A methodology to analyze changes in lipid core and calcification onto fibrous cap vulnerability: the human atherosclerotic carotid bifurcation as an illustratory example

Layer-specific residual strains in human carotid arteries revealed under layer separation

Residual stresses are considered as a significant factor influencing the stress-states in arteries. These stresses are typically observed through opening angle of a radially cut artery segment, often regarded as a primary descriptor of their stress-free state. However, the experimental evidence regarding the stress-free states of different artery layers is scarce. In this study, two experimental protocols, each employing different layer-separating sequences, were performed on 17 human common carotid arteries; the differences between both protocols were found statistically insignificant. While the media exhibited opening behaviour (reduced curvature), a contrasting trend was observed for the adventitia curvature, indicating its closing behaviour. In addition to the different bending effect, length changes of both layers after separation were observed, namely shortening of the adventitia and elongation of the media. The results point out that not all the residual stresses are released after a radial cut but a significant portion of them is released only after the layer separation. Considering the different mechanical properties of layers, this may significantly change the stress distribution in arterial wall and should be considered in its biomechanical models.

Modeling Fibrous Tissue in Vascular Fluid-Structure Interaction: A Morphology-Based Pipeline and Biomechanical Significance

Modeling fibrous tissue for vascular fluid-structure interaction analysis poses significant challenges due to the lack of effective tools for preparing simulation data from medical images. This limitation hinders the physiologically realistic modeling of vasculature and its use in clinical settings. Leveraging an established lumen modeling strategy, we propose a comprehensive pipeline for generating thick-walled artery models. A specialized mesh generation procedure is developed to ensure mesh continuity across the lumen and wall interface. Exploiting the centerline information, a series of procedures are introduced for generating local basis vectors within the arterial wall. The procedures are tailored to handle thick-walled tissues where basis vectors may exhibit transmural variations. Additionally, we propose methods for accurately identifying the centerline in multi-branched vessels and bifurcating regions. These modeling approaches are algorithmically implementable, rendering them readily integrable into mainstream cardiovascular modeling software. The developed fiber generation method is evaluated against the strategy using linear elastostatics analysis, demonstrating that the proposed approach yields satisfactory fiber definitions in the considered benchmark. Finally, we examine the impact of anisotropic arterial wall models on the vascular fluid-structure interaction analysis through numerical examples, employing the neo-Hookean model for comparative purposes. The first case involves an idealized curved geometry, while the second studies an image-based abdominal aorta model. Our numerical results reveal that the deformation and stress distribution are critically related to the constitutive model of the wall, whereas hemodynamic factors are less sensitive to the wall model. This work paves the way for more accurate image-based vascular modeling and enhances the prediction of arterial behavior under physiologically realistic conditions.

Investigation of the significance of the plaque morphology evolution in plaque rupture events using computational biomechanics

Forwarded by the technological urge of this era, several computational methods are implemented to give further insights into possible outcomes of diseases. In this context, atherosclerosis, which is one of the most fatal diseases nowadays, is treated alike, where several computational models are proposed annually allowing for the evaluation of several outcomes for patient specific cases. Among them, one of the most significant models is able to predict the atherosclerotic evolution over time. In this proof-of-concept study, we aim to investigate the effect of plaque morphology on plaque rupture in a two-case scenario - a longitudinal and a bulk plaque evolution in 3D-reconstructed patient-specific carotids arteries. Our approach is based on a three-step process: i) the implementation of a state-of-the-art plaque growth model that predicts evolving and new plaques in real patient specific carotid arteries, ii) the selection of 2 patient cases, one with longitudinal plaque evolution and one with bulk plaque evolution and, finally, iii) the evaluation the maximum principal stress over the plaques and the endothelium layers to assess the plaque rupture risk. The results indicate that the evolving plaques towards the lumen, not only cause stenoses but also are more prone to rupture. Clinical relevance- This proof-of-concept work establishes that the plaques that grow towards the luminal border present with a higher risk of potential rupture compared to plaques that grow longitudinally, thus giving valuable insights to clinicians for important decision making regarding potential endarterectomy procedures.

Review paper: The importance of consideration of collagen cross-links in computational models of collagen-based tissues

Collagen as the main protein in Extra Cellular Matrix (ECM) is the main load-bearing component of fibrous tissues. Nanostructure and architecture of collagen fibrils play an important role in mechanical behavior of these tissues. Extensive experimental and theoretical studies have so far been performed to capture these properties, but none of the current models realistically represent the complexity of network mechanics because still less is known about the collagen's inner structure and its effect on the mechanical properties of tissues. The goal of this review article is to emphasize the significance of cross-links in computational modeling of different collagen-based tissues, and to reveal the need for continuum models to consider cross-links properties to better reflect the mechanical behavior observed in experiments. In addition, this study outlines the limitations of current investigations and provides potential suggestions for the future work.

Patient-specific finite element simulation of peripheral artery percutaneous transluminal angioplasty to evaluate the procedure outcome without stent implantation

The purpose of this work is to present a patient-specific (PS) modeling approach for simulating percutaneous transluminal angioplasty (PTA) endovascular treatment and assessing the balloon sizing influence on short-term outcomes in peripheral arteries, i.e. without stent implantation. Two 3D PS stenosed femoral artery models, one with a dominant calcified atherosclerosis while the other with a lipidic plaque, were generated from pre-operative computed tomography angiography images. Elastoplastic constitutive laws were implemented within the plaque and artery models. Implicit finite element method (FEM) was used to simulate the balloon inflation and deflation for different sizings. Besides vessel strains, results were mainly evaluated in terms of the elastic recoil ratio (ERR) and lumen gain ratio (LGR) attained immediately after PTA. Higher LGR values were shown within the stenosed region of the lipidic patient. Simulated results also showed a direct and quantified correlation between balloon sizing and LGR and ERR for both patients after PTA, with a more significant influence on the lumen gain. The max principal strain values in the outer arterial wall increased at higher balloon sizes during inflation as well, with higher rates of increase when the plaque was calcified. Results show that our model could serve in finding a compromise for each stenosis type: maximizing the achieved lumen gain after PTA, but at the same time without damaging the arterial tissue. The proposed methodology can serve as a step toward a clinical decision support system to improve angioplasty balloon sizing selection prior to the surgery.

