Mathematical modeling of flows in blood vessels of complex shape

Mathematical modeling of flows in blood vessels of complex shape

Автор: Gromov Yuri Y., Gorbunov Alexey V., Tyutyunnik Viacheslav M., Kopylov Sergey A.

Журнал: Cardiometry @cardiometry

Статья в выпуске: 24, 2022 года.

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A study of the structure and topography of the cerebral arterial bed of 156 virtually healthy individuals verified 17 variants of the arterial circle of the great brain, most of which are shown in actual photographs. An analysis of various approaches to modeling of cerebral vessels was carried out and it is shown that all of them are based on the representation of a blood vessel in the form of a linear cylinder. In reality, in the blood system of the brain, such sections are only rare short elements of vessels that vary in diameter and direction. Cylindrical coordinates have been most commonly used to construct mathematical models of cerebral vessels, but they are not applicable to bending vessels. The aim of this work: to build a mathematical apparatus allowing to adequately describe various types of vessels containing sections with complex geometry (bends, especially U-shaped ones, spirals, etc.). Four typical sections of the vascular system were identified, in correspondence with which mathematical surfaces were introduced, and the corresponding mathematical description was selected for each of them. The mathematical apparatus introduced into consideration allowed us to build a description of hydrodynamic processes occurring in vessels of complex shape. The results of geometrical modeling in the Mathlab system and the corresponding fragments of the script are presented. The developed mathematical software made it possible to construct a system of transfer equations for vessels of complex shape

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Blood vessels, complex shape, blood flows, mathematical, modeling

Короткий адрес: https://sciup.org/148326580

ID: 148326580   |   DOI: 10.18137/cardiometry.2022.24.145158

Список литературы Mathematical modeling of flows in blood vessels of complex shape

