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A 3D nonlinear anisotropic spherical inflation model for intracranial saccular aneurysm elastodynamics. (English) Zbl 1197.74073

Summary: Cerebral aneurysms occur in weakened areas of artery walls resulting in a ballooning out of the wall filled with blood. A major catalyst for mathematical modeling of intracranial saccular aneurysms has been the axisymmetric membrane derivations in Shah and Humphrey [J. Biomech. 32, 593–599 (1999)] and David and Humphrey [J. Biomech. 36, 1143–1150 (2003)]. We expand on the foundational membrane dynamics to develop a blood-aneurysm-cerebrospinal fluid model from the fully three-dimensional nonlinear elastic equations of motion with system coupling at both inner and outer fluid- aneurysm boundaries consistent with Navier-Stokes. We derive the 3D elastodynamics and determine subsequent governing nonlinear ordinary differential equations for the three general material symmetries possible under the classic initial assumption of axisymmetry. We employ biologically motivated strain-energy functions to numerically solve the equations and observe resulting aneurysm cyclic stretches, thickness changes, effects of material and geometric parameters, and through-the-thickness stresses due to biological forcing for each type of material symmetry and constitutive model.

MSC:

74L15 Biomechanical solid mechanics
74E10 Anisotropy in solid mechanics
92C10 Biomechanics
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