Advertisement

The Bidomain Theory of Pacing

  • Deborah L. Janks
  • Bradley J. Roth

The implantable cardiac pacemaker is one of the most important medical innovations of the twentieth century.1 Yet until recently researchers have not understood the basic mechanisms governing how a pacemaker excites the heart. The development of a mathematical model describing the electrical properties of cardiac tissue — the bidomain model — helped unravel these mechanisms. This chapter outlines several important predictions of the bidomain model related to pacing. Several other chapters in this book examine related topics.

The bidomain model2,3 represents cardiac tissue as a multidimensional cable that can be represented by a network of resistors and capacitors. Figure 1 shows a network equivalent to the two-dimensional bidomain model. The lower grid of resistors represents the intracellular space, and the upper grid represents the extracellular space. The two spaces are coupled by resistors and capacitors representing the membrane. The electrical properties of cardiac muscle are markedly anisotropic; in Fig. 1 the resistors in the x direction may be different from the resistors in the y direction. Moreover, the degree of anisotropy differs within the intracellular and extracellular spaces. The ratio of conductivities in the x and y directions in the extracellular space is on the order of two, but in the intracellular space it is about ten, indicating the intracellular space is more anisotropic than the extracellular space.4 This condition of “unequal anisotropy ratios” leads to many of the interesting phenomena predicted by the bidomain model.5

