1,721,065 research outputs found
A fast DFA algorithm for multifractal multiscale analysis of physiological time series
No full textDetrended fluctuation analysis (DFA) is a popular tool in physiological and medical studies for estimating the self-similarity coefficient, α, of time series. Recent researches extended its use for evaluating multifractality (where α is a function of the multifractal parameter q) at different scales n. In this way, the multifractal-multiscale DFA provides a bidimensional surface α(q,n) to quantify the level of multifractality at each scale separately. We recently showed that scale resolution and estimation variability of α(q,n) can be improved at each scale n by splitting the series into maximally overlapped blocks. This, however, increases the computational load making DFA estimations unfeasible in most applications. Our aim is to provide a DFA algorithm sufficiently fast to evaluate the multifractal DFA with maximally overlapped blocks even on long time series, as usually recorded in physiological or clinical settings, therefore improving the quality of the α(q,n) estimate. For this aim, we revise the analytic formulas for multifractal DFA with first- and second-order detrending polynomials (i.e., DFA1 and DFA2) and propose a faster algorithm than the currently available codes. Applying it on synthesized fractal/multifractal series we demonstrate its numerical stability and a computational time about 1% that required by traditional codes. Analyzing long physiological signals (heart-rate tachograms from a 24-h Holter recording and electroencephalographic traces from a sleep study), we illustrate its capability to provide high-resolution α(q,n) surfaces that better describe the multifractal/multiscale properties of time series in physiology. The proposed fast algorithm might, therefore, make it easier deriving richer information on the complex dynamics of clinical signals, possibly improving risk stratification or the assessment of medical interventions and rehabilitation protocols
Effects of the ECG sampling frequency on the multiscale entropy of heart rate variability
No full textIt is known that the spectral analysis of heart rate variability requires an ECG sampling frequency Fs>1 00 Hz with parabolic interpolation to refine the R peak if Fs<250Hz. By contrast, the effects of quantization errors in Multiscale Entropy (MSE) analysis due to low Fs have never been evaluated systematically. Our aim is thus to describe the effects of low Fs and parabolic interpolation on MSE. We considered 21 ECG recordings of 10' duration sampled at 500Hz (reference). We decimated the ECG to simulate Fs between 250 and 50Hz, we extracted the tachograms without and with parabolic interpolation and estimated MSE at scales between 1 beat (=SampEn) and 50 beats. The estimates were expressed as the percentage of the reference and the error was quantified by the interquartile range (IQR) of their distribution. SampEn showed high sensitivity to Fs with IQR > 1 0% at 250Hz and >16% at 167Hz; however, the parabolic interpolation dramatically decreased the IQR below 2% up to Fs=71Hz. The MSE estimates at larger scales were less sensitive to Fs with IQR=2% even at Fs=50Hz. Thus the ECG sampling rate is more critical for SampEn than for MSE at larger scales and interpolation procedures are required when Fs<250Hz
Comparing Multiscale Estimators of the Degree of Multifractality by Detrended Fluctuation Analysis
No full textSome physiological series, like the cardiovascular signals, show multifractal structures that depend on the temporal scale. Thus, their fractal nature is better assessed by a Detrended Fluctuation Analysis (DFA) approach that provides multifractal coefficients scale by scale. Our aim is to compare two estimators of the degree of scale-by-scale multifractality based on the width of the singularity spectrum or on the statistical dispersion of the DFA coefficients. We synthesized 1000 series of white noise (monofractal and monoscale), of autoregressive noise (monofractal and multiscale) and of Cauchy-distributed noise (multifractal and monoscale) comparing the two estimators at scales between 8 and 228 samples. We found that the two estimators provide similar scale-by-scale profiles of multifractality. However, the statistical-dispersion estimator better distinguishes multifractal from monofractal noises at all the scales, thus appearing more suitable than the singularity-spectrum width to describe the fractal structure of physiological time series
Multifractal and Multiscale Detrended Fluctuation Analysis of Cardiovascular Signals: How the Estimation Bias Affects ShortTerm Coefficients and a Way to mitigate this Error
No full textThe Detrended Fluctuation Analysis (DFA) is a popular method for quantifying the self-similarity of the heart rate that may reveal complexity aspects in cardiovascular regulation. However, the self-similarity coefficients provided by DFA may be affected by an overestimation error associated with the shortest scales. Recently, the DFA has been extended to calculate the multifractal-multiscale self-similarity and some evidence suggests that overestimation errors may affect different multifractal orders. If this is the case, the error might alter substantially the multifractal-multiscale representation of the cardiovascular self-similarity. The aim of this work is 1) to describe how this error depends on the multifractal orders and scales and 2) to propose a way to mitigate this error applicable to real cardiovascular series.Clinical Relevance - The proposed correction method may extend the multifractal analysis at the shortest scales, thus allowing to better assess complexity alterations in the cardiac autonomic regulation and to increase the clinical value of DFA
Multiscale assessment of the degree of multifractality for physiological time series
