Mathematical modeling of the intrarenal arterial bed structure using regression models and a graph neural network
https://doi.org/10.20538/1682-0363-2026-2-21-31
Abstract
The aim was to develop models for numerical modeling of the diameters and lengths of bifurcation segments, structural units of the intrarenal arterial bed (IAB).
Materials and methods. The study is based on previously obtained morphometric data on the structure of 9,642 arterial bifurcations (AB) of 60 corrosion casts of the IAB. AB is a section of the IAB consisting of a proximal arterial segment (AS) (D), two distal AS (with a larger (dmax) and smaller (dmin) internal diameter) and a branching point. Regression models were used for numerical modeling of the AS diameters, while a graph attention network (GAT) was used for the lengths of AS.
Results. The developed models demonstrate high prediction accuracy: for AS diameters with a larger value (dmax), the training set reached an R2 value of 0.89, for AS with a smaller value (dmin) – R2 = 0.8. For the length of the AS with a larger diameter, the training set reached an R2 value of 0.75, and the test set reached an R2 value of 0.74; for the length of the AS with a smaller diameter, the training set reached an R2 value of 0.77, and the test set reached an R2 value of 0.73.
Conclusion. The proposed models can be used for numerical modeling of the IAB structure and assessment of the adequacy of renal blood supply.
About the Authors
O. K. Zenin
Penza State University (PSU)
Russian Federation
Russian Federation
40 Krasnaya St., 440026 Penza, Russian Federation
V. I. Gorbachenko
Penza State University (PSU)
Russian Federation
Russian Federation
40 Krasnaya St., 440026 Penza, Russian Federation
D. N. Gribkov
Penza State University (PSU)
Russian Federation
Russian Federation
40 Krasnaya St., 440026 Penza, Russian Federation
A. A. Sergienko
Penza State University (PSU)
Russian Federation
Russian Federation
40 Krasnaya St., 440026 Penza, Russian Federation
Ilias Miltiadis
The University of Palermo
Italy
Italy
61 Piazza Marina St., 90133 Palermo, Italy
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Review
For citations:
Zenin O.K., Gorbachenko V.I., Gribkov D.N., Sergienko A.A., Miltiadis I. Mathematical modeling of the intrarenal arterial bed structure using regression models and a graph neural network. Bulletin of Siberian Medicine. 2026;25(2):21-31. https://doi.org/10.20538/1682-0363-2026-2-21-31
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