On growth, buckling, and rupture of aneurysms: Cylindrical tube analogy.

Aneurysms are localized bulges of arteries; and they can rupture with fatal consequences. Complex mechanobiological factors preclude in vivo testing to assess the rupture risk of an aneurysm, and size based criteria are often used in clinical practice to guide surgical interventions. It is often found that tortuous and buckled aneurysms can exceed the size recommended for surgical intervention, and yet do not rupture. This study addresses why buckled aneurysms exhibit this intriguing behavior by combining in vitro inflation experiments on hyperelastic cylindrical tubes with finite element calculations. Using a biologically relevant material model for an arterial wall, we show that buckled aneurysms can grow in size without rupture under favorable arterial pre-tensions. Stretch reversal phenomenon exhibited by arteries governs whether buckling or bulging occurs first. Exponential stiffening favors the axial propagation of an aneurysm instead of radial growth or size. The choice of failure criteria based on Ogden's strain energy function, Gent's first stretch invariant, and Cauchy stress are discussed. Failure maps incorporating post-bifurcation (bulging and buckling) response are constructed to delineate the regimes of growth, buckling and rupture of an aneurysm.