Analysis of heart rate dynamics by methods derived from nonlinear mathematics

Clinical applicability and prognostic significance

Timo Mäkikallio

Department of Internal Medicine, University of Oulu
Merikoski Rehabilitation and Research Center, Oulu

Abstract

The traditional methods of analysing heart rate variability based on means and variance are unable to detect subtle but potentially important changes in interbeat heart rate behaviour. This research was designed to evaluate the clinical applicability and prognostic significance of new dynamical methods of analysing heart rate behaviour derived from nonlinear mathematics.

The study covered four different patient populations, their controls and one general population of elderly people. The first patient group consisted of 38 patients with coronary artery disease without previous myocardial infarction, the second of 40 coronary artery disease patients with a prior Q-wave myocardial infarction, and the third of 45 patients with a history of ventricular tachyarrhythmia. The fourth group comprised 10 patients with a previous myocardial infarction who had experienced ventricular fibrillation during electrocardiographic recordings. The fifth group comprised a random sample of 347 community-living elderly people invited for a follow-up of 10 years after electrocardiographic recordings.

Heart rate variability was analysed by traditional time and frequency domain methods. The new dynamical measures derived from nonlinear dynamics were: 1) approximate entropy, which reflects the complexity of the data, 2) detrended fluctuation analysis, which describes the presence or absence of fractal correlation properties of time series data, and 3) power-law relationship analysis, which demonstrates the distribution of spectral characteristics of RR intervals, but does not reflect the magnitude of spectral power in different spectral bands.

Approximate entropy was higher in postinfarction patients (1.17 0.22), but lower in coronary artery disease patients without myocardial infarction (0.93 0.17) than in healthy controls (1.03 014, p < 0.01, p < 0.05 respectively). It did not differ between patients with and without ventricular arrhythmia. The short term fractal-like scaling exponent of the detrended fluctuation analysis was higher in coronary artery disease patients without myocardial infarction (1.34 0.15, p < 0.001), but not in postinfarction patients without arrhythmia (1.06 0.13) compared with healthy controls (1.09 0.13). The short term exponent was markedly reduced in patients with life-threatening arrhythmia (0.85 0.25 ventricular tachycardia patients, 0.68 0.18 ventricular fibrillation patients, p < 0.001 for both). The long term power-law slope of the power-law scaling analysis was lower in the ventricular fibrillation group than in postinfarction controls without arrhythmia risk (-1.63 0.24 vs. -1.33 0.23, p < 0.01) and predicted mortality in a general elderly population with an adjusted relative risk of 1.74 (95% CI 1.42-2.13).

The present observations demonstrate that dynamic analysis of heart rate behaviour gives new insight into analysis of heart rate dynamics in various cardiovascular disorders. The breakdown of the normal fractal-like organising principle of heart rate variability is associated with an increased risk of mortality and vulnerability to life-threatening arrhythmias. .


Table of Contents
Acknowledgements
Abbrevations
List of original communications
1. Introduction
2. Review of the literature
2.1. History of heart rate variability
2.2. Physiological background of heart rate variability
2.3. Conventional methods of assessing heart rate variability
2.3.1. General
2.3.2. Time domain analysis of heart rate variability
2.3.3. Frequency domain measures of heart rate variability
2.4. Dynamical analysis methods of heart rate behaviour
2.4.1. History of chaotic and nonlinear dynamics
2.4.2. Approximate entropy analysis
2.4.3. Detrended fluctuation analysis
2.4.4. Power-law relationship analysis of heart rate dynamics
2.4.5. Two dimensional vector analysis
2.4.6. Other nonlinear analysis methods
2.5. Heart rate variability in pathological conditions
2.5.1. Heart rate variability in uncomplicated coronary artery disease
2.5.2. Heart rate variability after acute myocardial infarction
2.5.3. Prognostic significance of heart rate variability
2.5.4. Other risk markers of arrhythmic death
2.5.5. Heart rate variability in other disease states
2.5.6. Influence of physical training and drugs on heart rate variability
3. Purpose of the present study
4. Populations
5. Methods
5.1. Electrocardiographic recordings
5.2. Analysis of heart rate behaviour
5.2.1. Poincaré plot analysis
5.2.2. Approximate entropy analysis
5.2.3. Detrended fluctuation analysis
5.2.4. Power-law relationship analysis
5.3. Signal behaviour tests
5.4. Effects of editing
5.5. Electrophysiologic and angiographic examinations
5.6. Echocardiographic measurements
5.7. Exercise electrocardiographic measurements
5.8. Other analysis
5.9. Statistics
6. Results
6.1. Comparison of measures of heart rate behaviour between patients with stable angina pectoris and healthy controls
6.2. Comparison of measures of heart rate behaviour between postinfarction patients and healthy controls
6.3. Comparison of measures of heart rate behaviour between postinfarction patients with and without vulnerability to ventricular tachyarrhythmia and healthy controls
6.4. RR interval dynamics before spontaneous onset of ventricular fibrillation
6.5. Dynamical heart rate behaviour measures as a predictor of mortality in elderly population
6.6. Correlations between dynamical and conventional measures of heart rate behaviour
6.7. Correlations between dynamical measures of heart rate behaviour and clinical variables
7. Discussion
7.1. Heart rate dynamics in patients with stable angina pectoris
7.2. Heart rate dynamics in patients with prior myocardial infarction
7.3. Heart rate dynamics in patients with vulnerability to ventricular tachyarrhythmia
7.4. Heart rate dynamics before spontaneous onset of ventricular fibrillation
7.5. Dynamical measures of heart rate behaviour as a predictor of mortality in elderly people
7.6. Mathematical interpretation of dynamical analysis of RR intervals
7.7. Possible pathophysiological mechanisms of abnormal short and long term heart rate dynamics
8. Conclusions
References
List of Tables
4-1. Characteristics of patient populations
6-1. RR interval measurements
6-2. Significant Predictors of All-Cause Mortality in Proportional Hazards Regression analysis
List of Figures
6-1. (I,II,III,IV) Examples of power spectra, two dimensional vector analysis and detrended fluctuation analysis of fractal scaling exponents from 24-hour data in different patient populations. Healthy subject show power spectra with distinct low and high frequency peaks, a comet shape Poincarè plot and a short term scaling value ∼1 in DFA analysis. Patient with uncomplicated coronary artery disease shows a clear reduction in high frequency spectral power and an increased and short term scaling value α . Patients with previous myocardial infarction show reduced low frequency spectral power. Postinfarction patient with vulnerability to tachyarrhythmia shows a flatter spectrum and a reduced short term scaling value α. Ventricular fibrillation patient shows a widened high frequency spectral band, a ball-shaped Poincarè plot of successive RR intervals and a reduced short term scaling exponent (α ∼ 0.5). Abbreviations: α = short-term scaling exponent; VF = ventricular fibrillation; VT = ventricular tachycardia; MI = myocardial infarction; CAD = coronary artery disease.
6-2. (V) Examples of power law regression slopes computed over frequencies between 10-2 and 10-4 for a 70-year-old man who was alive 10 years after the 24-hour electrocardiographic recordings (left), and a 68-year-old man who had died of myocardial infarction 22 months after the 24-hour electrocardiographic recording (right). ULF = ultra low frequency power, VLF = very low frequency power, and slope = slope of the regression line computed from the log(power) - log(frequency) plot.