Analysis Of Physiological Time Series Research Articles

Frequency Detection and Change Point Estimation for Time Series of Complex Oscillation

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed to accurately detect all oscillatory frequencies. A further phase-adjusted local change point detection algorithm is applied in the frequency domain to detect the locations at which the oscillatory pattern changes. Our method is shown to be able to detect all oscillatory frequencies and the corresponding change points within an accurate range with a prescribed probability asymptotically. A Gaussian approximation scheme and an overlapping-block multiplier bootstrap methodology for sums of complex-valued high dimensional non-stationary time series without variance lower bounds are established, which could be of independent interest. This study is motivated by oscillatory frequency estimation and change point detection problems encountered in physiological time series analysis. An application to spindle detection and estimation in electroencephalogram recorded during sleep is used to illustrate the usefulness of the proposed methodology.

Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations.

While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve amounts of information shared by the processes within specific frequency bands which are otherwise not detectable by time-domain information measures, as well as coupling features which are not detectable by spectral measures. Then, it is applied to the time series of heart period, systolic and diastolic arterial pressure and respiration variability measured in healthy subjects monitored in the resting supine position and during head-up tilt. We show that the spectral measures of unique, redundant and synergistic information shared by these variability series, integrated within specific frequency bands of physiological interest and reflect the mechanisms of short-term regulation of cardiovascular and cardiorespiratory oscillations and their alterations induced by the postural stress. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Time\u2013frequency time\u2013space LSTM for robust classification of physiological signals

Automated analysis of physiological time series is utilized for many clinical applications in medicine and life sciences. Long short-term memory (LSTM) is a deep recurrent neural network architecture used for classification of time-series data. Here time–frequency and time–space properties of time series are introduced as a robust tool for LSTM processing of long sequential data in physiology. Based on classification results obtained from two databases of sensor-induced physiological signals, the proposed approach has the potential for (1) achieving very high classification accuracy, (2) saving tremendous time for data learning, and (3) being cost-effective and user-comfortable for clinical trials by reducing multiple wearable sensors for data recording.

Comparison of parametric and non-parametric Bayesian inference for fusing sensory estimates in physiological time-series analysis.

The rapid proliferation of wearable devices for medical applications has necessitated the need for automated algorithms to provide labelling of physiological time‐series data to identify abnormal morphology. However, such algorithms are less reliable than gold‐standard human expert labels (where the latter are typically difficult and expensive to obtain), due to their large inter‐ and intra‐subject variabilities. Actions taken in response to these algorithms can therefore result in sub‐optimal patient care. In a typical scenario where only unevenly sampled continuous or numeric estimates are provided, without access to the “ground truth”, it is challenging to choose which algorithms to trust and which to ignore, or even how to merge the outputs from multiple algorithms to form a more precise final estimate for individual patients. In this work, the novel application of two previously proposed parametric fully‐Bayesian graphical models is demonstrated for fusing labels from (i) independent and (ii) potentially correlated algorithms, validated on two publicly available datasets for the task of respiratory rate (RR) estimation. These unsupervised models aggregate RR labels and estimate jointly the assumed bias and precision of each algorithm. Fusing estimates in this way may then be used to infer the underlying ground truth for individual patients. It is shown that modelling the latent correlations between algorithms improves the RR estimates, when compared to commonly employed strategies in the literature. Finally, it is demonstrated that the adoption of a strongly Bayesian approach to inference using Gibbs sampling results in improved estimation over the current state‐of‐the‐art (e.g. hierarchical Gaussian processes) in physiological time‐series modelling.

Fractal analysis of muscle activity patterns during locomotion: pitfalls and how to avoid them.

Time-dependent physiological data sets are often difficult to interpret objectively. Biosignals such as electromyogram, electroencephalogram, or single-neuron recordings can be interpreted using various linear and nonlinear methods. Each analysis technique aims at the explanation of different data features that might be visible or not to the naked eye. Here, we used linear decomposition based on machine learning to extract motor primitives (the time-dependent coefficients of muscle synergies) from the hindlimb electromyographic activity of mice during normal and mechanically perturbed locomotion. We set out to investigate the effects of calculation parameters and data quality on two nonlinear metrics derived from fractal analysis: the Higuchi's fractal dimension (HFD) and the Hurst exponent (H). Both HFD and H proved to be exceptionally sensitive to changes in motor primitives induced by external perturbations to locomotion. We discuss the potential pitfalls that might arise from fractal analysis by using examples based on surrogate data. We conclude giving some simple, data-driven suggestions to reduce the chance of misinterpretations when metrics such as HFD and H are applied to any biological signal containing elements of periodicity.NEW & NOTEWORTHY Despite the lack of consensus on how to perform fractal analysis of physiological time series, many studies rely on this technique. Here, we shed light on the potential pitfalls of using the Higuchi's fractal dimension and the Hurst exponent. We expose and suggest how to solve the drawbacks of such methods when applied to data from normal and perturbed locomotion by combining in vivo recordings and computational approaches.

