The Biaxial Biomechanical Behavior of Abdominal Aortic Aneurysm Tissue

Experimental Protocols to Test Aortic Soft Tissues: A Systematic Review

Experimental protocols are fundamental for quantifying the mechanical behaviour of soft tissue. These data are crucial for advancing the understanding of soft tissue mechanics, developing and calibrating constitutive models, and informing the development of more accurate and predictive computational simulations and artificial intelligence tools. This paper offers a comprehensive review of experimental tests conducted on soft aortic tissues, employing the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology, based on the Scopus, Web of Science, IEEE, Google Scholar and PubMed databases. This study includes a detailed overview of the test method protocols, providing insights into practical methodologies, specimen preparation and full-field measurements. The review also briefly discusses the post-processing methods applied to extract material parameters from experimental data. In particular, the results are analysed and discussed providing representative domains of stress-strain curves for both uniaxial and biaxial tests on human aortic tissue.

Biomechanical effects of hemin and sildenafil treatments on the aortic wall of chronic-hypoxic lambs

Introduction: Gestation under chronic hypoxia causes pulmonary hypertension, cardiovascular remodeling, and increased aortic stiffness in the offspring. To mitigate the neonatal cardiovascular risk, pharmacological treatments (such as hemin and sildenafil) have been proposed to improve pulmonary vasodilation. However, little is known about the effects of these treatments on the aorta. Therefore, we studied the effect of hemin and sildenafil treatments in the aorta of lambs gestated and raised at highlands, thereby subjected to chronic hypoxia. Methods: Several biomechanical tests were conducted in the descending thoracic aorta (DTA) and the distal abdominal aorta (DAA), assessing 3 groups of study of hypoxic animals: non-treated (Control) and treated either with hemin or sildenafil. Based on them, the stiffness level has been quantified in both zones, along with the physiological strain in the unloaded aortic duct. Furthermore, a morphological study by histology was conducted in the DTA. Results: Biomechanical results indicate that treatments trigger an increment of axial pre-stress and circumferential residual stress levels in DTA and DAA of lambs exposed to high-altitude chronic hypoxia, which reveals a vasodilatation improvement along with an anti-hypertensive response under this characteristic environmental condition. In addition, histological findings do not reveal significant differences in either structure or microstructural content. Discussion: The biomechanics approach emerges as a valuable study perspective, providing insights to explain the physiological mechanisms of vascular function. According to established results, alterations in the function of the aortic wall may not necessarily be explained by morphostructural changes, but rather by the characteristic mechanical state of the microstructural components that are part of the studied tissue. In this sense, the reported biomechanical changes are beneficial in mitigating the adverse effects of hypobaric hypoxia exposure during gestation and early postnatal life.

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.

Mechanical and histological characteristics of aortic dissection tissues

AIMS

This study investigated the association between the macroscopic mechanical response of aortic dissection (AoD) flap, its fibre features, and patient physiological features and clinical presentations.

METHODS

Uniaxial test was performed with tissue strips in both circumferential and longitudinal directions from 35 patients with (AoD:CC) and without (AoD:w/oCC) cerebral/coronary complications, and 19 patients with rheumatic or valve-related heart diseases (RH). A Bayesian inference framework was used to estimate the expectation of material constants (C₁, D₁, and D₂) of the modified Mooney-Rivlin strain energy density function. Histological examination was used to visualise the elastin and collagen in the tissue strips and image processing was performed to quantify their area percentages, fibre misalignment and waviness.

RESULTS

The elastin area percentage was negatively associated with age (p = 0.008), while collagen increased about 6% from age 40 to 70 (p = 0.03). Elastin fibre was less dispersed and wavier in old patients and no significant association was found between patient age and collagen fibre dispersion or waviness. Features of fibrous microstructures, either elastin or collagen, were comparable between AoD:CC and AoD:w/oCC group. Elastin and collagen area percentages were positively correlated with C₁ and D₂, respectively, while the elastin and collagen waviness were negatively correlated with C₁ and D₂, respectively. Elastin dispersion was negatively correlated to D₂. Multivariate analysis showed that D₂ was an effective parameter which could differentiate patient groups with different age and clinical presentations, as well as the direction of tissue strip.

