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JOURNALS // Vestnik KRAUNC. Fiziko-Matematicheskie Nauki // Archive

Vestnik KRAUNC. Fiz.-Mat. Nauki, 2020 Volume 31, Number 2, Pages 79–91 (Mi vkam404)

MATHEMATICAL MODELING

Conformity of vein merging angles to the rules of Roux in the mathematical interpretation of Murray

N. R. Urmantsevaa, V. A. Galkinab, K. V. Mazayshvilia, M. A. Shushaeva, T. V. Gavrilenkoab

a Surgut State University
b Federal State Institution "Scientific Research Institute for System Analysis of the Russian Academy of Sciences", Surgut branch

Abstract: An algorithm has been developed to test the statistical hypothesis, which states that the Roux W. rule in Murray's mathematical interpretation is performed for merging veins located in the same plane between the fascia sheets of the anterior abdominal wall, using the Fisher and Student criteria. Using the author's technique, 100 fusions of the superficial veins of the anterior abdominal wall were studied in 50 patients (without venous pathology) on magnetic resonance images. For the first time, it was shown that the merging of superficial veins, as well as branching of arteries, occurs in accordance with the principle of minimum costs and the rules of thumb of Roux, using which, it is possible to identify anatomically the structure of veins predisposed to obvious diseases, including thrombosis. However, the range of applicability of these rules is limited by 2D geometry and requires refinement of the measurement procedure for the three-dimensional case

Keywords: Statistical hypothesis testing, Fisher test, Student test, Roux rules, magnetic resonance imaging, superficial veins.

UDC: 004.942

MSC: 34C60

DOI: 10.26117/2079-6641-2020-31-2-79-91



© Steklov Math. Inst. of RAS, 2024