The fractal structure of cardiovascular beat-to-beat series described over a broad range of scales: Differences between blood pressure and heart rate, and the effect of gender

The fractal characteristics of heart rate variability are usually assessed by estimating short- and long-term scale coefficients, α<;sub>1<;/sub>and α<;sub>2<;/sub>, by detrended fluctuation analysis. Recently we extended this approach introducing a temporal spectrum of scale coefficients, α(τ), that describes the deviations of self-similarity from the bi-fractal model at each scale τ. Until now relatively short recordings were considered and α(τ) was characterized only for scales τ<;100 s. Aim of this work is to describe α(τ) of cardiovascular signals extending the range τ by an order of magnitude with respect to previous studies. We considered 2-hour recordings of systolic and diastolic blood pressure (SBP and DBP) and of pulse interval (PI) in 68 volunteers (26 males, 42 females) sitting at rest. The α(τ) spectra were estimated for 5s ≤τ ≤1000s and compared. We found important differences between α(τ) of SBP, DBP and PI. In particular, α(τ) of PI was lower than α(τ) of SBP at all the scales τ, with a relative maximum at τ =26 s and a minimum at τ =300 s that were completely missing in α(τ) of DBP. Significant differences were also found between α(τ) of males and females, probably linked to gender differences in the cardiovascular autonomic tone.