Abstract
Cardiac Modeling may at present be considered as an important component of basic research in Cardiology. Theoretical studies have progressively been developed in multiple directions, from mechanical models in order to simulate hemodynamics or myocardial mechanics to electrophysiological models. A large part of cardiac action potential modelizations developed till now (Noble, 1975) (Beeler and Reuter, 1977) (Van Capelle and Durrer, 1980) (Luo and Rudy, 1991) have been derived from the model based on differential equations described by Hodgkin and Huxley on the giant squid axon in 1952 (Hodgkin and Huxley, 1952) (Hodgkin and Huxley, 1990).
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References
Auger P., Bardou A., Coulombe A. and Degonde J. Computer simulation of different mechanisms of ventricular fibrillation. Proceedings of the 9th IEEE/EMBS International Conference 171–174, 1987.
Auger P., Bardou A., Coulombe A. and Degonde J. Computer simulation of different electrophysiological mechanisms of ventricular fibrillation. Comput. in cardiol. Vol. no. 87: 527–530, 1987.
Auger P., Coulombe A., Govaere M.-C., Chesnais J.-M., Von Euw D. and Bardou A. Computer simulation of mechanisms of ventricular fibrillation and defibrillation. Innov. Technol. Biol. Med. Vol. no. 10: 299–312, 1989.
Auger P., Bardou A., Coulombe A., Govaere M.-C., Rochette L., Schreiber M.-C., Von Euw D. and Chesnais J.-M. Computer simulation of ventricular fibrillation and of defibrillating electric shocks. Effects of antiarrhythmic drugs. Mathl. Comput. Modelling Vol. no. 14: 576–581, 1990.
Auger P., Coulombe A., Dumée P., Govaere M.-C., Chesnais J.-M. and Bardou A. Computer simulation of cardiac arrhythmias and of defibrillating electric shocks. Effects of antiarrhythmic drugs. in Non linear coherent structures in Physics and Biology. Lecture Notes in Physics Vol. no. 393, Remoissenet, M. and Peyrard, M. Eds. Heidelberg: Springer Verlag, 133–140, 1990.
Auger P., Cardinal R, Bril A., Rochette L. and Bardou A. Interpretation of cardiac mapping by means of computer simulations: Applications to calcium, lidocaïne and to brl 34915. Acta Biotheoretica Vol. no. 40: 161–168, 1992.
Bardou A., Auger P., Cardinal R., Dumée P., Birkui P., Von Euw D. and Govaere M.-C. Theoretical study by means of computer simulation of conditions in which extrasystoles can trigger ventricular fibrillation. validation by epicardial mappings. Journal of Biological Systems Vol. no. 1: 147–158, 1993.
Bardou A., Auger P., Achour S., Dumée P., Birkui P. and Govaere M.-C. Effect of myocardial infarction and myocardial ischemia on induction of cardiac reentries and ventricular fibrillation. Acta Biotheoretica Vol. no. 43: 363–372, 1995.
Bardou A., Auger P., Chassé J.-L. and Achour S. Effects of local ischemia and transient conduction blocks on the induction of cardiac reentries. International Journal of Bifurcation and Chaos Vol. no. 6: 1657–1664, 1996.
Beeler G. and Reuter R. Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. Vol. no. 268: 177–210, 1977.
Bigger T. and Sahar D. Clinical types of proarrhythmic response to antiarrhythmic drugs. Amer. J. Cardiol. Vol. no. 59: 2E - 9E, 1987.
Cardinal R., Vermeulen M., Shenasa F., Roberge P., Page P., Hélie F. and Savard P. Anisotropic conduction and functional dissociation of ischemic tissue during reentrant ventricular tachycardia in canine myocardial infarction. Circulation. Vol. no. 77: 1162–1176, 1988.
