Single vessel hydrodynamic model in an arteriovenous malformation

Abstract

We study the hydrodynamics of a single vessel where the fluid follow a Poisseuillean flow condition. We introduce an analytic expression that approximates the arteriovenous malformation (AVM) vessel shape: a cylinder with Gaussian shape enlargement at the middle portion. Under conservation of mass and simplifications of the Navier-Stokes equation for Poiseuillean flow condition, we show that the relative pressure gradient across the wall of the enlarged area varies with enlargement volume. We also show that the dynamic pressure contribution play a vital role in the total pressure inside the vessel as determined by the average outgoing flow speed parameter 〈v_o〉. By looking at the variation of the pressure on the vessel walls, the model might be able to locate regions in a real AVM vessel that are prone to rupture and bleeding. The results might give new insights and better understanding of the nature of AVM.