Spectral Analysis and Invariant Measure in Studies of the Dynamics of the Hemostasis of a Blood Vessel
DOI:
https://doi.org/10.15407/ujpe66.3.221Keywords:
hemostasis, self-organization, strange attractor, Fourier series, invariant measure, low-density lipoproteins, cytokinesAbstract
A mathematical model of atherosclerosis of a blood vessel is advanced with regard for the entry of low-density lipoproteins (LDLs) into blood. For the first time, the influence of cytokines on the inflammation of a blood vessel at the formation of atherosclerotic plaques is taken into account. With the help of the expansion in a Fourier series and the calculation of an invariant measure, the scenario of the appearance of strange attractors depending on a change in the parameter of the dissipation of cholesterol is studied. The conclusion is made about the interconnection of the dynamics of the metabolic process in a blood vascular system and its physical state.
References
Great Medicinal Encyclopedia (Sovetsk. Entsikl., 1977), vol. 5, p. 223 (in Russian).
V.V. Verkhusha, V.M. Staroverov, P.V. Vrzhesh. The model of adhesive interaction of cells in the flow of a fluid. Biol. Membr. 11, No. 4, 437 (1994).
V.P. Baluda, M.V. Baluda, I.I. Deyanov. Physiology of the System of Hemostasis (Meditsina, 1995) (in Russian).
A.S. Shitikova. Thrombocytic Hemostasis (SPbSMU, 2000) (in Russian).
S.D. Varfolomeev, A.T. Mevkh. Prostaglandins - Molecular Bioregulators (Moscow University, 1985) (in Russian).
S.D. Varfolomeev, A.T. Mevkh, V.P. Gachok. Kinetic model of multienzyme system of blood prostanoid synthesis. 1. Mechanism of stabilization of the levels of thromboxane and prostacyclin. Molek. Biol. 20, No. 4, 957 (1986).
https://doi.org/10.1016/0303-2647(86)90033-X
S.D. Varfolomeev, V.P. Gachok, A.T. Mevkh. Kinetic behavior of the multienzyme system of blood prostanoid synthesis. BioSystems. 19, 45 (1986).
https://doi.org/10.1016/0303-2647(86)90033-X
P. Libby. The molecular bases of acute coronary syndromes. Circulation 91, No. 11, 2844 (1995).
https://doi.org/10.1161/01.CIR.91.11.2844
M.J. Davies. Stability and Instability: The two faces of coronary atherosclerosis. Paul Dudley White Lecture 1995. Circulation 94, No. 8, 2013 (1996).
https://doi.org/10.1161/01.CIR.94.8.2013
J. Berliner et al. Oxidized lipids in atherogenesis: Formation, destruction and action. Thrombosis and Haemostasis 78, No. 1, 195 (1997).
https://doi.org/10.1055/s-0038-1657525
D. Steinberg. Low density lipoprotein oxidation and its pathobiological significance. J. Biolog. Chem. 272, No. 34, 20963 (1997).
https://doi.org/10.1074/jbc.272.34.20963
P. Libby. Current concepts of the pathogenesis of the acute coronary syndroms. Circulation 104, No. 3, 365 (2001).
https://doi.org/10.1161/01.CIR.104.3.365
P. Libby. The vascular biology of atherosclerosis. In: Heart Disease: A Textbook of Cardiovascular Medicine. Edited by E. Braunwald, D.P. Zipes, P. Libby (Saunders, 2001) [ISBN: 0721685617, 9780721685618].
P. Libby, P.M. Ridker, A. Maseri. Inflammation and atherosclerosis. Circulation 105, No. 9, 1135 (2002).
https://doi.org/10.1161/hc0902.104353
P. Libby. Atherosclerosis: New look. Svit Nauky Nos. 4-5 (15-16), 19 (2002).
V.I. Grytsay, V.P. Gachok. Self-organization in fusion system of tromboxan and Prostacyclin. In: Abstracts of the V International Congress on Mathematical Modelling, V ICMM, September 30-October 6, 2002, Dubna, Moscow Region, Vol. II, p. 200.
V.I. Grytsay. Conditions of self-organization of the multienzyme prostacyclin-thromboxane system. Bulletin of the Univ. of Kiev. Ser. Phys. & Math. No. 3, 372 (2002).
