Annals of Biomedical Engineering

, Volume 39, Issue 8, pp 2203–2212

Stress Analysis of Carotid Atheroma in Transient Ischemic Attack Patients: Evidence for Extreme Stress-Induced Plaque Rupture

Authors

  • Hao Gao
    • Brunel Institute for BioengineeringBrunel University
    • Center for Excellence in Signal and Image Processing, Department of Electronic and Electrical EngineeringUniversity of Strathclyde
    • Brunel Institute for BioengineeringBrunel University
  • Saroj Kumar Das
    • Brunel Institute for BioengineeringBrunel University
    • Consultant SurgeonThe Hillingdon Hospital & Charing Cross Hospital
  • Umar Sadat
    • University Department of RadiologyCambridge University Hospitals NHS Foundation Trust
  • Martin Graves
    • University Department of RadiologyCambridge University Hospitals NHS Foundation Trust
  • Jonathan H. Gillard
    • University Department of RadiologyCambridge University Hospitals NHS Foundation Trust
  • Zhi-Yong Li
    • University Department of RadiologyCambridge University Hospitals NHS Foundation Trust
    • School of Biological Science & Medical EngineeringSoutheast University
Article

DOI: 10.1007/s10439-011-0314-5

Cite this article as:
Gao, H., Long, Q., Das, S.K. et al. Ann Biomed Eng (2011) 39: 2203. doi:10.1007/s10439-011-0314-5

Abstract

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.

Keywords

AtherosclerosisStress analysisPlaque ruptureTIAMRI

Introduction

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

An in house program developed in Matlab™ was used to segment the regions of the lipid core, the arterial wall, and the lumen, which have different signal characteristics from different MRI sequences. The image segmentation and 3D reconstruction procedure have been discussed in detail in previous works.5,6 Figure 1 is the segmentation for subject 1 (case S1) based on T1W and STIR sequences. Figure 1(a.1) shows the arterial wall segmentation in the healthy part; Fig. 1(a.2) shows the segmentation of the plaque region at the non-ruptured part, the lipid region is embedded inside arterial wall. Special attention was paid to the segmentation at the rupture site. The ruptured fibrous cap was deemed present if there was a clear defect, discontinuity or ulceration within the fibrous cap.24,25 In Fig. 1(a.3), the ruptured fibrous cap could be identified since only part of the fibrous cap remained, indicated by an arrow. The ruptured fibrous cap thickness was assumed to be one pixel (0.4 mm). The segmentation result of the ruptured fibrous cap is presented in Fig. 1(a.4), which was based on STIR image, and the lumen boundary was from the corresponding T1W image. Since the MRI slice thickness was 3 mm, the rupture site was assumed to cover a 3 mm range uniformly distributed up- and downstream of the ruptured slice. The whole segmentation for the plaque region is shown in Fig. 1b with the lipid region segmented from STIR images.
https://static-content.springer.com/image/art%3A10.1007%2Fs10439-011-0314-5/MediaObjects/10439_2011_314_Fig1_HTML.jpg
Figure 1

Carotid plaque component segmentation (represented by solid lines) for one patient. (a.1) Arterial wall segmentation with T1-weighted images; (a.2) lipid region segmentation with short T1 inversion recovery (STIR) images; (a.3) rupture site in the STIR image; (a.4) lipid and lumen segmentation in the rupture site, indicated by the arrow. (b) The whole segmentation based on T1 weighted and STIR images, superimposed in the T1-weighted images for the patient

