A fluid mechanical view on abdominal aortic aneurysms. (English) Zbl 1221.76262
Summary: Abdominal aortic aneurysms are a dilatation of the aorta, localized preferentially above the bifurcation of the iliac arteries, which increases in time. Understanding their localization and growth rate remain two open questions that can have either a biological or a physical origin. In order to identify the respective role of biological and physical processes, we address in this article these questions of the localization and growth using a simplified physical experiment in which water (blood) is pumped periodically (amplitude \(a\), pulsation \(\omega\)) in an elastic membrane (aorta) (length \(L\), cross-section \(A_{0}\) and elastic wave speed \(c_{0}\)) and study the deformation of this membrane while decharging in a rigid tube (iliac artery; hydraulic loss \(K\)). We first show that this pulsed flow either leads to a homogeneous deformation or inhomogeneous deformation depending on the value of the non-dimensional parameter \(c_{0}^{2}(aL\omega^{2}K)\). These different regimes can be related to the aneurysm locations. In the second part, we study the growth of aneurysms and show that they only develop above a critical flow rate which scales as \(A_{0}c_{0} \sqrt{k}\).
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