A model of growth and rupture of abdominal aortic aneurysm

Aortic tissue stiffness and tensile strength are correlated with density changes following proteolytic treatment

INTRODUCTION

Dissection or rupture of the aorta is accompanied by high mortality rates, and there is a pressing need for better prediction of these events for improved patient management and clinical outcomes. Biomechanically, these events represent a situation wherein the locally acting wall stress exceed the local tissue strength. Based on recent reports for polymers, we hypothesized that aortic tissue failure strength and stiffness are directly associated with tissue mass density. The objective of this work was to test this novel hypothesis for porcine thoracic aorta.

METHODS

Three tissue specimens from freshly harvested porcine thoracic aorta were treated with either collagenase or elastase to selectively degrade structural proteins in the tissue, or with phosphate buffer saline (control). The tissue mass and volume of each specimen were measured before and after treatment to allow for density calculation, then mechanically tested to failure under uniaxial extension.

RESULTS

Protease treatments resulted in statistically significant tissue density reduction (sham vs. collagenase p = 0.02 and sham vs elastase p = 0.003), which in turn was significantly and directly correlated with both ultimate tensile strength (sham vs. collagenase p = 0.02 and sham vs elastase p = 0.03) and tangent modulus (sham vs. collagenase p = 0.007 and sham vs elastase p = 0.03).

CONCLUSIONS

This work demonstrates for the first time that tissue stiffness and tensile strength are directly correlated with tissue density in proteolytically-treated aorta. These findings constitute an important step towards understanding aortic tissue failure mechanisms and could potentially be leveraged for non-invasive aortic strength assessment through density measurements, which could have implications to clinical care.

Modeling planar response of vascular tissues using quadratic functions of effective strain

Simulation-based studies of the cardiovascular structure such as aorta have become increasingly popular for many biomedical problems such as predictions of aneurysm rupture. A critical step in these simulations is the development of constitutive models that accurately describe the tissue's mechanical behavior. In this work, we present a new constitutive model, which explicitly accounts for the gradual recruitment of collagen fibers. The recruitment is considered using an effective stretch, which is a continuum-scale kinematic variable measuring the uncrimped stretch of the tissue in an average sense. The strain energy of a fiber bundle is described by a quadratic function of the effective strain. Constitutive models formulated in this manner are applied to describe the responses of ascending thoracic aortic aneurysm and porcine thoracic aorta tissues. The heterogeneous properties of the ATAA tissue are extracted from bulge inflation test data, and then used in finite element analysis to simulate the inflation test. The descriptive and predictive capabilities are further assessed using planar testing data of porcine thoracic aortic tissues. It is found that the constitutive model can accurately describe the stress-strain relations. In particular, the finite element simulation replicates the displacement, strain, and stress distributions with excellent fidelity.

A quarter of a century biomechanical rupture risk assessment of abdominal aortic aneurysms. Achievements, clinical relevance, and ongoing developments

Abdominal aortic aneurysm (AAA) disease, the local enlargement of the infrarenal aorta, is a serious condition that causes many deaths, especially in men exceeding 65 years of age. Over the past quarter of a century, computational biomechanical models have been developed towards the assessment of AAA risk of rupture, technology that is now on the verge of being integrated within the clinical decision-making process. The modeling of AAA requires a holistic understanding of the clinical problem, in order to set appropriate modeling assumptions and to draw sound conclusions from the simulation results. In this article we summarize and critically discuss the proposed modeling approaches and report the outcome of clinical validation studies for a number of biomechanics-based rupture risk indices. Whilst most of the aspects concerning computational mechanics have already been settled, it is the exploration of the failure properties of the AAA wall and the acquisition of robust input data for simulations that has the greatest potential for the further improvement of this technology.

Mechano-chemo-biological Computational Models for Arteries in Health, Disease and Healing: From Tissue Remodelling to Drug-eluting Devices

This review aims to highlight urgent priorities for the computational biomechanics community in the framework of mechano-chemo-biological models. Recent approaches, promising directions and open challenges on the computational modelling of arterial tissues in health and disease are introduced and investigated, together with in silico approaches for the analysis of drug-eluting stents that promote pharmacological-induced healing. The paper addresses a number of chemo-biological phenomena that are generally neglected in biomechanical engineering models but are most likely instrumental for the onset and the progression of arterial diseases. An interdisciplinary effort is thus encouraged for providing the tools for an effective in silico insight into medical problems. An integrated mechano-chemo-biological perspective is believed to be a fundamental missing piece for crossing the bridge between computational engineering and life sciences, and for bringing computational biomechanics into medical research and clinical practice.

