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

Haemodynamic Effects on the Development and Stability of Atherosclerotic Plaques in Arterial Blood Vessel

Studying the formation and stability of atherosclerotic plaques in the hemodynamic field is essential for understanding the growth mechanism and preventive treatment of atherosclerotic plaques. In this paper, based on a multiplayer porous wall model, we established a two-way fluid-solid interaction with time-varying inlet flow. The lipid-rich necrotic core (LRNC) and stress in atherosclerotic plaque were described for analyzing the stability of atherosclerotic plaques during the plaque growth by solving advection-diffusion-reaction equations with finite-element method. It was found that LRNC appeared when the lipid levels of apoptotic materials (such as macrophages, foam cells) in the plaque reached a specified lower concentration, and increased with the plaque growth. LRNC was positively correlated with the blood pressure and was negatively correlated with the blood flow velocity. The maximum stress was mainly located at the necrotic core and gradually moved toward the left shoulder of the plaque with the plaque growth, which increases the plaque instability and the risk of the plaque shedding. The computational model may contribute to understanding the mechanisms of early atherosclerotic plaque growth and the risk of instability in the plaque growth.

Automated finite element approach to generate anatomical patient-specific biomechanical models of atherosclerotic arteries from virtual histology-intravascular ultrasound

Despite advancements in early detection and treatment, atherosclerosis remains the leading cause of death across all cardiovascular diseases (CVD). Biomechanical analysis of atherosclerotic lesions has the potential to reveal biomechanically instable or rupture-prone regions. Treatment decisions rarely consider the biomechanics of the stenosed lesion due in-part to difficulties in obtaining this information in a clinical setting. Previous 3D FEA approaches have incompletely incorporated the complex curvature of arterial geometry, material heterogeneity, and use of patient-specific data. To address these limitations and clinical need, herein we present a user-friendly fully automated program to reconstruct and simulate the wall mechanics of patient-specific atherosclerotic coronary arteries. The program enables 3D reconstruction from patient-specific data with heterogenous tissue assignment and complex arterial curvature. Eleven arteries with coronary artery disease (CAD) underwent baseline and 6-month follow-up angiographic and virtual histology-intravascular ultrasound (VH-IVUS) imaging. VH-IVUS images were processed to remove background noise, extract VH plaque material data, and luminal and outer contours. Angiography data was used to orient the artery profiles along the 3D centerlines. The resulting surface mesh is then resampled for uniformity and tetrahedralized to generate the volumetric mesh using TetGen. A mesh convergence study revealed edge lengths between 0.04 mm and 0.2 mm produced constituent volumes that were largely unchanged, hence, to save computational resources, a value of 0.2 mm was used throughout. Materials are assigned and finite element analysis (FEA) is then performed to determine stresses and strains across the artery wall. In a representative artery, the highest average effective stress was in calcium elements with 235 kPa while necrotic elements had the lowest average stress, reaching as low as 0.79 kPa. After applying nodal smoothening, the maximum effective stress across 11 arteries remained below 288 kPa, implying biomechanically stable plaques. Indeed, all atherosclerotic plaques remained unruptured at the 6-month longitudinal follow up diagnosis. These results suggest our automated analysis may facilitate assessment of atherosclerotic plaque stability.

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.

Finite element analysis in clinical patients with atherosclerosis

Endovascular plaque composition is strongly related to stent strut stress and is responsible for strut fatigue, stent failure, and possible in-stent restenosis. To evaluate the effect of plaque on artery wall resistance to expansion we performed in silico analysis of atherosclerotic vessels. We generated finite element models from in vivo intravascular ultrasound virtual histology images to determine local artery surface stiffness and determined which plaque structures have the greatest influence. We validated the predictive capacity of our modeling approach by testing an atherosclerotic peripheral artery ex vivo with pressure-inflation testing at physiological pressures ranging from 10 to 200 mmHg. For this purpose, the in silico deformation of the arterial wall was compared to that observed ex vivo. We found that calcification had a positive effect on surface stiffness with fibrous plaque and necrotic core having negative effects. Additionally, larger plaque structures demonstrated significantly higher average surface stiffness and calcification located nearer the lumen was also shown to increase surface stiffness. Therefore, more developed plaques will have greater resistance to expansion and higher stent strut stress, with calcification located near the lumen further increasing stress in localized areas. Thus, it may be expected that such plaque structures may increase the likelihood of localized stent strut fracture.