The reconstruction of the carotid bifurcation beyond the plaque was based on the 2D TOF images. The center points of the lumen in TOF and T1W images were used to construct the center lines for the common carotid artery (CCA), internal carotid artery (ICA), and external carotid artery (ECA). After 2D segmentation, a linear transformation was applied for the registration of images obtained from different sequences based on the same features among the corresponding MR images. Furthermore, a proper shrinkage procedure to mimic the arterial stress free state was applied. In detail, the shrinkage procedure was: (a) 10% shrinkage in the axial direction13 from reconstructed geometry, and (b) 10% lumen area shrinkage determined by trial and error manor to best match with in vivo geometry under mean pressure loading condition (100 mmHg), that was about 5% shrinkage in diameter. In addition, the outer wall was also reduced to match the plaque volume in the in vivo state. The boundary points of segmented plaque regions in 2D transverse images were imported into Solidworks™; contours were generated by using closed spline interpolation. The region between the lumen and lipid core was treated as the fibrous cap, which was part of the arterial wall in our models with the same material properties as the healthy arterial wall. The same procedure was employed for the geometric reconstruction of cases S2 and S3, as shown in Fig. 2, and the rupture sites were highlighted for each subject. The stenosis degree for the three subjects was around 25%.
https://static-content.springer.com/image/art%3A10.1007%2Fs10439-011-0314-5/MediaObjects/10439_2011_314_Fig2_HTML.gif
Figure 2

Reconstructed plaque geometries for S1, S2, and S3, respectively. The rupture site is indicated by the arrow with gray band

Variations in Ruptured Fibrous Cap Reconstruction

Although STIR images can provide information about the lipid region in the rupture site, assumptions must be made on the thickness and location of fibrous cap in the rupture site in order to construct a pre-rupture geometry. The baseline model constructed above is one of the possible configurations. Since the pre-rupture fibrous cap structure was unknown for each plaque and fibrous cap thickness in the rupture sites is the most important geometry parameter for plaque stability, five more models were generated with varied fibrous cap thickness in the rupture sites to mimic possible pre-rupture statues. Thus six models were created for each subject, and divided into two groups for the study of the impacts of the local geometry variation in rupture sites on the stress analysis. In each group, three models were generated with an increasing fibrous cap thickness of half a pixel in the rupture site against the previous model. For group 1, the models were named as BL_Fth (baseline model presented above with normal fibrous cap thickness), BL_Fth+ and BL_Fth++; For group 2, the luminal wall at the rupture site was moved further towards the outer wall resulting in a slight increase in lumen size at the rupture site, while the reconstruction rule for the fibrous cap and the lipid core was the same as the group 1 models and named as SL_Fth (baseline for group 2), SL_Fth+, SL_Fth++. In detail:
  1. (1)

    BL_Fth: the baseline model used in the previous section.

     
  2. (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.
    https://static-content.springer.com/image/art%3A10.1007%2Fs10439-011-0314-5/MediaObjects/10439_2011_314_Fig3_HTML.jpg
    Figure 3

    Variations of plaque geometry reconstruction. (a) Models (BL_Fth+ and BL_Fth++) with thicker fibrous cap based on BL_Fth with a zoom-in view at right side. (b.1) Larger lumen region segmentation, (b.2) segmentation for SL_Fth, (b.3) Models (SL_Fth+ and SL_Fth++) with thicker fibrous cap based on SL_Fth

     
  3. (3)

    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.

     
Group 2
  1. (1)

    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).

     
  2. (2)

    SL_Fth+: has a thicker (half a pixel more) fibrous cap than SL_Fth, shown in Fig. 3(b.3).

     
  3. (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

Our previous study4 by using one-way FSI showed that one-way FSI is a good compromise but providing more realistic loading conditions in structure analysis, and less computational resource, therefore, one-way FSI was used for plaque stress analysis. The detailed description of material property and FSI procedure can be found in a previous study.4 The carotid arterial wall (including the fibrous cap) was assumed to be nonlinear, isotropic, and incompressible with the 5-parameter Mooney-Rivlin model (Ansys™) being used to describe its material properties. The strain-energy function is given by:
$$ W = C_{10} \left( {I_{1} - 3} \right) + C_{01} \left( {I_{2} - 3} \right) + C_{20} \left( {I_{1} - 3} \right)^{2} + C_{11} \left( {I_{1} - 3} \right)\left( {I_{2} - 3} \right) + C_{02} \left( {I_{2} - 3} \right)^{2} + \frac{1}{d}\left( {J - 1} \right)^{2} $$

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.

