Mathematical modeling and optimization of the embolization process of cerebral arteriovenous malformation

Cerebral arteriovenous malformation (AVM) is a disorderly tangle of degenerate fused blood vessels. One of the effective methods of treating AVM is embolization - filling pathological vessels with a special liquid hardening substance (embolic agent) in order to block blood flow through them. This method of surgical intervention is widely used, but still in some cases is accompanied by perioperative rupture of malformation vessels. The arteriovenous malformation embolization process is described as a process of joint filtration of two fluids inside the AVM: blood and embolic agent [1, 2]. To find optimal embolization scenarios, the task of optimal control is set. The target functionality and limitations are selected in accordance with medical indications, and the control is the embolic agent flow at the entrance to pathology. The influence of the amount of blood flow into the surrounding vascular system during embolization is studied [3]. There is a good coincidence of the calculated and clinical blood pressure when calculating the model with a given clinical blood flow [4, 5]. The solidification of the embolic agent between the stages of its supply by changing the cross-section of the AVM available for the flow of two liquid phases is taken into account [5]. In solving the problem, clinical data obtained during monitoring of hemodynamic parameters during neurosurgical embolization operations at the Academician E.N. Meshalkin National Medical Research Center. Literature: [1] Cherevko A. A. et al. Modeling of the optimal scenario of arteriovenous malformation embolization //Journal of Physics: Conference Series. – IOP Publishing, 2019. – Т. 1268. – №. 1. – С. 012017. [2] Cherevko A. A. et al. Modelling of the arteriovenous malformation embolization optimal scenario //Royal Society open science. – 2020. – Т. 7. – №. 7. – С. 191992. [3] Гологуш Т. С., Остапенко В. В., Черевко А. А. Математическое моделирование режима эмболизации артериовенозной мальформации с перетоками на основе модели двухфазной фильтрации //Журнал вычислительной математики и математической физики. – 2021. – Т. 61. – №. 9. – С. 1571-1584. English version: Gologush T. S., Ostapenko V. V., Cherevko A. A. Mathematical modeling of embolization of arteriovenous malformations with overflows on the basis of the two-phase filtering //Computational Mathematics and Mathematical Physics. – 2021. – Т. 61. – №. 9. – С. 1546-1558. [4] Черевко А. А., Гологуш Т. С., Остапенко В. В. Поиск оптимального решения задачи эмболизации артериовенозной мальформации методом роя частиц //Прикладная механика и техническая физика. – 2021. – Т. 62. – №. 4. – С. 9-21. English version: Cherevko A. A., Gologush T. S., Ostapenko V. V. Search for AN Optimal Solution of the Problem of Arteriovenous Malformation Embolization by the Particle Swarm Method //Journal of Applied Mechanics and Technical Physics. – 2021. – Т. 62. – №. 4. – С. 530-541. [5] Sharifullina T., Cherevko A., Ostapenko V. Optimal control problem arising in mathematical modeling of cerebral vascular pathology embolization //Scientific Reports. – 2022. – Т. 12. – №. 1. – С. 1-15.