Deterministic Chaos and Fractal Complexity in the Dynamics of Cardiovascular Behavior: Perspectives on a New Frontier

Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts

Moderate and heavy metabolic stress interval training improve arterial stiffness and heart rate dynamics in humans

Traditional continuous aerobic exercise training attenuates age-related increases of arterial stiffness, however, training studies have not determined whether metabolic stress impacts these favourable effects. Twenty untrained healthy participants (n = 11 heavy metabolic stress interval training, n = 9 moderate metabolic stress interval training) completed 6 weeks of moderate or heavy intensity interval training matched for total work and exercise duration. Carotid artery stiffness, blood pressure contour analysis, and linear and non-linear heart rate variability were assessed before and following training. Overall, carotid arterial stiffness was reduced (p  0.05). This study demonstrates the effectiveness of interval training at improving arterial stiffness and autonomic function, however, the metabolic stress was not a mediator of this effect. In addition, these changes were also independent of improvements in aerobic capacity, which were only induced by training that involved a high metabolic stress

Influence of mercury exposure on blood pressure, resting heart rate and heart rate variability in French Polynesians: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Populations which diet is rich in seafood are highly exposed to contaminants such as mercury, which could affect cardiovascular risk factors</p> <p>Objective</p> <p>To assess the associations between mercury and blood pressure (BP), resting heart rate (HR) and HR variability (HRV) among French Polynesians</p> <p>Methods</p> <p>Data were collected among 180 adults (≥ 18 years) and 101 teenagers (12-17 years). HRV was measured using a two-hour ambulatory electrocardiogram (Holter) and BP was measured using a standardized protocol. The association between mercury and HRV and BP parameters was studied using analysis of variance (ANOVA) and analysis of covariance (ANCOVA)</p> <p>Results</p> <p>Among teenagers, the high frequency (HF) decreased between the 2^ndand 3^rdtertile (380 vs. 204 ms², p = 0.03) and a similar pattern was observed for the square root of the mean squared differences of successive R-R intervals (rMSSD) (43 vs. 30 ms, p = 0.005) after adjusting for confounders. In addition, the ratio low/high frequency (LF/HF) increased between the 2^ndand 3^rdtertile (2.3 vs. 3.0, p = 0.04). Among adults, the standard deviation of R-R intervals (SDNN) tended to decrease between the 1^stand 2^ndtertile (84 vs. 75 ms, p = 0.069) after adjusting for confounders. Furthermore, diastolic BP tended to increase between the 2^ndand 3^rdtertile (86 vs. 91 mm Hg, p = 0.09). No significant difference was observed in resting HR or pulse pressure (PP)</p> <p>Conclusions</p> <p>Mercury was associated with decreased HRV among French Polynesian teenagers while no significant association was observed with resting HR, BP, or PP among teenagers or adults</p

The Prognostic Value of Non-Linear Analysis of Heart Rate Variability in Patients with Congestive Heart Failure—A Pilot Study of Multiscale Entropy

AIMS: The influences of nonstationarity and nonlinearity on heart rate time series can be mathematically qualified or quantified by multiscale entropy (MSE). The aim of this study is to investigate the prognostic value of parameters derived from MSE in the patients with systolic heart failure. METHODS AND RESULTS: Patients with systolic heart failure were enrolled in this study. One month after clinical condition being stable, 24-hour Holter electrocardiogram was recording. MSE as well as other standard parameters of heart rate variability (HRV) and detrended fluctuation analysis (DFA) were assessed. A total of 40 heart failure patients with a mea age of 56±16 years were enrolled and followed-up for 684±441 days. There were 25 patients receiving β-blockers treatment. During follow-up period, 6 patients died or received urgent heart transplantation. The short-term exponent of DFA and the slope of MSE between scale 1 to 5 were significantly different between patients with or without β-blockers (p = 0.014 and p = 0.028). Only the area under the MSE curve for scale 6 to 20 (Area(6-20)) showed the strongest predictive power between survival (n = 34) and mortality (n = 6) groups among all the parameters. The value of Area(6-20)21.2 served as a significant predictor of mortality or heart transplant (p = 0.0014). CONCLUSION: The area under the MSE curve for scale 6 to 20 is not relevant to β-blockers and could further warrant independent risk stratification for the prognosis of CHF patients

Unexpected Course of Nonlinear Cardiac Interbeat Interval Dynamics during Childhood and Adolescence

The fluctuations of the cardiac interbeat series contain rich information because they reflect variations of other functions on different time scales (e.g., respiration or blood pressure control). Nonlinear measures such as complexity and fractal scaling properties derived from 24 h heart rate dynamics of healthy subjects vary from childhood to old age. In this study, the age-related variations during childhood and adolescence were addressed. In particular, the cardiac interbeat interval series was quantified with respect to complexity and fractal scaling properties. The R-R interval series of 409 healthy children and adolescents (age range: 1 to 22 years, 220 females) was analyzed with respect to complexity (Approximate Entropy, ApEn) and fractal scaling properties on three time scales: long-term (slope β of the power spectrum, log power vs. log frequency, in the frequency range 10−4 to 10−2 Hz) intermediate-term (DFA, detrended fluctuation analysis, α2) and short-term (DFA α1). Unexpectedly, during age 7 to 13 years β and ApEn were higher compared to the age <7 years and age >13 years (β: −1.06 vs. −1.21; ApEn: 0.88 vs. 0.74). Hence, the heart rate dynamics were closer to a 1/f power law and most complex between 7 and 13 years. However, DFA α1 and α2 increased with progressing age similar to measures reflecting linear properties. In conclusion, the course of long-term fractal scaling properties and complexity of heart rate dynamics during childhood and adolescence indicates that these measures reflect complex changes possibly linked to hormonal changes during pre-puberty and puberty

