Computational Stress Analysis of Atherosclerotic Plaques in ApoE Knockout Mice
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- Vengrenyuk, Y., Kaplan, T.J., Cardoso, L. et al. Ann Biomed Eng (2010) 38: 738. doi:10.1007/s10439-009-9897-5
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The aortic sinus lesions of apolipoprotein E knockout (ApoE KO) mice seldom show any signs of fibrous cap disruption, whereas cap ruptures have been recently reported in the proximal part of their brachiocephalic arteries (BCA). We use histology based finite element analysis to evaluate peak circumferential stresses in aortic and BCA lesions from six 42–56 week-old fat-fed ApoE KO mice. This analysis is able to both explain the greater stability of aortic lesions in mice and provide new insight into the BCA lesion as a model for the stability of human lesions with and without microcalcifications in their fibrous caps. The predicted average peak stress in fibrous caps of aortic lesions of 205.8 kPa is significantly lower than the average value of maximum stresses of 568.8 kPa in BCA caps. The aortic plaque stresses only slightly depend on the cap thickness, while BCA lesions demonstrate an exponential growth of peak cap stresses with decreasing cap thickness similar to human vulnerable plaques. Murine BCA ruptured lesions with mean cap thickness of 2 μm show stresses ≈1400 kPa, three times higher than human ruptured plaques with a mean cap thickness of 23 μm without microcalcifications in the cap, but nearly identical to the peak stress around an elongated microcalcification with aspect ratio 2 in a human thin cap ≈50 μm thick. We predict biomechanical stress patterns in mouse BCA close to human vulnerable plaques without microcalcification in the cap, while aortic lesions show stress tendency similar to stable lesions in human.
KeywordsAtherosclerosisPlaque ruptureApolipoprotein EMouseStressCalcification
Cardiovascular disease remains the principal killer in the western world despite major advances in treatment of its patients. It is generally accepted that sudden rupture of vulnerable plaque followed by thrombus formation underlies most cases of myocardial infarction and is responsible for more than a half of 500,000 coronary heart disease deaths every year.7,36 Although histopathological analyses of postmortem specimens have provided important data on histological features of ruptured human plaques, there is an urgent need for good representative animal models of plaque rupture. Such experimental models would allow investigators to examine the events leading to plaque rupture and the rupture itself prospectively.
Over the last decade and a half, genetically engineered mice have been widely used to study the pathogenesis and potential treatment of atherosclerotic lesions, as well as genetic, hormonal and environmental influences on development of atherosclerosis.1,3,8 The development of the apolipoprotein E knockout (KO) and LDL receptor-deficient mouse models in inbred mouse strains greatly accelerated the pace of our knowledge about molecules and cellular phenotypes that affect lesion growth.11,24,38 The majority of these studies have focused on the development of the disease in the aorta which is the largest and the most accessible experimental vessel. Although fat-fed ApoE deficient mice have been demonstrated to develop atherosclerotic lesions very similar to those in humans,22,26 these murine models have long been regarded as poor models to study plaque rupture because the aortic sinus lesions seldom show any signs of fibrous cap disruption. Several recent studies reported potentially unstable atherosclerotic lesions in older ApoE KO mice in another anatomic site, the proximal part of the brachiocephalic artery (BCA)5,18,19,28,37 where visible defects in the fibrous caps are observed with thrombi extending from the lumen to the lipid core. These BCA lesions develop rapidly with advanced plaques present after as few as 5 weeks of lipid feeding. Williams et al.37 compared morphological characteristics of ruptured and intact BCA lesions in a large number of ApoE KO mice using histological analysis. Fifty-one of the 98 mice analyzed were found to have an acutely ruptured atherosclerotic plaque in the BCA.
A fundamental paradox in the murine BCA lesions is that the mean ruptured cap thickness 2.0 ± 0.3 μm,37 is an order of magnitude less than the mean thickness, 23 ± 19 μm, of caps in human ruptured coronary lesions4,36 although the average systolic and diastolic pressures 125 and 90 mmHg are almost the same as in human coronary arteries. This large difference in rupture thickness will be quantitatively explained herein using the microcalcification hypothesis proposed in Vengrenyuk et al.33,34 in which rupture is attributed to cavitation induced debonding at the interface of cellular calcifications in the fibrous cap proper of the human lesion.
