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(Circulation. 2000;101:8.)
© 2000 American Heart Association, Inc.
Editorials |
Chaos Theory, Heart Rate Variability, and Arrhythmic Mortality
From Cardiologia, Dipartimento di Medicina, Chirurgia e Odontoiatria, Ospedale San Paolo, Università degli Studi di Milano, Italy.
Correspondence to Prof Federico Lombardi, MD, FESC, Cardiologia, Dipartimento di Medicina, Chirurgia, e Odontoiatria, Ospedale San Paolo, University of Milan, Via A. di Rudini, 8, 20142 Milan, Italy. E-mail federico.lombardi{at}unimi.it
Key Words: Editorials • heart rate • nervous system, autonomic • myocardial infarction
Physiological rhythms are central to life. Some rhythms are maintained throughout life, and even a brief interruption leads to death. Glass and Mackey1
Since the original report by Wolf et al,2 analysis of spontaneous variations of beat-to-beat intervals has become a valuable tool, familiar to clinical cardiologists.
In 1987, Kleiger and coworkers3 published a pioneering work demonstrating that a reduced heart rate variability (HRV) was capable of identifying a subgroup of subjects with increased cardiac mortality after myocardial infarction (MI) and that its predictive value was independent of traditional clinical risk-stratifying factors. It was originally proposed that reduction in HRV might reflect, at the sinus node level, an autonomic imbalance characterized by increased sympathetic and reduced vagal activity. This interpretation was also supported by indirect findings, such as a tendency toward faster heart rates and a smaller day-night heart rate difference observed in these patients.
This initial observation was followed by several reports4 in which time-domain parameters or geometric indices of HRV, measured on Holter recordings, were found to be effective in identifying post-MI patients with increased cardiac mortality. Unfortunately, when sensitivity and specificity were determined, their value was less than expected, with a positive predictive value <30%. The confounding effect of the variety of computation methodologies present in commercial instrumentation also contributed to the limited application of this methodology in routine clinical practice.4
In 1987, spectral analysis of HRV was applied to post-MI
patients.4 5 6 7 8 The complexity of computation was partially
compensated for by the capability of spectral methodology to recognize
and quantify the power of the principal rhythmic components hidden in
the HRV signal. When it was shown4 5 6 7 8 that autonomic
modulation and, in particular, sympathetic and parasympathetic
influences were largely responsible for the low-frequency (LF; 
0.1
Hz) and high-frequency (HF; 0.25 Hz) components of HRV, it was
possible to evaluate alteration in autonomic control in a variety of
cardiovascular diseases4 and, in
particular, after MI. When short-term recordings were
analyzed,4 5 9 2 distinct spectral patterns were
identifiable: the first, in uncomplicated MI, was characterized by a
predominant LF and a smaller HF component, with an LF/HF ratio >2,
indicating a sympathetic activation and reduced vagal tone; the second,
occurring in complicated MI, was instead distinguished by a significant
reduction in total power, a small or absent LF component, and a
relatively predominant HF component, with >60% to 70% of power in
the VLF range. The autospectrum of these patients did not reflect the
clinical picture of neurohumoral sympathetic activation and was similar
to that subsequently reported in congestive heart failure patients in
the most advanced phases of the disease.4 10
When spectral analysis was instead applied to 24-hour
recordings, 90% of the power was present in the
ultralow-frequency (ULF; <0.00033 Hz) and very-low-frequency (VLF;
0.0033 to 0.04 Hz) range, whereas the LF and HF components accounted
for <10% of spectral energy.4 11 Moreover, a significant
reduction in total as well as fractional power distinguished patients
with increased cardiac mortality from those with a better prognosis.
Nevertheless, the sensitivity, specificity, and positive predictive
value of spectral parameters were similar to those of the
SD of the normal R-R interval (SDNN) or triangular
index.4 11 12
What was unexpected was the capability of time- and frequency-domain measures of HRV to predict total cardiac and arrhythmic mortality to a substantially similar extent, particularly when the amount of clinical and experimental evidence on the proarrhythmic role of sympathetic activation and reduced vagal tone was taken into account. Moreover, the interpretation of a markedly reduced LF in high-risk patients was difficult to explain. These and other unanswered questions have generated a new interest in the analysis of original R-R interval time series and in a more comprehensive appraisal of the central and peripheral mechanisms responsible for beat-to-beat fluctuations.
Nonlinear Dynamics
A 24-hour tachogram indicates that heart period fluctuates not only in response to environmental factors, such as posture or physical activity, but also during stationary conditions. This rhythmicity, which may have multiple interactions with other physiological rhythms, such as respiration, may also be affected by small perturbations (eg, premature ventricular contractions, atrioventricular block). As a result, the time series is not constant on time, does not show regular periodicity, and cannot be completely explained by a linear approach.