Constitutive models and failure properties of fibrous tissues of carotid artery atheroma based on their uniaxial testing

To obtain an experimental background for the description of mechanical properties of fibrous tissues of carotid atheroma, a cohort of 141 specimens harvested from 44 patients during endarterectomies, were tested. Uniaxial stress-strain curves and ultimate stress and strain at rupture were recorded. With this cohort, the impact of the direction of load, presence of calcifications, specimen location, patient's age and sex were investigated. A significant impact of sex was revealed for the stress-strain curves and ultimate strains. The response was significantly stiffer for females than for males but, in contrast to ultimate strain, the strength was not significantly different. The differences in strength between calcified and non-calcified atheromas have reached statistical significance in the female group. At most of the analysed stress levels, the loading direction was found significant for the male cohort which was also confirmed by large differences in ultimate strains. The representative uniaxial stress-strain curves (given by median values of strains at chosen stress levels) were fitted with an isotropic hyperelastic model for different groups specified by the investigated factors while the observed differences between circumferential and longitudinal direction were captured by an anisotropic hyperelastic model. The obtained results should be valid also for the tissue of the fibrous cap, the rupture of which is to be predicted in clinics using computational modelling because it may induce arterial thrombosis and consequently a brain stroke.

The Correlation Between Collagen Types and Ultrasound Feature Score in Evaluating the Vulnerability of Carotid Artery Plaque

Objectives: To investigate whether ultrasound score has clinical value in identifying carotid artery-vulnerable plaque and the impacts of collagen distribution on the stability of plaque.

Materials and Methods: Standard carotid artery ultrasound examinations were performed in 51 patients with carotid artery plaques before carotid endarterectomy. Hematoxylin-eosin staining and Sirius red–picric acid staining of plaque sections were performed to analyze the pathological features and collagen distribution. All plaques were classified into vulnerable and stable groups by pathological features. Ultrasound scores, cap thickness, and the ratios of different collagen types were recorded and analyzed between two groups and different parts of plaques.

Results: Ultrasound scores of the vulnerable group were higher than those of the stable group (4.35 ± 1.23 vs. 2.09 ± 1.04, P = 0.001). AUC was 0.894 (best cutoff point three) in differentiating vulnerable and stable plaques. Compared with the stable group, the fibrous caps of the vulnerable group were thinner (P = 0.012); the area ratios of collagen type I to all collagen in the vulnerable group were lower (P = 0.033); however, the area ratios of collagen type IV to all collagen were higher (P = 0.026). Compared with downstream shoulders, the ultrasound scores of upstream shoulders of plaque were higher (P = 0.001), the fibrous caps of upstream shoulders were thinner (P = 0.001), and the area ratios of collagen type I to all collagen were lower (P = 0.022).

Conclusion: Ultrasound score could have a clinical value in identifying vulnerable carotid artery plaque, and the collagen distribution could impact the stability of plaques, especially collagen type I and type IV. The results also prompted that the upstream shoulders were more vulnerable than the downstream shoulders.

Influence of balloon design, plaque material composition, and balloon sizing on acute post angioplasty outcomes: An implicit finite element analysis

In this work we propose a generic modeling approach for simulating percutaneous transluminal angioplasty (PTA) endovascular treatment, and evaluating the influence of balloon design, plaque composition, and balloon sizing on acute post-procedural outcomes right after PTA, without stent implantation. Clinically-used PTA balloons were classified into two categories according to their compliance characteristics, and were modeled correspondingly. Self-defined elastoplastic constitutive laws were implemented within the plaque and artery models, after calibration based on experimental and clinical data. Finite element method (FEM) implicit solver was used to simulate balloon inflation and deflation. Besides balloon profile at max inflation, results are mainly assessed in terms of the elastic recoil ratio (ERR) and lumen gain ratio (LGR) obtained immediately after PTA. No variations in ERR nor LGR values were detected when the balloon design changed, despite the differences observed in their profile at max inflation. Moreover, LGR and ERR inversely varied with the augmentation of calcification level within the plaque (-11% vs. +4% respectively, from fully lipidic to fully calcified plaque). Furthermore, results showed a direct correlation between balloon sizing and LGR and ERR, with noticeably higher rates of change for LGR (+18% and +2% for LGR and ERR respectively for a calcified plaque and a balloon pressure increasing from 10 to 14 atm). However a larger LGR comes with a higher risk of arterial rupture. This proposed methodology opens the way for evaluation of angioplasty balloon selections towards clinical procedure optimization.

An investigation into the critical role of fibre orientation in the ultimate tensile strength and stiffness of human carotid plaque caps

The development and subsequent rupture of atherosclerotic plaques in human carotid arteries is a major cause of ischaemic stroke. Mechanical characterization of atherosclerotic plaques can aid our understanding of this rupture risk. Despite this however, experimental studies on human atherosclerotic carotid plaques, and fibrous plaque caps in particular, are very limited. This study aims to provide further insights into atherosclerotic plaque rupture by mechanically testing human fibrous plaque caps, the region of the atherosclerotic lesion most often attributed the highest risk of rupture. The results obtained highlight the variability in the ultimate tensile stress, strain and stiffness experienced in atherosclerotic plaque caps. By pre-screening all samples using small angle light scattering (SALS) to determine the dominant fibre direction in the tissue, along with supporting histological analysis, this work suggests that the collagen fibre alignment in the circumferential direction plays the most dominant role for determining plaque structural stability. The work presented in this study could provide the basis for new diagnostic approaches to be developed, which non-invasively identify carotid plaques at greatest risk of rupture. STATEMENT OF SIGNIFICANCE: Mechanical characterisation of the atherosclerotic plaque cap is of utmost importance for understanding the mechanisms that govern the rupture strength of this tissue in-vivo. Studies has shown that plaque tissue is heterogenous and comprises of many structural components, each of which exhibits a varying mechanical response. However, rupture generally is located to the plaque cap, whereby the stress exerted on this location exceeds its mechanical strength causing failure. This work shows, for the first time, that the underlying collagen fibre architecture of carotid plaque caps governs their strength and stiffness. This study shows that plaque caps with collagen fibres aligned in the predominately circumferential direction experience higher stresses and lower strains before failure while those with predominately axial fibres display the opposite trend. Furthermore, total collagen content was found not to play a dominant role in determining the mechanical response of the tissue. The present study provides critical insights into human atherosclerotic plaque tissue mechanics and offers clinically relevant insights for mechanically sensitive imaging techniques, such as strain-based ultrasound or MRI.

