Crucial events, randomness, and multifractality in heartbeats

Abstract

We study the connection between multifractality and crucial events. Multifractality is frequently used as a measure of physiological variability, where crucial events are known to play a fundamental role in the transport of information between complex networks. To establish the connection of interest we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the past 20 years two apparently different diagnostic techniques have been established: the first is based on the observation that the multifractal spectrum of healthy patients is broader than the multifractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and uncorrelated Poisson-like events, with pathologic patients hosting uncorrelated Poisson-like events with larger probability than the healthy patients. In this paper, we prove that increasing the percentage of uncorrelated Poisson-like events hosted by heartbeats has the effect of making their multifractal spectrum narrower, thereby establishing that the two different diagnostic techniques are compatible with one another and, at the same time, establishing a dynamic interpretation of multifractal processes that had been previously overlooked.

Entropic Approach to the Detection of Crucial Events

“…Figure 4 shows that when the non-crucial events are a form of SFBM the tail of C(t) reveals the existence of a SFBM process to the time series under study. The analysis of heartbeats of References [37,42] in addition to finding the correct crucial scaling of heartbeats, corresponding to the parameter µ slightly larger than 2, with the method of stripes, yields for C(t) the slow tail that is a signature of SFBM.…”

“…The main theoretical result of the present paper allows us to reach some compelling conclusions about the nature of these two physiological processes. In fact, the heartbeats have been analyzed with the method of the stripes [37,42] leading the conclusion that the IPL index µ in the case of healthy individuals is close to the condition generating ideal noise, µ = 2. In a more recent paper, Bohara et al [54] using the method of the stripes analyzed the EEGs of healthy subjects in the same awake conditions as the human subjects of Reference [35] and confirmed that they have a power law index µ very close to the ideal condition µ = 2.…”

Bridging Waves and Crucial Events in the Dynamics of the Brain

“…The stripe method was originally adopted to detect the scaling of crucial events hosted by heartbeats (Allegrini et al, 2002 ) and was not used in the case of EEG time series in all likelihood because of the lack of a proper theoretical understanding of the connection between crucial events and periodicity. The same method was more recently applied by Bohara et al ( 2017 ) to establish a connection between the occurrence of crucial events and multifractality.…”

Order Through Disorder: The Characteristic Variability of Systems

“…The second was based on data showing that heartbeat dynamics are a superposition of crucial and uncorrelated Poisson-like events, with patients showing a higher probability of uncorrelated Poisson-like events than healthy subjects. Increasing the magnitude of uncorrelated Poisson-like events held by heartbeats leads to a narrowing of their multifractal spectrum (Bohara et al, 2017).…”