Numerical modelling of fracture in human arteries

On the Importance of Including Cohesive Zone Models in Modelling Mixed-Mode Aneurysm Rupture

INTRODUCTION

The precise mechanism of rupture in abdominal aortic aneurysms (AAAs) has not yet been uncovered. The phenomenological failure criterion of the coefficient of proportionality between von Mises stress and tissue strength does not account for any mechanistic foundation of tissue fracture. Experimental studies have shown that arterial failure is a stepwise process of fibrous delamination (mode II) and kinking (mode I) between layers. Such a mechanism has not previously been considered for AAA rupture.

METHODS

In the current study we consider both von Mises stress in the wall, in addition to interlayer tractions and delamination using cohesive zone models. Firstly, we present a parametric investigation of the influence of a range of AAA anatomical features on the likelihood of elevated interlayer traction and delamination.

RESULTS

We observe in several cases that the location of peak von Mises stress and tangential traction coincide. Our simulations also reveal however, that peak von Mises and intramural tractions are not coincident for aneurysms with Length/Radius less than 2 (short high-curvature aneurysms) and for aneurysms with symmetric intraluminal thrombus (ILT). For an aneurysm with (L/R = 2.0), the peak σ vm moves slightly towards the origin while the peak T t is near the peak bulge with a separation distance of ~ 17 mm. Additionally, we present three patient-specific AAA models derived directly from CT scans, which also illustrate that the location of von Mises stress does not correlate with the point of interlayer delamination.

CONCLUSION

This study suggests that incorporating cohesive zone models into clinical based FE analyses may capture a greater proportion of ruptures in-silico.

Fracture of the porcine aorta. Part 2: FEM modelling and inverse parameter identification

The mechanics of vascular tissue, particularly its fracture properties, are crucial in the onset and progression of vascular diseases. Vascular tissue properties are complex, and the identification of fracture mechanical properties relies on robust and efficient numerical tools. In this study, we propose a parameter identification pipeline to extract tissue properties from force-displacement and digital image correlation (DIC) data. The data has been acquired by symconCT testing porcine aorta wall specimens. Vascular tissue is modelled as a non-linear viscoelastic isotropic solid, and an isotropic cohesive zone model describes tissue fracture. The model closely replicated the experimental observations and identified the fracture energies of 1.57±0.82 kJ m^-2 and 0.96±0.34 kJ m^-2 for rupturing the porcine aortic media along the axial and circumferential directions, respectively. The identified strength was always below 350 kPa, a value significantly lower than identified through classical protocols, such as simple tension, and sheds new light on the resilience of the aorta. Further refinements to the model, such as considering rate effects in the fracture process zone and tissue anisotropy, could have improved the simulation results. STATEMENT OF SIGNIFICANCE: This paper identified porcine aorta's biomechanical properties using data acquired through a previously developed experimental protocol, the symmetry-constraint compact tension test. An implicit finite element method model mimicked the test, and a two-step approach identified the material's elastic and fracture properties directly from force-displacement curves and digital image correlation-based strain measurements. Our findings show a lower strength of the abdominal aorta as compared to the literature, which may have significant implications for the clinical evaluation of the risk of aortic rupture.

Long-term prognostic impact of paravalvular leakage on coronary artery disease requires patient-specific quantification of hemodynamics

