Ary L. Goldberger

Multifractality in Human Heartbeat Dynamics.

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report onevidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

Fractal Correlation Properties of R-R Interval Dynamics and Mortality in Patients With Depressed Left Ventricular Function After an Acute Myocardial Infarction

BACKGROUND Preliminary data suggest that the analysis of R-R interval variability by fractal analysis methods may provide clinically useful information on patients with heart failure. The purpose of this study was to compare the prognostic power of new fractal and traditional measures of R-R interval variability as predictors of death after acute myocardial infarction. METHODS AND RESULTS Time and frequency domain heart rate (HR) variability measures, along with short- and long-term correlation (fractal) properties of R-R intervals (exponents alpha(1) and alpha(2)) and power-law scaling of the power spectra (exponent beta), were assessed from 24-hour Holter recordings in 446 survivors of acute myocardial infarction with a depressed left ventricular function (ejection fraction </=35%). During a mean+/-SD follow-up period of 685+/-360 days, 114 patients died (25.6%), with 75 deaths classified as arrhythmic (17.0%) and 28 as nonarrhythmic (6.3%) cardiac deaths. Several traditional and fractal measures of R-R interval variability were significant univariate predictors of all-cause mortality. Reduced short-term scaling exponent alpha(1) was the most powerful R-R interval variability measure as a predictor of all-cause mortality (alpha(1) <0.75, relative risk 3.0, 95% confidence interval 2.5 to 4.2, P<0.001). It remained an independent predictor of death (P<0.001) after adjustment for other postinfarction risk markers, such as age, ejection fraction, NYHA class, and medication. Reduced alpha(1) predicted both arrhythmic death (P<0.001) and nonarrhythmic cardiac death (P<0.001). CONCLUSIONS Analysis of the fractal characteristics of short-term R-R interval dynamics yields more powerful prognostic information than the traditional measures of HR variability among patients with depressed left ventricular function after an acute myocardial infarction.

What is physiologic complexity and how does it change with aging and disease

1. IntroductionA defining but elusive feature of physiologic systems istheir daunting complexity. This complexity arises from theinteraction of a myriad of structural units and regulatoryfeedback loops that operate over a wide range of temporaland spatial scales, enabling the organism to adapt to thestresses of everyday life. Quantifying and modeling theremarkable and often bewildering repertoire of behaviorsexhibited by living organisms is one of the major challengesof contemporary science [4,7]. The combination of nonlin-earity and nonstationarity, more the rule than the exceptionin the output of physiologic systems, poses a major chal-lenge to conventional biostatistical assessments and stan-dard reductionist modeling stratagems. To describe andquantify the mechanisms of these “nonhomeostatic” behav-iors, investigators have employed new techniques derivedfrom complexity theory, including fractal analysis and non-linear dynamics. The appropriate application and interpre-tation of such metrics, however, remains incompletely ex-plored. What is clear is that reliance on any single test maygive a misleading representation of physiological complexity.In this issue, Vaillancourt and Newell critique and sug-gest modifications to a general dynamical model of patho-physiology that we and others have elaborated over the pasttwo decades [5,6,8,10,13,14,16,20,21,27]. The theory ofcomplexity loss in aging and disease, as currently formu-lated, has two central postulates:1. The output of healthy systems, under certain param-eter conditions, reveals a type of complex variabilityassociated with long-range (fractal) correlations,along with distinct classes of nonlinear interactions;2. This type of multi-scale, nonlinear complexity breaksdown with aging and disease, reducing the adaptivecapabilities of the individual.The term nonlinear applies to systems whose compo-nents interact in a non-additive way. Nonlinear couplingmay lead to an extraordinary range of dynamics, includingdifferent classes of abrupt changes, (such as bifurcations),deterministic chaos, nonlinear phase transitions, pacemakerentrainment and resetting, stochastic resonance, wave phe-nomena (including spiral waves, solitons, and scroll waves),emergent phenomena, and certain types of fractal scaling.Understanding the specific classes of nonlinear interactionsseen in healthy physiology and characterizing their pertur-bations with aging and disease is just beginning [4,16,27].The term fractal applies to complex-like objects, whichmay be generated by stochastic or nonlinear deterministicmechanisms. Fractal objects show self-similarity (scale-in-variance), such that the smaller-scale structure resemblesthe larger-scale form [10]. Examples in anatomy include theHis-Purkinje network and the tracheobronchial tree. Thefractal concept also extends to complex processes that lacka characteristic, or a single, time scale. Fractal processesgenerate fluctuations over multiple time scales, and theirfrequency spectra typically show an inverse power-law (1/f-like) scaling pattern. Of particular interest is a class offractal processes that demonstrates long-range correlations.This type of “memory” effect has been identified in thefluctuations of the healthy heartbeat, as well as in the inter-stride interval fluctuations in the walking patterns of healthyadults [14,15,21,22].A central caveat when applying concepts and techniquesfrom complexity theory to biomedicine is the recognition

Spectral characteristics of heart rate variability before and during postural tilt. Relations to aging and risk of syncope.

