Finite element based predictions of preferred material symmetries in saccular aneurysms

Over the years, various hypotheses have implicated the role of structural instabilities in the expansion of intracranial saccular aneurysms. Recent nonlinear analyses suggest, however, that particular subclasses of aneurysms are structurally stable (in the mechanics sense) and that we must consider different hypotheses. Indeed, based on an ever-increasing database, it appears that aneurysms may well expand via the remodeling of their constituents. Although more data and a kinetics-based formulation of remodeling are needed to examine this hypothesis, we present results from quasistatic finite element analyses of 12 subclasses of lesions that support the remodeling hypothesis. Briefly, we identify regional variations in material symmetry, for a class of noncomplicated axisymmetric lesions subjected to a uniform distension pressure, that minimize local maxima in multiaxial stress and tend to homogenize the stress field. Such symmetries are termed preferred. It is shown that the numerical predictions are consistent with the teleological concept that some intracranial saccular aneurysms will seek to become spherical, since the sphere is an optimal geometry for resisting a distension pressure. To achieve this, however, different subclasses must develop differently. Lesions having an initially large neck:height ratio must increase in height and therefore may seek to become increasingly stiffer circumferentially from the fundus to the neck. Conversely, lesions having an initially small neck:height ratio must increase in breadth and therefore may seek to become increasingly stiffer meridionally from the fundus to the neck. We submit that these results demonstrate the need for a detailed histological examination of regional variations in collagen organization in human lesions, for it is upon data that an analysis of remodeling must be founded.