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.     

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 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.     

New insights into the understanding of flow dynamics in an in vitro model for abdominal aortic aneurysms

An in vitro dynamics set-up of the flow in a compliant abdominal aortic aneurysm (AAA) model with an anterior posterior asymmetry, aorto-iliac bifurcation, and physiological inlet flow rate and outlet pressure waveforms was developed. The aims were first to show that the structural mechanical behavior of the used material to mimic the AAA wall was similar to this of patients with AAA and then to study the influence of the aorto-iliac bifurcation presence and to study the influence of the imbalanced flow rate in the iliac branches on the AAA flow field. 3D visualizations, never performed in the literature, have clearly put into evidence the development of a vortex ring generated at the AAA proximal neck during the decelerating phase of flow rate, which detaches and progresses downstream during the cardiac cycle, impinges on the anterior wall in the distal AAA region, breaks up, and separates into two vortices of which one rolls on upstream along the anterior wall. 2D particle image velocimetry measurements, swirling strength and enstrophy calculations allowed quantification of the vorticity, vortex trajectory and energy for the different geometrical and hydrodynamical conditions. The main results show that the instant and the intensity of the vortex ring impingement depend on the presence of the aorto-iliac bifurcation, with higher intensity, by about 90%, for an AAA without bifurcation. The imbalance of the flow rates into the iliac branches induces different propagation velocities of the vortex ring and lowers the intensity of the vortex impact by about 60%. The potential influence of the AAA dynamics is discussed in terms of AAA remodeling and rupture.     

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.     

In Vivo Three-Dimensional Surface Geometry of Abdominal Aortic Aneurysms

Abdominal aortic aneurysm (AAA) is a local, progressive dilation of the distal aorta that risks rupture until treated. Using the law of Laplace, in vivo assessment of AAA surface geometry could identify regions of high wall tensions as well as provide critical dimensional and shape data for customized endoluminal stent grafts. In this study, six patients with AAA underwent spiral computed tomography imaging and the inner wall of each AAA was identified, digitized, and reconstructed. A biquadric surface patch technique was used to compute the local principal curvatures, which required no assumptions regarding axisymmetry or other shape characteristics of the AAA surface. The spatial distribution of AAA principal curvatures demonstrated substantial axial asymmetry, and included adjacent elliptical and hyperbolic regions. To determine how much the curvature spatial distributions were dependent on tortuosity versus bulging, the effects of AAA tortuosity were removed from the three-dimensional (3D) reconstructions by aligning the centroids of each digitized contour to the z axis. The spatial distribution of principal curvatures of the modified 3D reconstructions were found to be largely axisymmetric, suggesting that much of the surface geometric asymmetry is due to AAA bending. On average, AAA surface area increased by 56% and abdominal aortic length increased by 27% over those for the normal aorta. Our results indicate that AAA surface geometry is highly complex and cannot be simulated by simple axisymmetric models, and suggests an equally complex wall stress distribution. © 1999 Biomedical Engineering Society. PAC99: 8719Rr, 8759Fm, 8757Gg     

Hemodynamics of the Normal Aorta Compared to Fusiform and Saccular Abdominal Aortic Aneurysms with Emphasis on a Potential Thrombus Formation Mechanism

Abdominal Aortic Aneurysms (AAAs), i.e., focal enlargements of the aorta in the abdomen are frequently observed in the elderly population and their rupture is highly mortal. An intra-luminal thrombus is found in nearly all aneurysms of clinically relevant size and multiply affects the underlying wall. However, from a biomechanical perspective thrombus development and its relation to aneurysm rupture is still not clearly understood. In order to explore the impact of blood flow on thrombus development, normal aortas (n = 4), fusiform AAAs (n = 3), and saccular AAAs (n = 2) were compared on the basis of unsteady Computational Fluid Dynamics simulations. To this end patient-specific luminal geometries were segmented from Computerized Tomography Angiography data and five full heart cycles using physiologically realistic boundary conditions were analyzed. Simulations were carried out with computational grids of about half a million finite volume elements and the Carreau–Yasuda model captured the non-Newtonian behavior of blood. In contrast to the normal aorta the flow in aneurysm was highly disturbed and, particularly right after the neck, flow separation involving regions of high streaming velocities and high shear stresses were observed. Naturally, at the expanded sites of the aneurysm average flow velocity and wall shear stress were much lower compared to normal aortas. These findings suggest platelets activation right after the neck, i.e., within zones of pronounced recirculation, and platelet adhesion, i.e., thrombus formation, downstream. This mechanism is supported by recirculation zones promoting the advection of activated platelets to the wall.     

