CLINICAL RESEARCH: CORONARY ARTERY DISEASE
Longitudinal Structural Determinants of Atherosclerotic Plaque Vulnerability
A Computational Analysis of Stress Distribution Using Vessel Models and Three-Dimensional Intravascular Ultrasound Imaging
Koji Imoto, MD*,
Takafumi Hiro, MD, PhD*,*,
Takashi Fujii, MD, PhD*,
Akihiro Murashige, MD, PhD*,
Yusaku Fukumoto, MD*,
Genta Hashimoto, MD*,
Takayuki Okamura, MD, PhD*,
Jutaro Yamada, MD, PhD*,
Koji Mori, PhD and
Masunori Matsuzaki, MD, PhD, FACC*
* Department of Molecular Cardiovascular Biology, Yamaguchi University Graduate School of Medicine, Yamaguchi, Ube, Japan
Department of Applied Medical Engineering Science, Yamaguchi University Graduate School of Medicine, Yamaguchi, Ube, Japan
Manuscript received February 6, 2005;
revised manuscript received June 10, 2005,
accepted June 14, 2005.
* Reprint requests and correspondence: Dr. Takafumi Hiro, Department of Molecular Cardiovascular Biology, Yamaguchi University Graduate School of Medicine, 1-1-1 Minami Kogushi, Ube, Yamaguchi, 755-8505, Japan. (Email: thiro{at}yamaguchi-u.ac.jp).
This study was presented in part at the 77th scientific sessions of the American Heart Association, New Orleans, Louisiana, 2004.
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Abstract
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OBJECTIVES: This study theoretically examined the longitudinal structural determinants of plaque vulnerability using a color-coded stress mapping technique for several hypothetical vessel models as well as three-dimensional intravascular ultrasound (IVUS) images with use of a finite element analysis.
BACKGROUND: It has been shown that an excessive concentration of stress is related to atherosclerotic plaque rupture. However, the local determinants of in-plaque longitudinal stress distribution along the coronary arterial wall remain unclear.
METHODS: Using a finite element analysis, we performed a color mapping of equivalent stress distribution within plaques for three-dimensional vessel models as well as longitudinal IVUS plaque images (n = 15). Then, the effects of plaque size, shape, expansive remodeling, calcification, and lipid core on the equivalent stress distribution were examined.
RESULTS: The color mapping of vessel models revealed a concentration of equivalent stress at the top of the hills and the shoulders of homogeneous fibrous plaques. Expansive remodeling and the lipid core augmented the surface equivalent stress, whereas luminal stenosis and superficial calcification attenuated the equivalent stress. The location of excessive stress concentration was modified by the distribution of the lipid core and calcification. The thickness of the fibrous cap was inversely related to the equivalent stress within the fibrous cap. However, the color mapping of IVUS plaque images showed that the equivalent stress value at the fibrous cap varied with changes in plaque shape and superficial calcification, even when the thickness of the fibrous cap remained constant.
CONCLUSIONS: A distribution analysis of longitudinal stress revealed specific effects of plaque shape, size, and remodeling, as well as effects of the interior distribution of tissue components, on the concentration of stress at the plaque surface. Moreover, fibrous caps of the same thickness did not consistently represent the same vulnerability to rupture.
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Abbreviations and Acronyms
| | E = Young moduli | | G = shear modulus | | IVUS = intravascular ultrasound | | P = Poisson ratios |
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Plaque rupture is a major cause of acute coronary syndrome (1,2). It has been shown that plaque rupture frequently occurs in a noncalcified eccentric atherosclerotic plaque with nonsevere stenosis (3–8), expansive remodeling (9–12), a thin fibrous cap (4,13–17), a large lipid core (4,13–16,18–21), and macrophage infiltration (17,22). Therefore, it is thought that a particular cluster of plaque, referred to as vulnerable plaques, is likely to exist, and the development of a modality for detecting this potentially vulnerable portion in the coronary arterial wall is greatly needed in the clinical setting.
