Complex patterns of abnormal heartbeats

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 66, Issue 3, 2002, Pages

  Schulte Frohlinde, Verena ^a,b   Ashkenazy, Yosef ^a,c   Goldberger, Ary L ^b   Ivanov, Plamen Ch ^a   Costa, Madalena ^b   Morley Davies, Adrian ^d   Stanley, H Eugene ^a   Glass, Leon ^e  

^a Boston University   (United States)

^b BETH ISRAEL DEACONESS MEDICAL CENTER   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d PILGRIM HOSPITAL   (United Kingdom)

^e MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

CARDIAC ARRHYTHMIAS; ELECTROCARDIOGRAM; HEARTBEATS; VENTRICULAR ECTOPIC BEATS;

COMPUTER SIMULATION; DATA PROCESSING; ELECTROCARDIOGRAPHY; ELECTROPHYSIOLOGY; INTERPOLATION; MATHEMATICAL MODELS; OSCILLATORS (ELECTRONIC); POLARIZATION; RISK ASSESSMENT;

CARDIOLOGY;

EID: 37649029529     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.031901     Document Type: Article

References (43)

1. E. N. Prystowsky and G. J. Klein, Cardiac Arrhythmias: An Integrated Approach for the Clinician (McGraw-Hill, New York, 1994).
2. P. F. Cranefield, The Conduction of the Cardiac Impulse: The Slow Response and Cardiac Arrhythmias (Futura Publishing Co., Mount Kisco, NY, 1975).
3. Multicenter Post-infarction Research Group, N. Engl. J. Med. 309, 331 (1983); J. Mukharji, et al., Am. J. Cardiol. 54, 31 (1984); J.T. Bigger Jr., J.L. Fleiss, R. Kleiger, J.P. Miller, and L.M. Rolnitzky, Circulation 69, 250 (1984).
4. Multicenter Post-infarction Research Group, N. Engl. J. Med. 309, 331 (1983); J. Mukharji, et al., Am. J. Cardiol. 54, 31 (1984); J.T. Bigger Jr., J.L. Fleiss, R. Kleiger, J.P. Miller, and L.M. Rolnitzky, Circulation 69, 250 (1984).
5. Multicenter Post-infarction Research Group, N. Engl. J. Med. 309, 331 (1983); J. Mukharji, et al., Am. J. Cardiol. 54, 31 (1984); J.T. Bigger Jr., J.L. Fleiss, R. Kleiger, J.P. Miller, and L.M. Rolnitzky, Circulation 69, 250 (1984).
6. The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, N. Engl. J. Med. 321, 406 (1989); D.S. Echt, P.R. Liebson, B. Mitchell, R.W. Peters, D. Obias-Manno, A.H. Barker, D. Arensberg, A. Baker, L. Friedman, H.L. Greene, M.L. Huther, and D.W. Richardson, ibid. 324, 781 (1991); The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, ibid. 327, 227 (1992).
7. The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, N. Engl. J. Med. 321, 406 (1989); D.S. Echt, P.R. Liebson, B. Mitchell, R.W. Peters, D. Obias-Manno, A.H. Barker, D. Arensberg, A. Baker, L. Friedman, H.L. Greene, M.L. Huther, and D.W. Richardson, ibid. 324, 781 (1991); The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, ibid. 327, 227 (1992).
8. The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, N. Engl. J. Med. 321, 406 (1989); D.S. Echt, P.R. Liebson, B. Mitchell, R.W. Peters, D. Obias-Manno, A.H. Barker, D. Arensberg, A. Baker, L. Friedman, H.L. Greene, M.L. Huther, and D.W. Richardson, ibid. 324, 781 (1991); The Cardiac Arrhythmia Suppression Trial (CAST) Investigators, ibid. 327, 227 (1992).
