Effectiveness of a home-based physical exercise intervention in patients with hip fragility fractures: a randomized controlled trial.

Brain functions as a complex, nonlinear system, making nonlinear analysis particularly suited for revealing the underlying dynamics of electroencephalographic (EEG) signals that may not be fully captured by traditional linear methods. Higuchi’s algorithm is a widely used nonlinear approach that estimates the fractal dimension as a measure of complexity and self-similarity in the time domain, without the need to embed the signal in a phase space. The resulting measure, known as Higuchi’s fractal dimension (HFD), is an effective biomarker for capturing dynamic changes in a signal, revealing its underlying scaling relationships. HFD has been applied to EEG signals for nearly three decades, with an early contribution from Inouye et al. in 1994, which analyzed wakefulness and sleep cycles to provide insights into transitions between different sleep stages. Accardo et al. later demonstrated its effectiveness in short EEG segments, leading to its gradual yet broader adoption in EEG analysis, including but not limited to the study of neurodegenerative diseases, such as Alzheimer’s and Parkinson’s, detecting seizure onsets and abnormal brain activity in epilepsy research, distinguishing various mental disorders from healthy individuals, including depression and schizophrenia, stress classification and monitoring the depth of anesthesia (DOA). Despite its widespread use and promising utility, reported HFD values vary considerably: even in healthy subjects, mean HFD values range from as low as 1.02 and 1.07 to nearly 1.94. Lower HFD values indicate a less complex signal, while values near two refer to a more complex signal or near-to-random white noise. These divergent values are influenced to some extent by individual differences in fractal dynamics, by different preprocessing methods, by different noise levels or hardware variability. While it has been shown that HFD is relatively independent of signal length (), the choice of sampling frequency () and parameter appears to have a substantial influence on the resulting HFD estimates.