Cap Stress Research Articles

Peak cap stress calculations in coronary atherosclerotic plaques with an incomplete necrotic core geometry.

BackgroundStress calculations in atherosclerotic coronary vulnerable plaques can aid in predicting coronary cap rupture. In vivo plaque geometry and composition of coronary arteries can merely be obtained via intravascular imaging. Only optical driven imaging techniques have sufficient resolution to visualize the fibrous cap, but due to limited penetration depth deeper components such as the backside of the necrotic core (NC) are generally not visible. The goal of this study was to investigate whether peak cap stresses can be approximated by reconstructing the backside of the NC.MethodsManual segmentations of coronary histological cross-sections served as a geometrical ground truth and were obtained from seven patients resulting in 73 NCs. Next, the backside was removed and reconstructed according to an estimation of the relative necrotic core thickness (rNCt). The rNCt was estimated at three locations along the NC angle and based on either group averaged parameters or plaque specific parameters. Stress calculations were performed in both the ground truth geometry and the reconstructed geometries and compared.ResultsGood geometrical agreement was found between the ground truth NC and the reconstructed NCs, based on group averaged rNCt estimation and plaque specific rNCt estimation, measuring the NC area difference (25.1 % IQR 14.0–41.3 % and 17.9 % IQR 9.81–32.7 %) and similarity index (0.85 IQR 0.77–0.90 and 0.88 IQR 0.79–0.91). The peak cap stresses obtained with both reconstruction methods showed a high correlation with respect to the ground truth, r2 = 0.91 and r2 = 0.95, respectively. For high stress plaques, the peak cap stress difference with respect to the ground truth significantly improved for the NC reconstruction based plaque specific features (6 %) compared to the reconstruction group averaged based (16 %).ConclusionsIn conclusion, good geometry and stress agreement was observed between the ground truth NC geometry and the reconstructed geometries. Although group averaged rNCt estimation seemed to be sufficient for the NC reconstruction and stress calculations, including plaque specific data further improved stress predictions, especially for higher stresses.

Carotid Plaque Morphological Classification Compared With Biomechanical Cap Stress: Implications for a Magnetic Resonance Imaging-Based Assessment

Carotid Plaque Morphological Classification Compared With Biomechanical Cap Stress: Implications for a Magnetic Resonance Imaging-Based Assessment

Coronary Calcification and Plaque Vulnerability: An Optical Coherence Tomographic Study.

Spotty superficial calcium deposits have been implicated in plaque vulnerability based on previous intravascular imaging studies. Biomechanical models suggest that microcalcifications between 5 and 65 µm in diameter can intensify fibrous cap stress, promoting plaque rupture. However, the 100- to 200-µm resolution of intravascular ultrasound limits its ability to discriminate single calcium deposits from clusters of smaller deposits, and a previous optical coherence tomographic investigation evaluated calcifications within a long segment of artery, which may not truly reflect the mechanics involved in potentiating focal plaque rupture. Detailed optical coherence tomographic assessment of coronary calcification at the culprit plaque (10-mm length) was performed in 53 patients with acute ST-segment-elevation myocardial infarction mediated by plaque rupture and 55 patients with stable angina pectoris. The number and longitudinal length of individual calcium deposits were recorded. Cross-sectional images were analyzed every 1 mm for calcium arc and depth, and these quantitative parameters were used to define individual deposits as spotty, large, and superficial. There was no significant difference between ST-segment-elevation myocardial infarction mediated by plaque rupture and stable angina pectoris groups in the number of total (P=0.58), spotty (P=0.87), or large calcium deposits (P=0.27). Minimum calcium depth was similar between groups (P=0.27), as was the number of superficial deposits (P=0.35 using a 65-µm depth threshold and P=0.84 using a 100-µm depth threshold). The number and pattern of culprit plaque calcifications did not differ between patients presenting with ST-segment-elevation myocardial infarction mediated by plaque rupture versus stable angina pectoris. The optical coherence tomographic assessment of coronary calcification may not be a useful marker of local plaque vulnerability as previously suspected. URL: http://www.clinicaltrials.gov. Unique identifier: NCT01110538.

