Stress Analysis of Carotid Atheroma in Transient Ischemic Attack Patients: Evidence for Extreme Stress-Induced Plaque Rupture
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- Gao, H., Long, Q., Das, S.K. et al. Ann Biomed Eng (2011) 39: 2203. doi:10.1007/s10439-011-0314-5
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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.
KeywordsAtherosclerosisStress analysisPlaque ruptureTIAMRI
Rupture of carotid atheroma has been considered to be associated with cerebrovascular ischemic events, including transient ischemic attacks (TIA) and stroke in both symptomatic and asymptomatic patients with carotid artery disease.18 Despite this importance and many years of research, the underlying mechanism for plaque rupture is still not fully understood.14 It is believed that several factors play important roles in the rupture process, including: (a) biological abnormalities,10 and (b) biomechanical factors.2,7,9,11
The hypothesis of local extremely high stress causing a plaque rupture is one of the most widely accepted theories for plaque rupture in terms of biomechanical factors. Attempts have been made to establish a possible link between extreme plaque stress and plaque rupture sites. Cheng et al.2 studied stress concentration locations and compared them with rupture sites based on 2D histological plaque samples. Lee et al.7 used in vitro balloon angioplasty to cause plaque rupture after intravascular ultrasound imaging of the plaques. By correlating rupture sites with structure analysis, they found 82% ruptures occurred in the regions with high circumferential stress. Ohayon et al.15 found that peak circumferential stress areas correlated well with plaque rupture sites in post-angioplasty intravascular ultrasound images. Tang et al.22 conducted stress analysis in plaques using fluid structure interaction (FSI) models based on in vivo and ex vivo magnetic resonance imaging (MRI), suggesting that a local increase in stress can be a cause of plaque rupture, and high stress could be used for plaque rupture risk assessment. Based on 2D computational models from in vivo MR images of carotid plaques, Li et al.8 found that symptomatic patients have significantly higher plaque stress than asymptomatic patients. A recent study by Tang et al.21 found that a ruptured site was normally associated with a high stress. Furthermore, Sadat et al.19 reported the association of high biomechanical stresses with subsequent cerebrovascular ischemic events. The recent study from Creane et al.3 suggested that plaque morphological features also could be useful for plaque rupture risk assessment.
The limitation of these studies is that only post-rupture plaque geometry is available for computational simulations, and the plaque model reconstruction based on MRI images in which the rupture was not clearly seen. The sooner the imaging is performed after plaque rupture, the better it is in investigating the relationship between structural stresses and their location at the plaque rupture sites, which lies in the facts that less remodeling and morphological changes compared to pre-rupture status. In this study, data from three patients, who had recently suffered a TIA (imaging within 72 h of acute event) and had MR evidence of carotid plaque rupture, were used. Based on plaque geometries constructed from the post-rupture status, the pre-rupture plaque models were reconstructed by artificially bridging the ruptured fibrous cap with various fibrous cap configurations. Stress analysis by FSI simulation was performed. The stress distributions of ruptured sites were examined. Furthermore, the sensitivity of stress analysis to the pre-rupture plaque geometry reconstruction was examined.
Materials and Methods
Three patients with symptomatic carotid disease were recruited from a specialist neurovascular clinic. The patients had suffered a recent TIA and underwent carotid MRI within 72 h. The study protocol was approved by the local Research Ethics Committee and written informed consent was given.
High Resolution MR Imaging
The detailed MRI procedure and parameters can be found in a previous study.6 Briefly, a 2D time of flight (TOF) sequence with a longitudinal range of 24 mm on carotid bifurcation was performed to acquire a general geometry. A series of scans were performed in the plaque region with different MRI sequences to examine different plaque components. They were 2D ECG-triggered, fat-suppressed fast spin echo pulse sequences employing double-inversion recovery blood suppression with a voxel size of 0.4 × 0.4 × 3 mm, including T1 weighted (T1W), short T1 inversion recovery (STIR). Those images were used to delineate various plaque components such as fibrous cap, lipid core and plaque hemorrhage as previously described in Gao et al.6
Plaque Geometry Reconstruction
Variations in Ruptured Fibrous Cap Reconstruction
BL_Fth: the baseline model used in the previous section.
