The effect of material model formulation in the stress analysis of abdominal aortic aneurysms

Fluid-structure interaction analysis for abdominal aortic aneurysms: the role of multi-layered tissue architecture and intraluminal thrombus

Introduction

Abdominal aortic aneurysm (AAA) is a life-threatening disease marked by localized dilatations of the infrarenal aortic wall. While clinical guidelines often use the aneurysm diameter as an indicator for surgical intervention, this metric alone may not reliably predict rupture risks, underscoring the need for detailed biomechanical analyses to improve risk assessments.

Methods

We investigate the effects of the multi-layered tissue architecture and the intraluminal thrombus (ILT) on the wall stress distribution of AAA. Using fluid-structure interaction, we analyze the biomechanical responses of fusiform and saccular AAAs under three conditions: without ILT, with ILT but no tissue degradation, and with both ILT and tissue degradation.

Results

The findings show that the media is the primary load-bearing layer, and the multi-layered model yields a more accurate stress profile than the single-layered tissue model. The ILT substantially reduces overall stress levels in the covered tissue, although its impact on the location of peak stress varies across different scenarios. Media degradation increases the stress in the intima and adventitia, but the cushioning effect of ILT largely mitigates this impact.

Discussion

The results underscore the importance of incorporating the multi-layered tissue architecture and ILT in patient-specific analyses of AAA. These factors may improve the predictive capabilities of biomechanical assessments for rupture risk.

On the Relative Effects of Wall and Intraluminal Thrombus Constitutive Material Properties in Abdominal Aortic Aneurysm Wall Stress

INTRODUCTION

An abdominal aortic aneurysm (AAA) is a dilation localized in the infrarenal segment of the abdominal aorta that can expand continuously and rupture if left untreated. Computational methods such as finite element analysis (FEA) are widely used with in silico models to calculate biomechanical predictors of rupture risk while choosing constitutive material properties for the AAA wall and intraluminal thrombus (ILT).

METHODS

In the present work, we investigated the effect of different constitutive material properties for the wall and ILT on 21 idealized and 10 unruptured patient-specific AAA geometries. Three material properties were used to characterize the wall and two for the ILT, leading to six material model combinations for each AAA geometry subject to appropriate boundary conditions.

RESULTS

The results of the FEA simulations indicate significant differences in the average peak wall stress (PWS), 99th percentile wall stress (99th WS), and spatially averaged wall stress (SAWS) for all AAA geometries subject to the choice of a material model combination. Specifically, using a material model combination with a compliant ILT yielded statistically higher wall stresses compared to using a stiff ILT, irrespective of the constitutive equation used to model the AAA wall.

DISCUSSION

This work provides quantitative insight into the variability of the wall stress distributions ensuing from AAA FEA modeling due to its strong dependency on population-averaged soft tissue material characterizations. This dependency leads to uncertainty about the true biomechanical state of stress of an individual AAA and the subsequent assessment of its rupture risk.

Design, Development, and Temporal Evaluation of a Magnetic Resonance Imaging-Compatible In Vitro Circulation Model Using a Compliant Abdominal Aortic Aneurysm Phantom

Biomechanical characterization of abdominal aortic aneurysms (AAAs) has become commonplace in rupture risk assessment studies. However, its translation to the clinic has been greatly limited due to the complexity associated with its tools and their implementation. The unattainability of patient-specific tissue properties leads to the use of generalized population-averaged material models in finite element analyses, which adds a degree of uncertainty to the wall mechanics quantification. In addition, computational fluid dynamics modeling of AAA typically lacks the patient-specific inflow and outflow boundary conditions that should be obtained by nonstandard of care clinical imaging. An alternative approach for analyzing AAA flow and sac volume changes is to conduct in vitro experiments in a controlled laboratory environment. In this study, we designed, built, and characterized quantitatively a benchtop flow loop using a deformable AAA silicone phantom representative of a patient-specific geometry. The impedance modules, which are essential components of the flow loop, were fine-tuned to ensure typical intraluminal pressure conditions within the AAA sac. The phantom was imaged with a magnetic resonance imaging (MRI) scanner to acquire time-resolved images of the moving wall and the velocity field inside the sac. Temporal AAA sac volume changes lead to a corresponding variation in compliance throughout the cardiac cycle. The primary outcome of this work was the design optimization of the impedance elements, the quantitative characterization of the resistive and capacitive attributes of a compliant AAA phantom, and the exemplary use of MRI for flow visualization and quantification of the deformed AAA geometry.

