Impact of calcifications on patient-specific wall stress analysis of abdominal aortic aneurysms

As a degenerative and inflammatory desease of elderly patients, about 80% of abdominal aortic aneurysms (AAA) show considerable wall calcification. Effect of calcifications on computational wall stress analyses of AAAs has been rarely treated in literature so far. Calcifications are heterogeneously distributed, non-fibrous, stiff plaques which are most commonly found near the luminal surface in between the intima and the media layer of the vessel wall. In this study, we therefore investigate the influence of calcifications as separate AAA constituents on finite element simulation results. Thus, three AAAs are reconstructed with regard to intraluminal thrombus (ILT), calcifications and vessel wall. Each patient-specific AAA is simulated twice, once including all three AAA constituents and once neglecting calcifications as it is still common in literature. Parameters for constitutive modeling of calcifications are thereby taken from experiments performed by the authors, showing that calcifications exhibit an almost linear stress–strain behavior with a Young’s modulus E ≥ 40 MPa. Simulation results show that calcifications exhibit significant load-bearing effects and reduce stress in adjacent vessel wall. Average stress within the vessel wall is reduced by 9.7 to 59.2%. For two out of three AAAs, peak wall stress decreases when taking calcifications into consideration (8.9 and 28.9%). For one AAA, simulated peak wall stress increases by 5.5% due to stress peaks near calcification borders. However, such stress singularities due to sudden stiffness jumps are physiologically doubtful. It can further be observed that large calcifications are mostly situated in concavely shaped regions of the AAA wall. We deduce that AAA shape is influenced by existent calcifications, thus crucial errors occur if they are neglected in computational wall stress analyses. A general increase in rupture risk for calcified AAAs is doubted.     

A comparison of modelling techniques for computing wall stress in abdominal aortic aneurysms

Background  

Aneurysms, in particular abdominal aortic aneurysms (AAA), form a significant portion of cardiovascular related deaths. There is much debate as to the most suitable tool for rupture prediction and interventional surgery of AAAs, and currently maximum diameter is used clinically as the determining factor for surgical intervention. Stress analysis techniques, such as finite element analysis (FEA) to compute the wall stress in patient-specific AAAs, have been regarded by some authors to be more clinically important than the use of a "one-size-fits-all" maximum diameter criterion, since some small AAAs have been shown to have higher wall stress than larger AAAs and have been known to rupture.     

Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability

Knowledge of the wall stresses in an abdominal aortic aneurysm (AAA) may be helpful in evaluating the need for surgical intervention to avoid rupture. This must be preceded by the development of a more suitable finite strain constitutive model for AAA, as none currently exists. Additionally, reliable stress analysis of in vivo AAA for the purposes of clinical diagnostics requires patient-specific values of the material parameters, which are difficult to determine noninvasively. The purpose of this work, therefore, was three-fold: (1) to develop a finite strain constitutive model for AAA; (2) to estimate the variation of model parameters within a sample population; and (3) to evaluate the sensitivity of computed stress distribution in AAA due to this biologic variation. We propose here a two parameter, hyperelastic, isotropic, incompressible material model and utilize experimental data from 69 freshly excised AAA specimens to both develop the functional form of the model and estimate its material parameters. Parametric analyses were performed via repeated finite element computations to determine the effect of varying each of the two model parameters on the stress distribution in a three-dimensional AAA model. The agreement between experimental data and the proposed functional form of the constitutive law was very good (R2 > 0.9). Our finite element simulations showed that the computed AAA wall stresses changed by only 4% or less when both the parameters were varied within the 95% confidence intervals for the patient population studied. This observation indicates that in lieu of the patient-specific material parameters, which are difficult to determine the use of population mean values is sufficiently accurate for the model to be reasonably employed in a clinical setting. We believe that this is an important advancement toward the development of a computational tool for the estimation of rupture potential for individual AAA, for which there is great clinical need.     

