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Predictability of normal heart rhythms and deterministic chaos
J. H. Lefebvre1, D. A. Goodings, M. V. Kamath
1Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada L8S 4M1Department of Medicine, McMaster University Medical Center, Hamilton, Ontario, Canada L8N 3Z5.
Insights
Normal heart rhythms show subtle signs of deterministic chaos, not strong or persistent. Analysis of R-R intervals reveals short-term predictability, suggesting nonlinear dynamics in cardiac function.
Area of Science:
- Cardiology
- Nonlinear Dynamics
- Physiology
Background:
- Normal heart rhythms are complex and influenced by various physiological factors.
- Understanding the underlying dynamics of heart rate variability is crucial for assessing cardiac health.
- Previous research has explored the potential for chaotic behavior in biological systems.
Purpose of the Study:
- To investigate the presence and characteristics of deterministic chaos in normal heart rhythms.
- To analyze the predictability of R-R intervals in healthy subjects and patients post-myocardial infarction.
- To identify parameters that quantify nonlinear dynamics in cardiac time series.
Main Methods:
- Electrocardiograms (ECGs) were recorded from 29 subjects across four groups (young healthy, older healthy, post-myocardial infarction).
- Time series of 1000 first differences of R-R intervals were constructed.
- Correlation integral and prediction methods (Sugihara-May, autoregressive linear predictor) were applied to analyze the data.
Main Results:
- No evidence for an attractor with a dimension less than 4 was found.
- Short-term predictability was observed in the differenced R-R intervals, inconsistent with a Gaussian random process.
- A small amount of nonlinear dynamical behavior was detected, suggesting deterministic chaos is present but not dominant.
Conclusions:
- Normal heart rhythms exhibit a degree of deterministic chaos, characterized by nonlinear dynamics and short-term predictability.
- The identified 'first step predictability' and 'predictability decay rate' are novel parameters for characterizing cardiac rhythm dynamics.
- These findings contribute to a deeper understanding of the complex physiological mechanisms governing heart rate variability.
Abstract:
The evidence for deterministic chaos in normal heart rhythms is examined. Electrocardiograms were recorded of 29 subjects falling into four groups-a young healthy group, an older healthy group, and two groups of patients who had recently suffered an acute myocardial infarction. From the measured R-R intervals, a time series of 1000 first differences was constructed for each subject. The correlation integral of Grassberger and Procaccia was calculated for several subjects using these relatively short time series. No evidence was found for the existence of an attractor having a dimension less than about 4. However, a prediction method recently proposed by Sugihara and May and an autoregressive linear predictor both show that there is a measure of short-term predictability in the differenced R-R intervals. Further analysis revealed that the short-term predictability calculated by the Sugihara-May method is not consistent with the null hypothesis of a Gaussian random process. The evidence for a small amount of nonlinear dynamical behavior together with the short-term predictability suggest that there is an element of deterministic chaos in normal heart rhythms, although it is not strong or persistent. Finally, two useful parameters of the predictability curves are identified, namely, the 'first step predictability' and the 'predictability decay rate,' neither of which appears to be significantly correlated with the standard deviation of the R-R intervals.
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