Effect of a lipid pool on stress/strain distributions in stenotic arteries: 3-D fluid-structure interactions (FSI) models

Patient-Specific Numerical Simulations of Coronary Artery Hemodynamics and Biomechanics: A Pathway to Clinical Use

PURPOSE

Numerical models that simulate the behaviors of the coronary arteries have been greatly improved by the addition of fluid-structure interaction (FSI) methods. Although computationally demanding, FSI models account for the movement of the arterial wall and more adequately describe the biomechanical conditions at and within the arterial wall. This offers greater physiological relevance over Computational Fluid Dynamics (CFD) models, which assume the walls do not move or deform. Numerical simulations of patient-specific cases have been greatly bolstered by the use of imaging modalities such as Computed Tomography Angiography (CTA), Magnetic Resonance Imaging (MRI), Optical Coherence Tomography (OCT), and Intravascular Ultrasound (IVUS) to reconstruct accurate 2D and 3D representations of artery geometries. The goal of this study was to conduct a comprehensive review on CFD and FSI models on coronary arteries, and evaluate their translational potential.

METHODS

This paper reviewed recent work on patient-specific numerical simulations of coronary arteries that describe the biomechanical conditions associated with atherosclerosis using CFD and FSI models. Imaging modality for geometry collection and clinical applications were also discussed.

RESULTS

Numerical models using CFD and FSI approaches are commonly used to study biomechanics within the vasculature. At high temporal and spatial resolution (compared to most cardiac imaging modalities), these numerical models can generate large amount of biomechanics data.

CONCLUSIONS

Physiologically relevant FSI models can more accurately describe atherosclerosis pathogenesis, and help to translate biomechanical assessment to clinical evaluation.

Update on cardiac imaging: A critical analysis

Imaging is instrumental in diagnosing and directing the management of atherosclerosis. In 1958 the first diagnostic coronary angiography (CA) was performed, and since then further development has led to new methods such as coronary CT angiography (CTA), optical coherence tomography (OCT), positron tomography (PET), and intravascular ultrasound (IVUS). Currently, CA remains powerful for visualizing coronary arteries; however, recent studies show the benefits of using other non-invasive techniques. This review identifies optimum imaging techniques for diagnosing and monitoring plaque stability. This becomes even direr now, given the rapidly rising incidence of atherosclerosis in society today. Many acute coronary events, including acute myocardial infarctions and sudden deaths, are attributable to plaque rupture. Although fatal, these events can be preventable. We discuss the factors affecting plaque integrity, such as increased inflammation, medications like statins, and increased lipid content. Some of these precipitating factors are identifiable through imaging. However, we also highlight significant complications arising in some modalities; in CA this can include ventricular arrhythmia and even death. Extending this, we elucidated from the literature that risk can also vary based on the location of arteries and their plaques. Promisingly, there are less invasive methods being trialled for assessing plaque stability, such as Cardiac Magnetic Resonance Imaging (CMR), which is already in use for other cardiac diseases like cardiomyopathies. Therefore, future research focusing on using imaging modalities in conjunction may be sensible, to bridge between the effectiveness of modalities, at the expense of increased complications, and vice versa.

Shear stress and plaque microenvironment induce heterogeneity: A multiscale microenvironment evolution model

BACKGROUND

Both clinical images and in vivo observations have demonstrated the heterogeneity in atherosclerotic plaque composition. However, the quantitative mechanisms that contribute to the heterogeneity, such as the wall shear stress (WSS) and the interplays among microenvironmental factors are still unclear.

METHODS

We develop a multiscale model coupling computational fluid dynamics, interactions of microenvironmental factors and evolutions of cellular behaviors to investigate the formation of plaque heterogeneity in a three-dimensional vessel segment. The model involves WSS, lipid deposition and inflammatory response to reveal the dynamic balance existed between the lipid metabolism and the phagocytosis of macrophages.

RESULTS

The dynamic balance in microenvironment is influenced by both the WSS and the interactions with microenvironmental factors, and consequently results in the longitudinal heterogeneity observed in plaque pathology. In addition, plaque heterogeneity can be reduced by decreasing low WSS area at downstream, as well as by altering the phagocytic abilities of macrophage on lipoproteins, which may be used to develop future plaque regression strategies.

CONCLUSIONS

This multiscale modeling provides a framework to understand the mechanisms in dynamics of plaque composition and also provides quantitative information to better risk stratification of plaque vulnerability in future clinical practice.

A spatiotemporal analysis of the left coronary artery biomechanics using fluid-structure interaction models

Biomechanics plays a critical role in coronary artery disease development. FSI simulation is commonly used to understand the hemodynamics and mechanical environment associated with atherosclerosis pathology. To provide a comprehensive characterization of patient-specific coronary biomechanics, an analysis of FSI simulation in the spatial and temporal domains was performed. In the current study, a three-dimensional FSI model of the LAD coronary artery was built based on a patient-specific geometry using COMSOL Multiphysics. The effect of myocardial bridging was simulated. Wall shear stress and its derivatives including time-averaged wall shear stress, wall shear stress gradient, and OSI were calculated across the cardiac cycle in multiple locations. Arterial wall strain (radial, circumferential, and longitudinal) and von Mises stress were calculated. To assess perfusion, vFFR was calculated. The results demonstrated the FSI model could identify regional and transient differences in biomechanical parameters within the coronary artery. The addition of myocardial bridging caused a notable change in von Mises stress and an increase in arterial strain during systole. The analysis performed in this manner takes greater advantage of the information provided in the space and time domains and can potentially assist clinical evaluation.