Initial stress and nonlinear material behavior in patient-specific AAA wall stress analysis

Rupture risk estimation of abdominal aortic aneurysms (AAA) is currently based on the maximum diameter of the AAA. A more critical approach is based on AAA wall stress analysis. For that, in most cases, the AAA geometry is obtained from CT-data and treated as a stress free geometry. However, during CT imaging, the AAA is subjected to a time-averaged blood pressure and is therefore not stress free. The aim of this study is to evaluate the effect of neglecting these initial stresses (IS) on the patient-specific AAA wall stress as computed by finite element analysis. Additionally, the contribution of the nonlinear material behavior of the AAA wall is evaluated.Thirty patients with maximum AAA diameters below the current surgery criterion were scanned with contrast-enhanced CT and the AAA's were segmented from the image data. The mean arterial blood pressure (MAP) was measured immediately after the CT-scan and used to compute the IS corresponding with the CT geometry and MAP. Comparisons were made between wall stress obtained with and without IS and with linear and nonlinear material properties.On average, AAA wall stresses as computed with IS were higher than without IS. This was also the case for the stresses computed with the nonlinear material model compared to the linear material model. However, omitting initial stress and material nonlinearity in AAA wall stress computations leads to different effects in the resulting wall stress for each AAA. Therefore, provided that other assumptions made are not predominant, IS cannot be discarded and a nonlinear material model should be used in future patient-specific AAA wall stress analyses.     

Including surrounding tissue improves ultrasound-based 3D mechanical characterization of abdominal aortic aneurysms

ObjectivesIn this study the influence of surrounding tissues including the presence of the spine on wall stress analysis and mechanical characterization of abdominal aortic aneurysms using ultrasound imaging has been investigated.MethodsGeometries of 7 AAA patients and 11 healthy volunteers were acquired using 3-D ultrasound and converted to finite element based models. Model complexity of externally unsupported (aorta-only) models was complemented with inclusion of both soft tissue around the aorta and a spine support dorsal to the aorta. Computed 3-D motion of the aortic wall was verified by means of ultrasound speckle tracking. Resulting stress, strain, and estimated shear moduli were analyzed to quantify the effect of adding surrounding material supports.ResultsAn improved agreement was shown between the ultrasound measurements and the finite element tissue and spine models compared to the aorta-only models. Peak and 99-percentile Von Mises stress showed an overall decrease of 23–30%, while estimated shear modulus decreased with 12–20% after addition of the soft tissue. Shear strains in the aortic wall were higher in areas close to the spine compared to the anterior region.ConclusionsImproving model complexity with surrounding tissue and spine showed a homogenization of wall stresses, reduction in homogeneity of shear strain at the posterior side of the AAA, and a decrease in estimated aortic wall shear modulus. Future research will focus on the importance of a patient-specific spine geometry and location.     

On the sensitivity of wall stresses in diseased arteries to variable material properties

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part I--steady flow hemodynamics

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Homogeneous, Newtonian blood flow is simulated under steady conditions for the range of Reynolds numbers 10 < or =Re < or =2265. Flow hemodynamics are quantified by calculating the distributions of wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG). A correlation between maximum values of hemodynamic stresses and Reynolds number is established, and the spatial distribution of WSSG is considered as a hemodynamic force that may cause damage to the arterial wall at an intermediate stage of AAA growth. The temporal distribution of hemodynamic stresses in pulsatile flow and their physical implications in AAA rupture are discussed in Part II of this paper.     

Haemodynamics and stresses in abdominal aortic aneurysms: A fluid-structure interaction study into the effect of proximal neck and iliac bifurcation angle