  • Gorbunov A.V. Evolution of Human Brain Arteries. Tambov: TSTU Publishing Center, 2022, 148 p.
  • Khananashvili Y.A. Blood supply to the cerebral cortex and its bioelectrical activity in the dynamics of spontaneous arterial hypertension. Dissertation Dr. in Medical Sciences. Scientific Research Institute of Experimental Medicine, Leningrad-Rostov, 1990, 242 p.
  • Vereshchagin N.V., Morgunov V.A., Gulevskaya T.S. Pathology of the brain in atherosclerosis and arterial hypertension. Moscow, Medicine, 1997, 288 p.
  • Nikhaeva O.A. Evaluation of functional efficiency of surgical treatment of vascular diseases of the brain. Dissertation ... Candidate of medical sciences. Kuban State Medical Academy, Krasnodar, 2003, 135 p.
  • Lachkepiani A.E., Majagaladze E.A. Adaptation-compensatory capabilities of the vilisian circle in pathology of the main vessels of the head. Tbilisi, Sabchota Sakartvelo, 1969, 88 p.
  • Mchedlishvili G.I. Spasm of cerebral arteries. Tbilisi, Metsniereba, 1977, 181 p.
  • Warlow C.P., Dennis M.S., Van Gijn J., Hankey G.J., Sadercock P.A.G., Bamford J.M., Wardlaw J. Stroke: A Practical Guide for Management of Patients. Transl. from Engl., Ed. by A.A. Skoromets, V.A. Sorokoumov. SPb., Polytechnic., 1998, 629 p.
  • Ott W.J. Middle cerebral artery blood flow in the fetus and central nervous system complications in the neonate. J. Matern. Fetal. Neonatal. Med., 2003, Vol. 14(1), pp. 26-29.
  • Korneev G.I. Age-related changes in human carotid and vertebral arteries. Abstract of dissertation.... Candidate of Medical Sciences. Kalinin, 1971, 19 p.
  • Kornienko V.I., Ozerova V.I. Pediatric neuroradiology. Мoscow, 1993, 448 p.
  • Khilko V.A., Gaidar B.V. Balloon catheter occlusion of false aneurysms of the subclinoid part of the internal carotid artery. In: Brain arterial aneurysms. Leningrad, 1983, pp. 36-43.
  • Sudakevich D.I. Architectonics of the intraocular blood supply system and its disorders. Moscow, 1971, 89 p.
  • Koshev V.I., Pirogov V.P., Ivanova V.D., Petrov E.S., Volobuyev A.N. Property of cardiovascular system to prevent hydrodynamic flutter in aorta, pulmonary trunk and their branches. Medical Biomechanics, Riga, 1986, Vol. IV, pp. 215-219.
  • Saratikov A.S., Belopasov V.V., Plotnikov M.B. Experimental and Clinical Pharmacology of the Brain Circulation. Tomsk, 1979, 156 p.
  • Zabrodskaya Y.M. Patalogoanatomical characterization of changes in the articulations of the cerebral base arteries (to the problem of aneurysm origin). Dissertation... Candidate of Medical Sciences. GU A.L. Polenov RSRI. SPb, 1996, 161 p.
  • Moskalenko E.Y., Weinstein G.B., Demchenko I.T. et al. Intracranial hemodynamics: biophysical aspects. Ltningrad, Nauka, 1975, 200 p.
  • Kulikov V.P., Smirnova Y.V., Smirnov K.V., Sidor M.V. Ultrasonic and functional diagnostics of pathological tortuosity of internal carotid arteries in children. Ultrasound and functional diagnostics, 2001, No.1, pp. 71-78.
  • Belenkaya, R.M. Stroke and variants of brain arteries. Moscow, Medicine, 1979, 176 p.
  • Gorbunov A.V. Variants of human cerebral arteries and cerebrovascular disorders: a monograph. Tambov, Pershina R.В., 2009, 310 p.
  • Pidgorny O.L. From the Theory of the Maps to Geometrical Modeling of Objects, Phenomena and Processes. The Applied Geometry and Engineering Graphics, Kiev, 2002, Issue 70, pp. 32-38.
  • Yarosh A.S., Filina N.A., Pirogova L.A. Current state of the problem of acute violations of cerebral circulation. Journal of GMU [Grodno, Inst. of Education “Grodno State Medical University”], 2014, No. 3, pp. 17–20.
  • Migliavacca F., Dubini G. Computational modeling of vascular anastomoses. Biomechanics and Modeling in Mechanobiology, 2005, Vol. 3, pp. 235–250.
  • Strong K., Chang P. Preventing chronic disease: a priority for global health. International Journal of Epidemiology. Oxford University Press, U.K., 2006, No. 35(2), pp. 492–494.
  • Simakov, S.S. Modern methods of mathematical modeling of blood flow by means of averaged models. Computer research, 2018, No. 5, pp. 581–604.
  • Hachinski V. The role of the neurologist: past, present and future. 1st International Congress: Cerebrovascular Pathology and Stroke, 2003, No. 3, pp. 33–35.
  • Sherwin J., Formaggia L., Ptiro J., Franke V. Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the arterial system. International journal for numerical methods in fluids, 2003, Vol. 43, pp. 673–700.
  • Burton A.C. Physical principles of circulatory phenomena: The physical equilibria of the heart and blood vessels. Handbook of physiology, Section 2: Circulation, 1962, Vol. 1, pp. 85–106.
  • Burton A.C. Relation of Structure to Function of Tissues of the Wall of Blood Vessels. Physiological Reviews, 1954, Vol. 34, No. 4, pp. 619–642.
  • McDonald D.A. Blood Flow in Arteries. London, UK, Williams & Wilkins, 1974, 496 p.
  • Taylor L.A., Cerrard J.H. Pressure-radius relationships for elastic tubes and their application to arteries: Theoretical relationships. Medical Biological Engineering and Computing, 1977, Vol. 15, pp. 11–17.
