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Evolvement of mathematical methods for analysis of heart rate variability: achievements and outlook

DOI 10.18127/j20700997-201902-05

Keywords:

P.B. Tatarintsev – Ph.D. (Eng.), Associate Professor, Department of Higher Mathematics, Ugra State University (Hanty-Mansijsk)
E-mail: pbt@ugrasu.ru
Z.I. Molchanova – Ph.D. (Med.), Associate Professor, Department of Neurology and Psychiatry, Khanty-Mansiysk State Medical Academy
E-mail: hmgmi2006@mail.ru
I.V. Radysh – Dr. Sc. (Med.), Professor, Аcademician REA, Head of the Department of Nursing Management Activities, Peoples' Friendship University of Russia (Moscow)
E-mail: iradysh@mail.ru
O.N. Ragozin – Dr Sc. (Med.), Professor, Department of Hospital Therapy, Khanty-Mansiysk State Medical Academy
E-mail: oragozin@mail.ru
N.V. Kokorina – Ph.D. (Agricultural), Associate Professor, Department of Ecology and Nature Management, Ugra State University
E-mail: N_Kokorina@ugrasu.ru


The literature review briefly describes the applicability of various mathematical methods of heart rate variability analysis in the time and frequency domains, methods of nonlinear dynamics. Heart rate variability is a manifestation of the variability of adjacent heartbeats. Either heart rate variability expresses in terms of heart rate or in terms of duration of RR intervals, it is a popular subject of physiology research. The aim – a brief historical overview of the development of the concept of heart rate variability, approaches and methods for its quantitative description. The advantages of developing and introducing into clinical practice of circular methods for the heart rate variability analysis described in connection with the quasi-periodicity of the cardiac rate, which is periodic, and in the same time random, close to almost periodic processes. Heart rhythm is partly periodic, partly random, representing a quasiperiodic oscillatory process, similar in its properties to almost periodic processes. Statistical indicators of generally accepted time domain methods for heart rate variability analysis cannot be adequate to the phenomenon under study: their statistical properties depend on the recording time T and the number of heart beats in the sample N. The temporal fluctuations in heart rate show a significant correlation with respiration as a reflection of changes in cardiac autonomic regulation. Despite the lack of certainty in the existing estimates of the contribution of the parasympathetic and the sympathetic divisions of the autonomic nervous system to this variability, a number of mathematical methods for the analysis of heart rate variability have been developed, allowing evaluate the effect of autonomous regulation of the heart. A variety of mathematical methods for analyzing data as a means of assessing for heart rate variability are characterized by unequal potential capabilities, their range of applications is limited. There is the problem of insufficient elaboration of standards. Depending on the capabilities of the data processing method, it is possible to obtain various information about the vegetative regulation of the heart rhythm and the functional state of the organism as a whole. To develop universal indicators of heart rate variability, the magnitude of which would have a clear physiological and clinical interpretation, it is necessary to involve mathematical models of quasi-periodic processes within the framework of the circular approach that are free from these drawbacks.

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