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Modelling: Big Data and Society Conference
Recent student publications
Dr. Alex White
During his PhD, Alex created a mathematical model of the embolization procedure in the treatment of Arteriovenous malformations (AVMs). Presently there are three main ways of treating Arteriovenous Malformations (AVMs): these are neurosurgery, embolization and radio-surgery. In embolization the surgeon guides a small catheter though the arterial network until the tip reaches the location of the AVM. The surgeon then injects a biological glue that will plug the abnormal vessels, reducing the blood flow through the AVM and diverting it (hopefully) to capillaries supplying normal brain tissue. AVMs are characterized by their complex branching geometries and it is of vital importance to predict the dynamics of the glue bolus when such procedures are carried out.
The main aim of his project was to derive a model for the multi-phase blood/glue flow at the branching site and to study the flow dynamics in such areas. The model comprises of two Newtonian fluids where the flow is assumed to be laminar. Alex’s work focuses on the case where glue and blood are both in the boundary layer by means of a high Reynolds number asymptotic analysis of the equations of motion. He did research on finding the solution of the boundary layer equations when the viscosity ratio is small. Finally he worked on a computational solution for the flow equations using a semi-explicit finite difference scheme and the analysis of the two-phase Navier-Stokes equations when both glue and blood are present in the core of the feeding artery.
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