Methods from nonlinear dynamics (NLD) have shown new insights into heart rate (HR) variability changes under various physiological and pathological conditions, providing additional prognostic information and complementing traditional time-and frequencydomain analyses. In this review, some of the most prominent indices of nonlinear and fractal dynamics are summarized and their algorithmic implementations and applications in clinical trials are discussed. Several of those indices have been proven to be of diagnostic relevance or have contributed to risk stratification. In particular, techniques based on mono-and multifractal analyses and symbolic dynamics have been successfully applied to clinical studies. Further advances in HR variability analysis are expected through multidimensional and multivariate assessments. Today, the question is no longer about whether or not methods from NLD should be applied; however, it is relevant to ask which of the methods should be selected and under which basic and standardized conditions should they be applied.

In the recent years, short-term heart rate variability (HRV) describing complex variations of beat-to-beat interval series that are mainly controlled by the autonomic nervous system (ANS) has been increasingly analyzed to assess the ANS activity in different diseases and under various conditions. In contrast to long-term HRV analysis, short-term investigations (<30 min) provide a test result almost immediately. Thus, short-term HRV analysis is suitable for ambulatory care, patient monitoring and all those applications where the result is urgently needed. In a previous study, we could show significant variations of 5-min HRV indices according to age in almost all domains (linear and nonlinear) in 1906 healthy subjects from the KORA S4 cohort. Based on the same group of subjects, general gender-related influences on HRV indices are to be determined in this study. Short-term 5-min HRV indices from linear time and frequency domain and from nonlinear methods (compression entropy, detrended fluctuation analysis, traditional and segmented Poincaré plot analysis, irreversibility analysis, symbolic dynamics, correlation and mutual information analysis) were determined from 782 females and 1124 males. First, we examined the gender differences in two age clusters (25–49 years and 50–74 years). Secondly, we investigated the gender-specific development of HRV indices in five age decade categories, namely for ages 25–34, 35–44, 45–54, 55–64 and 65–74 years. In this study, significant modifications of the indices according to gender could be obtained, especially in the frequency domain and correlation analyses. Furthermore, there were significant modifications according to age in nearly all of the domains. The gender differences disappeared within the last two age decades and the age dependencies disappeared in the last decade. To summarize gender and age influences need to be considered when performing HRV studies even if these influences only partly differ.

Recently, methods have been developed to analyse couplings in dynamic systems. In the field of medical analysis of complex cardiovascular and cardiorespiratory systems, there is growing interest in how insights may be gained into the interaction between regulatory mechanisms in healthy and diseased persons. The couplings within and between these systems can be linear or nonlinear. However, the complex mechanisms involved in cardiovascular and cardiorespiratory regulation very likely interact with each other in a nonlinear way. Recent advances in nonlinear dynamics and information theory have allowed the multivariate study of information transfer between time series. They therefore might be able to provide additional diagnostic and prognostic information in medicine and might, in particular, be able to complement traditional linear coupling analysis techniques. In this review, we describe the approaches (Granger causality, nonlinear prediction, entropy, symbolization, phase synchronization) most commonly applied to detect direct and indirect couplings between time series, especially focusing on nonlinear approaches. We will discuss their capacity to quantify direct and indirect couplings and the direction (driver–response relationship) of the considered interaction between different biological time series. We also give their basic theoretical background, their basic requirements for application, their main features and demonstrate their usefulness in different applications in the field of cardiovascular and cardiorespiratory coupling analyses.

Heart rate variability (HRV) analysis is an established method to characterize the autonomic regulation and is based mostly on 24h Holter recordings. The importance of short-term HRV (less than 30 min) for various applications is growing consistently. Major reasons for this are the suitability for ambulatory care and patient monitoring and the ability to provide an almost immediate test result. So far, there have been only a few studies that provided statistically relevant reference values for short-term HRV. In our study, 5 min short-term HRV indices were determined from 1906 healthy subjects. From these records, linear and nonlinear indices were extracted. To determine general age-related influences, HRV indices were compared from subjects aged 25-49 years with subjects aged 50-74 years. In a second approach, we examined the development of HRV indices by age in terms of age decades (25-34, 35-44, 45-54, 55-64 and 65-74 years). Our results showed significant variations of HRV indices by age in almost all domains. While marked dynamics in terms of parameter change (variability reduction) were observed in the first age decades, in particular the last two age decades showed certain constancy with respect to the HRV indices examined.

Dilated cardiomyopathy (DCM) has an incidence of about 20100 000 new cases per annum and accounts for nearly 10 000 deaths per year in the United States. Approximately 36% of patients with dilated cardiomyopathy (DCM) suffer from cardiac death within five years after diagnosis. Currently applied methods for an early risk prediction in DCM patients are rather insufficient. The objective of this study was to investigate the suitability of short-term nonlinear methods symbolic dynamics (STSD), detrended fluctuation (DFA), and Poincare plot analysis (PPA) for risk stratification in these patients. From 91 DCM patients and 30 healthy subjects (REF), heart rate and blood pressure variability (HRV, BPV), STSD, DFA, and PPA were analyzed. Measures from BPV analysis, DFA, and PPA revealed highly significant differences (p<0.0011) discriminating REF and DCM. For risk stratification in DCM patients, four parameters from BPV analysis, STSD, and PPA revealed significant differences between low and high risk (maximum sensitivity: 90%, specificity: 90%). These results suggest that STSD and PPA are useful nonlinear methods for enhanced risk stratification in DCM patients.