Introduction to Computational Cardiology pp 111-123 | Cite as
Computer Implementation of Mathematical Models
Chapter
First Online:
Abstract
Computer implementation of an AP mathematical model requires: A well-defined statement of the problem for computer simulation Selecting a computer architecture – a sequential or parallel Choosing the most effective numerical algorithms for the problem under investigation Investigating the possibility of utilizing standard (MATLAB, Mathematica, etc.) and specialized software (OXSOFT, Madonna, Visualization programs) packages Providing programming tools for measuring the conduction velocity of the wavefront and representing the cell’s state in time for chosen grid points in the spatial domain.
Keywords
Computer Implementation Local Truncation Error Adaptive Time Step Integration Step Size Explicit Euler Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- 1.Hamming, R.W., Numerical Methods for Scientists and Engineers. 1962, Columbus: McGraw-Hill.MATHGoogle Scholar
- 2.Bekey, G.A. and W.J. Karplus, Hybrid Computation. 1968, New York: Wiley Publishing.MATHGoogle Scholar
- 3.Aiken, R.C., ed. Stiff Computation. 1985, Oxford University Press: Oxford.MATHGoogle Scholar
- 4.Ashour, S.S. and O.T. Hanna, A new very simple explicit method for the integration of mildly stiff ordinary differential equations. Comp Chem Eng, 1990. 14(267–272).CrossRefGoogle Scholar
- 5.Moore, J.W. and F. Ramon, On numerical integration of the Hodgkin and Huxley equations for a membrane action potential. J Theor Biol, 1974. 45: 249–273.CrossRefGoogle Scholar
- 6.Rush, S. and H. Larsen, A practical algorithm for solving dynamic membrane equations. IEEE Trans Biomed Eng, 1978. 25: 389–392.CrossRefGoogle Scholar
- 7.Victorri, B., A. Vinet, F.A. Roberge, and J.P. Drouhard, Numerical integration in the reconstruction of cardiac action potentials using Hodgkin-Huxley-type models. Comput Biomed Res, 1985. 18: 10–23.CrossRefGoogle Scholar
- 8.Luo, C.H. and Y. Rudy, A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res, 1994. 74: 1071–1096.Google Scholar
- 9.Luo, C.H. and Y. Rudy, A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation. Circ Res, 1994. 74: 1097–1113.Google Scholar
- 10.Zeng, J., K.R. Laurita, D.S. Rosenbaum, and Y. Rudy, Two components of the delayed rectifier K+ current in ventricular myocytes of the guinea pig type. Theoretical formulation and their role in repolarization. Circ Res, 1995. 77: 140–152.Google Scholar
- 11.Strang, G., On the construction and comparison of difference schemes. SIAM J Numer Anal, 1968. 5: 506–517.MATHCrossRefMathSciNetGoogle Scholar
- 12.Winfree, A.T., Heart muscle as a reaction-diffusion medium: the roles of electrical potential diffusion, activation front curvature, and anisotropy. Int J Bif Chaos, 1997. 7: 487–526.MATHCrossRefMathSciNetGoogle Scholar
Copyright information
© Springer Science+Business Media, LLC 2010