Linear and non-linear analyses of heart rate variability: A minireview

Cardiovascular Research

Volumn 31, Issue 3, 1996, Pages 371-379

  Mansier, Pascale ^a   Clairambault, Jean ^b   Charlotte, Nathalie ^a   Médigue, Claire ^b   Vermeiren, Christophe ^b   LePape, Gilles ^c   Carré, François ^d   Gounaropoulou, Athanassia ^a   Swynghedauw, Bernard ^a  

^a HÔPITAL LARIBOISIÈRE   (France)

^b INRIA ROCQUENCOURT   (France)

^c UNIVERSITÉ DE TOURS   (France)

^d Inst de Med Légale   (France)

Author keywords

Heart rate variability; Linear analysis; Non linear analysis

Indexed keywords

ATROPINE;

CHAOS; HEART RATE; HEART RATE VARIABILITY; LINEAR SYSTEM; NONLINEAR SYSTEM; PRIORITY JOURNAL; REVIEW;

ANIMALS; ATROPINE; HEART RATE; HUMANS; MICE; MODELS, CARDIOVASCULAR; NONLINEAR DYNAMICS; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 0029918866     PISSN: 00086363     EISSN: None     Source Type: Journal    
DOI: 10.1016/0008-6363(96)00009-0     Document Type: Review

References (64)