EZ Entropy: a software application for the entropy analysis of physiological time-series

BackgroundEntropy analysis has been attracting increasing attentions in the recent two or three decades. It assesses complexity, or irregularity, of time-series which is extraordinarily relevant to physiology and diseases as demonstrated by tremendous studies. However, the complexity can hardly be appreciated by traditional methods including time-, frequency-domain analysis, and time-frequency analysis that are the common built-in options in commercialized measurement and statistical software. To facilitate the entropy analysis of physiological time-series, a new software application, namely EZ Entropy, was developed and introduced in this article.ResultsEZ Entropy was developed in MATLAB® environment. It was programmed in an object-oriented style and was constructed with a graphical user interface. EZ Entropy is easy to operate through its compact graphical interface, thus allowing researchers without knowledge of programming like clinicians and physiologists to perform such kind of analysis. Besides, it offers various settings to meet different analysis needs including (1) processing single data recording, (2) batch processing multiple data files, (3) sliding window calculations, (4) recall, (5) displaying intermediate data and final results, (6) adjusting input parameters, and (7) exporting calculation results after the run or in real-time during the analysis. The analysis results could be exported, either manually or automatically, to comma-separated ASCII files, thus being compatible to and easily imported into the common statistical analysis software. Code-wise, EZ Entropy is object-oriented, thus being quite easy to maintain and extend.ConclusionsEZ Entropy is a user-friendly software application to perform the entropy analysis of time-series, as well as to simplify and to speed up this useful analysis.

A New Approach for Physiological Time Series

In this paper, we developed a new approach for the analysis of physiological time series. An iterative convolution filter is used to decompose the time series into various components. Statistics of these components are extracted as features to characterize the mechanisms underlying the time series. Studies have shown that many normal physiological systems involve irregularity, while the decrease of irregularity usually implies abnormality. This motivates the use of the statistics for “outliers” in the components as features measuring irregularity. Support vector machines are used to select the most relevant features that are able to differentiate the time series from normal and abnormal systems. This new approach is successfully used in the study of congestive heart failure by heart beat interval time series.

Multitask Gaussian processes for multivariate physiological time-series analysis.

Gaussian process (GP) models are a flexible means of performing nonparametric Bayesian regression. However, GP models in healthcare are often only used to model a single univariate output time series, denoted as single-task GPs (STGP). Due to an increasing prevalence of sensors in healthcare settings, there is an urgent need for robust multivariate time-series tools. Here, we propose a method using multitask GPs (MTGPs) which can model multiple correlated multivariate physiological time series simultaneously. The flexible MTGP framework can learn the correlation between multiple signals even though they might be sampled at different frequencies and have training sets available for different intervals. Furthermore, prior knowledge of any relationship between the time series such as delays and temporal behavior can be easily integrated. A novel normalization is proposed to allow interpretation of the various hyperparameters used in the MTGP. We investigate MTGPs for physiological monitoring with synthetic data sets and two real-world problems from the field of patient monitoring and radiotherapy. The results are compared with standard Gaussian processes and other existing methods in the respective biomedical application areas. In both cases, we show that our framework learned the correlation between physiological time series efficiently, outperforming the existing state of the art.

Fractal Characterization of Gait in Parkinson's Disease Using Detrended Fluctuation Analysis

Fractal analysis of physiological time series have revealed many interesting features that were not so easily identified using conventional techniques 1. For example, altered gait dynamics has been reported for subjects with Huntingtons disease (HD) in comparison to healthy controls 2. Studies also showed that stride-interval fluctuations are more random in elderly subjects and in subjects with HD, which are apparently associated with changes in central nervous system control. In this paper, we perform fractal analysis on subject with Parkinsons disease (PD) using detrended fluctuation analysis (DFA)

Physiological time-series analysis using approximate entropy and sample entropy

Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.

Multiple-time scales analysis of physiological time series under neural control

We discuss multiple-time scale properties of neurophysiological control mechanisms, using heart rate and gait regulation as model systems. We find that scaling exponents can be used as prognostic indicators. Furthermore, detection of more subtle degradation of scaling properties may provide a novel early warning system in subjects with a variety of pathologies including those at high risk of sudden death.

