Revised microcalcification hypothesis for fibrous cap rupture in human coronary arteries

The initial formulation of the µCalc plaque rupture hypothesis (1) was based on an idealized model for a single spherical inclusion and the observation of three cellular-level µCalcs in the fibrous cap proper of a single fibroatheroma at 6.7-µm resolution HR-µCT. It is not unexpected that, with the current observation of nearly 35,000 µCalcs at significantly higher resolution and nondecalcified histology to see even smaller µCalcs, this original formulation requires major modification. Vengrenyuk et al. (1) suggested that the µCalcs were a relatively rare occurrence, that µCalcs derived from apoptotic macrophages trapped in the cap while moving to the necrotic core, and that rupture was caused by interfacial debonding at the µCalc interface. With evolved understanding of the biology of microcalcification and improved imaging resolution, our recent studies (10, 17) can be viewed as a critical transition, where each of these hypotheses is initially questioned.

The observation of nearly 35,000 µCalcs > 5 µm in 22 of 66 human fibrous caps provides indisputable evidence that µCalcs of these dimensions are, indeed, numerous and that the 81 µCalcs observed in ref. 10 in 15% of the caps at 6.7-µm resolution were a gross underestimation. Table 1 shows that the size of 80% of the µCalcs was between 5 and 15 µm, and thus, they were not visible at 6.7-µm resolution. Also, many µCalcs believed to be a single particle at 6.7-µm resolution were actually clusters of smaller µCalcs (Fig. S3). Similarly, particles between 30 and 50 µm seen at 6.7-µm resolution were clusters of 15- to 30-µm particles, causing a large percentage difference in the particle size distribution at 2.1- and 6.7-µm resolutions for the larger µCalcs. Not a single µCalc > 50 µm was seen in the fibrous cap proper, the current threshold for in vivo imaging. Additionally, histology images reveal the presence of µCalcs between 0.5 and 5.0 µm in the remaining 44 fibrous caps (Fig. S3C), confirming recent reports of µCalcs < 1 µm in fibrous caps in the works by New and Aikawa (22) and Roijers et al. (23).

With so many µCalcs, why are there not more ruptures? FEA and our criterion for identifying which of the thousands of µCalcs are potentially dangerous provide the key insights into this critical question. The data in Figs. 2 and 3 and Table 3 are crucial to understanding why these caps did not rupture. First, the µCalcs have to be in a local region where the background stress is already elevated, typically a region where the cap is thin. The minimum thickness of specimen 22 was only 35 µm, but no µCalcs were observed in this region where the PCS was 313 kPa, very close to the 300-kPa minimum threshold for rupture (12). Contrary to widely held beliefs, cap thickness by itself is not the only criterion. Even for a thin cap, a single µCalc at the right location would greatly increase rupture risk. Second, clusters of particles in close proximity, h/D < 0.4, produce a stress concentration factor that is much greater than a single µCalc provided that the particles are aligned with the tensile axis. This concept is supported by the study by Gent and Park (18) that shows that a tiny void has to preexist in the region of the stress concentration. This possibility is not likely for a single particle, because the region of increased stress is confined to small regions in the immediate vicinity of the tensile poles. In marked contrast, the entire region between two µCalcs in close proximity will be exposed to this high stress (Fig. 2B). Third, we observed that there were only three particle pairs with h/D ≤ 0.4 among all 22 caps with µCalcs > 5 µm that had not ruptured. In all three specimens 5, 7, and 17 in Table 3, FEA showed that the 300-kPa threshold for rupture had not been exceeded. In a dataset of 35,000 µCalcs, this finding is remarkable. We cannot confirm it in the present study, but a plausible conclusion is that the failure to find other particle pairs with h/D ≤ 0.4 meant that these caps had ruptured.

Our nondecalcified histology of human fibrous caps and EM of µCalcs in the cap of an apolipoprotein E knockout (APO-E^−/−) mouse in Fig. 4 strongly suggest that µCalcs are derived from matrix vesicles, which could be formed from smooth muscle cell or macrophage membrane blebs (24). These membrane-bound bodies, which are initially 100–300 nm, can merge to form larger vesicles or μCalcs (13–15). Bobryshev et al. (13) estimated that ∼1% of matrix vesicles calcify in their initial state. Fig. 4 suggests that these small vesicles first fuse to form larger vesicular bodies, typically 1- to 2-µm diameter, that then calcify and agglomerate. Calcification appears to start at the membrane and then may proceed inward. Even at 2.1-µm resolution HR-µCT, it is difficult to image the shape of small µCalcs. However, volume and sphericity measurements in Fig. S2 indicate that 65% of the µCalcs have an aspect ratio > 2.

Although µCalcs < 5 µm cannot be seen at 2.1-µm resolution HR-µCT, they are clearly visible in nondecalcified histology using either Alizarin Red S or von Kossa stain. These very small µCalcs do not initiate plaque rupture as explained in detail in ref. 17. Originally, Vengrenyuk et al. (1) proposed that the triggering event for rupture was an interfacial debonding that started at the poles of the inclusion. The theory for hyperelastic materials developed in ref. 18 and applied in ref. 17 for spherical µCalcs shows that, for debonding to occur, the strain energy stored in the tissue at the poles of a µCalc in tension must exceed the bonding energy at the surface of the particle. This stored energy increases with the size of the particle and for representative adhesion strengths debonding theory (18), predicts that the particle must exceed 65-µm diameter. No µCalcs of this dimension have been observed among 35,000 µCalcs in this study. A more plausible possibility is cavitation, the explosive growth of a small void when the tissue stress exceeds ∼5/6E, where E is the Young’s modulus of the material. Because the measured value of E is typically 500 kPa, this threshold for cavitation falls precisely in the range 300–545 kPa that has been widely used for cap rupture. Initial voids seldom exceed about 1/10th of the particle radius (18). Thus, a 5-µm inclusion would have an initial void < 500 nm. The calculations in ref. 17 show that the surface energy to expand such a tiny void would far exceed 5E/6 and that cavitation would not occur.

Unfortunately, the distribution of the µCalcs is heterogeneous, and thus, one cannot apply homogenization theory, such as in the work by Wenk et al. (25), for predicting local tissue stress. However, there is a single parameter, h/D, that seems to predict the local amplification factor for tissue stress when neighboring µCalcs are aligned along their tensile axis, the worst case scenario. This parameter enables one to quickly single out which µCalcs are the most dangerous in a cap with hundreds to thousands of µCalcs < 5 µm without doing very costly, if not insurmountable, FEA. The principle limitation of the present study is that it is based nearly exclusively on the analysis of caps that have not ruptured and the interpretation of now extensive data to explain why rupture has not occurred. Although they have not been treated in this paper, other biological processes can alter the Young’s modulus E of the tissue. Because the requirement for cavitation is that the local tissue stress exceed 5E/6, processes such as enzymatic degradation and erosion, which decrease E, will lower the threshold stress for cavitation, whereas matrix synthesis will increase E and increase this threshold. Another important factor, which is described in the work by Ohayon et al. (26), is the influence of residual stresses. These stresses typically put the inner wall of the artery in compression and can reduce the local background stress by as much as a factor of two, significantly reducing the PCS and hence, the likelihood of cavitation.

This research has been supported by National Institutes of Health Grant R01 HL114805-01 (to E.A.), National Science Foundation Major Research Instrumentation (MRI) Grants 0723027 (to L.C.) and 1229449 (to L.C.), and National Institutes of Health American Recovery and Reinvestment Act (ARRA) Grants RCI HL101151 (to S.W.) and AG034198.