In the process of plaque rupture, an excessive concentration of stress at a certain portion of the plaque surface is considered an important factor (23). An in vitro study reported by Loree et al. (13) showed that thinning of the fibrous cap over a subintimal lipid pool dramatically increased peak circumferential stress in the cross section, especially at the shoulder region of eccentric plaques. However, the local determinants of the distribution of in-plaque longitudinal stress along the coronary arterial wall remain unclear. Therefore, the purpose of this study was to clarify the determinants of the distribution of longitudinal stress within plaques, using a color mapping technique based on computational structural analysis. This color mapping was derived from several hypothetical vessel models as well as from three-dimensional intravascular ultrasound (IVUS) images. The structural computation was performed by a finite element analysis using established material parameters for vessel tissue components (13,19,23,24).
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Methods
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Design of vessel models.
Initially, various idealized vessel models were designed to examine the effects of plaque morphology and tissue components on longitudinal stress distribution inside the plaque. As shown in Figure 1, a cylindrical vessel model was used, in which an atherosclerotic plaque was formed by the revolution of the same longitudinal sectional structure, thereby avoiding the influence of cross-sectional geometrical factors. This cylindrical model had an inner radius of 1.7 mm and a vessel wall thickness of 0.5 mm at the reference site. In the computational simulation, various plaque morphologies were hypothesized with various stenosis severities and types of vessel remodeling. It was assumed that the plaque components consisted of collagen fibers, calcifications, homogenous lipid tissue, and smooth muscle cells. The blood pressure was considered to be uniform along the vessel walls. The effect of blood flow was neglected in this study. There were no structural limitations in terms of the degree of outward expansion.
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Figure 1 Three-dimensional model. In this vessel model, vessel diameter may vary when a remodeling model is considered.
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As in previous established studies (13,23), all of the components of the atherosclerotic plaques were considered to be orthotropic materials with linear elastic properties. In this study, arteries and fibers provided similar material properties in the circumferential ( ) direction, as well as in the axial (z) direction, which differed from those in the radial (r) direction. Each parameter for the material properties defined in this study is shown in Table 1. In Table 1, Er and E are the Young moduli in the radial and circumferential directions, respectively. Gr is the shear modulus in the r plane, where Gij is the ratio of the shear stress to the shear strain in the ij plane. Pr and Pz are the Poisson ratios in the r and z planes, respectively. All of these values have been accepted as the representative values of the material properties of atherosclerotic lesions (13,23). It was assumed that lipids and calcifications were nearly incompressible because of their isotropic properties (23). The Young modulus of lipids was estimated to be 1/100th of the circumferential modulus of a normal artery. The Young modulus of calcified plaques was estimated as 10 times that of the plaque E (13).
Structural analysis.
The computational structural analysis was performed with a finite element model using a commercially available application (ANSYS 6.0 software, ANSYS Inc., Pittsburgh, Pennsylvania). A complex structure of a vessel model was first divided into smaller subunits designated as elements. The total number of the subunits was approximately 10,000, with a spatial resolution of approximately 100 (10 µm x 10 µm) µm2. Then, the equivalent stress for each element was calculated. The equivalent stress represented all types of stress for a certain area analyzed, which was calculated from three principal stresses. The structure was automatically meshed with eight-noded quadrilateral plane-strain elements. Each mesh was modified by using an adaptive remeshing algorithm, which was installed in the program. An internal luminal static pressure of 13 kPa (100 mm Hg) was applied along the luminal wall, representing the mean physiological blood pressure in the coronary arteries. Finally, contour plots of equivalent stress were shown on a post-graphics terminal. These contour plots provided two types of colorized mapping, with color codes superimposed on the original structure. One type of mapping was absolute mapping, in which each color code represented a certain range of the absolute value of the equivalent stress; the other type of mapping was relative mapping, in which the color coding was performed by equal division of the range of stress between the maximum and minimum values. According to the computer algorithm, the resulted deformation, such as indentation at the soft part or outward bulging of the normal wall without plaques, was also illustrated.
