Fractal characterization of complexity in temporal physiological signals

Area of Science:

• Fractal Geometry
• Time Series Analysis
• Biomedical Research

Background:

• Fractal geometry describes complex structures with properties like self-similarity and power-law scaling.
• Time series analysis is crucial for understanding physiological signals.
• Existing methods may not adequately capture the fractal nature of biological data.

Purpose of the Study:

• To provide a comprehensive overview of fractal geometry and monofractal time series analysis.
• To introduce fractional Gaussian noise (fGn) and fractional Brownian motion (fBm) as essential models for physiological signals.
• To emphasize the necessity of signal classification before fractal analysis for reliable results.

Main Methods:

• Systematic introduction to fractal geometry concepts and terminology.
• Detailed explanation of monofractal time series analysis methods.
• Advocacy and demonstration of the fGn/fBm dichotomous model for signal classification.

Main Results:

• Classification of signals into fGn or fBm categories is critical for accurate fractal analysis.
• Failure to classify signals can lead to meaningless fractal estimates.
• Numerical experiments on ideal signals highlight the limitations and precision of fractal tools.

Conclusions:

• A robust fractal time series analysis of physiological signals necessitates a preceding classification step using appropriate models like fGn/fBm.
• Understanding fractal properties is vital for advancing biomedical research.
• The review critically evaluates current applications and methods in the field.