Machine Learning-Based Pulse Wave Analysis for Early Detection of Abdominal Aortic Aneurysms Using In Silico Pulse Waves

An abdominal aortic aneurysm (AAA) is usually asymptomatic until rupture, which is associated with extremely high mortality. Consequently, the early detection of AAAs is of paramount importance in reducing mortality; however, most AAAs are detected by medical imaging only incidentally. The aim of this study was to investigate the feasibility of machine learning-based pulse wave (PW) analysis for the early detection of AAAs using a database of in silico PWs. PWs in the large systemic arteries were simulated using one-dimensional blood flow modelling. A database of in silico PWs representative of subjects (aged 55, 65 and 75 years) with different AAA sizes was created by varying the AAA-related parameters with major impacts on PWs—identified by parameter sensitivity analysis—in an existing database of in silico PWs representative of subjects without AAAs. Then, a machine learning architecture for AAA detection was trained and tested using the new in silico PW database. The parameter sensitivity analysis revealed that the AAA maximum diameter and stiffness of the large systemic arteries were the dominant AAA-related biophysical properties considerably influencing the PWs. However, AAA detection by PW indexes was compromised by other non-AAA related cardiovascular parameters. The proposed machine learning model produced a sensitivity of 86.8 % and a specificity of 86.3 % in early detection of AAA from the photoplethysmogram PW signal measured in the digital artery with added random noise. The number of false positive and negative results increased with increasing age and decreasing AAA size, respectively. These findings suggest that machine learning-based PW analysis is a promising approach for AAA screening using PW signals acquired by wearable devices.

Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype

Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.

Effects of size and elasticity on the relation between flow velocity and wall shear stress in side-wall aneurysms: A lattice Boltzmann-based computer simulation study

Blood flow in an artery is a fluid-structure interaction problem. It is widely accepted that aneurysm formation, enlargement and failure are associated with wall shear stress (WSS) which is exerted by flowing blood on the aneurysmal wall. To date, the combined effect of aneurysm size and wall elasticity on intra-aneurysm (IA) flow characteristics, particularly in the case of side-wall aneurysms, is poorly understood. Here we propose a model of three-dimensional viscous flow in a compliant artery containing an aneurysm by employing the immersed boundary-lattice Boltzmann-finite element method. This model allows to adequately account for the elastic deformation of both the blood vessel and aneurysm walls. Using this model, we perform a detailed investigation of the flow through aneurysm under different conditions with a focus on the parameters which may influence the wall shear stress. Most importantly, it is shown in this work that the use of flow velocity as a proxy for wall shear stress is well justified only in those sections of the vessel which are close to the ideal cylindrical geometry. Within the aneurysm domain, however, the correlation between wall shear stress and flow velocity is largely lost due to the complexity of the geometry and the resulting flow pattern. Moreover, the correlations weaken further with the phase shift between flow velocity and transmural pressure. These findings have important implications for medical applications since wall shear stress is believed to play a crucial role in aneurysm rupture.

Patient-Specific Prediction of Abdominal Aortic Aneurysm Expansion Using Bayesian Calibration

Translating recent advances in abdominal aortic aneurysm (AAA) growth and remodeling (G&R) knowledge into a predictive, patient-specific clinical treatment tool requires a major paradigm shift in computational modeling. The objectives of this study are to develop a prediction framework that first calibrates the physical AAA G&R model using patient-specific serial computed tomography (CT) scan images, predicts the expansion of an AAA in the future, and quantifies the associated uncertainty in the prediction. We adopt a Bayesian calibration method to calibrate parameters in the G&R computational model and predict the magnitude of AAA expansion. The proposed Bayesian approach can take different sources of uncertainty; therefore, it is well suited to achieve our aims in predicting the AAA expansion process as well as in computing the propagated uncertainty. We demonstrate how to achieve the proposed aims by solving the formulated Bayesian calibration problems for cases with the synthetic G&R model output data and real medical patient-specific CT data. We compare and discuss the performance of predictions and computation time under different sampling cases of the model output data and patient data, both of which are simulated by the G&R computation. Furthermore, we apply our Bayesian calibration to real patient-specific serial CT data and validate our prediction. The accuracy and efficiency of the proposed method is promising, which appeals to computational and medical communities.

A chemo-mechano-biological formulation for the effects of biochemical alterations on arterial mechanics: the role of molecular transport and multiscale tissue remodelling

This paper presents a chemo-mechano-biological framework for arterial physiopathology. The model accounts for the fine remodelling in the multiscale hierarchical arrangement of tissue constituents and for the diffusion of molecular species involved in cell-cell signalling pathways. Effects in terms of alterations in arterial compliance are obtained. A simple instructive example is introduced. Although oversimplified with respect to realistic case studies, the proposed application mimics the biochemical activity of matrix metalloproteinases, transforming growth factors beta and interleukins on tissue remodelling. Effects of macrophage infiltration, of intimal thickening and of a healing phase are investigated, highlighting the corresponding influence on arterial compliance. The obtained results show that the present approach is able to capture changes in arterial mechanics as a consequence of the alterations in tissue biochemical environment and cellular activity, as well as to incorporate the protective role of both autoimmune responses and pharmacological treatments.

