Optimal control problem arising in mathematical modeling of cerebral vascular pathology embolization

Abstract

Arteriovenous malformation (AVM) of the brain is a congenital vascular abnormality, in which the arterial and venous blood pools are intertwined and directly connected. This dangerous disease causes a high risk of intracranial hemorrhage and disrupts brain functioning. The preferred method of AVM treating is embolization, which is the endovascular filling of abnormal AVM vessels with a special embolic agent. Despite the fact that this method is widely used in neurosurgery, in some cases its use is accompanied by perioperative AVM vessels rupture. In this regard, the aim of this work is to study the optimal scenarios for multi-stage AVM embolization from the effectiveness and safety of the procedure point of view. Mathematically, the joint movement of blood and embolic agent in the AVM body is described on the basis of a one-dimensional two-phase filtration model, which takes into account the redistribution of blood to surrounding healthy vessels. For the numerical solution of the resulting integro-differential system of equations, a monotonic modification of the CABARET scheme is used. To find optimal embolization scenarios, the optimal control problem with phase constraints arising from medicine is formulated. A modified particle swarm optimization method is used to solve this problem numerically. This technique is used to obtain optimal embolization scenarios on the basis of real patients clinical data collected during neurosurgical operations.

Rheological Properties of Non-Adhesive Embolizing Compounds—The Key to Fine-Tuning Embolization Process-Modeling in Endovascular Surgery

“…Furher, the concept of considering AVM nidus embolization as a model of two-component filtration, in which the displaced component was blood and the displacing component was embolization material, which is a Newtonian fluid, was formulated and implemented by Cherevko et al [ 41 ]. Such a simplification is essential, but it allowed the authors to solve the problem of optimal control of both single-stage (total) embolization and multi-stage embolization, when subtotal embolization is performed at all stages except the last one [ 42 ]. The use of rheological relations ( Table 3 ) with a known set of constants for the two tested polymers will make it possible to more accurately formulate the law of optimal embolization.…”