A pilot study on biaxial mechanical, collagen microstructural, and morphological characterizations of a resected human intracranial aneurysm tissue

Intracranial aneurysms (ICAs) are focal dilatations that imply a weakening of the brain artery. Incidental rupture of an ICA is increasingly responsible for significant mortality and morbidity in the American’s aging population. Previous studies have quantified the pressure-volume characteristics, uniaxial mechanical properties, and morphological features of human aneurysms. In this pilot study, for the first time, we comprehensively quantified the mechanical, collagen fiber microstructural, and morphological properties of one resected human posterior inferior cerebellar artery aneurysm. The tissue from the dome of a right posterior inferior cerebral aneurysm was first mechanically characterized using biaxial tension and stress relaxation tests. Then, the load-dependent collagen fiber architecture of the aneurysm tissue was quantified using an in-house polarized spatial frequency domain imaging system. Finally, optical coherence tomography and histological procedures were used to quantify the tissue’s microstructural morphology. Mechanically, the tissue was shown to exhibit hysteresis, a nonlinear stress-strain response, and material anisotropy. Moreover, the unloaded collagen fiber architecture of the tissue was predominantly aligned with the testing Y-direction and rotated towards the X-direction under increasing equibiaxial loading. Furthermore, our histological analysis showed a considerable damage to the morphological integrity of the tissue, including lack of elastin, intimal thickening, and calcium deposition. This new unified characterization framework can be extended to better understand the mechanics-microstructure interrelationship of aneurysm tissues at different time points of the formation or growth. Such specimen-specific information is anticipated to provide valuable insight that may improve our current understanding of aneurysm growth and rupture potential.

On the importance of tunica intima in the aging aorta: a three-layered in silico model for computing wall stresses in abdominal aortic aneurysms

Layer-specific experimental data for human aortic tissue suggest that, in aged arteries and arteries with non-atherosclerotic intimal thickening, the innermost layer of the aorta increases significantly its stiffness and thickness, becoming load-bearing. However, there are very few computational studies of abdominal aortic aneurysms (AAAs) that take into account the mechanical contribution of the three layers that comprise the aneurysmal tissue. In this paper, a three-layered finite element model is proposed from the simplest uniaxial stress state to geometrically parametrized models of AAAs with different asymmetry values. Comparisons are made between a three-layered artery wall and a mono-layered intact artery, which represents the complex behavior of the aggregate adventitia-media-intima in a single layer with averaged mechanical properties. Likewise, the response of our idealized geometries is compared with similar experimental and numerical models. Finally, the mechanical contributions of adventitia, media and intima are analyzed for the three-layered aneurysms through the evaluation of the mean stress absorption percentage. Results show the relevance and necessity of considering the inclusion of tunica intima in multi-layered models of AAAs for getting accurate results in terms of peak wall stresses and displacements.

The influence of fiber dispersion on the mechanical response of aortic tissues in health and disease: a computational study

Changes in the structural components of aortic tissues have been shown to play a significant role in the pathogenesis of aortic degeneration. Therefore, reliable stress analyses require a suitable and meaningful constitutive model that captures micro-structural changes. As recent data show, in-plane and out-of-plane collagen fiber dispersions vary significantly between healthy and aneurysmatic aortic walls. The aim of this study is to computationally investigate the influence of fiber dispersion on the mechanical response of aortic tissues in health and disease. In particular, the influence of three different fiber dispersions is studied: (i) non-rotationally symmetric dispersion, the most realistic assumption for aortic tissues; (ii) transversely isotropic dispersion, a special case; (iii) perfectly aligned fibers (no dispersion in either plane), another special case. Explicit expressions for the stress and elasticity tensors as needed for the implementation in a finite element code are provided. Three representative numerical examples are studied: planar biaxial extension, inflation of residually stressed and pre-stretched aortic segments and inflation of an idealized abdominal aortic aneurysm (AAA) geometry. For the AAA geometry the case of isotropic dispersion is additionally analyzed. Documented structural and mechanical parameters are taken from human aortas (healthy media/adventitia and AAA). The influence of fiber dispersions upon magnitudes and distributions of stresses and deformations are presented and analyzed. Stresses vary significantly, especially in the AAA case, where material stiffening is significantly influenced by fiber dispersion. The results highlight the need to incorporate the structural differences into finite element simulations to obtain more accurate stress predictions. Additionally, results show the capability of one constitutive model to represent different scenarios of aortic micro-structures allowing future studies of collagen reorientation during disease progression.

