Effects of wall calcifications in patient-specific wall stress analyses of abdominal aortic aneurysms

It is generally acknowledged that rupture of an abdominal aortic aneurysm (AAA) occurs when the stress acting on the wall over the cardiac cycle exceeds the strength of the wall. Peak wall stress computations appear to give a more accurate rupture risk assessment than AAA diameter, which is currently used for a diagnosis. Despite the numerous studies utilizing patient-specific wall stress modeling of AAAs, none investigated the effect of wall calcifications on wall stress. The objective of this study was to evaluate the influence of calcifications on patient-specific finite element stress computations. In addition, we assessed whether the effect of calcifications could be predicted directly from the CT-scans by relating the effect to the amount of calcification present in the AAA wall. For 6 AAAs, the location and extent of calcification was identified from CT-scans. A finite element model was created for each AAA and the areas of calcification were defined node-wise in the mesh of the model. Comparisons are made between maximum principal stress distributions, computed without calcifications and with calcifications with varying material properties. Peak stresses are determined from the stress results and related to a calcification index (CI), a quantification of the amount of calcification in the AAA wall. At calcification sites, local stresses increased, leading to a peak stress increase of 22% in the most severe case. Our results displayed a weak correlation between the CI and the increase in peak stress. Additionally, the results showed a marked influence of the calcification elastic modulus on computed stresses. Inclusion of calcifications in finite element analysis of AAAs resulted in a marked alteration of the stress distributions and should therefore be included in rupture risk assessment. The results also suggest that the location and shape of the calcified regions--not only the relative amount--are considerations that influence the effect on AAA wall stress. The dependency of the effect of the wall stress on the calcification elastic modulus points out the importance of determination of the material properties of calcified AAA wall.     

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.     

Nonlinear anisotropic stress analysis of anatomically realistic cerebral aneurysms

BACKGROUND: Static deformation analysis and estimation of wall stress distribution of patient-specific cerebral aneurysms can provide useful insights into the disease process and rupture. METHOD OF APPROACH: The three-dimensional geometry of saccular cerebral aneurysms from 27 patients (18 unruptured and nine ruptured) was reconstructed based on computer tomography angiography images. The aneurysm wall tissue was modeled using a nonlinear, anisotropic, hyperelastic material model (Fung-type) which was incorporated in a user subroutine in ABAQUS. Effective material fiber orientations were assumed to align with principal surface curvatures. Static deformation of the aneurysm models were simulated assuming uniform wall thickness and internal pressure load of 100 mm Hg. RESULTS: The numerical analysis technique was validated by quantitative comparisons to results in the literature. For the patient-specific models, in-plane stresses in the aneurysm wall along both the stiff and weak fiber directions showed significant regional variations with the former being higher. The spatial maximum of stress ranged from as low as 0.30 MPa in a small aneurysm to as high as 1.06 MPa in a giant aneurysm. The patterns of distribution of stress, strain, and surface curvature were found to be similar. Sensitivity analyses showed that the computed stress is mesh independent and not very sensitive to reasonable perturbations in model parameters, and the curvature-based criteria for fiber orientations tend to minimize the total elastic strain energy in the aneurysms wall. Within this small study population, there were no statistically significant differences in the spatial means and maximums of stress and strain values between the ruptured and unruptured groups. However, the ratios between the stress components in the stiff and weak fiber directions were significantly higher in the ruptured group than those in the unruptured group. CONCLUSIONS: A methodology for nonlinear, anisotropic static deformation analysis of geometrically realistic aneurysms was developed, which can be used for a more accurate estimation of the stresses and strains than previous methods and to facilitate prospective studies on the role of stress in aneurysm 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.     

The association of wall mechanics and morphology: a case study of abdominal aortic aneurysm growth

The purpose of this study is to evaluate the potential correlation between peak wall stress (PWS) and abdominal aortic aneurysm (AAA) morphology and how it relates to aneurysm rupture potential. Using in-house segmentation and meshing software, six 3-dimensional (3D) AAA models from a single patient followed for 28 months were generated for finite element analysis. For the AAA wall, both isotropic and anisotropic materials were used, while an isotropic material was used for the intraluminal thrombus (ILT). These models were also used to calculate 36 geometric indices characteristic of the aneurysm morphology. Using least squares regression, seven significant geometric features (p?相似文献   

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.     

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.     