A nonlinear deterministic approach appears to be more appropriate to describe more complex phenomena, showing that apparently erratic behavior can be generated even by a simple deterministic system with nonlinear structure.13 14
It is therefore not surprising that a specific subtype of nonlinear dynamics, chaos theory and fractals, has recently been applied to the study of HRV signal. Initially it was assumed that chaotic fluctuations could explain cardiac electrical activity during atrial or ventricular fibrillation. Later, it was proposed that the fluctuations of heartbeats during normal sinus rhythm could be partially attributed to deterministic chaos and that a decrease in this type of nonlinear variability could be observed in different cardiovascular diseases and before ventricular fibrillation.4 13 14
Different approaches have been used to show nonlinear dynamic mechanisms either by describing system trajectory in the space, by computing fractal dimensions, or by determining self-similarity properties.13 Of particular interest is the approach based on the assessment of the long-term correlation of R-R interval time series by determination of the long-range power-law correlation. When the power and frequency of HRV are plotted on a bilogarithmic scale, the plot within the 10-4- to 10-2-Hz frequency range, which corresponds to VLF, is described by a straight line with a slope of -1.15 This broadband spectrum indicates a fractal-like process with a long-term dependence, suggesting that fluctuations in R-R interval are related to variations that occurred hundreds of beats earlier and, at least in experimental animals, are dependent on the functional integrity of baroreflex mechanisms.16
In patients after MI,17 the presence of left ventricular dysfunction was associated with a significantly more negative slope of the power-frequency relationship. The exponent of 1/f slope was significantly correlated with extent of left ventricular dysfunction but not with total power. Another index of fractal dimension, D2, was smaller in patients with depressed ejection fraction than in control subjects. Both findings were consistent with the hypothesis that the altered HRV pattern observed in these patients, initially indicated by a marked reduction in total power, was also associated with a loss of complexity of the variability signal. The ability of power-law regression to predict death after MI was first reported by Bigger and coworkers.18 These authors demonstrated that a power-law regression parameter below -1.372 was significantly associated with total cardiac and arrhythmic mortality, with a predictive value similar to that of ULF and VLF power when considered individually but significantly greater when combined with zero correlation power.18
In the present issue of Circulation, Huikuri and coworkers19 report the results of a new application of nonlinear dynamics to the study of HRV signal in post-MI patients enrolled in the DIAMOND study. In addition to 1/f slope, the authors also analyzed short-range correlation of interbeat intervals by means of detrended fluctuation analysis,20 which allows us to compute 2 indices of the fractal scaling properties of short (<11 beats) and intermediate (>11 beats) R-R interval time series.
During a 2-year follow-up period, 114 deaths occurred; 75 were
classified as arrhythmic. Traditional time- and frequency-domain
parameters of HRV as well as indices of nonlinear dynamics
differed significantly between survivors and nonsurvivors. However,
among all R-R interval variability measures, the reduced short-term
scaling 
1 had the best overall independent
accuracy in predicting all-cause mortality after adjustment for other
variables. In addition, this index was the only
parameter that independently predicted arrhythmic death as
well.
These results, which stimulate new interest in the study of HRV, deserve a few considerations.
First, they indicate that the amount of information hidden in the variability signal cannot be completely extracted with a single approach. It is certain that not only the duration of recordings but also the specific pattern of fluctuations present in the variability signal might deserve different modalities of study. When HRV is depressed, as in high-risk post-MI patients, linear components of the variability signal are almost undetectable, as indicated by the absence or marked attenuation of the LF component and by the steeper slope of the power-frequency relation within the VLF range. The present results are in agreement with this hypothesis: lower values of the short scaling exponent (<11 beats) indicate a loss of short-term correlation properties of the R-R interval in the same time scale that corresponds to LF oscillation periodicity. Thus, the alteration of autonomic control mechanisms that characterize acute MI may span from a small reduction in HRV with a relative predominance of LF over HF to a marked attenuation of rhythmic oscillations with a loss of short- and long-term correlation of interbeat intervals.
In addition, the data of Huikuri and coworkers19 suggest that a loss of short-term correlation can predict not only total cardiac but also arrhythmic mortality. It is therefore possible that in high-risk patients, a persistent sympathetic activation and a reduced vagal tone may determine a marked reduction in dynamic complexity of heart rate fluctuations that would make heart period less adaptable and less able to cope with the requirements of a continuously changing environment.14 18
An additional advantage of this methodology is the possibility of performing analysis on raw data without the necessity of time-consuming and often disputable editing. Unfortunately, the model proposed by Huikuri and coworkers19 20 does not appear to be easily exported to clinical practice, in which frequency domain is still almost unconsidered. Nevertheless, only an approach based on an integrated analysis of linear and nonlinear dynamics of interbeat fluctuations seems to be adequate to properly evaluate the HRV signal and to better identify patients at risk. In this context, the short-term scaling exponent stands as one of the most promising new parameters.