Applicability of simplified computational models in prediction of peak wall stress in abdominal aortic aneurysms

In the paper impact of different material models on the calculated peak wall stress (PWS) and peak wall rupture risk (PWRR) in abdominal aortic aneurysms (AAAs) is assessed. Computational finite element models of 70 patient-specific AAAs were created using two different material models - a realistic one based on mean population results of uniaxial tests of AAA wall considered as reference, and a 100 times stiffer artificial model. The calculated results of PWS and PWRR were tested to evaluate statistical significance of differences caused by the non-realistic material model. It was shown that for majority of AAAs the differences are insignificant but for some 10% of them their relative differences exceed 20% which may lead to incorrect decisions on their surgical treatment. This percentage of failures favours application of realistic material models in clinical practise although they are much more time-consuming.

Fluid-Structure Interaction in Abdominal Aortic Aneurysm: Effect of Modeling Techniques

In this work, the impact of modeling techniques on predicting the mechanical behaviors of abdominal aortic aneurysm (AAA) is systematically investigated. The fluid-structure interaction (FSI) model for simultaneously capturing the transient interaction between blood flow dynamics and wall mechanics was compared with its simplified techniques, that is, computational fluid dynamics (CFD) or computational solid stress (CSS) model. Results demonstrated that CFD exhibited relatively smaller vortexes and tends to overestimate the fluid wall shear stress, compared to FSI. On the contrary, the minimal differences in wall stresses and deformation were observed between FSI and CSS models. Furthermore, it was found that the accuracy of CSS prediction depends on the applied pressure profile for the aneurysm sac. A large pressure drop across AAA usually led to the underestimation of wall stresses and thus the AAA rupture. Moreover, the assumed isotropic AAA wall properties, compared to the anisotropic one, will aggravate the difference between the simplified models with the FSI approach. The present work demonstrated the importance of modeling techniques on predicting the blood flow dynamics and wall mechanics of the AAA, which could guide the selection of appropriate modeling technique for significant clinical implications.

A Characteristic-Based Constitutive Law for Dispersed Fibers

Biological tissues are typically constituted of dispersed fibers. Modeling the constitutive laws of such tissues remains a challenge. Direct integration over all fibers is considered to be accurate but requires very expensive numerical integration. A general structure tensor (GST) model was previously developed to bypass this costly numerical integration step, but there are concerns about the model's accuracy. Here we estimate the approximation error of the GST model. We further reveal that the GST model ignores strain energy induced by shearing motions. Subsequently, we propose a new characteristic-based constitutive law to better approximate the direct integration model. The new model is very cost-effective and closely approximates the "true" strain energy as calculated by the direct integration when stress-strain nonlinearity or fiber dispersion angle is small.

Finite element simulation of the insertion of guidewires during an EVAR procedure: example of a complex patient case, a first step toward patient-specific parameterized models

Deformations of the vascular structure due to the insertion of tools during endovascular treatment of aneurysms of the abdominal aorta, unless properly anticipated during the preoperative planning phase, may be the source of intraoperative or postoperative complications. We propose here an explicit finite element simulation method which enables one to predict such deformations. This method is based on a mechanical model of the vascular structure which takes into account the nonlinear behavior of the arterial wall, the prestressing effect induced by the blood pressure and the mechanical support of the surrounding organs and structures. An analysis of the model sensitivity to the parameters used to represent this environment is done. This allows determining the parameters that have the largest influence on the quality of the prediction and also provides realistic values for each of them as no experimental data are available in the literature. Moreover, for the first time, the results are compared with 3D intraoperative data. This is done for a patient-specific case with a complex anatomy in order to assess the feasibility of the method. Finally, the predictive capability of the simulation is evaluated on a group of nine patients. The error between the final simulated and intraoperatively measured tool positions was 2.1 mm after the calibration phase on one patient. It results in a 4.6 ± 2.5 mm in average error for the blind evaluation on nine patients.

