Compute Wall Stress Research Articles

Biomechanical changes during abdominal aortic aneurysm growth.

The biomechanics-based Abdominal Aortic Aneurysm (AAA) rupture risk assessment has gained considerable scientific and clinical momentum. However, such studies have mainly focused on information at a single time point, and little is known about how AAA properties change over time. Consequently, the present study explored how geometry, wall stress-related and blood flow-related biomechanical properties change during AAA expansion. Four patients with a total of 23 Computed Tomography-Angiography (CT-A) scans at different time points were analyzed. At each time point, patient-specific properties were extracted from (i) the reconstructed geometry, (ii) the computed wall stress at Mean Arterial Pressure (MAP), and (iii) the computed blood flow velocity at standardized inflow and outflow conditions. Testing correlations between these parameters identified several nonintuitive dependencies. Most interestingly, the Peak Wall Rupture Index (PWRI) and the maximum Wall Shear Stress (WSS) independently predicted AAA volume growth. Similarly, Intra-luminal Thrombus (ILT) volume growth depended on both the maximum WSS and the ILT volume itself. In addition, ILT volume, ILT volume growth, and maximum ILT layer thickness correlated with PWRI as well as AAA volume growth. Consequently, a large ILT volume as well as fast increase of ILT volume over time may be a risk factor for AAA rupture. However, tailored clinical studies would be required to test this hypothesis and to clarify whether monitoring ILT development has any clinical benefit.

Impact of Wall Thickness and Saccular Geometry on the Computational Wall Stress of Descending Thoracic Aortic Aneurysms

Wall stress calculated using finite element analysis has been used to predict rupture risk of aortic aneurysms. Prior models often assume uniform aortic wall thickness and fusiform geometry. We examined the effects of including local wall thickness, intraluminal thrombus, calcifications, and saccular geometry on peak wall stress (PWS) in finite element analysis of descending thoracic aortic aneurysms. Computed tomographic angiography of descending thoracic aortic aneurysms (n=10 total, 5 fusiform and 5 saccular) underwent 3-dimensional reconstruction with custom algorithms. For each aneurysm, an initial model was constructed with uniform wall thickness. Experimental models explored the addition of variable wall thickness, calcifications, and intraluminal thrombus. Each model was loaded with 120 mm Hg pressure, and von Mises PWS was computed. The mean PWS of uniform wall thickness models was 410 ± 111 kPa. The imposition of variable wall thickness increased PWS (481 ± 126 kPa, P<0.001). Although the addition of calcifications was not statistically significant (506 ± 126 kPa, P=0.07), the addition of intraluminal thrombus to variable wall thickness (359 ± 86 kPa, P ≤ 0.001) reduced PWS. A final model incorporating all features also reduced PWS (368 ± 88 kPa, P<0.001). Saccular geometry did not increase diameter-normalized stress in the final model (77 ± 7 versus 67 ± 12 kPa/cm, P=0.22). Incorporation of local wall thickness can significantly increase PWS in finite element analysis models of thoracic aortic aneurysms. Incorporating variable wall thickness, intraluminal thrombus, and calcifications significantly impacts computed PWS of thoracic aneurysms; sophisticated models may, therefore, be more accurate in assessing rupture risk. Saccular aneurysms did not demonstrate a significantly higher normalized PWS than fusiform aneurysms.

Importance of material model in wall stress prediction in abdominal aortic aneurysms

BackgroundResults of biomechanical simulation of the abdominal aortic aneurysm (AAA) depend on the constitutive description of the wall. Based on in vitro and in vivo experimental data several constitutive models for the AAA wall have been proposed in the literature. Those models differ strongly from each other and their impact on the computed stress in biomechanical simulation is not clearly understood. MethodsFinite element (FE) models of AAAs from 7 patients who underwent elective surgical repair were used to compute wall stresses. AAA geometry was reconstructed from CT angiography (CT-A) data and patient-specific (PS) constitutive descriptions of the wall were derived from planar biaxial testing of anterior wall tissue samples. In total 28 FE models were used, where the wall was described by either patient-specific or previously reported study-average properties. This data was derived from either uniaxial or biaxial in vitro testing. Computed wall stress fields were compared on node-by-node basis. ResultsDifferent constitutive models for the AAA wall cause significantly different predictions of wall stress. While study-average data from biaxial testing gives globally the same stress field as the patient-specific wall properties, the material model based on uniaxial test data overestimates the wall stress on average by 30kPa or about 67% of the mean stress. A quasi-linear description based on the in vivo measured distensibility of the AAA wall leads to a completely altered stress field and overestimates the wall stress by about 75kPa or about 167% of the mean stress. ConclusionThe present study demonstrated that the constitutive description of the wall is crucial for AAA wall stress prediction. Consequently, results obtained using different models should not be mutually compared unless different stress gradients across the wall are not taken into account. Highly nonlinear material models should be preferred when the response of AAA to increased blood pressure is investigated, while the quasi-linear model with high initial stiffness produces negligible stress gradients across the wall and thus, it is more appropriate when response to mean blood pressure is calculated.

