Influence of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: potential impact for evaluating the risk of plaque rupture

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.

On the Impact of Residual Strains in the Stress Analysis of Patient-Specific Atherosclerotic Carotid Vessels: Predictions Based on the Homogenous Stress Hypothesis

The identification of carotid atherosclerotic lesion at risk for plaque rupture, eventually resulting in cerebral embolism and stroke, is of paramount clinical importance. High stress in the fibrous plaque cap has been proposed as risk factor. However, among others, residual strains influence said stress predictions, but quantitative and qualitative implications of residual strains in this context are not well explored. We therefore propose a multiplicative kinematics-based Growth and Remodeling (G&R) framework to predict residual strains from homogenizing tissue stress and then investigate its implication on plaque stress. Carotid vessel morphology of four patients was reconstructed from clinical Computed Tomography-Angiography (CT-A) images and equipped with heterogeneous tissue constitutive properties assigned through a histology-based artificial intelligence image segmentation tool. As compared to a purely elastic analysis and depending on patient-specific morphology and tissue distributions, the incorporation of residual strains reduced the maximum wall stress by up to 30 % and resulted in a fundamentally different distribution of stress across the atherosclerotic wall. Regardless residual strains homogenized tissue stresses, the fibrous plaque cap may persistently be exposed to spots of high stress. In conclusion, the incorporation of residual strains in biomechanical studies of atherosclerotic carotids may be important for a reliable assessment of fibrous plaque cap stress.

Impact of residual stress on coronary plaque stress/strain calculations using optical coherence tomography image-based multi-layer models

Introduction

Mechanical stress and strain conditions play an important role in atherosclerosis plaque progression, remodeling and potential rupture and may be used in plaque vulnerability assessment for better clinical diagnosis and treatment decisions. Single layer plaque models without residual stress have been widely used due to unavailability of multi-layer image segmentation method and residual stress data. However, vessel layered structure and residual stress have large impact on stress/strain calculations and should be included in the models.

Methods

In this study, intravascular optical coherence tomography (OCT) data of coronary plaques from 10 patients were acquired and segmented to obtain the three-layer vessel structure using an in-house automatic segmentation algorithm. Multi- and single-layer 3D thin-slice biomechanical plaque models with and without residual stress were constructed to assess the impact of residual stress on stress/strain calculations.

Results

Our results showed that residual stress led to a more uniform stress distribution across the vessel wall, with considerable plaque stress/strain decrease on inner wall and increase on vessel out-wall. Multi-layer model with residual stress inclusion reduced inner wall maximum and mean plaque stresses by 38.57% and 59.70%, and increased out-wall maximum and mean plaque stresses by 572.84% and 432.03%.

Conclusion

These findings demonstrated the importance of multi-layer modeling with residual stress for more accurate plaque stress/strain calculations, which will have great impact in plaque cap stress calculation and plaque rupture risk assessment. Further large-scale studies are needed to validate our findings.

Analysis of the geometrical influence of ring-opening samples on arterial circumferential residual stress reconstruction

This work consists of analyzing the impact of geometrical features (thickness and curvature) on the estimation of circumferential residual stresses in arteries. For this purpose, a specific sample of lamb abdominal artery is chosen for analysis and, through computational tools based on Python libraries, the stress-free geometry is captured after the ring opening test. Numerical simulations are then used to reconstruct the sample in order to estimate the circumferential residual stresses. Then, four stress-free geometry models are analyzed: an ideal geometry, i.e., constant curvature and thickness; a constant curvature and variable thickness geometry; a variable curvature and constant thickness geometry; and a variable curvature and thickness geometry. The numerical results show that models perform well from a geometric point of view, where the most different feature was the closed outer perimeter that differs about 14% from the closed real sample. As far as residual stress is concerned, differences up to 198% were found in more realistic models taking a constant curvature and thickness model as reference. Thus, the analysis of a realistic geometry with highly variable curvature and thickness can introduce, compared to an idealized geometry, significant differences in the estimation of residual stresses. This could indicate that the characterization of arterial residual stresses is not sufficient when considering only the opening angle and, therefore, it is also necessary to incorporate more geometrical variables.

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.

Fitting mechanical properties of the aortic wall and individual layers to experimental tensile tests including residual stresses

The authors have observed that a stress-strain curve for uniaxial tension of an aortic intact wall cannot be simply obtained by combining the strain energy functions of the three individual aortic layers - intima, media and adventitia - even taking into account the interaction among the three layers; the strain energy functions of the three layers are obtained fitting tensile tests on strips from the individual layers. Due to the layer separation, the residual stresses are released and thus they do not affect the stress-strain curves of the individual layers. The present study shows that it is instead possible to fit the intact wall experimental curves with the combination of the strain energy functions of the three individual layers if residual strains are added. The residual strains are used as optimization parameters with specific constraints and allowing for the buckling (wrinkling) of the intima under unpressurized condition of the aortic wall, as experimentally observed. By varying these parameters in the experimentally observed range of values, it is possible to find a solution with the combined responses of the individual layers matching the experimental stress-strain curves of the intact wall.

Quantification of patient-specific coronary material properties and their correlations with plaque morphological characteristics: An in vivo IVUS study

BACKGROUND

A method using in vivo Cine IVUS and VH-IVUS data has been proposed to quantify material properties of coronary plaques. However, correlations between plaque morphological characteristics and mechanical properties have not been studied in vivo.

METHOD

In vivo Cine IVUS and VH-IVUS data were acquired at 32 plaque cross-sections from 19 patients. Six morphological factors were extracted for each plaque. These samples were categorized into healthy vessel, fibrous plaque, lipid-rich plaque and calcified plaque for comparisons. Three-dimensional thin-slice models were constructed using VH-IVUS data to quantify in vivo plaque material properties following a finite element updating approach by matching Cine IVUS data. Effective Young's moduli were calculated to represent plaque stiffness for easy comparison. Spearman's rank correlation analysis was performed to identify correlations between plaque stiffness and morphological factor. Kruskal-Wallis test with Bonferroni correction was used to determine whether significant differences in plaque stiffness exist among four plaque groups.

RESULT

Our results show that lumen circumference change has a significantly negative correlation with plaque stiffness (r = -0.7807, p = 0.0001). Plaque burden and calcification percent also had significant positive correlations with plaque stiffness (r = 0.5105, p < 0.0272 and r = 0.5312, p < 0.0193) respectively. Among the four categorized groups, calcified plaques had highest stiffness while healthy segments had the lowest.

