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Calcium Oscillations and Ectopic Beats in Virtual Ventricular Myocytes and Tissues: Bifurcations, Autorhythmicity and Propagation

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Functional Imaging and Modeling of the Heart (FIMH 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3504))

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Abstract

One mechanism for the onset of arrhythmias is abnormal impulse initiation such as ventricular ectopic beats. These may be caused by abnormal calcium (Ca2 + ) cycling. The Luo-Rudy model was used to simulate the dynamics of intracellular Ca2 +  ([Ca2 + ]i) handling and the initiation of ectopic beats in virtual ventricular myocytes and tissues. [Ca2 + ]i in the reduced Ca2 +  handling equations settles to a steady state at low levels of intracellular sodium ([Na + ]i), but oscillates when [Na + ]i is increased. These oscillations emerge through a homoclinic bifurcation. In the whole cell, Ca2 +  overload, brought about by inhibition of the sodium-potassium pump and elevated [Na + ]i, can cause autorhythmic depolarisations. These oscillations interact with membrane currents to cause action potentials that propagate through one dimensional virtual tissue strands and two dimensional anisotropic virtual tissue sheets.

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References

  1. Wit, A.L., Rosen, M.R.: Afterdepolarizations and triggered activity: distinction from automaticity as an arrhythmogenic mechanism. In: Fozzard, H.A., Haber, E., Jennings, R.B., Katz, A.M., Morgan, H.E. (eds.) The heart and cardiovascular system: scientific foundations, 2nd edn., pp. 2113–2163. Raven Press, New York (1991)

    Google Scholar 

  2. Luo, C.H., Rudy, Y.: A dynamic model of the cardiac action potential. II. Afterdepolarizations, triggered activity, and potentiation. Circ. Res. 74, 1097–1113 (1994)

    Google Scholar 

  3. Bers, D.M.: Excitation-Contraction Coupling and Cardiac Contractile Force, 2nd edn. Klewer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  4. Verkerk, A.O., Veldkamp, M.W., Baartscheer, A., Schumacher, C.A., Klopping, C., van Ginneken, A.C., Ravesloot, J.H.: Ionic mechanism of delayed afterdepolarizations in ventricular cells isolated from human end-stage failing hearts. Circ. 104, 2728–2733 (2001)

    Article  Google Scholar 

  5. Spencer, C.I., Sham, J.S.: Effects of Na + /Ca2 +  exchange induced by SR Ca2 +  release on action potentials and afterdepolarizations in guinea pig ventricular myocytes. Am. J. Physiol. 285, H2552–H2562 (2003)

    Google Scholar 

  6. Noble, D., DiFrancesco, D., Denyer, J.: Ionic mechanisms in normal and abnormal cardiac pacemaker activity. In: Jacklet, J.W. (ed.) Neuronal and cellular oscillators, pp. 59–85. Marcel Dekker Inc., New York (1989)

    Google Scholar 

  7. Omichi, C., Lamp, S.T., Lin, S.-F., Yang, J., Baher, A., Zhou, S., Attin, M., Lee, M.-H., Karagueuzian, H.S., Kogan, B., Qu, Z., Garfinkel, A., Chen, P.-S., Weiss, J.N.: Intracellular Ca dynamics in ventricular fibrillation. Am. J. Physiol. 286, H1836–H1844 (2004)

    Google Scholar 

  8. Carmeliet, E.: Cardiac ionic currents and acute ischemia: from channels to arrhythmias. Physiol. Rev. 79, 917–1017 (1999)

    Google Scholar 

  9. Kass, R.S., Tsien, R.W., Weingart, R.: Ionic basis of transient inward current induced by strophanthidin in cardiac Purkinje fibres. J. Physiol. 281, 209–226 (1978)

    Google Scholar 

  10. Gheorghiade, M., Adams, K.F., Colucci, W.F.: Digoxin in the management of cardiovascular disorders. Circ. 109, 2959–2964 (2004)

    Article  Google Scholar 

  11. Varghese, A., Winslow, R.L.: Dynamics of the calcium subsystem in cardiac Purkinje fibers. Physica D 68, 364–386 (1993)

    Article  MATH  Google Scholar 

  12. DiFrancesco, D., Noble, D.: A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil. Trans. Roy. Soc. (Lond.) B 307, 353–398 (1985)

    Article  Google Scholar 

  13. Varghese, A., Winslow, R.L.: Dynamics of abnormal pacemaking activity in cardiac Purkinje fibers. J. Theor. Biol. 168, 407–420 (1994)