An approach for patient-specific multi-domain vascular mesh generation featuring spatially varying wall thickness modeling

In this work, we present a computationally efficient image-derived volume mesh generation approach for vasculatures that implements spatially varying patient-specific wall thickness with a novel inward extrusion of the wall surface mesh. Multi-domain vascular meshes with arbitrary numbers, locations, and patterns of both iliac bifurcations and thrombi can be obtained without the need to specify features or landmark points as input. In addition, the mesh output is coordinate-frame independent and independent of the image grid resolution with high dimensional accuracy and mesh quality, devoid of errors typically found in off-the-shelf image-based model generation workflows. The absence of deformable template models or Cartesian grid-based methods enables the present approach to be sufficiently robust to handle aneurysmatic geometries with highly irregular shapes, arterial branches nearly parallel to the image plane, and variable wall thickness. The assessment of the methodology was based on i) estimation of the surface reconstruction accuracy, ii) validation of the output mesh using an aneurysm phantom, and iii) benchmarking the volume mesh quality against other frameworks. For the phantom image dataset (pixel size 0.105 mm; slice spacing 0.7 mm; and mean wall thickness 1.401±0.120 mm), the average wall thickness in the mesh was 1.459±0.123 mm. The absolute error in average wall thickness was 0.060±0.036 mm, or about 8.6% of the largest image grid spacing (0.7 mm) and 4.36% of the actual mean wall thickness. Mesh quality metrics and the ability to reproduce regional variations of wall thickness were found superior to similar alternative frameworks.

Local Quantification of Wall Thickness and Intraluminal Thrombus Offer Insight into the Mechanical Properties of the Aneurysmal Aorta

Wall stress is a powerful tool to assist clinical decisions in rupture risk assessment of abdominal aortic aneurysms. Key modeling assumptions that influence wall stress magnitude and distribution are the inclusion or exclusion of the intraluminal thrombus in the model and the assumption of a uniform wall thickness. We employed a combined numerical-experimental approach to test the hypothesis that abdominal aortic aneurysm (AAA) wall tissues with different thickness as well as wall tissues covered by different thrombus thickness, exhibit differences in the mechanical behavior. Ultimate tissue strength was measured from in vitro tensile testing of AAA specimens and material properties of the wall were estimated by fitting the results of the tensile tests to a histo-mechanical constitutive model. Results showed a decrease in tissue strength and collagen stiffness with increasing wall thickness, supporting the hypothesis of wall thickening being mediated by accumulation of non load-bearing components. Additionally, an increase in thrombus deposition resulted in a reduction of elastin content, collagen stiffness and tissue strength. Local wall thickness and thrombus coverage may be used as surrogate measures of local mechanical properties of the tissue, and therefore, are possible candidates to improve the specificity of AAA wall stress and rupture risk evaluations.

Human thoracic and abdominal aortic aneurysmal tissues: Damage experiments, statistical analysis and constitutive modeling

Development of aortic aneurysms includes significant morphological changes within the tissue: collagen content increases, elastin content reduces and smooth muscle cells degenerate. We seek to quantify the impact of these changes on the passive mechanical response of aneurysms in the supra-physiological loading range via mechanical testing and constitutive modeling. We perform uniaxial extension tests on circumferentially and axially oriented strips from five thoracic (65.6 years ± 13.4, mean ± SD) and eight abdominal (63.9 years ± 11.4) aortic fusiform aneurysms to investigate both continuous and discontinuous softening during supra-physiological loading. We determine the significance of the differences between the fitted model parameters: diseased thoracic versus abdominal tissues, and healthy (Weisbecker et al., J. Mech. Behav. Biomed. Mater. 12, 93-106, 2012) versus diseased tissues. We also test correlations among these parameters and age, Body Mass Index (BMI) and preoperative aneurysm diameter, and investigate histological cuts. Tissue response is anisotropic for all tests and the anisotropic pseudo-elastic damage model fits the data well for both primary loading and discontinuous softening which we interpret as damage. We found statistically relevant differences between model parameters fitted to diseased thoracic versus abdominal tissues, as well as between those fitted to healthy versus diseased tissues. Only BMI correlated with fitted model parameters in abdominal aortic aneurysmal tissues.