Conclusions
Time- and frequency-domain analysis of HRV has been proved effective in evaluating autonomic modulation of the sinus node and in stratifying patients after MI. The marked reduction in HRV observed in high-risk patients seems to be associated with a significant attenuation of the linear and rhythmic components of HRV; thus, a nonlinear approach based on the evaluation of long- and short-term correlation of interbeat intervals seems to be more efficient in detecting the abnormal pattern of R-R fluctuations present in these patients and likely to reflect an abnormal autonomic modulation.
Footnotes
The opinions expressed in this editorial are not necessarily those of the editors or of the American Heart Association.
References
1. Glass L, Mackey MC. From Clocks to Chaos: The Rhythms of Life. Princeton, NJ: Princeton University Press; 1988.
2. Wolf MM, Varigos GA, Hunt D, Sloman JG. Sinus arrhythmia in acute myocardial infarction. Med J Aust. 1978;2:52–53.[Medline] [Order article via Infotrieve]
3. Kleiger RE, Miller JP, Bigger JT, Moss AR, Multicenter Post-Infarction Research Group. Decreased heart rate variability and its association with increased mortality after acute myocardial infarction. Am J Cardiol. 1987;59:256–262.[Medline] [Order article via Infotrieve]
4.
Task Force of the European Society of
Cardiology and the North American Society of Pacing and
Electrophysiology. Heart rate variability: standards of measurement,
physiological interpretation, and clinical use.
Circulation. 1996;93:1043–1065.
5. Lombardi F, Sandrone G, Perpruner S, Sala R, Garimoldi M, Cerutti S, Baselli G, Pagani M, Malliani A. Heart rate variability as an index of sympathovagal interaction after acute myocardial infarction. Am J Cardiol. 1987;60:1239–1245.[Medline] [Order article via Infotrieve]
6.
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.
7.
Pagani M, Lombardi F, Guzzetti S, Rimoldi O, Furlan R,
Pizzinelli P, Sandrone G, Malfatto G, Dell’Orto S, Piccaluga E, Turiel
M, Baselli G, Cerutti S, Malliani A. Power spectral analysis of
heart rate and arterial pressure variabilities as a marker
of sympathovagal interaction in man and conscious dog. Circ
Res. 1986;59:178–193.
8.
Malliani A, Pagani M, Lombardi F, Cerutti S.
Cardiovascular neural regulation explored in the
frequency domain. Circulation. 1991;84:482–492.
9.
Lombardi F, Malliani A, Pagani M, Cerutti S. Heart
rate variability and its sympatho-vagal modulation. Cardiovasc
Res. 1996;32:208–216.
10.
Lombardi F, Mortara A. Heart rate variability and
cardiac failure. Heart. 1998;80:213–214.
11.
Bigger JT, Fleiss J, 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.
12. La Rovere MT, Bigger JT Jr, Marcus FI, Mortara A, Schwartz PJ, for the ATRAMI Investigators. Baroreflex sensitivity and heart-rate variability in prediction of total cardiac mortality after myocardial infarction. Lancet. 1998;351:478–484.[Medline] [Order article via Infotrieve]
13. 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;120:1419–1440.[Medline] [Order article via Infotrieve]
14. Goldberger AL. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Lancet. 1996;347:1312–1314.[Medline] [Order article via Infotrieve]
15. Saul JP, Albrecht P, Berger RD, Cohen RJ. Analysis of long term heart rate variability: methods, 1/f scaling and implications. Computers in Cardiology. Silver Springs, Md: IEEE Computers Society Press; 1988:419–422.
16.
Parati G, Saul JP, Di Rienzo M, Mancia G. Spectral
analysis of blood pressure and heart rate variability in
evaluating cardiovascular regulation.
Hypertension. 1995;25:1276–1286.
17. Lombardi F, Sandrone G, Mortara A, Torzillo D, La Rovere MT, Signorini MG, Cerutti S, Malliani A. Linear and nonlinear dynamics of heart rate variability after acute myocardial infarction with normal and reduced left ventricular ejection fraction. Am J Cardiol. 1996;77:1283–1288.[Medline] [Order article via Infotrieve]
18. Bigger JT Jr, Steinman RC, Rolnitzky LM, Fleiss JL, Albrecht P, Cohen RJ. Power law behavior of RR-interval variability in healthy middle-aged persons, patients with recent acute myocardial infarction, and patients with heart transplants. Circulation. 1996;21:2142–2151.
19.
Huikuri HV, Mäkikallio TH, Peng CK, Goldberger
AL, Hintze U, Møller M, for the Diamond Study Group. Fractal
correlation properties of R-R interval dynamics and mortality in
patients with depressed left ventricular function after an
acute myocardial infarction. Circulation. 2000;101:47–53.
20. Peng CK, Havlin S, Stanley HE, Golberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 1995;5:82–87.[Medline] [Order article via Infotrieve]
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