CONCLUSION

There is a close link between plaque morphological characteristics and mechanical properties in vivo. Plaque stiffness tends to be higher as coronary atherosclerosis advances, indicating the potential to assess plaque mechanical properties in vivo based on plaque compositions.

Inverse material parameter estimation of patient-specific finite element models at the carotid bifurcation: The impact of excluding the zero-pressure configuration and residual stress

The carotid bifurcation experiences a complex loading environment due to its anatomical structure. Previous in-vivo material parameter estimation methods often use simplified model geometries, isotropic hyperelastic constitutive equations or neglect key aspects of the vessel, such as the zero-pressure configuration or residual stress, all of which have independently been shown to alter the stress environment of the vessel wall. Characterizing the location of high stress in the vessel wall has often been proposed as a potential indicator of structural weakness. However, excluding the afore-mentioned zero-pressure configuration, residual stress and patient-specific material parameters can lead to an incorrect estimation of the true stress values observed, meaning that stress alone as a risk indicator of rupture is insufficient. In this study, we investigate how the estimated material parameters and overall stress distributions in geometries of carotid bifurcations, extracted from in-vivo MR images, alter with the inclusion of the zero-pressure configuration and residual stress. This approach consists of the following steps: (1) geometry segmentation and hexahedral meshing from in-vivo magnetic resonance images (MRI) at two known phases; (2) computation of the zero-pressure configuration and the associated residual stresses; (3) minimization of an objective function built on the difference between the stress states of an "almost true" stress field at two known phases and a "deformed" stress field by altering the input material parameters to determine patient-specific material properties; and (4) comparison of the stress distributions throughout these carotid bifurcations for all cases with estimated material parameters. This numerical approach provides insights into the need for estimation of both the zero-pressure configuration and residual stress for accurate material property estimation and stress analysis for the carotid bifurcation, establishing the reliability of stress as a rupture risk metric.

Coronary artery plaque rupture and erosion: Role of wall shear stress profiling and biological patterns in acute coronary syndromes

AIMS

Wall shear stress (WSS) is involved in coronary artery plaque pathological mechanisms and modulation of gene expression. This study aims to provide a comprehensive haemodynamic and biological description of unstable (intact-fibrous-cap, IFC, and ruptured-fibrous-cap, RFC) and stable (chronic coronary syndrome, CCS) plaques and investigate any correlation between WSS and molecular pathways.

METHODS AND RESULTS

We enrolled 24 CCS and 25 Non-ST Elevation Myocardial Infarction-ACS patients with IFC (n = 11) and RFC (n = 14) culprit lesions according to optical coherence tomography analysis. A real-time PCR primer array was performed on peripheral blood mononuclear cells for 17 different molecules whose expression is linked to WSS. Computational fluid dynamics simulations were performed in high-fidelity 3D-coronary artery anatomical models for three patients per group. A total of nine genes were significantly overexpressed in the unstable patients as compared to CCS patients, with no differences between IFC and RFC groups (GPX1, MMP1, MMP9, NOS3, PLA2G7, PI16, SOD1, TIMP1, and TFRC) while four displayed different levels between IFC and RFC groups (TNFα, ADAMTS13, EDN1, and LGALS8). A significantly higher WSS was observed in the RFC group (p < 0.001) compared to the two other groups. A significant correlation was observed between TNFα (p < 0.001), EDN1 (p = 0.036), and MMP9 (p = 0.005) and WSS values in the RFC group.

CONCLUSIONS

Our data demonstrate that IFC and RFC plaques are subject to different WSS conditions and gene expressions, suggesting that WSS profiling may play an essential role in the plaque instability characterization with relevant diagnostic and therapeutic implications in the era of precision medicine.

The effect of plaque morphology, material composition and microcalcifications on the risk of cap rupture: A structural analysis of vulnerable atherosclerotic plaques

Background

The mechanical rupture of an atheroma cap may initiate a thrombus formation, followed by an acute coronary event and death. Several morphology and tissue composition factors have been identified to play a role on the mechanical stability of an atheroma, including cap thickness, lipid core stiffness, remodeling index, and blood pressure. More recently, the presence of microcalcifications (μCalcs) in the atheroma cap has been demonstrated, but their combined effect with other vulnerability factors has not been fully investigated.

Materials and methods

We performed numerical simulations on 3D idealized lesions and a microCT-derived human coronary atheroma, to quantitatively analyze the atheroma cap rupture. From the predicted cap stresses, we defined a biomechanics-based vulnerability index (VI) to classify the impact of each risk factor on plaque stability, and developed a predictive model based on their synergistic effect.

Results

Plaques with low remodeling index and soft lipid cores exhibit higher VI and can shift the location of maximal wall stresses. The VI exponentially rises as the cap becomes thinner, while the presence of a μCalc causes an additional 2.5-fold increase in vulnerability for a spherical inclusion. The human coronary atheroma model had a stable phenotype, but it was transformed into a vulnerable plaque after introducing a single spherical μCalc in its cap. Overall, cap thickness and μCalcs are the two most influential factors of mechanical rupture risk.

Conclusions

Our findings provide supporting evidence that high risk lesions are non-obstructive plaques with softer (lipid-rich) cores and a thin cap with μCalcs. However, stable plaques may still rupture in the presence of μCalcs.

Intravascular optical coherence elastography

Optical coherence elastography (OCE), a functional extension of optical coherence tomography (OCT), visualizes tissue strain to deduce the tissue's biomechanical properties. In this study, we demonstrate intravascular OCE using a 1.1 mm motorized catheter and a 1.6 MHz Fourier domain mode-locked OCT system. We induced an intraluminal pressure change by varying the infusion rate from the proximal end of the catheter. We analysed the pixel-matched phase change between two different frames to yield the radial strain. Imaging experiments were carried out in a phantom and in human coronary arteries in vitro. At an imaging speed of 3019 frames/s, we were able to capture the dynamic strain. Stiff inclusions in the phantom and calcification in atherosclerotic plaques are associated with low strain values and can be distinguished from the surrounding soft material, which exhibits elevated strain. For the first time, circumferential intravascular OCE images are provided side by side with conventional OCT images, simultaneously mapping both the tissue structure and stiffness.