- (2)BL_Fth+: the same lumen segmentation as BL_Fth, but has an additional half a pixel thicker fibrous cap, corresponding to half a pixel thinner lipid core at the luminal side compared with BL_Fth, as shown in Fig. 3a.
BL_Fth++: based on BL_Fth+, with another half a pixel more for the fibrous cap thickness, corresponding to half a pixel thinner lipid core at the luminal side compared with BL_Fth+, as shown in Fig. 3a.
SL_Fth: has an overestimation of luminal size at the rupture site, but the same arterial outer wall location compared with the BL_Fth models. The same criteria for the fibrous cap segmentation was used as the baseline model, named SL_Fth, shown in Fig. 3(b.1, b.2).
SL_Fth+: has a thicker (half a pixel more) fibrous cap than SL_Fth, shown in Fig. 3(b.3).
SL_Fth++: based on SL_Fth+, the fibrous cap thickness for this model was increased by half a pixel, shown in Fig. 3(b.3).
The order of the fibrous cap thickness in rupture sites for the models is BL_Fth < BL_Fth+ < BL_Fth++, and SL_Fth < SL_Fth+ <SL_Fth++, the ruptured cap thickness in BL_Fth and SL_Fth are the same.
One-Way FSI Simulation and Boundary Conditions
The material constants were C10 = 50.445 kPa, C01 = 30.491 kPa, C20 = 40 kPa, C11 = 120 kPa, C02 = 10 kPa, and d = 1.44e−7 according to the published experimental results.22 The lipid core was assumed to be very soft with a 2 kPa Young’s Modulus and a 0.49 Poisson ratio.23 Computational nodes at the efferent planes at ICA and ECA were fixed in all directions, and an axial pre-stretch of 11% (calculated based on the shrunk geometry model) was applied at the afferent plane of CCA for the stress analysis. The structure model was meshed with an unstructured mesh consisting of nearly 90,000 10-node 3D tetra elements.
One-way FSI coupling was used for stress analysis, which requires the computational fluid dynamics (CFD) code to pass pressure values at each computational node on the luminal surface for each time step to the finite element analysis solver for structure analysis. A total of 100 time steps were used in the CFD simulation for every cardiac cycle. However, the arterial wall displacement information is not transferred back to the CFD model as it is in fully coupled FSI simulation. This technique ensures a realistic pressure loading on the arterial wall compared with pure structure analysis (no flow), and much less computational resource and more robust convergence compared with fully coupled FSI simulation. The inner surface of the carotid arterial wall and the corresponding fluid boundary were defined as the fluid–structure interface, where the pressure was passed from blood flow domain to the arterial wall. Mesh density sensitivity tests were performed on both fluid and structure domains until the difference between solutions from two consecutive meshes was negligible, with less than 2% difference in stress values in a total of 30 selected points at different regions.
Baseline Case Study
Stress Prediction Sensitivity Study to Fibrous Cap Reconstruction Variations
Stress comparison between rupture locations and non-rupture locations
Stress at rupture location (kPa)
Stress at non-rupture location (kPa)
Recent advances in MRI technology have greatly enhanced plaque morphology classification and delineation with high resolution. With anatomically realistic plaque geometry, FSI simulation is able to provide detailed stress analysis of the plaque, which is believed to be helpful for plaque rupture risk assessment.5,8,20,21 Since the pre-rupture plaque geometry generally cannot be obtained, the computational reconstructed pre-rupture plaque geometry according to the post-rupture plaque may be useful to study the behaviors of plaque rupture under specific stress conditions.
In this study, we observed that the local high structural stress values were concentrated at the rupture sites. When examining the three plaques studied, stress concentration was maximum at the plaque shoulder (i.e., junction of atheroma with normal arterial wall) for patient 1 and 2, and at the middle of the plaque for the third patient. These findings were consistent with Shah et al.20 who concluded that the plaque shoulders were rupture prone sites responsible for 60% of plaque rupture in their study. Furthermore, plaque wall stress level comparison between rupture sites and non-rupture sites also showed that rupture sites experienced much higher stress than non-rupture site, even with a thicker fibrous cap. Similar results have been suggested in Tang’s study21 by using histological evidenced plaque rupture models.