V.I. Grytsay, V.P. Gachok. Regimes of self-organization in system of prostacyclin and tromboxan. Bulletin of the Univ. of Kiev. Ser. Phys. & Math. No. 4, 365 (2002).
V.I. Grytsay. Processes Modeling of the multienzyme prostacyclin and thromboxan system. Bulletin of the Univ. of Kiev. Ser. Phys. & Math., No. 4, 379 (2003).
V.I. Grytsay, V.P. Gachok. Ordered structures in mathematical system of prostacyclin and tromboxan model. Bulletin of the Univ. of Kiev. Ser. Phys. & Math. No. 1, 338 (2003).
V.I. Grytsay. Processes modelling of the multienzyme prostacyclin and tromboxan system. Bulletin of the Univ. of Kiev. Ser. Phys. & Math. No. 4, 379 (2003).
V.I. Grytsay. Self-organization and chaos in the metabolism of hemostasis in a blood vessel. Ukr. J. Phys. 61, No. 7, 648 (2016).
https://doi.org/10.15407/ujpe61.07.0648
V.I. Grytsay. A mathematical model of the metabolic process of atherosclerosis. Ukr. Biochem. J. 88, No. 4, 75 (2016).
https://doi.org/10.15407/ubj88.04.075
V.S. Anishchenko. Complex Oscillations in Simple Systems (Nauka, 1990) (in Russian).
S.P. Kuznetsov. Dynamical Chaos (Fizmatlit, 2001) (in Russian).
V.I. Grytsay. The self-organization in a macroporous structure of a gel with immobilized cells. The kinetic model of a bioselective membrane of biosensor. Dopov. NAN Ukr. No. 2, 175 (2000).
V.I. Grytsay. The self-organization in a reaction-diffusion porous medium. Dopov. NAN Ukr. No. 3, 201 (2000).
V.P. Gachok, V.I. Grytsay. The kinetic model of a macroporous granule with the regulation of biochemical proceses. Dokl. AN SSSR 282, No. 1, 51 (1985).
V.P. Gachok., V.I. Grytsay, A.Yu. Arinbasarova, A.G. Medentsev, K.A. Koshcheyenko, V.K. Akimenko. Kinetic model of hydrocortizone 1-en dehydrogenation by Arthrobacter globiformis. Biotechn. Bioengin. 33, 661 (1989).
https://doi.org/10.1002/bit.260330602
V.P. Gachok, V.I. Grytsay, A.Yu. Arinbasarova, A.G. Medentsev, K.A. Koshcheyenko, V.K. Akimenko. Kinetic model for the regulation of redox reactions in steroid transformation by Arthrobacter globiformis cells. Biotechn. Bioengin. 33, 668 (1989).
https://doi.org/10.1002/bit.260330603
V.I. Grytsay. Ordered structures in the mathematical model of a biosensor. Dopov. NAN Ukr. No. 11, 112 (2000).
V.I. Grytsay. The self-organization of the biochemical process of immobilized cells of a bioselective membrane of a biosensor. Ukr. Fiz. Zh. 46, No. 1, 124 (2001).
V.I. Grytsay. Ordered and chaotic structures in the reaction-diffusion medium. Visn. Kyiv. Univ. No. 2, 394 (2002).
V.I. Grytsay. Conditions of self-irganization of the prostacyclin-thromboxane system. Visn. Kyiv. Univ. No. 3, 372 (2002).
V.V. Andreev, V.I. Grytsay. Modeling of nonactive zones in porous granules of a catalyst and in a biosensor. Matem. Model. 17, No. 2, 57 (2005).
V.V. Andreev, V.I. Grytsay. Influence of the inhomogeneity of running of a diffusion-reaction process on the formation of structures in the porous medium. Matem. Modelir. 17, No. 6, 3 (2005).
V.I. Grytsay, V.V. Andreev. The role of diffusion in the formation of nonactive zones in porous reaction-diffusion media. Matem. Modelir. 18, No. 12, 88 (2006).
V.I. Grytsay. Unsteady conditions in porous reaction-diffusion medium. Romanian J. Biophys. 17, No. 1, 55 (2007).
V.I. Grytsay. Uncertainty of the evolution of structures in the reaction-diffusion medium of a bioreactor. Biofiz. Visn. Iss. 2 (19), 92 (2007).
