Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis

Abstract

A new method is proposed for estimating the elastic properties of the inhomogeneous and anisotropic structure of saccular cerebral aneurysms by inverse analysis. The aneurysm is modelled as a membrane and the constitutive response of each individual layer of the passive tissue is characterized by a transversely isotropic strain energy function of exponential type. The collagen fibres in the aneurysm wall are assumed to govern the mechanical response. Four parameters characterize the constitutive behaviour of the tissue: two initial stiffnesses of the collagen fabric in the two in-plane principal directions, one parameter describing the degree of nonlinearity that the collagen fibres exhibit and the other structural parameter, i.e. the angle which defines the orientation of the collagen fibres. The parameter describing the fibre nonlinearity is assumed to be constant, while all others are assumed to vary continuously over the aneurysm surface. Two model aneurysms, with the same initial geometry, boundary and loading conditions, constitutive behaviour and finite-element discretization, are defined: a 'reference model' with known distributions of material and structural properties and an 'estimation model' whose properties are to be estimated. An error function is defined quantifying the deviations between the deformations from the reference and the estimation models. The error function is minimized with respect to the unknown parameters in the estimation model, and in this way the reference parameter distributions are re-established. In order to achieve a robust parameter estimation, a novel element partition method is employed. The accordance between the estimated and the reference distributions is satisfactory. The deviations of the maximum stress distributions between the two models are below 1%. Consequently, the wall stresses in the cerebral aneurysm estimated by inverse analysis are accurate enough to facilitate the assessment of the risk of aneurysm rupture.

Effect of tendon stiffness on the generated force at the Achilles tendon - 3D finite element simulation of a human triceps surae muscle during isometric contraction

“…In many situations, to identify the material parameters is difficult or even impossible to perform. Hence, in several cases, an inverse analysis is used to obtain the material parameters (e.g., Kroon and Holzapfel, 2008). Our software would be also a useful tool for identifying the material parameters in the passive behavior of biological soft tissues, such as muscle and tendinous tissues by inverse FEM analysis.…”

Towards Regional Elastography of Intracranial Aneurysms

“…In terms of the model, we will study the incorporation of the anisotropy of the membrane [3] and the use of a different model for forward and inverse problems.…”

“…The aneurysm wall is usually characterized by a thin membrane [3], thus we modelled it as a shell object in which the surface is composed by triangles [4] and the thickness is then a variable of the mesh element. As a consequence, the stiffness of a shell element * E will be obtained as the product between the Young's modulus and the thickness of the wall.…”

“…In our application, the inverse problem framework will consist in estimating the mechanical parameters of a biomechanical model of the aneurysm based on non-invasive measurements of the dynamic pulsation and blood flow. The first theoretical framework addressed to the elasticity estimation of cerebral aneurysms has recently been proposed by Kroon and Holzapfel [3]. The authors present a numerical model characterized by a spherical shape discretized into a small number of mesh elements and by boundary conditions based on a uniform distribution of the pressure along the surface.…”

Toward integrated management of cerebral aneurysms

“…(ii) From anatomical models to the estimation of aneurysm mechanical properties A data assimilation framework can be designed to estimate the mechanical parameters of a computational model of the cerebral aneurysm wall based on available wall pulsation measurements, as Kroon & Holzapfel (2008) applied on idealized (spherical, axisymmetric) aneurysm geometries. In Balocco et al (2008), we incorporated information provided by in vivo imaging data into a data assimilation framework for estimating regional mechanical properties of cerebral aneurysms.…”