Plaque Ruptures Are Related to High Plaque Stress and Strain Conditions: Direct Verification by Using In Vivo OCT Rupture Data and FSI Models

Abstract

BACKGROUND:

While it has been hypothesized that high plaque stress and strain may be related to plaque rupture, its direct verification using in vivo coronary plaque rupture data and full 3-dimensional fluid-structure interaction models is lacking in the current literature due to difficulty in obtaining in vivo plaque rupture imaging data from patients with acute coronary syndrome. This case-control study aims to use high-resolution optical coherence tomography–verified in vivo plaque rupture data and 3-dimensional fluid-structure interaction models to seek direct evidence for the high plaque stress/strain hypothesis.

METHODS:

In vivo coronary plaque optical coherence tomography data (5 ruptured plaques, 5 no-rupture plaques) were acquired from patients using a protocol approved by the local institutional review board with informed consent obtained. The ruptured caps were reconstructed to their prerupture morphology using neighboring plaque cap and vessel geometries. Optical coherence tomography–based 3-dimensional fluid-structure interaction models were constructed to obtain plaque stress, strain, and flow shear stress data for comparative analysis. The rank-sum test in the nonparametric test was used for statistical analysis.

RESULTS:

Our results showed that the average maximum cap stress and strain values of ruptured plaques were 142% (457.70 versus 189.22 kPa; P=0.0278) and 48% (0.2267 versus 0.1527 kPa; P=0.0476) higher than that for no-rupture plaques, respectively. The mean values of maximum flow shear stresses for ruptured and no-rupture plaques were 145.02 dyn/cm² and 81.92 dyn/cm² (P=0.1111), respectively. However, the flow shear stress difference was not statistically significant.

CONCLUSIONS:

This preliminary case-control study showed that the ruptured plaque group had higher mean maximum stress and strain values. Due to our small study size, larger scale studies are needed to further validate our findings.

Highlights.

• Optical coherence tomography–verified plaque rupture data.

• Actual plaque cap thickness from repaired optical coherence tomography images.

• Three-dimensional fluid-structure interaction models that provided both plaque stress/strain and flow shear stress calculations.

Atherosclerotic plaque may rupture without warning and cause acute coronary syndrome, the leading cause of mortality worldwide.¹ It has been hypothesized that plaque rupture may be associated with high plaque stress, strain, and flow shear stress (FSS; called high plaque stress and strain hypothesis).^2–7 Although this hypothesis has been widely acknowledged or even accepted, its direct verification using real plaque rupture data is still lacking in the current literature due to difficulty in obtaining in vivo imaging data of plaque rupture from patients with acute coronary syndrome. Unlike carotid plaque studies where ex vivo histopathologic data could serve as the gold standard for rupture verification, coronary plaque samples could not be obtained from living patients to verify plaque rupture.⁸ To fill the gap in the literature, the goal of this study is to use optical coherence tomography (OCT)–verified in vivo plaque rupture data (similar to histopathology-verified carotid plaque data) and OCT-based patient-specific fluid-structure interaction (FSI) models to seek direct supporting evidence for the high plaque stress/strain hypothesis. It has been extremely challenging to detect plaque rupture and vulnerable plaques with thin fibrous cap (threshold cap thickness, <65 µm) using intravascular ultrasound (IVUS) and magnetic resonance imaging due to their imaging resolution limitations (150–200 µm for IVUS and 200–300 µm for magnetic resonance imaging, respectively). With its superior resolution (10–20 µm), recent development of OCT made it possible to use OCT to detect and verify plaque rupture in clinical settings.^9,10 In vivo OCT plaque data provided the basis for this modeling effort.⁶

It is believed that mechanical forces play an important role in plaque initiation, progression, and its eventual rupture, leading to drastic clinical cardiovascular events. Considerable effort has been made to seek and establish possible associations between biomechanical factors and plaque progression, vulnerability, and its eventual rupture.^11–14 The seminal paper by Loree et al¹² demonstrated that plaque circumferential stress was closely related to plaque cap thickness. From the flow side, Samady et al⁷ confirmed that low wall shear stress (WSS) segments developed greater plaque progression and constrictive remodeling. Bourantas et al² also proved that low WSS was the only independent predictor of disease progression at follow-up. Corban et al¹⁵ pointed out that combination of plaque burden, WSS, and plaque phenotype has incremental value for the prediction of coronary plaque progression and increased plaque vulnerability in patients with nonobstructive coronary artery disease. Thondapu et al¹⁶ reported in that high spatial endothelial shear stress gradient independently predicted site of acute coronary plaque rupture based on OCT data and computational hydrodynamic model. These studies suggested that hemodynamic factors (WSS) may be associated with future plaque rupture risk.^17,18