Transcatheter aortic valve replacement (TAVR) is a frequently used minimally invasive intervention for patient with aortic stenosis across a broad risk spectrum. While coronary artery disease (CAD) is present in approximately half of TAVR candidates, correlation of post-TAVR complications such as paravalvular leakage (PVL) or misalignment with CAD are not fully understood. For this purpose, we developed a multiscale computational framework based on a patient-specific lumped-parameter algorithm and a 3-D strongly-coupled fluid-structure interaction model to quantify metrics of global circulatory function, metrics of global cardiac function and local cardiac fluid dynamics in 6 patients. Based on our findings, PVL limits the benefits of TAVR and restricts coronary perfusion due to the lack of sufficient coronary blood flow during diastole phase (e.g., maximum coronary flow rate reduced by 21.73%, 21.43% and 21.43% in the left anterior descending (LAD), left circumflex (LCX) and right coronary artery (RCA) respectively (N = 6)). Moreover, PVL may increase the LV load (e.g., LV load increased by 17.57% (N = 6)) and decrease the coronary wall shear stress (e.g., maximum wall shear stress reduced by 20.62%, 21.92%, 22.28% and 25.66% in the left main coronary artery (LMCA), left anterior descending (LAD), left circumflex (LCX) and right coronary artery (RCA) respectively (N = 6)), which could promote atherosclerosis development through loss of the physiological flow-oriented alignment of endothelial cells. This study demonstrated that a rigorously developed personalized image-based computational framework can provide vital insights into underlying mechanics of TAVR and CAD interactions and assist in treatment planning and patient risk stratification in patients.

A Review on Damage and Rupture Modelling for Soft Tissues

Computational modelling of damage and rupture of non-connective and connective soft tissues due to pathological and supra-physiological mechanisms is vital in the fundamental understanding of failures. Recent advancements in soft tissue damage models play an essential role in developing artificial tissues, medical devices/implants, and surgical intervention practices. The current article reviews the recently developed damage models and rupture models that considered the microstructure of the tissues. Earlier review works presented damage and rupture separately, wherein this work reviews both damage and rupture in soft tissues. Wherein the present article provides a detailed review of various models on the damage evolution and tear in soft tissues focusing on key conceptual ideas, advantages, limitations, and challenges. Some key challenges of damage and rupture models are outlined in the article, which helps extend the present damage and rupture models to various soft tissues.

Potential damage in pulmonary arterial hypertension: An experimental study of pressure-induced damage of pulmonary artery

Pulmonary arterial hypertension (PAH) is associated with elevated pulmonary arterial pressure. PAH prognosis remains poor with a 15% mortality rate within 1 year, even with modern clinical management. Previous clinical studies proposed wall shear stress (WSS) to be an important hemodynamic factor affecting cell mechanotransduction, growth and remodeling, and disease progress in PAH. However, WSS in vivo is typically at most 2.5 Pa and a doubt has been cast whether WSS alone can drive disease progress. Furthermore, our current understanding of PAH pathology largely comes from small animals' studies in which caliber enlargement, a hallmark of PAH in humans, is rarely reported. Therefore, a large-animal experiment on pulmonary arteries (PAs) is needed to validate whether increased pressure can induce enlargement of PAs caliber. In this study, we use an inflation testing device to characterize the mechanical behavior, both nonlinear elastic behavior and irreversible damage of porcine arteries. The parameters of elastic behavior are estimated from the inflation test at a low-pressure range before and after over-pressurization. Then, histological images are qualitatively examined for medial and adventitial layers. This study sheds light on the relevance of pressure-induced damage mechanism in human PAH.

Review of Current Advances in the Mechanical Description and Quantification of Aortic Dissection Mechanisms

Aortic dissection is a life-threatening event associated with a very poor outcome. A number of complex phenomena are involved in the initiation and propagation of the disease. Advances in the comprehension of the mechanisms leading to dissection have been made these last decades, thanks to improvements in imaging and experimental techniques. However, the micro-mechanics involved in triggering such rupture events remains poorly described and understood. It constitutes the primary focus of the present review. Towards the goal of detailing the dissection phenomenon, different experimental and modeling methods were used to investigate aortic dissection, and to understand the underlying phenomena involved. In the last ten years, research has tended to focus on the influence of microstructure on initiation and propagation of the dissection, leading to a number of multiscale models being developed. This review brings together all these materials in an attempt to identify main advances and remaining questions.

