The Quasi-Static Failure Properties of the Abdominal Aortic Aneurysm Wall Estimated by a Mixed Experimental-Numerical Approach

Specimen width affects vascular tissue integrity for in-vitro characterisation

The preparation of slender specimens for in-vitro tissue characterisation could potentially alter mechanical tissue properties. To investigate this factor, rectangular specimens were prepared from the wall of the porcine aorta for uniaxial tensile loading. Varying strip widths of 16 mm, 8 mm, and 4 mm were achieved by excising zero, one, and three cuts within the specimen along the loading direction, respectively. While specimens loaded along the vessel's circumferential direction acquired consistent tissue properties, the width of test specimens influenced the results of axially loaded tissue; vascular wall stiffness was reduced by approximately 40% in specimens with strips 4 mm wide. In addition, the cross-loading stretch was strongly influenced by specimen strip width, and fiber sliding contributed to the softening of slender tensile specimens, an outcome from finite element analysis of test specimens. We may, therefore, conclude that cutting orthogonal to the main direction of collagen fibers introduces mechanical trauma that weakens slender tensile specimens, compromising the determination of representative mechanical vessel wall properties.

Energetically stable curve fitting to hyperelastic models based on uniaxial and biaxial tensile tests

Hyperelastic constitutive laws in biomechanics are used to model soft tissues, and material model parameters are often determined by performing curve fitting on data from uniaxial or biaxial tensile tests. The strain energy function of the applied constitutive law must to be energetically stable; however, this condition is not inherently provided by most currently available models. This study provides a procedure to determine stable strain energy functions in a biaxial strain space based on either uniaxial or biaxial tensile tests. Instead of conservative, strain-independent conditions, a stability region is defined in the strain space based on the sample's tensile tests, thus allowing optimisation within a wider parameter space, resulting in better approximations. An extension of the Levenberg-Marquardt algorithm incorporating user-defined stability constraints is proposed, and the constrained optimisation algorithm is applied to isotropic and anisotropic models. The uniqueness of solutions of the Fung model is also discussed. The material model parameters of stable solutions for soft tissue measurements from various literature sources are determined to demonstrate the proposed procedure. Applying appropriate constraints in the optimisation algorithm resulted in stable and physically permissible constrained solutions for the strain energy function, in contrast to the results of most unconstrained optimisation cases.

Layer-Specific Properties of the Human Infra-Renal Aorta During Aging Considering Pre/Post-Failure Damage

There is little information on the layer-specific failure properties of the adult human abdominal aorta, and there has been no quantification of postfailure damage. Infra-renal aortas were thus taken from forty-seven autopsy subjects and cut into 870 intact-wall and layer strips that underwent uni-axial-tensile testing. Intact-wall failure stress did not differ significantly (p > 0.05) from the medial value longitudinally, nor from the intimal and medial values circumferentially, which were the lowest recorded values. Intact-wall failure stretch did not differ (p > 0.05) from the medial value in either direction. Intact-wall prefailure stretch (defined as failure stretch-stretch at the initiation of the concave phase of the stress-stretch response) did not differ (p > 0.05) from the intimal and medial values, and intact-wall postfailure stretch (viz., full-rupture stretch-failure stretch) did not differ (p > 0.05) from the adventitial value since the adventitia was the last layer to rupture, being most extensible albeit under residual tension. Intact-wall failure stress and stretch declined from 20 to 60 years, explained by steady declines throughout the lifetime of their medial counterparts, implicating beyond 60 years the less age-varying failure properties of the intima under minimal residual compression. The positive correlation of postfailure stretch with age counteracted the declining failure stretch, serving as a compensatory mechanism against rupture. Hypertension, diabetes, and coronary artery disease adversely affected the intact-wall and layer-specific failure stretches while increasing stiffness.