The impact of personalized probabilistic wall thickness models on peak wall stress in abdominal aortic aneurysms

If computational models are ever to be used in high-stakes decision making in clinical practice, the use of personalized models and predictive simulation techniques is a must. This entails rigorous quantification of uncertainties as well as harnessing available patient-specific data to the greatest extent possible. Although researchers are beginning to realize that taking uncertainty in model input parameters into account is a necessity, the predominantly used probabilistic description for these uncertain parameters is based on elementary random variable models. In this work, we set out for a comparison of different probabilistic models for uncertain input parameters using the example of an uncertain wall thickness in finite element models of abdominal aortic aneurysms. We provide the first comparison between a random variable and a random field model for the aortic wall and investigate the impact on the probability distribution of the computed peak wall stress. Moreover, we show that the uncertainty about the prevailing peak wall stress can be reduced if noninvasively available, patient-specific data are harnessed for the construction of the probabilistic wall thickness model.

A new inverse method for estimation of in vivo mechanical properties of the aortic wall

The aortic wall is always loaded in vivo, which makes it challenging to estimate the material parameters of its nonlinear, anisotropic constitutive equation from in vivo image data. Previous approaches largely relied on either computationally expensive finite element models or simplifications of the geometry or material models. In this study, we investigated a new inverse method based on aortic wall stress computation. This approach consists of the following two steps: (1) computing an "almost true" stress field from the in vivo geometries and loading conditions, (2) building an objective function based on the "almost true" stress fields, constitutive equations and deformation relations, and estimating the material parameters by minimizing the objective function. The method was validated through numerical experiments by using the in vivo data from four ascending aortic aneurysm (AsAA) patients. The results demonstrated that the method is computationally efficient. This novel approach may facilitate the personalized biomechanical analysis of aortic tissues in clinical applications, such as in the rupture risk analysis of ascending aortic aneurysms.

Biomechanical rupture risk assessment of abdominal aortic aneurysms based on a novel probabilistic rupture risk index

A rupture risk assessment is critical to the clinical treatment of abdominal aortic aneurysm (AAA) patients. The biomechanical AAA rupture risk assessment quantitatively integrates many known AAA rupture risk factors but the variability of risk predictions due to model input uncertainties remains a challenging limitation. This study derives a probabilistic rupture risk index (PRRI). Specifically, the uncertainties in AAA wall thickness and wall strength were considered, and wall stress was predicted with a state-of-the-art deterministic biomechanical model. The discriminative power of PRRI was tested in a diameter-matched cohort of ruptured (n = 7) and intact (n = 7) AAAs and compared to alternative risk assessment methods. Computed PRRI at 1.5 mean arterial pressure was significantly (p = 0.041) higher in ruptured AAAs (20.21(s.d. 14.15%)) than in intact AAAs (3.71(s.d. 5.77)%). PRRI showed a high sensitivity and specificity (discriminative power of 0.837) to discriminate between ruptured and intact AAA cases. The underlying statistical representation of stochastic data of wall thickness, wall strength and peak wall stress had only negligible effects on PRRI computations. Uncertainties in AAA wall stress predictions, the wide range of reported wall strength and the stochastic nature of failure motivate a probabilistic rupture risk assessment. Advanced AAA biomechanical modelling paired with a probabilistic rupture index definition as known from engineering risk assessment seems to be superior to a purely deterministic approach.

A novel chemo-mechano-biological model of arterial tissue growth and remodelling

Arterial growth and remodelling (G&R) is mediated by vascular cells in response to their chemical and mechanical environment. To date, mechanical and biochemical stimuli tend to be modelled separately, however this ignores their complex interplay. Here, we present a novel mathematical model of arterial chemo-mechano-biology. We illustrate its application to the development of an inflammatory aneurysm in the descending human aorta. The arterial wall is modelled as a bilayer cylindrical non-linear elastic membrane, which is internally pressurised and axially stretched. The medial degradation that accompanies aneurysm development is driven by an inflammatory response. Collagen remodelling is simulated by adaption of the natural reference configuration of constituents; growth is simulated by changes in normalised mass-densities. We account for the distribution of attachment stretches that collagen fibres are configured to the matrix and, innovatively, allow this distribution to remodel. This enables the changing functional role of the adventitia to be simulated. Fibroblast-mediated collagen growth is represented using a biochemical pathway model: a system of coupled non-linear ODEs governs the evolution of fibroblast properties and levels of key biomolecules under the regulation of Transforming Growth Factor (TGF)-β, a key promoter of matrix deposition. Given physiologically realistic targets, different modes of aneurysm development can be captured, while the predicted evolution of biochemical variables is qualitatively consistent with trends observed experimentally. Interestingly, we observe that increasing the levels of collagen-promoting TGF-β results in arrest of aneurysm growth, which seems to be consistent with experimental evidence. We conclude that this novel Chemo-Mechano-Biological (CMB) mathematical model has the potential to provide new mechanobiological insight into vascular disease progression and therapy.

