Stochastic modelling of wall stresses in abdominal aortic aneurysms treated by a gene therapy

A stochastic mechanical model using the membrane theory was used to simulate the in vivo mechanical behaviour of abdominal aortic aneurysms (AAAs) in order to compute the wall stresses after stabilisation by gene therapy. For that, both length and diameter of AAAs rats were measured during their expansion. Four groups of animals, control and treated by an endovascular gene therapy during 3 or 28 days were included. The mechanical problem was solved analytically using the geometric parameters and assuming the shape of aneurysms by a 'parabolic-exponential curve'. When compared to controls, stress variations in the wall of AAAs for treated arteries during 28 days decreased, while they were nearly constant at day 3. The measured geometric parameters of AAAs were then investigated using probability density functions (pdf) attributed to every random variable. Different trials were useful to define a reliable confidence region in which the probability to have a realisation is equal to 99%. The results demonstrated that the error in the estimation of the stresses can be greater than 28% when parameters uncertainties are not considered in the modelling. The relevance of the proposed approach for the study of AAA growth may be studied further and extended to other treatments aimed at stabilisation AAAs, using biotherapies and pharmacological approaches.     

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.     

Blood flow in abdominal aortic aneurysms: pulsatile 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. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-averaged Reynolds numbers 50< or =Re(m)< or =300, corresponding to a range of peak Reynolds numbers 262.5< or =Re(peak) < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is characterized by a sequence of five different flow phases in one period of the flow cycle. Hemodynamic disturbance is evaluated for a modified set of indicator functions, which include wall pressure (p(w)), wall shear stress (tau(w)), and Wall Shear Stress Gradient (WSSG). At peak flow, the highest shear stress and WSSG levels are obtained downstream of both aneurysms, in a pattern similar to that of steady flow. Maximum values of wall shear stresses and wall shear stress gradients obtained at peak flow are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Mechanical instability of normal and aneurysmal arteries

Tortuous arteries associated with aneurysms have been observed in aged patients with atherosclerosis and hypertension. However, the underlying mechanism is poorly understood. The objective of this study was to determine the effect of aneurysms on arterial buckling instability and the effect of buckling on aneurysm wall stress. We investigated the mechanical buckling and post-buckling behavior of normal and aneurysmal carotid arteries and aorta’s using computational simulations and experimental measurements to elucidate the interrelationship between artery buckling and aneurysms. Buckling tests were done in porcine carotid arteries with small aneurysms created using elastase treatment. Parametric studies were done for model aneurysms with orthotropic nonlinear elastic walls using finite element simulations. Our results demonstrated that arteries buckled at a critical buckling pressure and the post-buckling deflection increased nonlinearly with increasing pressure. The presence of an aneurysm can reduce the critical buckling pressure of arteries, although the effect depends on the aneurysm’s dimensions. Buckled aneurysms demonstrated a higher peak wall stress compared to unbuckled aneurysms under the same lumen pressure. We conclude that aneurysmal arteries are vulnerable to mechanical buckling and mechanical buckling could lead to high stresses in the aneurysm wall. Buckling could be a possible mechanism for the development of tortuous aneurysmal arteries such as in the Loeys–Dietz syndrome.     

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.     

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.     

Characterization of arterial wall mechanical behavior and stresses from human clinical data

This paper demonstrates the feasibility of material identification and wall stress computation for human common carotid arteries based on non-invasive in vivo clinical data: dynamical intraluminal pressure measured by applanation tonometry, and medial diameter and intimal-medial thickness measured by high-resolution ultrasound echotracking. The mechanical behavior was quantified assuming an axially pre-stretched, thick-walled, cylindrical artery subjected to dynamical blood pressure and perivascular constraints. The wall was further assumed to be three-dimensional and to consist of a nonlinear, hyperelastic, anisotropic, incompressible material with smooth muscle activity and residual stresses. Mechanical contributions by individual constituents-an elastin-dominated matrix, collagen fibers, and vascular smooth muscle-were accounted for using a previously proposed microstructurally motivated constitutive relation. The in vivo boundary value problem was solved semi-analytically to compute the inner pressure during a mean cardiac cycle. Using a nonlinear least-squares method, optimal model parameters were determined by minimizing differences between computed and measured inner pressures over a mean cardiac cycle. The fit-to-data from two healthy patients was very good and the predicted radial, circumferential, and axial stretch and stress fields were sensible. Hence, the proposed approach was able to identify complex geometric and material parameters directly from non-invasive in vivo human data.     

Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms

Biomechanical factors play fundamental roles in the natural history of abdominal aortic aneurysms (AAAs) and their responses to treatment. Advances during the past two decades have increased our understanding of the mechanics and biology of the human abdominal aorta and AAAs, yet there remains a pressing need for considerable new data and resulting patient-specific computational models that can better describe the current status of a lesion and better predict the evolution of lesion geometry, composition, and material properties and thereby improve interventional planning. In this paper, we briefly review data on the structure and function of the human abdominal aorta and aneurysmal wall, past models of the mechanics, and recent growth and remodeling models. We conclude by identifying open problems that we hope will motivate studies to improve our computational modeling and thus general understanding of AAAs.     

Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease

Kawasaki disease (KD) is the leading cause of acquired heart disease in children and can result in life-threatening coronary artery aneurysms in up to 25 % of patients. These aneurysms put patients at risk of thrombus formation, myocardial infarction, and sudden death. Clinicians must therefore decide which patients should be treated with anticoagulant medication, and/or surgical or percutaneous intervention. Current recommendations regarding initiation of anticoagulant therapy are based on anatomy alone with historical data suggesting that patients with aneurysms \(\ge \) 8 mm are at greatest risk of thrombosis. Given the multitude of variables that influence thrombus formation, we postulated that hemodynamic data derived from patient-specific simulations would more accurately predict risk of thrombosis than maximum diameter alone. Patient-specific blood flow simulations were performed on five KD patients with aneurysms and one KD patient with normal coronary arteries. Key hemodynamic and geometric parameters, including wall shear stress, particle residence time, and shape indices, were extracted from the models and simulations and compared with clinical outcomes. Preliminary fluid structure interaction simulations with radial expansion were performed, revealing modest differences in wall shear stress compared to the rigid wall case. Simulations provide compelling evidence that hemodynamic parameters may be a more accurate predictor of thrombotic risk than aneurysm diameter alone and motivate the need for follow-up studies with a larger cohort. These results suggest that a clinical index incorporating hemodynamic information be used in the future to select patients for anticoagulant therapy.     

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.     

PD123319 Augments Angiotensin II-Induced Abdominal Aortic Aneurysms through an AT2 Receptor-Independent Mechanism

Background

AT2 receptors have an unclear function on development of abdominal aortic aneurysms (AAAs), although a pharmacological approach using the AT2 receptor antagonist PD123319 has implicated a role. The purpose of the present study was to determine the role of AT2 receptors in AngII-induced AAAs using a combination of genetic and pharmacological approaches. We also defined effects of AT2 receptors in AngII-induced atherosclerosis and thoracic aortic aneurysms.

Methods and Results

Male AT2 receptor wild type (AT2 +/y) and deficient (AT2 -/y) mice in an LDL receptor −/− background were fed a saturated-fat enriched diet, and infused with either saline or AngII (500 ng/kg/min). AT2 receptor deficiency had no significant effect on systolic blood pressure during AngII-infusion. While AngII infusion induced AAAs, AT2 receptor deficiency did not significantly affect either maximal width of the suprarenal aorta or incidence of AAAs. The AT2 receptor antagonist PD123319 (3 mg/kg/day) and AngII were co-infused into male LDL receptor −/− mice that were either AT2 +/y or −/y. PD123319 had no significant effect on systolic blood pressure in either wild type or AT2 receptor deficient mice. Consistent with our previous findings, PD123319 increased AngII-induced AAAs. However, this effect of PD123319 occurred irrespective of AT2 receptor genotype. Neither AT2 receptor deficiency nor PD123319 had any significant effect on AngII-induced thoracic aortic aneurysms or atherosclerosis.

Conclusions

AT2 receptor deficiency does not affect AngII-induced AAAs, thoracic aortic aneurysms and atherosclerosis. PD123319 augments AngII-induced AAAs through an AT2 receptor-independent mechanism.     

Hypoperfusion of the Adventitial Vasa Vasorum Develops an Abdominal Aortic Aneurysm

The aortic wall is perfused by the adventitial vasa vasorum (VV). Tissue hypoxia has previously been observed as a manifestation of enlarged abdominal aortic aneurysms (AAAs). We sought to determine whether hypoperfusion of the adventitial VV could develop AAAs. We created a novel animal model of adventitial VV hypoperfusion with a combination of a polyurethane catheter insertion and a suture ligation of the infrarenal abdominal aorta in rats. VV hypoperfusion caused tissue hypoxia and developed infrarenal AAA, which had similar morphological and pathological characteristics to human AAA. In human AAA tissue, the adventitial VV were stenotic in both small AAAs (30–49 mm in diameter) and in large AAAs (> 50 mm in diameter), with the sac tissue in these AAAs being ischemic and hypoxic. These results indicate that hypoperfusion of adventitial VV has critical effects on the development of infrarenal AAA.     

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.     

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.     

