Skip to main content

The Heart Pacemaker by Cellular Automata on Complex Networks

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5191))

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Klabunde, R.E.: Cardiovascular Physiology Concepts, http://www.cvphysiology.com

  2. Ermentrout, G.B., Edelstein-Keshet, L.: Cellular Automata Approaches to Biological Modeling. J. Theor. Biol. 160, 97–133 (1993)

    Article  Google Scholar 

  3. Greenberg, J.M., Hastings, S.P.: Spatial Patterns for Discrete Models of Diffusion in Exitable Media. SIAM J. Appl. Math. 34, 515–523 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  4. 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)

    Google Scholar 

  5. Markus, M., Hess, B.: Isotropic Cellular Automaton for Modeling Excital Media. Nature 347, 56–58 (1990)

    Article  Google Scholar 

  6. Bub, G., Shrier, A., Glass, L.: Spiral Wave Generation in Heteroneeous Excitable Media. Phys.Rev.Lett. 88, 058101–1–4 (2002)

    Article  Google Scholar 

  7. 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)

    Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Bub, G., Shrier, A., Glass, L.: Global Organization of Dynamics in Oscillatory Heterogeneous Excitable Media. Phys. Rev. Lett. 94, 028105-1–4 (2005)

    Article  Google Scholar 

  10. Makowiec, D.: On Cellular Automata Modeling of Cardiac Pacemaker. Journal of Cellular Automata (to appear, 2008)

    Google Scholar 

  11. Makowiec, D.: Cellular Automata Model of Cardiac Pacemaker. Acta Phys. Pol. B (to appear, 2008)

    Google Scholar 

  12. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Hiroshi Umeo Shin Morishita Katsuhiro Nishinari Toshihiko Komatsuzaki Stefania Bandini

Rights and permissions

Reprints 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)

Publish with us

Policies and ethics