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.

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.

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

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

Ex Vivo Evaluation of IVUS-VH Imaging and the Role of Plaque Structure on Peripheral Artery Disease

Peripheral artery disease (PAD) results from the buildup of atherosclerotic plaque in the arterial wall, can progress to severe ischemia and lead to tissue necrosis and limb amputation. We evaluated a means of assessing PAD mechanics ex vivo using ten human peripheral arteries with PAD. Pressure-inflation testing was performed at six physiological pressure intervals ranging from 10-200 mmHg. These vessels were imaged with IVUS-VH to determine plaque composition and change in vessel structure with pressure. Statistical analysis was performed to determine which plaque structures and distributions of these structures had the greatest influence on wall deformation. We found that fibrous plaque, necrotic core, and calcification had a statistically significant effect on all variables (p<0.05). The presence of large concentrations of fibrous plaque was linked to reduced vessel compliance and ellipticity, which could lead to stent fractures and restenosis. For the plaque distribution we found that clustered necrotic core increased overall compliance while clustered calcification decreased overall compliance. The effect of plaque distribution on vessel wall deformation must be considered equally important to plaque concentration.

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.

Stress-Relaxation and Cyclic Behavior of Human Carotid Plaque Tissue

Atherosclerotic plaque rupture is a catastrophic event that contributes to mortality and long-term disability. A better understanding of the plaque mechanical behavior is essential for the identification of vulnerable plaques pre-rupture. Plaque is subjected to a natural dynamic mechanical environment under hemodynamic loading. Therefore, it is important to understand the mechanical response of plaque tissue under cyclic loading conditions. Moreover, experimental data of such mechanical properties are fundamental for more clinically relevant biomechanical modeling and numerical simulations for risk stratification. This study aims to experimentally and numerically characterize the stress-relaxation and cyclic mechanical behavior of carotid plaque tissue. Instron microtester equipped with a custom-developed setup was used for the experiments. Carotid plaque samples excised at endarterectomy were subjected to uniaxial tensile, stress-relaxation, and cyclic loading protocols. Thirty percent of the underlying load level obtained from the uniaxial tensile test results was used to determine the change in mechanical properties of the tissue over time under a controlled testing environment (Control tests). The stress-relaxation test data was used to calibrate the hyperelastic (neo-Hookean, Ogden, Yeoh) and linear viscoelastic (Prony series) material parameters. The normalized relaxation force increased initially and slowly stabilized toward the end of relaxation phase, highlighting the viscoelastic behavior. During the cyclic tests, there was a decrease in the peak force as a function of the cycle number indicating mechanical distension due to repeated loading that varied with different frequencies. The material also accumulated residual deformation, which increased with the cycle number. This trend showed softening behavior of the samples. The results of this preliminary study provide an enhanced understanding of in vivo stress-relaxation and cyclic behavior of the human atherosclerotic plaque tissue.

Assessment of mechanical indicators of carotid plaque vulnerability: Geometrical curvature metric, plaque stresses and damage in tissue fibres