The importance of patient-specific regionally varying wall thickness in abdominal aortic aneurysm biomechanics

Abdominal aortic aneurysm (AAA) is a vascular condition where the use of a biomechanics-based assessment for patient-specific risk assessment is a promising approach for clinical management of the disease. Among various factors that affect such assessment, AAA wall thickness is expected to be an important factor. However, regionally varying patient-specific wall thickness has not been incorporated as a modeling feature in AAA biomechanics. To the best our knowledge, the present work is the first to incorporate patient-specific variable wall thickness without an underlying empirical assumption on its distribution for AAA wall mechanics estimation. In this work, we present a novel method for incorporating regionally varying wall thickness (the "PSNUT" modeling strategy) in AAA finite element modeling and the application of this method to a diameter-matched cohort of 28 AAA geometries to assess differences in wall mechanics originating from the conventional assumption of a uniform wall thickness. For the latter, we used both a literature-derived population average wall thickness (1.5 mm; the "UT" strategy) as well as the spatial average of our patient-specific variable wall thickness (the "PSUT" strategy). For the three different wall thickness modeling strategies, wall mechanics were assessed by four biomechanical parameters: the spatial maxima of the first principal stress, strain, strain-energy density, and displacement. A statistical analysis was performed to address the hypothesis that the use of any uniform wall thickness model resulted in significantly different biomechanical parameters compared to a patient-specific regionally varying wall thickness model. Statistically significant differences were obtained with the UT modeling strategy compared to the PSNUT strategy for the spatial maxima of the first principal stress (p = 0.002), strain (p = 0.0005), and strain-energy density (p = 7.83 e-5) but not for displacement (p = 0.773). Likewise, significant differences were obtained comparing the PSUT modeling strategy with the PSNUT strategy for the spatial maxima of the first principal stress (p = 9.68 e-7), strain (p = 1.03 e-8), strain-energy density (p = 9.94 e-8), and displacement (p = 0.0059). No significant differences were obtained comparing the UT and PSUT strategies for the spatial maxima of the first principal stress (p = 0.285), strain (p = 0.152), strain-energy density (p = 0.222), and displacement (p = 0.0981). This work strongly recommends the use of patient-specific regionally varying wall thickness derived from the segmentation of abdominal computed tomography (CT) scans if the AAA finite element analysis is focused on estimating peak biomechanical parameters, such as stress, strain, and strain-energy density.

Review: the role of biomechanical modeling in the rupture risk assessment for abdominal aortic aneurysms

AAA disease is a serious condition and a multidisciplinary approach including biomechanics is needed to better understand and more effectively treat this disease. A rupture risk assessment is central to the management of AAA patients, and biomechanical simulation is a powerful tool to assist clinical decisions. Central to such a simulation approach is a need for robust and physiologically relevant models. Vascular tissue senses and responds actively to changes in its mechanical environment, a crucial tissue property that might also improve the biomechanical AAA rupture risk assessment. Specifically, constitutive modeling should not only focus on the (passive) interaction of structural components within the vascular wall, but also how cells dynamically maintain such a structure. In this article, after specifying the objectives of an AAA rupture risk assessment, the histology and mechanical properties of AAA tissue, with emphasis on the wall, are reviewed. Then a histomechanical constitutive description of the AAA wall is introduced that specifically accounts for collagen turnover. A test case simulation clearly emphasizes the need for constitutive descriptions that remodels with respect to the mechanical loading state. Finally, remarks regarding modeling of realistic clinical problems and possible future trends conclude the article.