Image-Based Finite Element Modeling Approach for Characterizing In Vivo Mechanical Properties of Human Arteries

Mechanical properties of the arterial walls could provide meaningful information for the diagnosis, management and treatment of cardiovascular diseases. Classically, various experimental approaches were conducted on dissected arterial tissues to obtain their stress-stretch relationship, which has limited value clinically. Therefore, there is a pressing need to obtain biomechanical behaviors of these vascular tissues in vivo for personalized treatment. This paper reviews the methods to quantify arterial mechanical properties in vivo. Among these methods, we emphasize a novel approach using image-based finite element models to iteratively determine the material properties of the arterial tissues. This approach has been successfully applied to arterial walls in various vascular beds. The mechanical properties obtained from the in vivo approach were compared to those from ex vivo experimental studies to investigate whether any discrepancy in material properties exists for both approaches. Arterial tissue stiffness values from in vivo studies generally were in the same magnitude as those from ex vivo studies, but with lower average values. Some methodological issues, including solution uniqueness and robustness; method validation; and model assumptions and limitations were discussed. Clinical applications of this approach were also addressed to highlight their potential in translation from research tools to cardiovascular disease management.

Estimation of the zero-pressure computational start shape of atherosclerotic plaques: Improving the backward displacement method with deformation gradient tensor

Advances in medical imaging have enabled patient-specific biomechanical modelling of arterial lesions such as atherosclerosis and aneurysm. Geometry acquired from in-vivo imaging is already pressurized and a zero-pressure computational start shape needs to be identified. The backward displacement algorithm was proposed to solve this inverse problem, utilizing fixed-point iterations to gradually approach the start shape. However, classical fixed-point implementations were reported with suboptimal convergence properties under large deformations. In this paper, a dynamic learning rate guided by the deformation gradient tensor was introduced to control the geometry update. The effectiveness of this new algorithm was demonstrated for both idealized and patient-specific models. The proposed algorithm led to faster convergence by accelerating the initial steps and helped to avoid the non-convergence in large-deformation problems.

Multicomponent material property characterization of atherosclerotic human carotid arteries through a Bayesian Optimization based inverse finite element approach

OBJECTIVE

Plaque rupture in atherosclerotic carotid arteries is a main cause of ischemic stroke and it is correlated with high plaque stresses. Hence, analyzing stress patterns is essential for plaque specific rupture risk assessment. However, the critical information of the multicomponent material properties of atherosclerotic carotid arteries is still lacking greatly. This work aims to characterize component-wise material properties of atherosclerotic human carotid arteries under (almost) physiological loading conditions.

METHODS

An inverse finite element modeling (iFEM) framework was developed to characterize fibrous intima and vessel wall material properties of 13 cross sections from five carotids. The novel pipeline comprised ex-vivo inflation testing, pre-clinical high frequency ultrasound for deriving plaque deformations, pre-clinical high-magnetic field magnetic resonance imaging, finite element modeling, and a sample efficient machine learning based Bayesian Optimization.

RESULTS

The nonlinear Yeoh constants for the fibrous intima and wall layers were successfully obtained. The optimization scheme of the iFEM reached the global minimum with a mean error of 3.8% in 133 iterations on average. The uniqueness of the results were confirmed with the inverted Gaussian Process (GP) model trained during the iFEM protocol.

CONCLUSION

The developed iFEM approach combined with the inverted GP model successfully predicted component-wise material properties of intact atherosclerotic human carotids ex-vivo under physiological-like loading conditions.

SIGNIFICANCE

We developed a novel iFEM framework for the nonlinear, component-wise material characterization of atherosclerotic arteries and utilized it to obtain human atherosclerotic carotid material properties. The developed iFEM framework has great potential to be advanced for patient-specific in-vivo application.

Quantifying Patient-Specific in vivo Coronary Plaque Material Properties for Accurate Stress/Strain Calculations: An IVUS-Based Multi-Patient Study

Introduction: Mechanical forces are closely associated with plaque progression and rupture. Precise quantifications of biomechanical conditions using in vivo image-based computational models depend heavily on the accurate estimation of patient-specific plaque mechanical properties. Currently, mechanical experiments are commonly performed on ex vivo cardiovascular tissues to determine plaque material properties. Patient-specific in vivo coronary material properties are scarce in the existing literature.

Methods:In vivo Cine intravascular ultrasound and virtual histology intravascular ultrasound (IVUS) slices were acquired at 20 plaque sites from 13 patients. A three-dimensional thin-slice structure-only model was constructed for each slice to obtain patient-specific in vivo material parameter values following an iterative scheme. Effective Young's modulus (YM) was calculated to indicate plaque stiffness for easy comparison purposes. IVUS-based 3D thin-slice models using in vivo and ex vivo material properties were constructed to investigate their impacts on plaque wall stress/strain (PWS/PWSn) calculations.

Results: The average YM values in the axial and circumferential directions for the 20 plaque slices were 599.5 and 1,042.8 kPa, respectively, 36.1% lower than those from published ex vivo data. The YM values in the circumferential direction of the softest and stiffest plaques were 103.4 and 2,317.3 kPa, respectively. The relative difference of mean PWSn on lumen using the in vivo and ex vivo material properties could be as high as 431%, while the relative difference of mean PWS was much lower, about 3.07% on average.

Conclusion: There is a large inter-patient and intra-patient variability in the in vivo plaque material properties. In vivo material properties have a great impact on plaque stress/strain calculations. In vivo plaque material properties have a greater impact on strain calculations. Large-scale-patient studies are needed to further verify our findings.

Multicomponent Mechanical Characterization of Atherosclerotic Human Coronary Arteries: An Experimental and Computational Hybrid Approach

Atherosclerotic plaque rupture in coronary arteries, an important trigger of myocardial infarction, is shown to correlate with high levels of pressure-induced mechanical stresses in plaques. Finite element (FE) analyses are commonly used for plaque stress assessment. However, the required information of heterogenous material properties of atherosclerotic coronaries remains to be scarce. In this work, we characterized the component-wise mechanical properties of atherosclerotic human coronary arteries. To achieve this, we performed ex vivo inflation tests on post-mortem human coronary arteries and developed an inverse FE modeling (iFEM) pipeline, which combined high-frequency ultrasound deformation measurements, a high-field magnetic resonance-based artery composition characterization, and a machine learning-based Bayesian optimization (BO) with uniqueness assessment. By using the developed pipeline, 10 cross-sections from five atherosclerotic human coronary arteries were analyzed, and the Yeoh material model constants of the fibrous intima and arterial wall components were determined. This work outlines the developed pipeline and provides the knowledge of non-linear, multicomponent mechanical properties of atherosclerotic human coronary arteries.