The unusual stability of aortic lesions compared to the BCA lesions in ApoE knockout mice is an unexplained paradox in murine lesions. Jackson et al.16 have suggested that blood flow conditions or mechanical properties of the vessel wall protect the aortic sinus from rupture. One of these special conditions can be mean wall shear stress (WSS). A recent study by Greve et al.12 showed that mean WSS along the infrarenal aorta was significantly greater in mice and rats compared with humans (87.6, 70.5, and 4.8 dyn/cm2). Although the study doesn’t provide any data on mean WSS in mouse BCA, it would also in all likelihood be much higher than in humans and, therefore, not explain the difference in stability of the aorta and BCA lesions. Another possibility, which is explored herein for the first time, is the striking difference in lesion geometry.
Numerous computational stress analyses have been conducted to predict plaque rupture in human vulnerable plaque.6,9,13,14,21,27,30,31,33 The majority of these biomechanical models for vulnerable plaque stability are based on the premise that there is a critical tissue stress or rupture threshold for the integrity of the cap. This rupture threshold has been estimated to have an average value of 545 kPa and a minimum value of 300 kPa6 depending on the local elastin and collagen composition of the tissue. The peak circumferential stress (PCS) in the cap is considered to be the most important measure of this stress and is often used as a predictor of plaque rupture location. To our knowledge, there have been no previous attempts to perform equivalent numerical stress analysis for murine atherosclerotic lesions to estimate biomechanical stresses within murine lesions due to blood pressure.
To try and address these important paradoxes, we have applied two-dimensional (2D) histology based FEA to estimate stresses in intact advanced aortic and BCA lesions from 42 to 56 week-old high fat-fed ApoE KO mice. It is known that the size of the lipid core and fibrous cap thickness have the most significant effect on the stress level within a human atherosclerotic lesion.9,23,30,31,33 Fibrous cap thinning due to enzymatic degradation20 can lead in humans to increased stresses and conversion of a stable plaque to a rupture prone vulnerable lesion. To explore this possibility in mouse models we have created a series of idealized lesion geometries with cap thickness decreasing from 25 to 2 μm to investigate how PCS in the fibrous cap increases with decreasing cap thickness. In addition, the “cap thinning simulation” allowed us to predict the stress level within an idealized BCA lesion with fibrous cap thickness of 2 μm, the mean cap thickness in ruptured lesions,37 and compare it to the stresses in unstable human caps with and without microcalcifications.
We studied six 42–56 week-old female and male ApoE KO mice maintained on a high fat diet. They were housed in a specific pathogen-free environment at Mount Sinai School of Medicine and used in accordance with protocols approved by the Institutional Animal Care and Utilization Committee. Animals were sacrificed with CO2, then exsanguinated by intracardial perfusion with 40 mL of PBS/EDTA (2 mM), followed by 150–200 mL of freshly prepared 4% (para)formaldehyde in PBS. Perfusion was implemented with a peristaltic pump set to a constant flow rate, and allowed to continue for at least 30 min for maximal preservation of the vessels’ natural configuration. In addition, calcification in aortic arches and BCA (innominate) arteries of three older (58–60 week) mice was analyzed using calcium specific stain Alizarin Red S.34
Aortic arches and brachiocephalic arteries were embedded in optimum cutting temperature compound (OCT). Frozen sections of 6 μm thickness were collected at 30-μm intervals and stained with hematoxylin and eosin, Van Gieson, oil red O or Alizarin Red S. One cross-section containing the largest lipid core was selected for each lesion identified with histology staining.
Material properties used in the FE analysis
Isotropic material with E = 1 kPa and ν = 0.49
Isotropic material with E = 1000 kPa and ν = 0.27
Statement of Responsibility: “The authors had full access to the data and take responsibility for its integrity. All authors have read and agree to the manuscript as written”.
