Assessing the convolutedness of multivariate physiological time series

Area of Science:

• Physiology
• Complex Systems
• Time Series Analysis

Background:

• Time-series variability can indicate complex underlying dynamics.
• Quantifying this complexity, or 'convolutedness', is crucial for signal analysis.

Purpose of the Study:

• To propose and compare novel convolutedness indices for multivariate time series.
• To evaluate these indices on synthesized and real physiological data.

Main Methods:

• Developed convolutedness indices based on trail length (L) and planar extension (d).
• Compared classical indices (L/d ratio, Mandelbrot's fractal dimension - FD) with corrected estimators (FDKC, FDMC).
• Utilized synthesized fractional Brownian motions and real multivariate physiological recordings (muscular activity).

Main Results:

• All indices correlated with fractal dimension (FD) but varied in sensitivity to sample size (N) and ability to distinguish signal types.
• FDMC provided a refined estimation of FD by reducing bias over a running window.
• Indices successfully identified complex changes in physiological signals post-exercise-induced fatigue.

Conclusions:

• The proposed convolutedness indices offer valuable tools for analyzing complex dynamics in physiological signals.
• These methods can detect subtle changes in signal behavior, particularly in response to physiological challenges like fatigue.