Effect of Variation in Intraluminal Thrombus Constitutive Properties on Abdominal Aortic Aneurysm Wall Stress

The abdominal aortic aneurysm (AAA) is a degenerating disease for which the end stage is the rupture of the vessel wall. Accurate prediction of the stresses acting on the aneurysm tissue may be used to determine the actual risk of rupture of a specific aneurysm. To accomplish this, a correct constitutive model for the aneurysmal aortic wall and any intraluminal thrombus (ILT) present within it are needed. Our laboratory has previously reported the mechanical properties of ILT. The aim of this work is to investigate the reliability of using population-mean values of ILT constitutive parameters to estimate AAA wall stress distribution. For this, a three-dimensional asymmetric model of an aneurysm including ILT was generated and a parametric study was conducted varying ILT constitutive properties within a physiological range. Results show that the presence of any ILT reduces and redistributes the stresses in the aortic wall markedly. Maximum variation in the peak wall stresses for all the models analyzed was 5%. Adopting a nonhomogeneous ILT did not alter the stress distribution. On the basis of these results, we infer that population mean parameters for ILT material characteristics can be used to reasonably estimate the wall stresses in patient specific aneurysm models. © 2003 Biomedical Engineering Society. PAC2003: 8719Rr, 8719Xx, 8710+e     

Patient-Based Abdominal Aortic Aneurysm Rupture Risk Prediction with Fluid Structure Interaction Modeling

Elective repair of abdominal aortic aneurysm (AAA) is warranted when the risk of rupture exceeds that of surgery, and is mostly based on the AAA size as a crude rupture predictor. A methodology based on biomechanical considerations for a reliable patient-specific prediction of AAA risk of rupture is presented. Fluid–structure interaction (FSI) simulations conducted in models reconstructed from CT scans of patients who had contained ruptured AAA (rAAA) predicted the rupture location based on mapping of the stresses developing within the aneurysmal wall, additionally showing that a smaller rAAA presented a higher rupture risk. By providing refined means to estimate the risk of rupture, the methodology may have a major impact on diagnostics and treatment of AAA patients.     

A Comparison of Diameter,Wall Stress,and Rupture Potential Index for Abdominal Aortic Aneurysm Rupture Risk Prediction

An abdominal aortic aneurysm (AAA) is a balloon-like dilation of the aorta, which is potentially fatal in case of rupture. Computational finite element (FE) analysis is a promising approach to a more accurate and patient-specific rupture risk prediction. AAA wall strength and rupture potential index (RPI) calculation are implemented in our FE software. Static structural FE simulations are performed on n = 30 non-ruptured asymptomatic, n = 9 non-ruptured symptomatic, and n = 14 ruptured AAAs. We calculate maximum values for diameter, wall displacement, strain, stress, and RPI as well as minimum wall strength for every AAA. All investigated quantities, except minimum strength, show statistically significant differences between non-ruptured asymptomatic and symptomatic/ruptured AAAs. Maximum wall stress and especially the RPI are notably increased for symptomatic and ruptured AAAs. The biggest difference is found to be the RPI (Δ = 44.9%, p = 8.0e−5). Lowest RPI obtained for symptomatic or ruptured AAAs is 0.3. The RPI of more than 55% of the investigated asymptomatic AAAs falls below this value. Maximum wall stress and maximum RPI criteria enable a reliable rupture risk evaluation for AAAs. Especially in the diameter range where surgical indication is not obvious, the RPI holds great potential for improvement of clinical decisions.     

A novel approach for local abdominal aortic aneurysm growth quantification

Although aneurysm size still remains the most accepted predictor of rupture risk, abdominal aortic aneurysms (AAAs) with maximum diameter smaller than 5 cm may also rupture. Growth rate is an additional marker for rupture risk as it potentially reflects an undesirable wall remodeling that leads to fast regional growth. Currently, an indication for surgery is an expansion rate >10 mm/year, measured as change in maximum diameter over time. However, as AAA expansion is non-uniform, it is questionable whether measurement of maximum diameter change over time can capture increased localized remodeling activity. A method for estimating AAA surface area growth is introduced, providing a better measure of local wall deformation. The proposed approach is based on the non-rigid iterative closest point algorithm. Optimization and validation is performed using 12 patient-specific AAA geometries artificially deformed to produce a target surface with known nodal displacements. Mesh density sensitivity, range of uncertainty, and method limitations are discussed. Application to ten AAA patient-specific follow-ups suggested that maximum diameter growth does not correlate strongly with the maximum surface growth (R ² = 0.614), which is not always colocated with maximum diameter, or uniformly distributed. Surface growth quantification could reinforce the quality of aneurysm surveillance programs.     