Multi-patient study for coronary vulnerable plaque model comparisons: 2D/3D and fluid-structure interaction simulations

Several image-based computational models have been used to perform mechanical analysis for atherosclerotic plaque progression and vulnerability investigations. However, differences of computational predictions from those models have not been quantified at multi-patient level. In vivo intravascular ultrasound (IVUS) coronary plaque data were acquired from seven patients. Seven 2D/3D models with/without circumferential shrink, cyclic bending and fluid–structure interactions (FSI) were constructed for the seven patients to perform model comparisons and quantify impact of 2D simplification, circumferential shrink, FSI and cyclic bending plaque wall stress/strain (PWS/PWSn) and flow shear stress (FSS) calculations. PWS/PWSn and FSS averages from seven patients (388 slices for 2D and 3D thin-layer models) were used for comparison. Compared to 2D models with shrink process, 2D models without shrink process overestimated PWS by 17.26%. PWS change at location with greatest curvature change from 3D FSI models with/without cyclic bending varied from 15.07% to 49.52% for the seven patients (average = 30.13%). Mean Max-FSS, Min-FSS and Ave-FSS from the flow-only models under maximum pressure condition were 4.02%, 11.29% and 5.45% higher than those from full FSI models with cycle bending, respectively. Mean PWS and PWSn differences between FSI and structure-only models were only 4.38% and 1.78%. Model differences had noticeable patient variations. FSI and flow-only model differences were greater for minimum FSS predictions, notable since low FSS is known to be related to plaque progression. Structure-only models could provide PWS/PWSn calculations as good approximations to FSI models for simplicity and time savings in calculation.

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%).

The biology of vascular calcification

Vascular calcification (VC), characterized by different mineral deposits (i.e., carbonate apatite, whitlockite and hydroxyapatite) accumulating in blood vessels and valves, represents a relevant pathological process for the aging population and a life-threatening complication in acquired and in genetic diseases. Similarly to bone remodeling, VC is an actively regulated process in which many cells and molecules play a pivotal role. This review aims at: (i) describing the role of resident and circulating cells, of the extracellular environment and of positive and negative factors in driving the mineralization process; (ii) detailing the types of VC (i.e., intimal, medial and cardiac valve calcification); (iii) analyzing rare genetic diseases underlining the importance of altered pyrophosphate-dependent regulatory mechanisms; (iv) providing therapeutic options and perspectives.

Multi-scale modeling of the lamellar unit of arterial media

The heterogeneity of the lamellar unit (LU) of arterial media plays an important role in the biomechanics of artery. Current two-component (fibrous component and a homogenous matrix) constitutive model is inappropriate for capturing the micro-structural variations in the LU, such as contraction/relaxation of vascular smooth muscle cells (VSMCs), fragmentation of the elastin layer, and deposition/disruption of the collagen network. In this work, we developed a representative volume element (RVE) model with detailed micro-configurations, i.e., VSMCs at various phenotypes, collagen fibers, and elastin laminate embedded in the ground substance. The fiber architecture was generated based on its volume fraction and orientations. Our multi-scale model demonstrated the relation between the arterial expansion and the micro-structural variation of the lamellar unit. The obtained uniaxial response of the LU was validated against the published experimental data. The load sharing capacity of fibrous component and VSMCs of the LU were obtained. We found that the VSMC could take 30% of the circumferential load when contracted until the collagen fibers were recruited, while this value was less than 2% for the relaxed VSMC. In addition, the contribution of collagen fibers at low stretch levels was negligible but became predominant when straightened in high stretches.Moreover, aging effects by collagen deposition was modeled to estimate the arterial stiffening. It was revealed that the aortic stiffness is mainly controlled by collagen fibers, instead of VSMCs. Our findings could shed some light about the contribution of VSMCs in arterial stiffness which has been under debate in recent years.

Ventricle stress/strain comparisons between Tetralogy of Fallot patients and healthy using models with different zero-load diastole and systole morphologies

Patient-specific in vivo ventricle mechanical wall stress and strain conditions are important for cardiovascular investigations and should be calculated from correct zero-load ventricle morphologies. Cardiac magnetic resonance (CMR) data were obtained from 6 healthy volunteers and 12 Tetralogy of Fallot (TOF) patients with consent obtained. 3D patient-specific CMR-based ventricle models with different zero-load diastole and systole geometries due to myocardium contraction and relaxation were constructed to qualify right ventricle (RV) diastole and systole stress and strain values at begin-filling, end-filling, begin-ejection, and end-ejection, respectively. Our new models (called 2G models) can provide end-diastole and end-systole stress/strain values which models with one zero-load geometries (called 1G models) could not provide. 2G mean end-ejection stress value from the 18 participants was 321.4% higher than that from 1G models (p = 0.0002). 2G mean strain values was 230% higher than that of 1G models (p = 0.0002). TOF group (TG) end-ejection mean stress value was 105.4% higher than that of healthy group (HG) (17.54±7.42kPa vs. 8.54±0.92kPa, p = 0.0245). Worse outcome group (WG, n = 6) post pulmonary valve replacement (PVR) begin-ejection mean stress was 57.4% higher than that of better outcome group (BG, 86.94±26.29 vs. 52.93±22.86 kPa; p = 0.041). Among 7 selected parameters, End-filling stress was the best predictor to differentiate BG patients from WG patients with prediction accuracy = 0.8208 and area under receiver operating characteristic curve (AUC) value at 0.8135 (EE stress). Large scale studies are needed to further validate our findings.

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.

