Porohyperelastic finite element modeling of abdominal aortic aneurysms

Abdominal aortic aneurysm (AAA) is the gradual weakening and dilation of the infrarenal aorta. This disease is progressive, asymptomatic, and can eventually lead to rupture--a catastrophic event leading to massive internal bleeding and possibly death. The mechanical environment present in AAA is currently thought to be important in disease initiation, progression, and diagnosis. In this study, we utilize porohyperelastic (PHE) finite element models (FEMs) to investigate how such modeling can be used to better understand the local biomechanical environment in AAA. A 3D hypothetical AAA was constructed with a preferential anterior bulge assuming both the intraluminal thrombus (ILT) and the AAA wall act as porous materials. A parametric study was performed to investigate how physiologically meaningful variations in AAA wall and ILT hydraulic permeabilities affect luminal interstitial fluid velocities and wall stresses within an AAA. A corresponding hyperelastic (HE) simulation was also run in order to be able to compare stress values between PHE and HE simulations. The effect of AAA size on local interstitial fluid velocity was also investigated by simulating maximum diameters (5.5 cm, 4.5 cm, and 3.5 cm) at the baseline values of ILT and AAA wall permeability. Finally, a cyclic PHE simulation was utilized to study the variation in local fluid velocities as a result of a physiologic pulsatile blood pressure. While the ILT hydraulic permeability was found to have minimal affect on interstitial velocities, our simulations demonstrated a 28% increase and a 20% decrease in luminal interstitial fluid velocity as a result of a 1 standard deviation increase and decrease in AAA wall hydraulic permeability, respectively. Peak interstitial velocities in all simulations occurred on the luminal surface adjacent to the region of maximum diameter. These values increased with increasing AAA size. PHE simulations resulted in 19.4%, 40.1%, and 81.0% increases in peak maximum principal wall stresses in comparison to HE simulations for maximum diameters of 35 mm, 45 mm, and 55 mm, respectively. The pulsatile AAA PHE FEM demonstrated a complex interstitial fluid velocity field the direction of which alternated in to and out of the luminal layer of the ILT. The biomechanical environment within both the aneurysmal wall and the ILT is involved in AAA pathogenesis and rupture. Assuming these tissues to be porohyperelastic materials may provide additional insight into the complex solid and fluid forces acting on the cells responsible for aneurysmal remodeling and weakening.     

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.     

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.     

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   

Metabolites secreted by human atherothrombotic aneurysms revealed through a metabolomic approach

Abdominal aortic aneurysm (AAA) is perma-nent and localized dilation of the abdominal aorta. Intraluminal thrombus (ILT) is involved in evolution and rupture of AAA. Complex biological processes associated with AAA include oxidative stress, proteolysis, neovascularization, aortic inflammation, cell death, and extracellular matrix breakdown. Biomarkers of growth and AAA rupture could give a more nuanced indication for surgery, unveil novel pathogenic pathways, and open possibilities for pharmacological inhibition of growth. Differential analysis of metabolites released by normal and pathological arteries in culture may help to find molecules that have a high probability of later being found in plasma and start signaling processes or be useful diagnostic/prognostic markers. We used a LC-QTOF-MS metabolomic approach to analyze metabolites released by human ILT (divided into luminal and abluminal layers), aneurysm wall (AW), and healthy wall (HW). Statistical analysis was used to compare luminal with abluminal ILT layer, ILT with AW, and AW with HW to select the metabolites exchanged between tissue and external medium. Identified compounds are related to inflammation and oxidative stress and indicate the possible role of fatty acid amides in AAA. Some metabolites (e.g., hippuric acid) had not been previously associated to aneurysm, others (fatty acid amides) have arisen, indicating a very promising line of research.     

A model of growth and rupture of abdominal aortic aneurysm

We present here a coupled mathematical model of growth and failure of the abdominal aortic aneurysm (AAA). The failure portion of the model is based on the constitutive theory of softening hyperelasticity where the classical hyperelastic law is enhanced with a new constant indicating the maximum energy that an infinitesimal material volume can accumulate without failure. The new constant controls material failure and it can be interpreted as the average energy of molecular bonds from the microstructural standpoint. The constitutive model is compared to the data from uniaxial tension tests providing an excellent fit to the experiment. The AAA failure model is coupled with a phenomenological theory of soft tissue growth. The unified theory includes both momentum and mass balance laws coupled with the help of the constitutive equations. The microstructural alterations in the production of elastin and remodeling of collagen are reflected in the changing macroscopic parameters characterizing tissue stiffness, strength and density. The coupled theory is used to simulate growth and rupture of an idealized spherical AAA. The results of the simulation showing possible AAA ruptures in growth are reasonable qualitatively while the quantitative calibration of the model will require further clinical observations and in vitro tests. The presented model is the first where growth and rupture are coupled.     

