- Research
- Open Access
Impact of flow rates in a cardiac cycle on correlations between advanced human carotid plaque progression and mechanical flow shear stress and plaque wall stress
- Chun Yang^{1, 2}Email author,
- Gador Canton^{3},
- Chun Yuan^{3},
- Marina Ferguson^{3},
- Thomas S Hatsukami^{4} and
- Dalin Tang^{2}
https://doi.org/10.1186/1475-925X-10-61
© Yang et al; licensee BioMed Central Ltd. 2011
- Received: 16 May 2011
- Accepted: 19 July 2011
- Published: 19 July 2011
Abstract
Background
Mechanical stresses are known to play important roles in atherosclerotic plaque initiation, progression and rupture. It has been well-accepted that atherosclerosis initiation and early progression correlate negatively with flow wall shear stresses (FSS). However, mechanisms governing advanced plaque progression are not well understood.
Method
In vivo serial MRI data (patient follow-up) were acquired from 14 patients after informed consent. Each patient had 2-4 scans (scan interval: 18 months). Thirty-two scan pairs (baseline and follow-up scans) were formed with slices matched for model construction and analysis. Each scan pair had 4-10 matched slices which gave 400-1000 data points for analysis (100 points per slice on lumen). Point-wise plaque progression was defined as the wall thickness increase (WTI) at each data point. 3D computational models with fluid-structure interactions were constructed based on in vivo serial MRI data to extract flow shear stress and plaque wall stress (PWS) on all data points to quantify correlations between plaque progression and mechanical stresses (FSS and PWS). FSS and PWS data corresponding to both maximum and minimum flow rates in a cardiac cycle were used to investigate the impact of flow rates on those correlations.
Results
Using follow-up scans and maximum flow rates, 19 out of 32 scan pairs showed a significant positive correlation between WTI and FSS (positive/negative/no significance correlation ratio = 19/9/4), and 26 out of 32 scan pairs showed a significant negative correlation between WTI and PWS (correlation ratio = 2/26/4). Corresponding to minimum flow rates, the correlation ratio for WTI vs. FSS and WTI vs. PWS were (20/7/5) and (2/26/4), respectively. Using baseline scans, the correlation ratios for WTI vs. FSS were (10/12/10) and (9/13/10) for maximum and minimum flow rates, respectively. The correlation ratios for WTI vs. PWS were the same (18/5/9), corresponding to maximum and minimum flow rates.
Conclusion
Flow shear stress corresponding to the minimum flow rates in a cardiac cycle had slightly better correlation with WTI, compared to FSS corresponding to maximum flow rates. Choice of maximum or minimum flow rates had no impact on PWS correlations. Advanced plaque progression correlated positively with flow shear stress and negatively with plaque wall stress using follow-up scans. Correlation results using FSS at the baseline scan were inconclusive.
Keywords
- Magnetic Resonance Image Data
- Maximum Flow Rate
- Plaque Progression
- Correlation Ratio
- Wall Thickness Increase
Introduction
Cardiovascular diseases are the Number One cause of death in the developed countries and are becoming the Number One cause of death worldwide. Most cardiovascular diseases are related to atherosclerotic plaques whose rupture often leads to severe clinical event such as heart attack and stroke. It is of ultimate importance that we could understand the mechanisms governing plaque progression and rupture processes, and predict the drastic events (rupture, heart attack, and stroke) before their actual happening. It has been well accepted that low and oscillating blood flow shear stresses (LFSS) correlate positively with intimal thickening and atherosclerosis initiation [1–8]. However, results for advanced plaque progression based on patient-tracking data are relatively rare in the literature. Tang et al. used 2D structure-only models based on in vivo MRI patient-tracking data from 21 patients and their results indicated that 18 out of 21 patients studied showed significant negative correlation between plaque progression measured by wall thickness increase (WTI) and plaque wall stress (PWS, structure maximum principal stress taken at lumen wall) at follow-up time (T2). The 95% confidence interval for the Pearson correlation coefficient was (-0.443, -0.246), p < 0.0001 [9]. A recent paper from the same group reported that advanced human carotid plaque progression correlates positively with flow shear stress (FSS) using follow-up MRI scan data [10]. 3D models with fluid-structure interactions based on in vivo magnetic resonance images (MRI) of carotid plaques from 14 consented patients and 32 MRI scan pairs (baseline and follow-up) were used in that study. Two important observations from the study could be made: a) correlations between plaque progression with mechanical stresses (PWS and FSS) for advanced plaques may be different from those for plaques at their initiation and early development stage; b) correlations using follow-up time point data may be different from those using baseline time point data. Since it is generally believed that lower flow shear stress may promote plaque progression and our earlier analyses were performed only for data corresponding to the peak flow rate in a cardiac cycle. In an attempt to quantify the impact of flow rate on plaque progression, flow shear stress on the lumen corresponding to maximum and minimum flow rates in a cardiac cycle were calculated and their correlations with plaque progression were compared to investigate the flow rate impact. Correlation results for plaque wall stress were also reported.
