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Modelling of cardiac rhythm: from single cells to massive networks

  • D. Noble
  • J. C. Denyer
  • H. F. Brown
  • R. Winslow
  • A. Kimball
Conference paper
Part of the Perspectives in Neural Computing book series (PERSPECT.NEURAL)

Abstract

The development of models of the sinoatrial node cell is reviewed to show the steady progress from the early models based on voltage clamp of small multicellular preparations to permeabilized patch clamp of isolated single cells. It is shown that the kinetics of the hyperpolarizing-activated current, i f, are finely tuned to ‘buffer’ the cardiac pacemaker frequency against changes in other conductance parameters, in particular background conductances.

These single cell models have now been oncorporated into large scale network models: N x N meshes with neightbouring cells electrically coupled by resistors representing gap junctions. With 128 x 12 8 sinus cells, and random distribution of instrinsic properties, only two nexus channels (unit conductance 50 pS) between neighbouring cells are required to entrain the cells and between 20 and 200 channels will synchronize activity almost completely throughout the array. These very low densities of gap junctions are consistent with experimental observations (Masson-Pevet et al, 1979). When intrinsic properties are distributed between the node centre and periphery using a Gaussian function, and with the same magnitude of cell-to-cell coupling, and exitatory wave starts in the peripheral regions of the node and propagates towards the centre,i.e. the opposite direction to that in the normal heart. This occurs experimentally when the rabbit sinus node is separated from the atrium (Kirchhoff et al, 1987). Surrounding the node model with an atrial network shifts the origin of excitation towards the centre of the node.

Keywords

Sinus Node Node Cell Sinoatrial Node Pacemaker Potential Sinoatrial Node Cell 
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.

