Multifractality and scale invariance in human heartbeat dynamics

TL;DR

This paper clarifies the apparent paradox in human heartbeat dynamics by showing that scale invariance applies to summed heartbeat intervals, while individual increments are scale dependent, revealing a universal feature in health and disease.

Contribution

It resolves conflicting reports on multifractality and scale invariance in heartbeat fluctuations by distinguishing between different statistical measures.

Findings

Scale invariance applies to summed heartbeat intervals across different scales.

Detrended heartbeat increments are scale dependent.

Scale invariance is a universal feature in both healthy and pathological heart dynamics.

Abstract

Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov et al., Nature {\bf 399}, 461 (1999)]. This multifractal character could be manifested as a dependence on scale or beat number of the probability density functions (PDFs) of the heart rate increments. On the other hand, scale invariance has been recently reported in a detrended analysis of healthy heart rate increments [Kiyono et al., Phys. Rev. Lett. {\bf 93}, 178103 (2004)]. In this paper, we resolve this paradox by clarifying that the scale invariance reported is actually exhibited by the PDFs of the sum of detrended healthy heartbeat intervals taken over different number of beats, and demonstrating that the PDFs of detrended healthy heart rate increments are scale dependent. Our work also establishes that this scale invariance is a general feature of human heartbeat dynamics, which is shared by heart rate fluctuations in both healthy and pathological states.