Relationship between fractal dimension and power-law exponent of heart rate variability in normal and heart failure subjects

Among the plethora of indices that can describe the fractal-like behaviour of heart rate variability (HRV), the fractal dimension (FD) and the power-law exponent (β) have gained wide acceptance. Since HRV is generally modelled with fractional Brownian motion (fBm), the linear scaling relationship between β and FD, valid for fBm, is often applied to HRV series to derive one index from the other. In this paper the relationship between β and FD is calculated in normal (NR) and heart failure (HF) HRV series. Results revealed that a linear dependence between β and FD can be found only when the slope of the spectral density is calculated over the whole spectrum instead of considering more widespread very low frequency ranges. Moreover, the relationship is slightly different from that characterizing fBm and is not unique for the two categories of subjects. The common practice of estimating β from FD for HRV applying the theoretical relationship should be reconsidered.