Influence of Material Model and Aortic Root Motion in Finite Element Analysis of Two Exemplary Cases of Proximal Aortic Dissection

The risk of type-A dissection is increased in subjects with connective tissue disorders and dilatation of the proximal aorta. The location and extents of vessel wall tears in these patients could be potentially missed during prospective imaging studies. The objective of this study is to estimate the distribution of systolic wall stress in two exemplary cases of proximal dissection using finite element analysis (FEA) and evaluate the sensitivity of the distribution to the choice of anisotropic material model and root motion. FEA was performed for predissection aortas, without prior knowledge of the origin and extents of vessel wall tear. The stress distribution was evaluated along the wall tear in the postdissection aortas. The stress distribution was compared for the Fung and Holzapfel models with and without root motion. For the subject with spiral dissection, peak stress coincided with the origin of the tear in the sinotubular junction. For the case with root dissection, maximum stress was obtained at the distal end of the tear. The FEA predicted tear pressure was 20% higher for the subject with root dissection as compared to the case with spiral dissection. The predicted tear pressure was higher (9-11%) for root motions up to 10 mm. The Holzapfel model predicted a tear pressure that was lower (8-15%) than the Fung model. The FEA results showed that both material response and root motion could potentially influence the predicted dissection pressure of the proximal aorta at least for conditions tested in this study.

Effect of macro-calcification on the failure mechanics of intracranial aneurysmal wall tissue

BACKGROUND

Calcification was recently found to be present in the majority of cerebral aneurysms, though how calcification and the presence or absence of co-localized lipid pools affect failure properties is still unknown.

OBJECTIVE

The primary objective is to quantify the biomechanical effect of a macro-calcification with surrounding Near-Calcification Region (NCR) of varying mechanical properties on tissue failure behavior.

METHODS

We utilized a structurally informed finite element model to simulate pre-failure and failure behavior of a human cerebral tissue specimen modeled as a composite containing a macro-calcification and surrounding NCR, embedded in a fiber matrix composite. Data from multiple imaging modalities was combined to quantify the collagen organization and calcification geometry. An idealized parametric model utilizing the calibrated model was used to explore the impact of NCR properties on tissue failure.

RESULTS

Compared to tissue without calcification, peak stress was reduced by 82% and 49% for low modulus (representing lipid pool) and high modulus (simulating increase in calcification size) of the NCR, respectively. Failure process strongly depended on NCR properties with lipid pools blunting the onset of complete failure. When the NCR was calcified, the sample was able to sustain larger overall stress, however the failure process was abrupt with nearly simultaneous failure of the loaded fibers.

CONCLUSIONS

Failure of calcified vascular tissue is strongly influenced by the ultrastructure in the vicinity of the calcification. Computational modeling of failure in fibrous soft tissues can be used to understand how pathological changes impact the tissue failure process, with potentially important clinical implications.

Mechanical and structural contributions of elastin and collagen fibers to interlamellar bonding in the arterial wall

The artery relies on interlamellar structural components, mainly elastin and collagen fibers, for maintaining its integrity and resisting dissection propagation. In this study, the contribution of arterial elastin and collagen fibers to interlamellar bonding was studied through mechanical testing, multiphoton imaging and finite element modeling. Steady-state peeling experiments were performed on porcine aortic media and the purified elastin network in the circumferential (Circ) and longitudinal (Long) directions. The peeling force and energy release rate associated with mode-I failure are much higher for aortic media than for the elastin network. Also, longitudinal peeling exhibits a higher energy release rate and strength than circumferential peeling for both the aortic media and elastin. Multiphoton imaging shows the recruitment of both elastin and collagen fibers within the interlamellar space and points to in-plane anisotropy of fiber distributions as a potential mechanism for the direction-dependent phenomena of peeling tests. Three-dimensional finite element models based on cohesive zone model (CZM) of fracture were created to simulate the peeling tests with the interlamellar energy release rate and separation distance at damage initiation obtained directly from peeling test. Our experimental results show that the separation distance at damage initiation is 80 μm for aortic media and 40 μm for elastin. The damage initiation stress was estimated from the model for aortic media (Circ: 60 kPa; Long: 95 kPa) and elastin (Circ: 9 kPa; Long: 14 kPa). The interlamellar separation distance at complete failure was estimated to be 3 - 4 mm for both media and elastin. Furthermore, elastin and collagen fibers both play an important role in bonding of the arterial wall, while collagen has a higher contribution than elastin to interlamellar stiffness, strength and toughness. These results on microstructural interlamellar failure shed light on the pathological development and progression of aortic dissection.