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References

  1. Bleeker, W M, MacKaay, A J C, Masson-Pevet, M, Bouman, L N and Becker, A E (1980) Functional and morphological organization of the rabbit sinus node. Circulation Research 46 11–22.Google Scholar
  2. Denyer J C and Brown H F (1987) A method for isolating rabbit sinoatrial node cells which maintains their natural shape. Japanese Journal of Physiology 37 963–965.CrossRefGoogle Scholar
  3. Denyer J C and Brown H F (1990a) Rabbit sinoatrial node cells: isolation and electrophysiological properties. Journal of Physiology 428 405–424.Google Scholar
  4. Denyer J C and Brown H F (1990b) Pacemaking in rabbit isolated sinoatrial node cells during Cs+ block of the hyperpolarizing-activated current i f. Journal of Physiology 429 401–409.Google Scholar
  5. Denyer J C and Brown H F (1990c) Calcium window current in rabbit isolated sinoatrial node cells. Journal of Physiology 429 21 PGoogle Scholar
  6. DiFrancesco D (1984) Characterisation of the pacemaker current kinetics in calf Purkinje fibres. Journal of Physiology 348 341–367.Google Scholar
  7. DiFrancesco D, Ferroni, A, Mazzanti M and Tromba C (1986) Properties of the hyperpolarizing-activated current (If) in cells isolated from the rabbit sinoatrial node. Journal of Physiology 377 61–88.Google Scholar
  8. DiFrancesco D and Noble D (1982) Implications of the re-interpretation of i K2 for the modelling of the electrical activity of pacemaker tissues in the heart. In: Cardiac Rate and Rhythm Ed. Bouman, L.N. & Jongsma, H.J. pp. 93–128. The Hague, Boston, London: Martinus NijhoffGoogle Scholar
  9. DiFrancesco D and Noble D (1985) A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philosophical Transactions of the Royal Society B 307 353–398.Google Scholar
  10. DiFrancesco D and Noble D (1989) The current if and its contribution to cardiac pacemaking. In: Cellular and Neuronal Oscillators (Ed. JW Jacklet ) 31–57, New York: DekkerGoogle Scholar
  11. Earm Y E, Ho W K and So I S (1990) Inward current generated by Na-Ca exchange during the action potential in single atrial cells of the rabbit. Proceedings of The Royal Society B 240 61–81.Google Scholar
  12. Earm, Y. E. and Noble, D. (1990) A model of the single atrial cell: relation between calcium current and calcium release. Proceedings of The Royal Society 240, 83–96.CrossRefGoogle Scholar
  13. Fabiato A (1983) Calcium-induced release of calcium from the cardiac sarcoplasmic reticulum. American Journal of Physiology 245 C1–C14.Google Scholar
  14. Hagiwara, N, Irisawa, H and Kameyama, M (1988) Contribution of two types of calcium current to the pacemaker potentials of rabbit sinoatrial node cells. Journal of Physiology 395 233–253.Google Scholar
  15. Hilgemann DW and Noble D (1987) Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: Reconstruction of basic cellular mechanisms. Proceedings of the Royal Society B 230 163–205.Google Scholar
  16. Horn R and Marty A (1988) Muscarinic activation of ionic currents measured by a new whole-cell recording method. Journal of General Physiology 92 145–159.CrossRefGoogle Scholar
  17. Irisawa, H, Brown HF & Giles WR (1991) Cardiac pacemaking in the sinoatrial node. Physiological Reviews (in press)Google Scholar
  18. KirchhofF CJHJ (1989) The sinus node and atrial fibrillation. Ph. D. thesis, University of Maastricht.Google Scholar
  19. Kirchhoff CJHJ, Bonke FIM, Allessie MA and Lammers WJEP (1987) The influence of the atrial myocardium on impulse formation in the rabbit sinus node. Pflugers Arch 410 198–203CrossRefGoogle Scholar
  20. Kodama, I. and Boyett, M. R. (1985) Regional differences in the electrical activity of the rabbit sinus node. Pflugers Arch. 404, 214–226.CrossRefGoogle Scholar
  21. Masson-Pevet, M., Bleeker, W. K., Mackaay, A. J. C., and Bouman, L. N. (1979) Sinus node and atrium cells from the rabbit heart: a quantitative electron microscopic description after electrophysiological localisation. J. Molec. Cell. Cardiol. 11, 555–568.CrossRefGoogle Scholar
  22. Noble D. (1982) In discussion following De Haan, RL. (1972) In: Cardiac Rate and Rhythm ed. Bouman, L N &c Jongsma, H. J. pp 359–361. Martinus Nijhoff: The Hague.Google Scholar
  23. Noble D, Denyer JC, Brown H F and DiFrancesco D (1991) Modulation of pacemaker rhythm by conductance changes, (in preparation).Google Scholar
  24. Noble D, DiFrancesco D and Denyer JC (1989) Ionic mechanisms in normal and abnormal cardiac pacemaker activity. Neuronal and Cellular Oscillators J. W. Jacklet, Dekker: New York, 59–85Google Scholar
  25. Noble D and Noble SJ (1984) A model of S.A. node electrical activity using a modification of the DiFrancesco-Noble (1984) equations. Proceedings of the Royal Society B 222 295–304.Google Scholar
  26. Noble D and Powell T (1987) Electrophysiology of single cardiac cells. Academic Press.Google Scholar
  27. Noma A, and Irisawa, H. (1976) Membrane currents in rabbit sinoatrial node cells studied by the double microelectrode method. Pflügers Archiv 364 45–52.CrossRefGoogle Scholar
  28. Tanaguchi J, Kokubun S, Noma A and Irisawa H (1981) Spontaneously active cells isolated from the sino-atrial and atrio-ventricular nodes of the rabbit heart. Japanese Journal of Physiology 31 547–558.CrossRefGoogle Scholar
  29. van Ginneken, A G C (1987) Membrane currents in mammalian cardiac pacemaker cells. Ph. D. thesis. Amsterdam University.Google Scholar
  30. Winslow R, Kimball A, Noble D, Denyer J C and Varghese A (1991) Simulation of very large sinus node and atrial cell networks on the Connection Machine CM-2 massively parallel computer. Journal of Physiology 438 180 P.Google Scholar
  31. Winslow R L, Kimball A L, Varghese A and Noble D (1992) Simulating cardiac sinus and atrial network dynamics on the connection machine. Physica D: Nonlinear phenomena, in press.Google Scholar
  32. Yanagihara K, Noma A and Irisawa H (1980) Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments. Japanese Journal of Physiology 30 841–857.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1992

Authors and Affiliations

  • D. Noble
    • 1
  • J. C. Denyer
    • 1
  • H. F. Brown
    • 1
  • R. Winslow
    • 2
  • A. Kimball
    • 2
  1. 1.University Laboratory of PhysiologyParks RoadOxfordUK
  2. 2.Department of Physiology and Army High Performance Computer CenterUniversity of MinnesotaUSA

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