Multifractal multiscale dfa of cardiovascular time series: Differences in complex dynamics of systolic blood pressure, diastolic blood pressure and heart rate

The heart-rate fractal dynamics can be assessed by Detrended Fluctuation Analysis (DFA), originally proposed for estimating a short-term coefficient, α
₁
(for scales n≤12 beats), and a long-term coefficient α
₂
(for longer scales). Successively, DFA was extended to provide a multiscale α, i.e. a continuous function of n, α(n); or a multifractal α, i.e. a function of the order q of the fluctuations moment, α(q). Very recently, a multifractal-multiscale DFA was proposed for evaluating multifractality at different scales separately. Aim of this work is to describe the multifractal multiscale dynamics of three cardiovascular signals often recorded beat by beat in physiological and clinical settings: systolic blood pressure (SBP), diastolic blood pressure (DBP) and pulse interval (PI, inverse of the heart rate). We recorded SBP, DBP and PI for at least 90' in 65 healthy volunteers at rest, and adapted the previously proposed multifractal multiscale DFA to estimate α as function of the temporal scale, τ, between 15 and 450 s, and of the order q, between -5 and 5. We report, for the first time: 1) substantial differences among α(q,τ) surfaces of PI, SBP and DBP; 2) a strong dependency of the degree of multifractality on the temporal scale.