Numerical simulation of fenestrated graft deployment: Anticipation of stent graft and vascular structure adequacy

Fenestrated endovascular aneurism repair (FEVAR) is a minimally invasive technique, and its success depends on the adequacy of the correspondence between the visceral arteries ostia and position of the fenestrations of the stent graft (SG) during its deployment in juxtarenal aneurisms. However, the fenestration position is generally determined from a preoperative computerised tomography (CT) scan, without considering the vascular deformation induced by the insertion of the endovascular tools. Catheterisation difficulties may occur during clinical procedures. Accordingly, the objective of this work is to present an initial proof of concept aimed at anticipating and optimising the position of the fenestrations, while considering the vascular deformation induced by the insertion of the endovascular tools. The proposed method relies on the finite element method to simulate the SG deployment in a vascular structure (VS), and considers the vascular deformation induced by the tools. After determining the optimal simulation parameters for a patient-specific case, the robustness of the method is demonstrated on six other representative anatomies. The simulated SG is also compared with post-deployment CT observations, and demonstrates good adequacy. The results show that the numerically corrected fenestration positions, as determined from the simulated results following the insertion of the endovascular tools, deviate from those of the standard plan (as determined from the preoperative CT scan). This indicates that the SG-VS adequacy could be improved via simulation-based planning, to anticipate potential catheterisation difficulties.

The influence of angioplasty balloon sizing on acute post-procedural outcomes: a Finite Element Analysis

Atherosclerosis is one of the most common vascular pathologies in the world. Among the most commonly performed endovascular treatments, percutaneous transluminal angioplasty (PTA) has been showing significantly positive clinical outcomes. Due to the complex geometries, material properties and interactions that characterize PTA procedures, finite element analyses of acute angioplasty balloon deployment are limited. In this work, finite element method (FEM) was used to simulate the inflation and deflation of a semi-compliant balloon within the 3D model of a stenosed artery with two different plaque types (lipid and calcified). Self-defined constitutive models for the balloon and the plaque were developed based on experimental and literature data respectively. Balloon deployment was simulated at three different inflation pressures (10, 12 and 14 atm) within the two plaque types. Balloon sizing influence on the arterial elastic recoil obtained immediately after PTA was then investigated. The simulated results show that calcified plaques may lead to higher elastic recoil ratios compared to lipid stenosis, when the same balloon inflation pressures are applied. Also, elastic recoil increases for higher balloon inflation pressure independent of the plaque type. These findings open the way for a data-driven assessment of angioplasty balloon sizing selection and clinical procedures optimization.Clinical Relevance- The FE model developed in this work aims at providing quantitative evaluation of recoil after balloon angioplasty. It may be useful for both manufacturers and clinicians to improve efficiency of angioplasty balloon device design and sizing selection with respect to plaque geometry and constitution, consequently enhancing clinical outcomes.

Evaluating the Impact of Calcification on Plaque Vulnerability from the Aspect of Mechanical Interaction Between Blood Flow and Artery Based on MRI

Acute cerebral ischemic events and thrombosis are associated with the rupture/erosion of carotid atherosclerotic plaques. The aim of the present study was to determine the impact of calcification deposition on the wall shear stress (WSS) and stresses within the plaques using 3D fluid-structure interaction (FSI) models. Six patients with calcified carotid atherosclerosis underwent multisequence magnetic resonance imaging (MRI) and were divided into three groups according to the calcification volume. To evaluate the role of the calcification deposition on the stresses, the calcification content was replaced by lipids and arterial tissue, respectively. By comparing the results from the simulation with calcification, and when changing it to lipids there was a significant increment in the stresses at the fibrous cap (p = 0.004). Instead, by changing it to arterial tissue, there was no significant difference (p = 0.07). The calcification shapes that presented the highest stresses were thin concave arc-shaped (AS1) and thin convex arc-shaped (AS3), with mean stress values of 107 ± 54.2 and 99.6 ± 23.4 kPa, respectively. It was also observed that, the calcification shape has more influence on the level of stress than its distance to the lumen. Higher WSS values were associated with the presence of calcification. Calcification shape plays an important role in producing high stresses in the plaque. This work further clarifies the impact of calcification on plaque vulnerability.

Consideration of stiffness of wall layers is decisive for patient-specific analysis of carotid artery with atheroma

The paper deals with the impact of chosen geometric and material factors on maximal stresses in carotid atherosclerotic plaque calculated using patient-specific finite element models. These stresses are believed to be decisive for the plaque vulnerability but all applied models suffer from inaccuracy of input data, especially when obtained in vivo only. One hundred computational models based on ex vivo MRI are used to investigate the impact of wall thickness, MRI slice thickness, lipid core and fibrous tissue stiffness, and media anisotropy on the calculated peak plaque and peak cap stresses. The investigated factors are taken as continuous in the range based on published experimental results, only the impact of anisotropy is evaluated by comparison with a corresponding isotropic model. Design of Experiment concept is applied to assess the statistical significance of these investigated factors representing uncertainties in the input data of the model. The results show that consideration of realistic properties of arterial wall in the model is decisive for the stress evaluation; assignment of properties of fibrous tissue even to media and adventitia layers as done in some studies may induce up to eightfold overestimation of peak stress. The impact of MRI slice thickness may play a key role when local thin fibrous cap is present. Anisotropy of media layer is insignificant, and the stiffness of fibrous tissue and lipid core may become significant in some combinations.

