Fatigue crack propagation analysis of plaque rupture

Rupture of atheromatous plaque is the major cause of stroke or heart attack. Considering that the cardiovascular system is a classic fatigue environment, plaque rupture was treated as a chronic fatigue crack growth process in this study. Fracture mechanics theory was introduced to describe the stress status at the crack tip and Paris' law was used to calculate the crack growth rate. The effect of anatomical variation of an idealized plaque cross-section model was investigated. The crack initiation was considered to be either at the maximum circumferential stress location or at any other possible locations around the lumen. Although the crack automatically initialized at the maximum circumferential stress location usually propagated faster than others, it was not necessarily the most critical location where the fatigue life reached its minimum. We found that the fatigue life was minimum for cracks initialized in the following three regions: the midcap zone, the shoulder zone, and the backside zone. The anatomical variation has a significant influence on the fatigue life. Either a decrease in cap thickness or an increase in lipid pool size resulted in a significant decrease in fatigue life. Comparing to the previously used stress analysis, this fatigue model provides some possible explanations of plaque rupture at a low stress level in a pulsatile cardiovascular environment, and the method proposed here may be useful for further investigation of the mechanism of plaque rupture based on in vivo patient data.

MRI-based fatigue analysis predicts plaque vulnerability: A study comparing symptomatic and asymptomatic individuals

BACKGROUND: Rupture of atheromatous plaque in the carotid artery often leads to thrombosis and subsequent stroke. The mechanism of plaque rupture is not entirely clear but is thought to be a multi-factorial process involving thinning and weakening of the fibrous cap and biomechanical stress as the trigger leading to plaque rupture. As the cardiovascular system is a classic fatigue environment, the weakening of plaque leading to rupture may be a fatigue process, which is a symptomatically quiescent but potentially progressive failure process. In this study, we used a fatigue analysis based on in vivo magnetic resonance imaging (MRI) to investigate the rupture initiation location, crack propagation path and fatigue life within plaques of asymptomatic and symptomatic individuals. METHODS: Forty non-consecutive subjects (20 symptomatic and 20 asymptomatic) underwent high-resolution multi-sequence in vivo MRI of the carotid bifurcation. Fatigue analysis was performed based on the plaque geometry derived from in vivo MRI of the carotid artery at the point of maximum stenosis. Paris’ Law in fracture mechanics is adopted to determine the fatigue crack growth rate. Incremental crack propagation was dynamically simulated based on stress distributions. Plaque initiation location, crack propagation path and fatigue cycle of symptomatic and asymptomatic individuals were compared. RESULTS: Cracks were often found to begin at the lumen wall at areas of stress concentration. The preferred rupture direction was radial from the lumen center. The crack initially advanced slowly but accelerated as it developed, depending on plaque morphology. The fatigue cycles of symptomatic plaques were significantly less than those in the asymptomatic group (2.3 ± 0.9 vs 3.1 ± 0.7 (x106); p = 0.003). CONCLUSIONS: The number of cycles to rupture in symptomatic patients was higher than those predicted in asymptomatic patients by fatigue analysis, suggesting the possibility that plaques with a less fatigue life may be more prone to be symptomatic and rupture. If further validated by large-scale longitudinal studies, fatigue analysis based on high resolution in vivo MRI could potentially act as a useful tool for risk assessment of carotid atheroma.

Study of carotid arterial plaque stress for symptomatic and asymptomatic patients

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

Stress analysis of carotid atheroma in transient ischemic attack patients: Evidence for extreme stress-induced plaque rupture

Plaque rupture has been considered to be the result of its structural failure. The aim of this study is to suggest a possible link between higher stresses and rupture sites observed from in vivo magnetic resonance imaging (MRI) of transient ischemic attack (TIA) patients, by using stress analysis methods. Three patients, who had recently suffered a TIA, underwent in vivo multi-spectral MR imaging. Based on plaque geometries reconstructed from the post-rupture status, six pre-rupture plaque models were generated for each patient dataset with different reconstructions of rupture sites to bridge the gap of fibrous cap from original MRI images. Stress analysis by fluid structure interaction simulation was performed on the models, followed by analysis of local stress concentration distribution and plaque rupture sites. Furthermore, the sensitivity of stress analysis to the pre-rupture plaque geometry reconstruction was examined. Local stress concentrations were found to be located at the plaque rupture sites for the three subjects studied. In the total of 18 models created, the locations of the stress concentration regions were similar in 17 models in which rupture sites were always associated with high stresses. The local stress concentration region moved from circumferential center to the shoulder region (slightly away from the rupture site) for a case with a thick fibrous cap. Plaque wall stress level in the rupture locations was found to be much higher than the value in non-rupture locations. The good correlation between local stress concentrations and plaque rupture sites, and generally higher plaque wall stress level in rupture locations in the subjects studied could provide indirect evidence for the extreme stress-induced plaque rupture hypothesis. Local stress concentration in the plaque region could be one of the factors contributing to plaque rupture.