  • Oka S., Azuma T. Theoretical Studies in Blood Vessel Hemorheology. Theoretical and Clinical Hemorheology Copley. Berlin, Springer-Verlag Berlin Heidelberg, 1971, 78 p.
  • Bergel D.H. The static elastic properties of the arterial wall. The Journal of Physiology, 1961, Vol. 156, No. 3, pp. 445–457.
  • Purinya B.F., Kasyanov V.A. Biomechanics of large human blood vessels. Riga, Zinatne, 1980, 260 p.
  • Gorbunov A., Krasnianskaya S., Dolgov E. Nosological specificity of motor activity in the psychiatric clinic during night sleep. Archiv Euromedica, 2022, Vol. 12, No. 2, pp. 63–65.
  • Atabek H.B. Wave Propagation through a Viscous Fluid Contained in a Tethered, Initially Stressed, Orthotropic Elastic Tube. Biophysical Journal, 1968, Vol. 8, No. 5, pp. 626–649.
  • Fagula J., Sulla I. Angiographic demonstration of the congenital absence of one carotid artery. Case report. Zentralbl-Neurochir., 1984, No. 45(4), pp. 273–275.
  • Oka S., Azuma T. Physical theory of tension in thick-walled blood vessels in equilibrium. Biorheology, 1970, Vol. 7, pp. 109–117.
  • Ushida M. Cerebellar infarction due to vertebral artery dissection in a girl. To. Hattatsu, 1998, Vol. 30(6), pp. 535–541.
  • Krivoshapko S.N. Analytical surfaces in the architecture of buildings, structures and products: teaching complex. Moscow, PFUR, 2013, 94 p.
  • Kolosov S.M., Rusyak I.G. Numerical simulation of the incompressible fluid flow in a channel with a curvilinear formation. Khabarovsk, Nauka, 2008, No.1(8), pp. 61 – 74.
  • Pidgorny O.L. From the Theory of the Maps to Geometrical Modeling of Objects, Phenomena and Processes. The Applied Geometry and Engineering Graphics. Kiev, 2002, No.70, pp. 32–38.
  • Bagoutdinova A.G., Zolotonosov Ya.D., Mustakimova S.A. Geometric modeling of complex surfaces of spring-twisted channels of heat exchange devices. Proceedings of Kazan State University of Architecture and Civil Engineering, 2011, No. 4 (18), pp. 185–192.
  • Kolosov S.M., Rusyak I.G. Mathematical formulation of the problem of nonisothermal flow of viscous fluid in a curvilinear section of a pipeline. Proceedings of the Institute of Mathematics and Informatics, Udmurt State University, 2006, No.2 (36), pp. 177–180.
  • Nesnov D.V. Construction of helical surfaces of technical forms. Izvestiya Samara Scientific Center of the Russian Academy of Sciences, 2018, Vol.20, No. 4-2(84), pp. 265–270.
  • Nesnov D.V. Elements of Field Theory in Toroidal Coordinates. Construction and technogenic safety, 2019, No.16 (68), pp. 17–25.
  • Lyashkov A.A. A family of surfaces given by coordinate transformation formulas and its envelope. Bulletin of the Ivanovo State Institute, 2013, No.1 (24), pp. 55–59.
  • Lyashkov A.A. Mapping by orthogonal projection of hypersurfaces on a hypersurface. Bulletin of the Irkutsk State Technical University, 2012, No. 2, pp. 18–22.
  • Norden A.P. The theory of surfaces. Munich, GITTL, 1956, 261 p.
  • Krivoshapko S.N. To the question of aerodynamic surfaces defined by algebraic flat curves. Structural Mechanics of Engineering Structures and Constructions, 2010, No.2, pp. 98–103.
  • Gorbunov A.V. Variants of human cerebral arteries and cerebrovascular disorders: a monograph. Tambov: Pershina R.V., 2009, 310 p.
  • Belyavsky N.N. Clinical and pathogenetic variants of transient ischemic attacks in elderly and senile patients. Journal of Neurology, 2005, No. 5, pp. 9–12.
  • Krivoshapko S.N., Ivanov V.N., Halabi S.M. Analytical Surfaces: Materials on the Geometry of 500 Surfaces and Information for Calculating the Strength of Shells. Moscow, Nauka, 2006, 536 p.
  • Borisov V.V., Kruglov V.V. Fuzzy models and networks: tutorial. Moscow, Hot Line Telecom, 2012, 185 p.
  • Kofman A. Introduction to the theory of fuzzy sets. Moscow, Radio and Svyaz, 1982, 381 p.
  • Japaridze I.S. On the immersion of geometric correspondences in the model of multidimensional spaces. Applied Geometry and Engineering Graphics, 1968, No. 6, pp. 13–17.
  • Pidgorny O.L. From the Theory of the Maps to Geometrical Modeling of Objects, Phenomena and Processes. The Applied Geometry and Engineering Graphics, 2002, No.70, pp. 32–38.
  • Nigora V.N. Modeling of helical fluid motion in a cylindrical channel. Applied Geometry and Engineering Graphics, Kiev, KDTUBA, 1996, 119 p.
  • Lashnev S.I. Profiling tools for machining helical surfaces. Moscow, Mashinostroenie, 1965, 150 p.
  • Bykov V. I. Determination of a contour line on a surface given by an equation in an implicit form. All- Union Scientific Symposium “Application of Computer- Aided Design Systems in Mechanical Engineering”, 1983, No. 3, pp. 40–41.
  • Antonov S. Determination of the heat transfer coefficient elliptic spring-twisted channels of heat exchangers. CAGI, Proceedings of the XVII sch.-seminar of Young Scientists and Specialists Problems of Gas Dynamics and Heat and Mass Transfer in aerospace technology. Moscow, Zhukovsky, 2009, 283 p.
  • Gromov Yu.Yu., Gorbunov A.V., Tyutyunnik V.M. Intelligent digitalization of cardiovascular risks. Cardiometry, 2022, No.22 (May), pp.77-94. DOI: 10.18137/Cardiometry.2022.22.7794.
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