Advertisement

Computer Simulations and Nonlinear Dynamics of Cardiac Action Potentials

  • Daisuke SatoEmail author
Chapter
Part of the Handbook of Modern Biophysics book series (HBBT, volume 5)

Abstract

Sudden cardiac death accounts for >300,000 deaths per year in the United States alone. However, several clinical trials failed and tested drugs increased molarity. Therefore, deeper understanding of the mechanisms of arrhythmias is required. The goals of this chapter are (1) to learn how to make a mathematical model of the cardiac action potential, (2) to learn how to simulate the model and analyze the dynamics, (3) to learn how to parallelize the code to simulate computationally intensive models.

Keywords

Graphic Processing Unit Action Potential Duration Spiral Wave Cardiac Action Potential Inactivation Gate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I would like to acknowledge funding support from National Institutes of Health grant R00-HL111334, American Heart Association Grant-in-Aid 16GRNT31300018, and Amazon AWS Cloud Credits for Research.

References

  1. 1.
    Glass, L., Goldberger, A.L., Courtemanche, M., Shrier, A.: Nonlinear dynamics, chaos and complex cardiac arrhythmias. Proc. R. Soc. Lond. A 413, 9–26 (1987)CrossRefGoogle Scholar
  2. 2.
    Karma, A., Gilmour Jr., R.F.: Nonlinear dynamics of heart rhythm disorders. Phys. Today 60, 51 (2007)CrossRefGoogle Scholar
  3. 3.
    Glass, L., Hunter, P., McCulloch, A.: Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function. Springer, New York (2012)Google Scholar
  4. 4.
    Weiss, J.N., Chen, P.-S., Qu, Z., Karagueuzian, H.S., Garfinkel, A.: Ventricular fibrillation how do we stop the waves from breaking? Circ. Res. 87, 1103–1107 (2000)CrossRefPubMedGoogle Scholar
  5. 5.
    Hakim, V., Karma, A.: Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications. Phys. Rev. E 60, 5073 (1999)CrossRefGoogle Scholar
  6. 6.
    Kogan, B.J.: Introduction to Computational Cardiology: Mathematical Modeling and Computer Simulation. Springer, New York (2009)Google Scholar
  7. 7.
    Trayanova, N.A., O’Hara, T., Bayer, J.D., et al.: Computational cardiology: how computer simulations could be used to develop new therapies and advance existing ones. Europace 14, v82–v89 (2012)CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Adler, C.P., Costabel, U.: Cell number in human heart in atrophy, hypertrophy, and under the influence of cytostatics. Recent Adv. Stud. Cardiac Struct. Metab. 6, 343–355 (1975)PubMedGoogle Scholar
  9. 9.
    Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)CrossRefPubMedPubMedCentralGoogle Scholar
  10. 10.
    Bers, D.M.: Excitation Contraction Coupling and Cardiac Contractile Force. Kluwer, Boston (2001)CrossRefGoogle Scholar
  11. 11.
    Echebarria, B., Karma, A.: Mechanisms for initiation of cardiac discordant alternans. Eur. Phys. J. Spec. Top. 146, 217–231 (2007)CrossRefGoogle Scholar
  12. 12.
    Traube, L.: Ein Fall von Pulsus bigeminus nebst Bemerkungen über die Leberschwellungen bei Klappenfehlern und über acute Leberatrophie. Berliner Klinische Wochenschrift 9, 185–188 (1872)Google Scholar
  13. 13.
    Fox, J.J., McHarg, J.L., Gilmour Jr., R.F.: Ionic mechanism of electrical alternans. Am. J. Physiol. Heart Circ. Physiol. 282, H516–H530 (2002)CrossRefPubMedGoogle Scholar
  14. 14.
    Garfinkel, A., Kim, Y.H., Voroshilovsky, O., et al.: Preventing ventricular fibrillation by flattening cardiac restitution. Proc. Natl. Acad. Sci. U. S. A. 97, 6061–6066 (2000)CrossRefPubMedPubMedCentralGoogle Scholar
  15. 15.
    Groenendaal, W., Ortega, F.A., Krogh-Madsen, T., Christini, D.J.: Voltage and calcium dynamics both underlie cellular alternans in cardiac myocytes. Biophys. J. 106, 2222–2232 (2014)CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Hayashi, H., Shiferaw, Y., Sato, D., et al.: Dynamic origin of spatially discordant alternans in cardiac tissue. Biophys. J. 92, 448–460 (2007)CrossRefPubMedGoogle Scholar
  17. 17.
    Pastore, J.M., Girouard, S.D., Laurita, K.R., Akar, F.G., Rosenbaum, D.S.: Mechanism linking T-wave alternans to the genesis of cardiac fibrillation. Circulation 99, 1385–1394 (1999)CrossRefPubMedGoogle Scholar
  18. 18.
    Nolasco, J.B., Dahlen, R.W.: A graphic method for the study of alternation in cardiac action potentials. J. Appl. Physiol. 25, 191–196 (1968)CrossRefPubMedGoogle Scholar
  19. 19.
    Qu, Z., Garfinkel, A.: An advanced algorithm for solving partial differential equation in cardiac conduction. IEEE Trans. Biomed. Eng. 46, 1166–1168 (1999)CrossRefPubMedGoogle Scholar
  20. 20.
    Echebarria, B., Karma, A.: Instability and spatiotemporal dynamics of alternans in paced cardiac tissue. Phys. Rev. Lett. 88, 208101 (2002)CrossRefPubMedGoogle Scholar
  21. 21.
    Echebarria, B., Karma, A.: Amplitude equation approach to spatiotemporal dynamics of cardiac alternans. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76, 051911 (2007)CrossRefPubMedGoogle Scholar
  22. 22.
    Mines, G.R.: On dynamic equilibrium in the heart. J. Physiol. 46, 349–383 (1913)CrossRefPubMedPubMedCentralGoogle Scholar
  23. 23.
    Weiss, J.N., Garfinkel, A., Karagueuzian, H.S., Qu, Z., Chen, P.-S.: Chaos and the transition to ventricular fibrillation. A new approach to antiarrhythmic drug evaluation. Circulation 99, 2819–2826 (1999)CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Department of PharmacologyUniversity of California, DavisDavisUSA

Personalised recommendations