A relation between near-wall particle-hemodynamics and onset of thrombus formation in abdominal aortic aneurysms

A novel computational particle-hemodynamics analysis of key criteria for the onset of an intraluminal thrombus (ILT) in a patient-specific abdominal aortic aneurysm (AAA) is presented. The focus is on enhanced platelet and white blood cell residence times as well as their elevated surface-shear loads in near-wall regions of the AAA sac. The generalized results support the hypothesis that a patient’s AAA geometry and associated particle-hemodynamics have the potential to entrap activated blood particles, which will play a role in the onset of ILT. Although the ILT history of only a single patient was considered, the modeling and simulation methodology provided allow for the development of an efficient computational tool to predict the onset of ILT formation in complex patient-specific cases.     

A patient-specific computational model of fluid-structure interaction in abdominal aortic aneurysms

It is generally believed that knowledge of the wall stress distribution could help to find better rupture risk predictors of abdominal aortic aneurysms (AAAs). Although AAA wall stress results from combined action between blood, wall and intraluminal thrombus, previously published models for patient-specific assessment of the wall stress predominantly did not include fluid-dynamic effects. In order to facilitate the incorporation of fluid–structure interaction in the assessment of AAA wall stress, in this paper, a method for generating patient-specific hexahedral finite element meshes of the AAA lumen and wall is presented. The applicability of the meshes is illustrated by simulations of the wall stress, blood velocity distribution and wall shear stress in a characteristic AAA. The presented method yields a flexible, semi-automated approach for generating patient-specific hexahedral meshes of the AAA lumen and wall with predefined element distributions. The combined fluid/solid mesh allows for simulations of AAA blood dynamics and AAA wall mechanics and the interaction between the two. The mechanical quantities computed in these simulations need to be validated in a clinical setting, after which they could be included in clinical trials in search of risk factors for AAA rupture.     

A Numerical Implementation to Predict Residual Strains from the Homogeneous Stress Hypothesis with Application to Abdominal Aortic Aneurysms

Wall stress analysis of abdominal aortic aneurysm (AAA) is a promising method of identifying AAAs at high risk of rupture. However, neglecting residual strains (RS) in the load-free configuration of patient-specific finite element analysis models is a sever limitation that strongly affects the computed wall stresses. Although several methods for including RS have been proposed, they cannot be directly applied to patient-specific AAA simulations. RS in the AAA wall are predicted through volumetric tissue growth that aims at satisfying the homogeneous stress hypothesis at mean arterial pressure load. Tissue growth is interpolated linearly across the wall thickness and aneurysm tissues are described by isotropic constitutive formulations. The total deformation is multiplicatively split into elastic and growth contributions, and a staggered schema is used to solve the field variables. The algorithm is validated qualitatively at a cylindrical artery model and then applied to patient-specific AAAs (n = 5). The induced RS state is fully three-dimensional and in qualitative agreement with experimental observations, i.e., wall strips that were excised from the load-free wall showed stress-releasing-deformations that are typically seen in laboratory experiments. Compared to RS-free simulations, the proposed algorithm reduced the von Mises stress gradient across the wall by a tenfold. Accounting for RS leads to homogenized wall stresses, which apart from reducing the peak wall stress (PWS) also shifted its location in some cases. The present study demonstrated that the homogeneous stress hypothesis can be effectively used to predict RS in the load-free configuration of the vascular wall. The proposed algorithm leads to a fast and robust prediction of RS, which is fully capable for a patient-specific AAA rupture risk assessment. Neglecting RS leads to non-realistic wall stress values that severely overestimate the PWS.     

