Patient-Specific Wall Stress Analysis in Cerebral Aneurysms Using Inverse Shell Model

Abstract

Stress analyses of patient-specific vascular structures commonly assume that the reconstructed in vivo configuration is stress free although it is in a pre-deformed state. We submit that this assumption can be obviated using an inverse approach, thus increasing accuracy of stress estimates. In this paper, we introduce an inverse approach of stress analysis for cerebral aneurysms modeled as nonlinear thin shell structures, and demonstrate the method using a patient-specific aneurysm. A lesion surface derived from medical images, which corresponds to the deformed configuration under the arterial pressure, is taken as the input. The wall stress in the given deformed configuration, together with the unstressed initial configuration, are predicted by solving the equilibrium equations as opposed to traditional approach where the deformed geometry is assumed stress free. This inverse approach also possesses a unique advantage, that is, for some lesions it enables us to predict the wall stress without accurate knowledge of the wall elastic property. In this study, we also investigate the sensitivity of the wall stress to material parameters. It is found that the in-plane component of the wall stress is indeed insensitive to the material model.

Estimating an equivalent wall-thickness of a cerebral aneurysm through surface parameterization and a non-linear spring system

“…When compared against the 20% thickness, the thinner, equivalent wall-thickness produces a striking increase in the maximum principal-stress. The maximum stresses achieved with the equivalent wall-thickness fall well within a reasonable bound for cerebral aneurysms [40,41,[57][58][59].…”

An Inverse Finite Element u/p-Formulation to Predict the Unloaded State of In Vivo Biological Soft Tissues

“…Alternatively it can be assumed to be continuous across all finite elements and can incorporate more elaborate volumetric constitutive expressions, as opposed to the simplifications of Govindjee and Mihalic 14 and Lu et al 20 The present method encounters no difficulties reaching a stable solution of the reference configuration as opposed to existing techniques modelling arterial wall inverse biomechanics using shell or membrane elements. 11,19,22,43 The method is fully implicit thus achieving quadratic convergence, while simulations require very few load steps to reach final solution compared to explicit solvers, 17 and it can run quickly since no mesh updating is required during the analysis. 2,11 Additionally, the present algorithm ensures convergence using a combination of residual and energy criterion checks.…”

“…Their numerical approach was subsequently utilised for the stress analysis of patient-specific cerebral aneurysms. 43 More recently, Bols et al 2 formulated an iterative backward displacement method to recover the zero-pressure configuration of human blood vessel geometries and predict the in vivo stress distribution through a fixed-point algorithm.…”

Digital image correlation-based point-wise inverse characterization of heterogeneous material properties of gallbladder in vitro

“…The gallbladder was modelled as a shell structure for which the bending and transverse shear responses were also stipulated. As done previously [10,25], we used an approximate bending relation derived from the surface energy density. The bending moment m was assumed to be a linear function of curvature ρ as m = Hρ, where the bending moduli H = h 2 /12 (4∂ 2 w/∂C∂C| C=I ), which for the neo-Hookean function was worked out to be H = h 2 12 4μ 1 +2μ 2 2μ 1 +2μ 2 2μ 1 +2μ 2 4μ 1 +2μ 2 μ 1 .…”