Plaque Structural Stress: Detection, Determinants and Role in Atherosclerotic Plaque Rupture and Progression

Atherosclerosis remains a major cause of death worldwide, with most myocardial infarctions being due to rupture or erosion of coronary plaques. Although several imaging modalities can identify features that confer risk, major adverse cardiovascular event (MACE) rates attributable to each plaque are low, such that additional biomarkers are required to improve risk stratification at plaque and patient level. Coronary arteries are exposed to continual mechanical forces, and plaque rupture occurs when plaque structural stress (PSS) exceeds its mechanical strength. Prospective studies have shown that peak PSS is correlated with acute coronary syndrome (ACS) presentation, plaque rupture, and MACE, and provides additional prognostic information to imaging. In addition, PSS incorporates multiple variables, including plaque architecture, plaque material properties, and haemodynamic data into a defined solution, providing a more detailed overview of higher-risk lesions. We review the methods for calculation and determinants of PSS, imaging modalities used for modeling PSS, and idealized models that explore structural and geometric components that affect PSS. We also discuss current experimental and clinical data linking PSS to the natural history of coronary artery disease, and explore potential for refining treatment options and predicting future events.

Effect of Extended Lipid Core on the Hemodynamic Parameters: A Fluid-Structure Interaction Approach

Myocardial infarction is one of the leading causes of death in the developed countries. A majority of myocardial infarctions are caused by the rupture of coronary artery plaques. In order to achieve a better understanding of the effect of the extension of the lipid core into the artery wall on the change of flow field and its effect on plaque vulnerability, we have studied the hemodynamic parameters by utilizing a finite element method and taking into account the fluid-structure interaction (FSI). Four groups of stenosis models with different sizes of lipid core were used in the study. The fully developed pulsatile velocity profile of the right coronary artery was used as the inlet boundary condition, and the pressure pulse was applied as the outlet boundary condition. The non-Newtonian Carreau model was used to simulate the non-Newtonian behavior of blood. Results indicate that the extension of the lipid core into the artery wall influences the flow field; subsequently, creates favorable conditions for additional development of the lipid core which can lead to a higher risk of plaque rupture.

Characterizing Intracranial Hemodynamics in Sickle Cell Anemia: Impact of Patient-Specific Viscosity

PURPOSE

Pediatric and adult patients with sickle cell anemia (SCA) are at increased risk of stroke and cerebrovascular accident. In the general adult population, there is a relationship between arterial hemodynamics and pathology; however, this relationship in SCA patients remains to be elucidated. The aim of this work was to characterize circle of Willis hemodynamics in patients with SCA and quantify the impact of viscosity choice on pathophysiologically-relevant hemodynamics measures.

METHODS

Based on measured vascular geometries, time-varying flow rates, and blood parameters, detailed patient-specific simulations of the circle of Willis were conducted for SCA patients (n = 6). Simulations quantified the impact of patient-specific and standard blood viscosities on wall shear stress (WSS).

RESULTS

These results demonstrated that use of a standard blood viscosity introduces large errors into the estimation of pathophysiologically-relevant hemodynamic parameters. Standard viscosity models overpredicted peak WSS by 55% and 49% for steady and pulsatile flow, respectively. Moreover, these results demonstrated non-uniform, spatial patterns of positive and negative WSS errors related to viscosity, and standard viscosity simulations overpredicted the time-averaged WSS by 32% (standard deviation = 7.1%). Finally, differences in shear rate demonstrated that the viscosity choice alters the simulated near-wall flow field, impacting hemodynamics measures.

CONCLUSIONS

This work presents simulations of circle of Willis arterial flow in SCA patients and demonstrates the importance and feasibility of using a patient-specific viscosity in these simulations. Accurately characterizing cerebrovascular hemodynamics in SCA populations has potential for elucidating the pathophysiology of large-vessel occlusion, aneurysms, and tissue damage in these patients.

Nonlinear multiscale analysis of coronary atherosclerotic vulnerable plaque artery: fluid-structural modeling with micromechanics

A unique three-dimensional (3D) computational multiscale modeling approach is proposed to investigate the influence of presence of microcalcification particles on the stress field distribution in the thin cap layer of a coronary atherosclerotic vulnerable plaque system. A nested 3D modeling analysis framework spanning the multiscale nature of a coronary atherosclerotic vulnerable plaque is presented. At the microscale level, a micromechanical modeling approach, which is based on computational finite-element (FE) representative unit cell, is applied to obtain the homogenized nonlinear response of the calcified tissue. This equivalent response effectively allows the integration of extremely small microcalcification inclusions in a global biomechanical FE model. Next, at the macroscale level, a 3D patient-based fluid-structure interaction FE model, reconstructing a refined coronary artery geometry with calcified plaque lesion, is generated to study the mechanical behavior of such multi-component biomechanical system. It is shown that the proposed multiscale modeling approach can generate a higher resolution of stress and strain field distributions within the coronary atherosclerotic vulnerable plaque system and allow the assessment of the local concentration stress around the microcalcifications in plaque cap layers. A comparison of stress field distributions within cap layers with and without inclusion of microcalcifications is also presented.

Predicting plaque vulnerability change using intravascular ultrasound + optical coherence tomography image-based fluid-structure interaction models and machine learning methods with patient follow-up data: a feasibility study

Background

Coronary plaque vulnerability prediction is difficult because plaque vulnerability is non-trivial to quantify, clinically available medical image modality is not enough to quantify thin cap thickness, prediction methods with high accuracies still need to be developed, and gold-standard data to validate vulnerability prediction are often not available. Patient follow-up intravascular ultrasound (IVUS), optical coherence tomography (OCT) and angiography data were acquired to construct 3D fluid–structure interaction (FSI) coronary models and four machine-learning methods were compared to identify optimal method to predict future plaque vulnerability.

Methods

Baseline and 10-month follow-up in vivo IVUS and OCT coronary plaque data were acquired from two arteries of one patient using IRB approved protocols with informed consent obtained. IVUS and OCT-based FSI models were constructed to obtain plaque wall stress/strain and wall shear stress. Forty-five slices were selected as machine learning sample database for vulnerability prediction study. Thirteen key morphological factors from IVUS and OCT images and biomechanical factors from FSI model were extracted from 45 slices at baseline for analysis. Lipid percentage index (LPI), cap thickness index (CTI) and morphological plaque vulnerability index (MPVI) were quantified to measure plaque vulnerability. Four machine learning methods (least square support vector machine, discriminant analysis, random forest and ensemble learning) were employed to predict the changes of three indices using all combinations of 13 factors. A standard fivefold cross-validation procedure was used to evaluate prediction results.