Our knowledge of how geometry influences abdominal aortic aneurysm (AAA) biomechanics is still developing. Both iliac bifurcation angle and proximal neck angle could impact the haemodynamics and stresses within AAA. Recent comparisons of the morphology of ruptured and intact AAA show that cases with large iliac bifurcation angles are less likely to rupture than those with smaller angles. We aimed to perform fluid-structure interaction (FSI) simulations on a range of idealised AAA geometries to conclusively determine the influence of proximal neck and iliac bifurcation angle on AAA wall stress and haemodynamics.Peak wall shear stress (WSS) and time-averaged WSS (TAWSS) in the AAA sac region only increased when the proximal neck angle exceeded 30°. Both peak WSS (p < 0.0001) and peak von Mises wall stress (p = 0.027) increased with iliac bifurcation angle, whereas endothelial cell activation potential (ECAP) decreased with iliac bifurcation angle (p < 0.001) and increased with increasing neck angle.These observations may be important as AAAs have been shown to expand, develop thrombus and rupture in areas of low WSS. Here we show that AAAs with larger iliac bifurcation angles have higher WSS, potentially reducing the likelihood of rupture. Furthermore, ECAP was lower in AAA geometries with larger iliac bifurcation angles, implying less likelihood of thrombus development and wall degeneration. Therefore our findings could help explain the clinical observation of lower rupture rates associated with AAAs with large iliac bifurcation angles.     

A simple method of estimating the stress acting on a bilaterally symmetric abdominal aortic aneurysm

We extended a method of estimating the stress acting on an axisymmetric abdominal aortic aneurysm (AAA) under a load in vivo (Elger, D. F., Blackketter, D. M., Budwig, R. S., Johansen, K. H. (1996) The influence of shape on the stresses in model abdominal aortic aneurysms, Journal of Biomechanical Engineering, 118, pp. 326-32.) to bilaterally-symmetric AAAs, which are symmetric about the sagittal plane. Stresses were calculated along the anterior and posterior median lines of the AAA wall. Of the two force equilibrium equations, the Laplace equation held in this study. The longitudinal equilibrium was extended to hold by approximating the meridional tension and the directional cosine of the wall surface as constants along the circumference. The estimated stresses were compared with the results of a finite element analysis. Comparisons showed that the maximal principal stress, usually the circumferential stress or sometimes the meridional stress depending on location, sufficiently represented the wall stress. The proposed method provides a reasonable index for evaluating the rupture risk using the peak value of the maximal principal stress and its location without using the stress-free geometry and constitutive equation.     

Numerical identification of the rupture locations in patient-specific abdominal aortic aneurysmsusing hemodynamic parameters

The rupture of an abdominal aortic aneurysm (AAA) is generally an unexpected event. Up to now, there is no agreement on an accurate criteria to predict the rupture risk of AAAs. This paper aims to numerically investigate the hemodynamics of three ruptured and one non-ruptured patient-specific AAA models to correlate local hemodynamic parameters with the rupture sites, and for the first time, this study introduced helicity as a potential index for the rupture potential of AAAs.3D reconstructions from CT scans were done. The simulation revealed that all the rupture sites were in regions of stagnation with near zero wall shear stress (WSS) but large WSS gradient (WSSG), which may explain the observation by the former researchers that the rupture site in the ruptured AAA has the lowest recorded wall thickness compared to other non-ruptured regions. Moreover, all the ruptures occurred at regions of zero helicity which represents a purely axial or circumferential flow. In addition, this study revealed that the double low region for the non-ruptured AAA was present with a thick layer of plaques, it suggests that the AAA rupture and the formation of atherosclerotic plaques may share a lot common physiological features. However, the fact that there are no plaques present in the walls of three RAAAs also indicates that AAA is not always a result of atherosclerosis. The current computational study may complement the maximum diameter, peak wall stress and other clinically relevant factors in AAA ruptures to identify the rupture sites of AAAs.     

A planar biaxial constitutive relation for the luminal layer of intra-luminal thrombus in abdominal aortic aneurysms