Role of Vessel Microstructure in the Longevity of End-to-Side Grafts

Compliance mismatch between the graft and the host artery of an end-to-side (ETS) arterial bypass graft anastomosis increases the intramural stress in the ETS graft-artery junction, and thus may compromise its long-term patency. The present study takes into account the effects of collagen fibers to demonstrate how their orientations alter the stresses. The stresses in an ETS bypass graft anastomosis, as a man-made bifurcation, are compared to those of its natural counterpart with different fiber orientations. Both of the ETS bypass graft anastomosis and its natural counterpart have identical geometric and material models and only their collagen fiber orientations are different. The results indicate that the fiber orientation mismatch between the graft and the host artery may increase the stresses at both the heel and toe regions of the ETS anastomosis (the maximum principal stress at the heel and toe regions increased by 72% and 12%, respectively). Our observations, thus, propose that the mismatch between the collagen fiber orientations of the graft and the host artery, independent of the effect of the suture line, may induce aberrant stresses to the anastomosis of the bypass graft.

Calcification in Human Intracranial Aneurysms Is Highly Prevalent and Displays Both Atherosclerotic and Nonatherosclerotic Types

OBJECTIVE

Although the clinical and biological importance of calcification is well recognized for the extracerebral vasculature, its role in cerebral vascular disease, particularly, intracranial aneurysms (IAs), remains poorly understood. Extracerebrally, 2 distinct mechanisms drive calcification, a nonatherosclerotic, rapid mineralization in the media and a slower, inflammation driven, atherosclerotic mechanism in the intima. This study aims to determine the prevalence, distribution, and type (atherosclerotic, nonatherosclerotic) of calcification in IAs and assess differences in occurrence between ruptured and unruptured IAs. Approach and Results: Sixty-five 65 IA specimens (48 unruptured, 17 ruptured) were resected perioperatively. Calcification and lipid pools were analyzed nondestructively in intact samples using high resolution (0.35 μm) microcomputed tomography. Calcification is highly prevalent (78%) appearing as micro (<500 µm), meso (500 µm-1 mm), and macro (>1 mm) calcifications. Calcification manifests in IAs as both nonatherosclerotic (calcification distinct from lipid pools) and atherosclerotic (calcification in the presence of lipid pools) with 3 wall types: Type I-only calcification, no lipid pools (20/51, 39%), Type II-calcification and lipid pools, not colocalized (19/51, 37%), Type III-calcification colocalized with lipid pools (12/51, 24%). Ruptured IAs either had no calcifications or had nonatherosclerotic micro- or meso-calcifications (Type I or II), without macro-calcifications.

CONCLUSIONS

Calcification in IAs is substantially more prevalent than previously reported and presents as both nonatherosclerotic and atherosclerotic types. Notably, ruptured aneurysms had only nonatherosclerotic calcification, had significantly lower calcification fraction, and did not contain macrocalcifications. Improved understanding of the role of calcification in IA pathology should lead to new therapeutic targets.

A comparative study of methods used to generate the arterial fiber structure in a clinically relevant numerical analysis

The advanced constitutive material models of artery wall require the definition of the mean collagen fiber directions in the material configuration. There are several proposed methods; however, it is unclear how much does the fiber structures obtained by these methods differ one from the other and how much this difference may affect the results of the structural analysis of a clinically relevant scenario. Therefore, in this paper, we address this issue by presenting the results of the comparative study of our developed and currently state-of-the-art fiber definition methods. In addition, we present the verification of our developed numerical model that incorporates the extended Holzapfel-Gasser-Ogden (HGO) constitutive material model and the generalized prestressing algorithm (GPA). In the case of the patient-specific internal carotid artery (ICA), the percentage error of the mean fiber directions defined by different methods does not exceed 17.73% (at least 0.05%, at most 81.82%) and has negligible effect on the stress levels, as the percentage error of the mean circumferential Cauchy stress does not exceed 0.1%. Both fiber definition methods produce comparable fiber structure, but our proposed method has an advantage, as it does not depend on method and software used to model the arterial wall mechanics.

Vulnerability analysis on the interaction between Asymmetric stent and arterial layer

The utilization of Asymmetric stent for recovering atherosclerotic diseases, particularly non-symmetric obstruction, is a quite challenging breakthrough treatment. In terms of eccentric plaque, the non-uniform stiffness of arterial layer causes the increasingly complex issues of vulnerability. This study investigated the vulnerability of the interaction between the Asymmetric stent and the surrounding arterial layer using structural transient dynamic analysis in ANSYS. Four combinations of stent deployment, i.e. the Sinusoidal stent expanded by the offset balloon, the Sinusoidal stent expanded by the ordinary cylindrical balloon, the Asymmetric stent expanded by the offset balloon, and the Asymmetric stent expanded by the ordinary cylindrical balloon, are generated for this comparative study. Multilayer material properties from recent in vitro experiments are adopted for the surrounding arterial layer, such as a fibrous cap, lipid core, diseased-healthy intima, and diseased-healthy media. In order to address plaque vulnerability, the Cauchy stresses and Hencky strains are used for stress measure because of convenience in comparison with the uniaxial/biaxial tension test data. The location-specific threshold value from the diseased human carotid artery is adopted for rupture criteria. The simulation indicated that as regards the eccentric plaque, the plaque vulnerability is caused by the plaque shape and components rather than caused by the geometrical structure of the stent or balloon expansion method. Nevertheless, the non-symmetric inflation of balloon, which leads against the plaque, contributed to an increase in the vulnerability of fibrous cap of fibroatheroma plaque.

Mechanics of Atherosclerotic Plaques: Effect of Heart Rate

PURPOSE

Atherosclerotic plaques are highly heterogeneous, nonlinear materials with uncharacteristic structural behaviors. It is well known that mechanics of atherosclerotic plaques significantly depend on plaque geometry, location, composition, and loading conditions. There is no question that atherosclerotic plaques are viscoelastic. Plaques are characterized as the buildup of low-density lipoprotein cholesterol, macrophages, monocytes, and foam cells at a place of inflammation inside arterial walls. Lipid core and fibrous cap are the two major ingredients that are frequently used for the identification of main constituting quantities of atherosclerotic plaques. The lipid core contains of debris from dead cells, esterified cholesterol and cholesterol crystals. The fibrous cap contains smooth muscle cells and collagen fibers. All these materials contribute to the viscoelastic properties of atherosclerotic plaques. Computational studies have shown great potential to characterize this mechanical behavior. Different types of plaque morphologies and mechanical properties have been used in a computational platform to estimate the stability of rupture-prone plaques and detect their locations. In this study for the first time to the best of authors' knowledge, we hypothesize that heart rate is also one of the major factors that should be taken into account while mechanics of plaques is studied.