Results

For LPI change prediction using support vector machine, wall thickness was the optimal single-factor predictor with area under curve (AUC) 0.883 and the AUC of optimal combinational-factor predictor achieved 0.963. For CTI change prediction using discriminant analysis, minimum cap thickness was the optimal single-factor predictor with AUC 0.818 while optimal combinational-factor predictor achieved an AUC 0.836. Using random forest for predicting MPVI change, minimum cap thickness was the optimal single-factor predictor with AUC 0.785 and the AUC of optimal combinational-factor predictor achieved 0.847.

Conclusion

This feasibility study demonstrated that machine learning methods could be used to accurately predict plaque vulnerability change based on morphological and biomechanical factors from multi-modality image-based FSI models. Large-scale studies are needed to verify our findings.

Modeling Pulse Wave Propagation Through a Stenotic Artery With Fluid Structure Interaction: A Validation Study Using Ultrasound Pulse Wave Imaging

Pulse wave imaging (PWI) is an ultrasound-based method that allows spatiotemporal mapping of the arterial pulse wave propagation, from which the local pulse wave velocity (PWV) can be derived. Recent reports indicate that PWI can help the assessment of atherosclerotic plaque composition and mechanical properties. However, the effect of the atherosclerotic plaque's geometry and mechanics on the arterial wall distension and local PWV remains unclear. In this study, we investigated the accuracy of a finite element (FE) fluid-structure interaction (FSI) approach to predict the velocity of a pulse wave propagating through a stenotic artery with an asymmetrical plaque, as quantified with PWI method. Experiments were designed to compare FE-FSI modeling of the pulse wave propagation through a stenotic artery against PWI obtained with manufactured phantom arteries made of polyvinyl alcohol (PVA) material. FSI-generated spatiotemporal maps were used to estimate PWV at the plaque region and compared it to the experimental results. Velocity of the pulse wave propagation and magnitude of the wall distension were correctly predicted with the FE analysis. In addition, findings indicate that a plaque with a high degree of stenosis (>70%) attenuates the propagation of the pulse pressure wave. Results of this study support the validity of the FE-FSI methods to investigate the effect of arterial wall structural and mechanical properties on the pulse wave propagation. This modeling method can help to guide the optimization of PWI to characterize plaque properties and substantiate clinical findings.

Stress distribution analysis in healthy and stenosed carotid artery models reconstructed from in vivo ultrasonography

Purpose

This study investigated the accuracy of models reconstructed from ultrasound image processing by comparing the radial displacement waveforms of a subject-specific artery model and evaluated stress changes in the proximal shoulder, throat, and distal shoulder of the plaques depending on the degree of carotid artery stenosis.

Methods

Three groups of subjects (healthy and with less than 50% or more carotid stenosis) were evaluated with ultrasonography. Two-dimensional transverse imaging of the common carotid artery was performed to reconstruct the geometry. A longitudinal view of the same region was recorded to extract the Kelvin viscoelastic model parameters. The pulse pressure waveform and the effective pressure of perivascular tissue were loaded onto the internal and external walls of the model. Effective, circumferential, and principal stresses applied to the plaque throat, proximal shoulder, and distal shoulder in the transverse planes were extracted.

Results

The radial displacement waveforms of the model were closely correlated with those of image processing in all three groups. The mean of the effective, circumferential, and principal stresses of the healthy arteries were 15.01±4.93, 12.97±5.07, and 12.39±2.86 kPa, respectively. As stenosis increased from mild to significant, the mean values of the effective, circumferential, and first principal stresses increased significantly (97%, 74%, and 103% at the plaque throat, respectively) (P<0.05). The minimum effective stress was at the lipid pool. The effective stress in calcified areas was higher than in other parts of the artery wall.

Conclusion

This model can discriminate differences in stresses applied to mildly and severely stenotic plaques.

Rupture Risk Assessment of Cervical Spinal Manipulations on Carotid Atherosclerotic Plaque by a 3D Fluid-Structure Interaction Model

Method

The FSI model, based on MRI data of an atherosclerosis patient, was used to simulate the deformations of the plaque and lumen during the process of two kinds of typical cSMT (the high-speed, low-amplitude spinal manipulation and the cervical rotatory manipulation). The biomechanical parameters were recorded, such as the highest wall shear stress (WSS), the maximum plaque wall stress (PWS), the wall tensile stress (Von mises stress, VWTS), and the strain.

Result

The max_WSS was 33.77 kPa in the most extensive deformation. The highest WSS region on the plaque surface was also the highest PWS region. The max_PWS in a 12% stretch was 55.11 kPa, which was lower than the rupture threshold. The max_VWTS of the cap in 12% stretch which approached the fracture stress level was 116.75 kPa. Moreover, the vessel's max_VWTS values in 10% and 12% stretch were 554.21 and 855.19 kPa. They were higher than the fracture threshold, which might cause media fracture. Meanwhile, the 7% stretched strain was 0.29, closed to the smallest experimental green strains at rupture.

Conclusion

The carotid arteries' higher stretch generated the higher stress level of the plaque. Cervical rotatory manipulation might cause plaque at a high risk of rupture in deformation after 12% stretch and more. Lower deformation of the plaque and artery caused by the high-speed, low-amplitude spinal manipulation might be safer.