The rupture risk of abdominal aortic aneurysms (AAAs) is thought to be associated with increased levels of wall stress. Finite element analysis (FEA) allows the prediction of wall stresses in a patient-specific, non-invasive manner. We have recently shown that it is important to include the intra-luminal thrombus (ILT), present in approximately 70% of AAA, into FEA simulations of AAA. All FEA simulations to date assume an isotropic, homogeneous material behavior for this material. The purpose of this work was to investigate the multi-axial biomechanical behavior of ILT and to derive an appropriate constitutive relation. We performed planar biaxial testing on the luminal layer of nine ILT specimens obtained fresh in the operating room (9 patients, mean age 71+/-4.5 years, mean diameter 5.9+/-0.4 cm), and a constitutive relation was derived from this data. Peak stretch and maximum tangential modulus (MTM) values were recorded for the equibiaxial protocol in both the circumferential (theta) and longitudinal (L) directions. Stress contour plots were used to investigate the presence of mechanical anisotropy, after which an appropriate strain energy function was fit to each of the specimen datasets. The peak stretch values for the luminal layer of the ILT were (mean+/-SEM) 1.18+/-0.02 and 1.13+/-0.02 in the theta and L directions, respectively (p=0.14). The MTM values were 20+/-2 and 23+/-3N/cm(2) in the theta and L directions, respectively (p=0.37). From these results and our observation of the symmetry of the stress contour plots for each specimen, we concluded that the use of an isotropic strain energy function for ILT is appropriate. Each specimen data set was then fit to a second-order polynomial strain energy function of the first invariant of the left Cauchy-Green strain tensor, resulting in an accurate fit (average R(2)=0.92+/-0.02; range 0.80-0.99). Comparison of our previously reported, uniaxially derived constitutive relation with the biaxially derived relation derived here shows large differences in the predicted mechanical response, underscoring the importance of the appropriate experimental methods used to derive constitutive relations. Further work is merited in an effort to produce more accurate predictions of wall stresses in patient-specific AAA, and viscoelastic behaviors of the ILT.     

Probabilistic noninvasive prediction of wall properties of abdominal aortic aneurysms using Bayesian regression

Multiple patient-specific parameters, such as wall thickness, wall strength, and constitutive properties, are required for the computational assessment of abdominal aortic aneurysm (AAA) rupture risk. Unfortunately, many of these quantities are not easily accessible and could only be determined by invasive procedures, rendering a computational rupture risk assessment obsolete. This study investigates two different approaches to predict these quantities using regression models in combination with a multitude of noninvasively accessible, explanatory variables. We have gathered a large dataset comprising tensile tests performed with AAA specimens and supplementary patient information based on blood analysis, the patients medical history, and geometric features of the AAAs. Using this unique database, we harness the capability of state-of-the-art Bayesian regression techniques to infer probabilistic models for multiple quantities of interest. After a brief presentation of our experimental results, we show that we can effectively reduce the predictive uncertainty in the assessment of several patient-specific parameters, most importantly in thickness and failure strength of the AAA wall. Thereby, the more elaborate Bayesian regression approach based on Gaussian processes consistently outperforms standard linear regression. Moreover, our study contains a comparison to a previously proposed model for the wall strength.     

Use of the photoelastic method and finite element analysis in the assessment of wall strain in abdominal aortic aneurysm models

Abdominal aortic aneurysm (AAA) is a significant health problem. Current clinical rupture-risk relies primarily on the maximum diameter of the AAA and also growth rate. However, AAAs are a patient-specific problem and recently, numerical tools have been employed to estimate rupture-potential. Alternatively, experimental assessment of AAA biomechanics receives less attention, yet, rigorous validation of numerical tools is required prior to clinical acceptance. This paper examines the use of the photoelastic method to assess wall strain and its validation using finite element analysis (FEA) in a small number of patient-specific AAA models. Experimental models were manufactured in-house using the injection-moulding procedure together with a commercially available photoelastic material. The material was mechanically characterised prior to testing, with models examined under three loading regimes (80, 120 and 160mmHg). Each experimental model was imaged using computed tomography (CT) and reconstructed in three dimensions (3D) for numerical analyses. Experimental wall strain was measured and numerical wall strain calculated with finite element analysis (FEA). Results were qualitatively and quantitatively compared. There was good qualitative agreement between the experimental and numerical methods, with similar trends apparent throughout all models at all pressures. Overall, acceptable percentage errors between the techniques were observed for all models. Median errors of -6.5%, -0.4% and 3.9% for the models at 80, 120 and 160mmHg pressures, respectively, were determined. The photoelastic method is a very useful experimental tool that provides instant, easy to interpret, information regarding wall strain. The technique is useful for validation of numerical AAA studies.     