Association between biomechanical structural stresses of atherosclerotic carotid plaques and subsequent ischaemic cerebrovascular events - A longitudinal in vivo magnetic resonance imaging-based finite element study

Background: High-resolution magnetic resonance (MR) imaging has been used for MR imaging-based structural stress analysis of atherosclerotic plaques. The biomechanical stress profile of stable plaques has been observed to differ from that of unstable plaques; however, the role that structural stresses play in determining plaque vulnerability remains speculative. Methods: A total of 61 patients with previous history of symptomatic carotid artery disease underwent carotid plaque MR imaging. Plaque components of the index artery such as fibrous tissue, lipid content and plaque haemorrhage (PH) were delineated and used for finite element analysis-based maximum structural stress (M-C Stress) quantification. These patients were followed up for 2 years. The clinical end point was occurrence of an ischaemic cerebrovascular event. The association of the time to the clinical end point with plaque morphology and M-C Stress was analysed. Results: During a median follow-up duration of 514 days, 20% of patients (n=12) experienced an ischaemic event in the territory of the index carotid artery. Cox regression analysis indicated that M-C Stress (hazard ratio (HR): 12.98 (95% confidence interval (CI): 1.32-26.67, pZ0.02), fibrous cap (FC) disruption (HR: 7.39 (95% CI: 1.61e33.82), p Z 0.009) and PH (HR: 5.85 (95% CI: 1.27e26.77), p Z 0.02) are associated with the development of subsequent cerebrovascular events. Plaques associated with future events had higher M-C Stress than those which had remained asymptomatic (median (interquartile range, IQR): 330 kPa (229e494) vs. 254 kPa (166-290), p Z0.04). Conclusions: High biomechanical structural stresses, in addition to FC rupture and PH, are associated with subsequent cerebrovascular events.

Curvedness study on atherosclerosis plaques and its implications to plaque stress

Atherosclerosis plaque rupture has been considered to be a mechanical failure of the thin fibrous cap, resulted from extreme plaque stress. Plaque stress was affected by many factors from morphological features to biological abnormalities. In this study, geometrical factors (curvedness, fibrous cap thickness) were studied on assessing plaque vulnerability in comparison with stress analysis results obtained by fluid structure interaction from 20 human carotid atherosclerosis plaques. The results show that plaque surface curvedness could contribute to extreme stress level, especially in plaque shoulder region. General plaque stress distribution could be predicted by fibrous cap thickness and curvedness with multi-regression model. With more features included in the regression model, plaque stress could be easily calculated and used to assess plaque vulnerability.

Coronary calcium scoring: Calcium location needs to be integrated!

Coronary calcium scoring (CCS) has been a topic of great interest lately. In a large population-based study comprising 6,722 patients, Detrano et al. (1) have effectively shown that CCS can be a strong predictor of incident coronary heart disease among different racial groups. Henneman et al. (2) have, however, reported that CCS does not reliably exclude the presence of (significant) atherosclerosis. This topic is quite controversial as there is significant evidence from Detrano's work that higher CCS is associated with an increased risk of acute coronary events. We think that the location of calcium within the coronary arteries should also be considered. Li et al. (3,4) have shown that the position of the calcium in the plaque is a better determinant of plaque vulnerability than the total calcium load. Using a biomechanical model, predicted maximum stress was found to increase by 47.5% when calcium deposits were located in the thin fibrous cap. The presence of calcium deposits in the lipid core or remote from the fibrous cap resulted in no increase in maximum stress. It was also noted that the presence of calcification within the lipid core may even stabilize the plaque. Integration of calcium location in CCS will, therefore, enable better assessment of severity of atherosclerosis and prediction of future cardiovascular events.

Stress analysis on human arterial plaques by fluid structure interactions - Multi-case study

Atherosclerotic plaque rupture has been extensively considered as the leading cause of death in the world. It is believed that high stress within plaque can be an important factor which can trigger the rupture of the plaque. High resolution multi-spectral magnetic resonance imaging (MRI) has allowed the plaque components (arterial wall, lipids, and fibrous cap) to be visualized in vivo [1]. The patient specific finite element model can be generated from the image data to perform stress analysis and provide critical information on understanding plaque rupture mechanisms [2]. The present work is to apply the procedure to a total of 14 patients (S1 ∼ S14), to study the stress distributions on carotid artery plaque reconstructed from multi-spectral magnetic resonance images, and the possible relationships between stress and plaque burdens.