Patient-specific modelling of abdominal aortic aneurysms: The influence of wall thickness on predicted clinical outcomes

Rupture of abdominal aortic aneurysms (AAAs) is linked to aneurysm morphology. This study investigates the influence of patient-specific (PS) AAA wall thickness on predicted clinical outcomes. Eight patients under surveillance for AAAs were selected from the MA(3)RS clinical trial based on the complete absence of intraluminal thrombus. Two finite element (FE) models per patient were constructed; the first incorporated variable wall thickness from CT (PS_wall), and the second employed a 1.9mm uniform wall (Uni_wall). Mean PS wall thickness across all patients was 1.77±0.42mm. Peak wall stress (PWS) for PS_wall and Uni_wall models was 0.6761±0.3406N/mm(2) and 0.4905±0.0850N/mm(2), respectively. In 4 out of 8 patients the Uni_wall underestimated stress by as much as 55%; in the remaining cases it overestimated stress by up to 40%. Rupture risk more than doubled in 3 out of 8 patients when PS_wall was considered. Wall thickness influenced the location and magnitude of PWS as well as its correlation with curvature. Furthermore, the volume of the AAA under elevated stress increased significantly in AAAs with higher rupture risk indices. This highlights the sensitivity of standard rupture risk markers to the specific wall thickness strategy employed.

Aneurysm strength can decrease under calcification

Aneurysms are abnormal dilatations of vessels in the vascular system that are prone to rupture. Prediction of the aneurysm rupture is a challenging and unsolved problem. Various factors can lead to the aneurysm rupture and, in the present study, we examine the effect of calcification on the aneurysm strength by using micromechanical modeling. The calcified tissue is considered as a composite material in which hard calcium particles are embedded in a hyperelastic soft matrix. Three experimentally calibrated constitutive models incorporating a failure description are used for the matrix representation. Two constitutive models describe the aneurysmal arterial wall and the third one - the intraluminal thrombus. The stiffness and strength of the calcified tissue are simulated in uniaxial tension under the varying amount of calcification, i.e. the relative volume of the hard inclusion within the periodic unit cell. In addition, the triaxiality of the stress state, which can be a trigger for the cavitation instability, is tracked. Results of the micromechanical simulation show an increase of the stiffness and a possible decrease of the strength of the calcified tissue as compared to the non-calcified one. The obtained results suggest that calcification (i.e. the presence of hard particles) can significantly affect the stiffness and strength of soft tissue. The development of refined experimental techniques that will allow for the accurate quantitative assessment of calcification is desirable.

Effects of arterial blood flow on walls of the abdominal aorta: distributions of wall shear stress and oscillatory shear index determined by phase-contrast magnetic resonance imaging

Although abdominal aortic aneurysms (AAAs) occur mostly inferior to the renal artery, the mechanism of the development of AAA in relation to its specific location is not yet clearly understood. The objective of this study was to evaluate the hypothesis that even healthy volunteers may manifest specific flow characteristics of blood flow and alter wall shear or oscillatory shear stress in the areas where AAAs commonly develop. Eight healthy male volunteers were enrolled in this prospective study, aged from 24 to 27. Phase-contrast magnetic resonance imaging (MRI) was performed with electrocardiographic triggering. Flow-sensitive four-dimensional MR imaging of the abdominal aorta, with three-directional velocity encoding, including simple morphological image acquisition, was performed. Information on specific locations on the aortic wall was applied to the flow encodes to calculate wall shear stress (WSS) and oscillatory shear index (OSI). While time-framed WSS showed the highest peak of 1.14 ± 0.25 Pa in the juxtaposition of the renal artery, the WSS plateaued to 0.61 Pa at the anterior wall of the abdominal aorta. The OSI peaked distal to the renal arteries at the posterior wall of the abdominal aorta of 0.249 ± 0.148, and was constantly elevated in the whole abdominal aorta at more than 0.14. All subjects were found to have elevated OSI in regions where AAAs commonly occur. These findings indicate that areas of constant peaked oscillatory shear stress in the infra-renal aorta may be one of the factors that lead to morphological changes over time, even in healthy individuals.

A Review of Computational Methods to Predict the Risk of Rupture of Abdominal Aortic Aneurysms

Computational methods have played an important role in health care in recent years, as determining parameters that affect a certain medical condition is not possible in experimental conditions in many cases. Computational fluid dynamics (CFD) methods have been used to accurately determine the nature of blood flow in the cardiovascular and nervous systems and air flow in the respiratory system, thereby giving the surgeon a diagnostic tool to plan treatment accordingly. Machine learning or data mining (MLD) methods are currently used to develop models that learn from retrospective data to make a prediction regarding factors affecting the progression of a disease. These models have also been successful in incorporating factors such as patient history and occupation. MLD models can be used as a predictive tool to determine rupture potential in patients with abdominal aortic aneurysms (AAA) along with CFD-based prediction of parameters like wall shear stress and pressure distributions. A combination of these computer methods can be pivotal in bridging the gap between translational and outcomes research in medicine. This paper reviews the use of computational methods in the diagnosis and treatment of AAA.