Stroke is a major cause of death worldwide. The rupture of atherosclerotic carotid plaques is the leading single cause of stroke. Currently there is no accepted clinical measure to quantitatively assess the risk of carotid plaque rupture. Structural analyses of vulnerable plaques, using finite element (FE) analysis, have retrospectively found that regions of high stress tend to be the site of plaque rupture. The current study proposes a new clinical measure, based on plaque geometry, to assess the risk of carotid plaque rupture. This measure, named the weighted curvature difference, is based on the curvature of both the lumen and intima-media boundary, and the local plaque thickness. A series of idealized and realistic, 2-D and 3-D geometries are used to systematically assess this novel geometrical metric. The areas predicted to be at high risk of rupture using this geometrical metric are compared with areas of high stress, obtained from both isotropic and anisotropic material models. These results are also compared with areas in diseased carotid arteries that are predicted to have high damage accumulation in collagen fibres using a continuum damage model. Results show the new geometrical metric consistently predicts the locations of high stress in all of the vessel geometries examined. The drawbacks of using lumen curvature only as a risk measure are highlighted; particularly in the case of outward remodelled vessels. Weighted curvature difference shows great potential to be used as a metric to efficiently distinguish the rupture prone areas in a diseased vessels in a way that is independent of material properties.

STRESS ANALYSIS OF INTERNAL CAROTID ARTERY WITH LOW STENOSIS LEVEL: THE EFFECT OF MATERIAL MODEL AND PLAQUE GEOMETRY

Stress concentration in carotid stenosis has been proven to assist plaque morphology in disease diagnosis and vulnerability. This work focuses on numerical analysis of stress and strain distribution in the cross-section of internal carotid artery using a 2D structure-only method. The influence of four different idealized plaque geometries (circle, ellipse, oval and wedge) is investigated. Numerical simulations are implemented utilizing linear elastic model along with four hyperelastic constitutive laws named neo-Hookean, Ogden, Yeoh and Mooney–Rivlin. Each case is compared to the real geometry. Results show significant strength of oval and wedged geometries in predicting stress and strain values. Our results emphasize that Yeoh and Ogden hyperelastic materials are more reliable in stress prediction with errors less than 3%. The same concept is observed in locating critical stresses where oval and wedged plaque geometries are the most accurate models. Similar results are observed in predicting maximum principal elastic strain with errors less than 1%. However, the strain distribution in idealized plaque models showed a considerable difference in comparison with real geometry.

Influence of overlapping pattern of multiple overlapping uncovered stents on the local mechanical environment: A patient-specific parameter study

BACKGROUND

Multiple overlapping uncovered stents (MOUS) system has shown potentials in managing complex aortic aneurysms with side branches involvement. It promotes the development of thrombus by modulating local flow pattern that reduces the wall tension, while maintaining patency of side branches. However the modulation of local hemodynamic parameters depends on various factors that have not been assessed comprehensively.

METHODS

Aneurysm 3D geometry was reconstructed based on CT images. One-way fluid-structure interaction analysis was performed to quantify structural stress concentration in the wall, and changes of blood velocity, wall shear stress (WSS), oscillatory shear index (OSI), relative residence time (RRT) and pressure in the sac due to the stent deployment.

RESULTS

High structural stress concentration due to stent deployment was found in the landing zone and it increased linearly with the number of stents deployed. The wall tension in the sac was unaffected by the stent deployment. Stress within the wall was insensitive to the different overlapping pattern. After one stent was deployed, the mean flow velocity in the sac reduced by 36.4%. The deployment of the 2nd stent further reduced the mean sac velocity by 10%. WSS decreased while both OSI and RRT increased after stent deployment, however pressure in the sac remained nearly unchanged. Except for the cases with complete stents struts alignment, different overlapping pattern had little effect on flow parameters.

CONCLUSIONS

Mechanical parameters modulated by the MOUS are insensitive to different overlapping pattern suggesting that endovascular procedure can be performed with less attention to the overlapping pattern.

High Structural Stress and Presence of Intraluminal Thrombus Predict Abdominal Aortic Aneurysm 18F-FDG Uptake: Insights From Biomechanics

Supplemental Digital Content is available in the text.

Background—

Abdominal aortic aneurysm (AAA) wall inflammation and mechanical structural stress may influence AAA expansion and lead to rupture. We hypothesized a positive correlation between structural stress and fluorine-18-labeled 2-deoxy-2-fluoro-d-glucose (¹⁸F-FDG) positron emission tomography–defined inflammation. We also explored the influence of computed tomography–derived aneurysm morphology and composition, including intraluminal thrombus, on both variables.

