Further Roles of Geometry and Properties in the Mechanics of Saccular Aneurysms

Abstract

Rupture of intracranial saccular aneurysms continues to result in significant morbidity and mortality. Although it has long been thought that biomechanical factors play key roles in the genesis, growth, and rupture of these lesions, few analysis have employed realistic descriptions of the geometries and material properties. This paper presents parametric finite element studies for subclasses of elliptical and spherical lesions which complement those recently reported by Kyriacou and Humphrey. In particular, we show again that lesion shape, not size, is a primary determinant of aneurysmal wall stress. Moreover. material anisotropy and geometry can exhibit competing or synergistic effects on the stress fields -this suggests that these interactions may be important in the formulation of theories on lesion growth. Finally, we show that Laplace's equation (for spherical membranes) yields reasonable approximations for wall stress only for a very limited class of lesions. There is a need, t1herefore, for detailed analysis and thus more precise data on lesion geometry, material properties, and loading conditions.

Intracranial and Abdominal Aortic Aneurysms: Similarities, Differences, and Need for a New Class of Computational Models

“…Nonlinear finite element analyses (FEA) of idealized axisymmetric saccular aneurysms (23,42) confirmed that Laplace's relation yields reasonable results only when lesions have a small neck and are nearly spherical. For this sub-class, however, one can prove analytically that lesions described by either Fung or Skalak-Tozeren-Zarda-Chien (STZC) type stress-strain relations cannot exhibit a limit point instability (23,106,107); this is in contrast to rubber-like spherical membranes, which typically exhibit limit points (22).…”

“…42,43). The significance of this general finding was illustrated, using FEA, for classes of axisymmetric lesions (23,42,47). For example, "small" lesions with a large neck:height ratio can have much higher stresses than "large" lesions with a small neck:height ratio; contact constraints due to interactions between a lesion and surrounding tissue can decrease the maximum stresses in an otherwise large lesion, however.…”

“…Failure mechanisms remain unknown, but rupture usually occurs at the fundus (pole) despite the neck often being thinner (2,41). Although this was long perplexing, finite element calculations suggest that the maximum biaxial stresses typically occur near the fundus, where intramural shear stress is small (23,(42)(43). For this reason, it appears that a rupture criterion should be based on tensile, not shearing, stresses or strains.…”

“…For axisymmetric membranes, however, the principal (i.e., meridional and circumferential) Cauchy stress resultants T i can be found in closed form (109) and shown to depend directly on transmural pressure P and principal curvatures κ and κ 2 , not overall size: (2) Indeed, the continuing neglect of curvature is probably one reason why there is so much controversy over the elusive critical size (cf. 42,43). The significance of this general finding was illustrated, using FEA, for classes of axisymmetric lesions (23,42,47).…”

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

“…[4 -7]). Computations also suggest that wall stress is a better predictor of rupture potential than the commonly used clinical metric of maximum diameter [4,8]; rupture occurs when stress exceeds strength locally, which probably results from an imbalance in the production (synthesis) and removal (degradation) of fibrillar collagen. Nevertheless, all prior computational models of stresses in AAAs are limited by diverse simplifying assumptions, including neglect of spatial variations in the evolving mechanical properties of the wall.…”