This study first analyzed the longitudinal stress distribution within plaques for several vessel models with varying structural characteristics of plaque, such as plaque size, plaque shape, stenosis severity, remodeling type, lipid core size, fibrous cap thickness, location and degree of calcification, and so on.
IVUS study.
The present study also examined the longitudinal stress distribution in plaques, the structure of which was obtained from the three-dimensional IVUS images. Fifteen human ruptured coronary lesions selected from patients diagnosed with acute coronary syndrome were imaged by IVUS (Atlantis SR pro, 2.8-F, 40-MHz, Boston Scientific Corp./SCIMED, Maple Grove, Minnesota). The transducer was withdrawn automatically using a motorized pullback device (pullback speed, 0.5 mm/s). The IVUS images were all recorded on S-VHS videotape for off-line analysis. The images were then digitized and analyzed with commercially available software for longitudinal reconstructive IVUS image analysis (Netra IVUS, ScImage Inc., Los Altos, California).
The rupture was defined by an apparent morphology in IVUS images along with comparable clinical history, electrocardiograms, and echocardiograms. No definitive thrombus was detected around the plaque both in IVUS and in angiography. Ruptured plaques with a distinct cavity as well as a significant residual fibrous flap were selected to predict surface morphology before rupture by extrapolating the line of lumen-intima interface.
It was assumed that the ulceration cavity detected by IVUS used to be a lipid core, and that a fibrous cap of a certain thickness used to cover the lipid core. In this in vivo analysis, it was also presumed that the arteries and the plaque components had orthotropic linearly elastic material properties, and that the plaques consisted of homogeneous fibrous tissue, with the exception of the ulcerous cavities and calcifications. However, the original thickness of the fibrous cap of ruptured plaques was unknown. Therefore, in this study, fibrous caps with various thicknesses were considered for the same plaque. Previous in vitro study (19) of human atherosclerotic materials has shown that fibrous caps usually fracture when the static stress exceeds 300 kPa. Therefore, the critical value for fibrous cap thickness, under which the stress on the fibrous cap would exceed 300 kPa, was also calculated for each plaque. This critical thickness was obtained with the abovementioned computer simulation of finite element models. When the critical fibrous cap is thin, it means that the plaque therefore seemed to be less vulnerable. The data were then used to conduct a computational stress analysis using the finite element model for the purpose of color mapping the longitudinal stress distribution, which was superimposed onto the original IVUS images.
This study was approved by the Institutional Review Board of the Hospital of Yamaguchi University School of Medicine. All patients provided signed informed consent to participate in the study before IVUS was performed.
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Results
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Study of vessel models.
This study showed the longitudinal stress distribution within plaques using a color-coded representation. Figure 2A illustrates the longitudinal distribution of equivalent stress within a hill-like homogeneous plaque model by use of relative color mapping. The concentration of equivalent stress could be observed at the top of the plaque hills, as well as at its shoulders. When there was a distortion of plaque shape, the stress was concentrated not only at the summits and shoulders, but also at dips in the irregular surfaces of plaque hills. There was a negative relationship between equivalent stress and luminal stenosis (Fig. 2B). When there was a remodeling of the vascular diameter at a constant maximum plaque thickness, the equivalent stress at the plaque surface of arteries with expansive remodeling was greater than that of arteries with constrictive remodeling (Fig. 2C).
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Figure 2 Relationship between stress distribution and plaque shape, luminal stenosis, or vessel remodeling. (A1, A2) Color mapping of longitudinal stress distribution within a homogeneous hill-like fibrous plaque model and a complex-shaped model. Relative mapping (A2) was performed in the automatically determined window between the maximum and minimum value of stress. The arrows designate the sites of stress concentration. (B1, B2) Relationship between luminal stenosis and stress distribution. Absolute mapping (B2) represents the distribution of the absolute value of equivalent stress. There was a negative relationship between the equivalent stress and luminal stenosis. (C1, C2) Relationship between vessel remodeling and stress distribution. The equivalent stress at the plaque surface of arteries with expansive remodeling was greater than that of arteries with constrictive remodeling, when the plaque thickness remained constant.