The patients recruited for this study had the MRI session within 72 h of TIA which provided excellent opportunities to obtain true plaque geometry at rupture status. More importantly, the rupture sites were clearly demonstrated on the images. This protocol also showed that the comparison between stress analysis and rupture location would be more accurate than histological evidence of rupture location, because of the difficulties and uncertainties induced during the co-registration of results from MRI and histology, as well as the plaque structure remodeling after rupture.21 Because of the broken fibrous cap and unclear boundaries of enclosed components (such as lipid core), uncertainties exist in 3D geometrical reconstruction at the rupture site. Therefore, the impact of these uncertainties on the stress distribution needs to be quantified. For this purpose, five additional models for each subject were constructed with slightly varied fibrous cap morphology in the rupture sites. The consistent results of stress distribution at the rupture site for the 17 models with varied configuration of plaque geometry indicate that plaque rupture site is associated with local stress concentration according to these three patients.
The baseline model constructed in the study on bridging the ruptured fibrous cap was one of the possible configurations, thus five more models were generated with varied fibrous cap thickness in the rupture sites to mimic possible pre-rupture statues. In order to reconstruct those additional models, fibrous cap thickness at rupture site was increased by half a pixel in addition to baseline models as the first stage models, and increased again as the second stage models. Half a pixel size as a change unit is usually used on assessing the uncertainties of an imaged structure, which can address the partial volume errors. It is small enough to capture the rupture site geometry variations and large enough to avoid generating a large number of models. Further increase of fibrous cap thickness after 2 pixels, i.e., 2.5 pixels will make the total fibrous cap thickness larger than 1 mm, which would make the fibrous cap thickness at the ruptured sites larger than un-ruptured regions. According to Redgrave’s study,16 a combination of minimum fibrous cap thickness less than 0.2 mm and a representative cap thickness less than 0.5 mm could be used to identify ruptured plaques. Therefore, a further increase in fibrous cap thickness larger than 2 pixels can be unrealistic.
Major limitations include: (a) the arterial wall model was simple compared with the real anisotropic and viscous-elastic wall. Although many studies have been carried out to investigate material properties of carotid atherosclerotic plaques,12 it is still a challenge to characterize and incorporate in vivo material properties for patient specific plaque stress analysis; (b) the boundary conditions for the simulation were not patient specific, therefore, the absolute values of the stresses may not reflect the real values; (c) more subjects are needed to generate statistically significant results about the relationship between plaque stress distributions and rupture probability. (d) Rupture of vulnerable plaque is a very complex process,1,17 mechanical factors, morphological features, abnormalities in tissue and cells, etc., need to be considered together for predicting plaque rupture.
In the study, one-way FSI was performed in three patients who had a recent TIA. The assumed pre-rupture plaque geometry was constructed based on the in vivo post-TIA plaque MR images. To study the sensitivity of the local stress distribution to the uncertainties caused by the rupture site geometry reconstruction, six models with varied rupture site morphology were generated for each of the three simulation cases together with stress analysis. Generally, the local stress concentrations were found co-located with plaque rupture site, and rupture sites were associated with higher plaque wall stress compared to non-rupture sites. The location of the stress concentration region was unlikely to be influenced by varied fibrous cap thickness reconstruction procedure in a range of 0.4–0.8 mm in the rupture sites for the three studied subjects. The good co-location of local stress concentrations and plaque rupture sites, and higher plaque wall stress in plaque rupture sites in the subjects studied could provide indirect evidence for the local maximum stress hypothesis on plaque rupture.
This project was supported by the British Heart Foundation (FS/06/048). Dr Umar Sadat is supported by a Medical Research Council (UK) and Royal College of Surgeons of England Joint Clinical Research Training Fellowship.
Conflict of Interest