Cavitation instability as a trigger of aneurysm rupture

Aneurysm formation and growth is accompanied by microstructural alterations in the arterial wall. Particularly, the loss of elastin may lead to tissue disintegration and appearance of voids or cavities at the micron scale. Unstable growth and coalescence of voids may be a predecessor and trigger for the onset of macroscopic cracks. In the present work, we analyze the instability of membrane (2D) and bulk (3D) voids under hydrostatic tension by using two experimentally calibrated constitutive models of abdominal aortic aneurysm enhanced with energy limiters. The limiters provide the saturation value for the strain energy, which indicates the maximum energy that can be stored and dissipated by an infinitesimal material volume. We find that the unstable growth of voids can start when the critical stress is considerably less than the aneurysm strength. Moreover, this critical stress may even approach the arterial wall stress in the physiological range. This finding suggests that cavitation instability can be a rational indicator of the aneurysm rupture.

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.

Monitoring and staging abdominal aortic aneurysm disease with pulse wave imaging

The abdominal aortic aneurysm (AAA) is a silent and often deadly vascular disease caused by the localized weakening of the arterial wall. Previous work has indicated that local changes in wall stiffness can be detected with pulse wave imaging (PWI), which is a non-invasive technique for tracking the propagation of pulse waves along the aorta at high spatial and temporal resolutions. The aim of this study was to assess the capability of PWI to monitor and stage AAA progression in a murine model of the disease. ApoE/TIMP-1 knockout mice (N = 18) were given angiotensin II for 30 days via subcutaneously implanted osmotic pumps. The suprarenal sections of the abdominal aortas were imaged every 2-3 d after implantation using a 30-MHz VisualSonics Vevo 770 with 15-μm lateral resolution. Pulse wave propagation was monitored at an effective frame rate of 8 kHz by using retrospective electrocardiogram gating and by performing 1-D cross-correlation on the radiofrequency signals to obtain the displacements induced by the waves. In normal aortas, the pulse waves propagated at constant velocities (2.8 ± 0.9 m/s, r(2) = 0.89 ± 0.11), indicating that the composition of these vessels was relatively homogeneous. In the mice that developed AAAs (N = 10), the wave speeds in the aneurysm sac were 45% lower (1.6 ± 0.6 m/s) and were more variable (r(2) = 0.66 ± 0.23). Moreover, the wave-induced wall displacements were at least 80% lower within the sacs compared with the surrounding vessel. Finally, in mice that developed fissures (N = 5) or ruptures (N = 3) at the sites of their AAA, higher displacements directed out of the lumen and with no discernible wave pattern (r(2) < 0.20) were observed throughout the cardiac cycle. These findings indicate that PWI can be used to distinguish normal murine aortas from aneurysmal, fissured and ruptured ones. Hence, PWI could potentially be used to monitor and stage human aneurysms by providing information complementary to standard B-mode ultrasound.

Modeling rupture of growing aneurysms

Growth and rupture of aneurysms are driven by micro-structural alterations of the arterial wall yet precise mechanisms underlying the process remain to be uncovered. In the present work we examine a scenario when the aneurysm evolution is dominated by turnover of collagen fibers. In the latter case it is natural to hypothesize that rupture of individual fibers (or their bonds) causes the overall aneurysm rupture. We examine this hypothesis in computer simulations of growing aneurysms in which constitutive equations describe both collagen evolution and failure. Failure is enforced in constitutive equations by limiting strain energy that can be accumulated in a fiber. Within the proposed theoretical framework we find a range of parameters that lead to the aneurysm rupture. We conclude in a qualitative agreement with clinical observations that some aneurysms will rupture while others will not.

Microscale fiber network alignment affects macroscale failure behavior in simulated collagen tissue analogs

A tissue's microstructure determines its failure properties at larger length scales, however, the specific relationship between microstructure and macroscopic failure in native and engineered soft tissues (such as capsular ligaments, aortic aneurysms, or vascular grafts) has proven elusive. In this study, variations in the microscale fiber alignment in collagen gel tissue analogs were modeled in order to understand their effects on macroscale damage and failure outcomes. The study employed a multiscale finite-element (FE) model for damage and failure in collagen-based materials. The model relied on microstructural representative volume elements (RVEs) that consisted of stochastically-generated networks of discrete type-I collagen fibers. Fiber alignment was varied within RVEs and between layers of RVEs in a macroscopic FE model of a notched dogbone geometry. The macroscale stretch and the microscale response of fibers for each of the differently aligned cases were compared as the dogbone was uniaxially extended to failure. Networks with greater fiber alignment parallel to the direction of extension failed at smaller strains (with a 6-22% reduction in the Green strain at failure), however, at greater grip forces (a 28-60% increase) than networks with fibers aligned perpendicular to the extension. Alternating layers of crisscrossed network alignments (aligned ±45 deg to the direction of extension) failed at smaller strains but at greater grip forces than those created using one fiber alignment type. In summary, variations in microscale structure via fiber alignment produced different macroscale failure trends. To conclude, these findings may be significant in the realm of tissue engineering and in soft tissue biomechanics.