Mechanically speaking, plaque rupture occurs when stress and strain at the plaque fibrous cap exceed the strength of its material.¹⁹ From a solid mechanics point of view, plaque structural stress far exceeds WSS (10⁵× to 10⁶×) and may play a dominant role over WSS in the rupture process.^20,21 Most previously published vulnerable coronary plaque research papers (including our own) were based on IVUS data. IVUS resolution is a serious limitation that makes accurate quantification of plaque cap thickness nearly impossible. Based on IVUS virtual histology slices of plaques with evidence of rupture (verified by the Krakow Cardiovascular Research Institute Core Laboratory) and OCT slices of plaques without rupture, Costopoulos et al¹⁷ used 2-dimensional finite element models and showed that plaque stress from the ruptured plaques was higher than that from nonruptured plaques. Using numerical simulations on 3-dimensional (3D) idealized lesions and a micro-CT–derived human coronary atheroma, Corti et al²² indicated that inclusion of small microcalcification in thin cap could cause a 2.5-fold increase in plaque vulnerability. Considering the combined impact of 3D hemodynamics, solid mechanics, and their interactions on plaque progression and vulnerability changes, Yang et al,²¹ Tang et al,²³ Wang et al,²⁴ and Tang et al²⁵ developed 3D FSI models based on coronary vulnerable plaque in vivo images and reported that combining plaque morphology and mechanical factors may improve prediction accuracies for plaque progression and vulnerability changes. Still, direct verification of the high stress/strain hypothesis using real plaque rupture data is still needed, especially using full 3D FSI models to include both flow and solid mechanics factors in a more realistic blood flow and physiological modeling environment.

In this article, OCT imaging data of 5 ruptured plaques and 5 no-rupture plaques were selected for 3D FSI model construction and mechanical analysis. It should be noted that this is the first time plaques with in vivo OCT-identified ruptures were used in 3D FSI modeling study seeking associations between mechanical conditions and plaque rupture. The ruptured caps were repaired to their prerupture morphology using neighboring plaque cap and vessel geometries. Plaque stress, strain, and FSS conditions from these 2 groups were compared, and differences were identified and reported in Results.

The main features of our approach included (1) OCT-verified plaque rupture data; (2) actual plaque cap thickness from repaired OCT images using remaining ruptured cap flap and neighboring slices; (3) 3D FSI models with axial stretch and circumferential shrinking-expansion process to recover vessel in vivo morphology from its no-load condition (all models need to start from no-load morphology and zero pressure, zero stress/strain conditions); (4) more recent vessel material properties using nonlinear Mooney-Rivlin models with parameter values determined from in vivo IVUS cine images.²⁰

METHODS

The data used in this study and that supporting the findings of this study are available from the corresponding author upon reasonable request.

Data Acquisition, Coregistration, and Image Segmentation

OCT and angiography data were collected at Cardiovascular Research Foundation, Second Affiliated Hospital of Harbin Medical University, Zhongda Hospital, Southeast University, from patients with coronary heart diseases using the protocol approved by the local institute, and informed consents were obtained from the patients. Patients with severe calcified lesion, chronic total occlusion, or chronic kidney disease (creatinine, >1.5 mg/dL) were excluded. Ten lipid-rich plaques from different patients were identified for our analysis. Patient demographic data are shown in Table 1 (N=10; mean age, 65.2 years; male, n=6). OCT images were acquired with ILUMIEN OPTIS System and Dragonfly or Dragonfly JP Imaging Catheter (St. Jude Medical, Westford, MA). The frame thickness resolution of the OCT was 0.02 cm. The coronary angiography image matrix was 512×521, and the pixel size was 0.0258 cm. The length of the vessel with the plaque was set to be ≥2 cm. Plaque rupture was identified by the presence of fibrous cap discontinuity with a cavity inside the plaque overlying a lipid-rich core on the OCT image²⁶ (see Figure 1 for rupture sample). For ruptured plaques, it was required that the ruptured slices had obvious cavities caused by rupture, and there were at least 3 consecutive slices showing rupture. For no-rupture plaques, it must contain at least 8 consecutive slices with lipid cores, and the lipid angle must be ≥90°. We used the Strengthening the Reporting of Observational Studies in Epidemiology cross-sectional checklist when writing our report.²⁷

Table 1.

