Pavel Skacel

Importance of material model in wall stress prediction in abdominal aortic aneurysms

BACKGROUND Results of biomechanical simulation of the abdominal aortic aneurysm (AAA) depend on the constitutive description of the wall. Based on in vitro and in vivo experimental data several constitutive models for the AAA wall have been proposed in the literature. Those models differ strongly from each other and their impact on the computed stress in biomechanical simulation is not clearly understood. METHODS Finite element (FE) models of AAAs from 7 patients who underwent elective surgical repair were used to compute wall stresses. AAA geometry was reconstructed from CT angiography (CT-A) data and patient-specific (PS) constitutive descriptions of the wall were derived from planar biaxial testing of anterior wall tissue samples. In total 28 FE models were used, where the wall was described by either patient-specific or previously reported study-average properties. This data was derived from either uniaxial or biaxial in vitro testing. Computed wall stress fields were compared on node-by-node basis. RESULTS Different constitutive models for the AAA wall cause significantly different predictions of wall stress. While study-average data from biaxial testing gives globally the same stress field as the patient-specific wall properties, the material model based on uniaxial test data overestimates the wall stress on average by 30 kPa or about 67% of the mean stress. A quasi-linear description based on the in vivo measured distensibility of the AAA wall leads to a completely altered stress field and overestimates the wall stress by about 75 kPa or about 167% of the mean stress. CONCLUSION The present study demonstrated that the constitutive description of the wall is crucial for AAA wall stress prediction. Consequently, results obtained using different models should not be mutually compared unless different stress gradients across the wall are not taken into account. Highly nonlinear material models should be preferred when the response of AAA to increased blood pressure is investigated, while the quasi-linear model with high initial stiffness produces negligible stress gradients across the wall and thus, it is more appropriate when response to mean blood pressure is calculated.

Structure-based constitutive model can accurately predict planar biaxial properties of aortic wall tissue

Structure-based constitutive models might help in exploring mechanisms by which arterial wall histology is linked to wall mechanics. This study aims to validate a recently proposed structure-based constitutive model. Specifically, the models ability to predict mechanical biaxial response of porcine aortic tissue with predefined collagen structure was tested. Histological slices from porcine thoracic aorta wall (n=9) were automatically processed to quantify the collagen fiber organization, and mechanical testing identified the non-linear properties of the wall samples (n=18) over a wide range of biaxial stretches. Histological and mechanical experimental data were used to identify the model parameters of a recently proposed multi-scale constitutive description for arterial layers. The model predictive capability was tested with respect to interpolation and extrapolation. Collagen in the media was predominantly aligned in circumferential direction (planar von Mises distribution with concentration parameter bM=1.03 ± 0.23), and its coherence decreased gradually from the luminal to the abluminal tissue layers (inner media, b=1.54 ± 0.40; outer media, b=0.72 ± 0.20). In contrast, the collagen in the adventitia was aligned almost isotropically (bA=0.27 ± 0.11), and no features, such as families of coherent fibers, were identified. The applied constitutive model captured the aorta biaxial properties accurately (coefficient of determination R(2)=0.95 ± 0.03) over the entire range of biaxial deformations and with physically meaningful model parameters. Good predictive properties, well outside the parameter identification space, were observed (R(2)=0.92 ± 0.04). Multi-scale constitutive models equipped with realistic micro-histological data can predict macroscopic non-linear aorta wall properties. Collagen largely defines already low strain properties of media, which explains the origin of wall anisotropy seen at this strain level. The structure and mechanical properties of adventitia are well designed to protect the media from axial and circumferential overloads.

Impact of poroelasticity of intraluminal thrombus on wall stress of abdominal aortic aneurysms

BackgroundThe predictions of stress fields in Abdominal Aortic Aneurysm (AAA) depend on constitutive descriptions of the aneurysm wall and the Intra-luminal Thrombus (ILT). ILT is a porous diluted structure (biphasic solid–fluid material) and its impact on AAA biomechanics is controversially discussed in the literature. Specifically, pressure measurements showed that the ILT cannot protect the wall from the arterial pressure, while other (numerical and experimental) studies showed that at the same time it reduces the stress in the wall.MethodTo explore this phenomenon further a poroelastic description of the ILT was integrated in Finite Element (FE) Models of the AAA. The AAA model was loaded by a pressure step and a cyclic pressure wave and their transition into wall tension was investigated. To this end ILT’s permeability was varied within a microstructurally motivated range.ResultsThe two-phase model verified that the ILT transmits the entire mean arterial pressure to the wall while, at the same time, it significantly reduces the stress in the wall. The predicted mean stress in the AAA wall was insensitive to the permeability of the ILT and coincided with the results of AAA models using a single-phase ILT description.ConclusionAt steady state, the biphasic ILT behaves like a single-phase material in an AAA model. Consequently, computational efficient FE single-phase models, as they have been exclusively used in the past, accurately predict the wall stress in AAA models.

