Correlations between carotid plaque progression and mechanical stresses change sign over time: a patient follow up study using MRI and 3D FSI models
- Dalin Tang^{1, 2}Email author,
- Chun Yang^{2, 3},
- Gador Canton^{4},
- Zheyang Wu^{2},
- Thomas Hatsukami^{5} and
- Chun Yuan^{6}
https://doi.org/10.1186/1475-925X-12-105
© Tang et al.; licensee BioMed Central Ltd. 2013
Received: 18 August 2013
Accepted: 24 September 2013
Published: 14 October 2013
The Erratum to this article has been published in BioMedical Engineering OnLine 2013 12:126
Abstract
Background
Increasing evidence suggests that mechanisms governing advanced plaque progression may be different from those for early progression and require further investigation. Serial MRI data and 3D fluid–structure interaction (FSI) models were employed to identify possible correlations between mechanical stresses and advanced plaque progression measured by vessel wall thickness increase (WTI). Long-term patient follow up was used to gather data and investigate if the correlations identified above were reproducible.
Methods
In vivo MRI data were acquired from 16 patients in a follow-up study with 2 to 4 scans for each patient (scan interval: average 18 months and standard deviation 6.8 months). A total of 38 scan pairs (baseline and follow-up) were formed for analysis using the carotid bifurcation as the registration point. 3D FSI models were constructed to obtain plaque wall stress (PWS) and flow shear stress (FSS) to quantify their correlations with plaque progression. The Linear Mixed-Effects models were used to study possible correlations between WTI and baseline PWS and FSS with nodal dependence taken into consideration.
Results
Of the 38 scan pairs, 22 pairs showed positive correlation between baseline PWS and WTI, 1 pair showed negative correlation, and 15 pairs showed no correlation. Thirteen patients changed their correlation sign (81.25%). Between baseline FSS and WTI, 16 pairs showed negative correlation, 1 pair showed positive correlation. Twelve patients changed correlation sign (75%).
Conclusion
Our results showed that advanced plaque progression had an overall positive correlation with plaque wall stress and a negative correlation with flow shear stress at baseline. However, long-term follow up showed that correlations between plaque progress and mechanical stresses (FSS and PWS) identified for one time period were not re-producible for most cases (>80%). Further investigations are needed to identify the reasons causing the correlation sign changes.
Keywords
Introduction
Atherosclerosis development consists of three stages: early initiation, long-term (several decades) slow progression, and some of them final rupture. Low and oscillating blood flow shear stresses (LFSS) have been shown to correlate positively with intimal thickening and atherosclerosis initiation [1–7]. However, the mechanisms governing advanced plaque progression are not well understood. The LFSS hypothesis cannot explain why intermediate and advanced plaques continue to grow under elevated high shear stress conditions [8]. Several groups reported findings contrary to the LFSS hypothesis and suggested the growing importance of searching for other mechanical factors such as plaque wall (structural) stresses (PWS) and new hypotheses for mechanisms governing the plaque progression process [9, 10]. In a follow-up study for patients undertaking lipid-lowering therapy (10 patients, 24 months follow-up), Wentzel et al. (2005) reported that flow shear stress did not predict plaque regression [10]. The best predictor of plaque regression was baseline wall thickness. Using in vivo MRI of human carotid data, Tang et al. (2008) reported that 18 out of 21 patients showed negative correlations between human carotid atherosclerotic plaque progression and plaque wall stress on follow-up scan [8]. In the PREDICTION study, Stone et al. also reported that plaque area was a good predictor of change in plaque area (p<0.001), but flow shear stress was not (p=0.32) [11]. In a multi-patient (n=20) intravascular ultrasound (IVUS)-based follow-up study of patients with coronary atherosclerosis, by dividing slices into low (<10 dyn/cm^{2}), intermediate (between 10 and 25 dyn/cm^{2}), and high (>25 dyn/cm^{2}) flow shear stress (FSS) groups and comparing the low and high FSS groups with the intermediate-FSS group, Samady et al. found that low-FSS segments demonstrated greater reduction in vessel (P<0.001) and lumen area (P<0.001), and high-WSS segments demonstrated an increase in vessel (P<0.001) and lumen (P<0.001) area [12]. Using in vivo MRI-based models, Li et al. compared plaque stress conditions from asymptomatic and symptomatic individuals. High stress concentrations were found at the shoulder regions of symptomatic plaques [13].