Simultaneous evaluation of plaque stability and ischemic potential of coronary lesions in a fluid-structure interaction analysis

The measurement of fractional flow reserve (FFR) and superficial wall stress (SWS) identifies inducible myocardial ischemia and plaque vulnerability, respectively. A simultaneous evaluation of both FFR and SWS is still lacking, while it may have a major impact on therapy. A new computational model of one-way fluid-structure interaction (FSI) was implemented and used to perform a total of 54 analyses in virtual coronary lesion models, based on plaque compositions, arterial remodeling patterns, and stenosis morphologies under physiological conditions. Due to a greater lumen dilation and more induced strain, FFR in the lipid-rich lesions (0.81 ± 0.15) was higher than that in fibrous lesions (0.79 ± 0.16, P = 0.001) and calcified lesions (0.79 ± 0.16, P = 0.001). Four types of lesions were further defined, based on the combination of cutoff values for FFR (0.80) and maximum relative SWS (30 kPa): The level of risk increased from (1) plaques with mild-to-moderate stenosis but negative remodeling for lipid-rich (Type A: non-ischemic, stable) to (2) lipid-rich plaques with mild-to-moderate stenosis and without-to-positive remodeling (Type B: non-ischemic, unstable) or plaques with severe stenosis but negative remodeling for lipid-rich (Type C: ischemic, stable) to (3) lipid-rich plaques with severe stenosis and without-to-positive remodeling (Type D: ischemic, unstable). The analysis of FSI to simultaneously evaluate inducible myocardial ischemia and plaque stability may be useful to identify coronary lesions at a high risk and to ultimately optimize treatment. Further research is warranted to assess whether a more aggressive treatment may improve the prognosis of patients with non-ischemic, intermediate, and unstable lesions.

Intraluminal Ultrasonic Palpation Imaging Technique Revisited for Anisotropic Characterization of Healthy and Atherosclerotic Coronary Arteries: A Feasibility Study

Accurate mechanical characterization of coronary atherosclerotic lesions remains essential for the in vivo detection of vulnerable plaques. Using intravascular ultrasound strain measurements and based on the mechanical response of a circular and concentric vascular model, E. I. Céspedes, C. L. de Korte and A. F. van der Steen developed an elasticity-palpography technique in 2000 to estimate the apparent stress-strain modulus palpogram of the thick subendoluminal arterial wall layer. More recently, this approach was improved by our group to consider the real anatomic shape of the vulnerable plaque. Even though these two studies highlighted original and promising approaches for improving the detection of vulnerable plaques, they did not overcome a main limitation related to the anisotropic mechanical behavior of the vascular tissue. The present study was therefore designed to extend these previous approaches by considering the orthotropic mechanical properties of the arterial wall and lesion constituents. Based on the continuum mechanics theory prescribing the strain field, an elastic anisotropy index was defined. This new anisotropic elasticity-palpography technique was successfully applied to characterize ten coronary plaque and one healthy vessel geometries of patients imaged in vivo with intravascular ultrasound. The results revealed that the anisotropy index-palpograms were estimated with a good accuracy (with a mean relative error of 26.8 ± 48.8%) compared with ground true solutions.

Association Between Incomplete Circle of Willis and Carotid Vulnerable Atherosclerotic Plaques

Objective—

Carotid high-risk plaque, characterized by intraplaque hemorrhage, fibrous cap rupture, and large lipid-rich necrotic core, is associated with cerebrovascular events. This study sought to investigate the relationship between high-risk carotid plaque and an incomplete circle of Willis (COW).

Approach and Results—

Patients were recruited from a multicenter study, Chinese Atherosclerosis Risk Evaluation (CARE-II) and underwent 3-dimensional time-of-flight magnetic resonance angiography for intracranial arteries and 2-dimensional multicontrast magnetic resonance vessel wall imaging for carotid arteries on a 3.0T magnetic resonance scanner. The integrity of the COW in anterior and posterior portions was evaluated. Characteristics of carotid plaques were assessed. Correlation between incomplete COW and carotid plaque features was determined. Of 482 eligible patients, patients with carotid intraplaque hemorrhage showed significantly higher prevalence of an incomplete anterior COW (52.7% versus 38.5%; P =0.022) compared with those without. An incomplete anterior COW was associated with intraplaque hemorrhage before (odds ratio, 1.781; 95% CI, 1.083–2.931; P =0.023) and after adjusted for clinical risk factors (odds ratio, 1.945; 95% CI, 1.139–3.321; P =0.015). The unilateral carotid artery stenosis showed no correlation with incomplete anterior COW and posterior COW (all P >0.025). No significant associations were found between other plaque features and any type of incomplete COW (all P >0.025).

Conclusions—

An incomplete COW is independently associated with intraplaque hemorrhage of carotid atherosclerotic plaques.

Clinical Trial Registration—

URL: http://www.clinicaltrials.gov . Unique identifier: NCT02017756.

Biomechanical stress in coronary atherosclerosis: emerging insights from computational modelling

Coronary plaque rupture is the most common cause of vessel thrombosis and acute coronary syndrome. The accurate early detection of plaques prone to rupture may allow prospective, preventative treatment; however, current diagnostic methods remain inadequate to detect these lesions. Established imaging features indicating vulnerability do not confer adequate specificity for symptomatic rupture. Similarly, even though experimental and computational studies have underscored the importance of endothelial shear stress in progressive atherosclerosis, the ability of shear stress to predict plaque progression remains incremental. This review examines recent advances in image-based computational modelling that have elucidated possible mechanisms of plaque progression and rupture, and potentially novel features of plaques most prone to symptomatic rupture. With further study and clinical validation, these markers and techniques may improve the specificity of future culprit plaque detection.

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.

A General Approach to Derive Stress and Elasticity Tensors for Hyperelastic Isotropic and Anisotropic Biomaterials

Hyperelastic models are of particular interest in modeling biomaterials. In order to implement them, one must derive the stress and elasticity tensors from the given potential energy function explicitly. However, it is often cumbersome to do so because researchers in biomechanics may not be well-exposed to systematic approaches to derive the stress and elasticity tensors as it is vaguely addressed in literature. To resolve this, we present a framework of a general approach to derive the stress and elasticity tensors for hyperelastic models. Throughout the derivation we carefully elaborate the differences between formulas used in the displacement-based formulation and the displacement/pressure mixed formulation. Three hyperelastic models, Mooney-Rivlin, Yeoh and Holzapfel-Gasser-Ogden models that span from first-order to higher order and from isotropic to anisotropic materials, are served as examples. These detailed derivations are validated with numerical experiments that demonstrate excellent agreements with analytical and other computational solutions. Following this framework, one could implement with ease any hyperelastic model as user-defined functions in software packages or develop as an original source code from scratch.

