Abstract
Specially desinged network of Greenberg-Hastings (GH) cellular automata is shown to be a reliable approximation to cardiac pacemaker. A complex network is built basing on a square lattice where some edges are rewired locally and with preference to link to cells which are more connected to other cells. GH automata are systems with cyclic intrinsic dynamics where three possible cell’s states are characterized by timings — time steps spent in each state. Complex networks of GH automata evolve rhythmically with periods determined by timings. Diversity of oscillations coexisting in the system depends on network topology. Large variety in oscillations is interpreted as effectiveness to response to actual needs of a body.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Klabunde, R.E.: Cardiovascular Physiology Concepts, http://www.cvphysiology.com
Ermentrout, G.B., Edelstein-Keshet, L.: Cellular Automata Approaches to Biological Modeling. J. Theor. Biol. 160, 97–133 (1993)
Greenberg, J.M., Hastings, S.P.: Spatial Patterns for Discrete Models of Diffusion in Exitable Media. SIAM J. Appl. Math. 34, 515–523 (1978)
Greenberg, J.M., Greene, C., Hastings, S.P.: Remarks on a 25 Year Old Theorem on Two-dimensional Cellular Automata. Int. J. Unconv. Comp. 1, 399–402 (2005)
Markus, M., Hess, B.: Isotropic Cellular Automaton for Modeling Excital Media. Nature 347, 56–58 (1990)
Bub, G., Shrier, A., Glass, L.: Spiral Wave Generation in Heteroneeous Excitable Media. Phys.Rev.Lett. 88, 058101–1–4 (2002)
Saffitz, J.E., Lerner, D.L., Yamada, K.A.: Gap Junctions Distribution and Regulation in the Heart. In: Zipes, D.P., Jalive, J. (eds.) Cardiac Elecrophysiology. From Cell to Bedside, pp. 181–191. Saunders Co., Philadelphia (2004)
Luke, R.A., Saffitz, J.E.: Remodeling of Ventricular Conduction Pathways in Healed Canine Infarct Border Zones. J. Clin. Invest. 87(5), 1594–1602 (1991)
Bub, G., Shrier, A., Glass, L.: Global Organization of Dynamics in Oscillatory Heterogeneous Excitable Media. Phys. Rev. Lett. 94, 028105-1–4 (2005)
Makowiec, D.: On Cellular Automata Modeling of Cardiac Pacemaker. Journal of Cellular Automata (to appear, 2008)
Makowiec, D.: Cellular Automata Model of Cardiac Pacemaker. Acta Phys. Pol. B (to appear, 2008)
Kodama, I., Honyo, H., Boyett, M.R.: Are We Lost in the Labyrinth of the Sinoatrial Node Pacemaker Mechanism? Journal of Cardiovascular Electrophysiology 13(12), 1303–1305 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Makowiec, D. (2008). The Heart Pacemaker by Cellular Automata on Complex Networks. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_37
Download citation
DOI: https://doi.org/10.1007/978-3-540-79992-4_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79991-7
Online ISBN: 978-3-540-79992-4
eBook Packages: Computer ScienceComputer Science (R0)