Analysis of physiological time series using wavelet transforms.

Time-series analysis is the basis for characterization and modeling of an observed system. The aim of this analysis is the prediction of the short-term evolution of a dynamic system and the development of a model that captures features of its long-term behavior. Here, the authors present a a method of time-series analysis that uses wavelet transforms to analyze heart rhythm, chest volume, and blood oxygen saturation data from a patient suffering from sleep apnea.

New trends in electrophysiological signal parametrization and feature extraction.

New trends in physiological time series analysis are described. The discussed topics concern: parametric methods including their multi-channel version, non-linear formalism, artificial neural networks and wavelet analysis. The parametric methods which have been used mainly in EEG analysis are making their way into other fields. In their multi-channel version autoregressive models furnish information about the intrinsic relationship between signals. The chaotic formalism have brought new insight into the mechanisms of physiological processes. Nevertheless, in the description of physiological time series parameters estimated by means of non-linear formalism should be used with care. Artificial neural networks are becoming a popular method of time series classification. They are especially suitable in case of noisy and incomplete data. Interesting application of neural networks can be foreseen in the problems where not only classification but also control are involved. Wavelet analysis is a new method which makes possible the simultaneous estimation of signal frequency and localization in time with the accuracy superior to any previously known method. The method is especially suitable for the analysis of fast-varying non-stationary signals.

Physiological time-series analysis: what does regularity quantify?

Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity that appears to have potential application to a wide variety of physiological and clinical time-series data. The focus here is to provide a better understanding of ApEn to facilitate its proper utilization, application, and interpretation. After giving the formal mathematical description of ApEn, we provide a multistep description of the algorithm as applied to two contrasting clinical heart rate data sets. We discuss algorithm implementation and interpretation and introduce a general mathematical hypothesis of the dynamics of a wide class of diseases, indicating the utility of ApEn to test this hypothesis. We indicate the relationship of ApEn to variability measures, the Fourier spectrum, and algorithms motivated by study of chaotic dynamics. We discuss further mathematical properties of ApEn, including the choice of input parameters, statistical issues, and modeling considerations, and we conclude with a section on caveats to ensure correct ApEn utilization.

A nonstationarity test for the spectral analysis of physiological time series with an application to respiratory sinus arrhythmia.

The spectral analysis of time series requires the signal to be at least weakly stationary; i.e., the mean, (co-) variance, and spectrum of the time series should not vary from segment to segment. It is commonly assumed that psychophysiological time series are not stationary. This study introduces a nonstationarity test to the psychophysiological literature, which is derived from evolutionary spectral analysis. Basically, the test consists of a double window technique in both the time and frequency domains, leading to a two-way analysis of variance for times and frequencies. In the current study, the nonstationarity test is applied to heart rate data obtained in a typical psychophysiological setting. Heart rate and respiration were measured in four age groups under four conditions--rest, paced breathing, vigilance, and reaction time. The results indicate that only few physiological time series were completely stationary. However, for every subject, and in every condition stationary stretches could be found that were long enough to apply spectral analysis. Spectral measures (power, coherence, and phase spectra) were then compared for stationary parts of the data and the total data. This comparison indicated that nonstationarity affects all spectral measures. Most importantly, Stationarity x Task Condition x Frequency Band interactions were observed for coherence and phase spectra, and there were significant interactions with age for each of the spectral indices. These findings suggest that nonstationarity may result in biased outcomes of significance tests of the effects of task manipulations on the spectral indices of cardiac time series. Thus, it was concluded that the stationarity test should be routinely applied in the spectral analysis of physiological time series. In addition, it was suggested that the nonstationarity test has an even wider range of application that might be of interest to the psychophysiologist.

Spectral analysis of twin time series designs.

The genetic analysis of physiological time series has to accommodate the presence of autocorrelation. This can be accomplished by means of orthogonal transformation of the series, thus enabling the use of standard genetic analysis techniques for the sequence of uncorrelated transforms. In view of the oscillatory character which typifies various physiological time series, it is customary to invoke spectral techniques for the analysis of these series. It can be shown that spectral analysis is an orthogonal transformation that asymptotically resembles principal component analysis. Consequently, standard genetic analysis methods for the uncorrelated spectral transforms may be used. This approach will be illustrated with simulated and real (heart rate) data for univariate twin time series. Furthermore, it will be indicated that the proposed analysis can be readily generalized to multivariate time series.