Quantitative assessment of abdominal aortic aneurysm geometry

Recent studies have shown that the maximum transverse diameter of an abdominal aortic aneurysm (AAA) and expansion rate are not entirely reliable indicators of rupture potential. We hypothesize that aneurysm morphology and wall thickness are more predictive of rupture risk and can be the deciding factors in the clinical management of the disease. A non-invasive, image-based evaluation of AAA shape was implemented on a retrospective study of 10 ruptured and 66 unruptured aneurysms. Three-dimensional models were generated from segmented, contrast-enhanced computed tomography images. Geometric indices and regional variations in wall thickness were estimated based on novel segmentation algorithms. A model was created using a J48 decision tree algorithm and its performance was assessed using ten-fold cross validation. Feature selection was performed using the χ²-test. The model correctly classified 65 datasets and had an average prediction accuracy of 86.6% (κ = 0.37). The highest ranked features were sac length, sac height, volume, surface area, maximum diameter, bulge height, and intra-luminal thrombus volume. Given that individual AAAs have complex shapes with local changes in surface curvature and wall thickness, the assessment of AAA rupture risk should be based on the accurate quantification of aneurysmal sac shape and size.     

In vitro evaluation of the effects of intraluminal thrombus on abdominal aortic aneurysm wall dynamics

The optimum time to treat abdominal aortic aneurysms (AAAs) still remains an uncertain issue. The decision to intervene does not take in account the effects that wall curvature, intraluminal thrombus (ILT) properties and thickness have on rupture. The role of ILT in aneurysm dynamics and rupture has been controversial. In vitro testing of four silicone AAA models incorporating the ILT and aortic bifurcation was studied under physiological conditions. Pressures (P) and diameters (D) were analysed for models with and without ILT at different locations. The diametral strain, compliance and P/D curves were influenced by the presence, elastic stiffness and thickness of the ILT. In this case, the inclusion of ILT reduced the lumen area by 77% that resulted in a 0.5–81% reduction in compliance depending on ILT properties. With an increase in ILT stiffness from 0.05 to 0.2 MPa, the compliance was reduced by 81%. In the region of maximum diameter, there was a reduction of diametral strain and compliance except for the softer ILT which was more compliant throughout the proximal region. The shifting of the maximum diametral strain and compliance to the proximal neck was pronounced by an increase in ILT stiffness, thus creating a possible rupture site.     

The Effects of Anisotropy on the Stress Analyses of Patient-Specific Abdominal Aortic Aneurysms

The local dilation of the infrarenal abdominal aorta, termed an abdominal aortic aneurysm (AAA), is often times asymptomatic and may eventually result in rupture—an event associated with a significant mortality rate. The estimation of in-vivo stresses within AAAs has been proposed as a useful tool to predict the likelihood of rupture. For the current work, a previously-derived anisotropic relation for the AAA wall was implemented into patient-specific finite element simulations of AAA. There were 35 AAAs simulated in the current work which were broken up into three groups: elective repairs (n = 21), non-ruptured repairs (n = 5), and ruptured repairs (n = 9). Peak stresses and strains were compared using the anisotropic and isotropic constitutive relations. There were significant increases in peak stress when using the anisotropic relationship (p < 0.001), even in the absence of the ILT (p = 0.014). Rutpured AAAs resulted in elevated peak stresses as compared to non-ruptured AAAs when using both the isotropic and anisotropic simulations, however these comparisons did not reach significance (p _ani = 0.55, p _iso = 0.73). While neither the isotropic or anisotropic simulations were able to significantly discriminate ruptured vs. non-ruptured AAAs, the lower p-value when using the anisotropic model suggests including it into patient-specific AAAs may help better identify AAAs at high risk.     

Quantification of Hemodynamics in Abdominal Aortic Aneurysms During Rest and Exercise Using Magnetic Resonance Imaging and Computational Fluid Dynamics