A patient-specific numerical modeling of the spontaneous coronary artery dissection in relation to atherosclerosis

The spontaneous coronary artery dissection (SCAD) is a clinical complication of angioplasty leading to an initiation of a tear/crack in the intima layer of the artery. The crack can propagate to the interface of the intima-media layer following by intramural hematoma. The relation between the SCAD and atherosclerosis is a controversial issue, as some studies stated no correlation between them while others showed that a crack can initiate in the intima but cannot propagate into the atrophied media layer. To investigate the relation between the intraluminal crack propagation in the atherosclerotic artery and SCAD, this study numerically investigated the initiation and propagation of a crack in the intraluminal and radial locations of the healthy and atherosclerotic human coronary arterial walls. The energy release rate, namely J-integral, is computed as a numerical derivative of the strain energy with respect to a crack extension using a user-defined virtual crack method (VCE) of extended finite element method (XFEM). Experimental measurements were carried out to calculate the elasto-plastic mechanical properties of the healthy and atherosclerotic human coronary arteries. The experimental data were then assigned to our own established patient-specific FE model of the coronary artery. Cracks were sketched in the intraluminal and radial locations of the arterial wall and allowed to propagate to the virtual interface of the intima-media to form a false lumen. The results revealed a higher stress at the crack tip of the healthy arterial wall compared to the atherosclerotic one. Lower crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) were observed in the intraluminal crack of the atherosclerotic artery. J-integral of the atherosclerotic arterial wall was also found to be higher than the healthy one at the intraluminal crack. The results revealed that although a crack can initiate in the intraluminal of an atherosclerotic artery, it cannot propagate into the media layer due to a relatively higher rate of the strain energy release in the atherosclerotic arterial wall compared to the healthy one.

Computational modeling reveals the relationship between intrinsic failure properties and uniaxial biomechanical behavior of arterial tissue

Biomechanical failure of the artery wall can lead to rupture, a catastrophic event with a high rate of mortality. Thus, there is a pressing need to understand failure behavior of the arterial wall. Uniaxial testing remains the most common experimental technique to assess tissue failure properties. However, the relationship between intrinsic failure parameters of the tissue and measured uniaxial failure properties is not fully established. Furthermore, the effect of the experimental variables, such as specimen shape and boundary conditions, on the measured failure properties is not well understood. We developed a finite element model capable of recapitulating pre-failure and post-failure uniaxial biomechanical response of the arterial tissue specimen. Intrinsic stiffness, strength and fracture toughness of the vessel wall tissue were used as the input material parameters to the model. Two uniaxial testing protocols were considered: a conventional setup with a rectangular specimen held at the grips by cardboard inserts, and the other used a dogbone specimen with soft foam inserts at the grips. Our computational study indicated negligible differences in the peak stress and post-peak mechanical behavior between these two testing protocols. It was also found that the tissue experienced only modest localized failure until higher levels of applied stretch beyond the peak stress. A robust cohesive model was capable of modeling the post-peak biomechanical response, which was primarily governed by tissue fracture toughness. Our results suggest that the post-peak region, in conjunction with the peak stress, must be considered to evaluate the complete biomechanical failure behavior of the soft tissue.

