Numerical modeling of functional properties of different types of structural components (biunits) of the splenic venous vasculature in normal conditions

Objective - to establish functional (conducting, draining, pillar) properties of different types of structural components (biunites) of splenic venous vasculature by their numerical modelling based on the results of morphometry.

Materials and methods. Virtual (digital) models of different types of splenic venous biunites based on their morphometric characteristics obtained earlier were used as objects for the study. We distinguished 4 types of splenic venous biunites: 1 type - complete asymmetry, the diameter of the proximal segment (D) is not equal to the diameters of the larger (dmax) and smaller (dmin) distal segment D≠dmax≠dmin, 2 type - lateral asymmetry, D=dmax, D≠dmin, 3 type - unilateral symmetry, D≠dmax, dmin=dmax, 4 type - complete symmetry, D=dmax=dmin. ANSYS Student computer program was used to analyse the conductive function (haemodynamic resistance) and pillar function (structural rigidity) of virtual models of different types of splenic venous biunites. The drainage function of virtual models of different types of splenic venous biunites was analysed using the Vasculograph computer program.

Results. It was found that in the direction of increasing the value of the index characterising 1) hemodynamic resistance biunites of different types of splenic venous vasculature were arranged as follows: 1st type, 2nd type, 3rd type, and 4th type; 2) draining function: 4th type, 2nd type, 3rd type and 1st type; 3) pillar function: 4th type, 3rd type, 2nd type and 1st type.

Conclusion. Different types of splenic venous biunites take part in fulfilment of conducting, draining and pillar functions to an unequal extent. The main role in fulfilment of the functions of blood conduction, drainage of the spleen tissue and creation of the "soft skeleton" of the organ belongs to type 1 splenic venous biunites. The morphometric characteristics of type 1 biunites can be used as a morphometric standard of the splenic venous norm.

1. Jones C. Surgery of the spleen. Surgery (Oxford). 2022;40(4):274-276. DOI: 10.1016/j.mpsur.2022.01.006.

2. Lee J.E., Cho J.S., Shin K.S., Kim S.S., You S.K., Park J.W., Shin H.S., Yoon Y.C. Diffuse Infiltrative Splenic Lymphoma: Diagnostic Efficacy of Arterial-Phase CT. Korean Journal of Radiology. 2016;17(5):734-741. DOI: 10.3348/kjr.2016.17.5.734.

3. Asaadi S., Martins K.N., Lee M.M., Pantoja J.L. Artificial intelligence for the vascular surgeon. Seminars in Vascular Surgery. 2023;36(3):394-400. DOI: 10.1053/j.semvascsurg.2023.05.001.

4. Lareyre F., Yeung K.K., Guzzi L., Di Lorenzo G., Chaudhuri A., Behrendt C.A., Spanos K., Raffort J. Artificial intelligence in vascular surgical decision making. Seminars in Vascular Surgery. 2023;36(3): 448-453. DOI: 10.1053/j.semvascsurg.2023.05.004.

5. Miltykh I., Kafarov E.S., Covantsev S., Dadashev A.S., Skarlis A.A., Zenin O.K. A new dimension in medical education: Virtual reality in anatomy during COVID-19 pandemic. Clinical Anatomy. 2023;36(7):1007-1015. DOI: 10.1002/ca.24098.

6. Ishikawa Y., Ehara K., Yamada T., Matsuzawa N., Arai S., Ban D., Kudo A., Tanabe M., Kawashima Y., Sakamoto H. Three-dimensional computed tomography analysis of the vascular anatomy of the splenic hilum for gastric cancer surgery. Surgery Today. 2018;48(9):841-847. DOI: 10.1007/s00595-018-1679-y.

7. Bokor-Billmann T., Billmann F. Spleen. In: Billmann F, Keck T, eds. Essentials of Visceral Surgery : For Residents and Fellows. Springer; 2023:281-292. DOI: 10.1007/978-3-662-66735-4_11.

8. Wiik Larsen J., Søreide K., Søreide J.A., Tjosevik K., Kvaløy J.T., Thorsen K. Epidemiology of abdominal trauma: An age- and sex-adjusted incidence analysis with mortality patterns. Injury. 2022;53(10): 3130-3138. DOI: 10.1016/j.injury.2022.06.020.

9. Fredericks C.J., Galante J.M. Splenic injuries. In: Asensio JA, Meredith JW, eds. Current Therapy of Trauma and Surgical Critical Care (Third Edition). Elsevier; 2024:398-405. DOI: 10.1016/B978-0-323-69787-3.00068-X.

