The application of the normalized range method in the analysis of self-similar properties of complex living systems biomedical data

Abstract

Time signals, including experimental series of biomedical data, produced by complex systems, contain unique, inherent in highly organized composite objects, information about the evolution, organization, structure, as well as the nature and role of the interaction of individual components. The study of the unique properties of living systems: the nature of quantitative and qualitative relationships between the elements of the whole; collective phenomena of coordination and synchronization; mechanisms of self-organization and self-adjustment; power-law distributions and scale transformations, manifested in the behavior of the recorded parameters; interactions and correlations of individual components, linear and non-linear responses to external influences and excitations, becomes possible thanks to statistical methods for processing experimental data, in particular clinical and biomedical.
In this paper, 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 Hurst exponent allows differentiating temporal signals in the presence of minimal information about the complex system under study, depending on the nature of the correlations manifestation. The paper presents the basic mathematical relationships for the computer implementation of fast and slow (with averaging) algorithms for calculating the Hurst exponent. In the 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 temporal 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 temporal dynamics of the tremor rate in Parkinson's disease, the bioelectrical activity of the brain of patients with epilepsy, including those under external influences. The results of this work 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.

Speaker

Valentin A. Yunusov
1. Institute of Physics, Kazan Federal University, Kazan, Russia; 2. Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kazan, Russia
Russia

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