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A finite element implementation of a growth and remodeling model for soft biological tissues: verification and application to abdominal aortic aneurysms. (English) Zbl 1441.74127
Summary: The general framework for growth and remodeling (G&R) of soft biological tissues shows a great potential for expanding our current understanding of biochemical and biomechanical processes, and to predict disease progression. Yet, its use is held up by the lack of a reliable and verified 3D finite element (FE) implementation capable of describing G&R processes of soft biological tissues. Thus, in this study we present the implementation of a 3D constrained mixture G&R model in a FE analysis program. In contrast to traditional finite strain FE formulations, we show that the volumetric-isochoric decomposition not only introduces numerical problems and instabilities, it also provides unphysical results. As a verification of the implementation we present adaptations of realistic aorta models to changes in the hemodynamics, i.e. changes in blood flow and pressure. The obtained results show a correspondence with the membrane theory and with clinical expectations. Application to a fusiform aneurysm model provided realistic growth rates, evolution of thickness and stress, whereas changes in the kinetic parameters show good agreement to animal models. Finally, we present simulated expansions of an asymmetric fusiform aneurysm. Non-axisymmetric elastin degradation increased the curvature of the aorta, which is characteristic for abdominal aortic aneurysms.

74L15 Biomechanical solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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