CONCLUSION

Fibre dispersion and waviness in the aortic dissection flap changed with patient age and clinical presentations, and these can be captured by the material constants in the strain energy density function.

STATEMENT OF SIGNIFICANCE

Aortic dissection (AoD) is a severe cardiovascular disease. Understanding the mechanical property of intimal flap is essential for its risk evaluation. In this study, mechanical testing and histology examination were combined to quantify the relationship between mechanical presentations and microstructure features. A Bayesian inference framework was employed to estimate the expectation of the material constants in the modified Mooney-Rivlin constitutive equation. It was found that fibre dispersion and waviness in the AoD flap changed with patient age and clinical presentations, and these could be captured by the material constants. This study firstly demonstrated that the expectation of material constants can be used to characterise tissue microstructures and differentiate patients with different clinical presentations.

Micromechanical and Ultrastructural Properties of Abdominal Aortic Aneurysms

Abdominal aortic aneurysms are a common condition of uncertain pathogenesis that can rupture if left untreated. Current recommended thresholds for planned repair are empirical and based entirely on diameter. It has been observed that some aneurysms rupture before reaching the threshold for repair whilst other larger aneurysms do not rupture. It is likely that geometry is not the only factor influencing rupture risk. Biomechanical indices aiming to improve and personalise rupture risk prediction require, amongst other things, knowledge of the material properties of the tissue and realistic constitutive models. These depend on the composition and organisation of the vessel wall which has been shown to undergo drastic changes with aneurysmal degeneration, with loss of elastin, smooth muscle cells, and an accumulation of isotropically arranged collagen. Most aneurysms are lined with intraluminal thrombus, which has an uncertain effect on the underlying vessel wall, with some authors demonstrating a reduction in wall stress and others a reduction in wall strength. The majority of studies investigating biomechanical properties of ex vivo abdominal aortic aneurysm tissues have used low-resolution techniques, such as tensile testing, able to measure the global material properties at the macroscale. High-resolution engineering techniques such as nanoindentation and atomic force microscopy have been modified for use in soft biological tissues and applied to vascular tissues with promising results. These techniques have the potential to advance the understanding and improve the management of abdominal aortic aneurysmal disease.

Biomechanical properties of ascending aortic aneurysms: Quantification of inter- and intra-patient variability

This study investigates the biomechanical properties of ascending aortic aneurysms focusing on the inter-patient differences vs. the heterogeneity within a patient's aneurysm. Each specimen was tested on a biaxial testing device and the resulting stress-strain response was fitted to a four-parameter Fung constitutive model. We postulate that the inter-patient variability (differences between patients) blurs possible intra-patient variability (regional heterogeneity) and, thus, that both effects must be considered to shed light on the role of heterogeneity in aneurysm progression. We propose, demonstrate, and discuss two techniques to assess differences by, first, comparing conventional biomechanical properties and, second, the overall constitutive response. Results show that both inter- and intra-patient variability contribute to errors when using population averaged models to fit individual tissue behaviour. When inter-patient variability was accounted for and its effects excluded, intra-patient heterogeneity could be assessed, showing a wide degree of heterogeneity at the individual patient level. Furthermore, the right lateral region (from the patient's perspective) appeared different (stiffer) than the other regions. We posit that this heterogeneity could be a consequence of maladaptive remodelling due to altered loading conditions that hastens microstructural changes naturally occurring with age. Further validation of these results should be sought from a larger cohort study.

Sources of inconsistency in mean mechanical response of abdominal aortic aneurysm tissue

INTRODUCTION

There is a striking difference in the reported mean response of abdominal aortic aneurysm tissue in academic literature depending on the type of tests (uniaxial vs biaxial) performed. In this paper, the hypothesis variability caused by differences in experimental protocols is explored using porcine aortic tissue as a substitute for aneurysmal tissue.

