Cardiac Oscillations and Arrhythmia Analysis

  • Leon GlassEmail author
Part of the Topics in Biomedical Engineering International Book Series book series (ITBE)


In current medical practice, the diagnosis and treatment of cardiac arrhythmias in people is carried out without mathematical analysis of the underlying mechanisms of the underlying rhythm. In this article I describe how nonlinear dynamics is being used to formulate mathematical models of cardiac arrhythmias, and to demonstrate the ways the mathematics can be used to predict the changes in rhythms that occur as physiological parameters vary. In spatially heterogeneous cardiac tissue culture, a number of different patterns of spatiotemporal activity can be found, including propagating plane waves, rotating spiral waves, and spiral waves that spontaneously initiate and terminate. These paroxysmal patterns are similar to the paroxysmal rhythms observed during cardiac arrhythmias in people. Mathematical analyses of cardiac arrhythmias can be used to determine automatically if certain arrhythmias, such as atrial fibrillation, are present in individuals. Attempts are also underway to develop new methods to analyze normal and abnormal cardiac activity in patients to better assess the risk of fatal arrhythmias before they occur.


Cardiac Arrhythmia Action Potential Duration Excitable Medium Spiral Wave Ectopic Beat 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

6. References

  1. 1.
    Goldberger AL, Goldberger E. 1994. Clinical electrocardiography: a simplified approach, 5th ed. Mosby, St. Louis.Google Scholar
  2. 2.
    van der Pol B, van der Mark J. 1928. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Philos Mag 6:763–765.Google Scholar
  3. 3.
    Roberge FA, Nadeau RA. 1969. The nature of Wenckebach cycles. Can J Physiol Pharmacol 47:695–704.PubMedGoogle Scholar
  4. 4.
    Keener JP. 1981. On cardiac arrhythmia: AV conduction block. J Math Biol 12:215–225.Google Scholar
  5. 5.
    Shrier A, Dubarsky H, Rosengarten M, Guevara MR, Nattel S, Glass L. 1987. Prediction of complex atrioventricular conduction rhythms in humans with use of the atrioventricular nodal recovery curve. Circulation 76:1196–1205.PubMedGoogle Scholar
  6. 6.
    Glass L, Guevara MR, Shrier A. 1987. Universal bifurcations and the classification of cardiac arrhythmias. Ann NY Acad Sci 504:168–178.PubMedCrossRefGoogle Scholar
  7. 7.
    Guevara MR. 1991. Iteration of the human atrioventricular (AV) nodal recovery curve predicts many rhythms of AV block. In Theory of heart: biomechanics, biophysics, and nonlinear dynamics of cardiac function, pp. 313–358. Ed. L Glass, P Hunter, A McCulloch. Springer, New York.Google Scholar
  8. 8.
    Talajic M, Papadatos D, Villemaire C, Glass L, Nattel S. 1991. A unified model of atrioventricular nodal conduction predicts dynamic changes in Wenckebach periodicity. Circ Res 68:1280–1293.PubMedGoogle Scholar
  9. 9.
    Sun J, Amellal F, Glass L, Billette J. 1995. Alternans and period-doubling bifurcations in atrioventricular nodal conduction. J Theor Biol 173:79–91.PubMedCrossRefGoogle Scholar
  10. 10.
    Christini DJ, Stein KM, Markowitz SM, Mittal S, Slotwiner DJ, Scheiner MA, Iwai S, Lerman BB. 2001. Complex AV-nodal dynamics during ventricular-triggered atrial pacing in humans. Am J Physiol 281:H865–H872.Google Scholar
  11. 11.
    Glass L, Goldberger A, Bélair J. 1986. Dynamics of pure parasystole. Am J Physiol 251:H841–H847.PubMedGoogle Scholar
  12. 12.
    Castellanos A, Fernandez P, Moleiro F, Interian A, Myerburg R. 1991. Symmetry, broken symmetry, and restored symmetry of apparent pure ventricular parasystole. Am J Cardiol 68:256–259.PubMedCrossRefGoogle Scholar
  13. 13.
    Slater N. 1967. Gaps and steps for the sequence n2 mod 1. Proc Camb Phil Soc 63:1115–1123.Google Scholar
  14. 14.