METHOD

We propose a tunable viscoelastic constitutive material model for the fibrous cap tissue in order to calculate the peak cap stress in normal physiological (dynamic) conditions while heart rate changes from 60 bpm to 150 bpm in 2D plane stress models. A critical discussion on stress distribution in the fibrous cap area is made with respect to heart rate for the first time.

RESULTS

Results strongly suggest the viscoelastic properties of the fibrous cap tissue and heart rate together play a major role in the estimation of the pick cap stress values.

CONCLUSIONS

The results of current study may provide a better understanding on the mechanics of vulnerable atherosclerotic plaques and that any experimental methods assessing the viscoelasticity of plaque composition during progression are highly desirable.

Calcifications in atherosclerotic plaques and impact on plaque biomechanics

The catastrophic mechanical rupture of an atherosclerotic plaque is the underlying cause of the majority of cardiovascular events. The infestation of vascular calcification in the plaques creates a mechanically complex tissue composite. Local stress concentrations and plaque tissue strength properties are the governing parameters required to predict plaque ruptures. Advanced imaging techniques have permitted insight into fundamental mechanisms driving the initiating inflammatory-driven vascular calcification of the diseased intima at the (sub-) micron scale and up to the macroscale. Clinical studies have potentiated the biomechanical relevance of calcification through the derivation of links between local plaque rupture and specific macrocalcification geometrical features. The clinical implications of the data presented in this review indicate that the combination of imaging, experimental testing, and computational modelling efforts are crucial to predict the rupture risk for atherosclerotic plaques. Specialised experimental tests and modelling efforts have further enhanced the knowledge base for calcified plaque tissue mechanical properties. However, capturing the temporal instability and rupture causality in the plaque fibrous caps remains elusive. Is it necessary to move our experimental efforts down in scale towards the fundamental (sub-) micron scales in order to interpret the true mechanical behaviour of calcified plaque tissue interactions that is presented on a macroscale in the clinic and to further optimally assess calcified plaques in the context of biomechanical modelling.

Development of asymmetric stent for treatment of eccentric plaque

The selection of stent and balloon type is decisive in the stenting process. In the treatment of an eccentric plaque obstruction, a symmetric expansion from stent dilatation generates nonuniform stress distribution, which may aggravate fibrous cap prone to rupture. This paper developed a new stent design to treat eccentric plaque using structural transient dynamic analysis in ANSYS. A non-symmetric structural geometry of stent is generated to obtain reasonable stress distribution safe for the arterial layer surrounding the stent. To derive the novel structural geometry, a Sinusoidal stent type is modified by varying struts length and width, adding bridges, and varying curvature width of struts. An end ring of stent struts was also modified to eliminate dogboning phenomenon and to reduce the Ectropion angle. Two balloon types were used to deploy the stent, an ordinary cylindrical and offset balloon. Positive modification results were used to construct the final non-symmetric stent design, called an Asymmetric stent. Analyses of the deformation characteristics, changes in surface roughness and induced stresses within intact arterial layer were subsequently examined. Interaction between the stent and vessel wall was implemented by means of changes in surface roughness and stress distribution analyses. The Palmaz and the Sinusoidal stent were used for a comparative study. This study indicated that the Asymmetric stent types reduced the central radial recoiling and the dogboning phenomenon. In terms of changes in surface roughness and induced stresses, the Asymmetric stent has a comparable effect with that of the Sinusoidal stent. In addition, it could enhance the distribution of surface roughening as expanded by an offset balloon.

GPGPU-based explicit finite element computations for applications in biomechanics: the performance of material models, element technologies, and hardware generations

Finite element (FE) simulations are increasingly valuable in assessing and improving the performance of biomedical devices and procedures. Due to high computational demands such simulations may become difficult or even infeasible, especially when considering nearly incompressible and anisotropic material models prevalent in analyses of soft tissues. Implementations of GPGPU-based explicit FEs predominantly cover isotropic materials, e.g. the neo-Hookean model. To elucidate the computational expense of anisotropic materials, we implement the Gasser-Ogden-Holzapfel dispersed, fiber-reinforced model and compare solution times against the neo-Hookean model. Implementations of GPGPU-based explicit FEs conventionally rely on single-point (under) integration. To elucidate the expense of full and selective-reduced integration (more reliable) we implement both and compare corresponding solution times against those generated using underintegration. To better understand the advancement of hardware, we compare results generated using representative Nvidia GPGPUs from three recent generations: Fermi (C2075), Kepler (K20c), and Maxwell (GTX980). We explore scaling by solving the same boundary value problem (an extension-inflation test on a segment of human aorta) with progressively larger FE meshes. Our results demonstrate substantial improvements in simulation speeds relative to two benchmark FE codes (up to 300[Formula: see text] while maintaining accuracy), and thus open many avenues to novel applications in biomechanics and medicine.

Numerical modeling of experimental human fibrous cap delamination

Fibrous cap delamination is a critical process during the rupture of atherosclerotic plaque, which often leads to severe life-threatening clinical consequences such as myocardial infarction or stroke. In this study a finite element modeling and simulation approach is presented that enables the study of fibrous cap delamination experiments for the purpose of understanding the fibrous cap delamination process. A cohesive zone model (CZM) approach is applied to simulate delamination of the fibrous cap from the underlying plaque tissue. A viscoelastic anisotropic (VA) model for the bulk arterial material behavior is extended from existing studies so that the hysteresis phenomenon observed in the fibrous cap delamination experiments can be captured. A finite element model is developed for the fibrous cap delamination experiments, in which arterial layers (including the fibrous cap and the underlying plaque tissue) are represented by solid elements based on the VA model and the fibrous cap-underlying plaque tissue interface is characterized by interfacial CZM elements. In the CZM, the delamination process is governed by an exponential traction-separation law which utilizes critical energy release rates obtained directly from the fibrous cap delamination experiments. A set of VA model parameter values and CZM parameter values is determined based on values suggested in the literature and through matching simulation predictions of the load vs. load-point displacement curve with one set of experimental measurements. Using this set of parameter values, simulation predictions for other sets of experimental measurements are obtained and good agreement between simulation predictions and experimental measurements is observed. Results of this study demonstrate the applicability of the viscoelastic anisotropic model and the CZM approach for the simulation of diseased arterial tissue failure processes.