Patient Demographic Data

Figure 1.

Optical coherence tomography (OCT) images and segmented contour plots of ruptured and no-rupture plaques. A, Selected OCT slices with segmented contours of a plaque with no rupture. B, Selected OCT slices with segmented contours of a plaque with rupture. C, Three-dimensional (3D) reconstructed coronary geometry with ruptured cap repaired. Markers: *, lipid; yellow arrows, cavity or rupture site.

Segmentation was performed by the ImageJ 1.52v software to obtain plaque rupture cap, fibrous cap, plaque components, lumen, and outwall for all rupture and no-rupture plaques.^20,28 Small-size plaque components were neglected for simplicity. Three plaque compositions were considered: lipid necrotic core (short for lipid), calcification, and vessel tissue (fibrotic and fibrofatty). The ruptured cap was repaired to its prerupture morphology using remaining cap flaps and neighboring slice plaque cap information. Details of the rupture site cap repair, fibrous cap thickness determination, and stenosis severity with 1 figure and 2 tables are given in the Plaque Rupture Repair and Cap Thickness Determination section for better clarity. The 3D coordinates of the plaques were obtained based the coregistration of OCT and quantitative coronary angiography, and the spatial position information (called the centerline) was used for further 3D FSI model. Sample OCT slices with segmented contours, ruptured cap repaired, and 3D reconstruction process are shown in Figure 1.

Plaque Rupture Repair and Cap Thickness Determination

In this article, a key issue was to repair plaque rupture to restore (with best effort) plaque prerupture morphology so that we could have plaque prerupture morphology with enclosed lumen for 3D FSI model construction. Figure 2 shows details of a ruptured plaque and the repair process of the ruptured fibrous cap. The contours of lumen (with repaired cap), lipid, and outwall of a slice with rupture are shown in Figure 2B. Figure 2Bi gave the original OCT image showing the rupture site, torn flap, and cap discontinuity; Figure 2Bii showed the OCT image with partial lumen and lipid contours and outline of visible outwall contour (the torn flap was used to reconstruct the cap); Figure 2Biii gave the OCT image overlapped by complete lumen, lipid, and outwall contours. The torn flap was used to reconstruct the cap. The missing part of the fibrous cap was reconstructed using the torn flap as reference. Since plaques are often of irregular morphologies, a Four-Quarter Even-Spacing method has been developed to extract vessel and cap thickness data more evenly to be used in data analysis.²⁸ Points on lumen (100 points per slice, evenly spaced on the lumen) and outwall (points on each quarter were evenly spaced; quarters on outwall were determined by plaque shape to handle shape irregularity) were connected using Four-Quarter Even-Spacing method. Cap thickness was defined as the length of the line segment connecting the corresponding points on the lumen and the lipid core (Figure 2). Morphological parameters were then extracted on all data points for analysis. It should be noted that some ruptured plaques create cavities that support direct fibrous cap thickness acquisition, while others need to rely on the flaps. Therefore, an average extrapolation error of about 10% is calculated to reflect the error in quantifying the minimum fibrous cap thickness. Table 2 provided fibrous cap thickness, stenosis severity, and plaque burden for the ruptured and no-rupture plaques.

Figure 2.

Segmentation details of a ruptured plaque and the repair process of the ruptured fibrous cap. A, A slice with an untorn ruptured plaque cavity and repair segmentation process: optical coherence tomography (OCT) image and contour generation process (Ai–Aiii). B, A slice showing fibrous cap discontinuity and the cap repair process: OCT image showing rupture site, torn flap, and cap discontinuity, half and completely repaired cap (Bi–Biii).

