Day and night changes of cardiovascular complexity: A multi-fractal multi-scale analysis

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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, 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.

Original languageEnglish
Article number462
Issue number4
Publication statusPublished - Apr 1 2020


  • Blood pressure
  • Detrended fluctuation analysis
  • Heart rate
  • Multifractality
  • Multiscale complexity
  • Self-similarity

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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