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A 3D Nonlinear Anisotropic Spherical Inflation Model for Intracranial Saccular Aneurysm Elastodynamics

¹ Department of Biology, James Madison University, Harrisonburg, VA 22807, USA
² Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807, USA

^* To whom correspondence should be addressed.

	Abstract

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 (1999, Journal of Biomechanics, 32, 593–599) and David and Humphrey (2003, Journal of Biomechanics, 36, 1143–1150). 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.

Key Words: Cerebral saccular aneurysms, nonlinear elastodynamics, anisotropy, three-dimensional hyperelasticity, spherical inflation, coupled systems

First published on March 11, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286508100498


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