Carotid plaque elasticity estimation using ultrasound elastography, MRI, and inverse FEA - A numerical feasibility study

The material properties of atherosclerotic plaques govern the biomechanical environment, which is associated with rupture-risk. We investigated the feasibility of noninvasively estimating carotid plaque component material properties through simulating ultrasound (US) elastography and in vivo magnetic resonance imaging (MRI), and solving the inverse problem with finite element analysis. 2D plaque models were derived from endarterectomy specimens of nine patients. Nonlinear neo-Hookean models (tissue elasticity C1) were assigned to fibrous intima, wall (i.e., media/adventitia), and lipid-rich necrotic core. Finite element analysis was used to simulate clinical cross-sectional US strain imaging. Computer-simulated, single-slice in vivo MR images were segmented by two MR readers. We investigated multiple scenarios for plaque model elasticity, and consistently found clear separations between estimated tissue elasticity values. The intima C1 (160 kPa scenario) was estimated as 125.8 ± 19.4 kPa (reader 1) and 128.9 ± 24.8 kPa (reader 2). The lipid-rich necrotic core C1 (5 kPa) was estimated as 5.6 ± 2.0 kPa (reader 1) and 8.5 ± 4.5 kPa (reader 2). A scenario with a stiffer wall yielded similar results, while realistic US strain noise and rotating the models had little influence, thus demonstrating robustness of the procedure. The promising findings of this computer-simulation study stimulate applying the proposed methodology in a clinical setting.

A method for incorporating three-dimensional residual stretches/stresses into patient-specific finite element simulations of arteries

The existence of residual stresses in human arteries has long been shown experimentally. Researchers have also demonstrated that residual stresses have a significant effect on the distribution of physiological stresses within arterial tissues, and hence on their development, e.g., stress-modulated remodeling. Through progress in medical imaging, image analysis and finite element (FE) meshing tools it is now possible to construct in vivo patient-specific geometries and thus to study specific, clinically relevant problems in arterial mechanics via FE simulations. Classical continuum mechanics and FE methods assume that constitutive models and the corresponding simulations start from unloaded, stress-free reference configurations while the boundary-value problem of interest represents a loaded geometry and includes residual stresses. We present a pragmatic methodology to simultaneously account for both (i) the three-dimensional (3-D) residual stress distributions in the arterial tissue layers, and (ii) the equilibrium of the in vivo patient-specific geometry with the known boundary conditions. We base our methodology on analytically determined residual stress distributions (Holzapfel and Ogden, 2010, J. R. Soc. Interface 7, 787-799) and calibrate it using data on residual deformations (Holzapfel et al., 2007, Ann. Biomed. Eng. 35, 530-545). We demonstrate our methodology on three patient-specific FE simulations calibrated using experimental data. All data employed here are generated from human tissues - both the aorta and thrombus, and their respective layers - including the geometries determined from magnetic resonance images, and material properties and 3-D residual stretches determined from mechanical experiments. We study the effect of 3-D residual stresses on the distribution of physiological stresses in the aortic layers (intima, media, adventitia) and the layers of the intraluminal thrombus (luminal, medial, abluminal) by comparing three types of FE simulations: (i) conventional calculations; (ii) calculations accounting only for prestresses; (iii) calculations including both 3-D residual stresses and prestresses. Our results show that including residual stresses in patient-specific simulations of arterial tissues significantly impacts both the global (organ-level) deformations and the stress distributions within the arterial tissue (and its layers). Our method produces circumferential Cauchy stress distributions that are more uniform through the tissue thickness (i.e., smaller stress gradients in the local radial directions) compared to both the conventional and prestressing calculations. Such methods, combined with appropriate experimental data, aim at increasing the accuracy of classical FE analyses for patient-specific studies in computational biomechanics and may lead to increased clinical application of simulation tools.

A generalized prestressing algorithm for finite element simulations of preloaded geometries with application to the aorta

Finite element models reconstructed from medical imaging data, for example, computed tomography or MRI scans, generally represent geometries under in vivo load. Classical finite element approaches start from an unloaded reference configuration. We present a generalized prestressing algorithm based on a concept introduced by Gee et al. (Int. J. Num. Meth. Biomed. Eng. 26:52-72, 2012) in which an incremental update of the displacement field in the classical approach is replaced by an incremental update of the deformation gradient field. Our generalized algorithm can be implemented in existing finite element codes with relatively low implementation effort on the element level and is suitable for material models formulated in the current or initial configurations. Applicable to any finite element simulations started from preloaded geometries, we demonstrate the algorithm and its convergence properties on an academic example and on a segment of a thoracic aorta meshed from MRI data. Furthermore, we present an example to discuss the influence of neglecting prestresses in geometries obtained from medical images, a topic on which conflicting statements are found in the literature.

The influence of computational strategy on prediction of mechanical stress in carotid atherosclerotic plaques: comparison of 2D structure-only, 3D structure-only, one-way and fully coupled fluid-structure interaction analyses

BACKGROUND

Compositional and morphological features of carotid atherosclerotic plaques provide complementary information to luminal stenosis in predicting clinical presentations. However, they alone cannot predict cerebrovascular risk. Mechanical stress within the plaque induced by cyclical changes in blood pressure has potential to assess plaque vulnerability. Various modeling strategies have been employed to predict stress, including 2D and 3D structure-only, 3D one-way and fully coupled fluid-structure interaction (FSI) simulations. However, differences in stress predictions using different strategies have not been assessed.

