The complexity of clinically-normal sinus-rhythm ECGs is decreased in equine athletes with a diagnosis of paroxysmal atrial fibrillation

Abstract: Equine athletes have a pattern of exercise which is analogous to human athletes and the cardiovascular risks in both species are similar. Both species have a propensity for atrial fibrillation (AF), which is challenging to detect by ECG analysis when in paroxysmal form. We hypothesised that the proarrhythmic background present between fibrillation episodes in paroxysmal AF (PAF) might be detectable by complexity analysis of apparently normal sinus-rhythm ECGs. In this retrospective study ECG recordings were obtained during routine clinical work from 82 healthy horses and from 10 horses with a diagnosis of PAF. Artefact-free 60-second strips of normal sinus-rhythm ECGs were converted to binary strings using threshold crossing, beat detection and a novel feature detection parsing algorithm. Complexity of the resulting binary strings was calculated using Lempel-Ziv (‘76 & ‘78) and Titchener complexity estimators. Dependence of Lempel-Ziv ‘76 and Titchener T-complexity on the heart rate in ECG strips obtained at low heart rates (25–60 bpm) and processed by the feature detection method was found to be significantly different in control animals and those diagnosed with PAF. This allows identification of horses with PAF from sinus-rhythm ECGs with high accuracy

The application of Lempel-Ziv and Titchener complexity analysis for equine telemetric electrocardiographic recordings.

The analysis of equine electrocardiographic (ECG) recordings is complicated by the absence of agreed abnormality classification criteria. We explore the applicability of several complexity analysis methods for characterization of non-linear aspects of electrocardiographic recordings. We here show that complexity estimates provided by Lempel-Ziv '76, Titchener's T-complexity and Lempel-Ziv '78 analysis of ECG recordings of healthy Thoroughbred horses are highly dependent on the duration of analysed ECG fragments and the heart rate. The results provide a methodological basis and a feasible reference point for the complexity analysis of equine telemetric ECG recordings that might be applied to automate detection of equine arrhythmias in equine clinical practice.Funded by PetPlan Charitable Trust, grant S17-447-48

Lempel-Ziv Complexity Analysis of Local Field Potentials in Different Vigilance States with Different Coarse-Graining Techniques

Analysis of electrophysiological signals recorded from the brain with Lempel-Ziv (LZ) complexity, a measure based on coarse-graining of the signal, can provide valuable insights into understanding brain activity. LZ complexity of local field potential signals recorded from the neocortex of 11 adult male Wistar-Kyoto rats in different vigilance states - waking, non-rapid-eye movement (NREM) and REM sleep - was estimated with different coarse-graining techniques (median, LZCm, and k-means, LZCkm). Furthermore, surrogate data were used to test the hypothesis that LZ complexity results reveal effects accounted for by temporal structure of the signal, rather than merely its frequency content. LZ complexity values were significantly lower in NREM sleep as compared to waking and REM sleep, for both real and surrogate signals. LZCkm and LZCm values were similar, although in NREM sleep the values deviated in some epochs, where signals also differed significantly in terms of temporal structure and spectral content. Thus, the interpretation of LZ complexity results should take into account the specific algorithm used to coarse-grain the signal. Moreover, the occurrence of high amplitude slow waves during NREM sleep determines LZ complexity to a large extent, but characteristics such as the temporal sequence of slow waves or cross-frequency interactions might also play a role. © Springer International Publishing Switzerland 2014

Складність Лемпеля-Зіва та кризи ринку криптовалют

The informational (Kolmogorov) measure of complexity in accordance with the Lempel-Ziv algorithm (LZC) is calculated for the logarithmic returns of daily Bitcoin/$values. The calculations were carried out for a moving window with a variation in its size (50–250 days) in increments of one day in the framework of the implemented coarse graining procedure. It is shown that in both mono-and multi-scaling versions, LZC is sensitive to noticeable fluctuations in the Bitcoin price that occur as a result of critical events in the cryptocurrency market. In equilibrium, stable state, having a relatively low value, LZC rapidly increases immediately before the crisis, which proves the dominance of the chaotic component of the time series. The classification and periodization of crisis phenomena in the cryptocurrency market for the period 2010–2020 has been carried out. The results demonstrate the possibility of using the LZC measure as an indicator-precursor of crisis phenomena in the cryptocurrency market.Інформаційна (колмогоровской) міра складності відповідно до алгоритму Лемпеля-Зіва (LZC) розрахована для логарифмічного повернення денних значень біткойн/$. Розрахунки проводилися для рухомого вікна зі зміною його розміру (50-250 днів) з кроком в один день в рамках впровадженої процедури грубого гранулювання. Показано, що як в моно-, так і в багатомасштабних версіях LZC чутливий до помітних коливань ціни біткойнов, що виникають в результаті критичних подій на ринку криптовалюта. У рівноважному стабільному стані, що має відносно низьке значення, LZC швидко зростає безпосередньо перед кризою, що доводить домінування хаотичної складової часового ряду. Проведено класифікацію та періодизація кризових явищ на ринку криптовалюта за період 2010-2020 рр. Результати демонструють можливість використання показника LZC як індикатора-передвічника кризових явищ на ринку криптовалюта

