In June 2008, the editors of Chaos decided to institute a new section to appear from time to time that addresses timely and controversial topics related to nonlinear science. The first of these deals with the dynamical characterization of human heart rate variability. We asked authors to respond to the following questions: Is the normal heart rate chaotic? If the normal heart rate is not chaotic, is there some more appropriate term to characterize the fluctuations (e.g., scaling, fractal, multifractal)? How does the analysis of heart rate variability elucidate the underlying mechanisms controlling the heart rate? Do any analyses of heart rate variability provide clinical information that can be useful in medical assessment (e.g., in helping to assess the risk of sudden cardiac death)? If so, please indicate what additional clinical studies would be useful for measures of heart rate variability to be more broadly accepted by the medical community. In addition, as a challenge for analysis methods, PhysioNet [A. L. Goldberger et al., "PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals," Circulation 101, e215-e220 (2000)] provided data sets from 15 patients of whom five were normal, five had heart failure, and five had atrial fibrillation (http://www.physionet.org/challenge/chaos/). This introductory essay summarizes the main issues and introduces the essays that respond to these questions. ©2009 American Institute of Physics

Chaos 19, 028501 (2009)

DOI:10.1063/1.3156832 

Permalink:

http://link.aip.org/link/?CHAOEH/19/028501/1

Published 30 June 2009

 

This paper explores the possibility of applying statistical nonlinear physics methods to elucidate the underlying mechanisms controlling the heart rate. In particular, the presence of delays in RR interval dynamics is studied by using a lagged detrended fluctuation analysis. The results indicate that patients with congestive heart failure (CHF) have a prolonged time delay in the baroreflex response. Some implications of large delays for the functioning of autonomic control in subjects with CHF are discussed. ©2009 American Institute of Physics

 

Chaos 19, 028502 (2009)

DOI:10.1063/1.3152005

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http://link.aip.org/link/?CHAOEH/19/028502/1

Published 30 June 2009

We present new evidence that normal heartbeat series are nonchaotic, nonlinear, and multifractal. In addition to considering the largest Lyapunov exponent and the correlation dimension, the results of the parametric and semiparametric estimation of the long memory parameter (long-range dependence) unambiguously reveal that the underlying process is nonstationary, multifractal, and has strong nonlinearity. ©2009 American Institute of Physics

Chaos 19, 028503 (2009)

DOI:10.1063/1.3152006

Permalink:

http://link.aip.org/link/?CHAOEH/19/028503/1

Published 30 June 2009

 

 

Human heart rate is moderated by the autonomous nervous system acting predominantly through the sinus node (the main cardiac physiological pacemaker). One of the dominant factors that determine the heart rate in physiological conditions is its coupling with the respiratory rhythm. Using the language of stochastic processes, we analyzed both rhythms simultaneously taking the data from polysomnographic recordings of two healthy individuals. Each rhythm was treated as a sum of a deterministic drift term and a diffusion term (Kramers-Moyal expansion). We found that normal heart rate variability may be considered as the result of a bidirectional coupling of two nonlinear oscillators: the heart itself and the respiratory system. On average, the diffusion (noise) component measured is comparable in magnitude to the oscillatory (deterministic) term for both signals investigated. The application of the Kramers-Moyal expansion may be useful for medical diagnostics providing information on the relation between respiration and heart rate variability. This interaction is mediated by the autonomous nervous system, including the baroreflex, and results in a commonly observed phenomenon--respiratory sinus arrhythmia which is typical for normal subjects and often impaired by pathology. ©2009 American Institute of Physics 

Chaos 19, 028504 (2009)

DOI:10.1063/1.3152008

Permalink:

http://link.aip.org/link/?CHAOEH/19/028504/1

Published 30 June 2009  

Providing a conclusive answer to the question "is this dynamics chaotic?" remains very challenging when experimental data are investigated. We showed that such a task is actually a difficult problem in the case of heart rates. Nevertheless, an appropriate dynamical analysis can discriminate healthy subjects from patients. ©2009 American Institute of Physics 

Chaos 19, 028505 (2009)

DOI:10.1063/1.3139116

Permalink:

http://link.aip.org/link/?CHAOEH/19/028505/1

Published 30 June 2009 

 

Previous studies on heart rate variability (HRV) using chaos theory, fractal scaling analysis, and many other methods, while fruitful in many aspects, have produced much confusion in the literature. Especially the issue of whether normal HRV is chaotic or stochastic remains highly controversial. Here, we employ a new multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize HRV. SDLE has been shown to readily characterize major models of complex time series including deterministic chaos, noisy chaos, stochastic oscillations, random 1/f processes, random Levy processes, and complex time series with multiple scaling behaviors. Here we use SDLE to characterize the relative importance of nonlinear, chaotic, and stochastic dynamics in HRV of healthy, congestive heart failure, and atrial fibrillation subjects. We show that while HRV data of all these three types are mostly stochastic, the stochasticity is different among the three groups. ©2009 American Institute of Physics

Chaos 19, 028506 (2009)

DOI:10.1063/1.3152007

Permalink:

http://link.aip.org/link/?CHAOEH/19/028506/1

Published 30 June 2009 

In this paper, we participate to the discussion set forth by the editor of Chaos for the controversy, "Is the normal heart rate chaotic?" Our objective was to debate the question, "Is there some more appropriate term to characterize the heart rate variability (HRV) fluctuations?" We focused on the 24 h RR series prepared for this topic and tried to verify with two different techniques, generalized structure functions and wavelet transform modulus maxima, if they might be described as being multifractal. For normal and congestive heart failure subjects, the h_q exponents showed to be decreasing for increasing q with both methods, as it should be for multifractal signals. We then built 40 surrogate series to further verify such hypothesis. For most of the series (75%-80% of cases) multifractality stood the test of the surrogate data employed. On the other hand, series coming from patients in atrial fibrillation showed a small, if any, degree of multifractality. The population analyzed is too small for definite conclusions, but the study supports the use of multifractal series to model HRV. Also it suggests that the regulatory action of autonomous nervous system might play a role in the observed multifractality. ©2009 American Institute of Physics

Chaos 19, 028507 (2009)

DOI:10.1063/1.3152223

Permalink:

http://link.aip.org/link/?CHAOEH/19/028507/1

Published 30 June 2009

The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: "Is the normal heart rate `chaotic' due to respiration?" ©2009 American Institute of Physics  

Chaos 19, 028508 (2009)

DOI:10.1063/1.3133128

Permalink:

http://link.aip.org/link/?CHAOEH/19/028508/1

Published 30 June 2009 

 

Chaos 19, 028509 (2009)

DOI:10.1063/1.3141426

Permalink:

http://link.aip.org/link/?CHAOEH/19/028509/1

Published 30 June 2009