In this article, we advance a hypothesis for the rupture of thin fibrous cap atheroma, namely that minute (10-m-diameter) cellular-level microcalcifications in the cap, which heretofore have gone undetected because they lie below the visibility of current in vivo imaging techniques, cause local stress concentrations that lead to interfacial debonding. New theoretical solutions are presented for the local stress concentration around these minute spherical inclusions that predict a nearly 2-fold increase in interfacial stress that is relatively insensitive to the location of the hypothesized microinclusions in the cap. To experimentally confirm the existence of the hypothesized cellular-level microcalcifications, we examined autopsy specimens of coronary atheromatous lesions using in vitro imaging techniques whose resolution far exceeds conventional magnetic resonance imaging, intravascular ultrasound, and optical coherence tomography approaches. These high-resolution imaging modalities, which include confocal microscopy with calcium-specific staining and micro-computed tomography imaging, provide images of cellular-level calcifications within the cap proper. As anticipated, the minute inclusions in the cap are very rare compared with the numerous calcified macrophages observed in the necrotic core. Our mathematical model predicts that inclusions located in an area of high circumferential stress (>300 kPa) in the cap can intensify this stress to nearly 600 kPa when the cap thickness is <65 m. The most likely candidates for the inclusions are either calcified macrophages or smooth muscle cells that have undergone apoptosis. cellular-level calcification ͉ stress concentration ͉ thin-cap fibroatheroma T he rupture of the thin fibrous cap overlying the necrotic core of a vulnerable plaque is the principal cause of acute coronary syndrome. It has been widely assumed that plaque morphology is the major determinant of clinical outcome (1-6). Several pathological studies of ruptured plaques have provided morphological descriptions of the high-risk, or vulnerable, coronary plaque that is prone to rupture or erosion as a positively remodeled lesion rich in vasa-vasorium, containing a lipid-rich core with an overlying thin fibrous cap infiltrated by macrophages (7-10). Virmani et al. (6) described thin-cap fibroatheroma with a large necrotic core and a fibrous cap of Ͻ65 m as a more specific precursor of plaque rupture due to tissue stress.Despite the above observations, the mechanism of vulnerable plaque rupture has remained a mystery because ruptures often occur in regions where computational finite element (FEM) and fluid structure interaction (FSI) models do not predict maximal stress. Forty percent of ruptures occur in the central part of the cap rather than regions of high curvature at the shoulders of the lipid core where FEM models predict maximum tissue stresses (11-13). Similarly, the latest study by Tang et al. (14), using an FSI model applied to 3D MRI images of sample plaques, predicts that maximal stress often ...

Exact solutions are presented for the three-dimensional creeping motion of a sphere of arbitrary size and position between two plane parallel walls for the following conditions: (a) pure translation parallel to two stationary walls, (b) pure rotation about an axis parallel to the walls, (c) Couette flow past a rigidly held sphere induced by the motion of one of the boundaries and (d) two-dimensional Poiseuille flow past a rigidly held sphere in a channel. The combined analytic and numerical solution procedure is the first application for bounded flow of the three-dimensional boundary collocation theory developed in Ganatos, Pfeffer & Weinbaum (1978). The accuracy of the solution technique is tested by detailed comparison with the exact bipolar co-ordinate solutions of Goldman, Cox & Brenner (1967a, b) for the drag and torque on a sphere translating parallel to a single plane wall, rotating adjacent to the wall or in the presence of a shear field. In all cases, the converged collocation solutions are in perfect agreement with the exact solutions for all spacings tested. The new collocation solutions have also been used to test the accuracy of existing solutions for the motion of a sphere parallel to two walls using the method of reflexions technique. The first-order reflexion theory of Ho & Leal (1974) provides reasonable agreement with the present results for the drag when the sphere is five or more radii from both walls. At closer spacings first-order reflexion theory is highly inaccurate and predicts an erroneous direction for the torque on the sphere for a wide range of sphere positions. Comparison with the classical higher-order method of reflexions solutions of Faxen (1923) reveals that the convergence of the multiple reflexion series solution is poor when the sphere centre is less than two radii from either boundary.Solutions have also been obtained for the fluid velocity field. These solutions show that, for certain wall spacings and particle positions, a separated region of closed streamlines forms adjacent to the sphere which reverses the direction of the torque acting on a translating sphere.

This paper presents the first ‘exact’ solutions to the creeping-flow equations for the transverse motion of a sphere of arbitrary size and position between two plane parallel walls. Previous solutions to this classical Stokes flow problem (Ho & Leal 1974) were limited to a sphere whose diameter is small compared with the distance of the closest approach to either boundary. The accuracy and convergence of the present method of solution are tested by detailed comparison with the exact bipolar co-ordinate solutions of Brenner (1961) for the drag on a sphere translating perpendicular to a single plane wall. The converged series collocation solutions obtained in the presence of two walls show that for the best case where the sphere is equidistant from each boundary the drag on the sphere predicted by Ho & Leal (1974), using a first-order reflexion theory, is 40 per cent below the true value when the walls are spaced two sphere diameters apart and is one order-of-magnitude lower at a spacing of 1.1 diameters.