Using intravascular ultrasound image-based fluid-structure interaction models and machine learning methods to predict human coronary plaque vulnerability change

Plaque vulnerability prediction is of great importance in cardiovascular research. In vivo follow-up intravascular ultrasound (IVUS) coronary plaque data were acquired from nine patients to construct fluid-structure interaction models to obtain plaque biomechanical conditions. Morphological plaque vulnerability index (MPVI) was defined to measure plaque vulnerability. The generalized linear mixed regression model (GLMM), support vector machine (SVM) and random forest (RF) were introduced to predict MPVI change (ΔMPVI = MPVI_follow-up‒MPVI_baseline) using ten risk factors at baseline. The combination of mean wall thickness, lumen area, plaque area, critical plaque wall stress, and MPVI was the best predictor using RF with the highest prediction accuracy 91.47%, compared to 90.78% from SVM, and 85.56% from GLMM. Machine learning method (RF) improved the prediction accuracy by 5.91% over that from GLMM. MPVI was the best single risk factor using both GLMM (82.09%) and RF (78.53%) while plaque area was the best using SVM (81.29%).

Exploring the relationship between biomechanical stresses and coronary atherosclerosis

The pathophysiology of coronary atherosclerosis is multifaceted. Plaque initiation and progression are governed by a complex interplay between genetic and environmental factors acting through processes such as lipid accumulation, altered haemodynamics and inflammation. There is increasing recognition that biomechanical stresses play an important role in atherogenesis, and integration of these metrics with clinical imaging has potential to significantly improve cardiovascular risk prediction. In this review, we present the calculation of coronary biomechanical stresses from first principles and computational methods, including endothelial shear stress (ESS), plaque structural stress (PSS) and axial plaque stress (APS). We discuss the current experimental and human data linking these stresses to the natural history of coronary artery disease and explore the future potential for refining treatment options and predicting future ischaemic events.

Fluid-Structure Interaction Simulation of Blood Flow and Cerebral Aneurysm: Effect of Partly Blocked Vessel

In this study, using fluid-structure interaction (FSI), 3-dimensional blood flow in an aneurysm in the circle of Willis - which is located in the middle cerebral artery (MCA) - has been simulated. The purpose of this study is to evaluate the effect of a partly blocked vessel on an aneurysm. To achieve this purpose, two cases have been investigated using the FSI method: in the first case, an ideal geometry of aneurysm in the MCA has been simulated; in the second case, modeling is performed for an ideal geometry of the aneurysm in the MCA with a partly blocked vessel. All boundary conditions, properties and modeling methods were considered the same for both cases. The only difference between the two cases was that part of the MCA parent artery was blocked in the second case. In order to consider the hyperelastic property of the wall and the non-Newtonian properties of the blood, the Mooney-Rivlin model and the Carreau model have been used, respectively. In the second case, the Von Mises stress in the peak systole is 26% higher than in the first case. With regard to the high amount of Von Mises stress, the risk of rupture of the aneurysm is higher in this case. In the second case, the maximum wall shear stress (WSS) is 12% higher than in the first case. And maximum displacement in the second case is also higher than in the first. So, the risk of growth of the aneurysm is higher in cases with a partly blocked vessel.

Carotid Plaque CTA Analysis in Symptomatic Subjects with Bilateral Intraparenchymal Hemorrhage: A Preliminary Analysis

BACKGROUND AND PURPOSE

The presence of IPH is considered the most dangerous feature because it is significantly associated with clinical ipsilateral cerebrovascular events. Our aim was to explore the characterization of plaque with CT in symptomatic subjects with bilateral intraplaque hemorrhage.

MATERIALS AND METHODS

Three-hundred-forty-three consecutive patients with recent anterior circulation ischemic events (<2 weeks) and CT of the carotid arteries (performed within 14 days of the cerebrovascular event) evaluated between June 2012 and September 2017 were analyzed for plaque volume composition to identify all subjects with bilateral intraplaque hemorrhage. Plaque volume was semiautomatically measured, and tissue components were classified according to the attenuation values such as the following: calcified (for values of ≥130 HU), mixed (for values of ≥60 and <130 HU), lipid (for values of ≥25 and <60 HU), and intraplaque hemorrhage (for values of <25 HU). Twenty-one subjects (15 men; mean age, 70 ± 11 years; range, 44-87 years) had bilateral intraplaque hemorrhage and were included in the analysis.

RESULTS

Volume measurement revealed significantly larger plaques on the symptomatic side compared with the asymptomatic one (mean, 28 ± 9 versus 22 ± 8 mm, P = .007). Intraplaque hemorrhage volume and percentage were also significantly higher in the plaque ipsilateral to the cerebrovascular event (P < .001 and < .001, respectively). The volume of other plaque components did not show a statically significant association except for lipid and lipid + intraplaque hemorrhage percentages (23% versus 18% and 11% versus 15%), which were significantly different between the symptomatic and the asymptomatic sides (.016 and .011, respectively). The intraplaque hemorrhage/lipid ratio was higher on the symptomatic side (0.596 versus 0.171, P = .001).

CONCLUSIONS

In patients with bilateral intraplaque hemorrhage and recent ischemic symptoms, the plaque ipsilateral to the symptomatic side has significantly larger volume and a higher percentage of intraplaque hemorrhage compared with the contralateral, asymptomatic side.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Microcalcifications, Their Genesis, Growth, and Biomechanical Stability in Fibrous Cap Rupture

