Abstract
The stability of induced pacemaker activity in a virtual human ventricular cell is analysed by numerical simulations and continuation algorithms, with the conductance of the time independent inward rectifying potassium current (I K1) as the bifurcation parameter. Autorhythmicity is induced within a narrow range of this conductance, where periodic oscillations and bursting behaviour are observed. The frequency of the oscillations approaches zero as the parameter moves towards the bifurcation point, suggesting a homoclinic bifurcation. Intracellular sodium ([Na + ]i) and calcium ([Ca2 + ]i) concentration dynamics can influence the location of the bifurcation point and the stability of the periodic states. These two concentrations function as slow variables, pushing the fast membrane voltage system into and out of the periodic region, producing bursting behaviour. Moreover, suppressing I K1 will prolong action potential duration and may introduce risks of developing stable periodic intermittency and arrhythmia. A genetically engineered pacemaker may appear an attractive idea, but simple analysis suggests inherent problems.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Holden, A.V., Yoda, M.: Ionic channel density of excitable-membranes can act as a bifurcation parameter. Biol. Cyber. 42, 29–38 (1981)
Holden, A.V., Yoda, M.: The effects of ionic channel density on neuronal function. J. Theor. Neurobiol. 1, 60–81 (1981)
Miake, J., Marban, E., Nuss, H.B.: Biological pacemaker created by gene transfer. Nature 419, 132–133 (2002)
Miake, J., Marban, E., Nuss, H.B.: Functional role of inward rectifier current in heart probed by Kir2.1 over expression and dominant-negative suppression. J. Clin. Invest. 111, 1529–1536 (2003)
Silva, J., Rudy, Y.: Mechanism of Pacemaking in IK1-downregulated myocytes. Circ. Res. 92, 261–263 (2003)
Tristani-Firouzi, M., Jensen, J.L., Donaldson, M.R., Sansone, V., Meola, G., Hahn, A., Bendahhou, S., Kwiecinski, H., Fidzianska, A., Plaster, N., Fu, Y.H., Ptacek, L.J., Tawil, R.: Functional and clinical characterization of KCNJ2 mutations associated with LQT7 (Andersen syndrome). J. Clin. Invest. 110, 381–388 (2002)
ten Tusscher, K.H.W.J., Noble, D., Noble, P.J., Panfilov, A.V.: A model for human ventricular tissue. Am. J. Physiol. 286, H1573–H1589 (2004)
Iyer, V., Mazhari, R., Winslow, R.L.: A Computational Model of the Human Left-Ventricular Epicardial Myocyte. Biophys. J. 87, 1507–1525 (2004)
Priebe, L., Beuckelmann, D.J.: Simulation Study of Cellular Electric Properties in Heart Failure. Circ. Res. 82, 1206–1223 (1998)
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)
Faber, G.M.: The Luo-Rudy dynamic model of mammalian ventricular action potential (2000), http://www.cwru.edu/med/CBRTC/LRdOnline/
Benson, A.P., Tong, W.C., Holden, A.V., Clayton, R.H.: Induction of autorhythmicity in virtual ventricular myocytes and tissue. J. Physiol. (Proceedings) (2005) (to appear)
Koller, M.L., Riccio, M.L., Gilmour Jr., R.F.: Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am. J. Physiol. Heart. Circ. Physiol. 275, H1635–H1642 (1998)
Doedel, E.J.: AUTO: A program for the automatic bifurcation and analysis of autonomous systems. Cong. Num. 30, 265–284 (1981)
Ermentrout, G.B.: XPPAUT, http://www.math.pitt.edu/~bard/xpp/xpp.html
Hund, T.J., Kucera, J.P., Otani, N.F., Rudy, Y.: Ionic charge conservation and long-term steady state in the Luo-Rudy dynamic cell model. Biophys. J. 81, 3324–3331 (2001)
Bub, G., Glass, L., Publicover, N.G., Shrier, A.: Bursting calcium rotors in cultured cardiac myocyte monolayers. Proc. Natl. Acad. Sci. U. S. A. 95, 10283–10287 (1998)
Cohen, N., Soen, Y., Braun, E.: Spatio-temporal dynamics of networks of heart cells in culture. Physica. A. 249, 600–604 (1998)
Cohen, N.: The development of spontaneous beating activity in cultured heart cells: From cells to networks. PhD thesis, Technion – Israel Institute of Technology (2001)
Soen, Y., Cohen, N., Braun, E., Lipson, D.: Emergence of spontaneous rhythm disorders in self-assembled networks of heart cells. Phys. Rev. Lett. 82, 3556–3559 (1999)
Bertram, R., Butte, M., Kiemel, T., Sherman, A.: Topological and Phenomenological Classification of Bursting Oscillations. Bull. Math. Biol. 57, 413–439 (1995)
Rinzel, J., Ermentrout, B.: Analysis of neural excitability and oscillations. In: Koch, C., Segev, I. (eds.) Methods in Neuronal Modeling: From Synapses to Networks, 2nd edn., pp. 251–292. MIT Press, Cambridge (1999)
Wang, X.-J., Rinzel, J.: Oscillatory and bursting properties of neurons. In: Arbib, M.A. (ed.) Handbook of brain theory and neural networks, pp. 686–691. MIT Press, Cambridge (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tong, W.C., Holden, A.V. (2005). Induced Pacemaker Activity in Virtual Mammalian Ventricular Cells. 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_23
Download citation
DOI: https://doi.org/10.1007/11494621_23
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)