It should be noted that many authors have used wall shear stress (WSS) and endothelial shear stress (ESS) for flow shear stress. FSS was used in our paper because we are also studying plaque wall stress (PWS) which is the plaque structural maximal principal stress at the lumen wall.
Huge effort has been devoted to identify “mechanisms” governing plaque progression. Correlations between plaque progress and mechanical stresses (including both flow shear stress and plaque wall stress) are considered mechanisms and have been the objectives of many investigations. However, a mechanism has to be reproducible, at least in a statistical sense. That means the observation should remain true for large population and for many observation times. To date, no study was performed to investigate the long term plaque progression correlation behaviors, i.e., if certain correlation behavior (called mechanism) observed in one time interval could be observed in the following time intervals. In this paper, 3D fluid–structure interaction (FSI) models were constructed based on long-term patient follow-up (up to 5–6 years, 2–4 scans, 1–3 time intervals) in vivo MRI data. FSI models were used so that we could perform more complete investigations including both plaque wall stress and flow shear stress. Long-term patient follow-up data would enable us to observe if correlations observed at one time interval could be kept in the subsequent time intervals, i.e., if the observed correlation was “reproducible” in a sense. Details are given below.
Materials and methods
In vivo serial MRI data acquisition and segmentation
3D geometry re-construction and mesh generation
3D fluid–structure interaction plaque model 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, c_{i} and D_{i} are material parameters chosen to match experimental measurements and the current literature [21, 22]. Parameter values used in this paper: vessel/fibrous cap, c_{1}=36.8 KPa, D_{1}=14.4 KPa, D_{2}=2; calcification, c_{1}=368 KPa, D_{1}=144 KPa, D_{2}=2.0; lipid-rich necrotic core, c_{1}=2 KPa, D_{1}=2 KPa, D_{2}=1.5; loose matrix, c_{1}=18.4 KPa, D_{1}=7.2 KPa; D_{2}=1.5. c_{2} = 0 was set for all materials [17].
Blood flow was assumed to be laminar, Newtonian, viscous and incompressible. The incompressible Navier–Stokes equations with arbitrary Lagrangian–Eulerian (ALE) formulation were used as the governing equations. A no-slip condition, natural traction equilibrium boundary condition and continuity of displacement were assumed on the interface between solid and fluid. Inlet and outlet were fixed (after initial pre-stretch) in the longitudinal (axial) direction, but allowed to expand/contract with flow otherwise. Patient-specific systolic and diastolic pressure conditions from the last hospital admission were used as the maximum and minimum of the imposed pulsatile pressure waveforms at the inlet and outlet of the artery. Details of the FSI model were given in Tang, et al. (2004, 2009) [17, 20].
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. (2004, 2009) and Bathe (2002) [18–20]. 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
Statistical analysis
The Linear Mixed-Effects (LME) models [23] were used to study the correlation between WTI and the predictors (PWS and FSS) at the initial time point of each time pair. The measured points are nodes, and it seems reasonable to capture the dependence among nodes based on their 3-dimensional spatial locations on the vessel. The models are specified as follows.