Effect of macroscale formation of intraluminal thrombus on blood flow in abdominal aortic aneurysms

A mathematical approach of blood flow within an abdominal aortic aneurysm (AAA) with intraluminal thrombus (ILT) is presented. The macroscale formation of ILT is modeled as a growing porous medium with variable porosity and permeability according to values proposed in the literature. The model outlines the effect of a porous ILT on blood flow in AAAs. The numerical solution is obtained by employing a structured computational mesh of an idealized fusiform AAA geometry and applying the Galerkin weighted residual method in generalized curvilinear coordinates. Results on velocity and pressure fields of independent cases with and without ILT are presented and discussed. The vortices that develop within the aneurysmal cavity are studied and visualized as ILT becomes more condensed. From a mechanistic point of view, the reduction of bulge pressure, as ILT is thickening, supports the observation that ILT could protect the AAA from a possible rupture. The model also predicts a relocation of the maximum pressure region toward the zone proximal to the neck of the aneurysm. However, other mechanisms, such as the gradual wall weakening that usually accompany AAA and ILT formation, which are not included in this study, may offset this effect.     

Effect of intraluminal thrombus thickness and bulge diameter on the oxygen diffusion in abdominal aortic aneurysm.

The intraluminal thrombus (ILT) commonly found within abdominal aortic aneurysm (AAA) may serve as a barrier to oxygen diffusion from the lumen to the inner layers of the aortic wall. The purpose of this work was to address this hypothesis and to assess the effects of AAA bulge diameter (dAAA) and ILT thickness (delta) on the oxygen flow. A hypothetical, three-dimensional, axisymmetric model of AAA containing ILT was created for computational analysis. Commercial software was utilized to estimate the volume flow of O2 per cell, which resulted in zero oxygen tension at the AAA wall. Solutions were generated by holding one of the two parameters fixed while varying the other. The supply of O2 to the AAA wall increases slightly and linearly with dAAA for a fixed delta. This slight increase is due to the enlarged area through which diffusion of O2 may take place. The supply of O2 was found to decrease quickly with increasing delta for a fixed dAAA due to the increased resistance to O2 transport by the ILT layer. The presence of even a thin, 3 mm ILT layer causes a diminished O2 supply (less than 4 x 10(-10) mumol/min/cell). Normally functioning smooth muscle cells require a supply of 21 x 10(-10) mumol/min/cell. Thus, our analysis serves to support our hypothesis that the presence of ILT alters the normal pattern of O2 supply to the AAA wall. This may lead to hypoxic cell dysfunction in the AAA wall, which may further lead to wall weakening and increased potential for 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.     

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 thickness is not related to lower concentrations of trace elements in the wall of infrarenal abdominal aortic aneurysms

BackgroundIntraluminal thrombus (ILT) formation plays a significant role in the progression of infrarenal abdominal aortic aneurysms (AAA). Potentially, as ILT thickness increases the availability of trace elements in the aneurysm wall could decrease thereby leading to oxidative stress and intensifying pro-inflammatory cytokine generation.AimTo determine if thrombus thickness is related to the concentration of trace elements in the wall of infrarenal AAA.Patients and methodsThe concentrations of trace elements in the wall of the aneurysm sack and ILT obtained from 19 consecutive patients during surgery for infrarenal AAA were determined using emission spectrometry.ResultsThe concentrations of magnesium, zinc, manganese, and lead in the wall of AAA were significantly greater than in the ILT. Only the concentration of copper was lower in the AAA wall compared with the thrombus. The concentration of calcium, phosphorus, zinc, lead, copper, and magnesium increased with ILT thickness. The concentrations of no other trace elements in the wall of AAA were found to be related to the ILT thickness.ConclusionsIntraluminal thrombus thickness is not associated with a lower concentration of trace elements in the wall of the infrarenal AAA. Thus, the intraluminal thrombus participates in the progression of AAA by mechanisms independent of trace element supply to the wall of the aneurysm sack.     

Soft-cuticle biomechanics: A constitutive model of anisotropy for caterpillar integument

The mechanical properties of soft tissues are important for the control of motion in many invertebrates. Pressurized cylindrical animals such as worms have circumferential reinforcement of the body wall; however, no experimental characterization of comparable anisotropy has been reported for climbing larvae such as caterpillars. Using uniaxial, real-time fluorescence extensometry on millimeter scale cuticle specimens we have quantified differences in the mechanical properties of cuticle to circumferentially and longitudinally applied forces. Based on these results and the composite matrix-fiber structure of cuticle, a pseudo-elastic transversely isotropic constitutive material model was constructed with circumferential reinforcement realized as a Horgan-Saccomandi strain energy function. This model was then used numerically to describe the anisotropic material properties of Manduca cuticle. The constitutive material model will be used in a detailed finite-element analysis to improve our understanding of the mechanics of caterpillar crawling.     

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.     