Numerical aspects of anisotropic failure in soft biological tissues favor energy-based criteria: A rate-dependent anisotropic crack phase-field model

A deeper understanding to predict fracture in soft biological tissues is of crucial importance to better guide and improve medical monitoring, planning of surgical interventions and risk assessment of diseases such as aortic dissection, aneurysms, atherosclerosis and tears in tendons and ligaments. In our previous contribution (Gültekin et al., 2016) we have addressed the rupture of aortic tissue by applying a holistic geometrical approach to fracture, namely the crack phase-field approach emanating from variational fracture mechanics and gradient damage theories. In the present study, the crack phase-field model is extended to capture anisotropic fracture using an anisotropic volume-specific crack surface function. In addition, the model is equipped with a rate-dependent formulation of the phase-field evolution. The continuum framework captures anisotropy, is thermodynamically consistent and based on finite strains. The resulting Euler-Lagrange equations are solved by an operator-splitting algorithm on the temporal side which is ensued by a Galerkin-type weak formulation on the spatial side. On the constitutive level, an invariant-based anisotropic material model accommodates the nonlinear elastic response of both the ground matrix and the collagenous components. Subsequently, the basis of extant anisotropic failure criteria are presented with an emphasis on energy-based, Tsai-Wu, Hill, and principal stress criteria. The predictions of the various failure criteria on the crack initiation, and the related crack propagation are studied using representative numerical examples, i.e. a homogeneous problem subjected to uniaxial and planar biaxial deformations is established to demonstrate the corresponding failure surfaces whereas uniaxial extension and peel tests of an anisotropic (hypothetical) tissue deal with the crack propagation with reference to the mentioned failure criteria. Results favor the energy-based criterion as a better candidate to reflect a stable and physically meaningful crack growth, particularly in complex three-dimensional geometries with a highly anisotropic texture at finite strains.

Failure of the Porcine Ascending Aorta: Multidirectional Experiments and a Unifying Microstructural Model

The ascending thoracic aorta is poorly understood mechanically, especially its risk of dissection. To make better predictions of dissection risk, more information about the multidimensional failure behavior of the tissue is needed, and this information must be incorporated into an appropriate theoretical/computational model. Toward the creation of such a model, uniaxial, equibiaxial, peel, and shear lap tests were performed on healthy porcine ascending aorta samples. Uniaxial and equibiaxial tests showed anisotropy with greater stiffness and strength in the circumferential direction. Shear lap tests showed catastrophic failure at shear stresses (150-200 kPa) much lower than uniaxial tests (750-2500 kPa), consistent with the low peel tension (∼60 mN/mm). A novel multiscale computational model, including both prefailure and failure mechanics of the aorta, was developed. The microstructural part of the model included contributions from a collagen-reinforced elastin sheet and interlamellar connections representing fibrillin and smooth muscle. Components were represented as nonlinear fibers that failed at a critical stretch. Multiscale simulations of the different experiments were performed, and the model, appropriately specified, agreed well with all experimental data, representing a uniquely complete structure-based description of aorta mechanics. In addition, our experiments and model demonstrate the very low strength of the aorta in radial shear, suggesting an important possible mechanism for aortic dissection.

A phase-field approach to model fracture of arterial walls: Theory and finite element analysis

This study uses a recently developed phase-field approach to model fracture of arterial walls with an emphasis on aortic tissues. We start by deriving the regularized crack surface to overcome complexities inherent in sharp crack discontinuities, thereby relaxing the acute crack surface topology into a diffusive one. In fact, the regularized crack surface possesses the property of Gamma-Convergence, i.e. the sharp crack topology is restored with a vanishing length-scale parameter. Next, we deal with the continuous formulation of the variational principle for the multi-field problem manifested through the deformation map and the crack phase-field at finite strains which leads to the Euler-Lagrange equations of the coupled problem. In particular, the coupled balance equations derived render the evolution of the crack phase-field and the balance of linear momentum. As an important aspect of the continuum formulation we consider an invariant-based anisotropic constitutive model which is additively decomposed into an isotropic part for the ground matrix and an exponential anisotropic part for the two families of collagen fibers embedded in the ground matrix. In addition we propose a novel energy-based anisotropic failure criterion which regulates the evolution of the crack phase-field. The coupled problem is solved using a one-pass operator-splitting algorithm composed of a mechanical predictor step (solved for the frozen crack phase-field parameter) and a crack evolution step (solved for the frozen deformation map); a history field governed by the failure criterion is successively updated. Subsequently, a conventional Galerkin procedure leads to the weak forms of the governing differential equations for the physical problem. Accordingly, we provide the discrete residual vectors and a corresponding linearization yields the element matrices for the two sub-problems. Finally, we demonstrate the numerical performance of the crack phase-field model by simulating uniaxial extension and simple shear fracture tests performed on specimens obtained from a human aneurysmatic thoracic aorta. Model parameters are obtained by fitting the set of novel experimental data to the predicted model response; the finite element results agree favorably with the experimental findings.

