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

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.

Modelling of the arteriovenous malformation embolization optimal scenario.

Cerebral arteriovenous malformation (AVM) is a congenital brain vessels pathology, in which the arterial and venous blood channels are connected by tangles of abnormal blood vessels. It is a dangerous disease that affects brain functioning causing the high risk of intracerebral haemorrhage. One of AVM treatment methods is embolization-the endovascular filling of the AVM vessel bundle with a special embolic agent. This method is widely used, but still in some cases is accompanied by intraoperative AVM vessels rupture. In this paper, the optimal scenario of AVM embolization is studied from the safety and effectiveness of the procedure point of view. The co-movement of blood and embolic agent in the AVM body is modelled on the basis of a one-dimensional two-phase filtration model. Optimal control problem with phase constraints arising from medicine is formulated and numerically solved. In numerical analysis, the monotone modification of the CABARET scheme is used. Optimal embolization model is constructed on the basis of real patients' clinical data collected during neurosurgical operations. For the special case of embolic agent, input admissible and optimal embolization scenarios were calculated.