Fourier analysis of heart rate (HR) may be used to characterize overall HR variability as well as low- and high-frequency components attributable to sympathetic and vagal influences, respectively. We analyzed HR spectral characteristics of 12 healthy young (18-35 years) and 10 healthy old (71-94 years) subjects before and during 60 degrees head-up tilt. Total spectral power in the 0.01-0.40-Hz frequency range and low-frequency (0.06-0.10 Hz) and high-frequency (0.15-0.40 Hz) components of the HR power spectrum were significantly lower in old than in young subjects in supine and upright positions. To characterize and compare overall HR variability in young and old subjects, we computed the regression lines relating the log amplitude to the log frequency of the supine HR spectra (l/fx plots). The regression lines for old subjects were lower and steeper (mean slope, -0.78 [5%, 95% confidence limits (CL), -0.73, -0.83]) than in young (mean slope, -0.67 [CL, -0.62, -0.72]), indicating not only reduced overall spectral amplitude but also relatively greater attenuation of high-frequency HR components in the old subjects. This finding illustrates a novel way to quantify the loss of autonomic influences on HR regulation as a function of age. During postural tilt, HR variability was unchanged in the old subjects. For the entire group of young subjects, total HR variability increased during tilt. Six young subjects developed vasovagal syncope during tilt, enabling us to examine differences in the HR spectra of these subjects while they were asymptomatic before syncope.(ABSTRACT TRUNCATED AT 250 WORDS)

Increased gait unsteadiness in community-dwelling elderly fallers

OBJECTIVE To test the hypothesis that quantitative measures of gait unsteadiness are increased in community-dwelling elderly fallers. STUDY DESIGN Retrospective, case-control study. SETTING General community. PARTICIPANTS Thirty-five community-dwelling elderly subjects older than 70 years of age who were capable of ambulating independently for 6 minutes were categorized as fallers (age, 82.2 +/- 4.9 yrs [mean +/- SD]; n = 18) and nonfallers (age, 76.5 +/- 4.0 yrs; n = 17) based on history; 22 young (age, 24.6 +/- 1.9 yrs), healthy subjects also participated as a second reference group. MAIN OUTCOME MEASURES Stride-to-stride variability (standard deviation and coefficient of variation) of stride time, stance time, swing time, and percent stance time measured during a 6-minute walk. RESULTS All measures of gait variability were significantly greater in the elderly fallers compared with both the elderly nonfallers and the young subjects (p < .0002). In contrast, walking speed of the elderly fallers was similar to that of the nonfallers. There were little or no differences in the variability measures of the elderly nonfallers compared with the young subjects. CONCLUSIONS Stride-to-stride temporal variations of gait are relatively unchanged in community-dwelling elderly nonfallers, but are significantly increased in elderly fallers. Quantitative measurement of gait unsteadiness may be useful in assessing fall risk in the elderly.

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

BACKGROUND Despite much recent interest in quantification of heart rate variability (HRV), the prognostic value of conventional measures of HRV and of newer indices based on nonlinear dynamics is not universally accepted. METHODS AND RESULTS We have designed algorithms for analyzing ambulatory ECG recordings and measuring HRV without human intervention, using robust methods for obtaining time-domain measures (mean and SD of heart rate), frequency-domain measures (power in the bands of 0.001 to 0.01 Hz [VLF], 0.01 to 0.15 Hz [LF], and 0.15 to 0.5 Hz [HF] and total spectral power [TP] over all three of these bands), and measures based on nonlinear dynamics (approximate entropy [ApEn], a measure of complexity, and detrended fluctuation analysis [DFA], a measure of long-term correlations). The study population consisted of chronic congestive heart failure (CHF) case patients and sex- and age-matched control subjects in the Framingham Heart Study. After exclusion of technically inadequate studies and those with atrial fibrillation, we used these algorithms to study HRV in 2-hour ambulatory ECG recordings of 69 participants (mean age, 71.7+/-8.1 years). By use of separate Cox proportional-hazards models, the conventional measures SD (P<.01), LF (P<.01), VLF (P<.05), and TP (P<.01) and the nonlinear measure DFA (P<.05) were predictors of survival over a mean follow-up period of 1.9 years; other measures, including ApEn (P>.3), were not. In multivariable models, DFA was of borderline predictive significance (P=.06) after adjustment for the diagnosis of CHF and SD. CONCLUSIONS These results demonstrate that HRV analysis of ambulatory ECG recordings based on fully automated methods can have prognostic value in a population-based study and that nonlinear HRV indices may contribute prognostic value to complement traditional HRV measures.

Aging and the complexity of cardiovascular dynamics.

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Fractal analysis of heart rate dynamics as a predictor of mortality in patients with depressed left ventricular function after acute myocardial infarction

A number of new methods have been recently developed to quantify complex heart rate (HR) dynamics based on nonlinear and fractal analysis, but their value in risk stratification has not been evaluated. This study was designed to determine whether selected new dynamic analysis methods of HR variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction <35%) after an AMI. By the end of 4-year follow-up, 72 patients (45%) had died and 87 (55%) were still alive. Short-term scaling exponent alpha (1.07 +/- 0.26 vs 0.90 +/- 0.26, p <0.001) and power-law slope beta (-1.35 +/- 0.23 vs -1.44 +/- 0.25, p <0.05) differed between survivors and those who died, but none of the traditional HR variability measures differed between these groups. Among all analyzed variables, reduced scaling exponent alpha (<0.85) was the best univariable predictor of mortality (relative risk 3.17, 95% confidence interval 1.96 to 5.15, p <0.0001), with positive and negative predictive accuracies of 65% and 86%, respectively. In the multivariable Cox proportional hazards analysis, mortality was independently predicted by the reduced exponent alpha (p <0.001) after adjustment for several clinical variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death after AMI.

Magnitude and Sign Correlations in Heartbeat Fluctuations

We propose an approach for analyzing signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that signals with identical long-range correlations can exhibit different time organization for the magnitude and sign. We find that the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties. We apply our approach to the heartbeat interval series and find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications.

From 1'f noise to multifractal cascades in heartbeat dynamics

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.