Intraluminal thrombus and risk of rupture in patient specific abdominal aortic aneurysm - FSI modelling

Recent numerical studies of abdominal aortic aneurysm (AAA) suggest that intraluminal thrombus (ILT) may reduce the stress loading on the aneurysmal wall. Detailed fluid structure interaction (FSI) in the presence and absence of ILT may help predict AAA rupture risk better. Two patients, with varied AAA geometries and ILT structures, were studied and compared in detail. The patient specific 3D geometries were reconstructed from CT scans, and uncoupled FSI approach was applied. Complex flow trajectories within the AAA lumen indicated a viable mechanism for the formation and growth of the ILT. The resulting magnitude and location of the peak wall stresses was dependent on the shape of the AAA, and the ILT appeared to reduce wall stresses for both patients. Accordingly, the inclusion of ILT in stress analysis of AAA is of importance and would likely increase the accuracy of predicting AAA risk of rupture.     

Intraluminal thrombus and risk of rupture in patient specific abdominal aortic aneurysm – FSI modelling

Recent numerical studies of abdominal aortic aneurysm (AAA) suggest that intraluminal thrombus (ILT) may reduce the stress loading on the aneurysmal wall. Detailed fluid structure interaction (FSI) in the presence and absence of ILT may help predict AAA rupture risk better. Two patients, with varied AAA geometries and ILT structures, were studied and compared in detail. The patient specific 3D geometries were reconstructed from CT scans, and uncoupled FSI approach was applied. Complex flow trajectories within the AAA lumen indicated a viable mechanism for the formation and growth of the ILT. The resulting magnitude and location of the peak wall stresses was dependent on the shape of the AAA, and the ILT appeared to reduce wall stresses for both patients. Accordingly, the inclusion of ILT in stress analysis of AAA is of importance and would likely increase the accuracy of predicting AAA risk of rupture.     

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.     

Stress-modulated growth, residual stress, and vascular heterogeneity.

A simple phenomenological model is used to study interrelations between material properties, growth-induced residual stresses, and opening angles in arteries. The artery is assumed to be a thick-walled tube composed of an orthotropic pseudoelastic material. In addition, the normal mature vessel is assumed to have uniform circumferential wall stress, which is achieved here via a mechanical growth law. Residual stresses are computed for three configurations: the unloaded intact artery, the artery after a single transmural cut, and the inner and outer rings of the artery created by combined radial and circumferential cuts. The results show that the magnitudes of the opening angles depend strongly on the heterogeneity of the material properties of the vessel wall and that multiple radial and circumferential cuts may be needed to relieve all residual stress. In addition, comparing computed opening angles with published experimental data for the bovine carotid artery suggests that the material properties change continuously across the vessel wall and that stress, not strain, correlates well with growth in arteries.     

Computational analysis of type II endoleaks in a stented abdominal aortic aneurysm model

Insertion of a stent-graft into an aneurysm to form a new (synthetic) blood vessel and prevent the weakened artery wall from rupture is an attractive surgical intervention when compared to traditional open surgery. However, focusing on a stented abdominal aortic aneurysm (AAA), post-operative complications such as endoleaks may occur. An endoleak is the net influx of blood during the cardiac cycle into the cavity (or sac) formed by the stent-graft and the AAA wall. A natural endoleak source may stem from one or two secondary branches leading to and from the aneurysm, labeled types IIa and IIb endoleaks. Employing experimentally validated fluid-structure interaction solvers, the transient 3-D lumen and cavity blood flows, wall movements, pressure variations, maximum wall stresses and migration forces were computed for types IIa and IIb endoleaks. Simulation results indicate that the sac pressure caused by these endoleaks depends largely on the inlet branch pressure, where the branch inlet pressure increases, the sac pressure may reach the systemic level and AAA-rupture is possible. The maximum wall stress is typically located near the anterior-distal side in this model, while the maximum stent-graft stress occurs near the bifurcating point, in both cases, due to local stress concentrations. The time-varying leakage rate depends on the pressure difference between AAA sac and inlet branch. In contrast, the stent-graft migration force is reduced by type II endoleaks because it greatly depends on the pressure difference between the stent-graft and the aneurysm cavity.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part II--pulsatile flow hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50< or =Re(m) < or =300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG), time-average wall shear stress (tau(w)*), and time-average Wall Shear Stress Gradient WSSG*. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

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.     

Flat medial-lateral conformity in total knee replacements does not minimize contact stresses.