Elemental composition, morphology and mechanical properties of calcified deposits obtained from abdominal aortic aneurysms

Calcified deposits exist in almost all abdominal aortic aneurysms (AAAs). The significant difference in stiffness between these hard deposits and the compliant arterial wall may result in local stress concentrations and increase the risk of aneurysm rupture. Calcium deposits may also complicate AAA repair by hindering the attachment of a graft or stent-graft to the arterial wall or cause vessel wall injury at the site of balloon dilation or vascular clamp placement. Knowledge of the composition and properties of calcified deposits helps in understanding the risks associated with their presence. This work presents results of elemental composition, microscopic morphology, and mechanical property measurements of human calcified deposits obtained from within AAAs. The elemental analyses indicate the deposits are composed primarily of calcium phosphate with other assorted constituents. Microscopy investigations show a variety of microstructures within the deposits. The mechanical property measurements indicate an average elastic modulus in the range of cortical bone and an average hardness similar to nickel and iron.     

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。     

基于MRA的个体化腹主动脉瘤计算机仿真

目的探讨基于MRA图像进行个体化腹主动脉瘤(abdominal aortic aneurysm,AAA)计算机仿真研究的可行性,并从血流动力学层面探讨AAA的发生、发展和破裂机制。方法基于AAA患者的MRA数据采用逆向建模法建立AAA的三维几何模型;采用FLUENT软件进行数值模拟,假设血管壁为刚性壁,血液为不可压缩牛顿流体,建立瞬态模型。将收敛之后的数据导入到CFD-Post中进行结果分析,输出心动周期内不同时刻的血流流线图、流速分布图、血管壁面切应力分布图以及压力分布图。结果AAA瘤颈处血液流动的方式以层流为主,瘤腔内血流以涡流、湍流为主,且在瘤体膨大处较明显;瘤颈处血液流速快于瘤腔,瘤腔大部分区域在整个心动周期内都处于较低的流速水平,且波动不明显,瘤腔内的高流速区域多位于入口血流直接延续的部位;射血期的壁面切应力的量值及其变化幅度均大于充盈期,壁面切应力较高的区域总是分布于瘤颈附近,瘤腔的切应力在整个心动周期内始终处于较低水平;瘤体的壁面压力量值及其分布范围在射血峰值(t=0.08 s)时最大。加速射血期的壁面压力及其变化范围均较减速射血期及充盈期大。结论基于MRA图像可建立个体化的AAA计算机仿真模型,通过计算机仿真得到的AAA内血流分布规律对AAA的研究和临床个体化的诊治有一定的帮助。     

Geometrical factors as predictors of increased growth rate or increased rupture risk in small aortic aneurysms

Abdominal Aortic Aneurysms (AAAs) are focal dilation of the aorta that can lead to excessive enlargement and rupture over time. Current practice suggests intervention when the maximum diameter exceeds 5.5 cm, since in this diameter range the annual rupture risk outweighs the operative mortality. However, small AAA (<5.5 cm), though infrequently, may rupture or produce symptoms. Evidence from large randomized studies of small AAAs support the heterogeneity in patterns of growth and rupture potential among small AAAs. Elevated wall stress values have been implicated in AAAs rupture and rapid enlargement. Additionally, many studies have identified a strong correlation between certain geometric factors and elevated stress values. In this article we discuss the possibility that geometrical factors may have a predictive value to identify those small AAAs that have an increased risk of rupture or growth rate either during initial examination or during follow-up, making them amenable for early repair.     

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.     

腹主动脉瘤的数值计算模型比较研究

目的分别采用纯流体模型和流固耦合模型来计算腹主动脉瘤的血流动力学特征,比较两种数值模型的不同,并讨论在研究腹主动脉瘤中的应用。方法使用Gambit 2.2.30和COMSOL Multiphysics 4.2建立腹主动脉瘤的理想模型,分别基于有限体的方法分析纯流体模型,基于任意拉格朗日-欧拉算法(Arbitrary Lagrangian-Eulerian)计算流固耦合模型。结果同样的入口速度下,纯流体模型出现4个涡流和6个局部压力集中;流固耦合模型只有2个涡流和局部压力集中,且涡流中心更接近腹主动脉瘤的远端。在边界层分离点、血流回帖位置以及腹主动脉瘤的近端和远端,两种模型均出现壁剪切力极值。血管壁的最大形变和最大壁应力出现在腹主动脉瘤的近端和远端。结论两种模型的涡流个数和涡流中心的位置均不一样,与瘤体的生长有着密切的关联;流固耦合模型中的最大壁剪切力比纯流体模型要小36%;最大壁应力和最大血管壁的形变量与出口血压呈正相关。在研究血管瘤生长与血流动力学的关系时需要考虑使用流固耦合模型。     