On the Stability of Lung Parenchymal Lesions with Applications to Early Pneumothorax Diagnosis

Spontaneous pneumothorax, a prevalent medical challenge in most trauma cases, is a form of sudden lung collapse closely associated with risk factors such as lung cancer and emphysema. Our work seeks to explore and quantify the currently unknown pathological factors underlying lesion rupture in pneumothorax through biomechanical modeling. We hypothesized that lesion instability is closely associated with elastodynamic strain of the pleural membrane from pulsatile air flow and collagen-elastin dynamics. Based on the principles of continuum mechanics and fluid-structure interaction, our proposed model coupled isotropic tissue deformation with pressure from pulsatile air motion and the pleural fluid. Next, we derived mathematical instability criteria for our ordinary differential equation system and then translated these mathematical instabilities to physically relevant structural instabilities via the incorporation of a finite energy limiter. The introduction of novel biomechanical descriptions for collagen-elastin dynamics allowed us to demonstrate that changes in the protein structure can lead to a transition from stable to unstable domains in the material parameter space for a general lesion. This result allowed us to create a novel streamlined algorithm for detecting material instabilities in transient lung CT scan data via analyzing deformations in a local tissue boundary.

Opportunities in abdominal aortic aneurysm research: epidemiology, genetics, and pathophysiology

Aortic aneurysms are a complex genetic disorder with known environmental risk factors such as smoking. Along the length of the aorta, significant heterogeneity occurs in the distribution of aneurysmal disease. The prevalence of aneurysm in the abdominal aorta is at least nine times higher than that in the thoracic section of the aorta. A number of studies have shown that aortic aneurysms are frequently familial, even when they are not associated with rare heritable disorders such as Marfan syndrome or Ehlers-Danlos syndrome type IV. The pathobiology of aortic aneurysms is complex and largely unsolved. Unbiased whole-genome approaches are now being used to elucidate the genetic basis of aortic aneurysms to uncover the germline genetic variants that influence the disease risk. The findings will provide critical information about underlying biology of the disease and will help identify potential targets for pharmacological therapies. These studies may lead to therapies that may increase survival rates for individuals with aortic aneurysms and reduce the need for surgical interventions. Abdominal aortic aneurysms were the topic of an international conference "Abdominal Aortic Aneurysm: Epidemiology, Genetics, and Pathophysiology" held recently at the Geisinger Clinic, Danville, Pennsylvania.

Characterization of fracture toughness exhaustion in pig aorta

BACKGROUND

Spontaneous rupture of the aorta (SRA) without aneurysm, dissection, inflammation or infection of the aortic wall can be of two types: traumatic and non-traumatic. SRA is most of the time a fatal event. Consequently, it is important to understand the conditions which lead to the aortic rupture, and, in the case of non-traumatic SRA, to predict the temporal likelihood of rupture.

METHOD OF APPROACH

The present work incorporates the temporal aspect by examining the effects of fatigue on aortic wall properties, and adopts an energy approach, based on fracture toughness, to evaluate the aorta's resistance to rupture. Fracture toughness characterization is a destructive testing process and as a consequence cannot be implemented as a clinical tool. However, using concepts in damage mechanics, in theory, it should be possible to indirectly assess fracture toughness from other mechanical properties, such as aortic wall stiffness. Tissue samples from non-aneurysmal porcine aortas were fatigued and were subjected to both biaxial and guillotine tests to assess wall stiffness variations and fracture toughness exhaustion, respectively.

RESULTS

The experiments reveal that aortic wall stiffness variations and fracture toughness exhaustion decreased as a function of loading cycles and can be modeled with exponential functions. After one million loading cycles, the stiffness ratio between the non-fatigued sample and the fatigued sample, dropped to about 0.85, while the fracture toughness ratio counterpart fell to about 0.80.

CONCLUSION

Consequently, the changes in both stiffness and fracture toughness as a function of applied fatigue cycles can be measured in aortic tissues. Moreover, these results suggest the possibility to use fracture toughness exhaustion curves as a fatigue criterion.

A literature review of the numerical analysis of abdominal aortic aneurysms treated with endovascular stent grafts

The purpose of this paper is to present the basic principles and relevant advances in the computational modeling of abdominal aortic aneurysms and endovascular aneurysm repair, providing the community with up-to-date state of the art in terms of numerical analysis and biomechanics. Frameworks describing the mechanical behavior of the aortic wall already exist. However, intraluminal thrombus nonhomogeneous structure and porosity still need to be well characterized. Also, although the morphology and mechanical properties of calcifications have been investigated, their effects on wall stresses remain controversial. Computational fluid dynamics usually assumes a rigid artery wall, whereas fluid-structure interaction accounts for artery compliance but is still challenging since arteries and blood have similar densities. We discuss alternatives to fluid-structure interaction based on dynamic medical images that address patient-specific hemodynamics and geometries. We describe initial stresses, elastic boundary conditions, and statistical strength for rupture risk assessment. Special emphasis is accorded to workflow development, from the conversion of medical images into finite element models, to the simulation of catheter-aorta interactions and stent-graft deployment. Our purpose is also to elaborate the key ingredients leading to virtual stenting and endovascular repair planning that could improve the procedure and stent-grafts.

