we have devised an efficient numerical algorithm that carries out a simulation step-wise in time. At every time level, the ODE system is solved before a parabolic PDE, and then an elliptic PDE. The main focus of this paper is on the transformation of an existing sequential simulator into a parallel simulator that runs on multiprocessor platforms. Two important numerical ingredients used in the resulting parallel simulator are overlapping domain decomposition and multigrid, which together ensure good numerical efficiency. We also explain how object-oriented programming techniques enable the software parallelization in a simple and structured manner. In addition, we study the performance of the parallel simulator on different multiprocessor platforms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. M. Bruaset. A Survey of Preconditioned Iterative Methods. Addison-Wesley Pitman, 1995.
A. M. Bruaset, X. Cai, H. P. Langtangen, and A. Tveito. Numerical solution of PDEs on parallel computers utilizing sequential simulators. In Y. Ishikawa et al., editor, Scientific Computing in Object-Oriented Parallel Environment, Springer-Verlag Lecture Notes in Computer Science 1343, pages 161–168. Springer-Verlag, 1997.
X. Cai. Domain decomposition in high-level parallelization of pde codes. In C-H. Lai et al., editor, Domain Decompostion Methods in Science and Engineering, pages 382–389. Domain Decomposition Press, 1999.
X. Cai and K. Samuelsson. Parallel multilevel methods with adaptivity on unstructured grids. Computing and Visualization in Science, 3:133–146, 2000.
T. F. Chan and T. P. Mathew. Domain decomposition algorithms. In Acta Numerica 1994, pages 61–143. Cambridge University Press, 1994.
Diffpack World Wide Web home page. See URL http://www.nobjects.com/Diffpack .
D. B. Geselowitz and W. T. Miller. A bidomain model for anisotropic cardiac muscle. Annals of Biomedical Engineering, 11:191–206, 1983.
W. Hackbusch. Multigrid Methods and Applications. Springer, Berlin, 1985.
H. P. Langtangen. Computational Partial Differential Equations-Numerical Methods and Diffpack Programming. Lecture Notes in Computational Science and Engineering. Springer-Verlag, 1999.
H. P. Langtangen and X. Cai. A software framework for easy parallelization of pde solvers. In Proceedings of the Parallel Computational Fluid Dynamics 2000 Conference, 2001.
G. T. Lines. Simulating the electrical activity of the heart: a bidomain model of the ventricles embedded in a torso. PhD thesis, Department of Informatics, Faculty of Mathematics and Natural Sciences, University of Oslo, 1999.
G. T. Lines, P. Grøttum, and A. Tveito. Modeling the electrical activity of the heart, a bidomain model of the ventricles embedded in a torso. Preprint 2000 4, Department of Informatics, University of Oslo, 2000.
C. H. Luo and Y. Rudy. A dynamic model of the cardiac ventricular action potenial. Circulation Research, 74:1071–1096, 1994.
B. F. Smith, P. E. Bjørstad, and W. Gropp. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996.
J. Sundnes, G. T. Lines, and A. Tveito. Efficient solution of ordinary differential equations modeling electrical activity in cardiac cells. Mathematical Biosciences, 172:55–72, 2001.
L. Tung. A Bi-domain model for describing ischemic myocardial D-C potentials. PhD thesis, MIT, Cambridge, MA, 1978.
J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Review, 34(4):581–613, December 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cai, X., Lines, G.T. (2002). Enabling Numerical and Software Technologies for Studying the Electrical Activity in Human Heart. In: Fagerholm, J., Haataja, J., Järvinen, J., Lyly, M., Råback, P., Savolainen, V. (eds) Applied Parallel Computing. PARA 2002. Lecture Notes in Computer Science, vol 2367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48051-X_1
Download citation
DOI: https://doi.org/10.1007/3-540-48051-X_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43786-4
Online ISBN: 978-3-540-48051-8
eBook Packages: Springer Book Archive