Table 2.

Mean and Min Cap Thickness, Stenosis Severity (by Diameter), and Plaque Burden of Ruptured and No-Rupture Plaques

It should be noted that minimum cap thickness was found at the repaired portion (ie, extrapolated region) for all 5 ruptured cases. Strictly speaking, cap thickness extrapolation errors could not be calculated since we had no knowledge of the missing part of the cap. However, we could use the flap as a base to give some estimates. Figure 2Bii and 2Biii used yellow line for the repaired cap part with the flap and the location of minimum cap thickness marked. For this case, the minimum cap thickness and cap thickness of flap were 42.05 and 46.6 µm, respectively. Using flap cap thickness (where available) as the base, the extrapolation errors could be around 10%.

3D FSI Model

3D FSI models were constructed for the 10 selected plaques with preshrink-stretch process to obtain plaque stress, strain, and FSS/WSS conditions. For the fluid part, the blood was assumed as laminar, viscous, incompressible, and Newtonian. Patient-specific arm pressure was applied at the inlet and outlet of the vessel. No-slip boundary conditions and force balance were imposed on the blood vessel interfaces. The arbitrary Lagrangian-Eulerian description was adopted to handle the free-moving boundary (the interface). The full 3D FSI models were published before and are omitted here for simplicity.^21,23,24 For the structure model, the equilibrium equations (equation of motion), the nonlinear Cauchy-Green strain-displacement relation, and Mooney-Rivlin material properties were used. The vessel fibrous tissues (including cap tissue) were assumed to be hyperelastic, anisotropic, nearly incompressible, and homogeneous. The lipid core and calcification were assumed to be hyperelastic, isotropic, and nearly incompressible. Modified Mooney-Rivlin material models were used to describe the material properties of vessel tissues. The strain-energy density functions for tissue material properties are given below²⁰:

$${\displaystyle \begin{array}{l}{\displaystyle W_{iso}=c_1(I_1-3)+c_2(I_2-3)+D_1[exp\left(D_2(I_1-3)\right)-1]}\end{array}}$$ (1)

$${\displaystyle \begin{array}{l}{\displaystyle W_{aniso}=W_{iso}+\frac{K_1}{K_2}\{exp\left[K_2{(I_4-1)}^2\right]-1\}}\end{array}}$$ (2)

where $I_1=\sum \left(C_{ii}\right)$, $I_2=\frac{1}{2}[I_1^2-C_{ij}{C}_{ij}]$, $I_1$ and $I_2$ are the first and second invariants of right Cauchy-Green deformation tensor $C=\left[C_{ij}\right]=X^{T}X$, $X=\left[X_{ii}\right]=\left[\mathrm{\partial }{x}_i/\mathrm{\partial }{a}_j\right]$, $(x_i)$ is the current position, $\left(a_j\right)$ is the original position, $I_4=C_{ij}{(n_c)}_i{(n_c)}_j$, $n_c$ is the unit vector in the circumferential direction of the vessel, and $c_1$, $c_2$, $D_1$, $D_2$, $K_1$ and $K_2$ are material parameters. Material constants of isotropic Mooney-Rivlin model from existing literature were used: lipid: $c_1$=0.5 kPa, $c_2$=0 kPa, $D_1$=0.5 kPa, $D_2$=1.5 kPa; calcification: $c_1$=92 kPa,$c_2$=0 kPa, $D_1$=36 kPa, and $D_2$=2.0 kPa; vessel/fibrous tissue: $c_1$=−515.6 kPa, $c_2$=45.05 kPa,$D_1$=247.3 kPa, $D_2$=2.0 kPa, $K_1$=14.1 kPa, and $K_2$=23.5 kPa.²⁰

The 3D FSI models were solved by finite element software ADINA 9.6 (Adina R&D, Watertown, MA) following our established procedures.^20,21,23,24 Nonlinear incremental iterative procedures were used to solve the models. Mesh analysis was performed by refining mesh density by 10% until changes of solutions became <2%.