Investigation of fibrous cap stresses on vulnerable plaques leading to heart attacks.

Rupture-prone plaques in the coronary arteries, called ``vulnerable plaques'', are recognized as the key factor in acute myocardial infarction. Vulnerable plaques have a thin fibrous cap over a large fatty core and are highly susceptible to rupture. In general, this type of plaque rupture is mainly associated with stress concentrated on the fibrous cap. Fibrous cap stresses are counted among the most important factors in the plaque rupture process and must be taken into consideration when assessing the plaque vulnerability leading to heart attacks. The objective of this paper was to investigate the effects of nitinol stent deployment on the morphological changes of vulnerable plaques and then to propose a new stent design concept for effectively reducing fibrous cap stresses and the associated rupture risk. The deployment of a self-expanding nitinol stent was modeled, and the resulting stress distribution on the fibrous cap was investigated. The fibrous cap stresses were more uniformly distributed and the maximum stress was reduced by 13% when the crown number of the stent was increased. This study demonstrates an excellent approach to stent design that could effectively reduce the risk of a vulnerable plaque rupturing and causing a heart attack.

An intravascular coronary plaque elasticity reconstruction method using limited depth penetration ultrasound signals

Vulnerable atherosclerotic plaque (VP) rupture is the leading cause of acute coronary syndrome, myocardial infarction and stroke in the Western world (Go et al. 2013). Although past studies have identified fibrous cap thickness (Capthick) as the primary predictor of coronary plaque rupture (Virmani et al. 2006), biomechanical studies have recognized peak cap stress (PCS) as an additional key predictor of plaque disruption (Ohayon et al. 2008). Quantification of PCS amplitude requires not only an accurate description of plaque morphology but also a precise knowledge of the mechanical properties of plaque components. An early and accurate determination of these properties remains an essential step to implement preventive therapeutic strategies. A previous approach (named iMOD for imaging modulography) has been conducted by our group to reconstruct the Young’s modulus map (i.e. modulogram) from intravascular ultrasound (IVUS) strain-elastogram (Le Floc’h et al. 2009). However, one major limitation of such a method is the need to accurately estimate the strain field in the entire lesion, which may be often difficult when using HD-IVUS techniques with limited depth penetration signals (Kobayashi et al. 2014). Therefore, an extended iMOD approach (E-iMOD), based on the continuum mechanics theory prescribing the strain field in the limited atherosclerotic endoluminal region, was designed and successfully applied to coronary lesions of patients imaged in vivo with IVUS.

The effects of plaque morphology and material properties on peak cap stress in human coronary arteries

Heart attacks are often caused by rupture of caps of atherosclerotic plaques in coronary arteries. Cap rupture occurs when cap stress exceeds cap strength. We investigated the effects of plaque morphology and material properties on cap stress. Histological data from 77 coronary lesions were obtained and segmented. In these patient-specific cross sections, peak cap stresses were computed by using finite element analyses. The finite element analyses were 2D, assumed isotropic material behavior, and ignored residual stresses. To represent the wide spread in material properties, we applied soft and stiff material models for the intima. Measures of geometric plaque features for all lesions were determined and their relations to peak cap stress were examined using regression analyses. Patient-specific geometrical plaque features greatly influence peak cap stresses. Especially, local irregularities in lumen and necrotic core shape as well as a thin intima layer near the shoulder of the plaque induce local stress maxima. For stiff models, cap stress increased with decreasing cap thickness and increasing lumen radius (R = 0.79). For soft models, this relationship changed: increasing lumen radius and increasing lumen curvature were associated with increased cap stress (R = 0.66). The results of this study imply that not only accurate assessment of plaque geometry, but also of intima properties is essential for cap stress analyses in atherosclerotic plaques in human coronary arteries.