9. G.K. Moe, J.J. Jalife, W.J. Mueller, and B. Moe, Circulation 56, 968 (1977).
10. M. Courtemanche, L. Glass, M.D. Rosengarten, and A.L. Goldberger, Am. J. Physiol. 257, H693 (1989); M. Courtemanche, L. Glass, J. Bélair, D. Scagliotti, and D. Gordon, Physica D 40, 299 (1989); M. Courtemanche, L. Glass, and M.D. Rosengarten, Ann. N.Y. Acad. Sci. 591, 178 (1990).
11. M. Courtemanche, L. Glass, M.D. Rosengarten, and A.L. Goldberger, Am. J. Physiol. 257, H693 (1989); M. Courtemanche, L. Glass, J. Bélair, D. Scagliotti, and D. Gordon, Physica D 40, 299 (1989); M. Courtemanche, L. Glass, and M.D. Rosengarten, Ann. N.Y. Acad. Sci. 591, 178 (1990).
12. M. Courtemanche, L. Glass, M.D. Rosengarten, and A.L. Goldberger, Am. J. Physiol. 257, H693 (1989); M. Courtemanche, L. Glass, J. Bélair, D. Scagliotti, and D. Gordon, Physica D 40, 299 (1989); M. Courtemanche, L. Glass, and M.D. Rosengarten, Ann. N.Y. Acad. Sci. 591, 178 (1990).
13. N. Ikeda, S. Yoshizawa, and T. Sato, J. Theor. Biol. 103, 439 (1983).
14. J. Jalife, Ch. Antzelevitch, and G.K. Moe, PACE 5, 911 (1982).
15. L. Glass, A.L. Goldberger, and J. Bélair, Am. J. Physiol. 251, H841 (1986); L. Glass, A.L. Goldberger, M. Courtemanche, and A. Shrier, Proc. R. Soc. London, Ser. A 413, 9 (1987).
16. L. Glass, A.L. Goldberger, and J. Bélair, Am. J. Physiol. 251, H841 (1986); L. Glass, A.L. Goldberger, M. Courtemanche, and A. Shrier, Proc. R. Soc. London, Ser. A 413, 9 (1987).
17. S. Kinoshita, G. Konishi, M. Sakurai, and S. Ogawa, J. Electrocardiol. 28, 69 (1995).
18. R. De Paola, H.-X. Wang, and W.I. Norwood, Am. J. Physiol. 265, H1603 (1993); H.-X. Wang, R. De Paola, and W.I. Norwood, Phys. Rev. Lett. 70, 3671 (1993); 71, 3039 (1993).
19. R. De Paola, H.-X. Wang, and W.I. Norwood, Am. J. Physiol. 265, H1603 (1993); H.-X. Wang, R. De Paola, and W.I. Norwood, Phys. Rev. Lett. 70, 3671 (1993); 71, 3039 (1993).
20. R. De Paola, H.-X. Wang, and W.I. Norwood, Am. J. Physiol. 265, H1603 (1993); H.-X. Wang, R. De Paola, and W.I. Norwood, Phys. Rev. Lett. 70, 3671 (1993); 71, 3039 (1993).
21. K. Takayanagi, K. Tanaka, H. Kamishirado, Y. Sakai, T. Fujito, T. Inoue, T. Hayashi, S. Morooka, and N. Ikeda, J. Cardiovasc. Electrophysiol. 11, 168 (2000).
22. D. Sapoznikov and M.H. Luria, J. Electrocardiol. 34, 225 (2001).
23. L.S. Liebovitch, A.T. Todorov, M. Zochowski, D. Scheuerle, L. Colgin, M.A. Woods, K.A. Ellenbogen, J.K. Heere, and R.C. Bernstein, Phys. Rev. E 59, 3312 (1999).
24. K.M. Stein and P. Klingfleld, J. Electrocardiol. 23, S82 (1990).
25. A. Babloyantz and P. Maurer, Phys. Lett. A 221, 43 (1996).
26. V. Schulte-Frohlinde, Y. Ashkenazy, P.Ch. Ivanov, L. Glass, A.L. Goldberger, and H.E. Stanley, Phys. Rev. Lett. 87, 068104 (2001).
27. C.-K. Peng, S. Havlin, H.E. Stanley, and A. Goldberger, Chaos 5, 82 (1995).
28. P.Ch. Ivanov, L.A.N. Amaral, A.L. Goldberger, and H.E. Stanley, Europhys. Lett. 43, 363 (1998).
29. R.M. Berne and M.N. Levy, Cardiovascular Physiology, 6th ed. (C.V. Mosby, St. Louis, 1996).
