# Crucial events, randomness and multi-fractality in heartbeats

## TL;DR

This paper links multi-fractality and crucial events in heartbeat dynamics, showing how the proportion of Poisson events influences the multi-fractal spectrum, thereby unifying two diagnostic techniques for heart health assessment.

## Contribution

It demonstrates that increasing Poisson events narrows the multi-fractal spectrum, connecting two existing diagnostic methods and providing a new dynamic interpretation of multi-fractality in heartbeats.

## Key findings

- Poisson events reduce the multi-fractal spectrum width.
- The two diagnostic techniques are compatible.
- A dynamic interpretation of multi-fractality is proposed.

## Abstract

We study the connection between multi-fractality and crucial events. Multi-fractality is frequently used as a measure of physiological variability. Crucial events are known to play a fundamental role in the transport of information between complex networks. To establish a connection 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 last twenty years two apparently different diagnostic techniques have been established: the first is based on the observation that the multi-fractal spectrum of healthy patients is broader than the multi-fractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and Poisson events, with pathologic patients hosting Poisson events with larger probability than the healthy patients. In this paper, we prove that increasing the percentage of Poisson events hosted by heartbeats has the effect of making their multi-fractal 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 multi-fractal processes that has been previously overlooked.