The effect of angulation in abdominal aortic aneurysms: fluid–structure interaction simulations of idealized geometries

Abdominal aortic aneurysm (AAA) represents a degenerative disease process of the abdominal aorta that results in dilation and permanent remodeling of the arterial wall. A fluid structure interaction (FSI) parametric study was conducted to evaluate the progression of aneurysmal disease and its possible implications on risk of rupture. Two parametric studies were conducted using (i) the iliac bifurcation angle and (ii) the AAA neck angulation. Idealized streamlined AAA geometries were employed. The simulations were carried out using both isotropic and anisotropic wall material models. The parameters were based on CT scans measurements obtained from a population of patients. The results indicate that the peak wall stresses increased with increasing iliac and neck inlet angles. Wall shear stress (WSS) and fluid pressure were analyzed and correlated with the wall stresses for both sets of studies. An adaptation response of a temporary reduction of the peak wall stresses seem to correlate to a certain extent with increasing iliac angles. For the neck angulation studies it appears that a breakdown from symmetric vortices at the AAA inlet into a single larger vortex significantly increases the wall stress. Our parametric FSI study demonstrates the adaptation response during aneurysmal disease progression and its possible effects on the AAA risk of rupture. This dependence on geometric parameters of the AAA can be used as an additional diagnostic tool to help clinicians reach informed decisions in establishing whether a risky surgical intervention is warranted.     

The Role of Geometric and Biomechanical Factors in Abdominal Aortic Aneurysm Rupture Risk Assessment

The current clinical management of abdominal aortic aneurysm (AAA) disease is based to a great extent on measuring the aneurysm maximum diameter to decide when timely intervention is required. Decades of clinical evidence show that aneurysm diameter is positively associated with the risk of rupture, but other parameters may also play a role in causing or predisposing the AAA to rupture. Geometric factors such as vessel tortuosity, intraluminal thrombus volume, and wall surface area are implicated in the differentiation of ruptured and unruptured AAAs. Biomechanical factors identified by means of computational modeling techniques, such as peak wall stress, have been positively correlated with rupture risk with a higher accuracy and sensitivity than maximum diameter alone. The objective of this review is to examine these factors, which are found to influence AAA disease progression, clinical management and rupture potential, as well as to highlight on-going research by our group in aneurysm modeling and rupture risk assessment.     

Towards A Noninvasive Method for Determination of Patient-Specific Wall Strength Distribution in Abdominal Aortic Aneurysms

The spatial distributions of both wall stress and wall strength are required to accurately evaluate the rupture potential for an individual abdominal aortic aneurysm (AAA). The purpose of this study was to develop a statistical model to non-invasively estimate the distribution of AAA wall strength. Seven parameters–namely age, gender, family history of AAA, smoking status, AAA size, local diameter, and local intraluminal thrombus (ILT) thickness–were either directly measured or recorded from the patients hospital chart. Wall strength values corresponding to these predictor variables were calculated from the tensile testing of surgically procured AAA wall specimens. Backwards–stepwise regression techniques were used to identify and eliminate insignificant predictors for wall strength. Linear mixed-effects modeling was used to derive a final statistical model for AAA wall strength, from which 95% confidence intervals on the model parameters were formed. The final statistical model for AAA wall strength consisted of the following variables: sex, family history, ILT thickness, and normalized transverse diameter. Demonstrative application of the model revealed a unique, complex wall strength distribution, with strength values ranging from 56 N/cm² to 133 N/cm². A four-parameter statistical model for the noninvasive estimation of patient-specific AAA wall strength distribution has been successfully developed. The currently developed model represents a first attempt towards the noninvasive assessment of AAA wall strength. Coupling this model with our stress analysis technique may provide a more accurate means to estimate patient-specific rupture potential of AAA.     

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     

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.     

腹主动脉血管瘤的定常流动的模拟

目的 应用两维对称模型模拟腹主动肪血管瘤的定常流动。方法 运用计算力学软件（FLUENTv4.3.2)进行数值模拟。结果 该研究给出了各种情况下的流动状态、流线分布、壁面剪切力和壁面压降的分布。结论 结果表明，腹主动脉血管瘤的形状和大小对流动状态影响不大，而雷诺数的增大会增大腹主动脉血管瘤内涡的强度。