1. Angelone A, Coulter NA. Respiratory sinus arrhythmia: a frequency dependent phenomenon. J Appl Physiol 1964;19(3):479-482.
2. Mansier P, Charlotte N, Médigue C, Clairambault J, Vermeiren C, Carré F, Bertin B, Swynghedauw B. Heart rate variability is reduced in transgenic mice expressing human b1-adrenoceptors in atria. Circulation 1994;90:1-267(Abst).
3. Rosenblueth A, Simeone FA. The interrelations of vagal and accelerator effects on the cardiac rate. Am J Physiol 1934;110:42-55.
4. Akselrod S, Gordon D, Ubel FA, Shannon DC, Barger AC, Cohen RJ. Power spectrum analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control. Science 1981;213:220-222.
5. Pomeranz B, Macaulay RJB, Caudill MA, Kutz I, Adam D, Gordon D, Kilborn KM, Barger AC, Shannon DC, Cohen RJ, Benson H. Assessment of autonomic function in humans by heart rate spectral analysis. Am J Physiol 1985;248:H151-153.
6. Appel ML, Berger RD, Saul JP, Smith JM, Cohen RJ. Beat-to-beat variability in cardiovascular variables: noise or music?. J Am Coll Cardiol 1989;14:1139-1148.
7. Randall DC, Brown DR, Raisch RM, Yingling JD, Randall WC. SA nodal parasympathectomy delineates autonomic control of heart rate power spectrum. Am J Physiol 1991;260:H985-988.
8. Wolf M, Varigos G, Hunt D, Sloman J. Sinus arrhythmia in acute myocardial infarction. Med J Aust 1978;2:52-53.
9. Kleiger RE, Miller JP, Bigger JT Jr, Moss, and the Multicenter Postinfarction Research Group. Decreased heart rate variability and its association with increased mortality after acute myocardial infarction. Am J Cardiol 1987;59:256-262.
10. LaRovere MT, Spechhia G, Mortata A, Schwartz PJ. Baroreflex sensitivity, clinical correlates and cardiovascular mortality among patients with a first myocardial infarction: a prospective study. Circulation 1988;78:816-824.
11. Odemuyiwa O, Malik M, Farrell T, Bashir Y, Poloniecki J, Camm J. Comparison of the predictive characteristics of heart rate variability index and left ventricular ejection fraction for all-cause mortality, arrhythmic events and sudden death after acute myocardial infarction. Am J Cardiol 1991;68:434-439.
12. Bigger JT Jr, Fleiss JL, Rolnitzky LM, Steinman RC, Schneider WJ. Time course of recovery of heart period variability after myocardial infarction. J Am Coll Cardiol 1991;18:1643-1649.
13. Bigger JT Jr, Fleiss JL, Rolnitzky LM, Steinman RC. Predicting mortality after myocardial infarction from the response of RR variability to antiarrhythmic drug therapy. J Am Coll Cardiol 1994;23:733-740.
14. Carré F, Lessard Y, Coumel P, Ollivier S, Besse S, Lecarpentier Y, Swynghedauw B. Spontaneous arrhythmias in various models of cardiac hypertrophy and senescence in rats. A Holter monitoring study. Cardiovasc Res 1992;26:698-705.
15. Carré F, Maison-blanche P, Ollivier L, Mansier P, Chevalier B, Vicuna R, Lessard Y, Coumel P, Swynghedauw B. Heart rate variability in two models of cardiac hypertrophy in rats in relation to the new molecular phenotype. Am J Physiol 1994;266:H1872:1878.
16. Bertin B, Mansier P, Makeh I, Briand P, Rostene W, Swynghedauw B, Strosberg AD. Specific atrial overexpression of G-protein coupled human b1-adrenoceptors in transgenic mice. Cardiovasc Res 1993;27:1606-1612.
17. Brosnan J, Mullins J. Transgenic animals in hypertension and cardiovascular research. Exp Nephrol 1993;1:3-12.
18. Field L. Cardiovascular research in transgenic animals. Trends Cardiovasc Med 1992;2:237-245.
19. Koretsky A. Investigation of cell physiology in the animal using transgenic technology. Am J Physiol 1992;262:C261-C275.
20. Glass L, Kaplan D. Time series analysis of complex dynamics in physiology and medicine. Med Prog through Techn 1993;19:115-128.
21. Kitney RI, Rompelman O. The Study of Heart Rate Variability. Oxford: Clarendon Press, 1980.
22. Malliani A, Pagani M, Lombardi F, Cerutti S. Cardiovascular neural regulation explored in the frequency domain. Circulation 1991;84:482-492.
23. Parer WJ, Parer JT, Holbrook RH, Block BSB. Validity of mathematical methods of quantitating fetal heart rate variability. Am J Obstet Gynecol 1985;153:402-409.
24. Bigger JT, Fleiss JL, Steinman RC, Rolnitzky LM, Kleiger RE, Rottman JN. Frequency domain measures of heart period variability and mortality after myocardial infarction. Circulation 1992;85:164-171.
25. Coumel P, Hermida JS, Wennerblöm B, Leenhardt A, Maisonblanche P, Cauchemez B. Heart rate variability in left ventricular hypertrophy and heart failure and the effects of beta-blockade. A non-spectral analysis of heart rate variability in the frequency domain and in the time domain. Eur Heart J 1991;12:412-422.
26. Novak P, Novak V. Time/frequency mapping of the heart rate, blood pressure and respiratory signals. Med Biol Eng Comput 1993;31:103-110.
27. Novak V, Novak P, de Champlain J, Le Blanc AR, Martin R, Nadeau R. Influence of respiration on heart rate and blood pressure fluctuations. J Appl Physiol 1993;74(2):617-626.
28. Mandelbrot BB. The Fractal Geometry of Nature. New York: Freeman, 1983.