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When there was a lipid core, the stress was particularly concentrated at a localized surface area just above the lipid core (Fig. 3). The size of the lipid core had no influence on the surface stress value, given that the thickness of the fibrous cap remained constant. However, the thickness of the fibrous cap exerted a great impact on the surface equivalent stress of the plaque, namely, the thinner the fibrous cap, the greater the surface equivalent stress, given that the size of the lipid core remained constant (Fig. 4). In this idealized model, the peak equivalent stress reached beyond the empirical critical level leading to plaque rupture, when the fibrous cap was thinner than 80 µm. Superficial calcifications led to a decrease in surface stress, whereas calcification at the bottom of the plaque exerted no influence on the surface equivalent stress value. As in Figure 5, a superficial calcification adjacent to the lipid core attenuated the peak stress value at the plaque surface just above the lipid core. There was an inverse relationship between the surface equivalent stress and the thickness of the fibrous cap. The stress value increased dramatically when the fibrous cap was thinner than 80 µm. However, when there was a surface calcification near the lipid core, the surface equivalent stress was smaller with the same fibrous cap thickness, such that the inverse relationship shifted leftward and downward (Fig. 6).
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Figure 3 Effect of lipid core on stress distribution. The arrow indicates the point of stress concentration at a localized surface area just above the lipid core (A2). The size of the lipid core did not influence the value of the surface stress (B2), provided the fibrous cap thickness remained constant. (A1, B1) Plaque models used. (A2, B2) Mapping of stress distribution of the corresponded model.
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Figure 4 Effect of fibrous cap thickness (a, 90 µm; b, 80 µm; c, 40 µm) on stress distribution. When the fibrous cap was thinner than 80 µm, the stress was markedly elevated (arrow). (Aa, Ab, Ac) Plaque models used. (Ba, Bb, Bc) Mapping of stress distribution of the corresponded model.
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Figure 5 The effect of surface calcifications on the distribution of stress in the surrounding tissue. The size and the place of the lipid core remained constant. A superficial calcification adjacent to the lipid core attenuated the peak stress value at the plaque surface just above the lipid core (arrow). (Aa, Ab) Plaque models used. (Ba, Bb) Mapping of stress distribution of the corresponded model.
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Figure 6 Effect of superficial calcifications on the relationship between the fibrous cap thickness and the peak equivalent stress at the plaque surface. The equivalent stress increased dramatically when the fibrous cap thickness became <80 µm. This increase shifted leftward and downward when there was a superficial calcification close to the area of interest.
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IVUS study.
Figure 7 shows representative examples of the color mapping of longitudinal stress distribution using longitudinal IVUS images. In case 1, the critical thickness of the fibrous cap leading to rupture was 50 µm, whereas this value was 10 µm in case 2. In case 2, there was a superficial calcification close to the rupture point. Table 2 shows the profile of the 15 ruptured plaques analyzed. The IVUS study showed that the critical thickness of fibrous caps leading to rupture varied between <10 µm and 200 µm.
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Figure 7 Representative examples of the three-dimensional IVUS images and the color mappings of longitudinal stress distribution. The arrows show rupture points. In case 1, the critical thickness of the fibrous cap in terms of rupture was 50 µm (A). However, the thickness in case 2 had to be reduced to <10 µm to reach the critical point in terms of plaque rupture (B). Thus, case 2 seemed to represent a less vulnerable plaque than case 1, although the fibrous cap thickness was the same. (A) Case 1; (B) case 2.
