Modeling Aneurysm Growth and Failure

Aneurysms are abnormal dilatations of vessels in the vascular system. They exist in two major forms: fusiform and saccular. Fusiform aneurysms are found in the human abdominal aorta while saccular aneurysms are found in cerebral blood vessels. The growth and rupture of aneurysms is driven by micro-structural alterations of the vessel, yet precise mechanisms underlying the process remain to be uncovered. Medical treatments of aneurysms are both expensive and dangerous thus a biomechanical approach can be valuable in assisting medical doctors in the process of making decisions.Biomechanical theories ofaneurysm development should include a description of growth and failure. We argue that the growth description can be done within the framework of continuum mechanics based on the one-to-one mapping of material configurations during the tissue evolution. The latter evolution is accompanied by the alteration of mass density which, in turn, triggers deformations and changes of tissue shape. We also consider a constitutive description of failure based on the concept of energy limiters. The latter means that the strain energy density must be bounded by definition and, thus, the amount of energy that can be stored and dissipated by an infinitesimal material volume must be finite. We discuss some results of the aneurysm simulation based on the described approach.