Abstract 588: Cap Inflammation Leads to Large Plaque Cap Stress Decrease and Strain Increase: MRI-PET/CT-Based FSI Modeling

Introduction: Recent studies indicated that plaque rupture may be associated with: a) extreme mechanical stress/strain conditions; b) large lipid-rich necrotic core; c) thin and weakening fibrous cap; d) cap inflammation; e) intraplaque hemorrhage. Fayad et al and others have been developing multi-modality imaging technology using PET/CT (Positron Emission Tomography/ Computed Tomography) and MRI (magnetic resonance imaging) to identify inflammation in arteries. The goal of this paper is to investigate possible impact of cap inflammation on plaque stress/strain and flow shear stress conditions. Method: An MRI-PET/CT-based modeling approach is proposed to develop fluid-structure interaction (FSI) models for human carotid plaque assessment and quantify the effect of inflammation on plaque stress/strain conditions. The combined PET/CT and MRI data was acquired from a 74 year old male patient (with informed consent) to assess arterial inflammation. The patient was imaged with dark blood multi-contrast MRI and 18F-fluorodeoxyglucose (18F-FDG) PET/CT in separate imaging sessions 12 days apart. For the 15-slice MRI/PET/CT data set, inflammation was identified for S4-S11. The 3D FSI model was built following established procedures. Material stiffness for the fibrous cap was adjusted lower to reflect the cap weakening causing by cap inflammation. Setting stiffness ratio (SR) to be 1.0 for baseline, results for SR=0.5, 0.25, and 0.1 (smaller SR value indicates softer cap stiffness) were obtained. Results: Mean plaque cap stress (PC-Stress), strain (PC-Strain) and flow shear stress (PC-FSS) are reported in Table 1. Roughly, 30-50% decrease in PC-Stress and 50-100% increase in PC-Strain were observed. Greater changes were observed for SR=0.1. Conclusion: Since cap inflammation and extreme stress/strain conditions are of great interest, further investigations are warranted to validate our findings.

A computer-simulation study on the effects of MRI voxel dimensions on carotid plaque lipid-core and fibrous cap segmentation and stress modeling.

BackgroundThe benefits of a decreased slice thickness and/or in-plane voxel size in carotid MRI for atherosclerotic plaque component quantification accuracy and biomechanical peak cap stress analysis have not yet been investigated in detail because of practical limitations.MethodsIn order to provide a methodology that allows such an investigation in detail, numerical simulations of a T1-weighted, contrast-enhanced, 2D MRI sequence were employed. Both the slice thickness (2 mm, 1 mm, and 0.5 mm) and the in plane acquired voxel size (0.62x0.62 mm2 and 0.31x0.31 mm2) were varied. This virtual MRI approach was applied to 8 histology-based 3D patient carotid atherosclerotic plaque models.ResultsA decreased slice thickness did not result in major improvements in lumen, vessel wall, and lipid-rich necrotic core size measurements. At 0.62x0.62 mm2 in-plane, only a 0.5 mm slice thickness resulted in improved minimum fibrous cap thickness measurements (a 2–3 fold reduction in measurement error) and only marginally improved peak cap stress computations. Acquiring voxels of 0.31x0.31 mm2 in-plane, however, led to either similar or significantly larger improvements in plaque component quantification and computed peak cap stress.ConclusionsThis study provides evidence that for currently-used 2D carotid MRI protocols, a decreased slice thickness might not be more beneficial for plaque measurement accuracy than a decreased in-plane voxel size. The MRI simulations performed indicate that not a reduced slice thickness (i.e. more isotropic imaging), but the acquisition of anisotropic voxels with a relatively smaller in-plane voxel size could improve carotid plaque quantification and computed peak cap stress accuracy.