Plaque characteristics and cap stresses in aortic and BCA murine lesions
Cap thickness (μm)
Lipid content (%)
Plaque cross-sectional area (mm2)
Max cap stress (kPa)
Cap thickness (μm)
Lipid content (%)
Plaque cross-sectional area (mm2)
Max cap stress (kPa)
Our numerical analysis revealed a significant difference in stress distribution within the aortic and BCA lesion. The right panel of Fig. 1c shows that the maximum circumferential stress of 795 kPa in the BCA lesion was located in the thinnest area of the fibrous cap marked by an asterisk in Fig. 1b, while aortic lesion stress reached its maximum of 512 kPa under the lipid core as shown in the left panel. The most surprising result of the model is that the PCS in the 12 μm thick fibrous cap of the aortic lesion reached only 160 kPa, far below the minimum threshold for human plaque rupture of 300 kPa. A human lesion with this level of stress in the cap would have had a cap of about 100–120 μm thickness and been considered stable.9,33 This non-intuitive result can be explained by the striking difference in geometry of the typical aortic and BCA lesion. The left panel in Fig. 1 shows that the aortic lesion, in contrast to the BCA lesion, protrudes into the lumen taking the shape of a blister. This shape was observed in all five aortic lesions in Table 2. When the vessel is pressurized the tensile stresses are transferred to the outer layers of the wall, whereas the fibrous cap and the necrotic core are in a state of compression.
In order to compare the magnitudes of murine and human plaque stresses, we used Figs. 6 and 7 from our previous paper33 to plot cap PCS in a human coronary lesion as a function of fibrous cap thickness in the same Fig. 3. The baseline thick-capped human atheroma lesion analyzed in Vengrenyuk et al.33 had three spherical microcalcifications, ≈20 μm diameter, located in close vicinity to each other in the fibrous cap. Curve 3 in Fig. 3 shows global PCS in the human cap if these three microcalcifications were absent. Curve 4 demonstrates how the maximum cap stress is increased due to the presence of a single spherical microcalcification located at the point of background PCS, and line 5 predicts the effect of an elongated microcalcification with aspect ratio λ = b/a = 2 on cap stress. The plot shows that line 2 representing cap PCS in murine BCA plaques is shifted up by 500–600 kPa with respect to the stresses in the human lesion without microcalcifications in the cap (line 3). The predicted mouse BCA stresses also exceed significantly the human cap stresses around the spherical microcalcification (line 4). However, comparison of lines 2 and 5 indicates that the peak stress in the murine BCA cap at rupture (2 μm) is nearly identical to the peak stress in a 50 μm human cap with an elongated cellular microcalcification with aspect ratio two.
The purpose of the next numerical simulation was to validate our hypothesis that macrocalcifications at the plaque shoulders have a stabilizing effect. We replaced the two large shoulder calcifications in Fig. 4a by fibrotic tissue and recalculated stresses under the same loading and boundary conditions. Maximum circumferential stress for the section without calcium was 267.5 kPa, 8% more than in the original model, suggesting that macrocalcifications increase stability.
The first finite element solutions for the tissue stress distribution have been obtained for the murine animal model of atherosclerosis using histology images of high fat diet-induced lesions. These model predictions are of particular significance since they provide important insight into a fundamental paradox: why do the thin fibrous caps of human lesions rupture, whereas the much thinner caps of ApoE KO mice seldom rupture in aortic lesions although these caps can be thinner than 10 μm and are subject to similar lumen pressures. One would intuitively think that the tensile stress should easily exceed 300 kPa for such a thin cap and it would be highly prone to rupture. The results obtained have led to a most surprising prediction, namely that the PCS in the murine aortic lesion can be significantly less than humans although its cap thickness can be as little as 2 μm, see curve 1 Fig. 3. Our calculations showed that the average stress in aortic lesions was only 205.8 kPa, below the threshold for human plaque rupture of 300 kPa. A human lesion with this level of stress in the cap would have had a cap of approximately 100–120 μm thickness and have been considered stable (curve 3 in Fig. 3). In other words, the model showed that an aortic mouse lesion with a very thin, 10–20 μm fibrous cap is characterized by the same level of circumferential stresses as a thick-cap human fibroatheroma which seldom ruptures. Thin BCA caps (2–5 μm) in this simulation demonstrated high stresses of 1000–1400 kPa, while maximum tensile stresses in thin aortic caps of this thickness were 3–4 times lower, hardly reaching 300 kPa.