Effect of distal thickening and stiffening of plaque cap on arterial wall mechanics

To investigate the effect of longitudinal variations of cap thickness and tissue properties on wall stresses and strains along the atherosclerotic stenosis, stenotic plaque models (uniformly thick, distally thickened, homogenous, and distally stiffened) were constructed and subjected to computational stress analyses with due consideration of fluid-structure interactions (FSI). The analysis considered three different cap thicknesses-45, 65, and 200 μm-and tissue properties-soft, fibrous, and hard. The maximum peak cap stress (PCS) and strain were observed in the upstream throat section and demonstrated increases of the order of 345 and 190%, respectively, as the cap thickness was reduced from 200 to 45 μm in uniformly thick models. Distal stiffening increased PCS in the downstream region; however, the overall effect of this increase was rather small. Distal thickening did not affect maximum PCS and strain values for cap thicknesses exceeding 65 μm; however, a noticeable increase in maximum PCS and corresponding longitudinal variation (or spatial gradient) in stress was observed in the very thin (45-μm-thick) cap. It was, therefore, inferred that existence of a rather thin upstream cap demonstrating distal cap thickening indicates an increased risk of plaque progression and rupture. Graphical Abstract ᅟ.

Assessment of superficial coronary vessel wall deformation and stress: validation of in silico models and human coronary arteries in vivo

Cyclic biomechanical stress at the lumen-intima interface plays a crucial role in the rupture of coronary plaque. We performed a comprehensive assessment of a novel angiography-based method for four-dimensional (4D) dynamic assessment of superficial wall stress (SWS) and deformation with a total of 32 analyses in virtual stenosis models with equal lumen dimensions and 16 analyses in human coronary arteries in vivo. The in silico model analyses demonstrated that the SWS, derived by the proposed global displacement method without knowledge of plaque components or blood pressure, was comparable with the result calculated by traditional finite element method. Cardiac contraction-induced vessel deformation increased SWS. Softer plaque and positive arterial remodeling, associated with a greater plaque burden, showed more variation in mean lumen diameter within the cardiac cycle and resulted in higher SWS. In vivo patient analyses confirmed the accuracy of computed superficial wall deformation. The centerlines predicted by our method at random selected time instant matched well with the actual one in angiograms by Procrustes analysis (scaling: 0.995 ± 0.018; dissimilarity: 0.007 ± 0.014). Over 50% of the maximum SWS occurred at proximal plaque shoulders. This novel 4D approach could be successfully to predict superficial wall deformation of coronary artery in vivo. The dynamic SWS might be more realistic to evaluate the risk of plaque rupture.

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.

Fluid-structure interaction models based on patient-specific IVUS at baseline and follow-up for prediction of coronary plaque progression by morphological and biomechanical factors: A preliminary study

Plaque morphology and biomechanics are believed to be closely associated with plaque progression. In this paper, we test the hypothesis that integrating morphological and biomechanical risk factors would result in better predictive power for plaque progression prediction. A sample size of 374 intravascular ultrasound (IVUS) slices was obtained from 9 patients with IVUS follow-up data. 3D fluid-structure interaction models were constructed to obtain both structural stress/strain and fluid biomechanical conditions. Data for eight morphological and biomechanical risk factors were extracted for each slice. Plaque area increase (PAI) and wall thickness increase (WTI) were chosen as two measures for plaque progression. Progression measure and risk factors were fed to generalized linear mixed models and linear mixed-effect models to perform prediction and correlation analysis, respectively. All combinations of eight risk factors were exhausted to identify the optimal predictor(s) with highest prediction accuracy defined as sum of sensitivity and specificity. When using a single risk factor, plaque wall stress (PWS) at baseline was the best predictor for plaque progression (PAI and WTI). The optimal predictor among all possible combinations for PAI was PWS + PWSn + Lipid percent + Min cap thickness + Plaque Area (PA) + Plaque Burden (PB) (prediction accuracy = 1.5928) while Wall Thickness (WT) + Plaque Wall Strain (PWSn) + Plaque Area (PA) was the best for WTI (1.2589). This indicated that PAI was a more predictable measure than WTI. The combination including both morphological and biomechanical parameters had improved prediction accuracy, compared to predictions using only morphological features.

Intima heterogeneity in stress assessment of atherosclerotic plaques

Atherosclerotic plaque rupture is recognized as the primary cause of cardiac and cerebral ischaemic events. High structural plaque stresses have been shown to strongly correlate with plaque rupture. Plaque stresses can be computed with finite-element (FE) models. Current FE models employ homogeneous material properties for the heterogeneous atherosclerotic intima. This study aimed to evaluate the influence of intima heterogeneity on plaque stress computations. Two-dimensional FE models with homogeneous and heterogeneous intima were constructed from histological images of atherosclerotic human coronaries (n = 12). For homogeneous models, a single stiffness value was employed for the entire intima. For heterogeneous models, the intima was subdivided into four clusters based on the histological information and different stiffness values were assigned to the clusters. To cover the reported local intima stiffness range, 100 cluster stiffness combinations were simulated. Peak cap stresses (PCSs) from the homogeneous and heterogeneous models were analysed and compared. By using a global variance-based sensitivity analysis, the influence of the cluster stiffnesses on the PCS variation in the heterogeneous intima models was determined. Per plaque, the median PCS values of the heterogeneous models ranged from 27 to 160 kPa, and the PCS range varied between 43 and 218 kPa. On average, the homogeneous model PCS values differed from the median PCS values of heterogeneous models by 14%. A positive correlation (R² = 0.72) was found between the homogeneous model PCS and the PCS range of the heterogeneous models. Sensitivity analysis showed that the highest main sensitivity index per plaque ranged from 0.26 to 0.83, and the average was 0.47. Intima heterogeneity resulted in substantial changes in PCS, warranting stress analyses with heterogeneous intima properties for plaque-specific, high accuracy stress assessment. Yet, computations with homogeneous intima assumption are still valuable to perform sensitivity analyses or parametric studies for testing the effect of plaque geometry on PCS. Moreover, homogeneous intima models can help identify low PCS, stable type plaques with thick caps. Yet, for thin cap plaques, accurate stiffness measurements of the clusters in the cap and stress analysis with heterogeneous cap properties are required to characterize the plaque stability.