The Mechanical Properties Comparative Analysis for Socked and Non-Socketed Composite Pile

For socked and non-socketed piles in the different mechanical behavior under static and dynamic loads, the paper use ABAQUS to model, simulate the pile , the soil interlayer thickness between the bottom of the pile and bedrock are 2m, 4m under vertical load and Earthquake, cushion cap, pile and pile soil stress situation found non-socketed piles when the soil interlayer thickness within a certain range, the composite pile small subside under dynamic, static loads, the non-socketed piles can better take advantage of the pile soil has a good seismic performance in the earthquake.

The Influence of Inaccuracies in Carotid MRI Segmentation on Atherosclerotic Plaque Stress Computations

Biomechanical finite element analysis (FEA) based on in vivo carotid magnetic resonance imaging (MRI) can be used to assess carotid plaque vulnerability noninvasively by computing peak cap stress. However, the accuracy of MRI plaque segmentation and the influence this has on FEA has remained unreported due to the lack of a reliable submillimeter ground truth. In this study, we quantify this influence using novel numerical simulations of carotid MRI. Histological sections from carotid plaques from 12 patients were used to create 33 ground truth plaque models. These models were subjected to numerical computer simulations of a currently used clinically applied 3.0 T T1-weighted black-blood carotid MRI protocol (in-plane acquisition voxel size of 0.62 × 0.62 mm2) to generate simulated in vivo MR images from a known underlying ground truth. The simulated images were manually segmented by three MRI readers. FEA models based on the MRI segmentations were compared with the FEA models based on the ground truth. MRI-based FEA model peak cap stress was consistently underestimated, but still correlated (R) moderately with the ground truth stress: R = 0.71, R = 0.47, and R = 0.76 for the three MRI readers respectively (p < 0.01). Peak plaque stretch was underestimated as well. The peak cap stress in thick-cap, low stress plaques was substantially more accurately and precisely predicted (error of -12 ± 44 kPa) than the peak cap stress in plaques with caps thinner than the acquisition voxel size (error of -177 ± 168 kPa). For reliable MRI-based FEA to compute the peak cap stress of carotid plaques with thin caps, the current clinically used in-plane acquisition voxel size (∼0.6 mm) is inadequate. FEA plaque stress computations would be considerably more reliable if they would be used to identify thick-cap carotid plaques with low stresses instead.

Effects of mechanical properties and atherosclerotic artery size on biomechanical plaque disruption – Mouse vs. human

Mouse models of atherosclerosis are extensively being used to study the mechanisms of atherosclerotic plaque development and the results are frequently extrapolated to humans. However, major differences have been described between murine and human atherosclerotic lesions and the determination of similarities and differences between these species has been largely addressed recently. This study takes over and extends previous studies performed by our group and related to the biomechanical characterization of both mouse and human atherosclerotic lesions. Its main objective was to determine the distribution and amplitude of mechanical stresses including peak cap stress (PCS) in aortic vessels from atherosclerotic apoE-/- mice, in order to evaluate whether such biomechanical data would be in accordance with the previously suggested lack of plaque rupture in this model. Successful finite element analysis was performed from the zero-stress configuration of aortic arch sections and mainly indicated (1) the modest role of atherosclerotic lesions in the observed increase in residual parietal stresses in apoE-/- mouse vessels and (2) the low amplitude of murine PCS as compared to humans. Overall, the results from the present study support the hypothesis that murine biomechanical properties and artery size confer less propensity to rupture for mouse lesions in comparison with those of humans.

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.

A direct vulnerable atherosclerotic plaque elasticity reconstruction method based on an original material-finite element formulation: theoretical framework