Methods
The patient MRI data, 3D FSI model construction, solution methods, node type and data point selection procedures were the same as those reported in [10] and it is briefly outlined here.
In vivo serial MRI data acquisition and segmentation
A patient with 4 scans gave 3 scan pairs (Scan 1, Scan 2), (Scan 2, Scan 3), and (Scan 3, Scan 4). Scan pairs for patients with 2 or 3 scans were formed similarly. Once the pairs were formed, they were all treated equal. Scans in each pair were referred to as (baseline scan, follow-up scan), or (Time 1 scan, Time 2 scan). Time 1 (T1) and Time 2 (T2) were used for easy reference.
3D Fluid-structure interaction plaque model construction and solution methods
where I_{1} and I_{2} are the first and second strain invariants, C = [C_{ij}] = X^{T} X is the right Cauchy-Green deformation tensor, X = [X_{ij}] = [∂x_{i}/∂a_{j}], (x_{i}) is the current position, (a_{i}) is the original position, c_{i} and D_{i} are material parameters chosen to match experimental measurements and the current literature [10]. Parameter values used for the arterial vessel wall in this model were: c_{1} = 368000 dyn/cm^{2}, c_{2} = 0, D_{1} = 144000 dyn/cm^{2}, D_{2} = 2.0.
For FSI models based on in vivo MRI data, a shrink-stretch process was needed to obtain the no-load starting geometry and match in vivo geometry under pressurized and stretched condition. The shrinkage in axial direction was 9% so that the vessel would regain its in vivo length with a 10% axial stretch. Circumferential shrinkage for lumen (about 8-12%) and outer wall (about 2-5%) was determined by trial-and-error so that: 1) total mass of the vessel was conserved; 2) the loaded plaque geometry after 10% axial stretch and pressurization had the best match with the original in vivo geometry.
The 3D FSI models were solved by ADINA, using unstructured finite element methods for both fluid and solid domains. Nonlinear incremental iterative procedures were used to handle fluid-structure interactions. The governing finite element equations for both solid and fluid models were solved by Newton-Raphson iteration method. More details of the computational models and solution methods can be found in Tang et al. [13–15], Yang et al. [10] and Bathe [11]. Plaque wall stress and flow shear stress data corresponding to peak systolic pressure were recorded for analysis.
Plaque progression measurements and data extraction for correlation analysis
In view of the fact that advanced plaques have irregular geometries, a piecewise equal-step method was introduced to calculate wall thickness at each data point [10]. This method is better than the shortest-distance method used in our previous paper [9].
WTI, PWS and FSS were extracted from all data points for all the 32 pairs corresponding to both maximum and minimum flow rates in a cardiac cycle. The phrase "in a cardiac cycle" will be omitted when referring to maximum or minimum flow rates when no confusion arises. Standard statistical linear regression analysis was performed to quantify the correlation between plaque progression measured by WTI and both M-FSS and FSS at baseline and follow-up scans.