Noninvasive Vascular Modulography Method for Imaging the Local Elasticity of Atherosclerotic Plaques: Simulation and In Vitro Vessel Phantom Study

Mechanical and morphological characterization of atherosclerotic lesions in carotid arteries remains an essential step for the evaluation of rupture prone plaques and the prevention of strokes. In this paper, we propose a noninvasive vascular imaging modulography (NIV-iMod) method, which is capable of reconstructing a heterogeneous Young's modulus distribution of a carotid plaque from the Von Mises strain elastogram. Elastograms were computed with noninvasive ultrasound images using the Lagrangian speckle model estimator and a dynamic segmentation-optimization procedure to highlight mechanical heterogeneities. This methodology, based on continuum mechanics, was validated in silico with finite-element model strain fields and ultrasound simulations, and in vitro with polyvinyl alcohol cryogel phantoms based on magnetic resonance imaging geometries of carotid plaques. In silico, our results show that the NiV-iMod method: 1) successfully detected and quantified necrotic core inclusions with high positive predictive value (PPV) and sensitivity value (SV) of 81±10% and 91±6%; 2) quantified Young's moduli of necrotic cores, fibrous tissues, and calcium inclusions with mean values of 32±23, 515±30, and 3160±218 kPa (ground true values are 10, 600, and 5000 kPa); and 3) overestimated the cap thickness by . In vitro, the PPV and SV for detecting soft inclusions were 60±21% and 88±9%, and Young's modulus mean values of mimicking lipid, fibrosis, and calcium were 34±19, 193±14, and 649±118 kPa (ground true values are 25±3, 182±21, and 757±87 kPa).

Effects of Residual Stress, Axial Stretch, and Circumferential Shrinkage on Coronary Plaque Stress and Strain Calculations: A Modeling Study Using IVUS-Based Near-Idealized Geometries

Accurate stress and strain calculations are important for plaque progression and vulnerability assessment. Models based on in vivo data often need to form geometries with zero-stress/strain conditions. The goal of this paper is to use IVUS-based near-idealized geometries and introduce a three-step model construction process to include residual stress, axial shrinkage, and circumferential shrinkage and investigate their impacts on stress and strain calculations. In Vivo intravascular ultrasound (IVUS) data of human coronary were acquired for model construction. In Vivo IVUS movie data were acquired and used to determine patient-specific material parameter values. A three-step modeling procedure was used to make our model: (a) wrap the zero-stress vessel sector to obtain the residual stress; (b) stretch the vessel axially to its length in vivo; and (c) pressurize the vessel to recover its in vivo geometry. Eight models were constructed for our investigation. Wrapping led to reduced lumen and cap stress and increased out boundary stress. The model with axial stretch, circumferential shrink, but no wrapping overestimated lumen and cap stress by 182% and 448%, respectively. The model with wrapping, circumferential shrink, but no axial stretch predicted average lumen stress and cap stress as 0.76 kPa and -15 kPa. The same model with 10% axial stretch had 42.53 kPa lumen stress and 29.0 kPa cap stress, respectively. Skipping circumferential shrinkage leads to overexpansion of the vessel and incorrect stress/strain calculations. Vessel stiffness increase (100%) leads to 75% lumen stress increase and 102% cap stress increase.

Quantify patient-specific coronary material property and its impact on stress/strain calculations using in vivo IVUS data and 3D FSI models: a pilot study

Computational models have been used to calculate plaque stress and strain for plaque progression and rupture investigations. An intravascular ultrasound (IVUS)-based modeling approach is proposed to quantify in vivo vessel material properties for more accurate stress/strain calculations. In vivo Cine IVUS and VH-IVUS coronary plaque data were acquired from one patient with informed consent obtained. Cine IVUS data and 3D thin-slice models with axial stretch were used to determine patient-specific vessel material properties. Twenty full 3D fluid-structure interaction models with ex vivo and in vivo material properties and various axial and circumferential shrink combinations were constructed to investigate the material stiffness impact on stress/strain calculations. The approximate circumferential Young's modulus over stretch ratio interval [1.0, 1.1] for an ex vivo human plaque sample and two slices (S6 and S18) from our IVUS data were 1631, 641, and 346 kPa, respectively. Average lumen stress/strain values from models using ex vivo, S6 and S18 materials with 5 % axial shrink and proper circumferential shrink were 72.76, 81.37, 101.84 kPa and 0.0668, 0.1046, and 0.1489, respectively. The average cap strain values from S18 material models were 150-180 % higher than those from the ex vivo material models. The corresponding percentages for the average cap stress values were 50-75 %. Dropping axial and circumferential shrink consideration led to stress and strain over-estimations. In vivo vessel material properties may be considerably softer than those from ex vivo data. Material stiffness variations may cause 50-75 % stress and 150-180 % strain variations.

Mechanical characterization of intraluminal tissue with phase-resolved photoacoustic viscoelasticity endoscopy

We developed a phase-sensitive side-scanning photoacoustic viscoelasticity endoscopy (PAVEE) for mechanical characterization of intraluminal tissues. In PAVEE, the PA phase can be extracted from the optical absorption induced ultrasonic waves and provides an index of viscoelasticity that is closely linked to tissue compositions. The transverse resolution of the PAVEE measured by carbon fiber was about 32 μm. The imaging capability of the PAVEE was verified using a vessel-mimicking phantom with different agar density. Moreover, PAVEE was investigated in processed lumen-shaped vascular tissues to evaluate the biomechanical features, which was highly consistent with the histology. The results demonstrated that the PAVEE can obtain viscoelastic properties of intraluminal tissues, which puts a new insight into the intravascular disease and holds great promise for plaque vulnerability detection.