METHODS

Maximum principal stress (Stress-P1) within 8 human carotid atherosclerotic plaques was calculated based on geometry reconstructed from in vivo computerized tomography and high resolution, multi-sequence magnetic resonance images. Stress-P1 within the diseased region predicted by 2D and 3D structure-only, and 3D one-way FSI simulations were compared to 3D fully coupled FSI analysis.

RESULTS

Compared to 3D fully coupled FSI, 2D structure-only simulation significantly overestimated stress level (94.1 kPa [65.2, 117.3] vs. 85.5 kPa [64.4, 113.6]; median [inter-quartile range], p=0.0004). However, when slices around the bifurcation region were excluded, stresses predicted by 2D structure-only simulations showed a good correlation (R(2)=0.69) with values obtained from 3D fully coupled FSI analysis. 3D structure-only model produced a small yet statistically significant stress overestimation compared to 3D fully coupled FSI (86.8 kPa [66.3, 115.8] vs. 85.5 kPa [64.4, 113.6]; p<0.0001). In contrast, one-way FSI underestimated stress compared to 3D fully coupled FSI (78.8 kPa [61.1, 100.4] vs. 85.5 kPa [64.4, 113.7]; p<0.0001).

CONCLUSIONS

A 3D structure-only model seems to be a computationally inexpensive yet reasonably accurate approximation for stress within carotid atherosclerotic plaques with mild to moderate luminal stenosis as compared to fully coupled FSI analysis.

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.

Plaque hemorrhage in carotid artery disease: pathogenesis, clinical and biomechanical considerations

Stroke remains the most prevalent disabling illness today, with internal carotid artery luminal stenosis due to atheroma formation responsible for the majority of ischemic cerebrovascular events. Severity of luminal stenosis continues to dictate both patient risk stratification and the likelihood of surgical intervention. But there is growing evidence to suggest that plaque morphology may help improve pre-existing risk stratification criteria. Plaque components such a fibrous tissue, lipid rich necrotic core and calcium have been well investigated but plaque hemorrhage (PH) has been somewhat overlooked. In this review we discuss the pathogenesis of PH, its role in dictating plaque vulnerability, PH imaging techniques, marterial properties of atherosclerotic tissues, in particular, those obtained based on in vivo measurements and effect of PH in modulating local biomechanics.

Patient-specific finite element analysis of carotid artery stenting: a focus on vessel modeling

Finite element analysis is nowadays a well-assessed technique to investigate the impact of stenting on vessel wall and, given the rapid progression of both medical imaging techniques and computational methods, the challenge of using the simulation of carotid artery stenting as procedure planning tool to support the clinical practice can be approached. Within this context, the present study investigates the impact of carotid stent apposition on carotid artery anatomy by means of patient-specific finite element analysis. In particular, we focus on the influence of the vessel constitutive model on the prediction of carotid artery wall tensional state of lumen gain and of vessel straightening. For this purpose, we consider, for a given stent design and CA anatomy, two constitutive models for the CA wall, that is, a hyperelastic isotropic versus a fiber-reinforced hyperelastic anisotropic model. Despite both models producing similar patterns with respect to stress distribution, the anisotropic model predicts a higher vessel straightening and a more evident discontinuity of the lumen area near the stent ends as observed in the clinical practice. Although still affected by several simplifications, the present study can be considered as further step toward a realistic simulation of carotid artery stenting.

Does microcalcification increase the risk of rupture?

Rupture of atherosclerotic plaque, which is related to maximal stress conditions in the plaque among others, is a major cause of mortality. More careful examination of stress distributions in atherosclerotic plaques reports that it could be due to local stress behaviors at critical sites caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. However, the role of microcalcifications is not yet fully understood, and most finite element models of blood vessels with atheroma plaque ignore the heterogeneity of the plaque constituents at the microscale. The goal of this work is to investigate the effect of microcalcifications on the stress field of an atheroma plaque vessel section. This is achieved by performing a parametric finite element study, assuming a plane strain hypothesis, of a coronary artery section with eccentric atheroma plaque and one microcalcification incorporated. The geometrical parameters used to define and design the idealized coronary plaque anatomy and the microcalcification were the fibrous cap thickness and the microcalcification ratio, angle and eccentricity. We could conclude that microcalcifications should be considered in the modeling of this kind of problems since they cause a significant alteration of the vulnerable risk by increasing the maximum maximal principal stress up to 32%, although this increase of stress is not uniform (12% on average). The obtained results show that the fibrous cap thickness, the microcalcification ratio and the microcalcification eccentricity, in combination with the microcalcification angle, appear to be the key morphological parameters that play a determinant role in the maximal principal stress and accordingly in the rupture risk of the plaque.

Effect of calcification on the mechanical stability of plaque based on a three-dimensional carotid bifurcation model

Background

This study characterizes the distribution and components of plaque structure by presenting a three-dimensional blood-vessel modelling with the aim of determining mechanical properties due to the effect of lipid core and calcification within a plaque. Numerical simulation has been used to answer how cap thickness and calcium distribution in lipids influence the biomechanical stress on the plaque.

Method

Modelling atherosclerotic plaque based on structural analysis confirms the rationale for plaque mechanical examination and the feasibility of our simulation model. Meaningful validation of predictions from modelled atherosclerotic plaque model typically requires examination of bona fide atherosclerotic lesions. To analyze a more accurate plaque rupture, fluid-structure interaction is applied to three-dimensional blood-vessel carotid bifurcation modelling. A patient-specific pressure variation is applied onto the plaque to influence its vulnerability.

Results

Modelling of the human atherosclerotic artery with varying degrees of lipid core elasticity, fibrous cap thickness and calcification gap, which is defined as the distance between the fibrous cap and calcification agglomerate, form the basis of our rupture analysis. Finite element analysis shows that the calcification gap should be conservatively smaller than its threshold to maintain plaque stability. The results add new mechanistic insights and methodologically sound data to investigate plaque rupture mechanics.

Conclusion

Structural analysis using a three-dimensional calcified model represents a more realistic simulation of late-stage atherosclerotic plaque. We also demonstrate that increases of calcium content that is coupled with a decrease in lipid core volume can stabilize plaque structurally.