Data Extraction

The results of plaque stress, strain, and FSS on the lumen-wall interface under the maximum pressure of the 3D FSI model were extracted for analysis. The results of ruptured and no-rupture models from cap region were compared to investigate their differences. For each 3D FSI plaque model, all lipid slices were selected, and the model results of the fibrous cap region on their lumen were extracted. The maximum values of the extracted results were calculated to obtain the maximum values of the stress, strain, and FSS parameters for each model. The mean values of the extracted results were calculated to obtain the mean values of the stress, strain, and FSS parameters for each model.

Statistical Methods

The rank-sum test (right-tailed hypothesis test) in the nonparametric test was used for the statistical analysis of the biomechanical data. A 1-sided P<0.05 was considered statistically significant. Plaque rupture has been a hot research topic, and many publications demonstrated that ruptured plaque plaques may have higher structural stress values.^{5,6,8,12,15,17} With that, 1-sided P values were used in this study. To compare the relative errors, the no-rupture plaque was considered as the component parent (base), and the relative error between the ruptured and no-rupture plaque was calculated.

RESULTS

Maximum Cap Stress and Strain Values of Ruptured Plaques Were 142% and 48% Higher Than That of No-Rupture Plaques

Table 3 shows the maximum and mean cap stress and strain values of the ruptured and no-rupture plaques (the mean value results will be discussed in the Comparison of Mean Cap Stress and Strain Values of Ruptured and No-Rupture Plaques section). The average maximum cap stress for all ruptured plaques was 457.70 kPa, which was 142% higher than 189.22 kPa (P=0.0278) for all no-rupture plaques. The average maximum cap strain for all ruptured plaques was 0.2267 kPa, which was 48% higher than the average maximum cap strain (P=0.1527) for all no-rupture plaques (P=0.0476). Differences of mean cap stress and strain values can be observed in Table 3. However, those differences were not statistically significant. Figure 3 provided plots of plaque stress, strain, FSS, and velocity from ruptured and no-rupture plaque samples for clear direct comparisons.

Table 3.

Maximum and Mean Cap Stress and Strain Values of the Ruptured and No-Rupture Plaques

Figure 3.

Plaque wall stress, strain, FSS, and velocity distribution plots at maximum pressure showing their differences between ruptured and no-rupture plaques. A, Plaque stress, strain, flow shear stress, and velocity plots at maximum pressure from a ruptured plaque sample. B, Plaque stress, strain, flow shear stress, and velocity plots at maximum pressure from a no-rupture plaque sample.

Comparison of Mean Cap Stress and Strain Values of Ruptured and No-Rupture Plaques

The mean cap stress and strain values of the ruptured and no-rupture plaques are given in Table 3. The average mean cap stress for all ruptured plaques was 116.86 kPa, while that for all no-rupture plaques was 76.67 kPa. The average mean cap strain for all ruptured plaques was 0.1241 kPa, while that for all no-rupture plaques was 0.1030 kPa. Relative differences of 52% (P=0.1548) for mean cap stress and 20% for mean cap strain (P=0.754) were observed with no-rupture plaque average values used as the base. However, those differences were not statistically significant. Figure 4 provided plots of OCT image slice, segmented contour plot, plaque stress, and strain plots showing maximum cap stress/strain values from ruptured and no-rupture plaque samples for clear direct comparisons.

Figure 4.

Comparison of maximum (max) and mean cap stress and strain using slice plots of ruptured and no-rupture plaques. A, Max and mean cap stress/strain of a sample slice from a ruptured plaque. B, Max and mean cap stress/strain of a sample slice from a plaque with no rupture. Markers: Δ, location of max value on lumen; *, lipid, marked in OCT image in B. CapS indicates cap stress; and CapSn, cap strain.

Comparison of the Maximum and Mean FSS Values of Ruptured and No-Rupture Plaques

Table 4 gives the maximum and mean cap FSS (maximum FSS and mean FSS) values of the ruptured and no-rupture plaques. The average maximum FSS for all ruptured plaques was 145.02 dyn/cm², while that for all no-rupture plaques was 81.92 dyn/cm². The average mean FSSs for all ruptured and no-rupture plaques were 58.60 and 49.02 dyn/cm², respectively. Relative differences of 77% (P=0.1111) for maximum FSS and 20% (P=0.3452) for mean FSS were observed with no-rupture plaque average values used as the base. It should be noted that those differences were not statistically significant.

Table 4.

