Abstract
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.
Highlights
Cerebral arteriovenous malformation (AVM) is a congenital abnormality of brain vessels, in which a direct discharge of blood royalsocietypublishing.org/journal/rsos R
Blood conductivity dynamics for both scenarios are presented in figure 5. These cases demonstrate that operation success depends on embolic agent input g(t), which determines whether AVM cross-section will be cut off by embolic agent the best possible way, or over time a part of AVM section previously blocked by the embolic agent will be reopened for blood flow and blood conductivity will grow
The following formulation of the optimal embolization problem as an optimal control problem is proposed: To minimize the linear combination of AVM blood conductivity degree and AVM fullness by blood at terminal time using embolic agent input as control
Summary
Cerebral arteriovenous malformation (AVM) is a congenital abnormality of brain vessels, in which a direct discharge of blood royalsocietypublishing.org/journal/rsos R. AVM is simplified to one-dimensional case with even distribution of its physical characteristics ( porosity, permeability and cross-sectional area) along model length Some aspects such as capillary forces, embolic agent adsorption 3 effect and wall properties are neglected. It is optimal control problem with integral objective function for partial differential equation with state constraints considered in §§5 and 6. This approach can potentially be used in neurosurgical practice to provide a neurosurgeon with recommendation on the course of operation
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