Mathematical modelling of the embolization process in the treatment of arteriovenous malformations

• Main Author: White, A. H.
• Published: University College London (University of London) 2008
• Subjects: 617.4
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.719132

Arteriovenous malformations (AVMs) are neurological defects where the arte rial and venous systems are connected directly with no intervening capillaries. The absence of capillaries means that blood at high pressure is entering the venous system directly and so a venous haemorrhage is possible. AVMs can be treated by embolization in which a glue is injected into a local artery with the aim of diverting the blood flow away from the AVM and so reducing the risk of haemorrhage. The thesis introduces a mathematical model for the embolization process by considering a two phase fluid dynamical model. Both numerical and as ymptotic techniques are used to analyse the flow of the two fluids in different configurations. At the start of the thesis both the fluids are treated as inviscid and their interaction modelled using analytical techniques such as conformal mapping theory. Next, viscous effects are included in the model by assuming that both fluids are present in a thin wall layer as would be the case just be fore the glue has set. Finally the problem of both fluids being present in the core of the artery is treated numerically using the Volume of Fluid method. A detailed account of this method is given. The method essentially tracks the interface between the glue and the blood over time and thus can model how the glue spreads, for instance just after injection.