Automated methodology for determination of stress distribution in human abdominal aortic aneurysm

Knowledge of impending abdominal aortic aneurysm (AAA) rupture can help in surgical planning. Typically, aneurysm diameter is used as the indicator of rupture, but recent studies have hypothesized that pressure-induced biomechanical stress may be a better predictor Verification of this hypothesis on a large study population with ruptured and unruptured AAA is vital if stress is to be reliably used as a clinical prognosticator for AAA rupture risk. We have developed an automated algorithm to calculate the peak stress in patient-specific AAA models. The algorithm contains a mesh refinement module, finite element analysis module, and a postprocessing visualization module. Several aspects of the methodology used are an improvement over past reported approaches. The entire analysis may be run from a single command and is completed in less than 1 h with the peak wall stress recorded for statistical analysis. We have used our algorithm for stress analysis of numerous ruptured and unruptured AAA models and report some of our results here. By current estimates, peak stress in the aortic wall appears to be a better predictor of rupture than AAA diameter. Further use of our algorithm is ongoing on larger study populations to convincingly verify these findings.     

Mechanical stresses in abdominal aortic aneurysms: influence of diameter, asymmetry, and material anisotropy

Biomechanical studies suggest that one determinant of abdominal aortic aneurysm (AAA) rupture is related to the stress in the wall. In this regard, a reliable and accurate stress analysis of an in vivo AAA requires a suitable 3D constitutive model. To date, stress analysis conducted on AAA is mainly driven by isotropic tissue models. However, recent biaxial tensile tests performed on AAA tissue samples demonstrate the anisotropic nature of this tissue. The purpose of this work is to study the influence of geometry and material anisotropy on the magnitude and distribution of the peak wall stress in AAAs. Three-dimensional computer models of symmetric and asymmetric AAAs were generated in which the maximum diameter and length of the aneurysm were individually controlled. A five parameter exponential type structural strain-energy function was used to model the anisotropic behavior of the AAA tissue. The anisotropy is determined by the orientation of the collagen fibers (one parameter of the model). The results suggest that shorter aneurysms are more critical when asymmetries are present. They show a strong influence of the material anisotropy on the magnitude and distribution of the peak stress. Results confirm that the relative aneurysm length and the degree of aneurysmal asymmetry should be considered in a rupture risk decision criterion for AAAs.     

Improving the Efficiency of Abdominal Aortic Aneurysm Wall Stress Computations

An abdominal aortic aneurysm is a pathological dilation of the abdominal aorta, which carries a high mortality rate if ruptured. The most commonly used surrogate marker of rupture risk is the maximal transverse diameter of the aneurysm. More recent studies suggest that wall stress from models of patient-specific aneurysm geometries extracted, for instance, from computed tomography images may be a more accurate predictor of rupture risk and an important factor in AAA size progression. However, quantification of wall stress is typically computationally intensive and time-consuming, mainly due to the nonlinear mechanical behavior of the abdominal aortic aneurysm walls. These difficulties have limited the potential of computational models in clinical practice. To facilitate computation of wall stresses, we propose to use a linear approach that ensures equilibrium of wall stresses in the aneurysms. This proposed linear model approach is easy to implement and eliminates the burden of nonlinear computations. To assess the accuracy of our proposed approach to compute wall stresses, results from idealized and patient-specific model simulations were compared to those obtained using conventional approaches and to those of a hypothetical, reference abdominal aortic aneurysm model. For the reference model, wall mechanical properties and the initial unloaded and unstressed configuration were assumed to be known, and the resulting wall stresses were used as reference for comparison. Our proposed linear approach accurately approximates wall stresses for varying model geometries and wall material properties. Our findings suggest that the proposed linear approach could be used as an effective, efficient, easy-to-use clinical tool to estimate patient-specific wall stresses.     

