Heart rate variability (HRV) is a reliable reflection of the many physiological factors modulating the normal rhythm of the heart. In fact, they provide a powerful means of observing the interplay between the sympathetic and parasympathetic nervous systems. It shows that the structure generating the signal is not only simply linear, but also involves nonlinear contributions. Heart rate (HR) is a nonstationary signal; its variation may contain indicators of current disease, or warnings about impending cardiac diseases. The indicators may be present at all times or may occur at random-during certain intervals of the day. It is strenuous and time consuming to study and pinpoint abnormalities in voluminous data collected over several hours. Hence, HR variation analysis (instantaneous HR against time axis) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system. Computer based analytical tools for in-depth study of data over daylong intervals can be very useful in diagnostics. Therefore, the HRV signal parameters, extracted and analyzed using computers, are highly useful in diagnostics. In this paper, we have discussed the various applications of HRV and different linear, frequency domain, wavelet domain, nonlinear techniques used for the analysis of the HRV.

Heart rate variability: a review

We describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos. A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters. Computer programs that implement the resulting strategies are publicly available as the TISEAN software package. The use of each algorithm will be illustrated with a typical application. As to the theoretical background, we will essentially give pointers to the literature. (c) 1999 American Institute of Physics.

Practical implementation of nonlinear time series methods: The TISEAN package.

Nonlinear time series analysis is becoming a more and more reliable tool for the study of complicated dynamics from measurements. The concept of low-dimensional chaos has proven to be fruitful in the understanding of many complex phenomena despite the fact that very few natural systems have actually been found to be low dimensional deterministic in the sense of the theory. In order to evaluate the long term usefulness of the nonlinear time series approach as inspired by chaos theory, it will be important that the corresponding methods become more widely accessible. This paper, while not a proper review on nonlinear time series analysis, tries to make a contribution to this process by describing the actual implementation of the algorithms, and their proper usage. Most of the methods require the choice of certain parameters for each specific time series application. We will try to give guidance in this respect. The scope and selection of topics in this article, as well as the implementational choices that have been made, correspond to the contents of the software package TISEAN which is publicly available from this http URL . In fact, this paper can be seen as an extended manual for the TISEAN programs. It fills the gap between the technical documentation and the existing literature, providing the necessary entry points for a more thorough study of the theoretical background.

https://arxiv.org/pdf/chao-dyn/9810005.pdf

Practical implementation of nonlinear time series methods: The TISEAN package

Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field

The sudden and apparently unpredictable nature of seizures is one of the most disabling aspects of the disease epilepsy. A method capable of predicting the occurrence of seizures from the electroencephalogram (EEG) of epilepsy patients would open new therapeutic possibilities. Since the 1970s investigations on the predictability of seizures have advanced from preliminary descriptions of seizure precursors to controlled studies applying prediction algorithms to continuous multi-day EEG recordings. While most of the studies published in the 1990s and around the turn of the millennium yielded rather promising results, more recent evaluations could not reproduce these optimistic findings, thus raising a debate about the validity and reliability of previous investigations. In this review, we will critically discuss the literature on seizure prediction and address some of the problems and pitfalls involved in the designing and testing of seizure-prediction algorithms. We will give an account of the current state of this research field, point towards possible future developments and propose methodological guidelines for future studies on seizure prediction.

Seizure prediction: the long and winding road.

A practical method for calculating largest Lyapunov exponents from small data sets

Reconstruction expansion as a geometry-based framework for choosing proper delay times

Chaos and graphicsVisualizing the effects of filtering chaotic signals

It is well-known that filtered chaotic signals can exhibit increases in observed fractal dimension. However, there is still insufficient knowledge regarding the underlying causes of this phenomenon. We provide further insight into this problem through the use of computer animations and three-dimensional ray-tracings. Specifically, we show that lowpass filters can induce a nonuniform convergence to a dynamical system's mean state-space location. With chaotic attractors, this convergence distorts the attractor's normal geometrical configuration such that the observed system acquires increased dimensionality.

Visualizing the effects of filtering chaotic signals

Two mathematical techniques from dynamical systems theory - the reconstruction of phase portraits and correlation dimension calculations - were used to analyze and interpret centerof-pressure trajectories during quiet standing The analysis of experimental stabilogram time series generated complicated phase space attractors with small, non-integer dimensions The present results suggest that the human postural control system may be modelled as a nonlinear dynamical system which exhibits chaotic behavior

http://ieeexplore.ieee.org/iel4/1015/7498/00684969.pdf

Michael T. Rosenstein

Papers

A practical method for calculating largest Lyapunov exponents from small data sets

Reconstruction expansion as a geometry-based framework for choosing proper delay times

Chaos and graphicsVisualizing the effects of filtering chaotic signals

Visualizing the effects of filtering chaotic signals

A Nonlinear Dynamical Analysis Of The Human Postural Control System