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 frequency-domain 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.

In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, noninvasive diagnostic tools like Holter monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyze the HRV. Especially, some complexity measures that are based on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.

To investigate cardiac autonomic dysfunction in patients with major depressive disorder (MDD). Research in this area has faced several limitations because of the heterogeneity of the disease, the influence of medication, and methodological shortcomings. Participants were 75 patients suffering from an acute recurrent episode of MDD and 75 matched controls. All participants were assessed at baseline for linear and nonlinear parameters of heart rate variability, QT variability and baroreflex sensitivity. Participants with MDD were reassessed after 7 to 9 days of treatment with either a selective serotonin reuptake inhibitor (SSRI) or a serotonin and noradrenaline selective reuptake inhibitor (SNRI) antidepressant. In the initial examination, patients showed an overall shift of autonomic balance toward sympathetic predominance as compared with matched controls, with a decrease in parasympathetic parameters and baroreflex sensitivity, and an increase in sympathetically influenced QT variability. Overall, antidepressant treatment exacerbated this imbalance, with differential effects observed for SSRI and SNRI treatment. In contrast to autonomic dysfunction in other disorders, such as schizophrenia, autonomic dysfunction in MDD appeared to be independent of disease severity. Patients suffering from MDD show profound autonomic dysfunction, which is exacerbated by SNRI and to a lesser degree by SSRI treatment. This information could prove important when selecting antidepressant medication for patients at risk for cardiac arrhythmias.

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.