The Max and Mean FSS Values of the Ruptured and No-Rupture Plaques

DISCUSSION

Significance of Using In Vivo Plaque Rupture Data as the Final Verification for the Hypothesis That Higher Plaque Stress, Strain, and FSS Are Associated With Plaque Rupture

It has long been hypothesized that plaque rupture may be associated with higher plaque stress, strain, and FSS.^3,17,29–36 However, its direct verification by actual in vivo plaque rupture data is hard to find (if any) in the current literature, especially for coronary plaques. That is simply because we could not obtain coronary plaque samples from living patients to verify plaque rupture, while carotid plaque studies could get ex vivo plaque samples and histopathologic data to serve as the gold standard for rupture verification.⁸ This study used in vivo data of coronary plaque rupture verified by OCT in patients with acute coronary syndrome and patient-specific FSI models to perform comparisons for plaques with and without rupture and our results showed that mean maximum cap stress and strain from ruptured plaque group were higher than that from the no-rupture group. This is our effort using in vivo OCT plaque rupture data to verify the high stress/strain hypothesis, which is needed as the base for plaque vulnerability assessment using plaque stress/strain conditions.^25,37 Accurate plaque stress/strain conditions (used as additional risk factors) may improve plaque vulnerability assessment accuracy if combined with morphology features.^{4,5,17,20,21,23–25,38,39} In addition, the distribution of microcalcified and neovascularization between the fibrous cap and the lipid core may also be related to plaque rupture, which is a direction for future research.^40–42

Verification of the hypothesis that high plaque stress and strain are associated with plaque rupture provides the base for researchers to use plaque stress/strain values to introduce quantitative secondary plaque vulnerability indices (PVIs) for plaque classifications since plaque vulnerability (the likelihood that a plaque may rupture) is hard to quantify. While many articles focused on high plaque stress as a major risk factor for plaque rupture, it remains to be unsettled whether plaque stress/strain conditions could improve prediction accuracies. One long-term goal of our efforts was to show that combining morphological and biomechanical risk factors may lead to better prediction of plaque progress and vulnerability changes. Lv et al⁴³ introduced plaque stress/strain indices as substitute quantitative PVIs and used a machine learning method (random forest) to predict stress/strain index changes with actual patient IVUS+OCT follow-up data as the gold standard. Their prediction results showed that optimal prediction accuracies for changes in mean cap stress PVI and mean cap strain PVI were 85.6% (area under the curve [AUC], 0.867) and 83.3% (AUC, 0.809), which improved the prediction accuracies over the best single predictor by 10.0% for mean stress PVI and 8.0% for mean strain PVI. Wang et al⁴⁴ used IVUS follow-up data and 3D FSI models to obtain plaque stress, strain, and flow shear conditions and predict plaque progression measure by plaque area increase. Their results showed the optimal combination predictor achieved prediction accuracy of 1.5928 with an AUC of 0.852 while the best single predictor for plaque area increase was plaque wall stress with sensitivity and specificity of 1.4856 and AUC of 0.8116.

Use Caution When Interpreting Association Between High Plaque Stress/Strain and Rupture

While we are trying to verify the hypothesis that plaque rupture may be associated with high plaque stress and strain, caution should be exercised when interpreting our results. An intuitive prediction method is to use median (the cutoff value) of the maximum and mean cap stress and strain for the 10 plaques as a cutoff to predict plaque rupture, that is, the method predicts the plaque to be in the rupture group if the stress/strain value was greater than the median, otherwise the method predicts the plaque to be in the no-rupture group (no stress/strain values were equal to the median values). Table 5 showed that the correct prediction ratios (ruptured plaque predicted as ruptured; no-rupture plaque predicted as no-rupture) were 80% using maximum cap stress and maximum strain values as predictors. Prediction ratio using mean cap stress/strain values was lower (both 60%).

Table 5.

Using Max and Median Plaque Stress and Strain to Predict Plaque Rupture

It should be noted that the values of maximum cap stress for ruptured caps are only 150% greater than nonruptured caps, and the maximum strains for ruptured caps were only 48% higher. There was 1 ruptured plaque with maximum cap stress lower than the median (246.29 kPa) and 1 no-rupture plaque with maximum cap stress higher than the median. For mean cap stress, there were 2 ruptured plaques with mean cap stress lower than the median (94.94 kPa) and 1 no-rupture plaque with mean cap stress higher than the median. This is quite common due to the complexity of plaque structures, tissue property differences, and patient variations. Large-scale studies are needed to further verify (or defeat) the high stress/strain hypothesis.

