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

### Abstract

The healthcare process generates a vast quantity of data. Exploitation and analysis of such material might lead discoveries and potentially improve the clinical activity. Over the last years, several studies focused on the non-linear features exhibited by physiological signals and medical data. In general, the complex features of these signals have been demonstrated in some studies, ranging from heartbeat time intervals to neuron spikes series. Some works employed fractal and multifractal concepts to the analysis of such medical data. Similar evaluations of movement patterns recorded by actigraphy devices on individuals with fibromyalgia might provide new information that can be potentially translated into the clinical practice. Chronic pain is a condition characterised by sleep disturbances and psychological disorders that is correlated with impairment and reduced physical activity. This work aimed to determine the characteristics of activity series from fractal geometry concepts, 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 two weeks, all day long. The activity series were evaluated through fractal and multifractal methods. Hurst exponent analysis exhibited values according to other studies for both groups, 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 $α$q−−$α$0 in healthy subjects only, suggesting that there are not differences between awake and sleep state for patients with fibromyalgia. The approach has proven to be an option on the characterisation of such kind of signals and was able to (indirectly) differ between both healthy and fibromyalgia groups. This outcome suggests changes in the physiologic mechanisms of movement control.

Publication
Physica A: Statistical Mechanics and its Applications