Importance of experimental evaluation of structural parameters for constitutive modelling of aorta.

The study compares stresses and strains in the aortic wall derived using different constitutive models for various stress-strain conditions. Structure-based constitutive models with two fibre families with (GOH) and without (HGO) dispersion of collagen fibres are compared. The constitutive models were fitted to data from equibiaxial tension tests of two separated layers of the porcine aortic wall. The initial fit was evaluated with unrestricted parameters and subsequently, the mean angles of the fibre families and the angular dispersion were fixed to the values obtained from histology. Surprisingly, none of the tested models was capable to provide a good quality fit with histologically obtained structural parameters. Fitting the HGO model to experimental data resulted in two fibre families under angles close to ±45°, while the GOH model resulted in a nearly isotropic fibre distribution. These results indicate that both of these models suffer from the absence of isotropic strain stiffening. After having modified both models with corresponding additional members based on the Yeoh model of matrix, we obtained a perfect fit to the measured data while keeping the structural histology-based parameters. Finally, significant differences in compliance and resulting stresses and strains between different models are shown by means of simulations of uniaxial tension test, equibiaxial tension tests and inflation of the aorta.

Failure properties of abdominal aortic aneurysm tissue are orientation dependent.

INTRODUCTION: Biomechanical rupture risk assessment of abdominal aortic aneurysm (AAA) requires information about failure properties of aneurysmal tissue. There are large differences between reported values. Among others, studies vary in using either axially or circumferentially oriented samples. This study investigates the effect of sample orientation on failure properties. METHODS: Aneurysmal tissues from 45 patients (11 females) were harvested during open AAA repair, cut into uniaxial samples (90) and tested mechanically within 3 h. If possible, the samples were cut in both axial (49 samples) and circumferential (41 samples) directions. Wall thickness, First Piola-Kirchhoff strength Pult and ultimate tension Tult were recorded. Influence of sample orientation and other clinical parameters were investigated using non parametric tests. RESULTS: Medians of Pult (values 1100 kPa for circumferential vs. 715 kPa for axial direction, p < 10-4) and Tult (17.4 N/cm in circumferential vs. 11.2 N/cm in axial direction, p < 10-4) were significantly higher in circumferential direction. For paired data, the median of difference was 411 kPa (p < 10-3) in Pult and 7.4 N/cm (p < 10-4) in Tult in favor of circumferential direction. CONCLUSIONS: In this first study of anisotropy in AAA wall failure properties using paired comparisons, the strength in circumferential orientation was found to be higher than in axial orientation.

Biomechanical indices are more sensitive than diameter in predicting rupture of asymptomatic abdominal aortic aneurysms.

OBJECTIVE: Several studies of biomechanical rupture risk assessment (BRRA) showed its advantage over the diameter criterion in rupture risk assessment of abdominal aortic aneurysm (AAA). However, BRRA studies have not investigated the predictability of biomechanical risk indices at different time points ahead of rupture, nor have they been performed blinded for biomechanical analysts. The objective of this study was to test the predictability of the BRRA method against diameter-based risk indices in a quasi-prospective patient cohort study. METHODS: In total, 12 women and 31 men with intact AAAs at baseline have been selected retrospectively at two medical centers. Within 56 months, 19 cases ruptured, whereas 24 cases remained intact within 2 to 56 months. This outcome was kept confidential until all biomechanical activities in this study were finished. The biomechanical AAA rupture risk was calculated at baseline using high-fidelity and low-fidelity finite element method models. The capability of biomechanics-based and diameter-based risk indices to predict the known outcomes at 1 month, 3 months, 6 months, 9 months, and 12 months after baseline was validated. Besides common cohort statistics, the area under the curve (AUC) of receiver operating characteristic curves has been used to grade the different rupture risk indices. RESULTS: Up to 9 months ahead of rupture, the receiver operating characteristic analysis of biomechanics-based risk indices showed a higher AUC than diameter-based indices. Six months ahead of rupture, the largest difference was observed with an AUC of 0.878 for the high-fidelity biomechanical risk index, 0.859 for the low-fidelity biomechanical risk index, 0.789 for the diameter, and 0.821 for the sex-adjusted diameter. In predictions beyond 9 months, none of the risk indices proved to be superior. CONCLUSIONS: High-fidelity biomechanical modeling improves the predictability of AAA rupture. Asymptomatic AAA patients with high biomechanical AAA rupture risk indices have an increased risk of rupture. Integrating biomechanics-based diagnostic indices may significantly decrease the false-positive rate in AAA treatment. CLINICAL RELEVANCE: Rupture of abdominal aortic aneurysm (AAA) is the tenth leading cause of death in men older than 60 years; however, the currently used maximal diameter criterion has a high false-positive rate. In this study, we have compared this criterion with biomechanical rupture risk assessment on the unique data set of 43 asymptomatic AAAs, of which 19 ruptured later. Moreover, the AAA outcome was blinded to the operator for the first time. Our data demonstrated that the biomechanical rupture risk assessment is superior to maximal diameter in predicting AAA rupture up to 9 months ahead and significantly decreases the false-positive rate.

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.

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.