Turnover of fibrillar collagen in soft biological tissue with application to the expansion of abdominal aortic aneurysms

A better understanding of the inherent properties of vascular tissue to adapt to its mechanical environment is crucial to improve the predictability of biomechanical simulations. Fibrillar collagen in the vascular wall plays a central role in tissue adaptation owing to its relatively short lifetime. Pathological alterations of collagen turnover may fail to result in homeostasis and could be responsible for abdominal aortic aneurysm (AAA) growth at later stages of the disease. For this reason our previously reported multiscale constitutive framework (Martufi, G. & Gasser, T. C. 2011 J. Biomech. 44, 2544-2550 (doi:10.1016/j.jbiomech.2011.07.015)) has been enriched by a collagen turnover model. Specifically, the framework's collagen fibril level allowed a sound integration of vascular wall biology, and the impact of collagen turnover on the macroscopic properties of AAAs was studied. To this end, model parameters were taken from the literature and/or estimated from clinical follow-up data of AAAs (on average 50.7 mm-large). Likewise, the in vivo stretch of the AAA wall was set, such that 10 per cent of collagen fibres were engaged. Results showed that the stretch spectrum, at which collagen fibrils are deposed, is the most influential parameter, i.e. it determines whether the vascular geometry grows, shrinks or remains stable over time. Most importantly, collagen turnover also had a remarkable impact on the macroscopic stress field. It avoided high stress gradients across the vessel wall, thus predicted a physiologically reasonable stress field. Although the constitutive model could be successfully calibrated to match the growth of small AAAs, a rigorous validation against experimental data is crucial to further explore the model's descriptive and predictive capabilities.

A three-layer model for buckling of a human aortic segment under specific flow-pressure conditions

Human aortas are subjected to large mechanical stresses because of blood flow pressurization and through contact with the surrounding tissue. It is essential that the aorta does not lose stability by buckling with deformation of the cross-section (shell-like buckling) (i) for its proper functioning to ensure blood flow and (ii) to avoid high stresses in the aortic wall. A numerical bifurcation analysis employs a refined reduced-order model to investigate the stability of a straight aorta segment conveying blood flow. The structural model assumes a nonlinear cylindrical orthotropic laminated composite shell composed of three layers representing the tunica intima, media and adventitia. Residual stresses because of pressurization are evaluated and included in the model. The fluid is formulated using a hybrid model that contains the unsteady effects obtained from linear potential flow theory and the steady viscous effects obtained from the time-averaged Navier-Stokes equations. The aortic segment loses stability by divergence with deformation of the cross-section at a critical flow velocity for a given static pressure, exhibiting a strong subcritical behaviour with partial or total collapse of the inner wall. Preliminary results suggest directions for further study in relation to the appearance and growth of dissection in the aorta.

Correlation of biomechanics to tissue reaction in aortic aneurysms assessed by finite elements and [18F]-fluorodeoxyglucose-PET/CT

Mechanobiological interactions are essential for the adaption of the cardiovascular system to altered environmental and internal conditions, but are poorly understood with regard to abdominal aortic aneurysm (AAA) pathogenesis, growth and rupture. In the present study, we therefore calculated mechanical AAA quantities using nonlinear finite element methods and correlated these to [18F]-fluorodeoxyglucose (FDG)-metabolic activity in the AAA wall detected by positron emission tomography/computed tomography (PET/CT). The interplay between mechanics and FDG-metabolic activity was analyzed in terms of maximum values and the three-dimensional spatial relationship, respectively. Fluorodeoxyglucose-positron emission tomography/computed tomography (FDG-PET/CT) data sets of n = 18 AAA patients were studied. Maximum FDG-uptake (SUV max ) in the AAA wall varied from 1.32 to 4.60 (average SUV max 3.31 ± 0.87). Maximum wall stresses and strains ranged from 10.0 to 64.0 N∕cm(2) (38.2 ± 13.8  N∕cm(2)) and from 0.190 to 0.260 (0.222 ± 0.023), respectively. SUV max was significantly correlated to maximum wall stress and strain (SUV max to stress: r = 0.71, p = 0.0005; SUV max to strain: r = 0.66, p = 0.0013). To evaluate the three-dimensional spatial interaction between FDG-uptake and acting wall stress, element-wise correlations were performed. In all but 2 AAAs, positive element-wise correlation of FDG-uptake to wall stress was obtained, with the Pearson's correlation coefficient ranging from -0.168 to 0.738 ( 0.372 ± 0.263). The results indicate that mechanical stresses are correlated quantitatively and spatially to FDG-uptake in the AAA wall. It is hypothesized that unphysiologically increased loading in the AAA wall triggers biological tissue reaction, such as inflammation or regenerative processes, causing elevated FDG-metabolic activity. These findings strongly support experimental hypotheses of mechanotransduction mechanisms in vivo.