Methods and Results—

Twenty-one patients (19 males) with AAAs below surgical threshold (AAA size was 4.10±0.54 cm) underwent ¹⁸F-FDG positron emission tomography and contrast-enhanced computed tomography imaging. Structural stresses were calculated using finite element analysis. The relationship between maximum aneurysm ¹⁸F-FDG standardized uptake value within aortic wall and wall structural stress, patient clinical characteristics, aneurysm morphology, and compositions was explored using a hierarchical linear mixed-effects model. On univariate analysis, local aneurysm diameter, thrombus burden, extent of calcification, and structural stress were all associated with ¹⁸F-FDG uptake (P<0.05). AAA structural stress correlated with ¹⁸F-FDG maximum standardized uptake value (slope estimate, 0.552; P<0.0001). Multivariate linear mixed-effects analysis revealed an important interaction between structural stress and intraluminal thrombus in relation to maximum standardized uptake value (fixed effect coefficient, 1.68 [SE, 0.10]; P<0.0001). Compared with other factors, structural stress was the best predictor of inflammation (receiver-operating characteristic curve area under the curve =0.59), with higher accuracy seen in regions with high thrombus burden (area under the curve =0.80). Regions with both high thrombus burden and high structural stress had higher ¹⁸F-FDG maximum standardized uptake value compared with regions with high thrombus burdens but low stress (median [interquartile range], 1.93 [1.60–2.14] versus 1.14 [0.90–1.53]; P<0.0001).

Conclusions—

Increased aortic wall inflammation, demonstrated by ¹⁸F-FDG positron emission tomography, was observed in AAA regions with thick intraluminal thrombus subjected to high mechanical stress, suggesting a potential mechanistic link underlying aneurysm inflammation.

3D MRI-based multicomponent thin layer structure only plaque models for atherosclerotic plaques

MRI-based fluid-structure interactions (FSI) models for atherosclerotic plaques have been developed to perform mechanical analysis to investigate the association of plaque wall stress (PWS) with cardiovascular disease. However, the time consuming 3D FSI model construction process is a great hinder for its clinical implementations. In this study, a 3D thin-layer structure only (TLS) plaque model was proposed as an approximation with much less computational cost to 3D FSI models for better clinical implementation potential. 192 TLS models were constructed based on 192 ex vivo MRI Images of 12 human coronary atherosclerotic plaques. Plaque stresses were extracted from all lumen nodal points. The maximum value of Plaque wall stress (MPWS) and average value of plaque wall stress (APWS) of each slice were used to compare with those from corresponding FSI models. The relative errors for MPWS and APWS were 9.76% and 9.89%, respectively. Both MPWS and APWS values obtained from TLS models showed very good correlation with those from 3D FSI models. Correlation results from TLS models were in consistent with FSI models. Our results indicated that the proposed 3D TLS plaque models may be used as a good approximation to 3D FSI models with much less computational cost. With further validation, 3D TLS models may be possibly used to replace FSI models to save time and perform mechanical analysis for atherosclerotic plaques for clinical implementation.

Mechanical response of cardiovascular stents under vascular dynamic bending

Backround

Currently, the effect of vascular dynamic bending (VDB) has not been fully considered when studying cardiovascular stents’ long-term mechanical properties, as the previous studies about stent’s mechanical properties mostly focus on the effect of vascular pulsation (VP). More and more clinical reports suggested that the effect of VDB have a significant impact on stent.

Methods

In this paper, an explicit-implicit coupling simulation method was applied to analyze the mechanical responses of cardiovascular stents considering the effect of VDB. The effect of VP on stent mechanical properties was also studied and compared to the effect of VDB.