Abdominal aortic aneurysms (AAAs) affect 5–7% of older Americans. We hypothesize that exercise may slow AAA growth by decreasing inflammatory burden, peripheral resistance, and adverse hemodynamic conditions such as low, oscillatory shear stress. In this study, we use magnetic resonance imaging and computational fluid dynamics to describe hemodynamics in eight AAAs during rest and exercise using patient-specific geometric models, flow waveforms, and pressures as well as appropriately resolved finite-element meshes. We report mean wall shear stress (MWSS) and oscillatory shear index (OSI) at four aortic locations (supraceliac, infrarenal, mid-aneurysm, and suprabifurcation) and turbulent kinetic energy over the entire computational domain on meshes containing more than an order of magnitude more elements than previously reported results (mean: 9.0-million elements; SD: 2.3 M; range: 5.7–12.0 M). MWSS was lowest in the aneurysm during rest 2.5 dyn/cm² (SD: 2.1; range: 0.9–6.5), and MWSS increased and OSI decreased at all four locations during exercise. Mild turbulence existed at rest, while moderate aneurysmal turbulence was present during exercise. During both rest and exercise, aortic turbulence was virtually zero superior to the AAA for seven out of eight patients. We postulate that the increased MWSS, decreased OSI, and moderate turbulence present during exercise may attenuate AAA growth.     

A Pull-Back Algorithm to Determine the Unloaded Vascular Geometry in Anisotropic Hyperelastic AAA Passive Mechanics

Biomechanical studies on abdominal aortic aneurysms (AAA) seek to provide for better decision criteria to undergo surgical intervention for AAA repair. More accurate results can be obtained by using appropriate material models for the tissues along with accurate geometric models and more realistic boundary conditions for the lesion. However, patient-specific AAA models are generated from gated medical images in which the artery is under pressure. Therefore, identification of the AAA zero pressure geometry would allow for a more realistic estimate of the aneurysmal wall mechanics. This study proposes a novel iterative algorithm to find the zero pressure geometry of patient-specific AAA models. The methodology allows considering the anisotropic hyperelastic behavior of the aortic wall, its thickness and accounts for the presence of the intraluminal thrombus. Results on 12 patient-specific AAA geometric models indicate that the procedure is computational tractable and efficient, and preserves the global volume of the model. In addition, a comparison of the peak wall stress computed with the zero pressure and CT-based geometries during systole indicates that computations using CT-based geometric models underestimate the peak wall stress by 59 ± 64 and 47 ± 64 kPa for the isotropic and anisotropic material models of the arterial wall, respectively.     

腹主动脉瘤应力模型的建立及其应用

本研究用螺旋CT扫描腹主动脉瘤获得的断层图像合成腹主动脉瘤几何模型，通过设定瘤壁组织生物力学参数和边界条件，使用有限元分析的方法分析腹主动脉瘤瘤壁的应力分布。结果标明，本例腹主动脉瘤应力峰值位于远端分叉部位，瘤体应力峰值位于后壁，均小于瘤壁的承受极限。本研究所得结果对腹主动脉瘤应力模型有助于分析个体化腹主动脉瘤的破裂部位和生长方向，对研究疾病进程提供依据。     

MMP-9, homocysteine and CRP circulating levels are associated with intraluminal thrombus thickness of abdominal aortic aneurysms: new implication of the old biomarkers

Background: Abdominal aortic aneurysms (AAAs) are characterized by presence of high proteolytic activity, atherosclerotic lesions, extensive transmural inflammation and the presence of variably sized and shaped intraluminal thrombus (ILT). Therefore, we evaluated a possible association between plasma matrix metalloproteinase-9 (MMP-9), homocysteine (Hcy), high-sensitivity C-reactive protein (hsCRP) levels and ILT thickness in patients with AAA. Methods: Plasma concentrations of MMP-9, Hcy and hsCRP were determined and ILT thickness was measured in 71 patients with AAA. They were divided into 2 groups according to ILT thickness: 34 patients with ILT mean thickness ≥ 9 mm and 37 patients with ILT < 9 mm. Results: Plasma MMP-9 and CRP concentrations in patients with thin ILT were significantly higher than in group with thick ILT (medians 610 vs. 485 ng/mL, p = 0.00003, and 7.7 vs. 3.3 mg/L, p < 0.00001, respectively) In contrast, plasma Hcy concentrations in patients with thin ILT were significantly lower than in the group with thick ILT (medians 14.3 vs. 19.2 μmol/L, p < 0.00001). Multiple regression models adjusted for age and AAA diameter showed that thin ILT is an independent predictor of high MMP-9 and CRP concentrations, while thick ILT predicts high Hcy concentrations. Conclusions: Association of higher plasma levels of MMP-9 and CRP with thin ILT may be related to two phenomena: thin thrombi convey more elastolysis-stimulating factors from blood to the AAA wall and thin thrombi convey more factors involved in proteolysis and inflammation from AAA wall to blood. The association of thin ILT with lower plasma Hcy concentrations may be related to the role of Hcy as a prothrombotic marker and needs further research.     