The peak cap stress (PCS) amplitude is recognized as a biomechanical predictor of vulnerable plaque (VP) rupture. However, quantifying PCS in vivo remains a challenge since the stress depends on the plaque mechanical properties. In response, an iterative material finite element (FE) elasticity reconstruction method using strain measurements has been implemented for the solution of these inverse problems. Although this approach could resolve the mechanical characterization of VPs, it suffers from major limitations since (i) it is not adapted to characterize VPs exhibiting high material discontinuities between inclusions, and (ii) does not permit real time elasticity reconstruction for clinical use. The present theoretical study was therefore designed to develop a direct material-FE algorithm for elasticity reconstruction problems which accounts for material heterogeneities. We originally modified and adapted the extended FE method (Xfem), used mainly in crack analysis, to model material heterogeneities. This new algorithm was successfully applied to six coronary lesions of patients imaged in vivo with intravascular ultrasound. The results demonstrated that the mean relative absolute errors of the reconstructed Young's moduli obtained for the arterial wall, fibrosis, necrotic core, and calcified regions of the VPs decreased from 95.3±15.56%, 98.85±72.42%, 103.29±111.86% and 95.3±10.49%, respectively, to values smaller than 2.6 × 10−8±5.7 × 10−8% (i.e. close to the exact solutions) when including modified-Xfem method into our direct elasticity reconstruction method.

The influence of axial image resolution on atherosclerotic plaque stress computations

Biomechanical models are used extensively to study risk factors, such as peak stresses, for vulnerable atherosclerotic plaque rupture. Typically, 3D patient-specific arterial models are reconstructed by interpolating between cross sectional contour data which have a certain axial sampling, or image, resolution. The influence of the axial sampling resolution on computed stresses, as well as the comparison of 3D with 2D simulations, is quantified in this study. A set of histological data of four atherosclerotic human coronary arteries was used which were reconstructed in 3D with a high sampling (HS) and low sampling (LS) axial resolution, and 4 slices were treated separately for 2D simulations. Stresses were calculated using finite element analysis (FEA). High stresses were found in thin cap regions and regions of thin vessel walls, low stresses were found inside the necrotic cores and media and adventitia layers. Axial sampling resolution was found to have a minor effect on general stress distributions, peak plaque/cap stress locations and the relationship between peak cap stress and minimum cap thickness. Axial sampling resolution did have a profound influence on the error in computed magnitude of peak plaque/cap stresses (±15.5% for HS vs. LS geometries and ±24.0% for HS vs. 2D geometries for cap stresses). The findings of this study show that axial under sampling does not influence the qualitative stress distribution significantly but that high axially sampled 3D models are needed when accurate computation of peak stress magnitudes is required.

Microcalcifications Increase Coronary Vulnerable Plaque Rupture Potential: A Patient-Based Micro-CT Fluid–Structure Interaction Study

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

The Effect of Carotid Plaque Morphology on Longitudinal Fibrous Cap Stress Levels

Background and Purpose: Rupture of vulnerable carotid atherosclerotic plaques is a major cause of stroke. Stress levels may reflect risk of rupture in patients with carotid atherosclerotic plaques. Features thought to influence the risk of plaque rupture include the degree of stenosis, lipid-rich necrotic core (LR-NC) size, and thickness of the protective fibrous caps. We used computational models to investigate the effect of these variables on fibrous cap stress levels. Methods: Two-way coupled fluid-structure interaction longitudinal 2D simulations were performed on a bifurcation model based on idealized geometry derived from a symptomatic patient. Models with varying degrees of stenosis (50%-95%), fibrous cap thicknesses (0.05-1 mm), and LR-NC sizes (2 × 1 mm-6 × 3 mm) were simulated. The stress distribution for each model was calculated and peak principal stresses extracted. Regression analysis was used for assessing the relationship between the variables and stress levels. Results: Mechanical stresses increased with decreasing fibrous cap thicknesses ( β= -0.905, p Conclusions: Thin-capped plaques with large atheromas, known predictors of plaque vulnerability, were shown to exhibit the greatest mechanical stress levels.

