Inverse method of stress analysis for cerebral aneurysms

Abstract

We present a method for predicting the wall stress in a class of cerebral aneurysms. The method hinges on an inverse formulation of the elastostatic equilibrium problem; it takes as the input a deformed configuration and the corresponding pressure, and predicts the wall stress in the given deformed state. For a membrane structure, the inverse formulation possesses a remarkable feature, that is, it can practically determine the wall tension without accurate knowledge of the wall elastic properties. In this paper, we present a finite element formulation for the inverse membrane problem and perform material sensitivity studies on idealized lesions and an image-based cerebral aneurysm model.

Nondestructive mechanical characterization of developing biological tissues using inflation testing

“…These equations were initially derived for thin axisymmetric geometries [10,11], however it has been demonstrated that they can closely approximate the stress resultants in geometries that do not necessarily deform axisymmetrically due to material anisotropy [35,36] including anisotropic tissues subjected to inflation testing [19,20,37].…”

Local mechanical properties of human ascending thoracic aneurysms

“…The surface right Cauchy-Green tensor, C, and surface Green-Lagrange strains, E, were computed from the identified displacements using the local coordinate system of the NURBS mesh. The Cauchy membrane tension, t, at every Gauss point in the NURBS mesh was identified using an inverse membrane approach [5,22] which formulates the equilibrium problem directly on the deformed configuration. Additional details on the calculation of the surface strains and wall tension with respect to the NURBS coordinates can be found in [5].…”

“…In the inverse stress computation, the boundary of the analysis domain was fixed. Enforcing displacement based boundary conditions also causes a boundary layer effect whereby the stress solution near the boundary is expected to be inaccurate [21,22]. To minimize the influence of this boundary layer on the material property identification, the outer ring of elements were excluded from the material parameter identification and any further analysis.…”

Computational modelling for cerebral aneurysms: risk evaluation and interventional planning

“…Their diagnosis and the potentially dire consequences of rupture create a dilemma for patients and doctors, a dilemma centred on the risk of aneurysms growing or bleeding and amplified by the availability of minimally invasive endovascular treatments. Estimates of the incidence of aneurysmal subarachnoid haemorrhage range from 9 to 20 per 100 000 [1], considerably lower than aneurysm prevalence (3.6% at autopsy, 6.0% via angiography [2]). Thus, the majority of aneurysms do not rupture, a consistent finding in observation studies [3,4].…”

“…Accurate mechanical models, which can predict the stress distributions in an aneurysm, have the potential to assist diagnostic decisions [6]. However, the micro-structure, material properties, thickness and the strength of the aneurysm tissue are difficult to determine non-invasively.…”