METHODS

Nine samples of porcine aorta were created and both uniaxial and biaxial tests were performed. Three effects were investigated. (i) Effect of sample (non) preconditioning, (ii) effect of objective function used (normalised vs non-normalised), and (iii) effect of chosen procedure used for mean response calculation: constant averaging (CA) vs fit to averaged response (FAR) vs fit to all data (FAD). Both the overall shape of mean curve and mean initial stiffness were compared.

RESULTS

(i) Non-preconditioning led to a much stiffer response, and initial stiffness was about three times higher for a non-preconditioned response based on uniaxial data compared to a preconditioned biaxial response. (ii) CA led to a much stiffer response compared to FAR and FAD procedures which gave similar results. (iii) Normalised objective function produced a mean response with six times lower initial stiffness and more pronounced nonlinearity compared to non-normalised objective function.

DISCUSSION

It is possible to reproduce a mechanically inconsistent response purely by using the chosen experimental protocol. Non-preconditioned data from failure tests should be used for FE simulation of the elastic response of aneurysms. CA should not be used to obtain a mean response.

The influence of fiber dispersion on the mechanical response of aortic tissues in health and disease: a computational study

Changes in the structural components of aortic tissues have been shown to play a significant role in the pathogenesis of aortic degeneration. Therefore, reliable stress analyses require a suitable and meaningful constitutive model that captures micro-structural changes. As recent data show, in-plane and out-of-plane collagen fiber dispersions vary significantly between healthy and aneurysmatic aortic walls. The aim of this study is to computationally investigate the influence of fiber dispersion on the mechanical response of aortic tissues in health and disease. In particular, the influence of three different fiber dispersions is studied: (i) non-rotationally symmetric dispersion, the most realistic assumption for aortic tissues; (ii) transversely isotropic dispersion, a special case; (iii) perfectly aligned fibers (no dispersion in either plane), another special case. Explicit expressions for the stress and elasticity tensors as needed for the implementation in a finite element code are provided. Three representative numerical examples are studied: planar biaxial extension, inflation of residually stressed and pre-stretched aortic segments and inflation of an idealized abdominal aortic aneurysm (AAA) geometry. For the AAA geometry the case of isotropic dispersion is additionally analyzed. Documented structural and mechanical parameters are taken from human aortas (healthy media/adventitia and AAA). The influence of fiber dispersions upon magnitudes and distributions of stresses and deformations are presented and analyzed. Stresses vary significantly, especially in the AAA case, where material stiffening is significantly influenced by fiber dispersion. The results highlight the need to incorporate the structural differences into finite element simulations to obtain more accurate stress predictions. Additionally, results show the capability of one constitutive model to represent different scenarios of aortic micro-structures allowing future studies of collagen reorientation during disease progression.

Analysis of Iliac Artery Geometric Properties in Fenestrated Aortic Stent Graft Rotation

Introduction:

A complication of fenestrated endovascular aneurysm repair is the potential for stent graft rotation during deployment causing fenestration misalignment and branch artery occlusion. The objective of this study is to demonstrate that this rotation is caused by a buildup of rotational energy as the device is delivered through the iliac arteries and to quantify iliac artery geometric properties associated with device rotation.

Methods:

A retrospective clinical study was undertaken in which iliac artery geometric properties were assessed from preoperative imaging for 42 cases divided into 2 groups: 27 in the nonrotation group and 15 in the rotation group. Preoperative computed tomography scans were segmented, and the iliac artery centerlines were determined. Iliac artery tortuosity, curvature, torsion, and diameter were calculated from the centerline and the segmented vessel geometry.

Results:

The total iliac artery net torsion was found to be higher in the rotation group compared to the nonrotation group (23.5 ± 14.7 vs 14.6 ± 12.8 mm−1; P = .05). No statistically significant differences were found for the mean values of tortuosity, curvature, torsion, or diameter between the 2 groups.

Conclusion:

Stent graft rotation occurred in 36% of the cases considered in this study. Cases with high iliac artery total net torsion were found to be more likely to have stent graft rotation upon deployment. This retrospective study provides a framework for prospectively studying the influence of iliac artery geometric properties on fenestrated stent graft rotation.