Influence of plaque geometry on peak cap stress

Influence of plaque geometry on peak cap stress

Initial stress in biomechanical models of atherosclerotic plaques

Rupture of atherosclerotic plaques is the underlying cause for the majority of acute strokes and myocardial infarctions. Rupture of the plaque occurs when the stress in the plaque exceeds the strength of the material locally. Biomechanical stress analyses are commonly based on pressurized geometries, in most cases measured by in-vivo MRI. The geometry is therefore not stress-free. The aim of this study is to identify the effect of neglecting the initial stress state on the plaque stress distribution.Fifty 2D histological sections (7 patients, 9 diseased coronary artery segments), perfusion fixed at 100mmHg, were segmented and finite element models were created. The Backward Incremental method was applied to determine the initial stress state and the zero-pressure state. Peak plaque and cap stresses were compared with and without initial stress. The effect of initial stress on the peak stress was related to the minimum cap thickness, maximum necrotic core thickness, and necrotic core angle.When accounting for initial stress, the general relations between geometrical features and peak cap stress remain intact. However, on a patient-specific basis, accounting for initial stress has a different effect on the absolute cap stress for each plaque. Incorporating initial stress may therefore improve the accuracy of future stress based rupture risk analyses for atherosclerotic plaques.

Plaque geometry: determinant for fibrous cap stress levels

In clinical practice, the risk of cerebrovascular events originating from carotid atherosclerotic plaques is correlated to the degree of luminal narrowing, commonly designated the degree of stenosis. Though the degree of stenosis is a proven marker of plaque vulnerability, it is widely recognized that better risk markers for cerebrovascular events are needed. Known morphological features of plaque vulnerability are large lipid-rich necrotic cores (LR-NC) with thin fibrous caps that generate localized elevated mechanical stresses within the fibrous cap separating arterial lumen from LR-NC. Thus, determination of local biomechanics using computational simulations may have clinical implications.

Effects of intima stiffness and plaque morphology on peak cap stress

BackgroundRupture of the cap of a vulnerable plaque present in a coronary vessel may cause myocardial infarction and death. Cap rupture occurs when the peak cap stress exceeds the cap strength. The mechanical stress within a cap depends on the plaque morphology and the material characteristics of the plaque components. A parametric study was conducted to assess the effect of intima stiffness and plaque morphology on peak cap stress.MethodsModels with idealized geometries based on histology images of human coronary arteries were generated by varying geometric plaque features. The constructed multi-layer models contained adventitia, media, intima, and necrotic core sections. For adventitia and media layers, anisotropic hyperelastic material models were used. For necrotic core and intima sections, isotropic hyperelastic material models were employed. Three different intima stiffness values were used to cover the wide range reported in literature. According to the intima stiffness, the models were classified as stiff, intermediate and soft intima models. Finite element method was used to compute peak cap stress.ResultsThe intima stiffness was an essential determinant of cap stresses. The computed peak cap stresses for the soft intima models were much lower than for stiff and intermediate intima models. Intima stiffness also affected the influence of morphological parameters on cap stresses. For the stiff and intermediate intima models, the cap thickness and necrotic core thickness were the most important determinants of cap stresses. The peak cap stress increased three-fold when the cap thickness was reduced from 0.25 mm to 0.05 mm for both stiff and intermediate intima models. Doubling the thickness of the necrotic core elevated the peak cap stress by 60% for the stiff intima models and by 90% for the intermediate intima models. Two-fold increase in the intima thickness behind the necrotic core reduced the peak cap stress by approximately 25% for both intima models. For the soft intima models, cap thickness was less critical and changed the peak cap stress by 55%. However, the necrotic core thickness was more influential and changed the peak cap stress by 100%. The necrotic core angle emerged as a critical determinant of cap stresses where a larger angle lowered the cap stresses. Contrary to the stiff and intermediate intima models, a thicker intima behind the necrotic core increased the peak cap stress by approximately 25% for the soft intima models. Adventitia thickness and local media regression had limited effects for all three intima models.ConclusionsFor the stiff and intermediate intima models, the cap thickness was the most important morphological risk factor. However for soft intima models, the necrotic core thickness and necrotic core angle had a bigger impact on the peak cap stress. We therefore need to enhance our knowledge of intima material properties if we want to derive critical morphological plaque features for risk evaluation.