Poisson׳s ratio of arterial wall – Inconsistency of constitutive models with experimental data

Poisson׳s ratio of fibrous soft tissues is analyzed in this paper on the basis of constitutive models and experimental data. Three different up-to-date constitutive models accounting for the dispersion of fibre orientations are analyzed. Their predictions of the anisotropic Poisson׳s ratios are investigated under finite strain conditions together with the effects of specific orientation distribution functions and of other parameters. The applied constitutive models predict the tendency to lower (or even negative) out-of-plane Poisson׳s ratio. New experimental data of porcine arterial layer under uniaxial tension in orthogonal directions are also presented and compared with the theoretical predictions and other literature data. The results point out the typical features of recent constitutive models with fibres concentrated in circumferential-axial plane of arterial layers and their potential inconsistence with some experimental data. The volumetric (in)compressibility of arterial tissues is also discussed as an eventual and significant factor influencing this inconsistency.

Numerical implementation of constitutive model for arterial layers with distributed collagen fibre orientations

Several constitutive models have been proposed for the description of mechanical behaviour of soft tissues containing collagen fibres. Some of the commonly used approaches accounting for the dispersion of fibre orientations are based on the summation of (mechanical) contributions of differently oriented fibre families. This leads to the need of numerical integration on the sphere surface, and the related numerical consumption is the main disadvantage of this category of constitutive models. The paper is focused on the comparison of various numerical integration methods applied to a specific constitutive model applicable for arterial walls. Robustness and efficiency of several integration rules were tested with respect to application in finite element (FE) codes. Among all the analysed numerical integration rules, the best results were reached by Lebedev quadrature; the related parameters for the specific constitutive model are presented in the paper. The results were implemented into the commercial FE code ANSYS via user subroutines, and their applicability was demonstrated by an example of FE simulation with non-homogenous stress field.

Material parameter identification of arterial wall layers from homogenised stress–strain data

Multilayer structure of the artery can have significant effects on the resulting mechanical behaviour of the artery wall. Separation of the artery into individual layers is sometimes performed to identify the layer-specific parameters of constitutive model proposed by Holzapfel, Gasser and Ogden (HGO model). Inspired by this single-layer model, a double-layer model was formulated and used for identification of material parameters from homogenised stress–strain data (of non-separated artery wall). The paper demonstrates that the layer-specific parameters of the double-layer constitutive model can be identified without the need of artery separation. The resulting double-layer model can credibly describe the homogenised stress–strain behaviour of the real artery wall including large-strain stiffening effects attributed to multilayer nature of the artery.

Predictive capabilities of various constitutive models for arterial tissue

INTRODUCTION Aim of this study is to validate some constitutive models by assessing their capabilities in describing and predicting uniaxial and biaxial behavior of porcine aortic tissue. METHODS 14 samples from porcine aortas were used to perform 2 uniaxial and 5 biaxial tensile tests. Transversal strains were furthermore stored for uniaxial data. The experimental data were fitted by four constitutive models: Holzapfel-Gasser-Ogden model (HGO), model based on generalized structure tensor (GST), Four-Fiber-Family model (FFF) and Microfiber model. Fitting was performed to uniaxial and biaxial data sets separately and descriptive capabilities of the models were compared. Their predictive capabilities were assessed in two ways. Firstly each model was fitted to biaxial data and its accuracy (in term of R2 and NRMSE) in prediction of both uniaxial responses was evaluated. Then this procedure was performed conversely: each model was fitted to both uniaxial tests and its accuracy in prediction of 5 biaxial responses was observed. RESULTS Descriptive capabilities of all models were excellent. In predicting uniaxial response from biaxial data, microfiber model was the most accurate while the other models showed also reasonable accuracy. Microfiber and FFF models were capable to reasonably predict biaxial responses from uniaxial data while HGO and GST models failed completely in this task. CONCLUSIONS HGO and GST models are not capable to predict biaxial arterial wall behavior while FFF model is the most robust of the investigated constitutive models. Knowledge of transversal strains in uniaxial tests improves robustness of constitutive models.

Finite Element Model of Abdominal Aortic Aneurysm

Abdominal aortic aneurysm (AAA) is a pathological change in lumen (inner diameter) of aorta, with synchronous decrease of wall thickness, often in the whole part between renal arteries and aortic bifurcation. Whithout an adequate treatment the risk of aneurysm rupture increases in time so that an assessment of this risk is decisive for a surgical treatment. Stresses in AAA wall predict the risk of its rupture better than the mere maximum diameter of the aneurysm, used as a criterion for decision about its operability in clinical practice.

Computational Modelling of Spherical Cavity Behaviour in Rubber-Like Solids

A characteristic rubber failure process, termed cavitation, has been observed and analysed by several authors. This paper deals with the stress concentration effect of a hypothetical void (cavity) that is assumed to be present in rubber-like solids. Commercial software based on finite element method and up-to-date Arruda-Boyce material model is used here for rubber material behaviour modelling. A detailed study of the effects of particular material parameters on the cavity behaviour under far-field hydrostatic tension condition is presented. The results are compared to those, which can be obtained for the case of simple neo-hookean material model of rubber. In opposite to standard crystalline materials there is no general failure criterion applicable for elastomeric materials. This analysis is motivated by the endeavour to determine a general criterion describing the failure of elastomers as a consequence of static loading.