For many decades, cardiovascular calcification has been considered as a passive process, accompanying atheroma progression, correlated with plaque burden, and apparently without a major role on plaque vulnerability. Clinical and pathological analyses have previously focused on the total amount of calcification (calcified area in a whole atheroma cross section) and whether more calcification means higher risk of plaque rupture or not. However, this paradigm has been changing in the last decade or so. Recent research has focused on the presence of microcalcifications (μCalcs) in the atheroma and more importantly on whether clusters of μCalcs are located in the cap of the atheroma. While the vast majority of μCalcs are found in the lipid pool or necrotic core, they are inconsequential to vulnerable plaque. Nevertheless, it has been shown that μCalcs located within the fibrous cap could be numerous and that they behave as an intensifier of the background circumferential stress in the cap. It is now known that such intensifying effect depends on the size and shape of the μCalc as well as the proximity between two or more μCalcs. If μCalcs are located in caps with very low background stress, the increase in stress concentration may not be sufficient to reach the rupture threshold. However, the presence of μCalc(s) in the cap with a background stress of about one fifth to one half the rupture threshold (a stable plaque) will produce a significant increase in local stress, which may exceed the cap rupture threshold and thus transform a non-vulnerable plaque into a vulnerable one. Also, the classic view that treats cardiovascular calcification as a passive process has been challenged, and emerging data suggest that cardiovascular calcification may encompass both passive and active processes. The passive calcification process comprises biochemical factors, specifically circulating nucleating complexes, which would lead to calcification of the atheroma. The active mechanism of atherosclerotic calcification is a cell-mediated process via cell death of macrophages and smooth muscle cells (SMCs) and/or the release of matrix vesicles by SMCs.

Multi-objective optimization of coronary stent using Kriging surrogate model

Background

In stent design optimization, the functional relationship between design parameters and design goals is nonlinear, complex, and implicit and the multi-objective design of stents involves a number of potentially conflicting performance criteria. Therefore it is hard and time-consuming to find the optimal design of stent either by experiment or clinic test. Fortunately, computational methods have been developed to the point whereby optimization and simulation tools can be used to systematically design devices in a realistic time-scale. The aim of the present study is to propose an adaptive optimization method of stent design to improve its expansion performance.

Methods

Multi-objective optimization method based on Kriging surrogate model was proposed to decrease the dogboning effect and the radial elastic recoil of stents to improve stent expansion properties and thus reduce the risk of vascular in-stent restenosis injury. Integrating design of experiment methods and Kriging surrogate model were employed to construct the relationship between measures of stent dilation performance and geometric design parameters. Expected improvement, an infilling sampling criterion, was employed to balance local and global search with the aim of finding the global optimal design. A typical diamond-shaped coronary stent-balloon system was taken as an example to test the effectiveness of the optimization method. Finite element method was used to analyze the stent expansion of each design.

Results

27 iterations were needed to obtain the optimal solution. The absolute values of the dogboning ratio at 32 and 42 ms were reduced by 94.21 and 89.43%, respectively. The dogboning effect was almost eliminated after optimization. The average of elastic recoil was reduced by 15.17%.

Conclusion

This article presents FEM based multi-objective optimization method combining with the Kriging surrogate model to decrease both the dogboning effect and radial elastic recoil of stents. The numerical results prove that the proposed optimization method effectively decreased both the dogboning effect and radial elastic recoil of stent. Further investigations containing more design goals and more effective multidisciplinary design optimization method are warranted.

High shear stress induces atherosclerotic vulnerable plaque formation through angiogenesis

Rupture of atherosclerotic plaques causing thrombosis is the main cause of acute coronary syndrome and ischemic strokes. Inhibition of thrombosis is one of the important tasks developing biomedical materials such as intravascular stents and vascular grafts. Shear stress (SS) influences the formation and development of atherosclerosis. The current review focuses on the vulnerable plaques observed in the high shear stress (HSS) regions, which localizes at the proximal region of the plaque intruding into the lumen. The vascular outward remodelling occurs in the HSS region for vascular compensation and that angiogenesis is a critical factor for HSS which induces atherosclerotic vulnerable plaque formation. These results greatly challenge the established belief that low shear stress is important for expansive remodelling, which provides a new perspective for preventing the transition of stable plaques to high-risk atherosclerotic lesions.

The simulation of magnetic resonance elastography through atherosclerosis

The clinical diagnosis of atherosclerosis via the measurement of stenosis size is widely acknowledged as an imperfect criterion. The vulnerability of an atherosclerotic plaque to rupture is associated with its mechanical properties. The potential to image these mechanical properties using magnetic resonance elastography (MRE) was investigated through synthetic datasets. An image of the steady state wave propagation, equivalent to the first harmonic, can be extracted directly from finite element analysis. Inversion of this displacement data yields a map of the shear modulus, known as an elastogram. The variation of plaque composition, stenosis size, Gaussian noise, filter thresholds and excitation frequency were explored. A decreasing mean shear modulus with an increasing lipid composition was identified through all stenosis sizes. However the inversion algorithm showed sensitivity to parameter variation leading to artefacts which disrupted both the elastograms and quantitative trends. As noise was increased up to a realistic level, the contrast was maintained between the fully fibrous and lipid plaques but lost between the interim compositions. Although incorporating a Butterworth filter improved the performance of the algorithm, restrictive filter thresholds resulted in a reduction of the sensitivity of the algorithm to composition and noise variation. Increasing the excitation frequency improved the techniques ability to image the magnitude of the shear modulus and identify a contrast between compositions. In conclusion, whilst the technique has the potential to image the shear modulus of atherosclerotic plaques, future research will require the integration of a heterogeneous inversion algorithm.

Role of biomechanical forces in the natural history of coronary atherosclerosis

Atherosclerosis remains a major cause of morbidity and mortality worldwide, and a thorough understanding of the underlying pathophysiological mechanisms is crucial for the development of new therapeutic strategies. Although atherosclerosis is a systemic inflammatory disease, coronary atherosclerotic plaques are not uniformly distributed in the vascular tree. Experimental and clinical data highlight that biomechanical forces, including wall shear stress (WSS) and plaque structural stress (PSS), have an important role in the natural history of coronary atherosclerosis. Endothelial cell function is heavily influenced by changes in WSS, and longitudinal animal and human studies have shown that coronary regions with low WSS undergo increased plaque growth compared with high WSS regions. Local alterations in WSS might also promote transformation of stable to unstable plaque subtypes. Plaque rupture is determined by the balance between PSS and material strength, with plaque composition having a profound effect on PSS. Prospective clinical studies are required to ascertain whether integrating mechanical parameters with medical imaging can improve our ability to identify patients at highest risk of rapid disease progression or sudden cardiac events.

