Fractal Structure and Fractal Measurement of Pulmonary Vascular Systems
Downloads
This article is devoted to determining the fractal structure and fractal size of organs. There is a detailed description of the various mathematical methods for determining the size of fractal organs, and an analysis of errors in determining the fractal size of organs. In the article, the fractal structure, fractal size, properties of human organs were determined using the Mandelbrot-Richardson scale (or cell method). The fractal structure of the human lung was also studied by comparing the fractal structure of tree branches. In particular, tree branches, vascular systems in the human retina, and fractal measurements of the lungs were calculated. In determining the fractal scale, changes in human body parts were not taken into account. Most articles have used fractal measurement only in relation to geometric shapes. In this article, the fractal structure of human organisms is studied on the basis of mathematical formulas and special methods are used to calculate fractal dimensions, as well as the results of an appropriate number of experiments. In addition, based on these measurements, fractal measurements of the pulmonary vascular system of patients have been evaluated in several studies, widely used to describe vascular networks in various diseases, and data on their practical application have been provided.
Mandelbrot B.B. Les Objects Fractals: Forme, Hasard et Dimension.- Paris: Flammarion, 1975, 1984, 1989, 1995;
Balkhanov V.K. (2013) Fundamentals of fractal geometry and fractal calculus. Resp. ed. Ulan-Ude: Publishing house of the Buryat State University. – p. 224.
Bozhokin S.V., Parshin D.A. (2001) Fractals and multifractals. – Moscow: Izhevsk: “Regular and chaotic dynamics” (RCD).
Kronover R.M. (2000) Fractals and chaos in dynamical systems. Moscow. Postmarket.
Morozov A.D. (1999) Introduction to the theory of fractals. - Nizhny Novgorod: Nizhny Novgorod State University.
Kononyuk A.E. (2016) Discrete - continuous mathematics. (Surfaces). - In the 12th book. Book 6. Part 2.— Kiev: Osvita of Ukraine. - p. 618.
A.A. Potapov Fractal theory: sampling topology. - M .: University book, 2005, 868 p.
Pererva L.M., Yudin V.V. (2007) Fractal modeling // Tutorial. under total. ed. V.N. Gryanika. - Vladivostok: Publishing house of the Vladivostok State University of Economics and Service. – p. 186.
Richard M. Cronover. (2000) Fractals and chaos in dynamical systems. Fundamentals of the theory - Moscow: POSTMARKET. – p. 350.
Feder E. Fractals. (1991) Translated from English Moscow: Mir. – p. 254. (Jens Feder, Plenum Press, NewYork, 1988).
Bondarenko B.A. (1990) Generalized Pascal's triangles, their fractals, graphs and applications. – Tashkent: Fan. – p. 192.
Bondarenko B.A. (2010) Generalized Pascal Triangles and Pyramids, their Fractals, Graphs, and Applications – USA, Santa Clara: Fibonacci Associations, The Third Edition. – p. 296.
Gerald Elgar. (2008) Measure, Topology, and Fractal geometry. Second Edition. Springer Science+Business Media, LLC. – p. 272.
Kenneth Falconer. (2014) Fractal Geometry. Mathematical Foundations and Applications. Third Edition. University of St Andrews UK. Wiley. – p. 400.
Wellestead S. (2003) Fractals and wavelets for image compression in action. Study guide. Moscow: Triumph Publishing House. – p. 320.
Anarova, S., Nuraliev, F., Narzulloev, O. Construction of the equation of fractals structure based on the rvachev r-functions theories //Journal of Physics: Conference Series, 2019, 1260(7), 072001
Nuraliev F.M., Anarova Sh.A., Narzulloev O.M. Mathematical and software of fractal structures from combinatorial numbers. International Conference on Information Science and Communications Technologies ICISCT 2019 Applications, Trends and Opportunities 4th, 5th and 6th of November 2019, Tashkent University of Information Technologies TUIT, TASHKENT, UZBEKISTAN. (SCOPUS).
H.N.Zaynidinov, J.U.Juraev, I.Yusupov, J.S. Jabbarov Applying Two-Dimensional Piecewise-Polynomial Basis for Medical Image Processing// International Journal of Advanced Trends in Computer Science and Engineering (IJATCSE) – Scopus Volume 9, No.4, Jule -August 2020 [5259-5265] p.
https://doi.org/10.30534/ijatcse/2020/156942020.
A.A. Potapov Fractals, Scaling and Fractional Operators in Radio Engineering and Electronics: Current State and Development. Radioelectronics Journal No. 1, 2010.
Zainidinov Kh.N., Anarova Sh.A., Zhabbarov Zh.S. Fractal measurement and prospects for its application // Problems of computational and applied mathematics journal. – Toshkent. 2021. No. 3 (33), - pp. 105-114
All Content should be original and unpublished.