Compressive mechanical properties of the intraluminal thrombus in abdominal aortic aneurysms and fibrin-based thrombus mimics

An intraluminal thrombus (ILT) forms in the majority of abdominal aortic aneurysms (AAAs). While the ILT has traditionally been perceived as a byproduct of aneurysmal disease, the mechanical environment within the ILT may contribute to the degeneration of the aortic wall by affecting biological events of cells embedded within the ILT. In this study, the drained secant modulus (E₅～modulus at 5% strain) of ILT specimens (luminal, medial, and abluminal) procured from elective open repair was measured and compared using unconfined compression. Five groups of fibrin-based thrombus mimics were also synthesized by mixing various combinations of fibrinogen, thrombin, and calcium. Drained secant moduli were compared to determine the effect of the components’ concentrations on mimic stiffness. The stiffness of mimics was also compared to the native ILT. Preliminary data on the water content of the ILT layers and mimics was measured. It was found that the abluminal layer (E₅=19.3 kPa) is stiffer than the medial (2.49 kPa) and luminal (1.54 kPa) layers, both of which are statistically similar. E₅ of the mimics (0.63, 0.22, 0.23, 0.87, and 2.54 kPa) is dependent on the concentration of all three components: E₅ decreases with a decrease in fibrinogen (60–20 and 20–15 mg/ml) and a decrease in thrombin (3–0.3 units/ml), and E₅ increases with a decrease in calcium (0.1–0.01 M). E₅ from two of the mimics were not statistically different than the medial and luminal layers of ILT. A thrombus mimic with similar biochemical components, structure, and mechanical properties as native ILT would provide an appropriate test medium for AAA mechanobiology studies.     

Variations of dissection properties and mass fractions with thrombus age in human abdominal aortic aneurysms

Introduction

Thrombus ages, defined as four relative age phases, are related to different compositions of the intraluminal thrombus (ILT) in the abdominal aortic aneurysm (AAA) (Tong et al., 2011b). Experimental studies indicate a correlation between the relative thrombus age and the strength of the thrombus-covered wall.

Methods

On 32 AAA samples we performed peeling tests with the aim to dissect the material (i) through the ILT thickness, (ii) within the individual ILT layers and (iii) within the aneurysm wall underneath the thrombus by using two extension rates (1 mm/min, 1 mm/s). Histological investigations and mass fraction analysis were performed to characterize the dissected morphology, to determine the relative thrombus age, and to quantify dry weight percentages of elastin and collagen in the AAA wall.

Results

A remarkably lower dissection energy was needed to dissect within the individual ILT layers and through the thicknesses of old thrombi. With increasing ILT age the dissection energy of the underlying intima–media composite continuously decreased and the anisotropic dissection properties for that composite vanished. The quantified dissection properties were rate dependent for both tissue types (ILT and wall). Histology showed that single fibrin fibers or smaller protein clots within the ILT generate smooth dissected surfaces during the peeling. There was a notable decrease in mass fraction of elastin within the thrombus-covered intima–media composite with ILT age, whereas no significant change was found for that of collagen.

Conclusions

These findings suggest that intraluminal thrombus aging leads to a higher propensity of dissection for the ILT and the intima–media composite of the aneurysmal wall.     

Inflation of an artery leading to aneurysm formation and rupture

Formation and rupture of aneurysms due to the inflation of an artery with collagen fibers distributed in two preferred directions, subjected to internal pressure and axial stretch are examined within the framework of nonlinear elasticity. A two layer tube model with a fiber-reinforced composite based incompressible anisotropic hyperelastic constitutive material is employed to model the stress-strain behavior of the artery wall with distributed collagen fibers. The artery wall takes up a uniform inflation deformation, and there are no aneurysms in the artery under the normal condition. But an aneurysm may be formed in arteries when the stiffness of the fibers is decreased to a certain value or the direction of the fibers is changed to a certain degree towards the circumferential direction. The aneurysm may expand to much large extent and become complex in shape. One portion of the aneurysm becomes highly distended as a bubble while the rest remains lightly inflated. The rupture of the aneurysm is discussed along with the distribution of stresses. Critical pressures and the rupture pressures are given for different collagen fiber orientations or stiffness. Furthermore, the stability of the solutions is discussed to explain the formation of aneurysm.     

Epicardial suction: a new approach to mechanical testing of the passive ventricular wall

The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics.     

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.     

Adventitial Vasa Vasorum Arteriosclerosis in Abdominal Aortic Aneurysm

Abdominal aortic aneurysm (AAA) is a common disease among elderly individuals. However, the precise pathophysiology of AAA remains unknown. In AAA, an intraluminal thrombus prevents luminal perfusion of oxygen, allowing only the adventitial vaso vasorum (VV) to deliver oxygen and nutrients to the aortic wall. In this study, we examined changes in the adventitial VV wall in AAA to clarify the histopathological mechanisms underlying AAA. We found marked intimal hyperplasia of the adventitial VV in the AAA sac; further, immunohistological studies revealed proliferation of smooth muscle cells, which caused luminal stenosis of the VV. We also found decreased HemeB signals in the aortic wall of the sac as compared with those in the aortic wall of the neck region in AAA. The stenosis of adventitial VV in the AAA sac and the malperfusion of the aortic wall observed in the present study are new aspects of AAA pathology that are expected to enhance our understanding of this disease.