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.

Effects of dispersion of fiber orientation on the mechanical property of the arterial wall

Effects of dispersion of the fiber orientation on the mechanical property of the arterial wall in health and disease subjected to the combined internal pressure and axial loading are examined within the framework of the finite deformation hyper-elasticity theory. Taking into account the residual stress, a two layer thick-walled circular cylindrical tube model with the fiber-reinforced incompressible composite hyper-elastic material is employed. Stress-radius curves and stress distributions of the arterial wall are given in health and disease considering dispersion of the fiber orientation. With instability/bifurcation analysis, it is found that not only the uniform inflation of the arterial wall in health, but also the instability or bifurcation problem for the arterial wall in disease may be described by this model.

A continuum description of the damage process in the arterial wall of abdominal aortic aneurysms

In the present work, we develop a three-dimensional isotropic finite-strain damage model for abdominal aortic aneurysm (AAA) wall that considers both the characteristic softening of the material caused by damage and the spatial variation of the material properties. A strain energy function is formulated that accounts for a hyperelastic, slightly compressible, isotropic material behavior during the elastic phase, whereas the damage process only contributes to the material response when the elastic limit of the AAA wall is exceeded. Material and damage parameters are obtained by fitting the strain energy function to the experimental data obtained by uniaxial tensile tests of freshly harvested AAA wall samples. The damage model extends the validity of the material law to a strain range of up to 50%. Purely elastic material laws for AAA wall are only valid for a strain range of up to 17%. In a series of finite element simulations of patient-specific AAAs, serving as numerical examples, we investigate the applicability of the damage model. The use of the damage model does not yield a more distinct identification of rupture-prone AAAs than other computational-based risk indices. However, the benefit of the finite-strain damage model is the potential capability to trigger growth and remodeling processes in mechanobiological models.

An irreversible constitutive model for fibrous soft biological tissue: a 3-D microfiber approach with demonstrative application to abdominal aortic aneurysms

Understanding the failure and damage mechanisms of soft biological tissue is critical to a sensitive and specific characterization of tissue injury tolerance and its relation to biological responses. Despite increasing experimental and analytical efforts, failure-related irreversible effects of soft biological tissue are still poorly understood. There is still no clear definition of what "damage" of a soft biological material is, and conventional macroscopic indicators, as known from damage of engineering materials for example, may not identify the tissue's tolerance to injury appropriately. To account for the complex three-dimensional arrangement of collagen, a microfiber model approach is applied, where constitutive relations for collagen fibers are integrated over the unit sphere, which in turn defines the tissue's macroscopic properties. A collagen fiber is represented by a bundle of proteoglycan cross-linked collagen fibrils that undergoes irreversible deformations when exceeding its elastic tensile limit. The proposed constitutive model is able to predict strain stiffening at physiological strain levels and does not exhibit a clear macroscopic elastic limit, two typical features known from soft biological tissue testing. An elastic-predictor/plastic-corrector implementation of the model is followed and constitutive parameters are estimated from in vitro test data from a particular abdominal aortic aneurysm (AAA). Damage-based structural instabilities of the AAA under different inflation conditions are investigated, where the collagen orientation density has been estimated from its in vivo stress state.

Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms

A fluid-solid-growth (FSG) model of saccular cerebral aneurysm evolution is developed. It utilises a realistic two-layered structural model of the internal carotid artery and explicitly accounts for the degradation of the elastinous constituents and growth and remodelling (G&R) of the collagen fabric. Aneurysm inception is prescribed: a localised degradation of elastin results in a perturbation in the arterial geometry; the collagen fabric adapts, and the artery achieves a new homeostatic configuration. The perturbation to the geometry creates an altered haemodynamic environment. Subsequent degradation of elastin is explicitly linked to low wall shear stress (WSS) in a confined region of the arterial domain. A sidewall saccular aneurysm develops, the collagen fabric adapts and the aneurysm stabilises in size. A quasi-static analysis is performed to determine the geometry at diastolic pressure. This enables the cyclic stretching of the tissue to be quantified, and we propose a novel index to quantify the degree of biaxial stretching of the tissue. Whilst growth is linked to low WSS from a steady (systolic) flow analysis, a pulsatile flow analysis is performed to compare steady and pulsatile flow parameters during evolution. This model illustrates the evolving mechanical environment for an idealised saccular cerebral aneurysm developing on a cylindrical parent artery and provides the guidance to more sophisticated FSG models of aneurysm evolution which link G&R to the local mechanical stimuli of vascular cells.