A computational fluid–structure interaction model of the blood flow in the healthy and varicose saphenous vein

Objective

Varicose vein has become enlarged and twisted and, consequently, has lost its mechanical strength. As a result of the varicose saphenous vein (SV) mechanical alterations, the hemodynamic parameters of the blood flow, such as blood velocity as well as vein wall stress and strain, would change accordingly. However, little is known about stress and strain and there consequences under experimental conditions on blood flow and velocity within normal and varicose veins. In this study, a three-dimensional (3D) computational fluid–structure interaction (FSI) model of a human healthy and varicose SVs was established to determine the hemodynamic characterization of the blood flow as a function of vein wall mechanical properties, i.e. elastic and hyperelastic.

Methods

The mechanical properties of the human healthy and varicose SVs were experimentally measured and implemented into the computational model. The fully coupled fluid and structure models were solved using the explicit dynamics finite element code LS-DYNA.

Results

The results revealed that, regardless of healthy and varicose, the elastic walls reach to the ultimate strength of the vein wall, whereas the hyperelastic wall can tolerate more stress. The highest von Mises stress compared to the healthy ones was seen in the elastic and hyperelastic varicose SVs with 1.412 and 1.535 MPa, respectively. In addition, analysis of the resultant displacement in the vein wall indicated that the varicose SVs experienced a higher displacement compared to the healthy ones irrespective of elastic and hyperelastic material models. The highest blood velocity was also observed for the healthy hyperelastic SV wall.

Conclusion

The findings of this study may have implications not only for determining the role of the vein wall mechanical properties in the hemodynamic alterations of the blood, but also for employing as a null information in balloon-angioplasty and bypass surgeries.

Personalizing flow-diverter intervention for cerebral aneurysms: from computational hemodynamics to biochemical modeling

This paper presents the computational modeling of a variety of flow-diverting stents, deployed in a number of patient-specific aneurysm geometries. We consider virtual device deployment and hemodynamics as well as thrombus formation, with the scope to assess pre-operatively the efficacy of specific devices in treating particular aneurysms. An algorithm based on a linear and torsional spring analogy is developed for the fast virtual deployment of stents and similar minimally invasive devices in patient-specific vessel geometries. The virtual deployment algorithm is used to accurately deploy a total of four stent designs in three aneurysm geometries. A variety of different flow-diverting stent designs, representing the commercially available and the entirely novel, are presented, varying in both mesh design and porosity. Transient computational hemodynamics simulations are performed on multiple patient-specific geometries to predict the reduction in aneurysm inflow after the deployment of each device. Further, a thrombosis initiation and growth model is implemented, coupled with the hemodynamic computations. Hemodynamic simulations show large variations in flow reduction between devices and across different aneurysm geometries. The industry standard of flow-diverters with 70% porosity, assumed to offer the best compromise in flexibility and flow reduction, is challenged in at least one aneurysm geometry.

Fluid-Structure Interaction Analysis of a Soft Robotic Fish Using Piezoelectric Fiber Composite

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260005/13.jpg"" width=""300"" />Model of soft robotic fish</div> Designing a high-performance soft robotic fish requires considering the interaction between the flexible robot structure and surrounding fluid. This paper introduces fluid-structure interaction (FSI) analysis used to enhance the hydrodynamic performance of soft robotic fish using piezoelectric fiber composite (PFC) as the propulsion actuator. The basic FSI analysis scheme for soft robotic fish is presented, then the numerical model of the actuator, robot structure, and surrounding fluid are described based on the FSI analysis scheme. The FSI analysis of the soft robotic fish is performed through these numerical models. To evaluate the effectiveness of FSI analysis, coupling simulation and experimental results are compared. We found that the calculated results of propulsive force and deformation displacement were similar to those for experiments. These results suggest that FSI analysis is useful and is applicable to evaluating propulsion characteristics of the soft robotic fish to improve performance. </span>

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.

Optical measurement of arterial mechanical properties: from atherosclerotic plaque initiation to rupture

During the pathogenesis of coronary atherosclerosis, from lesion initiation to rupture, arterial mechanical properties are altered by a number of cellular, molecular, and hemodynamic processes. There is growing recognition that mechanical factors may actively drive vascular cell signaling and regulate atherosclerosis disease progression. In advanced plaques, the mechanical properties of the atheroma influence stress distributions in the fibrous cap and mediate plaque rupture resulting in acute coronary events. This review paper explores current optical technologies that provide information on the mechanical properties of arterial tissue to advance our understanding of the mechanical factors involved in atherosclerosis development leading to plaque rupture. The optical approaches discussed include optical microrheology and traction force microscopy that probe the mechanical behavior of single cell and extracellular matrix components, and intravascular imaging modalities including laser speckle rheology, optical coherence elastography, and polarization-sensitive optical coherence tomography to measure the mechanical properties of advanced coronary lesions. Given the wealth of information that these techniques can provide, optical imaging modalities are poised to play an increasingly significant role in elucidating the mechanical aspects of coronary atherosclerosis in the future.

Biomechanics of atherosclerotic coronary plaque: site, stability and in vivo elasticity modeling

Coronary atheroma develop in local sites that are widely variable among patients and are considerably variable in their vulnerability for rupture. This article summarizes studies conducted by our collaborative laboratories on predictive biomechanical modeling of coronary plaques. It aims to give insights into the role of biomechanics in the development and localization of atherosclerosis, the morphologic features that determine vulnerable plaque stability, and emerging in vivo imaging techniques that may detect and characterize vulnerable plaque. Composite biomechanical and hemodynamic factors that influence the actual site of development of plaques have been studied. Plaque vulnerability, in vivo, is more challenging to assess. Important steps have been made in defining the biomechanical factors that are predictive of plaque rupture and the likelihood of this occurring if characteristic features are known. A critical key in defining plaque vulnerability is the accurate quantification of both the morphology and the mechanical properties of the diseased arteries. Recently, an early IVUS based palpography technique developed to assess local strain, elasticity and mechanical instabilities has been successfully revisited and improved to account for complex plaque geometries. This is based on an initial best estimation of the plaque components' contours, allowing subsequent iteration for elastic modulus assessment as a basis for plaque stability determination. The improved method has also been preliminarily evaluated in patients with successful histologic correlation. Further clinical evaluation and refinement are on the horizon.

