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Growth and remodeling with application to abdominal aortic aneurysms. (English) Zbl 1408.74038
Summary: In this paper, we apply a mixture theory of growth and remodeling to study the formation and dilatation of abdominal aortic aneurysms. We adapt the continuum theory of mixtures to formalize the processes of production and removal of constituents from a loaded body. Specifically, we consider a mixture of elastin and collagen fibers which endow the material with anisotropic properties. An evolving recruitment variable defines the intermediate configuration from which the elastic stretch of collagen is measured. General formulations of the equations governing homeostatic state and aneurysm development are provided. In the homeostatic state, the idealized geometry of the aorta is a thick-walled tube subject to constant internal pressure and axial stretch. The formation of an aneurysm induces an increase of mass locally achieved via production of new material that exceeds the removal of old material. The combined effects of loss of elastin, degradation of existing and deposition of new collagen, as well as fiber remodeling results in a continuous enlargement of the aneurysm bulge. The numerical method makes use of a purposely written material subroutine, called UMAT, which is based on the constitutive formulation provided in the paper. Numerical results based on patient-based material parameters are illustrated.

MSC:
74L15 Biomechanical solid mechanics
92C30 Physiology (general)
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