Results

The results showed that the dynamic bending deformation occurred in stents due to the effect of VDB. The effects of VDB and VP resulted in alternating stress states of the stent, while the VDB alternate stresses effective on the stent were almost three times larger than that of the VP. The stress concentration under VDB mainly occurred in bridge struts and the maximal stress was located in the middle loops of the stent. However, the stress distributed uniformly in the stents under the effect of VP. Stent fracture occurred more frequently as a result of VDB with the predicted fracture position located in the bridging struts of the stent. These results are consistent with the reported data in clinical literatures. The stress of the vessel under VDB was higher, than that caused by VP.

Conclusions

The results showed that the effect of VDB has a significant impact on the stent’s stress distribution, fatigue performance and overall stress on the vessel, thus it is necessary to be considered when analyzing stent’s long-term mechanical properties. Meanwhile, the results showed that the explicit-implicit coupling simulation can be applied to analyze stent mechanical properties.

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.

MRI-based biomechanical parameters for carotid artery plaque vulnerability assessment

Carotid atherosclerotic plaques are a major cause of ischaemic stroke. The biomechanical environment to which the arterial wall and plaque is subjected to plays an important role in the initiation, progression and rupture of carotid plaques. MRI is frequently used to characterize the morphology of a carotid plaque, but new developments in MRI enable more functional assessment of carotid plaques. In this review, MRI based biomechanical parameters are evaluated on their current status, clinical applicability, and future developments. Blood flow related biomechanical parameters, including endothelial wall shear stress and oscillatory shear index, have been shown to be related to plaque formation. Deriving these parameters directly from MRI flow measurements is feasible and has great potential for future carotid plaque development prediction. Blood pressure induced stresses in a plaque may exceed the tissue strength, potentially leading to plaque rupture. Multi-contrast MRI based stress calculations in combination with tissue strength assessment based on MRI inflammation imaging may provide a plaque stress-strength balance that can be used to assess the plaque rupture risk potential. Direct plaque strain analysis based on dynamic MRI is already able to identify local plaque displacement during the cardiac cycle. However, clinical evidence linking MRI strain to plaque vulnerability is still lacking. MRI based biomechanical parameters may lead to improved assessment of carotid plaque development and rupture risk. However, better MRI systems and faster sequences are required to improve the spatial and temporal resolution, as well as increase the image contrast and signal-to-noise ratio.

Detecting the vulnerable plaque in patients

Atherosclerosis is a systemic condition that eventually evolves into vulnerable plaques and cardiovascular events. Pathology studies reveal that rupture-prone atherosclerotic plaques have a distinct morphology, namely a thin, inflamed fibrous cap covering a large lipidic and necrotic core. With the fast development of imaging techniques in the last decades, detecting vulnerable plaques thereby identifying individuals at high risk for cardiovascular events has become of major interest. Yet, in current clinical practice, there is no routine use of any vascular imaging modality to assess plaque characteristics as each unique technique has its pros and cons. This review describes the techniques that may evolve into screening tool for the detection of the vulnerable plaque. Finally, it seems that plaque morphology has been changing in the last decades leading to a higher prevalence of 'stable' atherosclerotic plaques, possibly due to the implementation of primary prevention strategies or other approaches. Therefore, the nomenclature of vulnerable plaque lesions should be very carefully defined in all studies.

Subject-Specific Fully-Coupled and One-Way Fluid-Structure Interaction Models for Modeling of Carotid Atherosclerotic Plaques in Humans

Background

Hemodynamics play an important role in the development and progression of carotid atherosclerosis, and may be important in the assessment of plaque vulnerability. The aim of this study was to develop a system to assess the hemodynamics of carotid atherosclerotic plaques using subject-specific fluid-structure interaction (FSI) models based on magnetic resonance imaging (MRI).

Material/Methods

Models of carotid bifurcations (n=86 with plaques from 52 patients, n=14 normal carotids from 12 participants) were obtained at the Department of Radiology, Beijing Tian Tan Hospital between 2010 and 2013. The maximum von Mises stress, minimum pressure, and flow velocity values were assessed at the most stenotic site in patients, or at the carotid bifurcations in healthy volunteers. Results of one-way FSI were compared with fully-coupled FSI for the plaques of 19 randomly selected models.