Cholesterol is associated with the presence of a lipid core in carotid plaque of asymptomatic, young-to-middle-aged African Americans with and without HIV infection and cocaine use residing in inner-city Baltimore, Md., USA

BACKGROUND

Stroke remains a leading cause of death in the United States. While stroke-related mortality in the USA has declined over the past decades, stroke death rates are still higher for blacks than for whites, even at younger ages. The purpose of this study was to estimate the frequency of a lipid core and explore risk factors for its presence in asymptomatic, young-to-middle-aged urban African American adults recruited from inner-city Baltimore, Md., USA.

METHODS

Between August 28, 2003, and May 26, 2005, 198 African American participants aged 30-44 years from inner-city Baltimore, Md., were enrolled in an observational study of subclinical atherosclerosis related to HIV and cocaine use. In addition to clinical examinations and laboratory tests, B-mode ultrasound for intima-media thickness of the internal carotid arteries was performed. Among these 198, 52 were selected from the top 30th percentile of maximum carotid intima-media thickness by ultrasound, and high-resolution black blood MRI images were acquired through their carotid plaque before and after the intravenous administration of gadodiamide. Of these 52, 37 with maximum segmental thickness by MRI >1.0 mm were included in this study. Lumen and outer wall contours were defined using semiautomated analysis software. The frequency of a lipid core in carotid plaque was estimated and risk factors for lipid core presence were explored using logistic regression analysis.

RESULTS

Of the 37 participants in this study, 12 (32.4%) were women. The mean age was 38.7 ± 4.9 years. A lipid core was present in 9 (17%) of the plaques. Seventy percent of the study participants had a history of cigarette smoking. The mean total cholesterol level was 176.1 ± 37.3 mg/dl, the mean systolic blood pressure was 113.1 ± 13.3 mm Hg, and the mean diastolic blood pressure was 78.9 ± 9.5 mm Hg. There were 5 participants with hypertension (13.5%). Twelve (32%) participants had a history of chronic cocaine use, and 23 (62%) were HIV positive. Among the factors investigated, including age, sex, blood pressure, cigarette smoking, C-reactive protein, fasting glucose, triglycerides, serum total cholesterol, coronary calcium, cocaine use, and HIV infection, only total cholesterol was significantly associated with the presence of a lipid core.

CONCLUSIONS

This study revealed an unexpectedly high rate of the presence of lipid core in carotid plaque and highlights the importance of cholesterol lowering to prevent cerebrovascular disease in this population. Further population-based studies are warranted to confirm these results.

Effects of intima stiffness and plaque morphology on peak cap stress

BACKGROUND

Rupture of the cap of a vulnerable plaque present in a coronary vessel may cause myocardial infarction and death. Cap rupture occurs when the peak cap stress exceeds the cap strength. The mechanical stress within a cap depends on the plaque morphology and the material characteristics of the plaque components. A parametric study was conducted to assess the effect of intima stiffness and plaque morphology on peak cap stress.

METHODS

Models with idealized geometries based on histology images of human coronary arteries were generated by varying geometric plaque features. The constructed multi-layer models contained adventitia, media, intima, and necrotic core sections. For adventitia and media layers, anisotropic hyperelastic material models were used. For necrotic core and intima sections, isotropic hyperelastic material models were employed. Three different intima stiffness values were used to cover the wide range reported in literature. According to the intima stiffness, the models were classified as stiff, intermediate and soft intima models. Finite element method was used to compute peak cap stress.

RESULTS

The intima stiffness was an essential determinant of cap stresses. The computed peak cap stresses for the soft intima models were much lower than for stiff and intermediate intima models. Intima stiffness also affected the influence of morphological parameters on cap stresses. For the stiff and intermediate intima models, the cap thickness and necrotic core thickness were the most important determinants of cap stresses. The peak cap stress increased three-fold when the cap thickness was reduced from 0.25 mm to 0.05 mm for both stiff and intermediate intima models. Doubling the thickness of the necrotic core elevated the peak cap stress by 60% for the stiff intima models and by 90% for the intermediate intima models. Two-fold increase in the intima thickness behind the necrotic core reduced the peak cap stress by approximately 25% for both intima models. For the soft intima models, cap thickness was less critical and changed the peak cap stress by 55%. However, the necrotic core thickness was more influential and changed the peak cap stress by 100%. The necrotic core angle emerged as a critical determinant of cap stresses where a larger angle lowered the cap stresses. Contrary to the stiff and intermediate intima models, a thicker intima behind the necrotic core increased the peak cap stress by approximately 25% for the soft intima models. Adventitia thickness and local media regression had limited effects for all three intima models.

CONCLUSIONS

For the stiff and intermediate intima models, the cap thickness was the most important morphological risk factor. However for soft intima models, the necrotic core thickness and necrotic core angle had a bigger impact on the peak cap stress. We therefore need to enhance our knowledge of intima material properties if we want to derive critical morphological plaque features for risk evaluation.

Prediction of fibre architecture and adaptation in diseased carotid bifurcations

Many studies have used patient-specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. In complex geometries, few studies have incorporated the anisotropic material response of arterial tissue. This paper presents a fibre remodelling algorithm to predict the fibre architecture, and thus anisotropic material response in four patient-specific models of the carotid bifurcation. The change in fibre architecture during disease progression and its affect on the stress environment in the plaque were predicted. The mean fibre directions were assumed to lie at an angle between the two positive principal strain directions. The angle and the degree of dispersion were assumed to depend on the ratio of principal strain values. Results were compared with experimental observations and other numerical studies. In non-branching regions of each model, the typical double helix arterial fibre pattern was predicted while at the bifurcation and in regions of plaque burden, more complex fibre architectures were found. The predicted change in fibre architecture in the arterial tissue during plaque progression was found to alter the stress environment in the plaque. This suggests that the specimen-specific anisotropic response of the tissue should be taken into account to accurately predict stresses in the plaque. Since determination of the fibre architecture in vivo is a difficult task, the system presented here provides a useful method of estimating the fibre architecture in complex arterial geometries.

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.