Measuring and modeling patient-specific distributions of material properties in abdominal aortic aneurysm wall

Both the clinically established diameter criterion and novel approaches of computational finite element (FE) analyses for rupture risk stratification of abdominal aortic aneurysms (AAA) are based on assumptions of population-averaged, uniform material properties for the AAA wall. The presence of inter-patient and intra-patient variations in material properties is known, but has so far not been addressed sufficiently. In order to enable the preoperative estimation of patient-specific AAA wall properties in the future, we investigated the relationship between non-invasively assessable clinical parameters and experimentally measured AAA wall properties. We harvested n = 163 AAA wall specimens (n = 50 patients) during open surgery and recorded the exact excision sites. Specimens were tested for their thickness, elastic properties, and failure loads using uniaxial tensile tests. In addition, 43 non-invasively assessable patient-specific or specimen-specific parameters were obtained from recordings made during surgery and patient charts. Experimental results were correlated with the non-invasively assessable parameters and simple regression models were created to mathematically describe the relationships. Wall thickness was most significantly correlated with the metabolic activity at the excision site assessed by PET/CT (ρ = 0.499, P = 4 × 10^?7) and to thrombocyte counts from laboratory blood analyses (ρ = 0.445, P = 3 × 10^?9). Wall thickness was increased in patients suffering from diabetes mellitus, while it was significantly thinner in patients suffering from chronic kidney disease (CKD). Elastic AAA wall properties had significant correlations with the metabolic activity at the excision site (PET/CT), with existent calcifications, and with the diameter of the non-dilated aorta proximal to the AAA. Failure properties (wall strength and failure tension) had correlations with the patient’s medical history and with results from laboratory blood analyses. Interestingly, AAA wall failure tension was significantly reduced for patients with CKD and elevated blood levels of potassium and urea, respectively, both of which are associated with kidney disease. This study is a first step to a future preoperative estimation of AAA wall properties. Results can be conveyed to both the diameter criterion and FE analyses to refine rupture risk prediction. The fact that AAA wall from patients suffering from CKD featured reduced failure tension implies an increased AAA rupture risk for this patient group at comparably smaller AAA diameters.     

Fluid-structure interaction in abdominal aortic aneurysms: effects of asymmetry and wall thickness

Background  

Abdominal aortic aneurysm (AAA) is a prevalent disease which is of significant concern because of the morbidity associated with the continuing expansion of the abdominal aorta and its ultimate rupture. The transient interaction between blood flow and the wall contributes to wall stress which, if it exceeds the failure strength of the dilated arterial wall, will lead to aneurysm rupture. Utilizing a computational approach, the biomechanical environment of virtual AAAs can be evaluated to study the affects of asymmetry and wall thickness on this stress, two parameters that contribute to increased risk of aneurysm rupture.     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.     

A decoupled fluid structure approach for estimating wall stress in abdominal aortic aneurysms

Abdominal aortic aneurysm (AAA) is a localized dilatation of the aortic wall. The lack of an accurate AAA rupture risk index remains an important problem in the clinical management of the disease. To accurately estimate AAA rupture risk, detailed information on patient-specific wall stress distribution and aortic wall tissue yield stress is required. A complete fluid structure interaction (FSI) study is currently impractical and thus of limited clinical value. On the other hand, isolated static structural stress analysis based on a uniform wall loading is a widely used approach for AAA rupture risk estimation that, however, neglects the flow-induced wall stress variation. The aim of this study was to assess the merit of a decoupled fluid structure analysis of AAA wall stress. Anatomically correct, patient specific AAA wall models were created by 3D reconstruction of computed tomography images. Flow simulations were carried out with inflow and outflow boundary conditions obtained from patient extracted data. Static structural stress analysis was performed applying both a uniform pressure wall loading and a flow induced non-uniform pressure distribution obtained during early systolic deceleration. For the structural analysis, a hyperelastic arterial wall model and an elastic intraluminal thrombus model were assumed. The results of this study demonstrate that although the isolated static structural stress analysis approach captures the gross features of the stress distribution it underestimates the magnitude of the peak wall stress by as much as 12.5% compared to the proposed decoupled fluid structure approach. Furthermore, the decoupled approach provides potentially useful information on the nature of the aneurysmal sac flow.