    Moe GK, Jalife J, Mueller WJ, Moe B. 1977. A mathematical model of parasystole and its application to clinical arrhythmias. Circulation 56:968–979.PubMedGoogle Scholar
  15. 15.
    Ikeda N, Yoshizawa S, Sato T. 1983. Difference equation model of ventricular parasystole as an interaction of pacemakers based on the phase response curve. J Theor Biol 103:439–465.PubMedCrossRefGoogle Scholar
  16. 16.
    Courtemanche M, Glass L, Bélair J, Scagliotti D, Gordon D. 1989. A circle map in a human heart. Physica D 40:299–310.CrossRefGoogle Scholar
  17. 17.
    Schulte-Frohlinde V, Ashkenazy Y, Ivanov PCh, Glass L, Goldberger AL, Stanley HE. 2001. Noise effects on the complex patterns of abnormal heartbeats. Phys Rev Lett 87:068104.PubMedCrossRefGoogle Scholar
  18. 18.
    Josephson ME. 2002. Clinical cardiac electrophysiology: techniques and interpretations. Williams and Wilkins, Philadelphia.Google Scholar
  19. 19.
    Rudy Y. 1995. Reentry: insights from theoretical simulations in a fixed pathway. J Cardiovasc Electrophysiol 6:294–312.PubMedCrossRefGoogle Scholar
  20. 20.
    Frame LH, Simpson MB. 1988. Oscillations of conduction, action potential duration, and refractoriness: a mechanism for spontaneous termination of reentrant tachycardias. Circulation 78:1277–1287.PubMedGoogle Scholar
  21. 21.
    Quan WL, Rudy Y. 1991. Termination of reentrant propagation by a single stimulus: a model study. Pacing Clin Electrophysiol 14:1700–1706.PubMedCrossRefGoogle Scholar
  22. 22.
    Courtemanche M, Glass L, Keener JP. 1993. Instabilities of a propagating pulse in a ring of excitable media. Phys Rev Lett 70:2182–2185.CrossRefPubMedGoogle Scholar
  23. 23.
    Vinet A, Roberge FA. 1994. The dynamics of sustained reentry in a ring model of cardiac tissue. Annu Biomed Eng 22:568–591.CrossRefGoogle Scholar
  24. 24.
    Glass L, Josephson ME. 1995. Resetting and annihilation of reentrant abnormally rapid heartbeat. Phys Rev Lett 75:2059–2063.CrossRefPubMedGoogle Scholar
  25. 25.
    Sinha S, Stein KM, Christini DJ. 2002. Critical role of inhomogeneities in pacing termination of cardiac reentry. Chaos 12:893–902.PubMedCrossRefGoogle Scholar
  26. 26.
    Comtois A, Vinet A. 2002. Resetting and annihilation of reentrant activtiy in a model of a onedimensional loop of ventricular tissue. Chaos 12:903–923.PubMedCrossRefGoogle Scholar
  27. 27.
    Glass L, Nagai Y, Hall K, Talajic M, Nattel S. 2002. Predicting the entrainment of reentrant cardiac waves using phase resetting curves. Phys Rev E 65:021908.CrossRefGoogle Scholar
  28. 28.
    Stevenson WG, Delacretaz E. 2000. Strategies for catheter ablation of scar-related ventricular tachycardia. Curr Cardiol Rep 2:537–544.PubMedCrossRefGoogle Scholar
  29. 29.
    Stein KM, Markowitz SM, Mittal S, Slotwiner DJ, Iwai S, Lerman BB. 2002. Anatomic determinants of atrial arrhythmias: new insights from three-dimensional mapping. Chaos 12:740–746.PubMedCrossRefGoogle Scholar
  30. 30.
    Gray RA, Jalife J, Panfilov A, Baxter WT, Cabo C, Davidenko JM, Pertsov AM. 1995. Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart. Circulation 91:2454–2469.PubMedGoogle Scholar
  31. 31.
    Winfree AT. 2001. The geometry of biological time, 2nd ed. Springer, New York.Google Scholar
  32. 32.
    Fenton FH, Cherry EM, Hastings HM, Evans SJ. 2002. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity. Chaos 12:852–892.PubMedCrossRefGoogle Scholar
  33. 33.
    Qu Z, Kil J, Xie F, Garfinkel A, Weiss JN. 2000. Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation. Biophys J 78:2761–2775.PubMedCrossRefGoogle Scholar
  34. 34.
    Virag N, Jacquemet V, Henriquez CS, Zozor S, Blanc O, Vesin J-M, Pruvot E, Kappenberger L. 2002. Study of atrial arrhythmias in a computer model based on magnetic resonance images of human atria. Chaos 12:754–763.PubMedCrossRefGoogle Scholar
  35. 35.
    Kovacs SJ, McQueen DM, Peskin CS. 2001. Modeling cardiac fluid dynamics and diastolic function. Phil Trans R Soc Lond A 359:1299–1314.CrossRefGoogle Scholar