The non-intuitive result for murine lesions arises from the observation that there is a distinctly different behavior for aortic and BCA lesions. The former deform in such a way as to reduce peak circumferential stress in the cap, whereas the latter deform like human lesions in a manner that increases PCS. This prediction could explain why ruptures are seldom seen in high fat-diet induced aortic mouse lesions, whereas there appear to be at least occasional ruptures in BCA lesions.19,28 This is due to a negative remodeling (decreased luminal area) that occurs when the lesions take the shape of blisters that protrude into the lumen. All of the aortic lesions that we have observed in the six mice in this study have had this geometry. In marked contrast, BCA lesions appear to have a flat geometry that is closer to that observed in human lesions. One can think of this as a positive remodeling that leads to instability.
The process of coronary artery enlargement in response to plaque growth which maintains the lumen area was first described by Glagov et al.10 Their histopathology study discovered that due to the compensatory enlargement of human atherosclerotic lesions lumen stenosis may be delayed until the lesion occupies 40 percent of the area above the internal elastic lamina. Despite the fact that positive remodeling avoids vessel stenosis, it can have dangerous consequences since it promotes plaque vulnerability. An in vivo study with intravascular ultrasound established a relationship between positive remodeling and plaque stability.29 In this study, positive remodeling was more frequent in unstable than in stable lesions, while negative remodeling, or vessel shrinkage, was more common in patients with stable clinical presentation. One of the explanations for the observed in vivo increase in plaque vulnerability at the sites of outward vessel wall remodeling is that coronary artery plaques have been shown to have higher lipid content and macrophage count, both markers of plaque vulnerability.32 The importance of considering arterial remodeling index in addition to fibrous cap thickness for evaluating biomechanical plaque vulnerability was demonstrated by a recent FEA of cap stresses as a function of remodeling index.23 Our computational predictions for stress distribution within an aortic lesion shown in Fig. 1c, left panel, can explain the higher stability of negatively remodeled lesions. The color map of lesion stresses shows that some parts of the cap may be even compressed in a lesion protruding inside the lumen.
The difference in size between human and mice arteries requires development of different quantitative criteria for vulnerable plaque rupture. For example, a thin-cap fibroatheroma with cap thickness <65 μm and large lipid core has been defined as a more specific precursor of plaque rupture in humans.4,35 Even though all fibrous caps in mice are thinner than this, it would be unreasonable to conclude on this basis that all mouse plaques can be considered as vulnerable thin-capped lesions.15 Our histology based FEA allows one to compare biomechanical stresses in human and mouse vulnerable lesions. The results shown in Fig. 3 predict that murine BCA ruptured lesions with mean cap thickness of 2 μm have stresses about 1400 kPa, three times higher than human ruptured plaques with a mean cap thickness of 23 μm without calcifications in the cap proper, but nearly identical to the local stress around an elongated microcalcification with aspect ratio two embedded in a 50 μm thick human cap. In addition, our “cap thinning” simulations further support previous observations5,18,19,28,37 that BCA lesions more closely mimic cap rupture in human vulnerable lesions. Curve 2 in Fig. 3 demonstrates an exponential growth of peak cap stresses with decreasing cap thickness as predicted for human plaques in several computational studies.9,31,33 In sharp contrast, aortic plaque stresses are shown in Fig. 3 to only slightly depend on cap thickness.