Study of reproducibility of human arterial plaque reconstruction and its effects on stress analysis based on multispectral in vivo magnetic resonance imaging

Purpose: To quantify the uncertainties of carotid plaque morphology reconstruction based on patient-specific multispectral in vivo magnetic resonance imaging (MRI) and their impacts on the plaque stress analysis. Materials and Methods: In this study, three independent investigators were invited to reconstruct the carotid bifurcation with plaque based on MR images from two subjects to study the geometry reconstruction reproducibility. Finite element stress analyses were performed on the carotid bifurcations, as well as the models with artificially modified plaque geometries to mimic the image segmentation uncertainties, to study the impacts of the uncertainties to the stress prediction. Results: Plaque reconstruction reproducibility was generally high in the study. The uncertainties among interobservers are around one or the subpixel level. It also shows that the predicted stress is relatively less sensitive to the arterial wall segmentation uncertainties, and more affected by the accuracy of lipid region definition. For a model with lipid core region artificially increased by adding one pixel on the lipid region boundary, it will significantly increase the maximum Von Mises Stress in fibrous cap (>100%) compared with the baseline model for all subjects. Conclusion: The current in vivo MRI in the carotid plaque could provide useful and reliable information for plaque morphology. The accuracy of stress analysis based on plaque geometry is subject to MRI quality. The improved resolution/quality in plaque imaging with newly developed MRI protocols would generate more realistic stress predictions.

Carotid arterial plaque stress analysis using fluid-structure interactive simulation based on in-vivo magnetic resonance images of four patients

The rupture of atherosclerotic plaques is known to be associated with the stresses that act on or within the arterial wall. The extreme wall tensile stress (WTS) is usually recognized as a primary trigger for the rupture of vulnerable plaque. The present study used the in-vivo high-resolution multi-spectral magnetic resonance imaging (MRI) for carotid arterial plaque morphology reconstruction. Image segmentation of different plaque components was based on the multi-spectral MRI and co-registered with different sequences for the patient. Stress analysis was performed on totally four subjects with different plaque burden by fluid-structure interaction (FSI) simulations. Wall shear stress distributions are highly related to the degree of stenosis, while the level of its magnitude is much lower than the WTS in the fibrous cap. WTS is higher in the luminal wall and lower at the outer wall, with the lowest stress at the lipid region. Local stress concentrations are well confined in the thinner fibrous cap region, and usually locating in the plaque shoulder; the introduction of relative stress variation during a cycle in the fibrous cap can be a potential indicator for plaque fatigue process in the thin fibrous cap. According to stress analysis of the four subjects, a risk assessment in terms of mechanical factors could be made, which may be helpful in clinical practice. However, more subjects with patient specific analysis are desirable for plaque-stability study.

Assessment of carotid plaque vulnerability using structural and geometrical determinants

Background Because many acute cerebral ischemic events are caused by rupture of vulnerable carotid atheroma and subsequent thrombosis, the present study used both idealized and patient-specific carotid atheromatous plaque models to evaluate the effect of structural determinants on stress distributions within plaque. Methods and Results Using a finite element method, structural analysis was performed using models derived from in vivo high-resolution magnetic resonance imaging (MRI) of carotid atheroma in 40 non-consecutive patients (20 symptomatic, 20 asymptomatic). Plaque components were modeled as hyper-elastic materials. The effects of varying fibrous cap thickness, lipid core size and lumen curvature on plaque stress distributions were examined. Lumen curvature and fibrous cap thickness were found to be major determinants of plaque stress. The size of the lipid core did not alter plaque stress significantly when the fibrous cap was relatively thick. The correlation between plaque stress and lumen curvature was significant for both symptomatic (p = 0.01; correlation coefficient: 0.689) and asymptomatic patients (p = 0.01; correlation coefficient: 0.862). Lumen curvature in plaques of symptomatic patients was significantly larger than those of asymptomatic patients (1.50±1.0mm-1 vs 1.25±0.75 mm-1; p = 0.01). Conclusion Specific plaque morphology (large lumen curvature and thin fibrous cap) is closely related to plaque vulnerability. Structural analysis using high-resolution MRI of carotid atheroma may help in detecting vulnerable atheromatous plaque and aid the risk stratification of patients with carotid disease.

Does PGA external stenting reduce compliance mismatch in venous grafts?

