Hydraulic model of cerebral arteriovenous malformations

Abstract

The paper presents a model of a cerebral vascular system including two types of vessel networks (arterial and venous) joined by a porous medium as a substitute to a microcapillary system. The aim of the paper is to reproduce numerically experimental data on endovascular measurements of fluid velocity and pressure in the afferent artery and the efferent vein of the arteriovenous malformation (AVM). The suggested model qualitatively simulates all the main features of the experimental $vp$-diagrams: presence of the time shift between velocity and pressure waves, semicircular shape of the diagram, difference in the direction of circulation in the arterial and venous parts and upper-left drift of the diagram during the embolisation of the AVM. The velocity–pressure time shift is analysed on the modelling example of pulsation flow within a vessel in a cylindrical porous medium. The demonstrated adequacy of the model allows its further use for simulation of various strategies of AVM treatment, haemorrhage risk estimations, etc.