Geodesic
Conformity of vein merging angles to the rules of Roux in the mathematical interpretation of Murray
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 79-91 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, magnetic resonance imaging, superficial veins.
Mots-clés : Roux rules 
@article{VKAM_2020_31_2_a5,
     author = {N. R. Urmantseva and V. A. Galkin and K. V. Mazayshvili and M. A. Shushaev and T. V. Gavrilenko},
     title = {Conformity of vein merging angles to the rules of {Roux} in the mathematical interpretation of {Murray}},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {79--91},
     year = {2020},
     volume = {31},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a5/}
}
TY  - JOUR
AU  - N. R. Urmantseva
AU  - V. A. Galkin
AU  - K. V. Mazayshvili
AU  - M. A. Shushaev
AU  - T. V. Gavrilenko
TI  - Conformity of vein merging angles to the rules of Roux in the mathematical interpretation of Murray
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2020
SP  - 79
EP  - 91
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a5/
LA  - ru
ID  - VKAM_2020_31_2_a5
ER  - 
%0 Journal Article
%A N. R. Urmantseva
%A V. A. Galkin
%A K. V. Mazayshvili
%A M. A. Shushaev
%A T. V. Gavrilenko
%T Conformity of vein merging angles to the rules of Roux in the mathematical interpretation of Murray
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2020
%P 79-91
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a5/
%G ru
%F VKAM_2020_31_2_a5
N. R. Urmantseva; V. A. Galkin; K. V. Mazayshvili; M. A. Shushaev; T. V. Gavrilenko. Conformity of vein merging angles to the rules of Roux in the mathematical interpretation of Murray. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 31 (2020) no. 2, pp. 79-91. http://geodesic.mathdoc.fr/item/VKAM_2020_31_2_a5/

[1] Passariello A., “Wilhelm Roux (1850-1924) and blood vessel branching”, Journal of Theoretical and Applied Vascular Research, 1:1 (2016) | DOI

[2] Sveshnikov A. V., Computer analysis of microvascular networks, dissertation for the degree of candidate of medical sciences, Smolensk, 2007, 133 pp.

[3] Murray C. D., “The physiological principle of minimum work applied to the angle of branching of arteries”, J. Gen. Physiol, 9:6 (1926), 835–841 | DOI

[4] Rossitti S., Lofgren J., “Vascular dimensions of the cerebral arteries follow the principle of minimum work”, Stroke, 24:3 (1993), 371–377 | DOI

[5] Willems P. W. A., Han K. S., Hillen B., “Evaluation by solid vascular casts of arterial geometric optimisation and the influence of ageing”, J. Anat., 196:2 (2000), 161–171 | DOI

[6] Bagaev S. N., Zakharov V. N., Orlov V. A., “The law of branching of blood vessels”, Russian Journal of Biomechanics, 6:4 (2002), 13–29

[7] Elshin M. A., One-dimensional mathematical model of blood flow dynamics in the mainstream of the human arterial system and a variant of its practical application, dissertation for the degree of candidate of medical sciences, Saratov, 2009, 145 pp.

[8] Bogachenko S. E., Ustinov Yu. A., “The model of blood movement in the arterial vessel during systole and the analysis of the stress state of the wall taking into account helical anisotropy”, Russian Journal of Biomechanics, 13:1(43) (2009), 29–42

[9] Rossitti S., Lofgren J., “Vascular Dimensions of the Cerebral Arteries Follow the Principle of Minimum Work”, Stroke, 24:3, March (1993), 371–377 | DOI

[10] Willems P. W. A., Han K. S., Hillen B., “Evaluation by solid vascular casts of arterial geometric optimization and the influence of ageing”, J. Anat., 2000, no. 196, 161–171 | DOI

[11] Zamir M., “The Role of Shear Forces in Arterial Branching”, The journal of general physiology, 67, March (1976), 213–222 | DOI

[12] Smorodinov A. V., A synthetic model of microvascular networks based on modeling of the microvascular bed (morphological, biological, biophysical, mathematical aspects), dissertation for the degree of candidate of medical sciences, Smolensk, 2007, 183 pp.

[13] Hughes A. D., “Optimality, Cost Minimization and the Design of Arterial Networks”, Stroke, 2015, no. 10, March, 1–20 | Zbl

[14] Willems P. W. A., Han, K. S., Hillen B., “Evaluation by solid vascular casts of arterial geometric optimisation and the influence of ageing”, Journal of Anatomy, 196:2 (2000), 161–171 | DOI

[15] Zamir M., “Nonsymmetrical bifurcations in arterial branching”, The Journal of General Physiology, 72:6 (2004), 837–845 | DOI