Eur J VascSurg 7, 667-674 (1993) Biomechanical Factors in Abdominal Aortic Aneurysm Rupture Fabio Inzoli 1, Federica BoschettP, Mario Zappa 2, Tito Longo 2 and Roberto Fumero ~ 1 Dipartimento di Bioingegneria, Politecnico di Milano and 2Isituto di Chirurgia Generale e Cardiovascolare, Policlinico di Milano, Milano, Italy Hitherto the size of abdominal aortic aneurysms (AAA) has been considered the most important factor in determining the risk of rupture. For this reason most interest had been devoted to physical, echographic and tomographic analyses of the shape of AAA. However, it is known that rupture can also occur in small AAA. Other factors must be considered to have an important role in the natural history of aneurysms. The aim of this study was to characterise the mechanical stress in the wall of an AAA due to pressure in the presence of atherosclerosis, intraluminal thrombus and anatomical restraints. The Finite Elements Method (FEM) was used to determine wall stress distribution. Due to the simplicity of the AAA structure an axisymmetric model has been built. The results of the structural analysis confirms that maximum stress increases with diameter. These effects may be reduced by the presence of intraluminal thrombus, which in the models reduces maximum stress by up to 30%; however this is not the case for dissecting thrombus. On the other hand atherosclerotic plaques cause stress concentration and a significant increase in maximum wail stress. The risk of rupture can increase by about 200%. Finally the investigation shows the FEM is a versatile tool for studying the mechanics of vascular structures. It enables the influence of various parameters on wall stress to be quantified in diagnostic settings, and so could be useful for predicting the rupture of AAA, although at present such predictions are limited by data leakage and by the approximations used in the model. K~ Words: Aneurysm; Mathematical model; Finite Element Method; Mechanical stress. Introduction According to clinical, pathological and biochemical observations 1-9 a number of risk factors have been identified for rupture of abdominal aortic aneurysms (AAA). Since the early studies of Szilagyi et al. 4-5 the size of AAA seems to be the principal risk factor. It has been suggested ! that patients with AAAs that are more than 5-7cm in diameter should undergo sur- gery, but this can be safely deferred for smaller aneurysms. This strategy has been challenged because small diameter AAAs also rupture, l°-n Since rupture occurs when the stress exceeds the ultimate strength in the arterial wall, the knowledge of stress distri- bution may be a useful factor in evaluating of the risk of rupture. Finite Element Method (FEM), a computer-based method for solving complex structural problems, has been used in AAA models to determine the relative Please address all correspondence to: Ing. Federica Boschetti, Dipartimento di Bioingegneria--Politecnico di Milano, PiazzaLeo- nardo da Vinci32, 20133Milano, Italy. contribution of aneurysm size, wall thickness and geometry to wall stress distribution. 2 The influence of other variables, such as wall composition and throm- bus formation, albeit related to the natural history of the lesion, has not been evaluated. The geometrical parameters of AAA and the re- lationship with internal aneurysm components such as mural calcification and lumen thrombus have been correlated by Computer Axial Tomography (CAT). So far, CAT imaging descriptors have been considered predictors of uncertain value. 12" 13 The aim of this study was to assess the influence of these variables upon the maximum stress which contributes to aneurysm rupture. In order to evaluate the relative influence of geometry, internal and exter- nal restraints and internal thrombus to variations in stress distribution in the vessel wall, data recorded by CAT analyses of different sizes of AAA have been used in mathematical models. Method During the period 1988-1990, 30 cases of AAA under- went CAT examination (General Electric 9800). The 0950-821X/93/060667+08 $08.00/0© 1993Grune & StrattonLtd.