The question that still needs to be resolved for the murine BCA lesions is why there aren’t more frequent ruptures despite such high stresses in their fibrous caps. One possible explanation is that the WSS in mice is an order of magnitude greater than in human arteries.12 This elevated WSS may lead to compensatory changes in the density of the extracellular matrix and collagen content within mouse plaques that render them consequently more resistant to rupture.17 Another reason for the greater stability of murine lesions can be related to plaque calcification. Several recent computational studies of calcified human lesions demonstrated that coronary calcifications have a significant effect on plaque stability depending on their size, shape and localization. While large millimeter size calcifications frequently observed adjacent to or under the lipid core have been shown to have a stabilizing effect,13,30,33 cellular level microcalcifications, 10–20 μm diameter, in the fibrous cap proper have been predicted to increase plaque vulnerability dramatically by creating local stress concentrations around these rigid inclusions.33,34 Curves 3 and 4 in Fig. 3 show that the presence of spherical microcalcifications embedded in the fibrous cap of a human plaque can almost double cap PCS due to the mismatch of mechanical properties at the inclusion/tissue interface and this amplification can be substantially increased for elongated microcalcifications, curve 5. A striking observation is that a 50 μm cap with an aspect ratio of two in a human lesion can have the same peak stress as a cap in a murine BCA lesion whose cap is 25 times thinner.
Despite the fact that calcification in human lesions is a well-known occurrence, the tendency of plaques in ApoE KO mice to calcify has only recently been studied. Aging ApoE-deficient mice show progressively increased degrees of medial and intimal calcification in the aorta and BCA,2 with a marked elevation in total extractable calcium particularly in females aged for 60 weeks.25 Our computational results shown in Fig. 4 predicted that macrocalcifications in murine lesions, as observed for humans,13,30,33 are reinforcing and increase stability. At the same time we haven’t been able to identify microcalcifications in the fibrous caps of any of the lesions in this study, probably, because, unlike a human lesion, the murine cap is too thin to contain a 10–20 μm cellular level microcalcification. All the above factors combined can make the ApoE KO BCA lesion highly resistant to rupture despite their very thin caps and high level biomechanical stresses.
One of limitations of our present analysis of mouse lesions is the use of linear FEA. Although Cheng et al.6 used linear analysis to predict plaque rupture threshold as their main approach, they also ran an additional secondary analysis on all their samples using a large strain isotropic model instead of the linearly elastic transversely isotropic model. The results showed that the locations of the peak stress values using the isotropic model were virtually identical to those obtained using the transversely isotropic model. The predicted large strain model stresses were significantly lower; however, the peak stresses in the ruptured lesions were still significantly higher than peak stresses in control lesions. In addition, all lesion components in our study were approximated by linearly elastic material parameters taken from the literature. Although FEM can be created based on nonlinear material properties, there is little published data on the nonlinear mechanical behavior of atherosclerotic lesions in the physiological literature and none for mice. We also haven’t considered viscoelastic effects, since our stress analysis was performed for a static pressure load.
Another limitation of our study is that we used human material properties described in literature6,9 for our histology based FEM, because there are no reliable data on the structural properties of mouse arteries. It is possible, if not likely, that there are differences in mechanical properties between human and mice—since the wall shear stress is an order of magnitude higher in mice.12 Furthermore, there is a possibility that differences in plaque geometry are the result of mechanical property differences. Experiments need to be done to see whether the collagen structure of the fibrous caps in the aortic and BCA arteries differ and whether differences in collagen content are reflected in cap thickness and lesion geometry. However, the most striking result is that the fibrous caps in the mice are an order of magnitude thinner than humans and there are relatively few ruptures even for the BCA at equivalent lumen pressures. This strongly suggests that the caps themselves might have stronger material properties. Furthermore, there is no evidence of microcalcifications in the cap proper, as in human lesions, to induce cavitation induced debonding, a primary feature of human lesions as proposed in Vengrenyuk et al.34
In conclusion, our computational model predicts biomechanical stress patterns in mouse BCA that are close to human vulnerable plaques, while murine aortic lesions showed stress behavior similar to stable lesions. Our FEA predicts similar stress levels in ruptured BCA plaques and thin-cap human atheromas with an elongated microcalcification in the cap proper. The results suggest that the proximal BCA artery of the fat-fed ApoE KO mouse is a better site to study pathophysiology of plaque rupture although they are too thin to contain cellular microcalcifications in the cap proper. Despite the absence of these microcalcifications, the murine BCA lesions have stress levels that are quite similar to the PCS of the much thicker vulnerable caps of humans with such microcalcifications as shown in Vengrenyuk et al.33