Aging and cardiovascular complexity: effect of the length of RR tachograms

As we age, our hearts undergo changes that result in a reduction in complexity of physiological interactions between different control mechanisms. This results in a potential risk of cardiovascular diseases which are the number one cause of death globally. Since cardiac signals are nonstationary and nonlinear in nature, complexity measures are better suited to handle such data. In this study, three complexity measures are used, namely Lempel–Ziv complexity (LZ), Sample Entropy (SampEn) and Effort-To-Compress (ETC). We determined the minimum length of RR tachogram required for characterizing complexity of healthy young and healthy old hearts. All the three measures indicated significantly lower complexity values for older subjects than younger ones. However, the minimum length of heart-beat interval data needed differs for the three measures, with LZ and ETC needing as low as 10 samples, whereas SampEn requires at least 80 samples. Our study indicates that complexity measures such as LZ and ETC are good candidates for the analysis of cardiovascular dynamics since they are able to work with very short RR tachograms

Multivariate multiscale complexity analysis

Established dynamical complexity analysis measures operate at a single scale and thus fail to quantify inherent long-range correlations in real world data, a key feature of complex systems. They are designed for scalar time series, however, multivariate observations are common in modern real world scenarios and their simultaneous analysis is a prerequisite for the understanding of the underlying signal generating model. To that end, this thesis first introduces a notion of multivariate sample entropy and thus extends the current univariate complexity analysis to the multivariate case. The proposed multivariate multiscale entropy (MMSE) algorithm is shown to be capable of addressing the dynamical complexity of such data directly in the domain where they reside, and at multiple temporal scales, thus making full use of all the available information, both within and across the multiple data channels. Next, the intrinsic multivariate scales of the input data are generated adaptively via the multivariate empirical mode decomposition (MEMD) algorithm. This allows for both generating comparable scales from multiple data channels, and for temporal scales of same length as the length of input signal, thus, removing the critical limitation on input data length in current complexity analysis methods. The resulting MEMD-enhanced MMSE method is also shown to be suitable for non-stationary multivariate data analysis owing to the data-driven nature of MEMD algorithm, as non-stationarity is the biggest obstacle for meaningful complexity analysis. This thesis presents a quantum step forward in this area, by introducing robust and physically meaningful complexity estimates of real-world systems, which are typically multivariate, finite in duration, and of noisy and heterogeneous natures. This also allows us to gain better understanding of the complexity of the underlying multivariate model and more degrees of freedom and rigor in the analysis. Simulations on both synthetic and real world multivariate data sets support the analysis

Investigation of the stability of fluctuations in electrocardiography data

A new algebraic algorithm based on the concept of the rank of a sequence for the analysis of electrocardiography (ECG) signals is proposed in this paper. The task of the proposed algorithm is to develop strategy for finding the nearest algebraic progression to each segment of time series of the ECG parameters. ECG parameters of different duration were used to investigate the dynamics of different physiological processes in human heart during load. It indicates that proposed algebraic algorithm can be effectively used for the analysis of ECG parameters. Different behavior can be observed in fluctuations of ECG parameters in different fractal levels

Methods for heart rate variability analysis during sleep

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Refined Multiscale Fuzzy Entropy based on Standard Deviation for Biomedical Signal Analysis

Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of fluctuations in the local mean value of biomedical time series. Recent developments in the field have tried to improve the MSE by reducing its variability in large scale factors. On the other hand, there has been recent interest in using other statistical moments than the mean, i.e. variance, in the coarse-graining step of the MSE. Building on these trends, here we introduce the so-called refined composite multiscale fuzzy entropy based on the standard deviation (RCMFE{\sigma}) to quantify the dynamical properties of spread over multiple time scales. We demonstrate the dependency of the RCMFE{\sigma}, in comparison with other multiscale approaches, on several straightforward signal processing concepts using a set of synthetic signals. We also investigate the complementarity of using the standard deviation instead of the mean in the coarse-graining process using magnetoencephalograms in Alzheimer disease and publicly available electroencephalograms recorded from focal and non-focal areas in epilepsy. Our results indicate that RCMFE{\sigma} offers complementary information to that revealed by classical coarse-graining approaches and that it has superior performance to distinguish different types of physiological activity