An Invariant-Based Damage Model for Human and Animal Skins

Constitutive modelling of skins that account for damage effects is important to provide insight for various clinical applications, such as skin trauma and injury, artificial skin design, skin aging, disease diagnosis, surgery, as well as comparative studies of skin biomechanics between species. In this study, a new damage model for human and animal skins is proposed for the first time. The model is nonlinear, anisotropic, invariant-based, and is based on the Gasser-Ogden-Holzapfel constitutive law initially developed for arteries. Taking account of the mean collagen fibre orientation and its dispersion, the new model can describe a wide range of skins with damage. The model is first tested on the uniaxial test data of human skin and then applied to nine groups of uniaxial test data for the human, swine, rabbit, bovine and rhino skins. The material parameters can be inversely estimated based on uniaxial tests using the optimization method in MATLAB with a root mean square error ranged between 2.15% and 12.18%. A sensitivity study confirms that the fibre orientation dispersion and the mean fibre angle are among the most important factors that influence the behaviour of the damage model. In addition, these two parameters can only be reliably estimated if some histological information is provided. We also found that depending on the location of skins, the tissue damage may be brittle controlled by the fibre breaking limit (i.e., when the fibre stretch is greater than 1.13-1.32, depending on the species), or ductile (due to both the fibre and the matrix damages). The brittle damages seem to occur mostly in the back, and the ductile damages are seen from samples taken from the belly. The proposed constitutive model may be applied to various clinical applications that require knowledge of the mechanical response of human and animal skins.

Damage Models for Soft Tissues: A Survey

Damage to soft tissues in the human body has been investigated for applications in healthcare, sports, and biomedical engineering. This paper reviews and classifies damage models for soft tissues to summarize achievements, identify new directions, and facilitate finite element analysis. The main ideas of damage modeling methods are illustrated and interpreted. A few key issues related to damage models, such as experimental data curve-fitting, computational effort, connection between damage and fractures/cracks, damage model applications, and fracture/crack extension simulation, are discussed. Several new challenges in the field are identified and outlined. This review can be useful for developing more advanced damage models and extending damage modeling methods to a variety of soft tissues.

Computational approaches for analyzing the mechanics of atherosclerotic plaques: a review

Vulnerable and stable atherosclerotic plaques are heterogeneous living materials with peculiar mechanical behaviors depending on geometry, composition, loading and boundary conditions. Computational approaches have the potential to characterize the three-dimensional stress/strain distributions in patient-specific diseased arteries of different types and sclerotic morphologies and to estimate the risk of plaque rupture which is the main trigger of acute cardiovascular events. This review article attempts to summarize a few finite element (FE) studies for different vessel types, and how these studies were performed focusing on the used stress measure, inclusion of residual stress, used imaging modality and material model. In addition to histology the most used imaging modalities are described, the most common nonlinear material models and the limited number of models for plaque rupture used for such studies are provided in more detail. A critical discussion on stress measures and threshold stress values for plaque rupture used within the FE studies emphasizes the need to develop a more location and tissue-specific threshold value, and a more appropriate failure criterion. With this addition future FE studies should also consider more advanced strain-energy functions which then fit better to location and tissue-specific experimental data.