Keywords

Wave Front Cardiac Tissue Virtual Cathode Anodal Stimulation Break Excitation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jeffrey K. Machines in Our Hearts: The Cardiac Pacemaker, the Implantable Defibrillator, and American Health Care. Baltimore: Johns Hopkins University Press; 2001Google Scholar
  2. 2.
    Henriquez CS. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit Rev Biomed Eng 1993;21:1–77PubMedGoogle Scholar
  3. 3.
    Roth BJ. How the anisotropy of the intracellular and extracellular conductivities influences stimulation of cardiac muscle. J Math Biol 1992;30:633–646PubMedCrossRefGoogle Scholar
  4. 4.
    Roth BJ. Electrical conductivity values used with the bidomain model of cardiac tissue. IEEE Trans Biomed Eng 1997;44:326–328PubMedCrossRefGoogle Scholar
  5. 5.
    Roth BJ. How to explain why “unequal anisotropy ratios” is important using pictures but no mathematics. 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Aug. 30–Sept. 3, 2006, New YorkGoogle Scholar
  6. 6.
    Sepulveda NG, Roth BJ, Wikswo JP Jr. Current injection into a two-dimensional anisotropic bidomain. Biophys J 1989;55:987–999PubMedGoogle Scholar
  7. 7.
    Neunlist M, Tung L. Spatial distribution of cardiac transmembrane potentials around an extracellular electrode: dependence on fiber orientation. Biophys J 1995;68:2310–2322PubMedGoogle Scholar
  8. 8.
    Knisley SB. Transmembrane voltage changes during unipolar stimulation of rabbit ventricle. Circ Res 1995;77:1229–1239PubMedGoogle Scholar
  9. 9.
    Wikswo JP Jr, Lin S-F, Abbas RA. Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation. Biophys J 1995;69:2195–2210PubMedGoogle Scholar
  10. 10.
    Roth BJ. A mathematical model of make and break electrical stimulation of cardiac tissue by a unipolar anode or cathode. IEEE Trans Biomed Eng 1995;42:1174–1184PubMedCrossRefGoogle Scholar
  11. 11.
    Roth BJ. Strength-interval curves for cardiac tissue predicted using the bidomain model. J Cardiovasc Electrophysiol 1996;7:722–737PubMedCrossRefGoogle Scholar
  12. 12.
    Roth BJ. Nonsustained reentry following successive stimulation of cardiac tissue through a unipolar electrode. J Cardiovasc Electrophysiol 1997;8:768–778PubMedCrossRefGoogle Scholar
  13. 13.
    Goto M, Brooks C McC. Membrane excitability of the frog ventricle examined by long pulses. Am J Physiol 1969;217:1236–1245PubMedGoogle Scholar
  14. 14.
    Dekker E. Direct current make and break thresholds for pacemaker electrodes on the canine ventricle. Circ Res 1970;27:811–823PubMedGoogle Scholar
  15. 15.
    Lindemans FW, Heethaar RM, Denier van der Gon JJ, Zimmerman ANE. Site of initial excitation and current threshold as a function of electrode radius in heart muscle. Cardiovasc Res 1975;9:95–104PubMedCrossRefGoogle Scholar
  16. 16.
    Lindemans FW, Denier van der Gon JJ. Current thresholds and liminal size in excitation of heart muscle. Cardiovasc Res 1978;12:477–485PubMedCrossRefGoogle Scholar
  17. 17.
    Roth BJ. Artifacts, assumptions, and ambiguity: Pitfalls in comparing experimental results to numerical simulations when studying electrical stimulation of the heart. Chaos 2002;12:973–981PubMedCrossRefGoogle Scholar
  18. 18.
    van Dam RTh, Durrer D, Strackee J, van der Tweel LH. The excitability cycle of the dog's left ventricle determined by anodal, cathodal, and bipolar stimulation. Circ Res 1956;4:196–203Google Scholar
  19. 19.
    Cranefield PF, Hoffman BF, Siebens AA. Anodal excitation of cardiac muscle. Am J Physiol 1957;190:383–390PubMedGoogle Scholar
  20. 20.
    Sidorov VY, Woods MC, Baudenbacher P, Baudenbacher F. Examination of stimulation mechanism and strength-interval curve in cardiac tissue. Am J Physiol 2005;289:H2602–H2615Google Scholar
  21. 21.
    Roth BJ. A mechanism for the “no-response” phenomenon during anodal stimulation of cardiac tissue. 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Chicago, Oct. 30–Nov. 2, 1997Google Scholar
  22. 22.
    Cheng Y, Mowrey KA, van Wagoner DR, Tchou PJ, Efimov IR. Virtual electrode-induced reexcitation: a mechanism of defibrillation. Circ Res 1999;85:1056–1066PubMedGoogle Scholar
  23. 23.
    Rodriguez B, Trayanova N. Upper limit of vulnerability in a defibrillation model of the rabbit ventricles. J Electrocardiol 2003;36(Suppl):51–56PubMedCrossRefGoogle Scholar
  24. 24.
    Roth BJ, Patel SG. Effects of elevated extracellular potassium ion concentration on anodal excitation of cardiac tissue. J Cardiovasc Electrophysiol 2003;14:1351–1355PubMedCrossRefGoogle Scholar
  25. 25.
    Sidorov VY, Woods MC, Wikswo JP. Effects of elevated extracellular potassium on the stimulation mechanism of diastolic cardiac tissue. Biophys J 2003;84:3470–3479PubMedCrossRefGoogle Scholar
  26. 26.
    Rodriguez B, Tice BM, Eason JC, Aguel F, Trayanova N. Cardiac vulnerability to electric shocks during phase 1A of acute global ischemia. Heart Rhythm 2004;1:695–703PubMedCrossRefGoogle Scholar
  27. 27.
    Mehra R, McMullen M, Furman S. Time dependence of unipolar cathodal and anodal strength-interval curves. PACE 1980;3:526–530PubMedGoogle Scholar
  28. 28.
    Bennett JA, Roth BJ. Time dependence of anodal and cathodal refractory periods in cardiac tissue. PACE 1999;22:1031–1038PubMedGoogle Scholar
  29. 29.
    Janks DL, Roth BJ. Quatrefoil reentry caused by burst pacing. J Cardiovasc Electro-physiol 2006;17:1362–1368CrossRefGoogle Scholar
  30. 30.
    Saypol JM, Roth BJ. A mechanism for anisotropic reentry in electrically active tissue. J Cardiovasc Electrophysiol 1992;3:558–566Google Scholar
  31. 31.
    Lin S-F, Roth BJ, Wikswo JP Jr. Quatrefoil reentry in myocardium: an optical imaging study of the induction mechanism. J Cardiovasc Electrophysiol 1999;10:574–586PubMedCrossRefGoogle Scholar
  32. 32.
    Efimov IR, Gray RA, Roth BJ. Virtual electrodes and de-excitation: new insights into fibrillation induction and defibrillation. J Cardiovasc Electrophysiol 2000;11:339–353PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Deborah L. Janks
    • 1
  • Bradley J. Roth
    • 1
  1. 1.Department of PhysicsOakland UniversityRochesterUSA

Personalised recommendations