where y_{ ij } is the WTI value at the i th node on the j th slice, x_{ ij } is the corresponding value of FSS (or PWS). β_{0} and β_{1} are the fixed effects of the predictor for the baseline and the changing rate of WTI, respectively. The spatial dependence structure among y_{ ij } is accounted for by the exponential isotropic variogram model in 3D space, which is analogous to the autoregressive model in 1D space [23]. Specifically, the vector of random error terms (∈_{ ij }) follows a joint Gaussian distribution with mean 0, and the correlation between ${\in}_{{i}_{1}}{{j}_{1}}_{}$ and ${\in}_{{i}_{2}}{{j}_{2}}_{}$ is assumed an exponential function ϕ^{s}, where s is the Euclidean distance between the 3-dimensional spatial locations of the two nodes on the vessel, ϕ is the correlation parameter to be estimated in the model fitting by restricted maximum likelihood (REML) algorithm. The null hypothesis that no correlation exists between WTI and FSS (or PWS) indicates β_{1} = 0. A small p-value of the Student’s t-test for the coefficient [23] provides a strong statistical evidence to reject the null and accept the existence of correlation.
where y_{ ijk } is the WTI value at the i th node on the j th slice of the k th patient, x_{ ijk } is the corresponding value of FSS (or PWS). β_{0} and β_{1} have the same meanings as those in equation (4). For the k th patient, random effect b_{ k } follows a Gaussian distribution with mean 0, which models the clustering dependence of WTI values within this patient. The vector of error terms (∈_{ ijk }) follows a joint Gaussian distribution with mean 0. The patients are assumed to be independent so the correlation between the error terms from different patients is 0. The correlation between ${\in}_{{i}_{1}}{{{j}_{1}}_{}}_{k}$ and ${\in}_{{i}_{2}}{{j}_{2}k}_{}$ from the same k th patients is assumed an exponential function ${\varphi}_{k}^{s}$, where s is the Euclidean distance between the 3D spatial locations, ϕ_{ k } is the patient-specific correlation parameter to be estimated in model fitting. To test the correlation, we again use the p-value for testing β_{1} = 0.
To assess the above 3D spatial LME models, we randomly permuted the response WTI values and then calculated the p-values. Such a permutation breaks potential correlations between WTI and FSS (or PWS), so the corresponding p-value is expected to follow a Uniform (0, 1) distribution. Our results verified that the empirical distributions of these p-values after permutations were close to such expectation, which evidenced that our models have the type I error well controlled at the level of individual hypothesis test. That is, these models are appropriate in fitting the correlations between WTI and FSS (or PWS), and the observed small p-values are reliable to indicate the significance of the correlations. We controlled the type I error rate at 0.05.
where ${\widehat{\beta}}_{1}$ is the estimated slope coefficient by fitting FSS (or PWS) to WTI with the LME model (4) or (5). Because ${\widehat{\beta}}_{1}$ is estimated in the models that have adjusted the 3D spatial dependence structure among the observations of FSS (or PWS), r is the dependence-adjusted correlation coefficient.
Results
Plaque progression (WTI) correlates positively with plaque wall stress at baseline
Correlation summary between WTI and PWS at baseline
Patient | Nodes | TP1-TP2 | Nodes | TP2-TP3 | Nodes | TP3-TP4 | |||
---|---|---|---|---|---|---|---|---|---|
p | r | p | r | p | r | ||||
P1 | 800 | 0.0000 | 0.6048 | 800 | 0.0019 | 0.0972 | |||
P2 | 800 | 0.0000 | 0.2946 | 900 | 0.0000 | 0.0889 | 900 | 0.1063 | −0.0508 |