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Discussion
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This study was the first showing the longitudinal structural determinants of plaque vulnerability by use of a simplified computational analysis of stress distribution within atherosclerotic plaques using vessel models and three-dimensional intravascular ultrasound imaging. Furthermore, this study also showed that the critical thickness of fibrous caps leading to rupture varied substantially with differences in plaque structure, especially with differences in the degree of calcification.
Plaque size, shape, vessel remodeling, and plaque stress.
Previous cross-sectional structural analyses of plaque stress distribution have shown that the shoulder regions of eccentric plaques are likely to exhibit stress concentration, leading to a susceptibility to rupture (13). However, the results of this study indicated that longitudinal plaque shape is also important for predicting the location of stress concentration within plaques.
Our study showed that increasing either plaque volume or the severity of stenosis decreased the degree of stress concentration. These findings were compatible with those of a previous cross-sectional structural analysis of plaques (13). According to the LaPlace law, the tensile stress on the wall of a luminal structure is correlated with luminal pressure and diameter, and is inversely related to the thickness of the wall. Increasing plaque volume thus increases the thickness of a wall and decreases the luminal diameter (unless there is vessel remodeling), thereby leading to a decrease in the surface stress of the plaque. The present results may therefore account for previous serial angiographic analyses showing that the culprit lesion before the acute event frequently had <50% diameter stenosis (3–8). Based on recent IVUS studies, it is likely that plaque regression or less progression that may not lead to stress attenuation is associated with a decrease in the risk of future cardiac events (9–11). Therefore, this paradoxical consequence could be attributed to simultaneous changes in plaque composition and fibrous cap thickness.
In this study, when the plaque thickness remained constant, expansive remodeling led to a greater concentration of stress than did constrictive remodeling. Expansive remodeling is frequently observed as a compensatory process for an increase in plaque thickness. In such a case, stress attenuation by the increase in plaque thickness is canceled by expansion in vessel diameter, which consequently maintains or enhances stress value on the plaque surface. Therefore, the present results may be consistent with the findings of previous reports (9–12) showing that unstable plaques are usually associated with expansive remodeling.
Subintimal plaque structure and stress.
The significant impact of decreases in fibrous cap thickness on stress concentration within plaques has been widely shown in various studies using postmortem pathological analyses and intravascular imaging modalities (4,13–17). Our findings showed that the stress on a fibrous cap was dramatically increased when its thickness was <80 µm. This value of 80 µm actually depends on the vessel diameter. The range of cap thickness of 60 to 100 µm corresponds to vessel diameters of 2.5 to 4mm. Previous empirical cross-sectional studies have shown that a fibrous cap thickness of less than 65 to 150 µm is critical in terms of the risk of plaque rupture (15,16,25–27). Therefore, the critical thickness of fibrous caps in terms of plaque rupture might be similar in both the cross-sectional and the longitudinal direction. However, the present study using longitudinal IVUS showed that the critical thickness of a fibrous cap leading to rupture varies greatly because of differences in the distribution of surrounding calcifications, even with the same vessel diameter. The involvement of calcification, and variabilities in plaque thickness and shape, may account for inconsistencies regarding the critical thickness reported in several previous studies, which has been shown to vary between 65 and 150 µm (15,16,25–27). The effect of vessel size would also account for a range of the critical thickness varying from 60 to 100 µm as noted above. Furthermore, our results suggest that the measurement of fibrous cap thickness alone is inadequate for identifying plaques vulnerable to rupture.
The presence of a lipid core was also an important factor in stress concentration, according to our study of the longitudinal vessel axis. However, increasing the size of a lipid core did not affect the surface stress of plaques, provided the thickness of the fibrous cap remained constant. These studies, as well as our own, may support the findings of previous reports showing that plaque rupture can be observed in the region of a fibrous cap, even in the presence of a very small lipid core (18,25,28).
