The use of Laplace's equation in aneurysm mechanics

It is widely thought that the genesis, expansion, and rupture of intracranial aneurysms are each governed, in part, by mechanical mechanisms, and consequently that continuum mechanics has an important role to play in increasing our understanding of the natural history of these lesions. Mechanical analyses must, of course, be mathematically and conceptually consistent with fundamental principles, definitions, and findings. In this note, we identify and correct fundamental errors that appear in three recent papers on the mechanics of human intracranial aneurysms. In addition, we also show that, based on a simple analysis, it is unlikely that saccular aneurysms expand or rupture due to a limit point instability, and discuss directions for future mechanical analyses of aneurysms.