P3 | 700 | 0.0000 | 0.1222 | 800 | 0.0014 | 0.0573 | 800 | 0.0042 | 0.0904 |
P4 | 700 | 0.0000 | 0.1512 | 700 | 0.6773 | −0.0108 | |||
P5 | 900 | 0.0000 | 0.1889 | 900 | 0.0066 | 0.0600 | |||
P6 | 800 | 0.0020 | 0.0449 | 800 | 0.0000 | 0.1304 | 800 | 0.1876 | −0.0249 |
P7 | 700 | 0.1892 | 0.0160 | 400 | 0.3004 | 0.0266 | |||
P8 | 400 | 0.8234 | 0.0049 | 900 | 0.0038 | 0.0536 | |||
P9 | 700 | 0.0053 | 0.0422 | 700 | 0.3353 | −0.0258 | |||
P10 | 400 | 0.0279 | 0.0244 | ||||||
P11 | 800 | 0.0080 | 0.0519 | 900 | 0.1847 | −0.0228 | |||
P12 | 800 | 0.0000 | 0.1727 | 800 | 0.0633 | 0.0323 | 800 | 0.0655 | 0.0477 |
P13 | 600 | 0.0000 | 0.2123 | 600 | 0.8811 | 0.0051 | 500 | 0.0000 | 0.3827 |
P14 | 700 | 0.2534 | −0.0199 | 700 | 0.1829 | 0.0393 | 600 | 0.0149 | −0.0793 |
P15 | 1000 | 0.3021 | −0.0162 | 1000 | 0.0006 | 0.0644 | |||
P16 | 900 | 0.1409 | −0.0446 | 800 | 0.0000 | 0.1858 | 800 | 0.0001 | 0.1129 |
All | T1-T2 | 0.0000 | 0.0570 | T2-T3 | 0.0000 | 0.0498 | T3-T4 | 0.0130 | 0.0283 |
Total | |||||||||
P=22 | 16 pairs | P=11 | 15 pairs | P= 8 | 7 pairs | P=3 | |||
N=1 | N=0 | N=0 | N=1 | ||||||
NS=15 | NS=5 | NS=7 | NS=3 |
Only 16 pairs out of 38 showed negative correlation between WTI and FSS at baseline
Correlation summary between WTI and FSS at baseline
Patient | Nodes | TP1-TP2 | Nodes | TP2-TP3 | Nodes | TP3-TP4 | |||
---|---|---|---|---|---|---|---|---|---|
p | r | p | r | p | r | ||||
P1 | 800 | 0.0000 | 0.7795 | 800 | 0.0048 | −0.1168 | |||
P2 | 800 | 0.0003 | −0.1432 | 900 | 0.7463 | 0.0132 | 900 | 0.5646 | −0.0157 |
P3 | 700 | 0.0787 | −0.0495 | 800 | 0.2754 | −0.0303 | 800 | 0.0000 | −0.1859 |
P4 | 700 | 0.8717 | 0.0074 | 700 | 0.0316 | −0.0761 | |||
P5 | 900 | 0.0026 | −0.1257 | 900 | 0.0535 | −0.0538 | |||
P6 | 800 | 0.3243 | 0.0256 | 800 | 0.5825 | −0.0165 | 800 | 0.0757 | −0.0459 |
P7 | 700 | 0.0015 | −0.1208 | 400 | 0.0002 | −0.1705 | |||
P8 | 400 | 0.0051 | −0.1524 | 900 | 0.0909 | 0.0553 | |||
P9 | 700 | 0.0000 | −0.2104 | 700 | 0.0012 | −0.1732 | |||
P10 | 400 | 0.0003 | −0.0749 | ||||||
P11 | 800 | 0.4927 | 0.0207 | 900 | 0.0003 | −0.1034 | |||
P12 | 800 | 0.0000 | −0.0900 | 800 | 0.2037 | −0.0482 | 800 | 0.1904 | 0.0376 |
P13 | 600 | 0.1071 | −0.0864 | 600 | 0.0281 | −0.0865 | 500 | 0.6058 | 0.0355 |
P14 | 700 | 0.6729 | 0.0127 | 700 | 0.4306 | −0.0322 | 600 | 0.0788 | −0.0591 |
P15 | 1000 | 0.8519 | −0.0044 | 1000 | 0.4461 | 0.0220 | |||
P16 | 900 | 0.5383 | 0.0179 | 800 | 0.0071 | −0.0906 | 800 | 0.0082 | −0.0853 |
All | T1-T2 | 0.0350 | −0.0182 | T2-T3 | 0.0003 | −0.0308 | T3-T4 | 0.0001 | −0.05210 |
Total | |||||||||
P=1 | 16 pairs | P=1 | 15 pairs | P=0 | 7 pairs | P=0 | |||
N=16 | N=7 | N=7 | N=2 | ||||||
NS=21 | NS=8 | NS=8 | NS=5 |
Most patients changed correlation sign during the long-term follow-up study
Correlation sign change summary between WTI and PWS at baseline
Pts | WTI vs. PWS | Sign kept | WTI vs. FSS | Sign kept | ||||
---|---|---|---|---|---|---|---|---|
T1-T2 | T2-T3 | T3-T4 | T1-T2 | T2-T3 | T3-T4 | |||
P1 | + | + | Yes | + | − | |||
P2 | + | + | N | − | N | N | ||
P3 | + | + | + | Yes | N | N | − | |
P4 | + | N | N | − | ||||
P5 | + | + | Yes | − | N | |||
P6 | + | + | N | N | N | N | ||
P7 | N | N | − | − | yes | |||
P8 | N | + | − | N | ||||
P9 | + | N | − | − | yes | |||
P10 | + | − | ||||||
P11 | + | N | N | − | ||||
P12 | + | N | N | − | N | N | ||
P13 | + | N | + | N | − | N | ||
P14 | N | N | − | N | N | N | ||
P15 | N | + | N | N | ||||
P16 | N | + | + | N | − | − | ||
Patients kept correlation sign | 3 | Patients kept correlation sign | 2 |
Discussion
Re-thinking about mechanisms governing advanced plaque progression