  36. 36.
    Bub G, Glass L, Shrier A. 1998. Bursting calcium rotors in cultured cardiac myocyte monolayers. Proc Natl Acad Sci USA 123:10283–10287.CrossRefGoogle Scholar
  37. 37.
    Nagai Y, González H, Shrier A, Glass L. 2000. Paroxysmal starting and stopping of circulating waves in excitable media, Phys Rev Lett 84:4248–4251.PubMedCrossRefGoogle Scholar
  38. 38.
    Bub G, Tateno K, Shrier A, Glass L. 2003. Spontaneous initiation and termination of complex rhythms in cardiac cell culture. J Cardiovasc Electrophysiol 14:S229–S236.PubMedCrossRefGoogle Scholar
  39. 39.
    Hwang S, Yea K, Lee KJ. 2004. Regular and alternant spiral waves of contractile motion on rat ventricle cell cultures. Phys Rev Lett 92:198103.PubMedCrossRefGoogle Scholar
  40. 40.
    Bub G, Shrier A, Glass L. 2002. Spiral wave generation in heterogeneous excitable media. Phys Rev Lett 88:058101.PubMedCrossRefGoogle Scholar
  41. 41.
    Hohnloser H, Klingenheben T, Bloomfield D, Dabbous O, Cohen RJ. 2003. Usefulness of microvolt T-wave alternans for prediction of ventricular tachyarrhythmic events in patients with dilated cardiomyopathy: results from a prospective observational study. J Am Coll Cardiol 41:2220–2224.PubMedCrossRefGoogle Scholar
  42. 42.
    Verrier RL, Tolat AV, Josephson ME. 2003. T-wave alternans for arrhythmia risk stratification in patients with idiopathic dilated cardiomyopathy. J Am Coll Cardiol 41:2225–2227.PubMedCrossRefGoogle Scholar
  43. 43.
    Guevara MR, Ward G, Shrier A, Glass L. 1984. Electrical alternans and period-doubling bifurcations. IEEE Comput Cardiol 11:167–170.Google Scholar
  44. 44.
    Goldberger AL, Amaral LA, Hausdorff JM, Ivanov PCh, Peng CK, Stanley HE. 2002. Fractal dynamics in physiology: alterations with disease and aging. Proc Natl Acad Sci USA 99(suppl 1):2466–2472.PubMedCrossRefGoogle Scholar
  45. 45.
    La Rovere MT, Pinna GD, Maestri R, Mortara A, Capomolla S, Febo O, Ferrari R, Franchini M, Gnemmi M, Opasich C, Riccardi PG, Traversi E, Cobelli F. 2003. Short-term heart rate variability strongly predicts sudden cardiac death in chronic heart failure patients. Circulation 107:565–570.PubMedCrossRefGoogle Scholar
  46. 46.
    Schulte-Frohlinde V, Ashkenazy Y, Goldberger AL, Ivanov PCh, Costa M, Morley-Davies A, Stanley HE, Glass L. 2002. Complex patterns of abnormal heartbeats. Phys Rev E 66:031901.CrossRefGoogle Scholar
  47. 47.
    Krogh-Madsen T, Glass L, Doedel EJ, Guevara MR, 2004. Apparent discontinuities in the phase-setting response of cardiac pacemakers. J Theor Biol 230:499–519.PubMedCrossRefGoogle Scholar
  48. 48.
    Tateno K, Glass L. 2001. Automatic detection of atrial fibrillation using the coefficient of variation and density histograms of RR and )RR intervals. Med Biol Eng Comput 39:664–671.PubMedCrossRefGoogle Scholar
  49. 49.
    Trayanova N, Eason J. 2002. Shock-induced arrhythmogenesis in the myocardium. Chaos 12:962–972.PubMedCrossRefGoogle Scholar
  50. 50.
    Hall K, Christini DJ, Tremblay M, Collins JJ, Glass L, Billette J. 1997. Dynamic control of cardiac alternans. Phys Rev Lett 78:4518–4521.CrossRefGoogle Scholar
  51. 51.
    Christini DJ, Stein KM, Markowitz SM, Mittal S, Slotwiner DJ, Scheiner MA, Iwai S, Lerman BB. 2001. Nonlinear-dynamical arrhythmia control in humans. Proc Natl Acad Sci USA 98:5827–5832.PubMedCrossRefGoogle Scholar
  52. 52.
    Garfinkel A, Spano ML, Ditto WL, Weiss JN. 1992. Controlling cardiac chaos. Science 257:1230–1235.PubMedCrossRefGoogle Scholar
  53. 53.
    Gauthier DJ, Hall GM, Oliver RA, Dixon-Tulloch EG, Wolf PD, Bahar S. 2002. Progress toward controlling in vivo fibrillating sheep atria using a nonlinear-dynamics-based-closed-loop feedback method. Chaos 12:952–962.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Inc. 2006

Authors and Affiliations

  1. 1.Department of PhysiologyMcGill UniversityMontreal

Personalised recommendations