Results
Summary of correlation results between flow shear stress (FSS) and plaque progression from 32 scan pairs using both baseline and follow-up scans and corresponding to maximum and minimum flow rates in a cardiac cycle
Case # | # of Data Pts | FSS Baseline Max-Q | FSS Baseline Min-Q | FSS Follow-Up Max-Q | FSS Follow-Up Min-Q | ||||
---|---|---|---|---|---|---|---|---|---|
r | p | r | p | r | p | r | p | ||
C1 | 400 | 0.015 | 0.761 | 0.025 | 0.619 | 0.125 | 0.013 | 0.130 | 0.009 |
C2 | 400 | -0.108 | 0.032 | -0.110 | 0.027 | 0.058 | 0.247 | 0.057 | 0.256 |
C3 | 900 | 0.338 | < .001 | 0.337 | < .001 | 0.401 | < .001 | 0.403 | < .000 |
C4 | 400 | -0.450 | < .001 | -0.460 | < .001 | -0.144 | 0.004 | -0.173 | 0.001 |
C5 | 800 | 0.170 | < .001 | 0.181 | < .001 | 0.432 | < .000 | 0.439 | < .000 |
C6 | 800 | -0.379 | < .001 | -0.384 | < .001 | 0.123 | 0.001 | 0.114 | 0.001 |
C7 | 800 | 0.117 | 0.001 | 0.108 | 0.002 | 0.125 | < .001 | 0.126 | < .001 |
C8 | 800 | -0.088 | 0.013 | -0.090 | 0.011 | 0.183 | < .001 | 0.181 | < .001 |
C9 | 600 | -0.305 | < .001 | -0.300 | < .001 | -0.288 | < .001 | -0.293 | < .001 |
C10 | 600 | 0.392 | < .001 | 0.391 | < .001 | 0.348 | < .001 | 0.352 | < .001 |
C11 | 700 | -0.313 | < .001 | -0.307 | < .001 | -0.311 | < .001 | -0.312 | < .001 |
C12 | 700 | 0.005 | 0.887 | 0.008 | 0.834 | -0.077 | 0.043 | -0.072 | 0.056 |
C13 | 600 | -0.117 | 0.004 | -0.110 | 0.007 | -0.027 | 0.513 | -0.013 | 0.745 |
C14 | 1000 | 0.188 | < .001 | 0.193 | < .001 | 0.337 | < .001 | 0.340 | < .001 |
C15 | 1000 | 0.108 | < .001 | 0.102 | 0.001 | 0.257 | < .001 | 0.252 | < .001 |
C16 | 900 | 0.007 | 0.845 | -0.010 | 0.760 | -0.146 | < .001 | 0.310 | < .001 |
C17 | 800 | 0.188 | < .001 | -0.199 | < .001 | 0.273 | < .001 | 0.288 | < .001 |
C18 | 800 | 0.056 | 0.116 | 0.054 | 0.128 | 0.154 | < .001 | 0.159 | < .001 |
C19 | 800 | -0.032 | 0.361 | -0.025 | 0.484 | 0.274 | < .001 | 0.283 | < .001 |
C20 | 800 | -0.587 | < .001 | -0.588 | < .001 | -0.468 | < .001 | -0.463 | < .001 |
C21 | 900 | 0.135 | < .001 | 0.134 | < .001 | 0.139 | < .001 | 0.137 | < .001 |
C22 | 900 | -0.036 | 0.282 | -0.053 | 0.111 | 0.006 | 0.858 | 0.002 | 0.947 |
C23 | 700 | -0.051 | 0.182 | -0.041 | 0.281 | 0.263 | < .001 | 0.272 | < .001 |
C24 | 800 | 0.028 | 0.436 | 0.021 | 0.548 | 0.082 | 0.020 | 0.081 | 0.022 |
C25 | 800 | -0.021 | 0.547 | -0.029 | 0.421 | 0.193 | < .001 | 0.203 | < .001 |
C26 | 700 | 0.054 | 0.150 | 0.058 | 0.128 | 0.153 | < .001 | 0.162 | < .001 |
C27 | 700 | -0.382 | < .001 | -0.389 | < .001 | -0.044 | 0.246 | -0.037 | 0.329 |
C28 | 900 | -0.369 | < .001 | -0.373 | < .001 | -0.223 | < .001 | -0.225 | < .001 |
C29 | 900 | 0.207 | < .001 | 0.215 | < .001 | 0.207 | < .001 | 0.205 | < .001 |
C30 | 800 | 0.332 | < .001 | 0.336 | < .001 | 0.361 | < .001 | 0.364 | < .001 |
C31 | 800 | -0.420 | < .001 | -0.418 | < .001 | -0.357 | < .001 | -0.354 | < .001 |
C32 | 800 | -0.489 | < .001 | -0.498 | < .001 | -0.170 | < .001 | -0.175 | < .001 |
Positive | 10 | 9 | 19 | 20 | |||||
Negative | 12 | 13 | 9 | 7 | |||||
No Signifi. | 10 | 10 | 4 | 5 | |||||
95% CI | (-0.15, 0.037) | (-.163, 0.024) | (-0.015, 0.155) | (0.01, 0.172) |
Summary of correlation results between plaque wall stress (PWS) and plaque progression from 32 scan pairs using both baseline/follow-up scans and maximum and minimum flow rates in a cardiac cycle
Case # | # of Data Pts | PWS Baseline Max-Q | PWS Baseline Min-Q | PWS Follow-Up Max-Q | PWS Follow-Up Min-Q | ||||
---|---|---|---|---|---|---|---|---|---|
r | p | r | p | r | p | r | p | ||