Development of an FEA framework for analysis of subject-specific aortic compliance based on 4D flow MRI

This paper presents a subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel during the cardiac cycle uncovered through our MRI investigations. A microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle cell stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle cell contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin digestion and SMC activation experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower distally. The analyses presented in this paper provide new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. Furthermore, this subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development. STATEMENT OF SIGNIFICANCE: This study provides a significant advance in in-silico medicine by capturing the structure/function relationship of the subject-specific human aorta presented in our previous MRI analyses. A physiologically based aortic constitutive model is developed, and simulations reveal that internal vessel contractility must be incorporated, along with collagen strain stiffening, to accurately predict the in-vivo non-linear pressure-area relationship. Furthermore, this is the first subject-specific model to predict spatial variation in the volume fractions of aortic wall constituents. Previous studies perform phenomenological hyperelastic curve fits to medical imaging data and ignore the prestress contribution of elastin, collagen, and SMCs and the associated zero-pressure reference state of the vessel. This novel MRI/FEA framework can be used as an in-silico diagnostic tool for the early stage detection of aortic pathologies.

A Chemomechanobiological Model of the Long-Term Healing Response of Arterial Tissue to a Clamping Injury

Vascular clamping often causes injury to arterial tissue, leading to a cascade of cellular and extracellular events. A reliable in silico prediction of these processes following vascular injury could help us to increase our understanding thereof, and eventually optimize surgical techniques or drug delivery to minimize the amount of long-term damage. However, the complexity and interdependency of these events make translation into constitutive laws and their numerical implementation particularly challenging. We introduce a finite element simulation of arterial clamping taking into account acute endothelial denudation, damage to extracellular matrix, and smooth muscle cell loss. The model captures how this causes tissue inflammation and deviation from mechanical homeostasis, both triggering vascular remodeling. A number of cellular processes are modeled, aiming at restoring this homeostasis, i.e., smooth muscle cell phenotype switching, proliferation, migration, and the production of extracellular matrix. We calibrated these damage and remodeling laws by comparing our numerical results to in vivo experimental data of clamping and healing experiments. In these same experiments, the functional integrity of the tissue was assessed through myograph tests, which were also reproduced in the present study through a novel model for vasodilator and -constrictor dependent smooth muscle contraction. The simulation results show a good agreement with the in vivo experiments. The computational model was then also used to simulate healing beyond the duration of the experiments in order to exploit the benefits of computational model predictions. These results showed a significant sensitivity to model parameters related to smooth muscle cell phenotypes, highlighting the pressing need to further elucidate the biological processes of smooth muscle cell phenotypic switching in the future.

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 P_ult and ultimate tension T_ult were recorded. Influence of sample orientation and other clinical parameters were investigated using non parametric tests.

RESULTS

Medians of P_ult (values 1100 kPa for circumferential vs. 715 kPa for axial direction, p < 10^-4) and T_ult (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 P_ult and 7.4 N/cm (p < 10^-4) in T_ult 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.

Outcomes of Endovascular Repair for Abdominal Aortic Aneurysms: A Nationwide Survey in Japan

OBJECTIVE

To analyze data on patients treated with a bifurcated stent graft for abdominal aortic aneurysm (AAA).

BACKGROUND

The Japan Committee for Stentgraft Management (JACSM) was established in 2007 to manage the safety of endovascular aortic aneurysm repair (EVAR) in Japan. The JACSM registry includes detailed anatomical and clinical data of all patients who undergo stent graft insertion in Japan.

METHODS

Among 51,380 patients treated with bifurcated stent graft for AAA, we identified 38,008 eligible patients (excluding those with rupture or insufficient data). The analyzed factors included age, sex, comorbidities, AAA pathology and etiology, aneurysm and neck diameters, 7 anti-instructions for use (IFU) factors, and endoleaks at hospital discharge. The endpoints were death, adverse events, sac dilatation (≥5 mm), and reintervention.