29. Keipes M, Ries F, Dicato M. Of the British coastline and the interest of fractals in medicine. Biomed Pharmac 1993;47:409-415.
30. Goldberger AL, Rigney DR, West BJ. Chaos and fractals in human physiology. Sci Am 1990;46:42-51.
31. Glenny RW, Robertson HT, Yamashiro S, Bassingthwaighte. Applications of fractal analysis to physiology. J Appl Physiol 1991;70:2351-2367.
32. Kobayashi M, Musha T. 1/f fluctuation of heartbeat period. IEEE Trans Biomed Eng 1982;29:456-457.
33. Butler GC, Yamamoto Y, Xing HC, Northey DR, Hughson RL. Heart rate variability and fractal dimension during orthostatic challenges. J Appl Physiol 1993;75:2602-2612.
34. Yamamoto Y, Hughson RL. Extracting fractal components from time series. Physica D 1993;68:250-264.
35. Yamamoto Y, Hughson RL. On the fractal nature of heart rate variability in humans: effects of data length and β-adrenergic blockade. Am J Physiol 1994;268:R40-R49.
36. Bergé P, Pomeau Y, Vidal C. L'ordre dans le Chaos. Paris: Hermann, 1984.
37. Baker GL, Gollub JP. Chaotic Dynamics, an Introduction. Cambridge University Press, 1990.
38. Schuster HG. Deterministic Chaos. Weinheim, Germany: VCH Verlag, 1989.
39. Drazin PG. Nonlinear Systems. Cambridge University Press, 1992.
40. Ruelle D, Takens F. On the nature of turbulence. Commun Math Phys 1971;20:167-192 and 23:343-344.
41. Li T, Yorke J. Period three implies chaos. Am Math Monthly 1975;82:985-992.
42. Denton TA, Diamond GA, Helfant RH, Khan S, Karagueuzian H. Fascinating rhythm: a primer on chaos theory and its application to cardiology. Am Heart J 1990;6:1419-1440.
43. Skinner JE, Molnar M, Vybiral T, Mitra M. Application of chaos theory to biology and medicine. Int Physiol Behav Sci 1992;27:39-53.
44. Elbert T, Ray WJ, Kowalik ZJ, Skinner JE, Graf KE, Bimbaumer N. Chaos and physiology: deterministic chaos in excitable cell assemblies. Physiol Rev 1994;74:1-47.
45. Schechtman VL, Raetz SL, Harper RK, Garfinkel A, Wilson AJ, Southall DP, Harper RM. Dynamic analysis of cardiac RR intervals in normal infants and in infants who subsequently succumbed to the sudden infant death syndrome. Pediatr Res 1992;31:606-614.
46. Copie X, Le Heuzey JY, Iliou MC, Khouri R, Lavergne T, Pousset P, Guize L. Correlation between time-domain measures of heart rate variability and scatterplots in post-infarction patients. Pace 1995; in press.
47. Zbilut JP, Mayer-Kress G, Geist K. Dimensional analysis of heart rate variability in heart transplant recipients. Math Biosci 1988;90:49-70.
48. Eckmann JP, Ruelle D. Ergodic theory of chaos and strange attractors. Rev Modern Phys 1985;57:617-656.
49. Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D 1983;9:189-208.
50. Ding M, Grebogi C, Ott E, Sauer T, Yorke JA. Estimating correlation dimension from a chaotic time series: when does plateau onset occur? Physica D 1993;69:404-424.
51. Kruel Th-M, Freund A. SCOUNT: a program to calculate the correlation and information dimension from attractors by the method of sphere-counting. 1986-1993. Documentation to the program (1986, last revised 1993) available on internet by anonymous ftp from the archive lyapunov.ucsd.edu.
52. Fraedrich K, Wang R. Estimating the correlation dimension of an attractor from noisy and small data sets based on re-embedding. Physica D 1993;65:373-398.
53. Eckmann JP, Ruelle D. Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems. Physica D 1992;56:185-187.
54. Wolf A, Swift JB, Swinney HL, Vastano JA. Determining Lyapunov exponents from a time series. Physica D 1985;16:285-317.
55. Eckmann JP, Oliffson Kamphorst S, Ruelle D, Ciliberto S. Lyapunov exponents from time series. Phys Rev A 1986;34:4971-4979.
56. Briggs K. An improved method for estimating Lyapunov exponents of chaotic time series. Physics Lett A 1990;151:27-36.
57. Brown R, Bryant P, Arbanel HDI. Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys Rev A 1991;43:2787-2806.
58. Kruel TM, Eiswirth M, Schneider FW. Computation of Lyapunov spectra: effect of interactive noise and application to a chemical oscillator. Physica D 1993;63:117-137.
59. Pincus SM, Goldberger AL. Physiological time-series analysis: what does regulatory quantify? Am J Physiol 1994;266:H1643-H1656.
60. Pincus SM, Cummins TR, Haddad GG. Heart rate control in normal and aborted-SIDS infants. Am J Physiol 1993;264:R638-646.
61. Sugihara G, May RM. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 1990;344:734-741.
62. Theiler J, Eubank S, Longtin A, Galdrikian B. Testing for non-linearity in time series: the method of surrogate data. Physica D 1992;58:77-94.
63. Skinner JE, Carpeggiani C, Landisman CE, Fulton KW. Correlation dimension of heartbeat intervals is reduced in conscious pigs in myocardial ischemia. Circ Res 1991;68:966-976.
64. Yamamoto Y, Hughson RL, Sutton JR, Houston CS, Cymerman A, Fallen EL, Kamath MV. Operation Everest II: an indication of deterministic chaos in human heart rate variability at simulated extreme altitude. Biol Cybern 1993;69:205-212.