A “mechanism” governing a physical or biological process should be something that is true for a majority of events from any given observations, both in terms of samples such as patients and observation time intervals. Then the “mechanism” could be used to predict future trends and possible clinical events, and the prediction should be true at least statistically. There have been huge efforts seeking mechanisms governing plaque progression. It is intuitively natural that low and oscillating flow shear stress would create more favorable flow conditions for cell adhesion and atherosclerosis initiation. Recent advance of medical imaging technology made it possible to track patients non-invasively, obtain patient-specific plaque progression data and quantify possible correlations between plaque progression and various factors such as flow shear stress and plaque wall stress. While the research community has yet to come to a consensus, it is becoming clearer that correlations between advanced plaque progression and mechanical stresses, if they exist, may not be as strong as we thought they were. Results from this study indicated that more than 80% of the patients could not hold their correlation sign over time. If we insist on finding some mechanisms which remained true for all observation intervals for the same patient, those “mechanisms” would be applicable only to 18.75% patients for a positive correlation between plaque progression and plaque wall stress, and 12.5% patients for negative correlation between plaque progression and flow shear stress.
Our results give strong motivations to seeking other mechanisms governing plaque progression, or investigating the reasons causing the correlation sign change. Use of lipid-lowering medications such as statin could be a contributing factor. Diet, cholesterol, mental stress, sudden change of life style, or other disease or illness could all be contributing factors. Growth of plaques depends not only on stress and strain, but a complex biology and physiology environments. Investigation with more possible factors included may lead to new findings.
Limitations
We are limiting our research to the correlation study between plaque progression and mechanical stresses (FSS and PWS). Other risk factors such as stenosis severity, lipid-rich necrotic cores, and intraplaque hemorrhage will be studies in our subsequent investigations. Other model limitations include: a) the use of an isotropic material model for the vessel because patient-specific anisotropic material properties were not available in vivo [24]; b) flow was assumed laminar because the average stenosis severity (by diameter) of the 54 plaques was 50% and laminar flow assumption was considered acceptable at this level [25]; c) arm systole and diastole pressures taken at scan visit were used to scale the pressure profile used in the simulations since pressure conditions right at the location of the plaque were not available; d) effect of statin use and presence of intraplaque hemorrhage (IPH) were not included in the current study due to lack of complete patient data. Development of IPH would be expected to increase FSS on follow-up scans due to progression in luminal narrowing, but result in continued increase in wall thickness. We are continuing our effort and results will be reported as they become available.
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.
Notes
Declarations
Acknowledgement
This research was supported in part by NSF grant DMS-0540684, NIH/NIBIB 2R01EB004759, and NIH R01 HL073401. Chun Yang’s research was partially supported by National Sciences Foundation of China grant 10871028.
Authors’ Affiliations
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