Risk Factor Statistic Associations With Plaque Rupture

Due to our small data size, association/correlation may not be able to achieve statistically significant P values. That was why we chose to report comparative study results in this article. Student t test was performed, and Table 6 gives the statistic association results of 12 risk factors with plaque rupture. Positive t-statistic value indicates that the no-rupture group had a larger average than the rupture group. The commonly known risk factors (age, mean, and minimum cap thickness, stenosis severity, plaque burden, and blood pressure) had a P value <0.05, indicating significant associations. P values for maximum stress and strain were 0.0410 and 0.0279, respectively, also indicating statistical significance. Due to our small sample size, the association results should be interpreted with caution and large size samples are needed to get more solid association results.

Table 6.

Risk Factor Statistic Associations With Plaque Rupture

Using the Repaired Approach to Estimate the Morphology of the Plaque Rupture Site

The process of the plaque ruptures considered in the article (macroplaque rupture) can be described as follows: the fibrous cap covering a large lipid pool became so thin that it broke. Then the contents in the lipid pool flew out, and the fibrous cap became free and formed flap. Our repaired approach was to restore the floating flap to its previous position when the rupture was about to occur, based on the flap’s own thickness and the images of the no-rupture plaque before and after the ruptured segment. This repaired approach is conducive to the study of the direct factors related to plaque rupture and has been proved to be reliable to a certain extent by researchers.^45,46 For some cases where the thickness of the fibrous cap cannot be estimated, we use the parameter values from the work of Chandran et al.⁴⁷ The source of plaque instability has been shown to be associated with a large lipid core, and the rebuild of the contents of the vessel wall at the site of rupture (thought to be lipid) has also strengthened the validity of this repaired approach to some extent.

Limitations

This study has the following limitations. (1) Due to the small sample size, we would like to emphasize that the findings from this study are not definitive as the sample size is too small. While it is true that plaque rupture cases are hard to have, large-scale studies are needed to further validate the high stress/strain hypothesis and obtain more definitive results and conclusions. Some comparison results do not meet the statistical requirements. It is also difficult to consider the sex and age differences between patients. (2) Patient-specific material properties were not available in this study. It is challenging to obtain patient-specific vessel material properties (especially cap material properties as it involves smaller scales) in a clinical setting as it requires additional catheterization or special devices/techniques.^19,22 Collagen fiber in the fibrous cap is the most important component to withstand external force, and the effects of matrix metalloproteinases on collagen and other components were not considered in this article. It is not possible to take the patient’s living tissue out for material testing. (3) Our 3D reconstruction of coronary vessels was done by hanging all segmented slices on the centerline and keeping the slices perpendicular to the centerline. In OCT acquisition, the operators tried to get image slices as perpendicular to vessel centerline as possible. But errors are unavoidable and OCT may not show the cross-sectional area perpendicular to the centerline. This is a limitation of our model construction. (4) Coronary cycle bending secondary to heart beat was not included. (5) The FSI model did not consider the bifurcation due to the lack of flow rate information at the bifurcation locations.^7,48 (6) The FSI model only considered the tunica media and did not consider the adventitia. The adventitia may have a supporting role and an impact on the results at the thin vessel wall.

Conclusions

This preliminary case-control study showed that the ruptured plaque group had higher mean maximum stress and strain values based on in vivo OCT plaque rupture data. Due to our small study size, larger scale studies are needed to further validate our findings.

ARTICLE INFORMATION

Acknowledgments

The manuscript review and checking by Prof Zheyang Wu at Worcester Polytechnic Institute (Professor of Statistics) is happily acknowledged.

Sources of Funding

This research was supported, in part by, the Natural Science Foundation of China (grant numbers: 11972117, 11672001, 81827806, 62135002, 81722025, and 82072031); and Key R&D Project of Heilongjiang Province (grant number: 2022ZX06C07).

Disclosures

None.