C1 | 400 | -0.060 | 0.232 | -0.059 | 0.243 | -0.301 | < .001 | -0.299 | < .001 |
C2 | 400 | 0.192 | < .001 | 0.192 | < .001 | -0.209 | < .001 | -0.209 | < .001 |
C3 | 900 | 0.019 | 0.564 | 0.022 | 0.505 | -0.440 | < .001 | -0.437 | < .001 |
C4 | 400 | 0.467 | < .001 | 0.469 | < .001 | -0.079 | 0.116 | -0.085 | 0.091 |
C5 | 800 | 0.270 | < .001 | 0.260 | < .001 | -0.108 | 0.002 | -0.129 | < .001 |
C6 | 800 | -0.039 | 0.274 | -0.023 | 0.508 | -0.279 | < .001 | -0.275 | < .001 |
C7 | 800 | 0.133 | < .001 | 0.145 | < .001 | -0.179 | < .001 | -0.166 | < .001 |
C8 | 800 | 0.267 | < .001 | 0.263 | < .001 | -0.133 | < .001 | -0.141 | < .001 |
C9 | 600 | 0.457 | < .001 | 0.457 | < .001 | 0.208 | < .001 | 0.208 | < .001 |
C10 | 600 | -0.297 | < .001 | -0.297 | < .001 | -0.622 | < .001 | -0.622 | < .001 |
C11 | 700 | -0.048 | 0.208 | -0.043 | 0.252 | -0.325 | < .001 | -0.329 | < .001 |
C12 | 700 | -0.024 | 0.530 | -0.015 | 0.695 | -0.228 | < .001 | -0.218 | < .001 |
C13 | 600 | -0.119 | 0.004 | -0.120 | 0.003 | -0.229 | < .001 | -0.242 | < .001 |
C14 | 1000 | -0.098 | 0.002 | -0.097 | 0.002 | -0.341 | < .001 | -0.342 | < .001 |
C15 | 1000 | 0.235 | < .001 | 0.240 | < .001 | -0.101 | 0.001 | -0.100 | 0.002 |
C16 | 900 | -0.037 | 0.269 | -0.037 | 0.262 | -0.302 | < .001 | -0.307 | < .001 |
C17 | 800 | -0.125 | < .001 | -0.121 | < .001 | -0.386 | < .001 | -0.383 | < .001 |
C18 | 800 | 0.030 | 0.397 | 0.030 | 0.396 | -0.368 | < .001 | -0.369 | < .001 |
C19 | 800 | -0.017 | 0.632 | -0.016 | 0.649 | -0.228 | < .001 | -0.228 | < .001 |
C20 | 800 | 0.492 | < .001 | 0.491 | < .001 | 0.253 | < .001 | 0.252 | < .001 |
C21 | 900 | 0.097 | 0.004 | 0.094 | 0.005 | -0.080 | 0.016 | -0.081 | 0.015 |
C22 | 900 | -0.135 | < .001 | -0.135 | < .001 | -0.241 | < .001 | -0.241 | < .001 |
C23 | 700 | 0.408 | < .001 | 0.412 | < .001 | -0.144 | < .001 | -0.143 | < .001 |
C24 | 800 | 0.242 | < .001 | 0.242 | < .001 | -0.402 | < .001 | -0.403 | < .001 |
C25 | 800 | 0.227 | < .001 | 0.226 | < .001 | -0.374 | < .001 | -0.375 | < .001 |
C26 | 700 | 0.107 | 0.005 | 0.107 | 0.005 | -0.221 | < .001 | -0.220 | < .001 |
C27 | 700 | 0.024 | 0.531 | 0.019 | 0.609 | -0.416 | < .001 | -0.415 | < .001 |
C28 | 900 | 0.470 | < .001 | 0.470 | < .001 | -0.011 | 0.741 | -0.014 | 0.673 |
C29 | 900 | 0.080 | 0.017 | 0.087 | 0.009 | 0.013 | 0.694 | 0.016 | 0.639 |
C30 | 800 | 0.110 | 0.002 | 0.112 | 0.002 | -0.052 | 0.140 | -0.051 | 0.152 |
C31 | 800 | 0.127 | < .001 | 0.125 | < .001 | -0.149 | < .001 | -0.154 | < .001 |
C32 | 800 | 0.119 | 0.001 | 0.117 | < .001 | -0.158 | < .001 | -0.161 | < .001 |
Positive | 18 | 18 | 2 | 2 | |||||
Negative | 5 | 5 | 26 | 26 | |||||
No Signifi. | 9 | 9 | 4 | 4 | |||||
95% CI | (0.039, 0.184) | (0.041, 0.185) | (-0.273, -0.142) | (-0.273, -0.143) |
Wall flow shear stress (FSS) correlates positively with wall thickness increase (WTI) using time 2 data, maximum and minimum flow
Table 1 summarizes correlation results between WTI and FSS at Time 1 and Time 2. Using FSS at Time 2 with maximum flow rate, statistically significant positive correlation between WTI and FSS was found in 19 of the 32 cases examined (9 negative, 4 no significance). The 95% confidence interval (CI) for Pearson correlation (PC) coefficient values was (-0.015, 0.155). The correlation ratio (positive: negativess: no significance) was (20:7:5) corresponding to the minimum flow rate. The 95% confidence interval (CI) was (0.01, 0.172). The correlation results corresponding to minimum flow rates were slightly better than those for maximum flow rates. Only 1 case (C16) changed from negative correlation under maximum flow to positive correlation under negative flow. And the p-value for one case changed from 0.043 to 0.056 (therefore became no significance). The correlations were weak in general and results were very close using either maximum or minimum flows.