Changing views of the biomechanics of vulnerable plaque rupture: a review

This review examines changing perspectives on the biomechanics of vulnerable plaque rupture over the past 25 years from the first finite element analyses (FEA) showing that the presence of a lipid pool significantly increases the local tissue stress in the atheroma cap to the latest imaging and 3D FEA studies revealing numerous microcalcifications in the cap proper and a new paradigm for cap rupture. The first part of the review summarizes studies describing the role of the fibrous cap thickness, tissue properties, and lesion geometry as main determinants of the risk of rupture. Advantages and limitations of current imaging technologies for assessment of vulnerable plaques are also discussed. However, the basic paradoxes as to why ruptures frequently did not coincide with location of PCS and why caps >65 μm thickness could rupture at tissue stresses significantly below the 300 kPa critical threshold still remained unresolved. The second part of the review describes recent studies in the role of microcalcifications, their origin, shape, and clustering in explaining these unresolved issues including the actual mechanism of rupture due to the explosive growth of tiny voids (cavitation) in local regions of high stress concentration between closely spaced microinclusions oriented along their tensile axis.

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.

Hemodynamic characteristics of the vertebrobasilar system analyzed using MRI-based models

The vertebrobasilar system (VBS) is unique in human anatomy in that two arteries merge into a single vessel, and it is especially important because it supplies the posterior circulation of the brain. Atherosclerosis develops in this region, and atherosclerotic plaques in the vertebrobasilar confluence can progress with catastrophic consequences, including artery occlusion. Quantitative assessments of the flow characteristics in the VBS could elucidate the factors that influence flow patterns in this confluence, and deviations from normal patterns might then be used to predict locations to monitor for potential pathological changes, to detect early signs of disease, and to evaluate treatment options and efficacy. In this study, high-field MRI was used in conjunction with computational fluid dynamics (CFD) modeling to investigate the hemodynamics of subject-specific confluence models (n = 5) and to identify different geometrical classes of vertebrobasilar systems (n = 12) of healthy adult subjects. The curvature of the vessels and their mutual orientation significantly affected flow parameters in the VBS. The basilar artery geometry strongly influenced both skewing of the velocity profiles and the wall shear stress distributions in the VBS. All five subjects modeled possessed varying degrees of vertebral asymmetry, and helical flow was observed in four cases, suggesting that factors other than vertebral asymmetry influence mixing of the vertebral artery flow contributions. These preliminary studies verify that quantitative, MR imaging techniques in conjunction with subject-specific CFD models of healthy adult subjects may be used to characterize VBS hemodynamics and to predict flow features that have been related to the initiation and development of atherosclerosis in large arteries. This work represents an important first step towards applying this approach to study disease initiation and progression in the VBS.

A simplified murine intimal hyperplasia model founded on a focal carotid stenosis

Murine models offer a powerful tool for unraveling the mechanisms of intimal hyperplasia and vascular remodeling, although their technical complexity increases experimental variability and limits widespread application. We describe a simple and clinically relevant mouse model of arterial intimal hyperplasia and remodeling. Focal left carotid artery (LCA) stenosis was created by placing 9-0 nylon suture around the artery using an external 35-gauge mandrel needle (middle or distal location), which was then removed. The effect of adjunctive diet-induced obesity was defined. Flowmetry, wall strain analyses, biomicroscopy, and histology were completed. LCA blood flow sharply decreased by ∼85%, followed by a responsive right carotid artery increase of ∼71%. Circumferential strain decreased by ∼2.1% proximal to the stenosis in both dietary groups. At 28 days, morphologic adaptations included proximal LCA intimal hyperplasia, which was exacerbated by diet-induced obesity. The proximal and distal LCA underwent outward and negative inward remodeling, respectively, in the mid-focal stenosis (remodeling indexes, 1.10 and 0.53). A simple, defined common carotid focal stenosis yields reproducible murine intimal hyperplasia and substantial differentials in arterial wall adaptations. This model offers a tool for investigating mechanisms of hemodynamically driven intimal hyperplasia and arterial wall remodeling.

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.

Microcalcifications increase coronary vulnerable plaque rupture potential: a patient-based micro-CT fluid-structure interaction study

Asymptomatic vulnerable plaques (VP) in coronary arteries accounts for significant level of morbidity. Their main risk is associated with their rupture which may prompt fatal heart attacks and strokes. The role of microcalcifications (micro-Ca), embedded in the VP fibrous cap, in the plaque rupture mechanics has been recently established. However, their diminutive size offers a major challenge for studying the VP rupture biomechanics on a patient specific basis. In this study, a highly detailed model was reconstructed from a post-mortem coronary specimen of a patient with observed VP, using high resolution micro-CT which captured the microcalcifications embedded in the fibrous cap. Fluid-structure interaction (FSI) simulations were conducted in the reconstructed model to examine the combined effects of micro-Ca, flow phase lag and plaque material properties on plaque burden and vulnerability. This dynamic fibrous cap stress mapping elucidates the contribution of micro-Ca and flow phase lag VP vulnerability independently. Micro-Ca embedded in the fibrous cap produced increased stresses predicted by previously published analytical model, and corroborated our previous studies. The 'micro-CT to FSI' methodology may offer better diagnostic tools for clinicians, while reducing morbidity and mortality rates for patients with vulnerable plaques and ameliorating the ensuing healthcare costs.