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.

Peak Wall Stress Predicts Expansion Rate in Descending Thoracic Aortic Aneurysms

Aortic diseases, including aortic aneurysms, are the 12th leading cause of death in the United States. The incidence of descending thoracic aortic aneurysms is estimated at 10.4 per 100,000 patient-years. Growing evidence suggests that stress measurements derived from structural analysis of aortic geometries predict clinical outcomes better than diameter alone. Twenty-five patients undergoing clinical and radiologic surveillance for thoracic aortic aneurysms were retrospectively identified. Custom MATLAB algorithms were employed to extract aortic wall and intraluminal thrombus geometry from computed tomography angiography scans. The resulting reconstructions were loaded with 120 mm Hg of pressure using finite element analysis. Relationships among peak wall stress, aneurysm growth, and clinical outcome were examined. The average patient age was 71.6 ± 10.0 years, and average follow-up time was 17.5 ± 9 months (range, 6 to 43). The mean initial aneurysm diameter was 47.8 ± 8.0 mm, and the final diameter was 52.1 ± 10.0 mm. Mean aneurysm growth rate was 2.9 ± 2.4 mm per year. A stronger correlation (r = 0.894) was found between peak wall stress and aneurysm growth rate than between maximal aortic diameter and growth rate (r = 0.531). Aneurysms undergoing surgical intervention had higher peak wall stresses than aneurysms undergoing continued surveillance (300 ± 75 kPa versus 229 ± 47 kPa, p = 0.01). Computational peak wall stress in thoracic aortic aneurysms was found to be strongly correlated with aneurysm expansion rate. Aneurysms requiring surgical intervention had significantly higher peak wall stresses. Peak wall stress may better predict clinical outcome than maximal aneurysmal diameter, and therefore may guide clinical decision-making.

Response to Letter Regarding Article, “Association Between Aneurysm Shoulder Stress and Abdominal Aortic Aneurysm Expansion: A Longitudinal Follow-Up Study”

We appreciate the interest from Drs Frydrychowicz and Markl in our study,1 in which we found an association between the computed wall stress (WS) at the shoulder region and the expansion rate in abdominal aortic aneurysms. In our study, we did not calculate wall shear stress (WSS) or use a computational fluid dynamics method. Wall stress was calculated on the basis of the structural analysis using a finite element method. We have to emphasize that WS is different from WSS. In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is …

The impact of model assumptions on results of computational mechanics in abdominal aortic aneurysm

In principle, superiority of computational wall stress analyses compared with the maximum diameter criterion for rupture risk evaluation of abdominal aortic aneurysm (AAA) has been demonstrated. The results of finite element analyses should be evaluated carefully, however, because computational strains and stresses are highly dependent on the quality and complexity of each step of AAA simulation. Most clinically active vascular specialists are not familiar with the processes of computational mechanics to evaluate the quality of AAA simulations. For better understanding and to provide insights in computational biomechanics of AAA, the effect of different computational model assumptions on the results of simulation are explained and demonstrated. Four patients with asymptomatic (n = 3) and symptomatic (n = 1) infrarenal AAAs with distinctly different aneurysm morphologies were exemplarily studied. For segmentation and 3-dimensional (3D) reconstruction of AAA and thrombus, 3-mm computed tomography (CT) slices were used, and a high-density hexahedral element-dominated finite element mesh was generated. Subsequent AAAs were simulated on seven different levels, culminating in the most realistic ortho-pressure-finite element analyses simulations, including thrombus, wall calcifications, and prestress state of AAA geometry with nonlinear hyperelastic material and geometric model assumptions. Alterations in displacements due to model assumptions are up to 740% for a specific aneurysm. The average maximum discrepancy among the four morphologies between simple and advanced models is 607%. Differences in peak wall stress between simple and realistic models are up to 210% individually and 170% on average. Differences of model assumptions are more important for simulation results than differences between patient-specific morphologies. Because the biomechanical behavior of AAA is nonlinear in many senses, comparisons between individual morphologies and statistics are only valid when detailed information about preconditions and model assumptions is provided.

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.

I034 Mechanical modeling of in vivo human carotid arteries from non-invasive clinical data. application to normal subjects