RESULTS

The rates of intraoperative and in-hospital mortality were 0.08% and 1.07%, respectively. Infectious aneurysm and pseudo-aneurysm were associated with overall survival and reintervention. Older age, large aneurysm diameter, and all types of persistent endoleaks were strong predictors of adverse events, sac dilatation, and reintervention. Comorbid cerebrovascular disease, renal dysfunction, and respiratory disorders were also risk factors. In total, 47.6% of patients violated the IFU; among the anti-IFU factors assessed, poor access and severe neck calcification were strong risk factors for mortality, reintervention, and adverse events. The sac dilatation rate at 5 years was 23.3%.

CONCLUSIONS

Although the analysis included EVAR with poor anatomy, the perioperative mortality rate was acceptable compared with that in previous large population studies.

Computational modeling reveals the relationship between intrinsic failure properties and uniaxial biomechanical behavior of arterial tissue

Biomechanical failure of the artery wall can lead to rupture, a catastrophic event with a high rate of mortality. Thus, there is a pressing need to understand failure behavior of the arterial wall. Uniaxial testing remains the most common experimental technique to assess tissue failure properties. However, the relationship between intrinsic failure parameters of the tissue and measured uniaxial failure properties is not fully established. Furthermore, the effect of the experimental variables, such as specimen shape and boundary conditions, on the measured failure properties is not well understood. We developed a finite element model capable of recapitulating pre-failure and post-failure uniaxial biomechanical response of the arterial tissue specimen. Intrinsic stiffness, strength and fracture toughness of the vessel wall tissue were used as the input material parameters to the model. Two uniaxial testing protocols were considered: a conventional setup with a rectangular specimen held at the grips by cardboard inserts, and the other used a dogbone specimen with soft foam inserts at the grips. Our computational study indicated negligible differences in the peak stress and post-peak mechanical behavior between these two testing protocols. It was also found that the tissue experienced only modest localized failure until higher levels of applied stretch beyond the peak stress. A robust cohesive model was capable of modeling the post-peak biomechanical response, which was primarily governed by tissue fracture toughness. Our results suggest that the post-peak region, in conjunction with the peak stress, must be considered to evaluate the complete biomechanical failure behavior of the soft tissue.

Determination of the Material Parameters in the Holzapfel-Gasser-Ogden Constitutive Model for Simulation of Age-Dependent Material Nonlinear Behavior for Aortic Wall Tissue under Uniaxial Tension

In this study, computational simulations and experiments were performed to investigate the mechanical behavior of the aorta wall because of the increasing occurrences of aorta-related diseases. The study focused on the deformation and strength of porcine and healthy human abdominal aortic tissues under uniaxial tensile loading. The experiments for the mechanical behavior of the arterial tissue were conducted using a uniaxial tensile test apparatus to validate the simulation results. In addition, the strength and stretching of the tissues in the abdominal aorta of a healthy human as a function of age were investigated based on the uniaxial tensile tests. Moreover, computational simulations using the ABAQUS finite element analysis program were conducted on the experimental scenarios based on age, and the Holzapfel–Gasser–Ogden (HGO) model was applied during the simulation. The material parameters and formulae to be used in the HGO model were proposed to identify the failure stress and stretch correlation with age.

The role of tissue remodeling in mechanics and pathogenesis of abdominal aortic aneurysms