The fluid domain was meshed in ICEM CFX11.0 with a much finer mesh of 1 million 3D tetra cells. Blood was treated as an incompressible, Newtonian fluid with a viscosity of 4 × 10−3 Pa s and a density of 1,067 kg m−3. The flow was assumed to be laminar; transient simulations were carried out with time-dependent pressure at the inlet of the CCA and mass flow rates at the ICA and ECA. In this study, the boundary conditions for the three subjects were assumed to be the same, and obtained from our previous study,5 shown in Fig. 4.
https://static-content.springer.com/image/art%3A10.1007%2Fs10439-011-0314-5/MediaObjects/10439_2011_314_Fig4_HTML.gif
Figure 4

Boundary conditions. (a) Mass flow rates in internal and external carotid arteries. (b) Pressure profile for common carotid artery

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.

Results

Baseline Case Study

Wall tensile stress is believed to be an important factor for rupturing the thin fibrous cap.8 First principle stress (FPS), which is the highest stretching stress component in the wall, was used to represent wall tensile stress distributions for the three subjects. Figure 5 shows FPS distribution at a systolic phase. For case S1, FPS is higher at the luminal wall, lower at the arterial outer wall and the lowest in the lipid region (shown in Fig. 5(a.1, a.2)), the maximum value for each cross-section in Fig. 5(a.2) was presented in Fig. 5(a.3). An FPS concentration region, where the stress is particularly high, could be found in the fibrous cap, especially when the fibrous cap is thin. Figure 5(a.4) shows FPS distribution in the lumen surface, the local maximum stress regions can be found in the plaque region, indicated by the arrow, which is around the rupture site of the plaque. Similar results can be found in cases S2 (Fig. 5b) and S3 (Fig. 5c) with the local stress concentrations occurring around the rupture sites. Due to the 3 mm slice thickness in MR images, the rupture location has been assumed to cover 3 mm in axial direction across the rupture slice. Therefore, the averaged maximum stress at the cross-sections above and below ruptured sites plus the ruptured slice (three cross-sections in total) was compared with the average maximum stress in the remaining cross-sections. It showed that the stress was much higher in ruptured region than the non-rupture region. They were 157.8 kPa vs. 97.4 kPa for S1, 160.6 kPa vs. 93.6 kPa for S2, and 181.4 kPa vs. 106 kPa for S3.
https://static-content.springer.com/image/art%3A10.1007%2Fs10439-011-0314-5/MediaObjects/10439_2011_314_Fig5_HTML.gif
Figure 5

General plaque wall stress distributions for (a) S1, (b) S2, and (c) S3, respectively with three different views: (1) view with longitudinal cut, (2) cross-sectional view with 1.5 mm gap in axial direction, (3) maximum stress value for each cross-section, and (4) fibrous cap surface on the luminal side. Local stress concentrations at plaque regions are indicated by arrows

Stress Prediction Sensitivity Study to Fibrous Cap Reconstruction Variations

The wall tensile stress distributions in the fibrous cap surface of the luminal side for each subject (in a total of six models) is provided in Fig. 6, in which (a.1), (b.1), and (c.1) show the FPS distributions of the baseline models for S1, S2, and S3, respectively. Maximum stress value is presented for each model in Fig. 6. From the baseline model analysis (first part of this section), the local stress concentrations are located in rupture sites. For group 1, models in case S1 shown in Fig. 6(a.1, a.2, a.3), stress distributions for BL_Fth+ and BL_Fth++ have similar patterns as for BL_Fth. It can be seen that the rupture site experiences a local stress concentration with high stress values. In group 2 models of case 1 (Fig. 6(a.4, a.5, a.6), stress concentrations can still be found in the rupture site as in BL_Fth’s. Similar results for FPS distributions can be found for cases S2 and S3. With different fibrous cap thickness and lipid region configurations in the rupture sites for the different models, the local FPS concentration positions may vary slightly from baseline models in the cases of S1 and S2. In S3, the local stress concentration location changes from the middle part of the fibrous cap to the circumferential shoulder region when a thicker fibrous cap was present compared with the baseline model (Fig. 6(c.2)). Nevertheless, the stress concentrations are still around the rupture sites except for SL_Fth++ in S3 (Fig. 6(c.6)). Therefore, local stress concentration is generally located in the rupture sites of the studied plaques, and does not move away with varied plaque morphology induced by different rupture site reconstructions.
https://static-content.springer.com/image/art%3A10.1007%2Fs10439-011-0314-5/MediaObjects/10439_2011_314_Fig6_HTML.gif
Figure 6