Numerical simulation of arterial dissection during balloon angioplasty of atherosclerotic coronary arteries

Balloon angioplasty is a standard clinical treatment for symptomatic coronary artery disease. In this procedure, controlled damage is applied intraluminally to the wall of a stenotic artery. Dissection of the coronary artery is a commonly observed clinical complication of angioplasty; however, not all dissections can be detected angioscopically. This work focuses on studying the dissection mechanisms triggered during the early stages of angioplasty in an atherosclerotic coronary artery, addressing the problem by means of a parametric study based on a simplified finite element model and cohesive interface modeling. Our results emphasize the presence of several damage mechanisms, at different locations, that are triggered near the very beginning of the process and evolve competitively, depending on both geometry and material properties of the atherosclerotic vessel. Small-scale damage was evidenced, which would not be detectable by angiography or intravascular ultrasound, but could potentially be sufficient to stimulate smooth muscle cell activation, promoting late-onset complications such as restenosis.

COMPUTER-BASED MECHANICAL ANALYSIS OF STENOSED ARTERY WITH THROMBOTIC PLAQUE: THE INFLUENCES OF IMPORTANT PHYSIOLOGICAL PARAMETERS

The thrombus is the inappropriate activation of hemostasis in vascular system. In this paper, biomechanical factors affecting the behaviors of artery with intraluminal thrombus were studies. Results indicated that heart rate and blood viscosity had strong impact on the compliance of the stenosis artery and flow pattern. The alteration in blood viscosity had stronger influence than cardiac cycle on the volume change of the fluid region surrounded by thrombus. von Mises stress measured at the thinnest region of the plaque had the largest time-averaged value. The alteration of these parameters could potentially lead to stress redistribution at intraluminal thrombus.

Evaluation of carotid stent scaffolding through patient-specific finite element analysis

After carotid artery stenting, the plaque remains contained between the stent and the vessel wall, moving consequently physicians' concerns toward the stent capability of limiting the plaque protrusion, that is, toward vessel scaffolding, to avoid that some debris is dislodged after the procedure. Vessel scaffolding is usually measured as the cell area of the stent in free-expanded configuration, neglecting thus the actual stent configuration within the vascular anatomy. In the present study, we measure the cell area of four different stent designs deployed in a realistic carotid artery model through patient-specific finite element analysis. The results suggest that after deployment, the cell area change along the stent length and the related reduction with respect to the free-expanded configuration are functions of the vessel tapering. Hence, the conclusions withdrawn from the free-expanded configuration appear to be qualitatively acceptable for comparative purposes, but they should be carefully handled because they neglect the post-implant variability, which seems to be more pronounced in open-cell designs, especially at the bifurcation segment. Even though the investigation is limited to few stent designs and one vascular anatomy, our study confirms the capability of dedicated computer-based simulations to provide useful information about complex stent features as vessel scaffolding.

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.

Carotid atheroma rupture observed in vivo and FSI-predicted stress distribution based on pre-rupture imaging

Atherosclerosis at the carotid bifurcation is a major risk factor for stroke. As mechanical forces may impact lesion stability, finite element studies have been conducted on models of diseased vessels to elucidate the effects of lesion characteristics on the stresses within plaque materials. It is hoped that patient-specific biomechanical analyses may serve clinically to assess the rupture potential for any particular lesion, allowing better stratification of patients into the most appropriate treatments. Due to a sparsity of in vivo plaque rupture data, the relationship between various mechanical descriptors such as stresses or strains and rupture vulnerability is incompletely known, and the patient-specific utility of biomechanical analyses is unclear. In this article, we present a comparison between carotid atheroma rupture observed in vivo and the plaque stress distribution from fluid–structure interaction analysis based on pre-rupture medical imaging. The effects of image resolution are explored and the calculated stress fields are shown to vary by as much as 50% with sub-pixel geometric uncertainty. Within these bounds, we find a region of pronounced elevation in stress within the fibrous plaque layer of the lesion with a location and extent corresponding to that of the observed site of plaque rupture.