Modelling the impulse distribution, delay and block in the electrical conduction system of the heart bundles

Authors

  • I.N. Vasserman Institute of Continuous Media Mechanics UB RAS
  • A.P. Shestakov Institute of Continuous Media Mechanics UB RAS

DOI:

https://doi.org/10.7242/1998-2097/2018.3.2

Keywords:

electrical conduction system of the heart, bundle branch block, electrodynamics, finite element method

Abstract

In the article the excitatory irradiation in the electrical conduction system was numerically modeled. The overview of transmembrane potential of electrical conduction system was given. The Luo-Rudi model (2011) was chosen for the investigation. A finite element model of the electrical conduction system was built in which the latter was regarded as a one-dimensional sequence of cells connected at the edges. Based on the elaborated model one of the mechanisms of a bundle branch block was investigated. A Y-shaped structure which models the move from the common trunk of the bundle of His to the bundle branches was investigated. The results show that depending on the conductivity of certain parts of the electrical conduction system of the heart three regimes might occur: excitation advancing through branching, complete block or excitation advancing with delay. Conductivity Value Domains for the common trunk of the bundle of His and the bundle branches in which each of the regimes occurs were obtained. The role of quick and slow sodium channels when the regime with delay occurs is considered

Author Biographies

  • I.N. Vasserman, Institute of Continuous Media Mechanics UB RAS
    кандидат физико-математических наук, научный сотрудник
  • A.P. Shestakov, Institute of Continuous Media Mechanics UB RAS
    младший научный сотрудник, ИМСС УрО РАН

References

  1. Ten Tusscher K.H.W.J., Panfilov A.W. Modelling of the ventricular conduction system // Progress in Biophysics and Molecular Biology. - 2008. - Vol. 96. - R. 152-170.
  2. Noble D. A Modification of the Hodgkin-Huxley Equations Applicable to Purkinje Fibre Action and Pacemaker Potentials // J. of Physiology. - 1962. - Vol. 160. - R. 317-352.
  3. Hodgkin L., Huxley A.F. A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve // The J. of Physiology. - 1952. - Vol. 117. - R. 500-544.
  4. McAllister R.E., Noble D., Tsien R.W. Reconstruction of the Electrical Activity of Cardiac Purkinje Fibres // J. of Physiology. - 1975. - Vol. 251. - R 1-59.
  5. Francesco Di, Noble D. A Model of the Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes - Simulations of Ionic Currents and Concentration Changes // Phil. Trans. R. Soc. Lond. - 1985. - Vol. 307. - R. 353-398.
  6. Ten Tusscher K.H.W.J., Noble D., Noble P.J., Panfilov A.V. A model for human ventricular tissue // American J. of Physiology. - 2004. - Vol. 286. - No 4. - R. 1573-1589.
  7. Ten Tusscher K.H.W.J., Panfilov A.V. Alternans and spiral breakup in a human ventricular tissue model // American J. of Physiology, Heart and Circulatory Physiology. - 2006. - Vol. 291. - R. 1088-1100.
  8. Aslanidi O.V., Stewart P., Boyett M.R., Zhang H. Optimal velocity and safety of discontinuous conduction through the heterogeneous Purkinje-ventricular junction // Biophysical J. - 2009. - Vol. 97. - R. 20-39.
  9. Stewart P., Aslanidi O.V., Noble D., Noble P.J., Boyett M.R., Zhang H. Mathematical models of the electrical action potential of Purkinje fibre cells // Philosophical Transactions of the Royal Society. - 2009. - Vol. 367. - R. 2225-2255.
  10. Sampson K.J., Iyer V., Marks A.R., Kass R.S. A computational model of Purkinje fibre single cell electrophysiology: implications for the long QT syndrome // J. Physiol. - 2010. - Vol. 588. - No 14. - R. 2643-2655.
  11. Corrias A., Giles W., Rodriguez B. Ionic mechanisms of electrophysiological properties and repolarization abnormalities in rabbit Purkinje fibers // Am. J. Physiol. Heart Circ. Physiol. - 2011. - Vol. 300. - No 5. - R. 1806-1813.
  12. Li P., Rudy Y. A Model of Canine Purkinje Cell Electrophysiology and Ca2+ Cycling. Rate Dependence, Triggered Activity, and comparison to Ventricular Myocites // Circulation Reesearch. - 2011. - Vol. 109. - R. 71-79.
  13. Cherry E.M., Fenton F.H. Contribution of the Purkinje network to wave propagation in the canine ventricle: insights from a combined electrophysiological-anatomical model // Nonlinear Dyn. - 2012. - Vol. 68. - R. 365-379.
  14. Garzon A., Grigoriev R.O., Fenton F.H. Continuous-time control of alternans in long Purkinje fibers // Chaos. - 2014. - Vol. 24. - No 3. - 033124.
  15. URL:http://rudylab.wustl.edu/research/cell/code/AllCodes.html (data obrasenia: 18.09.2018).
  16. The CellML project [Elektronnyj resurs] URL:https://models.cellml.org/cellml (data obrasenia: 18.09.2018).
  17. Clerx M., Collins P., de Lange E., Volders P.G. Myokit: A simple interface to cardiac cellular electrophysiology // Progress in Biophysics and Molecular Biology. - 2016. - Vol. 120. - No1-3. - R. 100-114.
  18. URL:http://myokit.org/ (data obrasenia: 18.09.2018).
  19. Keener J., Sneyd J. Mathematical Physiology. Springer, 2009.
  20. Laske T.G., Iaizzo P.A. The Cardiac Conduction System // In: Handbook of Cardiac Anatomy, Physiology and Devices. Humana Press. - 2005. - Chapter 9. - R. 123-136.
  21. Iaizzo P.A., Laske T.G. Anatomy and Physiology of the Cardiac Conduction System. // In: Cardiac Electrophysiology Methods and Models. Springer. - 2010. - Chapter 4. - P. 73-89

Published

2018-11-02

Issue

Section

Research: theory and experiment

How to Cite

Vasserman, I. ., & Shestakov, A. . (2018). Modelling the impulse distribution, delay and block in the electrical conduction system of the heart bundles. Perm Federal Research Centre Journal, 3, 17-24. https://doi.org/10.7242/1998-2097/2018.3.2