The Study of Spatiotemporal Scaling Features and Correlations in Complex Biomedical Data

In this research, we demonstrate the capabilities of the normalized range method (R/S analysis) in the study of fractal patterns in biomedical data of complex living systems. The paper presents the basic mathematical relationships for the computer implementation of fast and slow (with averaging) algorithms for calculating the Hurst exponent. In case of a complex image of the resulting logarithmic curve, a piecewise linear approximation is proposed for calculating the generalized value of the Hurst exponent. The analysis of self-similar properties in separate sections of the time evolution of living systems is performed using the localization procedure. The capabilities of the proposed algorithms were demonstrated by analyzing the scaling features of the time dynamics of the tremor velocity in Parkinson's disease, the bioelectrical activity of the brain of patients with epilepsy. The results can be used in computational biophysics and physics of complex systems to search for diagnostic criteria for neurological and neurodegenerative diseases, as well as to study the processes of biological aging and changes in the "physiological complexity" of the human body.