Reduced Physiological Complexity in Robust Elderly Adults with the APOE ε4 Allele

BACKGROUND:It is unclear whether the loss of physiological complexity during the aging process is due to genetic variations. The APOE gene has been studied extensively in regard to its relationship with aging-associated medical illness. We hypothesize that diminished physiological complexity, as measured by heart rate variability, is influenced by polymorphisms in the APOE allele among elderly individuals. METHODOLOGY/PRINCIPAL FINDINGS:A total of 102 robust, non-demented, elderly subjects with normal functions of daily activities participated in this study (97 males and 5 females, aged 79.2+/-4.4 years, range 72-92 years). Among these individuals, the following two APOE genotypes were represented: epsilon4 non-carriers (n = 87, 85.3%) and epsilon4 carriers (n = 15, 14.7%). Multi-scale entropy (MSE), an analysis used in quantifying complexity for nonlinear time series, was employed to analyze heart-rate dynamics. Reduced physiological complexity, as measured by MSE, was significantly associated with the presence of the APOE epsilon4 allele in healthy elderly subjects, as compared to APOE epsilon4 allele non-carriers (24.6+/-5.5 versus 28.9+/-5.2, F = 9.429, p = 0.003, respectively). CONCLUSIONS/SIGNIFICANCE:This finding suggests a role for the APOE gene in the diminished physiological complexity seen in elderly populations

Effects of antidepressant treatment on heart rate variability in major depression: A quantitative review

<p>Abstract</p> <p>Background</p> <p>The literature measuring effects of antidepressant and electroconvulsive therapy (ECT) for major depression on heart rate variability (HRV) in medically well individuals was reviewed.</p> <p>Methods</p> <p>Fourteen studies evaluating HRV were included. Twenty three pre-post or within group comparisons were available. Treatment impact on measures of HRV was pooled over studies. We examined different classes of antidepressants, and for short and long electrocardiogram (ECG) recordings separately.</p> <p>Results</p> <p>Tricyclic antidepressants (TCAs) were associated with declines in most measures of HRV and significant increase in heart rate (HR) in studies with short recording intervals. No significant changes were found for longer recording times.</p> <p>Treatment effects with selective serotonin reuptake inhibitors (SSRIs) were more variable. Short-recording studies revealed a significant decrease in HR and an increase in one HRV measure. In two 24-hour recording studies no significant changes were observed. No relationship between ECT and HRV has been established in the literature. The effects of other drugs are reported.</p> <p>Limitations</p> <p>Few studies measure the effects of treatment of depression on HRV. Existing studies have generally used very small samples, employing a variety of measurements and methodologies.</p> <p>Conclusion</p> <p>We confirm that TCAs are associated with a large decrease in HRV and increase HR. However, data for SSRIs is not clear. Although the effect of SSRIs on HRV is weaker than for TCAs, evidence shows that SSRIs are associated with a small decrease in HR, and an increase in one measure of HRV. The use of TCAs in depression leads to changes in HRV that are associated with increased risk of mortality.</p

A quantitative comparison of different methods to detect cardiorespiratory coordination during night-time sleep

BACKGROUND: The univariate approaches used to analyze heart rate variability have recently been extended by several bivariate approaches with respect to cardiorespiratory coordination. Some approaches are explicitly based on mathematical models which investigate the synchronization between weakly coupled complex systems. Others use an heuristic approach, i.e. characteristic features of both time series, to develop appropriate bivariate methods. OBJECTIVE: In this study six different methods used to analyze cardiorespiratory coordination have been quantitatively compared with respect to their performance (no. of sequences with cardiorespiratory coordination, no. of heart beats coordinated with respiration). Five of these approaches have been suggested in the recent literature whereas one method originates from older studies. RESULTS: The methods were applied to the simultaneous recordings of an electrocardiogram and a respiratory trace of 20 healthy subjects during night-time sleep from 0:00 to 6:00. The best temporal resolution and the highest number of coordinated heart beats were obtained with the analysis of 'Phase Recurrences'. Apart from the oldest method, all methods showed similar qualitative results although the quantities varied between the different approaches. In contrast, the oldest method detected considerably fewer coordinated heart beats since it only used part of the maximum amount of information available in each recording. CONCLUSIONS: The method of 'Phase Recurrences' should be the method of choice for the detection of cardiorespiratory coordination since it offers the best temporal resolution and the highest number of coordinated sequences and heart beats. Excluding the oldest method, the results of the heuristic approaches may also be interpreted in terms of the mathematical models

Complex systems and the technology of variability analysis

Characteristic patterns of variation over time, namely rhythms, represent a defining feature of complex systems, one that is synonymous with life. Despite the intrinsic dynamic, interdependent and nonlinear relationships of their parts, complex biological systems exhibit robust systemic stability. Applied to critical care, it is the systemic properties of the host response to a physiological insult that manifest as health or illness and determine outcome in our patients. Variability analysis provides a novel technology with which to evaluate the overall properties of a complex system. This review highlights the means by which we scientifically measure variation, including analyses of overall variation (time domain analysis, frequency distribution, spectral power), frequency contribution (spectral analysis), scale invariant (fractal) behaviour (detrended fluctuation and power law analysis) and regularity (approximate and multiscale entropy). Each technique is presented with a definition, interpretation, clinical application, advantages, limitations and summary of its calculation. The ubiquitous association between altered variability and illness is highlighted, followed by an analysis of how variability analysis may significantly improve prognostication of severity of illness and guide therapeutic intervention in critically ill patients