Calcification is commonly found in atherosclerosis, but the role of calcification in plaque rupture is still unknown. Some studies indicate beneficial effects in stabilizing plaque (19,23,29), whereas some suggest its worsening effects to plaque vulnerability (30–34). In our study, calcification significantly affected the stress on fibrous caps that were either adjacent to or at a slight distance from calcifications. The exact mechanisms of the attenuation of stress by surface calcification are unclear.
Clinical implications.
Although a variety of factors may participate in the process of plaque rupture, including hemodynamic shear stress (20), turbulent pressure fluctuations (35), transient compression (36), sudden increase in intraluminal pressure (37), rupture of the vaso vasorum (38), material fatigue (4,18,39), and cellular inflammatory reactions (3,4,22,40), this study suggests that assessment of stress concentration within a plaque along the longitudinal axis of a vessel is also important for identifying vulnerable plaques. Therefore, this approach may help identify vulnerable plaques or even help predict the point of future rupture.
Study limitations.
To simplify the present finite element analysis, the materials were assumed to be isotropic, incompressible, and uniform solids. By assuming that plaques, lipids, calcium, and normal arterial walls could each be characterized by a single set of structural parameters, spatial and interspecimen variations within a particular component were not considered here. However, the assumptions used in this study have been widely accepted as allowable for the assessment of the biomechanical properties of atherosclerotic lesions (13,23). The model used in this study was a linear one, although almost all of the biomaterials have nonlinear properties. Actually, there are only limited data available with regard to the nonlinear biomechanical behavior of atherosclerotic lesions. Furthermore, in the present study, we examined factors affecting relative stress values and not exact absolute stress magnitudes.
In this study, we used an axisymmetric model, although clinical plaques are not always axisymmetric in geometry. The purpose of this study was limited to assess the longitudinal determinants of plaque vulnerability, but not cross-sectional determinants, which were already clarified in the numerous previous studies. Therefore, the axisymmetric model was used to exclude the cross-sectional determinants of stress distribution within plaques.
It was also assumed in this study that there were no shear stresses, torques, time-varying forces, or flow-related forces; only static blood pressure was considered to be acting on the lesion in the models. It has been documented that the effect of fluid shear stress is insignificant when compared with the effect of tensile wall stresses (19) as a direct component in plaque fracture dynamics. The estimation of stresses induced by static pressure load alone has already shown its usefulness in identifying stress concentration in human lesions (23), because the location of stress concentration does not significantly differ between the single static pressure model and the complex dynamic pressure model.
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Footnotes
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This study was partly supported by a grant-in-aid for scientific research of the Ministry of Education, Japan (grant No. (C)(2)14570666), Health and Labour Sciences Research Grants: Comprehensive Research on Cardiovascular Diseases from Ministry of Health, Labour, and Welfare of Japan, and Knowledge Cluster Initiative of the Ministry of Education, Japan. The first two authors contributed equally to this work.
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A. Tanaka, K. Shimada, M. Namba, T. Sakamoto, Y. Nakamura, Y. Nishida, J. Yoshikawa, and T. Akasaka
Relationship between longitudinal morphology of ruptured plaques and TIMI flow grade in acute coronary syndrome: a three-dimensional intravascular ultrasound imaging study
Eur. Heart J.,
January 1, 2008;
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[Abstract]
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P. H. Stone, A. U. Coskun, S. Kinlay, J. J. Popma, M. Sonka, A. Wahle, Y. Yeghiazarians, C. Maynard, R. E. Kuntz, and C. L. Feldman
Regions of low endothelial shear stress are the sites where coronary plaque progresses and vascular remodelling occurs in humans: an in vivo serial study
Eur. Heart J.,
March 8, 2007;
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[Abstract]
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Y. Vengrenyuk, S. Carlier, S. Xanthos, L. Cardoso, P. Ganatos, R. Virmani, S. Einav, L. Gilchrist, and S. Weinbaum
A hypothesis for vulnerable plaque rupture due to stress-induced debonding around cellular microcalcifications in thin fibrous caps
PNAS,
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14678 - 14683.
[Abstract]
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