The potential for wear in UHMWPE components for total knee replacements can be reduced by decreasing the stresses and strains arising from tibial-femoral contact. The conformity of the articular surfaces has a large effect on the resultant stresses, and components that achieve flat medial-lateral contact have been assumed to produce the lowest stresses due to their perfect conformity. We computed the stresses arising from curved and flat contact on a half-space using two-dimensional, plane strain elasticity solutions and finite element analyses to compare the performance of curved and flat indenters. These indenters were represented by a polynomial so the profiles could be continuously varied from curved to flat. Curved contact resulted in maximum stresses at the center of contact, while flat contact produced maximum stresses at the edge of contact. In addition, three contemporary tibial configurations (flat-on-flat, curved-on-flat, and curved-on-curved geometries) were analyzed using the finite element method with nonlinear material properties. The maximum contact stress, von Mises stress, and von Mises strain were lowest for the curved-on-curved model. The other configurations resulted in higher contact stresses, von Mises stresses, and von Mises strains. The perfect conformity arising from flat contact did not reduce the contact stresses in the UHMWPE component. The tensile stresses, however, were lowest for the flat-on-flat geometry compared with the other two configurations. Relating these distinct differences could prove useful in interpretation of data from simulator and retrieval studies.     

Accurate prediction of wall shear stress in a stented artery: newtonian versus non-newtonian models

A significant amount of evidence linking wall shear stress to neointimal hyperplasia has been reported in the literature. As a result, numerical and experimental models have been created to study the influence of stent design on wall shear stress. Traditionally, blood has been assumed to behave as a Newtonian fluid, but recently that assumption has been challenged. The use of a linear model; however, can reduce computational cost, and allow the use of Newtonian fluids (e.g., glycerine and water) instead of a blood analog fluid in an experimental setup. Therefore, it is of interest whether a linear model can be used to accurately predict the wall shear stress caused by a non-Newtonian fluid such as blood within a stented arterial segment. The present work compares the resulting wall shear stress obtained using two linear and one nonlinear model under the same flow waveform. All numerical models are fully three-dimensional, transient, and incorporate a realistic stent geometry. It is shown that traditional linear models (based on blood's lowest viscosity limit, 3.5 Pa s) underestimate the wall shear stress within a stented arterial segment, which can lead to an overestimation of the risk of restenosis. The second linear model, which uses a characteristic viscosity (based on an average strain rate, 4.7 Pa s), results in higher wall shear stress levels, but which are still substantially below those of the nonlinear model. It is therefore shown that nonlinear models result in more accurate predictions of wall shear stress within a stented arterial segment.     

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.     

Patient-specific initial wall stress in abdominal aortic aneurysms with a backward incremental method

Patient-specific wall stress simulations on abdominal aortic aneurysms may provide a better criterion for surgical intervention than the currently used maximum transverse diameter. In these simulations, it is common practice to compute the peak wall stress by applying the full systolic pressure directly on the aneurysm geometry as it appears in medical images. Since this approach does not account for the fact that the measured geometry is already experiencing a substantial load, it may lead to an incorrect systolic aneurysm shape. We have developed an approach to compute the wall stress on the true diastolic geometry at a given pressure with a backward incremental method. The method has been evaluated with a neo-Hookean material law for several simple test problems. The results show that the method can predict an unloaded configuration if the loaded geometry and the load applied are known. The effect of incorporating the initial diastolic stress has been assessed by using three patient-specific geometries acquired with cardiac triggered MR. The comparison shows that the commonly used approach leads to an unrealistically smooth systolic geometry and therefore provides an underestimation for the peak wall stress. Our backward incremental modelling approach overcomes these issues and provides a more plausible estimate for the systolic aneurysm volume and a significantly different estimate for the peak wall stress. When the approach is applied with a more complex material law which has been proposed specifically for abdominal aortic aneurysm similar effects are observed and the same conclusion can be drawn.     

A fluid–structure interaction-based numerical investigation on the evolution of stress,strength and rupture potential of an abdominal aortic aneurysm

An abdominal aortic aneurysm (AAA) is an irreversible dilation of the abdominal artery. Once an aneurysm is detected by doctors, clinical intervention is usually recommended. The interventions involve traditional open surgery repair and endovascular aneurysm repair with a stent graft. Both types of prophylactic procedures are expensive and not without any risk to the patient. It is very difficult to balance the risk of aneurysm repair and the chance of rupture. The reason lies in that the changing trend of characteristic physical quantities with the evolution of AAA and the mechanisms that give rise to it are still not completely clear. In this study, computational 3D patient-specific model for investigating AAA development was established based on computed tomography (CT) images. Results showed that as the aneurysm evolved, peak wall stress and time-averaged wall shear stress distribution patterns changed. The expansion of AAA wall resulted in the increment of peak stress. The AAA wall compliance not only showed different magnitudes at different cross-sections of the aneurismal body, but also changed with the development of the aneurysm. Furthermore, minimum wall strength and rupture potential index during the three stages of AAA evolution were also investigated in detail. This study might provide valuable information on how to further explore the mechanical basis and the rupture potential during AAA evolution, and that it may assist clinical diagnostic procedures and avoid the potential risk of unnecessary surgical intervention.