Arterial walls can be regarded as composite materials consisting of collagen fibers embedded in an elastic matrix and smooth muscle cells. Remodeling of the structural proteins has been shown to play a significant role in the mechanical behavior of walls during pathogenesis of abdominal aortic aneurysms (AAA). In this study, we systematically studied the change in the microstructure, histology and mechanics to link them to AAA disease progression. We performed biaxial extension tests, second-harmonic generation imaging and histology on 15 samples from the anterior part of AAA walls harvested during open aneurysm surgery. Structural data were gained by fitting to a bivariate von Mises distribution and yielded the mean fiber direction and in- and out-of-plane fiber dispersions of collagen. Mechanical and structural data were fitted to a recently proposed material model. Additionally, the mechanical data were used to derive collagen recruitment points in the obtained stress-stretch curves. We derived 14 parameters from histology such as smooth muscle cell-, elastin-, and abluminal adipocyte content. In total, 22 parameters were obtained and statistically evaluated. Based on the collagen recruitment points we were able to define three different stages of disease progression. Significant differences in elastin content, collagen orientation and adipocyte contents were discovered. Nerves entrapped inside AAA walls pointed towards a significant deposition of newly formed collagen abluminally, which we propose as neo-adventitia formation. We were able to discriminate two types of remodeled walls with a high collagen content - potentially safe and possibly vulnerable walls with a high adipocyte content inside the wall and significant amounts of inflammation. The study yielded a hypothesis for disease progression, derived from the systematic comparison of mechanical, microstructural and histological changes in AAAs. STATEMENT OF SIGNIFICANCE: Remodeling of the structural proteins plays an important role in the mechanical behavior of walls during pathogenesis of abdominal aortic aneurysms (AAA). We analyzed changes in the microstructure, histology and biomechanics of 15 samples from the anterior part of AAA walls and, for the first time, linked the results to three different stages of disease progression. We identified significant differences in elastin content, collagen orientation, adipocyte contents, and also a deposition of newly formed collagen forming a neoadventitia. We could discriminate two types of remodeled walls: (i) potentially safe and (ii) possibly vulnerable associated with inflammation and a high amount of adipocytes.

Computational Evaluation for Age-Dependent Material Nonlinear Behavior of Aortic Wall Tissue on Abdominal Aortic Aneurysms

An abdominal aortic aneurysm is a localized expansion of the abdominal aorta with a diameter >3 cm or >50% larger than the normal diameter. In this study, the stretch and strength of the materials in the abdominal aorta in patients with aneurysms were examined based on the results of tensile tests, and databases of failure stress and stretch were established according to age. Generally, the tensile test results of the axial and circumferential directions have become a priority in the tests of aortic materials. However, this study focused on the results of the axial direction. In addition, finite element analysis, where the Holzapfel model and the test results were applied, was performed. As a result, the behavior characteristics of the abdominal aortic materials were precisely simulated. The formula and material constants used in the Holzapfel model were studied and proposed in order to simulate the failure stress and stretch according to age as well as simulation.

A Uniaxial Testing Approach for Consistent Failure in Vascular Tissues

Although uniaxial tensile testing is commonly used to evaluate failure properties of vascular tissue, there is no established protocol for specimen shape or gripping method. Large percentages of specimens are reported to fail near the clamp and can potentially confound the studies, or, if discarded will result in sample waste. The objective of this study is to identify sample geometry and clamping conditions that can achieve consistent failure in the midregion of small arterial specimens, even for vessels from older individuals. Failure location was assessed in 17 dogbone specimens from human cerebral and sheep carotid arteries using soft inserts. For comparison with commonly used protocols, an additional 22 rectangular samples were tested using either sandpaper or foam tape inserts. Midsample failure was achieved in 94% of the dogbone specimens, while only 14% of the rectangular samples failed in the midregion, the other 86% failing close to the clamps. Additionally, we found midregion failure was more likely to be abrupt, caused by cracking or necking. In contrast, clamp failure was more likely to be gradual and included a delamination mode not seen in midregion failure. Hence, this work provides an approach that can be used to obtain consistent midspecimen failure, avoiding confounding clamp-related artifacts. Furthermore, with consistent midregion failure, studies can be designed to image the failure process in small vascular samples providing valuable quantitative information about changes to collagen and elastin structure during the failure process.

Fatigue of soft fibrous tissues: Multi-scale mechanics and constitutive modeling

In recent experimental studies a possible damage mechanism of collagenous tissues mainly caused by fatigue was disclosed. In this contribution, a multi-scale constitutive model ranging from the tropocollagen (TC) molecule level up to bundles of collagen fibers is proposed and utilized to predict the elastic and inelastic long-term tissue response. Material failure of collagen fibrils is elucidated by a permanent opening of the triple helical collagen molecule conformation, triggered either by overstretching or reaction kinetics of non-covalent bonds. This kinetics is described within a probabilistic framework of adhesive detachments of molecular linkages providing collagen fiber integrity. Both intramolecular and interfibrillar linkages are considered. The final constitutive equations are validated against recent experimental data available in literature for both uniaxial tension to failure and the evolution of fatigue in subsequent loading cycles. All material parameters of the proposed model have a clear physical interpretation.

