D.N. Gribkov1, O.K. Zenin2, A.A. Sergienko3, Z.M. Yuldashev4, V.I. Gorbachenko5

1–3, 5 Penza State University (Penza, Russia)
4 St. Petersburg State Electrotechnical University "LETI" (Saint Petersburg, Russia)

In the diagnosis, prevention, and treatment of ischemic heart disease, it is important to predict the diameters of coronary arteries in order to detect stenosis, assess hemodynamic risk, and optimize revascularization.

Arterial networks within organs are fractal systems consisting of bifurcations. Predicting the diameters of daughter vessels based on the known diameter of the parent segment is of great practical interest. Known prediction models are empirical. This paper proposes the use of graph neural networks to predict the diameters of daughter vessels of bifurcations.

Purpose – to develop graph neural networks for predicting the diameters of coronary arteries of the heart.

Graph neural networks were used for the first time to predict the diameters of coronary arteries. A graph convolution network, a graph attention network, a GraphSAGE network, and a graph neural network based on a transformer were implemented and studied. The quality of the implemented networks, as well as a multilayer perceptron and two well-known hydrodynamic models, was evaluated on a test data set, showing the advantage of graph neural networks over known models, especially when predicting smaller diameters of bifurcation vessels. The best results were demonstrated by a graph neural network based on a transformer with determination coefficients of 0.96 when predicting the larger diameter of the daughter vessel and 0.73 for the smaller vessel diameter.

The developed neural networks can serve as the basis for prediction systems for clinical practice.

Gribkov D.N., Zenin O.K., Sergienko A.A., Yuldashev Z.M., Gorbachenko V.I. Forecasting using graph neural networks of coronary artery diameters. Biomedicine Radioengineering. 2026. V. 29. № 1. P. 84–89. DOI: https:// doi.org/10.18127/ j15604136-202601-16 (In Russian)

1. Chen Y.-li, Bai G.-Q., Ren L.-xing, Bai Y., Sun M.-y, Shang T., Ma C.-y, Ma D.-s. Blood physiological and flow characteristics within coronary artery circulatory network for human heart based on vascular fractal theory. Advances in Mechanical Engineering. 2020. V. 12. № 7. P. 1–13. DOI: 10.1177/1687814020933385.
2. Dadashev A.Sh., Zenin O.K., Miltyh I.S., Kafarov E.S. Morfometricheskie osobennosti razlichnogo vida bifurkacij vnutriorgannogo arterial'nogo rusla selezenki u lic raznogo pola i vozrasta. Rossijskij mediko-biologicheskij vestnik im. akad. I.P. Pavlova. 2024. T. 32. № 1. S. 81–92. DOI:10.17816/PAVLOVJ321742 (In Russian)
3. Huo Y., Kassab G.S. Intraspecific scaling laws of vascular trees. Journal of the Royal Society Interface. 2012, V. 9. № 66. P. 190–200. DOI: 10.1098/rsif.2011.0270.
4. Labon M., Gruzdev A. Grafovye nejronnye seti na Python. M.: DMK Press. 2024. 342 s. (In Russian).
5. Svidetel'stvo o gosudarstvennoj registracii bazy dannyh № 2021623064. Baza dannyh rezul'tatov morfometrii angiogramm vnutriorgannogo arterial'nogo rusla serdca cheloveka // O.K. Zenin, A.V. Dmitriev, I.S. Miltyh. 2021 (In Russian).
6. PyG Documentation. URL: https://pytorch-geometric.readthedocs.io/en/latest/#
7. NetworkX. URL: https://networkx.org/
8. scikit-learn. URL: https://scikit-learn.org/stable/
9. Veličković P., Cucurull G., Casanova A., Romero A., Liò P., Bengio Y. Graph Attention Networks. URL: https://arxiv.org/abs/1710.10903
10. Hamilton W.L., Ying R., Leskovec J. Inductive Representation Learning on Large Graphs. URL: https://arxiv.org/abs/1706.02216
11. Shi Y., Huang Z., Feng S., Zhong H., Wang W., Sun Y. Masked Label Prediction: Unified Message Passing Model for Semi-Supervised Classification. URL: https://arxiv.org/abs/2009.03509
12. Vaswani A., Shazeer N., Parmar N., Uszkoreit J., Jones L., Gomez A.N., Kaiser L., Polosukhin I. Attention Is All You Need. URL: https://arxiv.org/abs/1706.03762
13. Optuna. URL: https://optuna.org/
14. AdamW. URL: https://docs.pytorch.org/docs/stable/generated/torch.optim.AdamW.html
15. Why Do We Need Weight Decay in Modern Deep Learning? / F. D'Angelo, M. Andriushchenko, A. Varre, N. Flammarion. URL: https://arxiv.org/abs/2310.04415
16. HuberLoss. URL: https://docs.pytorch.org/docs/stable/generated/torch.nn.HuberLoss.html
17. Olufsen M.S., Peskin C.S., Kim W.Y. et al. Numerical Simulation and Experimental Validation of Blood Flow in Arteries with Structured-Tree Outflow Conditions. Annals of Biomedical Engineering. 2000. V. 28. P. 1281–1299. DOI: 10.1114/1.1326031.
18. Huo Y., Kassab G. Scaling Laws of Coronary Circulation in Health and Disease. Journal of Biomechanics. 2016. V. 49. № 12. P. 2531–2539. DOI: 10.1016/j.jbiomech.2016.01.044.