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BioMed Research International
Volume 2015, Article ID 170768, 8 pages
http://dx.doi.org/10.1155/2015/170768
Research Article

Characterizing Spatial Dynamics of Bifurcation to Alternans in Isolated Whole Rabbit Hearts Based on Alternate Pacing

1Department of Biomedical Engineering, University of Minnesota, 312 Church Street SE, Minneapolis, MN 55455, USA
2Department of Mechanical, Aerospace, and Biomedical Engineering, University of Tennessee, 1506 Middle Drive, Knoxville, TN 37996, USA

Received 10 November 2014; Accepted 6 February 2015

Academic Editor: Sergio Alonso

Copyright © 2015 Kanchan Kulkarni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. L. George Jr., “Molecular and genetic basis of sudden cardiac death,” The Journal of Clinical Investigation, vol. 123, no. 1, pp. 75–83, 2013. View at Publisher · View at Google Scholar · View at Scopus
  2. D. P. Zipes and H. J. J. Wellens, “Sudden cardiac death,” Circulation, vol. 98, no. 21, pp. 2334–2351, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Karma, “Electrical alternans and spiral wave breakup in cardiac tissue,” Chaos, vol. 4, no. 3, pp. 461–472, 1994. View at Publisher · View at Google Scholar · View at Scopus
  4. R. F. Gilmour Jr., “Electrical restitution and ventricular fibrillation: negotiating a slippery slope,” Journal of Cardiovascular Electrophysiology, vol. 13, no. 11, pp. 1150–1151, 2002. View at Publisher · View at Google Scholar · View at Scopus
  5. M. Watanabe, N. F. Otani, and R. F. Gilmour Jr., “Biphasic restitution of action potential duration and complex dynamics in ventricular myocardium,” Circulation Research, vol. 76, no. 5, pp. 915–921, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. J. J. Fox, J. L. McHarg, and R. F. Gilmour Jr., “Ionic mechanism of electrical alternans,” The American Journal of Physiology—Heart and Circulatory Physiology, vol. 282, no. 2, pp. H516–H530, 2002. View at Google Scholar · View at Scopus
  7. J. B. Nolasco and R. W. Dahlen, “A graphic method for the study of alternation in cardiac action potentials,” Journal of Applied Physiology, vol. 25, no. 2, pp. 191–196, 1968. View at Publisher · View at Google Scholar · View at Scopus
  8. E. G. Tolkacheva, D. G. Schaeffer, D. J. Gauthier, and W. Krassowska, “Condition for alternans and stability of the 1:1 response pattern in a ‘memory’ model of paced cardiac dynamics,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 67, no. 3, part 1, Article ID 031904, 2003. View at Publisher · View at Google Scholar · View at Scopus
  9. M. L. Riccio, M. L. Koller, and R. F. Gilmour Jr., “Electrical restitution and spatiotemporal organization during ventricular fibrillation,” Circulation Research, vol. 84, no. 8, pp. 955–963, 1999. View at Publisher · View at Google Scholar · View at Scopus
  10. M. L. Koller, M. L. Riccio, and R. F. Gilmour Jr., “Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation,” The American Journal of Physiology—Heart and Circulatory Physiology, vol. 275, no. 5, pp. H1635–H1642, 1998. View at Google Scholar · View at Scopus
  11. H. M. Hastings, F. H. Fenton, S. J. Evans et al., “Alternans and the onset of ventricular fibrillation,” Physical Review E, vol. 62, no. 3, pp. 4043–4048, 2000. View at Google Scholar
  12. A. Petrie and X. Zhao, “Estimating eigenvalues of dynamical systems from time series with applications to predicting cardiac alternans,” Proceedings of The Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, vol. 468, no. 2147, pp. 3649–3666, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. J. Sun, F. Amellal, L. Glass, and J. Billette, “Alternans and period-doubling bifurcations in atrioventricular nodal conduction,” Journal of Theoretical Biology, vol. 173, no. 1, pp. 79–91, 1995. View at Publisher · View at Google Scholar · View at Scopus
  14. C. M. Berger, X. Zhao, D. G. Schaeffer, H. M. Dobrovolny, W. Krassowska, and D. J. Gauthier, “Period-doubling bifurcation to alternans in paced cardiac tissue: crossover from smooth to border-collision characteristics,” Physical Review Letters, vol. 99, no. 5, Article ID 058101, 2007. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Heldstab, H. Thomas, T. Geisel, and G. Radons, “Linear and nonlinear response of discrete dynamical systems. I. Periodic attractors,” Zeitschrift für Physik B Condensed Matter, vol. 50, no. 2, pp. 141–150, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. X. Zhao and D. G. Schaeffer, “Alternate pacing of border-collision period-doubling bifurcations,” Nonlinear Dynamics, vol. 50, no. 3, pp. 733–742, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. X. Zhao, D. G. Schaeffer, C. M. Berger, D. J. Gauthier, and W. Krassowska, “Cardiac alternans arising from an unfolded border-collision bifurcation,” Journal of Computational and Nonlinear Dynamics, vol. 3, no. 4, Article ID 041004, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. R. M. Smith, R. Visweswaran, I. Talkachova, J. K. Wothe, and E. G. Tolkacheva, “Uncoupling the mitochondria facilitates alternans formation in the isolated rabbit heart,” American Journal of Physiology—Heart and Circulatory Physiology, vol. 305, no. 1, pp. H9–H18, 2013. View at Publisher · View at Google Scholar · View at Scopus
  19. A. R. Cram, H. M. Rao, and E. G. Tolkacheva, “Toward prediction of the local onset of alternans in the heart,” Biophysical Journal, vol. 100, no. 4, pp. 868–874, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. J. N. Weiss, A. Karma, Y. Shiferaw, P.-S. Chen, A. Garfinkel, and Z. Qu, “From pulsus to pulseless: the saga of cardiac alternans,” Circulation Research, vol. 98, no. 10, pp. 1244–1253, 2006. View at Publisher · View at Google Scholar · View at Scopus