No significant correlation between FSS and WTI using time 1 data, maximum and minimum flow
The positive, negative and no significance correlation cases between WTI and FSS were 10, 12, and 10 out of 32 cases corresponding to maximum flow rates, respectively. The 95% confidence interval (CI) was (-0.15, 0.037). Using minimum flow rates, the correlation ratio was (9:13:10) with 95% CI interval (-0.163, 0.024). Correlation results for both maximum and minimum flow rates were very similar; with minimum flow rates gave slightly better results. Only 1 case (C17) changed from positive correlation under maximum flow to negative correlation under minimum flow.
Plaque wall stress (PWS) correlates negatively with wall thickness increase (WTI) using time 2 data, maximum and minimum flow
Table 2 summarizes correlation results between PWS and WTI at Time 1 and Time 2. Using PWS at Time 2 with maximum flow rate, statistically significant negative correlation between PWS and FSS was found in 26 of the 32 cases examined (2 positive, 4 no significance). The 95% confidence interval (CI) for Pearson correlation (PC) coefficient values was (-0.273, -0.142). The correlation ratio and 95% CI interval corresponding to the minimum flow rate was exactly the same. That was not surprising since changing flow rates (actually it was the change of pressure for PWS) only caused proportional change in PWS which did not change correlation results.
Plaque wall stress (PWS) correlates positively with WTI using time 1 data, maximum and minimum flow
The positive, negative and no significance correlation cases between PWS and WTI and FSS were 18, 5, and 9, respectively, corresponding to both maximum and minimum flow rates. The 95% confidence interval (CI) corresponding to maximum and minimum flow rates were (0.039, 0.184) and (0.041, 0.185), respectively.
Discussion
An attempt was made to quantify impact of flow rates in a cardiac cycle on correlations between plaque progression and mechanical stresses. Correlation ratio for FSS vs. WTI corresponding to minimum flow rate at follow-up was (20:7:5), better than (19:9:4) corresponding to maximum flow rate. Overall, our results from the 32 pairs indicated that there is a positive correlation between advanced carotid plaque progression and flow shear stress using follow-up scan data, corresponding to both maximum and minimum flow rates. The correlation between plaque wall stress (PWS) and WTI was negative using follow-up data and positive using baseline data. Flow rate had almost no impact on correlations between PWS and WTI. The study using baseline FSS data for possible correlation between advanced carotid plaque progression and flow shear stress was inconclusive. All of these weak or inclusive correlation results suggest that more detailed data analysis [3, 4] may be needed to discover localized plaque progression and mechanical stress (FSS and PWS) behaviors that the overall correlation analysis could not reveal. It also suggests that non-mechanical factors such as cellular activities, chemical factors (medication), genetic factors (genes), and diseases (diabetes, high cholesterol, high blood pressure) may contribute to plaque progression and their impact should be investigated.