The role of geometric and biomechanical factors in abdominal aortic aneurysm rupture risk assessment

The current clinical management of abdominal aortic aneurysm (AAA) disease is based to a great extent on measuring the aneurysm maximum diameter to decide when timely intervention is required. Decades of clinical evidence show that aneurysm diameter is positively associated with the risk of rupture, but other parameters may also play a role in causing or predisposing the AAA to rupture. Geometric factors such as vessel tortuosity, intraluminal thrombus volume, and wall surface area are implicated in the differentiation of ruptured and unruptured AAAs. Biomechanical factors identified by means of computational modeling techniques, such as peak wall stress, have been positively correlated with rupture risk with a higher accuracy and sensitivity than maximum diameter alone. The objective of this review is to examine these factors, which are found to influence AAA disease progression, clinical management and rupture potential, as well as to highlight on-going research by our group in aneurysm modeling and rupture risk assessment.

A pull-back algorithm to determine the unloaded vascular geometry in anisotropic hyperelastic AAA passive mechanics

Biomechanical studies on abdominal aortic aneurysms (AAA) seek to provide for better decision criteria to undergo surgical intervention for AAA repair. More accurate results can be obtained by using appropriate material models for the tissues along with accurate geometric models and more realistic boundary conditions for the lesion. However, patient-specific AAA models are generated from gated medical images in which the artery is under pressure. Therefore, identification of the AAA zero pressure geometry would allow for a more realistic estimate of the aneurysmal wall mechanics. This study proposes a novel iterative algorithm to find the zero pressure geometry of patient-specific AAA models. The methodology allows considering the anisotropic hyperelastic behavior of the aortic wall, its thickness and accounts for the presence of the intraluminal thrombus. Results on 12 patient-specific AAA geometric models indicate that the procedure is computational tractable and efficient, and preserves the global volume of the model. In addition, a comparison of the peak wall stress computed with the zero pressure and CT-based geometries during systole indicates that computations using CT-based geometric models underestimate the peak wall stress by 59 ± 64 and 47 ± 64 kPa for the isotropic and anisotropic material models of the arterial wall, respectively.

AN OSMOTICALLY INFLATABLE SEAL TO TREAT ENDOLEAKS OF TYPE 1, FOLLOWING ENDOVASCULAR ANEURYSM REPAIR

Stent-grafts of various designs are currently used in endoluminal treatment of abdominal aortic aneurysm. Two of the remaining possible complications are endoleaks and stent migrations. To treat endoleaks of type 1, a new system is studied here: An inflatable osmotic seal. It is set up at the extremities of the endograft and swollen using osmotic process against the vessels in case of endoleak without any invasive re-intervention. Mechanical modeling of the device and finite element simulations are performed to evaluate the efficiency of the seal and the consequences on the arteries as function of the osmotic pressure.

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 < 0.05) were found to characterize the AAA morphology during the surveillance period. By means of nonlinear regression, PWS estimated with the anisotropic material was found to be highly correlated with three of these features: maximum diameter (r = 0.992, p = 0.002), sac volume (r = 0.989, p = 0.003) and diameter to diameter ratio (r = 0.947, p = 0.033). The correlation of wall mechanics with geometry is nonlinear and reveals that PWS does not increase concomitantly with aneurysm diameter. This suggests that a quantitative characterization of AAA morphology may be advantageous in assessing rupture risk.

Experimental and modeling study of collagen scaffolds with the effects of crosslinking and fiber alignment

Collagen type I scaffolds are commonly used due to its abundance, biocompatibility, and ubiquity. Most applications require the scaffolds to operate under mechanical stresses. Therefore understanding and being able to control the structural-functional integrity of collagen scaffolds becomes crucial. Using a combined experimental and modeling approach, we studied the structure and function of Type I collagen gel with the effects of spatial fiber alignment and crosslinking. Aligned collagen scaffolds were created through the flow of magnetic particles enmeshed in collagen fibrils to mimic the anisotropy seen in native tissue. Inter- and intra- molecular crosslinking was modified chemically with Genipin to further improve the stiffness of collagen scaffolds. The anisotropic mechanical properties of collagen scaffolds were characterized using a planar biaxial tensile tester and parallel plate rheometer. The tangent stiffness from biaxial tensile test is two to three orders of magnitude higher than the storage moduli from rheological measurements. The biphasic nature of collagen gel was discussed and used to explain the mechanical behavior of collagen scaffolds under different types of mechanical tests. An anisotropic hyperelastic constitutive model was used to capture the characteristics of the stress-strain behavior exhibited by collagen scaffolds.

On constitutive descriptors of the biaxial mechanical behaviour of human abdominal aorta and aneurysms

The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological 'four-fibre family' constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.