For mechanical modeling, in vivo data are relatively incomplete in comparison to in vitro results. However, identification of mechanical properties from human clinical data to compute wall stress fields can play an important role in understanding better pathological evolutions. Demonstrate the feasibility of material identification and stress computation from clinical data for normal subjects. In vivo human common carotid arteries (CCAs) were explored non-invasively for 16 normal subjects. During several cardiac cycles, medial diameter, intimal-medial thickness and blood pressure were measured by a high-resolution echotracking (Art. Lab®) and applanation tonometry (SphygmoCor®), respectively. To study the wall mechanical behavior, the CCA was assumed to be a 3D hollow cylinder subjected to dynamical intraluminal pressure and perivascular constraints. We also assumed that the arterial wall is made of hyperelastic, fibrous, and incompressible material with smooth muscle activity and residual stresses. We included wall mechanical contributions by microconstituents: an elastin-dominated matrix, collagen fibers, and vascular smooth muscle (VSM). We solved the in vivo boundary value problem semianalytically to compute the intraluminal pressure during a cardiac cycle. Minimizing the difference between computed and measured inner pressures over the cardiac cycle provided the identification of optimal model parameters employing a nonlinear regression. The fit-to-data gave very good results and was possible in all cases. There was a convergence of parameters for major constituents such as collagen, elastin and VSM tone. Age was correlated with collagen content and residual stresses. The predicted radial, circumferential, and axial stretches and stresses within the wall during the cardiac cycle were sensible. We were able to reproduce the evolution of inner blood pressure identifying experimentally unknown geometric and material parameters directly from in vivo human data, in order to compute wall stresses and stretches over a cardiac cycle. We can extend the proposed approach to pathological cases such as hypertension.

Impact of calcification and intraluminal thrombus on the computed wall stresses of abdominal aortic aneurysm

Increased biomechanical stresses within the abdominal aortic aneurysm (AAA) wall contribute to its rupture. Calcification and intraluminal thrombus can be commonly found in AAAs, but the relationship between calcification/intraluminal thrombus and AAA wall stress is not completely described. Patient-specific three-dimensional AAA geometries were reconstructed from computed tomographic images of 20 patients. Structural analysis was performed to calculate the wall stresses of the 20 AAA models and their altered models when calcification or intraluminal thrombus was not considered. A nonlinear large-strain finite element method was used to compute the wall stress distribution. The relationships between wall stresses and volumes of calcification and intraluminal thrombus were sought. Maximum stress was not correlated with the percentage of calcification, and was negatively correlated with the percentage of intraluminal thrombus (r = -0.56; P = .011). Exclusion of calcification from analysis led to a significant decrease in maximum stress by a median of 14% (range, 2%-27%; P < .01). When intraluminal thrombus was eliminated, maximum stress increased significantly by a median of 24% (range, 5%-43%; P < .01). The presence of calcification increases AAA peak wall stress, suggesting that calcification decrease the biomechanical stability of AAA. In contrast, intraluminal thrombus reduces the maximum stress in AAA. Calcification and intraluminal thrombus should both be considered in the evaluation of wall stress for risk assessment of AAA rupture.

Effect of intraluminal thrombus on wall stress in patient-specific models of abdominal aortic aneurysm

Purpose: The role of intraluminal thrombus (ILT) on abdominal aortic aneurysm rupture is still not clear. Rupture of an aneurysm occurs when the wall stress exceeds the wall strength at any location on the wall. The purpose of this study was to address the hypothesis that the presence of ILT alters the wall stress distribution or wall stress magnitude in AAA. Methods: Patient-specific 3D AAA geometries were reconstructed from computed tomographic images. Two geometric features, ILT surface ratio (ILT surface area divided by the total AAA surface area) and ILT volume ratio (ILT volume divided by the total AAA volume), were calculated for each AAA. Two models were created for each patient: one with ILT and one without ILT. Systolic pressure measured at the time of computed tomographic imaging was applied to the internal surface of each model. A nonlinear large deformation algorithm was used to compute wall stress distribution with the finite element method. The Wilcoxon matched pairs test was used to compare the peak wall stress between the two models of each patient. Results: Four patients were studied with ILT surface ratios that ranged from 0.29 to 0.72 and ILT volume ratios that ranged from 0.12 to 0.66. The peak wall stress was reduced (range, 6% to 38% reduction; P = .067) for all models with ILT included (range, 28 to 37 N/cm 2) as compared with models with no ILT (range, 30 to 44 N/cm 2). Visual inspection also revealed a marked effect of ILT on the wall stress distribution. Conclusion: The presence of ILT alters the wall stress distribution and reduces the peak wall stress in AAA.For this reason, ILT should be included in all patient-specific models of AAA for evaluation of AAA wall stresses. (J Vasc Surg 2002;36:598-604.)

High Reynolds number calculations using the dynamic subgrid-scale stress model

The dynamic subgrid-scale eddy viscosity model has been used in the large-eddy simulation of the turbulent flow in a plane channel for Reynolds numbers based on friction velocity and channel half-width ranging between 200 and 2000, a range including values significantly higher than in previous simulations. The computed wall stress, mean velocity, and Reynolds stress profiles compare very well with experimental and direct simulation data. Comparison of higher moments is also satisfactory. Although the grid in the near-wall region is fairly coarse, the results are quite accurate: the turbulent kinetic energy peaks at y+≂12, and the near-wall behavior of the resolved stresses is captured accurately. The model coefficient is o(10−3) in the buffer layer and beyond, where the cutoff wave numbers are in the decaying region of the spectra; in the near-wall region the cutoff wave numbers are nearer the energy-containing range, and the resolved turbulent stresses become a constant fraction of the resolved stresses. This feature is responsible for the correct near-wall behavior of the model coefficient. In the near-wall region the eddy viscosity is reduced to account for the energy transfer from small to large scales that may occur locally.