Very few correlation studies for plaque progression using patient follow-up could be found in the current literature, mainly due to the fact that it is expensive to conduct large-scale patient studies and it takes a long time to observe plaque progression. Gibson et al. (1993) studied 20 human coronary arteries (time interval: 3 years) and found that there were negative correlations between flow shear stress at baseline and vessel diameter changes (15 negative correlation, 5 no significance) [4]. They did not use vessel wall thickness change as plaque progression measurements. Wentzel et al. (2005) used serial MRI (time interval: 24 months) to investigate the role of FSS in plaque progression and regression in the thoracic aorta. Ten patients participated in their study. Velocity was measured at each 2 cm starting from the arch using phase-contrast MRI and FSS was calculated based on pc-MRI measurements. Each cross-section was divided into 4 quadrants and wall thickness of each quadrants at baseline and follow-up were calculated. Each patient had 16 locations (4 segments × 4 quadrants) for analysis. Their results indicated that FSS at baseline was a good predictor for wall thickness (which was not a surprise since WT correlated strongly with stenosis severity), but did not predict plaque regression. This is consistent with our findings.
Comparison of correlation results using flow maximum shear stress (FMSS) and traditional flow wall shear stress (FSS)
FMSS Baseline Max-Q | FMSS Follow-Up Max-Q | FSS Baseline Max-Q | FSS Follow-Up Max-Q | |
---|---|---|---|---|
Positive | 10 | 21 | 10 | 19 |
Negative | 15 | 8 | 12 | 9 |
No Signifi. | 7 | 3 | 10 | 4 |
95% CI | (-0.167, 0.025) | (0.012, 0.187) | (-0.15, 0.037) | (-0.015, 0.155) |
Modeling limitations include the following items: a) arm cuff systolic/diastolic pressures were used since on-site pressures were not available; b) isotropic material properties from the literature were used for the vessel since no patient-specific material properties were available. Layer-specific anisotropic material properties were not used in our models [16]; c) to reduce the model construction effort, plaque components were not included in the vessel wall. This certainly effected the accuracy of stress calculations and error estimates were given in [10]; d) blood flow was assumed laminar because the average stenosis severity (by diameter) of the 47 plaques was 50% and laminar flow assumption could be accepted [17].
Conclusion
Lower flow rates in a cardiac cycle led to slightly better correlation between WTI and FSS, but had no impact on PWS correlation. Advanced plaque progression correlated positively with flow shear stress and negatively with plaque wall stress using follow-up scans. Correlation results using FSS at the baseline scan were inconclusive.
Authors' information
Tang's group has been publishing image-based modeling work in recent years. For more information, please visit Tang's website: http://users.wpi.edu/~dtang/.
Dr. Yuan's group and their lab (Vascular Imaging Laboratory, University of Washington) have been developing MR imaging methods and have published extensively in this area. Website: http://www.rad.washington.edu/research/our-research/groups/vil.
Declarations
Acknowledgements
This research was supported in part by NSF grant DMS-0540684, NIH/NIBIB 2R01EB004759, and NIH R01 HL073401. Professor Chun Yang's research was partially supported by a grant for priority discipline of Beijing Normal University and the Fundamental Research Funds for the Central Universities. Many helpful discussions and advice from Professor Roger Kamm at MIT are gratefully acknowledged.