10. Savage S.A. Management of blunt splenic injury: down the rabbit hole and into the bucket. Trauma Surg Acute Care Open. 2023;8(Suppl 1):e001119. DOI: 10.1136/tsaco-2023-001119.

11. Zenin O.K., Kafarov E.S., Kosnikov Yu.N., Baysultanov I.Kh., Dmitriev A.V., Bataev Kh.M. Analytical and three-dimensional (3D) anatomy of the vascular bed of the human kidney. Grozny: Chechen State University Publishing House; 2021. 218 p. (in Russ.)

12. Roux W. Ueber die verzweigungen der blutgefsse. Eine morphologische studie. Z Naturwiss. 1878;12:205-266.

13. Murray C.D. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proceedings of the National Academy of Sciences. 1926;12(3):207-214. DOI: 10/d4n7kt

14. Murray C.D. The physiological principle of minimum work applied to the angle of branching of arteries. Journal of General Physiology. 1926;9(6):835-841. DOI: 10/dq9qn9

15. Taylor D.J., Saxton H., Halliday I., Newman T., Hose D.R., Kassab G.S., Gunn J.P., Morris P.D. Systematic review and meta-analysis of Murray’s law in the coronary arterial circulation. American Journal of Physiology-Heart and Circulatory Physiology. 2024;327(1):H182-H190. DOI: 10.1152/ajpheart.00142.2024

16. Dadashev A.S., Miltykh I.S., Zenin O.K., Kafarov E.S. Morphometric characteristics of different types of splenic venous vasculature’s structural components. Humans and their health. 2024;27(1):30-38 (in Russ.). DOI: 10.21626/vestnik/2024-1/04. EDN: MKLSCV.

17. Kafarov E.S., Dadashev A.Sh., Miltykh I.S., Zenin O., inventors; FGBOU VO Penzenskiy gosudarstvennyy universitet, assignee. Kolichestvennaya anatomiya vnutriorgannogo venoznogo rusla selezenki.Russian Federation Certificate of State Registration of Database No. 2023621572. 2023 May 18. (in Russ.). EDN: JTQAFX.

18. Gharahi H., Zambrano B.A., Zhu D.C., DeMarco J.K., Baek S.Computational fluid dynamic simulation of human carotid artery bifurcation based on anatomy and volumetric blood flow rate measured with magnetic resonance imaging.International Journal of Advances in Engineering Sciences and Applied Mathematics. 2016;8(1):46-60. DOI: 10/f9tbwm.

19. Issa R.I. Solution of the implicitly discretised fluid flow equations by operator-splitting. Journal of Computational Physics. 1986;62(1):40-65. DOI: 10/fxgbtt.

20. Lechowicz R., Elwertowski M. Standards of the Polish Ultrasound Society. Ultrasound examination of the portal system and hepatic vessels. Journal of Ultrasonography. 2015;61:208-226. DOI: 10.15557/JoU.2015.0018

21. Zenіn O.K., Nіkіtіn O.V., Chvala O.O., Beshulya O.O., Tomash D.S., authors. Spetsіal'na komp’yuterna sistema modelyuvannya arterіal'nogo krovonosnogo rusla lyudini («Vasculograph»)». Ukraine. Certificate of registration of intellectual property rights 29585. 2009 July 27. (in Ukr.)

22. Xiong Z., Yan Y., Wang X., Liu Z., Luo X., Zheng T. The effect of splenic vein diameter on the diagnosis of portal vein thrombosis. Medical Physics. 2023;50(10):6614-6623. DOI: 10.1002/mp.16481

23. Vekilov D.P., Grande-Allen K.J. Mechanical Properties of Diseased Veins. 2018;14(3):182-187. DOI: 10.14797/mdcj-14-3-182

24. Rosen R. Optimality Principles in Biology. Springer US; 1967. DOI: 10.1007/978-1-4899-6419-9

25. Crandall C.L., Lin C.J., Wagenseil J.E. Major vascular ECM components, differential distribution supporting structure, and functions of the vasculome. In: The Vasculome. Elsevier; 2022:77-86. DOI: 10.1016/B978-0-12-822546-2.00010-1

26. Valaris S., Kostourou V. Cell-Extracellular Matrix Adhesions in Vascular Endothelium. In: Papadimitriou E, Mikelis CM, eds. Matrix Pathobiology and Angiogenesis. Vol. 12. Biology of Extracellular Matrix. Springer International Publishing; 2023:175-204. DOI: 10.1007/978-3-031-19616-4_7