30. The sinus beat interval is computed from the average of four consecutive sinus beats where concealed sinus beats are in cluded. Since not all sinus beat intervals are equally probable, we normalized each line in each of the gray scale plots by dividing by the corresponding value in the sinus beat interval histogram. In constructing the gray scale plots, we collect all episodes with the same sinus beat interval independent of the time of day at which they occur. For long sinus beat intervals, both in the clinical records and in the models to follow, it often happens that the sinus beat following an ectopic beat is not blocked. Such beats are called interpolated sinus beats. When counting the numbers of sinus beats between ectopic beats, we do not include the interpolated beats in this count.
31. Numerical simulations of the models are carried out for each mechanism with sinus cycle lengths from 0.5 s to 1.25 s. Each sinus cycle length is simulated for 1000 beats and then increased by 1/128 = 0.0078125 s, the typical resolution of clinical records. This amounts to 96000 sinus beats, which span a time period of 83 625 s (that is almost 86 400 s = 24 h). As refractory time we choose θ=0.4 s, a value typically found in clinical data.
32. To realize a random distribution of V beats we choose equally distributed random numbers between 0 and 1, sort them, and then multiply them with the length of the time period under consideration (86 400 s=24 h). We choose to have a probability of V beats of 0.5 per second, and therefore we generate N = 43 200 V beats.
33. A similar function was introduced to explain a phenomenon called AV block in which the passage from the upper chambers to the lower chambers is slowed down in dependence on the time that has elapsed since the last beat.
34. This ratio is similar to the ratio of expressed ectopic or expressed sinus beats which can be derived from a Farey construction: H.-X. Wang, R. De Paola, and W.I. Norwood, Phys. Rev. Lett. 70, 3671 (1993).
35. Y. Murakawa, H. Inoue, T. Koide, A. Nozaki, and T. Sugimoto, Br. Heart J. 68, 589 (1992).
36. In the clinical literature such a coupling effect is referred to as modulated or irregular parasystole.
37. S. Kinoshita, F. Okada, and G. Konishi, Am. Heart J. 124, 816 (1992).
38. L. Glass, C. Graves, G.A. Petrillo, and M.C. Mackey, J. Theor. Biol. 86, 455 (1980); A. Lasota and M.C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics (Springer-Verlag, New York, 1994).
39. L. Glass, C. Graves, G.A. Petrillo, and M.C. Mackey, J. Theor. Biol. 86, 455 (1980); A. Lasota and M.C. Mackey, Chaos, Fractals and Noise: Stochastic Aspects of Dynamics (Springer-Verlag, New York, 1994).
40. S≥0.5). This form is similar to physiologically motivated phase resetting curves [5,8].
41. A. Longtin, Chaos 5, 209 (1995).
42. V. Santinelli, M. De Paola, D. Smimmo, P. Turco, and M. Condorelli, Clin. Cardiol. 10, 49 (1987); S. Kinoshita, G. Konishi, and F. Okada, Cardiol. 81, 100 (1992).
43. V. Santinelli, M. De Paola, D. Smimmo, P. Turco, and M. Condorelli, Clin. Cardiol. 10, 49 (1987); S. Kinoshita, G. Konishi, and F. Okada, Cardiol. 81, 100 (1992).