V.I. Grytsay. Formation and stability of the morphogenetic field of immobilized cells of a bioreactor. Biofiz. Visn., Iss. 1 (20), 48 (2008).
V.I. Grytsay. Prediction structural instability and type attractor of biochemical process. Biofiz. Visn. Iss. 23 (2), 77 (2009).
V.I. Grytsay. Structural instability of a biochemical process. Ukr. J. Phys. 55 (5), 599 (2010).
V.I. Grytsay, I.V. Musatenko. The structure of a chaos of strange attractors within a mathematical model of the metabolism of a cell. Ukr. J. Phys. 58, No. 7, 677 (2013).
https://doi.org/10.15407/ujpe58.07.0677
V.I. Grytsay, I.V. Musatenko. Self-oscillatory dynamics of the metabolic process in a cell. Ukr. Biochim. Zh. 85, No. 2, 93 (2013).
https://doi.org/10.15407/ubj85.02.093
V.I. Grytsay, I.V. Musatenko. A mathematical model of the metabolism of a cell. CMSIM 2, No. 4, 539 (2013).
V.I. Grytsay, I.V. Musatenko. Self-organization and fractality in a metabolic processes of the Krebs cycle. Ukr. Biokhim. Zh. 85, No. 5, 191 (2013).
https://doi.org/10.15407/ubj85.05.191
V.I. Grytsay, I.V. Musatenko. Self-organization and chaos in the metabolism of a cell, Biopolymers and Cells, 30, No. 5, 404 (2014).
https://doi.org/10.7124/bc.0008B9
V. Grytsay, I. Musatenko. Nonlinear self-organization dynamics of a metabolic process of the Krebs cycle. CMSIM 3, 207 (2014).
V. Grytsay. Lyapunov indices and the Poincar'e mapping in a study of the stability of the Krebs cycle. Ukr. J. Phys. 60, No. 6, 564 (2015).
https://doi.org/10.15407/ujpe60.06.0561
V.I. Grytsay. Self-organization and fractality in the metabolic process of glycolysis. Ukr. J. Phys. 60, No. 12, 1253 (2015).
https://doi.org/10.15407/ujpe60.12.1251
V.I. Grytsay. Self-organization and fractality created by gluconeogenesis in the metabolic process. CMSIM 5, 113 (2016).
V.I. Grytsay. Spectral analysis and invariant measure in the study of a nonlinear dynamics of the metabolic process in cells. Ukr. J. Phys. 62, No. 5, 448 (2017).
https://doi.org/10.15407/ujpe62.05.0448
V.P. Gachok. Kinetics of Biochemical Processes (Naukova Dumka, 1988) (in Russian).
V.P. Gachok. Strange Attractors in Biosystems (Naukova Dumka, 1989) (in Russian).
G.Yu. Riznichenko. Mathematical Models in Biophysics and Ecology (Inst. of Computer. Studies, Moscow, Izhevsk, 2003) (in Russian).
Yu.M. Romanovskii, N.V. Stepanova, D.S. Chernavskii. Mathematical Biophysics (Nauka, 1984) (in Russian).
E.E. Selkov. Self-oscillations in glycolysis. Europ. J. Biochem. 4, 79 (1968).
https://doi.org/10.1111/j.1432-1033.1968.tb00175.x
O.P. Matyshevska, A. Yu. Karlash, Ya. V. Shtogum, A. Benilov, Yu. Kirgizov, K. O. Gorchinskyy, E.V. Buzaneva, Yu. I. Prylutskyy, P. Scharff. Self-organizing DNA/carbon nanotube molecular films. Mater. Sci. Engin. C 15, Nos. 1-2, 249 (2001).
https://doi.org/10.1016/S0928-4931(01)00309-5
S.V. Prylutska, O.P. Matyshevska, I.I. Grynyuk, Yu.I. Prylutskyy, U. Ritter, P. Scharff. Biological effects of C60 fullerenes in vitro and in a model system. Mol. Cryst. Liq. Cryst. 468, 265-274 (2007).
Downloads
Published
How to Cite
Issue
Section
License
Copyright Agreement
License to Publish the Paper
Kyiv, Ukraine
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4. Duration.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5. Loyalty.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.
.png){kind=small}