Chassé J.-L., Auger P., Bardou A. and Achour S. Some mechanisms of initiation of ventricular fibrillation: Transient blocks and ischemic zones. IEEE/Engin. Med. Biol., Soc. 17th Conf. Proceed.: 1755–1758, 1995.
Chiaso D., Michaels D. and Jalife J. Supernormal excitability as a mechanism of chaotic dynamics of activation in cardiac purkinje fiber. Circ. Res. Vol. no. 90: 525–545, 1990.
Hélie F., Cossette F., Vermeulen M. and Cardinal R. Differential effects of lignocaine and hypercalcemia on anisotropic conduction and reentry in the ischemically damaged canine ventricle. Cardiovascular research. Vol. no. 29: 359–372, 1995.
Hodgkin A. and Huxley A. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. Vol. no. 117: 500–544, 1952.
Hodgkin A. and Huxley A. A quantitative description of membrane current and its application to conduction and excitation in nerve. Bul.Math.Bio. Vol.no. 52: 25–71, 1990.
Horowitz L., Zipes D., Campbell R., Morganroth J., Podrid B., Rosen M. and Woosley R. Proarrhythmia, arrhythmogenesis or aggravation of arrhythmia-a status report. Amer. J. Cardiol. Vol. no. 59: 54E - 56E, 1987.
Luo C. and Rudy Y. A model of the ventricular action potential. depolarization, repolarization and their interaction. Circ. Res. Vol. no. 68: 1501–1526, 1991.
Moe G., Rheinboldt W. and Abildskov J. R. A computer model of atrial fibrillation. Am. Heart J. Vol. no. 67: 200–220, 1964.
Noble D. The initiation of the heart beat. Oxford University Press, 1975.
Pertsov A., Davidenko J., Salomonsz R., Baxter W. and Jalife J. Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. Circ. Res. Vol. no. 72: 63 1650, 1993.
Saxberg B. and Cohen R. Cellular automata models of cardiac conduction. in Theory of the heart., Glass L., Hunter P. and McCulloch A., Eds, Springer Verlag, New-York: 437–476, 1991.
Smith J. and Cohen R. Simple computer model predicts a wide range of ventricular dysrhyythmias. P.N.A.S. Vol. no. 81: 233–237, 1984.
Smith J., Ritzenberg R. and Cohen R. Percolation theory and cardiac conduction. Computers in Cardiology, Washington, DC: IEEE Computer Society Press: 201–204, 1984.
Solomon J. and Selvester R. Simulation of measured activation sequence in the human heart. Am. Heart J. Vol. no. 85: 518–523, 1973.
Szathmary V. and Osvald R. An intercative computer model of propagated activation with analytically defined geometry of ventricles. Computers and Biomed. Res. Vol. no. 27: 27–38, 1994.
The Cardiac Arrhythmia Suppresion Trial Investigators [CAST89]: Preliminary report: effect of encaidine and flecaidine on mortality in a randomized trial of arrhythmia suppression after myocardial infarction. New Engl. J. Med. Vol. no. 321: 406–412, 1989.
Van Capelle F. and Durrer D. Computer simulation of arrhythmias in a network of coupled excitable elements. Circ. Res. Vol. no. 47: 454–466, 1980.
Velbit V., Podrid P., Lown B., Cohen B. and Graboys T. Aggravation and provocation of ventricular arrhythmias by antiarrhythmic drugs. Circulation Vol. no. 65: 886–894, 1982.
Zhou X., Daubert J., Lown B., Wolf P., Smith W. and Ideker R. Size of the critical mass for defibrillation. Circulation Vol. no. 80: II - 531, 1989.
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Bardou, A.L., Auger, P.M., Seigneuric, R., Chassé, JL. (1999). Cellular Automata Models and Cardiac Arrhythmias. In: Delorme, M., Mazoyer, J. (eds) Cellular Automata. Mathematics and Its Applications, vol 460. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9153-9_10
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DOI: https://doi.org/10.1007/978-94-015-9153-9_10
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