A Fast DFA Algorithm for Multifractal Multiscale Analysis of Physiological Time Series

Castiglioni, Paolo; Faini, Andrea

doi:10.3389/fphys.2019.00115

Cited by 39 publications

(54 citation statements)

References 37 publications

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“…We estimated the multifractal multiscale structure of the IBI, SBP, and DBP time series by the fast DFA algorithm available in [17]. Given the beat-by-beat series x i of length L beats, we calculated its cumulative sum, y i .…”

Section: Multifractal-multiscale Detrended Fluctuation Analysismentioning

confidence: 99%

“…We evaluated Equation (1) for q between −5 and +5 and block sizes n between 6 and L/4 beats. We evaluated the multifractal multiscale coefficients as a function of the beat-scale n, α B (q,n), calculating the derivative of log F q (n) vs. log n [17]. This was done for detrending polynomials of order 1 and 2 (see examples of the corresponding F q (n) estimates in Figure 1.…”

Section: Multifractal-multiscale Detrended Fluctuation Analysismentioning

confidence: 99%

“…This was done for detrending polynomials of order 1 and 2 (see examples of the corresponding F q (n) estimates in Figure 1. Previous empirical analyses suggested that the second-order polynomial overfits block sizes shorter than 12 beats, but at the same time, it appears to more efficiently remove long-term trends [17][18][19]. Therefore, we estimated a single α B (q,n) function combining the estimates after detrending of order 1 and 2 with a weighted average which weights more the order one at the shorter scales as proposed in [17].…”

Section: Multifractal-multiscale Detrended Fluctuation Analysismentioning

confidence: 99%

“…We considered scales between 8 and 2048 s. The largest scale (τ = 2048 s) is estimated on more than seven independent blocks of data even in the case of the recording with the shortest duration: this assures sufficient stability of the estimate as shown empirically in previous validations [5,20]. Scales shorter than τ = 8 s were not considered because at negative q orders high levels of estimation bias may be present [17]. We introduced multifractal short-term and long-term coefficients to concisely describe the multifractal multiscale structure.…”

Section: Figurementioning

confidence: 99%

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Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis

Castiglioni

Omboni

Parati

et al. 2020

Entropy

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Recently, a multifractal-multiscale approach to detrended fluctuation analysis (DFA) was proposed to evaluate the cardiovascular fractal dynamics providing a surface of self-similarity coefficients α(q,τ), function of the scale τ, and moment order q. We hypothesize that this versatile DFA approach may reflect the cardiocirculatory adaptations in complexity and nonlinearity occurring during the day/night cycle. Our aim is, therefore, to quantify how α(q, τ) surfaces of cardiovascular series differ between daytime and night-time. We estimated α(q,τ) with −5 ≤ q ≤ 5 and 8 ≤ τ ≤ 2048 s for heart rate and blood pressure beat-to-beat series over periods of few hours during daytime wake and night-time sleep in 14 healthy participants. From the α(q,τ) surfaces, we estimated short-term (<16 s) and long-term (from 16 to 512 s) multifractal coefficients. Generating phase-shuffled surrogate series, we evaluated short-term and long-term indices of nonlinearity for each q. We found a long-term night/day modulation of α(q,τ) between 128 and 256 s affecting heart rate and blood pressure similarly, and multifractal short-term modulations at q < 0 for the heart rate and at q > 0 for the blood pressure. Consistent nonlinearity appeared at the shorter scales at night excluding q = 2. Long-term circadian modulations of the heart rate DFA were previously associated with the cardiac vulnerability period and our results may improve the risk stratification indicating the more relevant α(q,τ) area reflecting this rhythm. Furthermore, nonlinear components in the nocturnal α(q,τ) at q ≠ 2 suggest that DFA may effectively integrate the linear spectral information with complexity-domain information, possibly improving the monitoring of cardiac interventions and protocols of rehabilitation medicine.