Elasticity and geometry: a computational model of the Heineke–Mikulicz strictureplasty

Crohn’s disease is a challenging inflammatory process with a propensity for focal gastro-intestinal tract inflammation and stricture. Surgically, Crohn’s is often treated with resection. However, a subtype of diffuse disease with multiple strictures is treated by strictureplasty procedures in hope of avoiding short-gut syndrome. Prior work by Pocivavsek et al. defined the geometry of a Heineke–Mikulicz strictureplasty. Here, we bring this analysis one step closer to clinical and biological relevance by calculating the mechanical stresses and strains that the strictureplasty deformation generates on a model intestinal wall. The small bowel is simulated as a linearly elastic isotropic deformable cylindrical shell using finite element modeling. Data show a divergence in elastic response between the anti-mesenteric and mesenteric halves. The anti-mesenteric surface shows a bending dominated elastic response that correlates with the prior purely geometric analysis. However, the mesenteric half is not a neutral bystander during strictureplasty formation, as geometric arguments predict. Strong in-plane stretching strains develop in a rim around the image of the transverse closure, which may impact local perfusion and serve as sites of disease recurrence. Lastly, nearly all the deformation energy is stored in the central vertex stitch, placing this part at highest risk of dehiscence. This study enhances our understanding of mechanical response in complex nonlinear cylindrical geometries like the surgically manipulated intestinal tract. The developed framework serves as a platform for future addition of more complex clinically relevant parameters to our model, including real tissue properties, anisotropy, blood supply modeling, and patient deriver anatomic factors.     

The effects of stent interaction on porcine urinary bladder matrix employed as stent-graft materials

Deployment of stent-grafts, derived from synthetic biomaterials, is an established minimally invasive approach for effectively treating abdominal aortic aneurysms (AAAs). However, a notable disadvantage associated with this surgical technique is migration of the deployed stent-graft due to poor biocompatibility and inadequate integration in vivo. Recently, tissue-engineered extracellular matrices (ECMs) have shown early promise as integrating stabilisation collars in this setting due to their ability to induce a constructive tissue remodelling response after in vivo implantation. In the present study the effects of stent loading on an ECM?s mechanical properties were investigated by characterising the compression and loading effects of endovascular stents on porcine urinary bladder matrix (UBM) scaffolds. Results demonstrated that the maximum stress was induced when the stent force was 8-times higher than a standard commercially available stent-graft and this represented about 20% of the failure strength of the UBM material. In addition, the influence of stent shape was also investigated. Findings demonstrated that the stress induced was higher for circular stents at low forces and a higher stress was induced on square stents when increased force was applied. Our findings demonstrate that porcine UBM possesses sufficient mechanical strength to withstand the compression and loading effects of commercially available stent-grafts in the setting of endovascular aneurysm repair.     

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.     

Hemodynamic stress in lateral saccular aneurysms

The flow velocities in glass and silastic lateral aneurysm models were quantitatively measured with the non-invasive laser Doppler method. The influences of the elasticity of the wall, the pulse wave and the properties of the perfusion medium on the intra-aneurysmal circulation were investigated. As shown previously, the inflow into the aneurysm arose from the downstream lip and was directed toward the center of the fundus. Backflow to the parent vessel took place along the walls of the fundus. With non-pulsatile perfusion, flow velocities in the center of the standardized aneurysms varied between 0.4 and 2% of the maximum velocity in the parent vessel. With pulsatile perfusion, flow velocities in the center of the fundus ranged between 8 and 13% of the flow velocity in the axis of the parent vessel. Flow velocities in the aneurysms were slower with a polymer suspension with blood-like properties compared to a glycerol/water solution. Flow velocity measurements near the aneurysmal wall allowed the estimation of the shear stresses at critical locations. The maximum shear stresses at the downstream lip of the aneurysm were in the range of the stresses measured at the flow divider of an arterial bifurcation. The present results suggest that in human saccular aneurysms intra-aneurysmal flow and shear stress on the wall are directly related to the pulsatility of perfusion, i.e. the systolic/diastolic pressure difference and that the tendency to spontaneous thrombosis depends on the viscoelastic properties of the blood, namely the hematocrit.     

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.     

Abdominal aortic aneurysms: an autoimmune disease?

Abdominal aortic aneurysms (AAAs) are a multifactorial degenerative vascular disorder. One of the defining features of the pathophysiology of aneurysmal disease is inflammation. Recent developments in vascular and molecular cell biology have increased our knowledge on the role of the adaptive and innate immune systems in the initiation and propagation of the inflammatory response in aortic tissue. AAAs share many features of autoimmune disease, including genetic predisposition, organ specificity and chronic inflammation. Here, this evidence is used to propose that the chronic inflammation observed in AAAs is a consequence of a dysregulated autoimmune response against autologous components of the aortic wall that persists inappropriately. Identification of the molecular and cellular targets involved in AAA formation will allow the development of therapeutic agents for the treatment of AAA.