INFLUENCE OF THE LOCAL MEAN CURVATURE ON THE ABDOMINAL AORTIC ANEURYSM STRESS DISTRIBUTION

An abdominal aortic aneurysm (AAA) is a permanent focal dilatation of the abdominal aorta of at least 1.5 times its normal diameter. Although the criterion of maximum diameter is still used in clinical practice to decide when to proceed with surgical intervention, numerical studies have demonstrated the importance of other geometric factors. In this work, the influence of the local mean curvature on AAA stress distribution has been analyzed in synthetic AAA geometries via finite element analysis. The results show a significant correlation between this geometric parameter and stress, suggesting that local mean curvature should also be considered along with the diameter criterion when making decisions about surgery.

Anisotropic and nonlinear biaxial mechanical response of porcine small bowel mesentery

Intestinal malrotation places pediatric patients at the risk of midgut volvulus, a complication that can lead to ischemic bowel, short gut syndrome, and even death. Even though the treatments for symptomatic patients of this complication are clear, it is still a challenge to identify asymptomatic patients who are at a higher risk of midgut volvulus and decide on a suitable course of treatment. Development of an accurate computerized model of this intestinal abnormality could help in gaining a better understanding of its integral behavior. To aid in developing such a model, in the current study, we have characterized the biaxial mechanical properties of the porcine small bowel mesentery. First, the tissue stress-strain response was determined using a biaxial tensile testing equipment. The stress-strain data were then fitted into a Fung-type phenomenological constitutive model to quantify the tissue material parameters. The stress-strain responses were highly nonlinear, showing more compliance at the lower strains following by a rapid transition into a stiffer response at higher strains. The tissue was anisotropic and showed more stiffness in the radial direction. The data fitted the Fung-type constitutive model with an average R-squared value of 0.93. An averaging scheme was used to produce a set of material parameters which can represent the generic mechanical behavior of the tissue in the models.

Mechanical Characterization and Material Modeling of Diabetic Aortas in a Rabbit Model

Diabetes has been recognized as a major risk factor to cause macrovascular diseases and plays a key role in aortic wall remodeling. However, the effects of diabetes on elastic properties of aortas remain largely unknown and quantitative mechanical data are lacking. Thirty adult rabbits (1.6-2.2 kg) were collected and the type 1 diabetic rabbit model was induced by injection of alloxan. A total of 15 control and 15 diabetic rabbit (abdominal) aortas were harvested. Uniaxial and biaxial tensile tests were performed to measure ultimate tensile strength and to characterize biaxial mechanical behaviors of the aortas. A material model was fitted to the biaxial experimental data to obtain constitutive parameters. Histological and mass fraction analyses were performed to investigate the underlying microstructure and dry weight percentages of elastin and collagen in the control and the diabetic aortas. No statistically significant difference was found in ultimate tensile strength between the control and the diabetic aortas. Regarding biaxial mechanical responses, the diabetic aortas exhibited significantly lower extensibility and significantly higher tissue stiffness than the control aortas. Notably, tissue stiffening occurred in both circumferential and axial directions for the diabetic aortas; however, mechanical anisotropy does not change significantly. The material model was able to fit biaxial experimental data very well. Histology showed that a number of isolated foam cells were embedded in the diabetic aortas and hyperplasia of collagen was identified. The dry weight percentages of collagen within the diabetic aortas increased significantly as compared to the control aortas, whereas no significant change was found for that of elastin. Our data suggest that the diabetes impairs elastic properties and alters microstructure of the aortas and consequently, these changes may further contribute to complex aortic wall remodeling.

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.

