Modeling of a False Aneurysm in an Artery: Equilibrium and Development of a Hematoma

Abstract

We present a new one-dimensional model of a false aneurysm in an artery describing several stages of development of aneurysm by expanding a hematoma that exchanges blood with a vessel channel through a small hole in the thin elastic vessel wall. The model involves one hyperbolic and two parabolic partial differential equations joined by common unknowns (the artery and hematoma pressures and the radial displacement of the wall) and by the classical Kirchhoff transmission conditions on the pressure and blood flows which simulate the blood exchange through the hole. We obtain the equilibrium state condition for an aneurysm and propose criteria for aneurysm developing by hematoma thickening or lengthening. We propose a simplified “0-dimensional” model applicable only for detecting an aneurysm by using peripheral examination and solving inverse problems.