Results

The maximum von Mises stress and the minimum pressure and velocity were significantly increased in the stenosis group compared with controls based on one-way FSI (all P<0.05). The maximum von Mises stress and the minimum pressure were significantly higher and the velocity was significantly lower based on fully coupled FSI compared with on-way FSI (all P<0.05). Although there were differences in numerical values, both methods were equivalent. The maximum von Mises stress of vulnerable plaques was significantly higher than stable plaques (P<0.001). The maximum von Mises stress of the group with fibrous cap defect was significantly higher than the group without fibrous cap defect (P=0.001).

Conclusions

The hemodynamics of atherosclerotic plaques can be assessed noninvasively using subject-specific models of FSI based on MRI.

The influence of constitutive law choice used to characterise atherosclerotic tissue material properties on computing stress values in human carotid plaques

Calculating high stress concentration within carotid atherosclerotic plaques has been shown to be complementary to anatomical features in assessing vulnerability. Reliability of stress calculation may depend on the constitutive laws/strain energy density functions (SEDFs) used to characterize tissue material properties. Different SEDFs, including neo-Hookean, one-/two-term Ogden, Yeoh, 5-parameter Mooney–Rivlin, Demiray and modified Mooney–Rivlin, have been used to describe atherosclerotic tissue behavior. However, the capacity of SEDFs to fit experimental data and the difference in the stress calculation remains unexplored. In this study, seven SEDFs were used to fit the stress–stretch data points of media, fibrous cap, lipid and intraplaque hemorrhage/thrombus obtained from 21 human carotid plaques. Semi-analytic solution, 2D structure-only and 3D fully coupled fluid-structure interaction (FSI) analyses were used to quantify stress using different SEDFs and the related material stability examined. Results show that, except for neo-Hookean, all other six SEDFs fitted the experimental points well, with vessel stress distribution in the circumferential and radial directions being similar. 2D structural-only analysis was successful for all seven SEDFs, but 3D FSI were only possible with neo-Hookean, Demiray and modified Mooney–Rivlin models. Stresses calculated using Demiray and modified Mooney–Rivlin models were nearly identical. Further analyses indicated that the energy contours of one-/two-term Ogden and 5-parameter Mooney–Rivlin models were not strictly convex and the material stability indictors under homogeneous deformations were not always positive. In conclusion, considering the capacity in characterizing material properties and stabilities, Demiray and modified Mooney–Rivlin SEDF appear practical choices for mechanical analyses to predict the critical mechanical conditions within carotid atherosclerotic plaques.

Influence of material property variability on the mechanical behaviour of carotid atherosclerotic plaques: a 3D fluid-structure interaction analysis

Mechanical analysis has been shown to be complementary to luminal stenosis in assessing atherosclerotic plaque vulnerability. However, patient-specific material properties are not available and the effect of material properties variability has not been fully quantified. Media and fibrous cap (FC) strips from carotid endarterectomy samples were classified into hard, intermediate and soft according to their incremental Young's modulus. Lipid and intraplaque haemorrhage/thrombus strips were classified as hard and soft. Idealised geometry-based 3D fluid-structure interaction analyses were performed to assess the impact of material property variability in predicting maximum principal stress (Stress-P1 ) and stretch (Stretch-P1 ). When FC was thick (1000 or 600 µm), Stress-P1 at the shoulder was insensitive to changes in material stiffness, whereas Stress-P1 at mid FC changed significantly. When FC was thin (200 or 65 µm), high stress concentrations shifted from the shoulder region to mid FC, and Stress-P1 became increasingly sensitive to changes in material properties, in particular at mid FC. Regardless of FC thickness, Stretch-P1 at these locations was sensitive to changes in material properties. Variability in tissue material properties influences both the location and overall stress/stretch value. This variability needs to be accounted for when interpreting the results of mechanical modelling.