Background: Autogenous vein grafting is widely used in regular bypassing procedures. Due to its mismatch with the host artery in both mechanical property and geometry, the graft often over expands under high arterial blood pressure and forms a step-depth where eddy flow develops, thus causing restenosis, fibrous graft wall, etc. External stents, such as sheaths being used to cuff the graft, have been introduced to eliminate these mismatches and increase the patency. Although histological and immunochemical studies have shown some positive effects of the external stent, the mechanical mismatch under the protection of an external stent remains poorly analyzed. Methods: In this study, the jugular veins taken from hypercholesterolemic rabbits were transplanted into the carotid arteries, and non-woven polyglycolic acid (PGA) fabric was used to fabricate the external stents to study the effect of the biodegradable external stent. Eight weeks after the operation, the grafts were harvested to perform mechanical tests and histological examinations. An arc tangent function was suggested to describe the relationship between pressure and cross-sectional area to analyse the compliance of the graft. Results: The results from the mechanical tests indicated that grafts either with or without external stents displayed large compliance in the low-pressure range and were almost inextensible in the high-pressure range. This was very different from the behavior of the arteries or veins in vivo. The data from histological tests showed that, with external stents, collagen fibers were more compact, whilst those in the graft without protection were looser and thicker. No elastic fiber was found in either kind of grafts. Furthermore, grafts without protection were over-expanded which resulted in much bigger cross-sectional areas. Conclusion: The PGA external extent contributes little to the reduction of the mechanical mismatch between the graft and its host artery while remodeling develops. For the geometric mismatch, it reduces the cross-section area, therefore matching with the host artery much better. Although there are some positive effects, conclusively the PGA is not an ideal material for external stent.

Does calcium deposition play a role in the stability of atheroma? Location may be the key

Background: Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The role of calcium deposition and its contribution to plaque stability is controversial. This study uses both an idealized and a patient-specific model to evaluate the effect of a calcium deposit on the stress distribution within an atheromatous plaque. Methods: Using a finite-element method, structural analysis was performed on an idealized plaque model and the location of a calcium deposit within it was varied. In addition to the idealized model, in vivo high-resolution MR imaging was performed on 3 patients with carotid atheroma and stress distributions were generated. The individual plaques were chosen as they had calcium at varying locations with respect to the lumen and the fibrous cap. Results: The predicted maximum stress was increased by 47.5% when the calcium deposit was located in the thin fibrous cap in the model when compared with that in a model without a deposit. The result of adding a calcium deposit either to the lipid core or remote from the lumen resulted in almost no increase in maximal stress. Conclusion: Calcification at the thin fibrous cap may result in high stress concentrations, ultimately increasing the risk of plaque rupture. Assessing the location of calcification may, in the future, aid in the risk stratification of patients with carotid stenosis.

Simulation of the interaction between blood flow and atherosclerotic plaque

It has been well accepted that over 50% of cerebral ischemic events are the result of rupture of vulnerable carotid atheroma and subsequent thrombosis. Such strokes are potentially preventable by carotid interventions. Selection of patients for intervention is currently based on the severity of carotid luminal stenosis. It has been, however, widely accepted that luminal stenosis alone may not be an adequate predictor of risk. To evaluate the effects of degree of luminal stenosis and plaque morphology on plaque stability, we used a coupled nonlinear time-dependent model with flow-plaque interaction simulation to perform flow and stress/strain analysis for stenotic artery with a plaque. The Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations for the fluid. The Ogden strain energy function was used for both the fibrous cap and the lipid pool. The plaque Principal stresses and flow conditions were calculated for every case when varying the fibrous cap thickness from 0.1 to 2mm and the degree of luminal stenosis from 10% to 90%. Severe stenosis led to high flow velocities and high shear stresses, but a low or even negative pressure at the throat of the stenosis. Higher degree of stenosis and thinner fibrous cap led to larger plaque stresses, and a 50% decrease of fibrous cap thickness resulted in a 200% increase of maximum stress. This model suggests that fibrous cap thickness is critically related to plaque vulnerability and that, even within presence of moderate stenosis, may play an important role in the future risk stratification of those patients when identified in vivo using high resolution MR imaging.

Correlation of macrophage location and plaque stress distribution using USPIO-enhanced MRI in a patient with symptomatic severe carotid stenosis: A new insight into risk stratification

High resolution, USPIO-enhanced MR imaging can be used to identify inflamed atherosclerotic plaque. We report a case of a 79-year-old man with a symptomatic carotid stenosis of 82%. The plaque was retrieved for histology and finite element analysis (FEA) based on the preoperative MR imaging was used to predict maximal Von Mises stress on the plaque. Macrophage location correlated with maximal predicted stresses on the plaque. This supports the hypothesis that macrophages thin the fibrous cap at points of highest stress, leading to an increased risk of plaque rupture and subsequent stroke.