Authors’ Affiliations
References
- Friedman MH, Bargeron CB, Deters OJ, Hutchins GM, Mark FF: Correlation between wall shear and intimal thickness at a coronary artery branch. Atherosclerosis 1987, 68: 27–33. 10.1016/0021-9150(87)90090-6View ArticleGoogle Scholar
- Friedman MH: Arteriosclerosis research using vascular flow models: from 2-D branches to compliant replicas. J Biomech Eng 1993, 115: 595–601. 10.1115/1.2895546View ArticleGoogle Scholar
- Ku DN, Giddens DP, Zarins CK, Glagov S: Pulsatile flow and atherosclerosis in the human carotid bifurcation: positive correlation between plaque location and low and oscillating shear stress. Arteriosclerosis 1985, 5: 293–302. 10.1161/01.ATV.5.3.293View ArticleGoogle Scholar
- Gibson CM, Diaz L, Kandarpa K, Sacks FM, Pasternak RC, Sandor T, Feldman C, Stone PH: Relation of vessel wall shear stress to atherosclerosis progression in human coronary arteries. Arterioscler Thromb 1993, 13(2):310–5. 10.1161/01.ATV.13.2.310View ArticleGoogle Scholar
- Giddens DP, Zarins CK, Glagov S: The role of fluid mechanics in the localization and detection of atherosclerosis. J Biomech Eng 1993, 115: 588–594. 10.1115/1.2895545View ArticleGoogle Scholar
- Nerem RM: Vascular fluid mechanics, the arterial wall, and atherosclerosis. J Biomech Eng 1992, 114: 274–282. 10.1115/1.2891384View ArticleGoogle Scholar
- Suo J, Oshinski JN, Giddens DP: Blood flow patterns in the proximal human coronary arteries: relationship to atherosclerotic plaque occurrence. Mol Cell Biomech 2008, 5(1):9–18.MATHGoogle Scholar
- Wentzel JJ, Corti R, Fayad ZA, Wisdom P, Macaluso F, Winkelman MO, Fuster V, Badimon JJ: Does shear stress modulate both plaque progression and regression in the thoracic aorta? Human study using serial magnetic resonance imaging. J Am Coll Cardiol 2005, 45(6):846–854. 10.1016/j.jacc.2004.12.026View ArticleGoogle Scholar
- Tang D, Yang C, Mondal S, Liu F, Canton G, Hatsukami TS, Yuan C: A negative correlation between human carotid atherosclerotic plaque progression and plaque wall stress: in vivo MRI-based 2D/3D FSI models. J Biomech 2008, 41(4):727–736. 10.1016/j.jbiomech.2007.11.026View ArticleGoogle Scholar
- Yang C, Canton G, Yuan C, Ferguson M, Hatsukami TS, Tang D: Advanced human carotid plaque progression correlates positively with flow shear stress: an in vivo MRI multi-patient 3D FSI study. J Biomechanics 2010, 43(13):2530–2538. 10.1016/j.jbiomech.2010.05.018View ArticleGoogle Scholar
- Bathe KJ: Theory and Modeling Guide, Vol I: ADINA; Vol II: ADINA-F, ADINA R&D, Inc., Watertown, MA. 2002.Google Scholar
- Huang H, Virmani R, Younis H, Burke AP, Kamm RD, Lee RT: The impact of calcification on the biomechanical stability of atherosclerotic plaques. Circulation 2001, 103: 1051–1056.View ArticleGoogle Scholar
- Tang D, Yang C, Zheng J, Woodard PK, Sicard GA, Saffitz JE, Yuan C: 3D MRI-based multicomponent fsi models for atherosclerotic plaques. Ann Biomed Eng 2004, 32: 947–960.View ArticleGoogle Scholar
- Tang D, Teng Z, Canton G, Yang C, Ferguson M, Huang X, Zheng J, Woodard PK, Yuan C: Sites of rupture in human atherosclerotic carotid plaques are associated with high structural stresses: an in vivo MRI-based 3D fluid-structure interaction study. Stroke 2009, 40(10):3258–63. 10.1161/STROKEAHA.109.558676View ArticleGoogle Scholar
- Teng Z, Canton G, Yuan C, Ferguson M, Yang C, Huang X, Zheng J, Woodard PK, Tang D: 3D critical plaque wall stress is a better predictor of carotid plaque rupture sites than flow shear stress: An in vivo MRI-based 3D FSI study. J Biomech Eng 2010, 132(3):031007. 10.1115/1.4001028View ArticleGoogle Scholar
- Holzapfel GA, Stadler M, Schulze-Bause CAJ: A layer-specific three-dimensional model for the simulation of balloon angioplasty using magnetic resonance imaging and mechanical testing. Ann Biomed Eng 2002, 30(6):753–767.View ArticleGoogle Scholar
- Ku DN: Blood flow in arteries. Annu Rev Fluid Mech 1997, 29: 399–434. 10.1146/annurev.fluid.29.1.399MathSciNetView ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.