Intravascular optical imaging technology for investigating the coronary artery

There is an ever-increasing demand for new imaging methods that can provide additional information about the coronary wall to better characterize and stratify high-risk plaques, and to guide interventional and pharmacologic management of patients with coronary artery disease. While there are a number of imaging modalities that facilitate the assessment of coronary artery pathology, this review paper focuses on intravascular optical imaging modalities that provide information on the microstructural, compositional, biochemical, biomechanical, and molecular features of coronary lesions and stents. The optical imaging modalities discussed include angioscopy, optical coherence tomography, polarization sensitive-optical coherence tomography, laser speckle imaging, near-infrared spectroscopy, time-resolved laser induced fluorescence spectroscopy, Raman spectroscopy, and near-infrared fluorescence molecular imaging. Given the wealth of information that these techniques can provide, optical imaging modalities are poised to play an increasingly significant role in the evaluation of the coronary artery in the future.

Intracranial collateralization determines hemodynamic forces for carotid plaque disruption

INTRODUCTION

Percent diameter reduction provides an imperfect assessment of the risk for stroke from carotid atheroembolism. Stroke associated with atherosclerotic carotid stenosis commonly results from plaque disruption brought about by hemodynamic shear stress and Bernoulli forces. The aim of the present study was to predict the effect of incomplete intracranial collateralization through the circle of Willis (COW) on disruptive hemodynamic forces acting on carotid plaques.

METHODS

A simple circuit model of the major pathways and collaterals that form and supply the COW was developed. We modeled the intra- and extracranial arterial circuits from standard anatomic references, and the pressure-flow relationships within these conduits from standard fluid mechanics. The pressure drop caused by (laminar and turbulent) flow along the internal carotid artery path was then computed. Carotid circulation to the brain was classified as being with or without collateral connections through the COW, and the extracranial carotid circuit as being with or without severe stenosis. The pressure drop was computed for each scenario. Finally, a linear circuit model was used to compute brain blood flow in the presence/absence of a disconnected COW.

RESULTS

Pressure drop across a carotid artery stenosis increased as the flow rate within the carotid conduit increased. Poststenotic turbulence from a sudden expansion distal to the stenosis resulted in an additional pressure drop. Despite the stenosis, mean brain blood flow was sustained at 4.15 mL/s bilaterally. In the presence of an intact (collateralized) COW, this was achieved by enhanced flow in the contralateral (normal) carotid artery. However, in a disconnected COW, this was achieved by sustained systolic and enhanced diastolic flow through the stenosed artery. For a similar degree of stenosis, flow and velocity across the plaque was much higher when the COW was disconnected compared with an intact COW. Furthermore, the pressure drop across a similar stenosis was significantly higher with a disconnected COW compared with an intact COW.

CONCLUSIONS

Incomplete intracranial collateralization through the COW results in increased flow rates and velocities, and therefore large pressure drops across a carotid artery stenosis. This exerts large disruptive shear stress on the plaque compared with patients with an intact COW. Percent diameter reduction provides an inaccurate assessment of risk for atheroembolic stroke. An assessment of carotid flow rates, flow velocities, and the intracranial collateral circulation may add independent information to refine the estimation of stroke risk in patients with asymptomatic carotid atherosclerosis.

Study of carotid arterial plaque stress for symptomatic and asymptomatic patients

Stroke is one of the leading causes of death in the world, resulting mostly from the sudden ruptures of atherosclerosis carotid plaques. Until now, the exact plaque rupture mechanism has not been fully understood, and also the plaque rupture risk stratification. The advanced multi-spectral magnetic resonance imaging (MRI) has allowed the plaque components to be visualized in-vivo and reconstructed by computational modeling. In the study, plaque stress analysis using fully coupled fluid structure interaction was applied to 20 patients (12 symptomatic and 8 asymptomatic) reconstructed from in-vivo MRI, followed by a detailed biomechanics analysis, and morphological feature study. The locally extreme stress conditions can be found in the fibrous cap region, 85% at the plaque shoulder based on the present study cases. Local maximum stress values predicted in the plaque region were found to be significantly higher in symptomatic patients than that in asymptomatic patients (200 ± 43 kPa vs. 127 ± 37 kPa, p=0.001). Plaque stress level, defined by excluding 5% highest stress nodes in the fibrous cap region based on the accumulative histogram of stress experienced on the computational nodes in the fibrous cap, was also significantly higher in symptomatic patients than that in asymptomatic patients (154 ± 32 kPa vs. 111 ± 23 kPa, p<0.05). Although there was no significant difference in lipid core size between the two patient groups, symptomatic group normally had a larger lipid core and a significantly thinner fibrous cap based on the reconstructed plaques using 3D interpolation from stacks of 2D contours. Plaques with a higher stenosis were more likely to have extreme stress conditions upstream of plaque throat. The combined analyses of plaque MR image and plaque stress will advance our understanding of plaque rupture, and provide a useful tool on assessing plaque rupture risk.

Carotid artery stenting simulation: from patient-specific images to finite element analysis

The outcome of carotid artery stenting (CAS) depends on a proper selection of patients and devices, requiring dedicated tools able to relate the device features with the target vessel. In the present study, we use finite element analysis to evaluate the performance of three self-expanding stent designs (laser-cut open-cell, laser-cut closed-cell, braided closed-cell) in a carotid artery (CA). We define six stent models considering the three designs in different sizes and configurations (i.e. straight and tapered), evaluating the stress induced in the vessel wall, the lumen gain and the vessel straightening in a patient-specific CA model based on computed angiography tomography (CTA) images. For the considered vascular anatomy and stents, the results suggest that: (i) the laser-cut closed-cell design provides a higher lumen gain; (ii) the impact of the stent configuration and of the stent oversizing is negligible with respect to the lumen gain and relevant with respect to the stress induced in the vessel wall; (iii) stent design, configuration and size have a limited impact on the vessel straightening. The presented numerical model represents a first step towards a quantitative assessment of the relation between a given carotid stent design and a given patient-specific CA anatomy.