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Section: Multifractal-multiscale Detrended Fluctuation Analysismentioning

confidence: 99%

Section: Multifractal-multiscale Detrended Fluctuation Analysismentioning

confidence: 99%

Section: Multifractal-multiscale Detrended Fluctuation Analysismentioning

confidence: 99%

Section: Figurementioning

confidence: 99%

See 2 more Smart Citations

Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis

Castiglioni

Omboni

Parati

et al. 2020

Entropy

Self Cite

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“…Accordingly, in controlled conditions, a logical expected system behavior should help in strengthening the link between system complexity if one can demonstrate that signal complexity change concurrently [ 1 ]. Ultimately, changes in output signal complexity should reflect interconnectivity at neurophysiological levels [ 2 , 3 , 4 ].…”

Section: Introductionmentioning

confidence: 99%

Entropy in Heart Rate Dynamics Reflects How HRV-Biofeedback Training Improves Neurovisceral Complexity during Stress-Cognition Interactions

Deschodt-Arsac

Blons

Gilfriche

et al. 2020

Entropy

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Despite considerable appeal, the growing appreciation of biosignals complexity reflects that system complexity needs additional support. A dynamically coordinated network of neurovisceral integration has been described that links prefrontal-subcortical inhibitory circuits to vagally-mediated heart rate variability. Chronic stress is known to alter network interactions by impairing amygdala functional connectivity. HRV-biofeedback training can counteract stress defects. We hypothesized the great value of an entropy-based approach of beat-to-beat biosignals to illustrate how HRVB training restores neurovisceral complexity, which should be reflected in signal complexity. In thirteen moderately-stressed participants, we obtained vagal tone markers and psychological indexes (state anxiety, cognitive workload, and Perceived Stress Scale) before and after five-weeks of daily HRVB training, at rest and during stressful cognitive tasking. Refined Composite Multiscale Entropy (RCMSE) was computed over short time scales as a marker of signal complexity. Heightened vagal tone at rest and during stressful tasking illustrates training benefits in the brain-to-heart circuitry. The entropy index reached the highest significance levels in both variance and ROC curves analyses. Restored vagal activity at rest correlated with gain in entropy. We conclude that HRVB training is efficient in restoring healthy neurovisceral complexity and stress defense, which is reflected in HRV signal complexity. The very mechanisms that are involved in system complexity remain to be elucidated, despite abundant literature existing on the role played by amygdala in brain interconnections.

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Persistence of Basal Ganglia Oscillatory Activity During Tremor Attenuation by Movement in Parkinson's Disease Patients

Wilken,

Andres,

Bianchi

et al. 2024

Movement Disorders

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BackgroundOne of the characteristics of parkinsonian tremor is that its amplitude decreases with movement. Current models suggest an interaction between basal ganglia (BG) and cerebello‐thalamo‐cortical circuits in parkinsonian tremor pathophysiology.ObjectiveWe aimed to correlate central oscillation in the BG with electromyographic activity during re‐emergent tremor in order to detect changes in BG oscillatory activity when tremor is attenuated by movement.MethodsWe performed a prospective, observational study on consecutive parkinsonian patients who underwent deep brain stimulation surgery and presented re‐emergent tremor. Coherence analysis between subthalamic nucleus/globus pallidus internus (STN/GPi) tremorous activity measured by microrecording (MER) and electromyogram (EMG) from flexor and extensor wrist muscles during rest, posture, and re‐emergent tremor pause was performed during surgery. The statistical significance level of the MER‐EMG coherence was determined using surrogate data analysis, and the directionality of information transfer between BG and muscle was performed using entropy transfer analysis.ResultsWe analyzed 148 MERs with tremor‐like activity from 6 patients which were evaluated against the simultaneous EMGs, resulting in 296 correlations. Of these, 26 presented a significant level of coherence at tremor frequency, throughout rest and posture, with a complete EMG stop in between. During the pause, all recordings showed sustained MER peaks at tremor frequency (±1.5 Hz). Information flows preferentially from BG to muscle during rest and posture, with a loss of directionality during the pause.ConclusionsOur results suggest that oscillatory activity in STN/GPi functionally linked to tremor sustains firing frequency during re‐emergent tremor pause, thus suggesting no direct role of the BG circuit on tremor attenuation due to voluntary movements. © 2024 International Parkinson and Movement Disorder Society.

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A Fast DFA Algorithm for Multifractal Multiscale Analysis of Physiological Time Series

Cited by 39 publications

References 37 publications

Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis

Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis

Entropy in Heart Rate Dynamics Reflects How HRV-Biofeedback Training Improves Neurovisceral Complexity during Stress-Cognition Interactions

Persistence of Basal Ganglia Oscillatory Activity During Tremor Attenuation by Movement in Parkinson's Disease Patients

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