    Article  Google Scholar 

  14. Winslow, R.L., Varghese, A., Noble, D., Adlakha, C., Hoythya, A.: Generation and propagation of ectopic beats induced by spatially localized Na-K pump inhibition in atrial network models. Proc. Roy. Soc. (Lond.) B 254, 55–61 (1993)

    Article  Google Scholar 

  15. Earm, Y.E., Noble, D.: A model of the single atrial cell: relation between calcium current and calcium release. Proc. Roy. Soc. (Lond.) B 240, 83–96 (1990)

    Article  Google Scholar 

  16. Joyner, R.W., Wang, Y.-G., Wilders, R., Golod, D.A., Wagner, M.B., Kumar, R., Goolsby, W.N.: A spontaneously active focus drives a model atrial sheet more easily than a model ventricular sheet. Am. J. Physiol. 279, H752–H763 (2000)

    Google Scholar 

  17. Wilders, R., Wagner, M.B., Golod, D.A., Kumar, R., Wang, Y.-G., Goolsby, W.N., Joyner, R.W., Jongsma, H.J.: Effects of anisotropy on the development of cardiac arrhythmias associated with focal activity. Pflug. Arch. 441, 301–312 (2000)

    Article  Google Scholar 

  18. Luo, C.H., Rudy, Y.: A dynamic model of the cardiac action potential. I. Simulations of ionic currents and concentration changes. Circ. Res. 74, 1071–1096 (1994)

    Google Scholar 

  19. 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)

    Google Scholar 

  20. Luo, C.H., Rudy, Y.: A model of the ventricular cardiac action potential: depolarization, repolarization, and their interaction. Circ. Res. 68, 1501–1526 (1991)

    Google Scholar 

  21. Zeng, J., Laurita, K.R., Rosenbaum, D.S., Rudy, Y.: Two components of the delayed rectifier K +  current in ventricular myocytes of the guinea pig type: theoretical formulation and their role in repolarization. Circ. Res. 77, 140–152 (1995)

    Google Scholar 

  22. Viswanathan, P.C., Shaw, R.M., Rudy, Y.: Effects of I Kr and I Ks heterogeneity on action potential duration and its rate-dependence: a simulation study. Circ. 99, 2466–2474 (1999)

    Google Scholar 

  23. Faber, G.M., Rudy, Y.: Action potential and contractility changes in [Na + ]i overloaded cardiac myocytes: a simulation study. Biophys. J. 78, 2392–2404 (2000)

    Article  Google Scholar 

  24. Rush, S., Larsen, H.: A practical algorithm for solving dynamic membrane equations. IEEE Trans. Biomed. Eng. 25, 389–392 (1978)

    Article  Google Scholar 

  25. Guckenheimer, J., Labouriau, I.S.: Bifurcation of the Hodgkin and Huxley equations: a new twist. Bull. Math. Biol. 55, 937–952 (1993)

    MATH  Google Scholar 

  26. Benson, A.P., Holden, A.V., Kharche, S., Tong, W.C.: Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling. Phil. Trans. Roy. Soc. (Lond.) A (to appear)

    Google Scholar 

  27. Fast, V.G., Kléber, A.G.: Role of wavefront curvature in propagation of cardiac impulse. Cardiovasc. Res. 33, 258–271 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. Computational Biology Laboratory, School of Biomedical Sciences, University of Leeds, Leeds, LS2 9JT, UK

    Alan P. Benson & Arun V. Holden

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  1. Alan P. Benson
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  2. Arun V. Holden
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Editor information

Editors and Affiliations

  1. Computational Imaging Lab, Department of Technology - D.326, Pompeu Fabra University, Barcelona, Spain

    Alejandro F. Frangi

  2. Computer Vision Center, Campus UAB, Edifici O, 08193, Bellaterra, Spain, Dept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Petia I. Radeva

  3. School of Engineering in Telecommunication, Polytechnic University of Madrid, 28040, Madrid, Spain

    Andres Santos

  4. GTC, Aragon Institute of Engineering Research (I3A), University of Zaragoza, Spain

    Monica Hernandez

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© 2005 Springer-Verlag Berlin Heidelberg

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Benson, A.P., Holden, A.V. (2005). Calcium Oscillations and Ectopic Beats in Virtual Ventricular Myocytes and Tissues: Bifurcations, Autorhythmicity and Propagation. In: Frangi, A.F., Radeva, P.I., Santos, A., Hernandez, M. (eds) Functional Imaging and Modeling of the Heart. FIMH 2005. Lecture Notes in Computer Science, vol 3504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494621_31

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  • DOI: https://doi.org/10.1007/11494621_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26161-2

  • Online ISBN: 978-3-540-32081-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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