×

zbMATH — the first resource for mathematics

Fractal thermodynamics of the states of instantaneous heart rhythm. (English) Zbl 1465.92020
Summary: The paper considers the concept of fractal thermodynamics for studying the states of instantaneous cardiac rhythm (ICR) according to Holter monitoring (HM) data. An effective method cardiac rhythms analysis using the quantum phase space of the ICR Sq is presented. The space Sq is a powerful tool for studying nondeterministic chaotic systems which allows to identify statistical regularities adequately covering the patients’ cardiovascular system states in the context of nondeterministic chaos of ICR states [A. N. Kudnikov et al., “Kvantovanie fazovogo prostranstva mgnovennogo serdechnogo ritma” (Russian), in: V. D. Lahno (ed.), Doklady mezhdunarodnoy konferentsii “matematicheskaya biologiya i bioinformatika”. Puschino: IMPB RAN (2018); the first author et al., “Visualisation of the quantum phase space of instantaneous heart rhythm”, CEUR Workshop Proc. 2267, 359–363 (2018)]. The results of our papers show with high accuracy Sq is a fractal.
MSC:
92C30 Physiology (general)
28A80 Fractals
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baevskiy, R. M.; Berseneva, A. P., Vvedenie v donozologicheskuyu diagnostiku, 220 (2008), notfound: Slovo, notfound
[2] Ryabikina, G. V.; Sobolev, A. V., Variabel’nost’ ritma serdtsa, 135 (1998), Moskva: notfound, Moskva
[3] Kudinov, A. N.; Mikheev, S. A.; Tsvetkov, V. P.; Tsvetkov, I. V., Kvantovanie Fazovogo Prostranstva Mgnovennogo Serdechnogo Ritma, Doklady Mezhdunarodnoy konferentsii “Matematicheskaya biologiya i bioinformatika” Ed. V. D. Lahno. V. 7. Puschino: IMPB RAN, 0, 15, 0 (2018)
[4] Mikheev, S. A.; Tsvetkov, V. P.; Tsvetkov, I. V., Visualisation of the Quantum Phase Space of Instantaneous Heart Rhythm, CEUR Workshop Proc., 2267, 359-363 (2018)
[5] Tsvetkov, V. P.; Mikheyev, S. A.; Tsvetkov, I. V., Fractal Phase Space and Fractal Entropy of Instantaneous Cardiac Rhythm, Chaos Solitons Fractals, 108, 71-76 (2018)
[6] Kudinov, A. N.; Tsvetkov, V. P.; Tsvetkov, I. V., Catastrophes in the Multi-Fractal Dynamics of Social-Economic Systems, Russ. J. Math. Phys., 18, 2, 149-155 (2011) · Zbl 1260.91167
[7] Maslov, V. P., Thermodynamics, Idempotent Analysis, and Tropical Geometry as a Return to Primitivism, Russ. J. Math. Phys., 23, 2, 278-280 (2016) · Zbl 1351.82029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.