Plaque wall stress distributions at fibrous cap surface for three models (classified by two groups) of each subject: (a) S1, (b) S2, and (c) S3. Rupture sites are indicated in the baseline models by arrows

In order to compare the wall stress level experienced in rupture location and non-rupture location in fibrous cap surface, three stress values for each model were introduced, they were the maximum FPS (FPSmax), mean FPS (FPSmean), and a cut-off FPS value named FPS95 in both rupture location and non-rupture location. The rupture location was defined as the region across the rupture slice along the axial direction with a total axial distance of 3 mm, and the remaining part was considered to be non-rupture region. FPS95 was defined by excluding 5% of all nodes containing the highest stress in the region, which can better represent plaque wall stress level in the local high stress regions on the fibrous cap. Table 1 summarizes the three stress values on all models, which shows that maximum FPS, mean FPS, and FPS95 generally were higher in rupture location than non-rupture location, except for the models BL_Fth++ in S1 and SL_Fth++ in S3 due to the thicker fibrous cap. If taking the stress value in non-rupture location to be the baseline value, maximum FPS, mean FPS, and FPS95 in the studied 18 models were 24.5, 34, and 49.5% higher in rupture sites than the values in non-rupture locations.
Table 1

Stress comparison between rupture locations and non-rupture locations

Subjects

Models

Stress at rupture location (kPa)

Stress at non-rupture location (kPa)

FPSmax

FPSmean

FPS95

FPSmax

FPSmean

FPS95

S1

BL_Fth

139.7

62.5

99.4

88.1

44.4

68.0

BL_Fth+

115.6

51.7

94.9

77.2

43.4

67.3

BL_Fth++

98.4

40.7

81.5

80.8

43.2

68.6

SL_Fth

276.2

71.3

151.4

206

48

73.1

SL_Fth+

158.1

53.9

95.9

129.3

46.2

72.5

SL_Fth++

109.6

46.2

83.1

96.9

45.8

70.8

S2

BL_Fth

222.9

84.7

163.3

159.8

53.4

83.9

BL_Fth+

181.4

70.9

139.9

164.3

49.6

80.5

BL_Fth++

163.9

56.3

114.6

148.7

46.5

78.8

SL_Fth

273

69.3

219.6

214.1

51.4

93.1

SL_Fth+

156.1

53.4

120.8

122

46.9

82.8

SL_Fth++

149

51.1

112.7

131.9

47.2

86.7

S3

BL_Fth

282.4

115.9

188.7

233.4

54.8

106.5

BL_Fth+

147.8

86.6

129.7

119.5

49.9

90.9

BL_Fth++

123.1

62.1

109.5

113.9

47.6

86.5

SL_Fth

192.7

75.4

129.5

127.9

47.1

86.8

SL_Fth+

128.7

64.4

102.9

120.7

50.6

91.6

SL_Fth++

88.9

33.9

56.5

85.7

31.2

59.7

BL_Fth, BL_Fth+, BL_Fth++, SL_Fth, SL_Fth+, SL_Fth++ were the six models for the studied three subjects S1, S2, and S3, respectively

FPSmax, maximum plaque wall stress; FPSmean, mean plaque wall stress; and FPS95 the cut-off plaque wall stress value. The model with higher stress value in non-rupture location than rupture location has been changed to be italic

Discussion

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.

Conclusions

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.

Acknowledgments

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

None.

Copyright information

© Biomedical Engineering Society 2011