The Relationship Between Surface Curvature and Abdominal Aortic Aneurysm Wall Stress

The maximum diameter (MD) criterion is the most important factor when predicting risk of rupture of abdominal aortic aneurysms (AAAs). An elevated wall stress has also been linked to a high risk of aneurysm rupture, yet is an uncommon clinical practice to compute AAA wall stress. The purpose of this study is to assess whether other characteristics of the AAA geometry are statistically correlated with wall stress. Using in-house segmentation and meshing algorithms, 30 patient-specific AAA models were generated for finite element analysis (FEA). These models were subsequently used to estimate wall stress and maximum diameter and to evaluate the spatial distributions of wall thickness, cross-sectional diameter, mean curvature, and Gaussian curvature. Data analysis consisted of statistical correlations of the aforementioned geometry metrics with wall stress for the 30 AAA inner and outer wall surfaces. In addition, a linear regression analysis was performed with all the AAA wall surfaces to quantify the relationship of the geometric indices with wall stress. These analyses indicated that while all the geometry metrics have statistically significant correlations with wall stress, the local mean curvature (LMC) exhibits the highest average Pearson's correlation coefficient for both inner and outer wall surfaces. The linear regression analysis revealed coefficients of determination for the outer and inner wall surfaces of 0.712 and 0.516, respectively, with LMC having the largest effect on the linear regression equation with wall stress. This work underscores the importance of evaluating AAA mean wall curvature as a potential surrogate for wall stress.

Histology and Biaxial Mechanical Behavior of Abdominal Aortic Aneurysm Tissue Samples

Abdominal aortic aneurysms (AAAs) represent permanent, localized dilations of the abdominal aorta that can be life-threatening if progressing to rupture. Evaluation of risk of rupture depends on understanding the mechanical behavior of patient AAA walls. In this project, a series of patient AAA wall tissue samples have been evaluated through a combined anamnestic, mechanical, and histopathologic approach. Mechanical properties of the samples have been characterized using a novel, strain-controlled, planar biaxial testing protocol emulating the in vivo deformation of the aorta. Histologically, the tissue ultrastructure was highly disrupted. All samples showed pronounced mechanical stiffening with stretch and were notably anisotropic, with greater stiffness in the circumferential than the axial direction. However, there were significant intrapatient variations in wall stiffness and stress. In biaxial tests in which the longitudinal stretch was held constant at 1.1 as the circumferential stretch was extended to 1.1, the maximum average circumferential stress was 330 ± 70 kPa, while the maximum average axial stress was 190 ± 30 kPa. A constitutive model considering the wall as anisotropic with two preferred directions fit the measured data well. No statistically significant differences in tissue mechanical properties were found based on patient gender, age, maximum bulge diameter, height, weight, body mass index, or smoking history. Although a larger patient cohort is merited to confirm these conclusions, the project provides new insight into the relationships between patient natural history, histopathology, and mechanical behavior that may be useful in the development of accurate methods for rupture risk evaluation.

Investigation on the Regional Loss Factor and Its Anisotropy for Aortic Aneurysms

An aortic aneurysm is a lethal arterial disease that mainly occurs in the thoracic and abdominal regions of the aorta. Thoracic aortic aneurysms are prevalent in the root/ascending parts of the aorta and can lead to aortic rupture resulting in the sudden death of patients. Understanding the biomechanical and histopathological changes associated with ascending thoracic aortic aneurysms (ATAAs), this study investigates the mechanical properties of the aorta during strip-biaxial tensile cycles. The loss factor-defined as the ratio of dissipated energy to the energy absorbed during a tensile cycle-the incremental modulus, and their anisotropy indexes were compared with the media fiber compositions for aneurysmal (n = 26) and control (n = 4) human ascending aortas. The aneurysmal aortas were categorized into the aortas with bicuspid aortic valves (BAV) and tricuspid aortic valves (TAV). The strip-biaxial loss factor correlates well with the diameter of the aortas with BAV and TAV (for the axial direction, respectively, R² = 0.71, p = 0.0022 and R² = 0.54, p = 0.0096). The loss factor increases significantly with patients' age in the BAV group (for the axial direction: R² = 0.45, p = 0.0164). The loss factor is isotropic for all TAV quadrants, whereas it is on average only isotropic in the anterior and outer curvature regions of the BAV group. The results suggest that loss factor may be a useful surrogate measure to describe the histopathology of aneurysmal tissue and to demonstrate the differences between ATAAs with the BAV and TAV.

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.

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).