STATEMENT OF SIGNIFICANCE

Irreversible changes take place at different length scales of soft fibrous tissues under supra-physiological loading and alter their macroscopic mechanical properties. Understanding the evolution of those histologic pathologies under loading and incorporating them into a continuum mechanical framework appears to be crucial in order to predict long-term evolution of various diseases and to support the development of tissue engineering.

Structural modeling reveals microstructure-strength relationship for human ascending thoracic aorta

High lethality of aortic dissection necessitates accurate predictive metrics for dissection risk assessment. The not infrequent incidence of dissection at aortic diameters <5.5 cm, the current threshold guideline for surgical intervention (Nishimura et al., 2014), indicates an unmet need for improved evidence-based risk stratification metrics. Meeting this need requires a fundamental understanding of the structural mechanisms responsible for dissection evolution within the vessel wall. We present a structural model of the repeating lamellar structure of the aortic media comprised of elastic lamellae and collagen fiber networks, the primary load-bearing components of the vessel wall. This model was used to assess the role of these structural features in determining in-plane tissue strength, which governs dissection initiation from an intimal tear. Ascending aortic tissue specimens from three clinically-relevant patient populations were considered: non-aneurysmal aorta from patients with morphologically normal tricuspid aortic valve (CTRL), aneurysmal aorta from patients with tricuspid aortic valve (TAV), and aneurysmal aorta from patients with bicuspid aortic valve (BAV). Multiphoton imaging derived collagen fiber organization for each patient cohort was explicitly incorporated in our model. Model parameters were calibrated using experimentally-measured uniaxial tensile strength data in the circumferential direction for each cohort, while the model was validated by contrasting simulated tissue strength against experimentally-measured strength in the longitudinal direction. Orientation distribution, controlling the fraction of loaded collagen fibers at a given stretch, was identified as a key feature governing anisotropic tissue strength for all patient cohorts.

Microstructure and mechanics of healthy and aneurysmatic abdominal aortas: experimental analysis and modelling

Soft biological tissues such as aortic walls can be viewed as fibrous composites assembled by a ground matrix and embedded families of collagen fibres. Changes in the structural components of aortic walls such as the ground matrix and the embedded families of collagen fibres have been shown to play a significant role in the pathogenesis of aortic degeneration. Hence, there is a need to develop a deeper understanding of the microstructure and the related mechanics of aortic walls. In this study, tissue samples from 17 human abdominal aortas (AA) and from 11 abdominal aortic aneurysms (AAA) are systematically analysed and compared with respect to their structural and mechanical differences. The collagen microstructure is examined by analysing data from second-harmonic generation imaging after optical clearing. Samples from the intact AA wall, their individual layers and the AAA wall are mechanically investigated using biaxial stretching tests. A bivariate von Mises distribution was used to represent the continuous fibre dispersion throughout the entire thickness, and to provide two independent dispersion parameters to be used in a recently proposed material model. Remarkable differences were found between healthy and diseased tissues. The out-of-plane dispersion was significantly higher in AAA when compared with AA tissues, and with the exception of one AAA sample, the characteristic wall structure, as visible in healthy AAs with three distinct layers, could not be identified in AAA samples. The collagen fibres in the abluminal layer of AAAs lost their waviness and exhibited rather straight and thick struts of collagen. A novel set of three structural and three material parameters is provided. With the structural parameters fixed, the material model was fitted to the mechanical experimental data, giving a very satisfying fit although there are only three material parameters involved. The results highlight the need to incorporate the structural differences into finite-element simulations as otherwise simulations of AAA tissues might not be good predictors for the actual in vivo stress state.

