Relationship between detrended fluctuation analysis and spectral analysis of heart-rate variability.

The recently-introduced technique of detrended fluctuation analysis (DFA) for heart-rate variability appears to yield improved prognostic power in cardiovascular disease through calculation of the fractal scaling exponent alpha. However, the physiological meaning of alpha remains unclear. In DFA, the signal is segmented into lengths from 4 to 64 beats. For each segmentation length (n), the individual segments are cumulated, detrended and the sum of the squares (F2) of residuals calculated. Alpha is the slope of log(F) against log(n). We show mathematical equivalence between alpha calculated by DFA and by a novel alternative method using frequency-weighted power spectra. We show F2 (and thus alpha) can be obtained from a frequency-weighted power spectrum without DFA. To do this, we cumulate and detrend the Taylor series of individual Fourier components. F2 is found to depend on the relationship between the signal period and segment length. F2 can therefore be expressed in terms of frequency-weighted power spectra. From this, the alpha coefficient of DFA can then be described in power-spectral terms, which facilitates exploration of its physiological basis. We confirm these findings using samples from 20 healthy volunteers and 40 patients with heart failure.

[1]  D. T. Kaplan,et al.  Aging and the complexity of cardiovascular dynamics. , 1991, Biophysical journal.

[2]  D. Eckberg.  Sympathovagal balance: a critical appraisal. , 1997, Circulation.

[3]  A L Goldberger,et al.  Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infarction. , 2000, Circulation.

[4]  C. Peng,et al.  Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory. , 1999, Circulation.

[5]  M. Turiel,et al.  Power Spectral Analysis of Heart Rate and Arterial Pressure Variabilities as a Marker of Sympatho‐Vagal Interaction in Man and Conscious Dog , 1986, Circulation research.

[6]  H. Huikuri,et al.  Is abnormal heart rate variability a specific feature of congestive heart failure? , 2001, The American journal of cardiology.

[7]  Peter J. Schwartz,et al.  Baroreflex Sensitivity and Heart Rate Variability in the Identification of Patients at Risk for Life-Threatening Arrhythmias Implications for Clinical Trials , 2001 .

[8]  V. Yeragani,et al.  Effect of age on long-term heart rate variability. , 1997, Cardiovascular research.

[9]  A. Antoniadis,et al.  Maximal blood lactate level acts as a major discriminant variable in exercise testing for coronary artery disease detection in men. , 1996, Circulation.

[10]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[11]  A. Stefanovska,et al.  Spectral components of heart rate variability determined by wavelet analysis. , 2000, Physiological measurement.

[12]  D. Levy,et al.  Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics. , 1997, Circulation.

[13]  P. Ponikowski,et al.  Very-low-frequency oscillations in heart rate and blood pressure in periodic breathing: role of the cardiovascular limb of the hypoxic chemoreflex. , 2000, Clinical science.

[14]  Simon C Malpas,et al.  The rhythmicity of sympathetic nerve activity , 1998, Progress in Neurobiology.

[15]  Jacob Levitan,et al.  COMPARISON OF RECENT METHODS OF ANALYZING HEART RATE VARIABILITY , 2000 .

[16]  J. Bigger,et al.  Baroreflex sensitivity and heart-rate variability in prediction of total cardiac mortality after myocardial infarction , 1998, The Lancet.

[17]  A. Malliani,et al.  Cardiovascular Neural Regulation Explored in the Frequency Domain , 1991, Circulation.

[18]  C L Feldman,et al.  Determinants of heart rate variability. , 1996, Journal of the American College of Cardiology.

[19]  G D Pinna,et al.  Abnormal awake respiratory patterns are common in chronic heart failure and may prevent evaluation of autonomic tone by measures of heart rate variability. , 1997, Circulation.

[20]  H V Huikuri,et al.  Comparability of nonlinear measures of heart rate variability between long- and short-term electrocardiographic recordings. , 2001, The American journal of cardiology.

[21]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.