The influence of shape on the stresses in model abdominal aortic aneurysms

Presence of a small abdominal aortic aneurysm (AAA) often presents a difficult clinical dilemma--a reparative operation with its inherent risks versus monitoring the growth of the aneurysm, with the accompanying risk of rupture. The risk of rupture is conventionally believed to be a function of the AAA bulge diameter. In this work, we hypothesized that the risk of rupture depends on AAA shape. Because rupture is inevitably linked to stress, membrane theory was used to predict the stresses in the walls of an idealized AAA, using a model which was axisymmetric and fusiform, with the ends merged into straight opened-ended tubes. When the stresses for many different shapes of model AAAs were examined, a number of conclusions became evident: (i) maximum hoop stress typically exceeded maximum meridional stress by a factor of 2 to 3 (ii) the shape of an AAA had a small effect on the meridional stresses and a rather dramatic effect on the hoop stresses, (iii) maximum stress typically occurred near the inflection point of a curve drawn coincident with the AAA wall, and (iv) the maximum stress was a function--not of the bulge diameter---but of the curvatures (i.e. shape) of the AAA wall. This last result suggested that rupture probability should be based on wall curvatures, not on AAA bulge diameter. Because curvatures are not much harder to measure than bulge diameter, this concept may be useful in a clinical setting in order to improve prediction of the likelihood of AAA rupture.