No full textRecent advancements in detrended fluctuation analysis (DFA) allow evaluating multifractal coefficients scale-by-scale, a promising approach for assessing the complexity of biomedical signals. The multifractality degree is typically quantified by the singularity spectrum width (W SS), a method that is critically unstable in multiscale applications. Thus, we aim to propose a robust multiscale index of multifractality, compare it with W SS and illustrate its performance on real biosignals. The proposed index is the cumulative function of squared increments between consecutive DFA coefficients at each scale n: α CF (n). We compared it with W SS calculated scale-by-scale considering monofractal/monoscale, monofractal/multiscale, multifractal/monoscale and multifractal/multiscale random processes. The two indices provided qualitatively similar descriptions of multifractality, but α CF (n) differentiated better the multifractal components from artefacts due to crossovers or detrending overfitting. Applied on 24 h heart rate recordings of 14 participants, the singularity spectrum failed to always satisfy the concavity requirement for providing meaningful W SS, while α CF (n) demonstrated a statistically significant heart rate multifractality at night in the scale ranges 16-100 and 256-680 s. Furthermore, α CF (n) did not reject the hypothesis of monofractality at daytime, coherently with previous reports of lower nonlinearity and monoscale multifractality during the day. Thus, α CF (n) appears a robust index of multiscale multifractality that is useful for quantifying complexity alterations of physiological series. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'
The HRV Multifractality Spectrum and not the Power Spectrum Is Altered in Paraplegic Individuals with Low-Level Lesion
No full textThe autonomic nervous system may contribute to the multifractal-multiscale dynamics of heart rate variability (HRV). Aim of this work is to evaluate multifractal-multiscale features of HRV complexity when the integrative autonomic regulation is altered. We recorded R-R intervals for 10 minutes in 14 spinal cord injured (SCI) individuals with lesion below the 12th thoracic vertebra, which have intact autonomic cardiac innervations with partially altered autonomic integrative control, and in 34 matched able-bodied (AB) controls. We calculated powers spectra by FFT and generalized Hurst coefficients, α(q,τ), with scales τ between 6 and 120 seconds and q between -4 and +4, by multifractal multiscale detrended fluctuation analysis. At each scale we calculated α SD(τ) standard deviation of α(q, τ). α SD(τ) is ≥0 and tends to zero at scales where the series is monofractal. AB and SCI groups were compared by Mann-Whitney test. While SCI and AB spectra were similar, α SD(τ) was significantly lower at τ < 7 s and at τ around 24 s in the SCI group. Thus, in low-level SCI individuals, the HRV multifractal-multiscale detrended fluctuation analysis reveals alterations in the autonomic integrative control, likely due to loss of multifractality at specific scales, that are completely undetected by traditional spectral analysis
Information-domain analysis of cardiovascular complexity: Night and day modulations of entropy and the effects of hypertension
No full textMultiscale entropy (MSE) provides information-domain measures of the systems' complexity. The increasing interest in MSE of the cardiovascular system lies in the possibility of detecting interactions with other regulatory systems, as higher neural networks. However, most of the MSE studies considered the heart-rate (HR) series only and a limited number of scales: actually, an integrated approach investigating HR and blood-pressure (BP) entropies and cross-entropy over the range of scales of traditional spectral analyses is missing. Therefore, we aim to highlight influences of higher brain centers and of the autonomic control on multiscale entropy and cross-entropy of HR and BP over a broad range of scales, by comparing different behavioral states over 24 h and by evaluating the influence of hypertension, which reduces the autonomic control of BP. From 24-h BP recordings in eight normotensive and eight hypertensive participants, we selected subperiods during daytime activities and nighttime sleep. In each subperiod, we derived a series of 16,384 consecutive beats for systolic BP (SBP), diastolic BP (DBP), and pulse interval (PI). We applied a modified MSE method to obtain robust estimates up to time scales of 334 s, covering the traditional frequency bands of spectral analysis, for three embedding dimensions and compared groups (rank-sum test) and conditions (signed-rank test) at each scale. Results demonstrated night-and-day differences at scales associable with modulations in vagal activity, in respiratory mechanics, and in local vascular regulation, and reduced SBP-PI cross-entropy in hypertension, possibly representing a loss of complexity due to an impaired baroreflex sensitivity
Are inter-beat intervals from blood pressure a valid alternative to R-R intervals for the multiscale entropy analysis of heart rate variability?
No full textWhen an ECG recording is not available to derive the R-R interval (RRI) series, the heart rate variability (HRV) may be evaluated considering the inter-beat intervals (IBI) from other cardiovascular signals, like the arterial blood pressure (ABP).
However, it is unknown how the ABP-derived IBI series quantify the multiscale entropy (MSE) of HRV.
Thus our aim is to describe differences between RRI and the ABP-derived IBI in MSE estimates.
We recorded the ECG and the finger ABP in 40 volunteers.
We derived the RRI series from the ECG (reference IBI) and the series of systolic-systolic intervals (SSI), diastolic-diastolic intervals (DDI), and intervals between maxima of the first- (d'PI) and second- (d"PI) derivative of ABP.
For each IBI series, we estimated the MSE at the scale s=1 beat (SampEn), at high-frequency scales (MSEHF, for 2≤s≤7 beats) and low-frequency scales (MSELF, for
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