Stability of membrane elastodynamics with applications to cylindrical aneurysms. (English) Zbl 1330.74101

Summary: The enlargement and rupture of intracranial and abdominal aortic aneurysms constitutes a major medical problem. It has been suggested that enlargement and rupture are due to mechanical instabilities of the associated complex fluid-solid interaction in the lesions. In this paper, we examine a coupled fluid-structure mathematical model for a cylindrical geometry representing an idealized aneurysm using both analytical and numerical techniques. A stability analysis for this subclass of aneurysms is presented. It is shown that this subclass of aneurysms is dynamically stable both with and without a viscoelastic contribution to the arterial wall.


74K15 Membranes
34D20 Stability of solutions to ordinary differential equations
76Z05 Physiological flows
92C35 Physiological flow
Full Text: DOI


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