On arterial fiber dispersion and auxetic effect

There are two polar contemporary approaches to the constitutive modeling of arterial wall with anisotropy induced by collagen fibers. The first one is based on the angular integration (AI) of the strain energy on a unit sphere for the analytically defined fiber dispersion. The second one is based on the introduction of the generalized structure tensors (GST). AI approach is very involved computationally while GST approach requires somewhat complicated procedure for the exclusion of compressed fibers. We present some middle ground models, which are based on the use of 16 and 8 structure tensors. These models are moderately involved computationally and they allow excluding compressed fibers easily. We use the proposed models to study the role of the fiber dispersion in the constitutive modeling of the arterial wall. Particularly, we study the auxetic effect which can appear in anisotropic materials. The effect means thickening of the tissue in the direction perpendicular to its stretching. Such an effect was not observed in experiments while some simple anisotropic models do predict it. We show that more accurate account of the fiber dispersion suppresses the auxetic effect in a qualitative agreement with experimental observations.

Diameter and thickness-related variations in mechanical properties of degraded arterial wall in the rat xenograft model

The purpose of this study was to evaluate the diameter and thickness-related variations in mechanical properties of degraded arterial wall. To this end, ring tests were performed on 31 samples from the rat xenograft model of abdominal aortic aneurysm (AAA) and failure properties were determined. An inverse finite element method was then employed to identify the material parameters of a hyperelastic and incompressible strain energy function. Correlations with outer diameter and wall thickness of the rings were examined. Furthermore, we investigated the changes in mechanical properties between the grafts, which consist in guinea pig decellularized aortas, native murine aortas and degraded aortas (AAAs). Decellularized aortas presented a significantly lower ultimate strain associated with a higher stiffening rate compared to native aortas. AAAs exhibited a significantly lower ultimate stress than other groups and an extensible-but-stiff behavior. The proposed approach revealed correlations of ultimate stress and material parameters of aneurysmal aortas with outer diameter and thickness. In particular, the negative correlations of the material parameter accounting for the response of the non-collagenous matrix with diameter and thickness (r=-0.67 and r=-0.73, p<0.001) captured the gradual loss of elastin with dilatation observed in histology (r=-0.97, p<0.001). Moreover, it exposed the progressive weakening of the wall with enlargement and thickening (r=-0.64 and r=-0.69, p<0.001), suggesting that wall thickness and diameter may be indicators of rupture risk in the rat xenograft model.

Biomechanical rupture risk assessment of abdominal aortic aneurysms based on a novel probabilistic rupture risk index

A rupture risk assessment is critical to the clinical treatment of abdominal aortic aneurysm (AAA) patients. The biomechanical AAA rupture risk assessment quantitatively integrates many known AAA rupture risk factors but the variability of risk predictions due to model input uncertainties remains a challenging limitation. This study derives a probabilistic rupture risk index (PRRI). Specifically, the uncertainties in AAA wall thickness and wall strength were considered, and wall stress was predicted with a state-of-the-art deterministic biomechanical model. The discriminative power of PRRI was tested in a diameter-matched cohort of ruptured (n = 7) and intact (n = 7) AAAs and compared to alternative risk assessment methods. Computed PRRI at 1.5 mean arterial pressure was significantly (p = 0.041) higher in ruptured AAAs (20.21(s.d. 14.15%)) than in intact AAAs (3.71(s.d. 5.77)%). PRRI showed a high sensitivity and specificity (discriminative power of 0.837) to discriminate between ruptured and intact AAA cases. The underlying statistical representation of stochastic data of wall thickness, wall strength and peak wall stress had only negligible effects on PRRI computations. Uncertainties in AAA wall stress predictions, the wide range of reported wall strength and the stochastic nature of failure motivate a probabilistic rupture risk assessment. Advanced AAA biomechanical modelling paired with a probabilistic rupture index definition as known from engineering risk assessment seems to be superior to a purely deterministic approach.