A uni-extension study on the ultimate material strength and extreme extensibility of atherosclerotic tissue in human carotid plaques

Atherosclerotic plaque rupture occurs when mechanical loading exceeds its material strength. Mechanical analysis has been shown to be complementary to the morphology and composition for assessing vulnerability. However, strength and stretch thresholds for mechanics-based assessment are currently lacking. This study aims to quantify the ultimate material strength and extreme extensibility of atherosclerotic components from human carotid plaques. Tissue strips of fibrous cap, media, lipid core and intraplaque hemorrhage/thrombus were obtained from 21 carotid endarterectomy samples of symptomatic patients. Uni-extension test with tissue strips was performed until they broke or slid. The Cauchy stress and stretch ratio at the peak loading of strips broken about 2 mm away from the clamp were used to characterize their ultimate strength and extensibility. Results obtained indicated that ultimate strength of fibrous cap and media were 158.3 [72.1, 259.3] kPa (Median [Inter quartile range]) and 247.6 [169.0, 419.9] kPa, respectively; those of lipid and intraplaque hemorrhage/thrombus were 68.8 [48.5, 86.6] kPa and 83.0 [52.1, 124.9] kPa, respectively. The extensibility of each tissue type were: fibrous cap – 1.18 [1.10, 1.27]; media – 1.21 [1.17, 1.32]; lipid – 1.25 [1.11, 1.30] and intraplaque hemorrhage/thrombus – 1.20 [1.17, 1.44]. Overall, the strength of fibrous cap and media were comparable and so were lipid and intraplaque hemorrhage/thrombus. Both fibrous cap and media were significantly stronger than either lipid or intraplaque hemorrhage/thrombus. All atherosclerotic components had similar extensibility. Moreover, fibrous cap strength in the proximal region (closer to the heart) was lower than that of the distal. These results are helpful in understanding the material behavior of atherosclerotic plaques.

A Framework for Local Mechanical Characterization of Atherosclerotic Plaques: Combination of Ultrasound Displacement Imaging and Inverse Finite Element Analysis

Biomechanical models have the potential to predict plaque rupture. For reliable models, correct material properties of plaque components are a prerequisite. This study presents a new technique, where high resolution ultrasound displacement imaging and inverse finite element (FE) modeling is combined, to estimate material properties of plaque components. Iliac arteries with plaques were excised from 6 atherosclerotic pigs and subjected to an inflation test with pressures ranging from 10 to 120 mmHg. The arteries were imaged with high frequency 40 MHz ultrasound. Deformation maps of the plaques were reconstructed by cross correlation of the ultrasound radiofrequency data. Subsequently, the arteries were perfusion fixed for histology and structural components were identified. The histological data were registered to the ultrasound data to construct FE model of the plaques. Material properties of the arterial wall and the intima of the atherosclerotic plaques were estimated using a grid search method. The computed displacement fields showed good agreement with the measured displacement fields, implying that the FE models were able to capture local inhomogeneities within the plaque. On average, nonlinear stiffening of both the wall and the intima was observed, and the wall of the atheroslcerotic porcine iliac arteries was markedly stiffer than the intima (877 ± 459 vs. 100 ± 68 kPa at 100 mmHg). The large spread in the data further illustrates the wide variation of the material properties. We demonstrated the feasibility of a mixed experimental–numerical framework to determine the material properties of arterial wall and intima of atherosclerotic plaques from intact arteries, and concluded that, due to the observed variation, plaque specific properties are required for accurate stress simulations.

In vitro simulation research on the hoop stress of myocardial bridge--coronary artery

Aims

The aim of this study is to investigate how the myocardial bridge oppression affects the hoop stress of mural coronary artery.

Methods

The “myocardial bridge – coronary artery” simulative device records the hoop stress which is changed by adjusting the external pressure of the simulated coronary artery and the oppression degree of the respectively.

Results

Simulation experiment in vitro indicates that the abnormal hoop stress mainly occurs in the proximal end of mural coronary artery. As the oppression degree of myocardial bridge increases, the mean and the oscillatory value (maximum-minimum) of hoop stress in the proximal end increase markedly.

Conclusions

The “myocardial bridge – coronary artery” simulation device can provide an experiment method of studying the hoop stress influence on mural coronary artery in vitro.

Effect of residual stress on peak cap stress in arteries

Vulnerable plaques are a subset of atherosclerotic plaques that are prone to rupture when high stresses occur in the cap. The roles of residual stress, plaque morphology, and cap stiffness on the cap stress are not completely understood. Here, arteries are modeled within the framework of nonlinear elasticity as incompressible cylindrical structures that are residually stressed through differential growth. These structures are assumed to have a nonlinear, anisotropic, hyperelastic response to stresses in the media and adventitia layers and an isotropic response in the intima and necrotic layers. The effect of differential growth on the peak stress is explored in a simple, concentric geometry and it is shown that axial differential growth decreases the peak stress in the inner layer. Furthermore, morphological risk factors are explored. The peak stress in residually stressed cylinders is not greatly affected by changing the thickness of the intima. The thickness of the necrotic layer is shown to be the most important morphological feature that affects the peak stress in a residually stressed vessel.

Biomechanical factors in atherosclerosis: mechanisms and clinical implications

Blood vessels are exposed to multiple mechanical forces that are exerted on the vessel wall (radial, circumferential and longitudinal forces) or on the endothelial surface (shear stress). The stresses and strains experienced by arteries influence the initiation of atherosclerotic lesions, which develop at regions of arteries that are exposed to complex blood flow. In addition, plaque progression and eventually plaque rupture is influenced by a complex interaction between biological and mechanical factors-mechanical forces regulate the cellular and molecular composition of plaques and, conversely, the composition of plaques determines their ability to withstand mechanical load. A deeper understanding of these interactions is essential for designing new therapeutic strategies to prevent lesion development and promote plaque stabilization. Moreover, integrating clinical imaging techniques with finite element modelling techniques allows for detailed examination of local morphological and biomechanical characteristics of atherosclerotic lesions that may be of help in prediction of future events. In this ESC Position Paper on biomechanical factors in atherosclerosis, we summarize the current 'state of the art' on the interface between mechanical forces and atherosclerotic plaque biology and identify potential clinical applications and key questions for future research.

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.

Image-based modeling for better understanding and assessment of atherosclerotic plaque progression and vulnerability: data, modeling, validation, uncertainty and predictions

Medical imaging and image-based modeling have made considerable progress in recent years in identifying atherosclerotic plaque morphological and mechanical risk factors which may be used in developing improved patient screening strategies. However, a clear understanding is needed about what we have achieved and what is really needed to translate research to actual clinical practices and bring benefits to public health. Lack of in vivo data and clinical events to serve as gold standard to validate model predictions is a severe limitation. While this perspective paper provides a review of the key steps and findings of our group in image-based models for human carotid and coronary plaques and a limited review of related work by other groups, we also focus on grand challenges and uncertainties facing the researchers in the field to develop more accurate and predictive patient screening tools.