Abstract: We have presented a mathematical model to study the evolution, growth and risk rupture of nontraumatic aneurysms contained within a cylindrical region of blood vessels. Analytical and numerical solutions are studied. Results affirmed that the intra-aneurysmal pressure and bloodstream flow account for the evolution and growth of aneurysms, and we find that an aneurysm may rupture when the ratio of the lateral membrane contraction to longitudinal membrane extension approaches one. Numerical properties of intra-aneurysmal pressure, impact fluid velocity, membrane displacement and the deformed radius with respect to the Poisson ratio, membrane thickness and extensional rigidity are studied. The importance of the findings is rested on the fact that they can be used to improve noninvasive means for predicting aneurysm rupture, and treatment and management decisions after rupture.
Keywords: Elastodynamics, Filtration, Navier-Stokes, Numerical Solutions, Permeability, Poisson Ratio, Aneurysm.