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

Assessing the risk for abdominal aortic aneurysm (AAA) rupture is critical in the management of aneurysm patients and an individual assessment is possible with the biomechanical rupture risk assessment. Such an assessment could potentially be improved by a constitutive AAA wall model that accounts for irreversible damage-related deformations. Because of that the present study estimated the elastic and inelastic properties of the AAA wall through a mixed experimental-numerical approach. Specifically, finite element (FE) models of bone-shaped tensile specimens were used to merge data from failure testing of the AAA wall with their measured collagen orientation distribution. A histo-mechanical constitutive model for collagen fibers was employed, where plastic fibril sliding determined not only remaining deformations but also weakening of the fiber. The developed FE models were able to replicate the experimentally recorded load–displacement property of all 16 AAA wall specimens that were investigated in the study. Tensile testing in longitudinal direction of the AAA defined a Cauchy strength of 569(SD 411) kPa that was reached at a stretch of 1.436(SD 0.118). The stiffness and strength of specimens decreased with the wall thickness and were elevated (p = 0.018; p = 0.030) in patients with chronic obstructive pulmonary disease (COPD). Smoking affected the tissue parameters that were related to the irreversible deformation response, and no correlation with gender and age was found. The observed effects on the biomechanical properties of the AAA wall could have long-term consequences for the management of aneurysm patients, i.e., specifically they might influence future AAA rupture risk assessments. However, in order to design appropriate clinical validation studies our findings should firstly be verified in a larger patient cohort.     

Micromechanical Characterization of Intra-luminal Thrombus Tissue from Abdominal Aortic Aneurysms

The reliable assessment of Abdominal Aortic Aneurysm rupture risk is critically important in reducing related mortality without unnecessarily increasing the rate of elective repair. Intra-luminal thrombus (ILT) has multiple biomechanical and biochemical impacts on the underlying aneurysm wall and thrombus failure might be linked to aneurysm rupture. Histological slices from 7 ILTs were analyzed using a sequence of automatic image processing and feature analyzing steps. Derived microstructural data was used to define Representative Volume Elements (RVE), which in turn allowed the estimation of microscopic material properties using the non-linear Finite Element Method. ILT tissue exhibited complex microstructural arrangement with larger pores in the abluminal layer than in the luminal layer. The microstructure was isotropic in the abluminal layer, whereas pores started to orient along the circumferential direction towards the luminal site. ILT’s macroscopic (reversible) deformability was supported by large pores in the microstructure and the inhomogeneous structure explains in part the radially changing macroscopic constitutive properties of ILT. Its microscopic properties decreased just slightly from the luminal to the abluminal layer. The present study provided novel microstructural and micromechanical data of ILT tissue, which is critically important to further explore the role of the ILT in aneurysm rupture. Data provided in this study allow an integration of structural information from medical imaging for example, to estimate ILT’s macroscopic mechanical properties.     

基于个性化颈内动脉瘤模型的流固耦合分析

目的在考虑血管壁弹性条件下,分析颈内动脉血液流动和壁面切应力的分布特性,探讨动脉瘤破裂的生物力学因素。方法依据二维医学扫描图像构建三维个性化颈内动脉瘤模型。依据人体生理统计数据构建出血管壁模型。根据人体颈内动脉生理流动条件,利用有限体积法和有限元法模拟分析流固耦合作用下颈内动脉瘤中的血流动力学。结果在动脉瘤腔中有一个明显的涡旋存在,此涡旋流动的方向在心动周期内没有改变;在动脉瘤颈和动脉瘤壁面处存在一个壁面切应力值相对较大区域;在动脉瘤颈和动脉瘤顶有两个区域的Von Mises应力处于局部最大值。从材料强度角度考虑,这几个区域都是动脉瘤容易破裂的地方。结论通过流固耦合计算可以获得血管壁面应力分布特性,进而推断动脉瘤破裂的可能位置。     