Prior Distributions of Material Parameters for Bayesian Calibration of Growth and Remodeling Computational Model of Abdominal Aortic Wall

For the accurate prediction of the vascular disease progression, there is a crucial need for developing a systematic tool aimed toward patient-specific modeling. Considering the interpatient variations, a prior distribution of model parameters has a strong influence on computational results for arterial mechanics. One crucial step toward patient-specific computational modeling is to identify parameters of prior distributions that reflect existing knowledge. In this paper, we present a new systematic method to estimate the prior distribution for the parameters of a constrained mixture model using previous biaxial tests of healthy abdominal aortas (AAs). We investigate the correlation between the estimated parameters for each constituent and the patient's age and gender; however, the results indicate that the parameters are correlated with age only. The parameters are classified into two groups: Group-I in which the parameters ce, ck1, ck2, cm2,Ghc, and ϕe are correlated with age, and Group-II in which the parameters cm1, Ghm, G1e, G2e, and α are not correlated with age. For the parameters in Group-I, we used regression associated with age via linear or inverse relations, in which their prior distributions provide conditional distributions with confidence intervals. For Group-II, the parameter estimated values were subjected to multiple transformations and chosen if the transformed data had a better fit to the normal distribution than the original. This information improves the prior distribution of a subject-specific model by specifying parameters that are correlated with age and their transformed distributions. Therefore, this study is a necessary first step in our group's approach toward a Bayesian calibration of an aortic model. The results from this study will be used as the prior information necessary for the initialization of Bayesian calibration of a computational model for future applications.

Biomechanical Rupture Risk Assessment: A Consistent and Objective Decision-Making Tool for Abdominal Aortic Aneurysm Patients

Abdominal aortic aneurysm (AAA) rupture is a local event in the aneurysm wall that naturally demands tools to assess the risk for local wall rupture. Consequently, global parameters like the maximum diameter and its expansion over time can only give very rough risk indications; therefore, they frequently fail to predict individual risk for AAA rupture. In contrast, the Biomechanical Rupture Risk Assessment (BRRA) method investigates the wall's risk for local rupture by quantitatively integrating many known AAA rupture risk factors like female sex, large relative expansion, intraluminal thrombus-related wall weakening, and high blood pressure. The BRRA method is almost 20 years old and has progressed considerably in recent years, it can now potentially enrich the diameter indication for AAA repair. The present paper reviews the current state of the BRRA method by summarizing its key underlying concepts (i.e., geometry modeling, biomechanical simulation, and result interpretation). Specifically, the validity of the underlying model assumptions is critically disused in relation to the intended simulation objective (i.e., a clinical AAA rupture risk assessment). Next, reported clinical BRRA validation studies are summarized, and their clinical relevance is reviewed. The BRRA method is a generic, biomechanics-based approach that provides several interfaces to incorporate information from different research disciplines. As an example, the final section of this review suggests integrating growth aspects to (potentially) further improve BRRA sensitivity and specificity. Despite the fact that no prospective validation studies are reported, a significant and still growing body of validation evidence suggests integrating the BRRA method into the clinical decision-making process (i.e., enriching diameter-based decision-making in AAA patient treatment).

Relaxed incremental variational approach for the modeling of damage-induced stress hysteresis in arterial walls