Trans-Thrombus Blood Pressure Effects in Abdominal Aortic Aneurysms

How much and how the thrombus supports the wall of an abdominal aortic aneurysm (AAA) is unclear. While some previous studies have indicated that thrombus lacks the mechanical integrity to support much load compared with the aneurysm wall, others have shown that removing thrombus in computational AAA models drastically changes aneurysm wall stress. Histopathological studies have shown that thrombus properties vary through the thickness and it can be porous. The goal of this study is to explore the variations in thrombus properties, including the ability to isolate pressure from the aneurysm wall, incomplete attachment, and their effects on aneurysm wall stress, an important parameter in determining risk for rupture. An analytical model comprised of cylinders and two patient specific models were constructed with pressurization boundary conditions applied at the lumen or the thrombus/aneurysm wall interface (to simulate complete transmission of pressure through porous thrombus). Aneurysm wall stress was also calculated in the absence of thrombus. The potential importance of partial thrombus attachment was also analyzed. Pressurizing at either surface (lumen versus interface) made little difference to mean von Mises aneurysm wall stress values with thrombus completely attached (3.1% analytic, 1.2% patient specific) while thrombus presence reduced mean von Mises stress considerably (79% analytic, 40–46% patient specific) in comparison to models without it. Peak von Mises stresses were similarly influenced with pressurization surface differing slightly (3.1% analytic, 1.4% patient specific) and reductions in stress by thrombus presence (80% analytic, 28–37% patient specific). The case of partial thrombus attachment was investigated using a cylindrical model in which there was no attachment between the thrombus and aneurysm wall in a small area (10 deg). Applying pressure at the lumen resulted in a similar stress field to fully attached thrombus, whereas applying pressure at the interface resulted in a 42% increase in peak aneurysm wall stress. Taken together, these results show that the thrombus can have a wall stress reducing role even if it does not shield the aneurysm wall from direct pressurization—as long as the thrombus is fully attached to the aneurysm wall. Furthermore, the potential for porous thrombus to transmit pressure to the interface can result in a considerable increase in aneurysm wall stress in cases of partial attachment. In the search for models capable of accurately assessing the risk for rupture, the nature of the thrombus and its attachment to the aneurysm wall must be carefully assessed.

Semiautomatic vessel wall detection and quantification of wall thickness in computed tomography images of human abdominal aortic aneurysms

PURPOSE

Quantitative measurements of wall thickness in human abdominal aortic aneurysms (AAAs) may lead to more accurate methods for the evaluation of their biomechanical environment.

METHODS

The authors describe an algorithm for estimating wall thickness in AAAs based on intensity histograms and neural networks involving segmentation of contrast enhanced abdominal computed tomography images. The algorithm was applied to ten ruptured and ten unruptured AAA image data sets. Two vascular surgeons manually segmented the lumen, inner wall, and outer wall of each data set and a reference standard was defined as the average of their segmentations. Reproducibility was determined by comparing the reference standard to lumen contours generated automatically by the algorithm and a commercially available software package. Repeatability was assessed by comparing the lumen, outer wall, and inner wall contours, as well as wall thickness, made by the two surgeons using the algorithm.

RESULTS

There was high correspondence between automatic and manual measurements for the lumen area (r = 0.978 and r = 0.996 for ruptured and unruptured aneurysms, respectively) and between vascular surgeons (r = 0.987 and r = 0.992 for ruptured and unruptured aneurysms, respectively). The authors' automatic algorithm showed better results when compared to the reference with an average lumen error of 3.69%, which is less than half the error between the commercially available application Simpleware and the reference (7.53%). Wall thickness measurements also showed good agreement between vascular surgeons with average coefficients of variation of 10.59% (ruptured aneurysms) and 13.02% (unruptured aneurysms). Ruptured aneurysms exhibit significantly thicker walls (1.78 +/- 0.39 mm) than unruptured ones (1.48 +/- 0.22 mm), p = 0.044.

CONCLUSIONS

While further refinement is needed to fully automate the outer wall segmentation algorithm, these preliminary results demonstrate the method's adequate reproducibility and low interobserver variability.

Constitutive modelling of arteries

This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.