Surface Curvature as a Classifier of Abdominal Aortic Aneurysms: A Comparative Analysis

An abdominal aortic aneurysm (AAA) carries one of the highest mortality rates among vascular diseases when it ruptures. To predict the role of surface curvature in rupture risk assessment, a discriminatory analysis of aneurysm geometry characterization was conducted. Data was obtained from 205 patient-specific computed tomography image sets corresponding to three AAA population subgroups: patients under surveillance, those that underwent elective repair of the aneurysm, and those with an emergent repair. Each AAA was reconstructed and their surface curvatures estimated using the biquintic Hermite finite element method. Local surface curvatures were processed into ten global curvature indices. Statistical analysis of the data revealed that the L2-norm of the Gaussian and Mean surface curvatures can be utilized as classifiers of the three AAA population subgroups. The application of statistical machine learning on the curvature features yielded 85.5% accuracy in classifying electively and emergent repaired AAAs, compared to a 68.9% accuracy obtained by using maximum aneurysm diameter alone. Such combination of non-invasive geometric quantification and statistical machine learning methods can be used in a clinical setting to assess the risk of rupture of aneurysms during regular patient follow-ups.     

Decision Tree Based Classification of Abdominal Aortic Aneurysms Using Geometry Quantification Measures

Abdominal aortic aneurysm (AAA) is an asymptomatic aortic disease with a survival rate of 20% after rupture. It is a vascular degenerative condition different from occlusive arterial diseases. The size of the aneurysm is the most important determining factor in its clinical management. However, other measures of the AAA geometry that are currently not used clinically may also influence its rupture risk. With this in mind, the objectives of this work are to develop an algorithm to calculate the AAA wall thickness and abdominal aortic diameter at planes orthogonal to the vessel centerline, and to quantify the effect of geometric indices derived from this algorithm on the overall classification accuracy of AAA based on whether they were electively or emergently repaired. Such quantification was performed based on a retrospective review of existing medical records of 150 AAA patients (75 electively repaired and 75 emergently repaired). Using an algorithm implemented within the MATLAB computing environment, 10 diameter- and wall thickness-related indices had a significant difference in their means when calculated relative to the AAA centerline compared to calculating them relative to the medial axis. Of these 10 indices, nine were wall thickness-related while the remaining one was the maximum diameter (D_max). D_max calculated with respect to the medial axis is over-estimated for both electively and emergently repaired AAA compared to its counterpart with respect to the centerline. C5.0 decision trees, a machine learning classification algorithm implemented in the R environment, were used to construct a statistical classifier. The decision trees were built by splitting the data into 70% for training and 30% for testing, and the properties of the classifier were estimated based on 1000 random combinations of the 70/30 data split. The ensuing model had average and maximum classification accuracies of 81.0 and 95.6%, respectively, and revealed that the three most significant indices in classifying AAA are, in order of importance: AAA centerline length, L2-norm of the Gaussian curvature, and AAA wall surface area. Therefore, we infer that the aforementioned three geometric indices could be used in a clinical setting to assess the risk of AAA rupture by means of a decision tree classifier. This work provides support for calculating cross-sectional diameters and wall thicknesses relative to the AAA centerline and using size and surface curvature based indices in classification studies of AAA.     

Effects of blood flow and vessel geometry on wall stress and rupture risk of abdominal aortic aneurysms

Sudden rupture of abdominal aortic aneurysm (AAA), often without prior medical warning, is the 13th leading cause of mortality in the US. The local rupture is triggered when the elusive maximum local wall stress exceeds the patient's yield stress. Employing a validated fluid – structure interaction code, the coupled blood flow and AAA wall dynamics were simulated and analysed for two representative asymmetric AAAs with different neck angles and iliac bifurcations. It turned out that the AAA morphology plays an important role in wall deformation and stress distribution, and hence possible rupture. The neck angle substantially impacts flow fields. A large neck angle may cause strong irregular vortices in the AAA cavity and may influence the wall stress distribution remarkably. The rupture risk of lateral asymmetric AAAs is higher than for the anterior – posterior asymmetric types. The most likely rupture site is located near the anterior distal side for the anterior – posterior asymmetric AAA and the left distal side in the lateral asymmetric AAA.