Mathematical model of the change in hemodynamics around a vascular pathology in neurosurgical intervention

An approach is proposed to model hemodynamics in an arteriovenous malformation and its vascular environment during neurosurgical embolization. This approach is based on a combination of the filtration model of blood flow and the embolic agent in the malformation with a hydraulic approach for the vessels surrounding the malformation. The model is described mathematically by a system of integrodifferential hyperbolic equations. The parameters and functions included in the model are determined using real clinical data from patients. Based on the model, the problem of optimal control of multistage embolization was formulated and studied numerically. Optimal embolization regimens were found for which there is good agreement between the calculated and clinical data. The proposed approach can be used to develop preoperative recommendations about the optimal tactics of surgical intervention.