In this paper, a three-dimensional relaxed incremental variational damage model is proposed, which enables the description of complex softening hysteresis as observed in supra-physiologically loaded arterial tissues, and which thereby avoids a loss of convexity of the underlying formulation. The proposed model extends the relaxed formulation of Balzani and Ortiz [2012. Relaxed incremental variational formulation for damage at large strains with application to fiber-reinforced materials and materials with truss-like microstructures. Int. J. Numer. Methods Eng. 92, 551-570], such that the typical stress-hysteresis observed in arterial tissues under cyclic loading can be described. This is mainly achieved by constructing a modified one-dimensional model accounting for cyclic loading in the individual fiber direction and numerically homogenizing the response taking into account a fiber orientation distribution function. A new solution strategy for the identification of the convexified stress potential is proposed based on an evolutionary algorithm which leads to an improved robustness compared to solely Newton-based optimization schemes. In order to enable an efficient adjustment of the new model to experimentally observed softening hysteresis, an adjustment scheme using a surrogate model is proposed. Therewith, the relaxed formulation is adjusted to experimental data in the supra-physiological domain of the media and adventitia of a human carotid artery. The performance of the model is then demonstrated in a finite element example of an overstretched artery. Although here three-dimensional thick-walled atherosclerotic arteries are considered, it is emphasized that the formulation can also directly be applied to thin-walled simulations of arteries using shell elements or other fiber-reinforced biomembranes.

Computational Growth and Remodeling of Abdominal Aortic Aneurysms Constrained by the Spine

Abdominal aortic aneurysms (AAAs) evolve over time, and the vertebral column, which acts as an external barrier, affects their biomechanical properties. Mechanical interaction between AAAs and the spine is believed to alter the geometry, wall stress distribution, and blood flow, although the degree of this interaction may depend on AAAs specific configurations. In this study, we use a growth and remodeling (G&R) model, which is able to trace alterations of the geometry, thus allowing us to computationally investigate the effect of the spine for progression of the AAA. Medical image-based geometry of an aorta is constructed along with the spine surface, which is incorporated into the computational model as a cloud of points. The G&R simulation is initiated by local elastin degradation with different spatial distributions. The AAA-spine interaction is accounted for using a penalty method when the AAA surface meets the spine surface. The simulation results show that, while the radial growth of the AAA wall is prevented on the posterior side due to the spine acting as a constraint, the AAA expands faster on the anterior side, leading to higher curvature and asymmetry in the AAA configuration compared to the simulation excluding the spine. Accordingly, the AAA wall stress increases on the lateral, posterolateral, and the shoulder regions of the anterior side due to the AAA-spine contact. In addition, more collagen is deposited on the regions with a maximum diameter. We show that an image-based computational G&R model not only enhances the prediction of the geometry, wall stress, and strength distributions of AAAs but also provides a framework to account for the interactions between an enlarging AAA and the spine for a better rupture potential assessment and management of AAA patients.

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 model's 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.

Biomechanical properties of the thoracic aneurysmal wall: differences between bicuspid aortic valve and tricuspid aortic valve patients

BACKGROUND

The prevalence for thoracic aortic aneurysms (TAAs) is significantly increased in patients with a bicuspid aortic valve (BAV) compared with patients who have a normal tricuspid aortic valve (TAV). TAA rupture is a life-threatening event, and biomechanics-based simulations of the aorta may help to disentangle the molecular mechanism behind its development and progression. The present study used polarized microscopy and macroscopic in vitro tensile testing to explore collagen organization and mechanical properties of TAA wall specimens from BAV and TAV patients.

METHODS

Circumferential sections of aneurysmal aortic tissue from BAV and TAV patients were obtained during elective operations. The distribution of collagen orientation was captured by a Bingham distribution, and finite element models were used to estimate constitutive model parameters from experimental load-displacement curves.

RESULTS

Collagen orientation was almost identical in BAV and TAV patients, with a highest probability of alignment along the circumferential direction. The strength was almost two times higher in BAV samples (0.834 MPa) than in TAV samples (0.443 MPa; p<0.001). The collagen-related stiffness (Cf) was significantly increased in BAV compared with TAV patients (Cf=7.45 MPa vs 3.40 MPa; p=0.003), whereas the elastin-related stiffness was similar in both groups. A trend toward a decreased wall thickness was seen in BAV patients (p=0.058).

CONCLUSIONS

The aneurysmal aortas of BAV patients show a higher macroscopic strength, mainly due to an increased collagen-related stiffness, compared with TAV patients. The increased wall stiffness in BAV patients may contribute to the higher prevalence for TAAs in this group.