# On multifractals: a non-linear study of actigraphy data

## TL;DR

This study applied fractal and multifractal analysis to activity data from healthy and fibromyalgia subjects, finding differences in sleep and awake states that could help characterize movement control alterations in fibromyalgia.

## Contribution

It demonstrates the use of multifractal analysis to distinguish activity patterns between healthy individuals and fibromyalgia patients, revealing physiological differences.

## Key findings

- Hurst exponent values were similar for both groups, indicating similar fractal properties.
- Multifractal spectra showed significant differences between sleep and awake states.
- The method can differentiate between healthy and fibromyalgia activity patterns.

## Abstract

This work aimed, to determine the characteristics of activity series from fractal geometry concepts application, in addition to evaluate the possibility of identifying individuals with fibromyalgia. Activity level data were collected from 27 healthy subjects and 27 fibromyalgia patients, with the use of clock-like devices equipped with accelerometers, for about four weeks, all day long. The activity series were evaluated through fractal and multifractal methods. Hurst exponent analysis exhibited values according to other studies ($H>0.5$) for both groups ($H=0.98\pm0.04$ for healthy subjects and $H=0.97\pm0.03$ for fibromyalgia patients), however, it is not possible to distinguish between the two groups by such analysis. Activity time series also exhibited a multifractal pattern. A paired analysis of the spectra indices for the sleep and awake states revealed differences between healthy subjects and fibromyalgia patients. The individuals feature differences between awake and sleep states, having statistically significant differences for $\alpha_{q-} - \alpha_{0}$ in healthy subjects ($p = 0.014$) and $D_{0}$ for patients with fibromyalgia ($p = 0.013$). The approach has proven to be an option on the characterisation of such kind of signals and was able to differ between both healthy and fibromyalgia groups. This outcome suggests changes in the physiologic mechanisms of movement control.