Peter Ganatos

A hypothesis for vulnerable plaque rupture due to stress-induced debonding around cellular microcalcifications in thin fibrous caps

In this article, we advance a hypothesis for the rupture of thin fibrous cap atheroma, namely that minute (10-μm-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 μm. The most likely candidates for the inclusions are either calcified macrophages or smooth muscle cells that have undergone apoptosis.

A numerical-solution technique for three-dimensional Stokes flows, with application to the motion of strongly interacting spheres in a plane

This paper describes how the collocation technique previously developed by the authors for treating both unbounded (Gluckman, Pfeffer & Weinbaum 1971; Leichtberg, Weinbaum, Pfeffer & Gluckman 1976) and bounded (Leichtberg, Pfeffer & Weinbaum 1976) multiparticle axisymmetric Stokes flows can be extended to handle a wide variety of non-axisymmetric creeping-motion problems with planar symmetry where the boundaries conform to more than a single orthogonal co-ordinate system. The present paper examines in detail the strong hydrodynamic interaction between two or more closely spaced identical spheres in a plane. The various two-sphere configurations provide a convenient means of carefully testing the accuracy and convergence of the numerical solution technique for three dimensional flow with known exact spherical bipolar solutions. The important difficulty encountered in applying the collocation technique to multi-particle non-axisymmetric flows is that the selection of boundary points is rather sensitive to the flow orientation. Despite this shortcoming one is able to obtain solutions for the quasi-steady particle velocities and drag for as many as 15 spheres in less than 30 s on an IBM 370/168 computer. The method not only gives accurate global results, but is able to predict the local fluid velocity and to resolve fine features of the flow such as the presence of separated regions of closed streamlines. Time-dependent numerical solutions are also presented for various three-sphere assemblages falling in a vertical plane. These solutions, in which the motion of each sphere is traced for several hundred diameters, are found to be in very good agreement with experimental measurements. The concluding section of the paper describes how the present collocation procedure can be extended to a number of important unsolved three-dimensional problems in Stokes flow with planar symmetry such as the arbitrary off-axis motion of a sphere in a circular cylinder or between parallel walls, or the motion of a neutrally buoyant particle at the entrance to a slit or pore.

Gravitational and zero-drag motion of a spheroid adjacent to an inclined plane at low Reynolds number

The first highly accurate solutions for the resistance tensor of an oblate or prolate spheroid moving near a planar wall obtained by Hsu & Ganatos are used to compute the translational and angular velocities and trajectories of a neutrally buoyant spheroid in shear flow and the gravitational settling motion of a non-neutrally buoyant spheroid adjacent to an inclined plane. The neutrally buoyant spheroid in shear flow undergoes a periodical motion toward and away from the wall as it continually tumbles forward. For some orientation angles, the wall actually enhances the angular velocity of the particle. For certain inclinations a spheroid settling under gravity near an inclined plane reaches an equilibrium position, after which it translates parallel to the wall without rotation

Motion of a sphere near planar confining boundaries in a Brinkman medium

A general numerical method using the boundary integral equation technique of Pozrikidis (1994) for Stokes flow in an axisymmetric domain is used to obtain the first solutions to the Brinkman equation for the motion of a particle in the presence of planar confining boundaries. The method is first applied to study the perpendicular and parallel motion of a sphere in a fibre-filled medium bounded by either a solid wall or a planar free surface which remains undeformed. By accurately evaluating the singular integrals arising from the discretization of the resulting integral equation, one can efficiently and accurately treat flow problems with high α defined by r s / K 1/2 p in which r s is the radius of the sphere and K p is the Darcy permeability. Convergence and accuracy of the new technique are tested by comparing results for the drag with the solutions of Kim & Russell (1985 a ) for the motion of two spheres perpendicular to their line of centres in a Brinkman medium. Numerical results for the drag and torque exerted on the particle moving either perpendicular or parallel to a confining planar boundary are presented for e[ges ]0.1, in which e r s is the gap between the particle and the boundary. When the gap width is much smaller than r s , a local analysis using stretched variables for motion of a sphere indicates that the leading singular term for both drag and torque is independent of α provided that α = O (1). These results are of interest in modelling the penetration of the endothelial surface glycocalyx by microvilli on rolling neutrophils and the motion of colloidal gold and latex particles when they are attached to membrane receptors and observed in nanovid (video enhanced) microscopy. The method is then applied to investigate the motion of a sphere translating in a channel. The drag and torque exerted on the sphere are obtained for various values of α, the channel height H and particle position b . These numerical results are used to describe the diffusion of a spherical solute molecule in a parallel walled channel filled with a periodic array of cylindrical fibres and to assess the accuracy of a simple multiplicative formula proposed in Weinbaum et al . (1992) for diffusion of a solute in the interendothelial cleft.

On the electrophysiological response of bone cells using a Stokesian fluid stimulus probe for delivery of quantifiable localized picoNewton level forces

A Stokesian fluid stimulus probe (SFSP), capable of delivering quantifiable pN level hydrodynamic forces, is developed to distinguish the electrophysiological response of the cell process and cell body of osteocyte-like MLO-Y4 cells without touching the cell or its substrate. The hydrodynamic disturbance is a short lived (100 ms), constant strength pressure pulse that propagates nearly instantaneously through the medium creating a nearly spherical expanding fluid bolus surrounding a 0.8 μm micropipette tip. Laboratory model experiments show that the growth of the bolus and the pressure field can be closely modeled by quasi-steady Stokes flow through a circular orifice provided the tip Reynolds number, Re(t)<0.03. By measuring the deflection of the dendritic processes between discrete attachment sites, and applying a detailed ultrastructural model for the central actin filament bundle within the process, one is able to calculate the forces produced by the probe using elastic beam theory. One finds that forces between 1 and 2.3 pN are sufficient to initiate electrical signaling when applied to the cell process, but not the much softer cell body. Even more significantly, cellular excitation by the process only occurs when the probe is directed at discrete focal attachment sites along the cell process. This suggests that electrical signaling is initiated at discrete focal attachments along the cell process and that these sites are likely integrin-mediated complexes associated with stretch-activated ion channels though their molecular structure is unknown.

On the time-dependent diffusion of macromolecules through transient open junctions and their subendothelial spread. I: Short-time model for cleft exit region

In this two-part study we shall quantitatively study, using time-dependent models, the hypothesis that transient open junctions associated with widely scattered endothelial cells undergoing mitosis are the structural equivalent for the large pore pathway via which macromolecules the size of albumin or larger cross the vascular endothelium. In an earlier steady-state model [Am. J. Physiol. 248, H945-960 (1985)], the authors demonstrated that such an open-junction pathway could quantitatively account for the regional differences in macromolecular permeability observed in various mammalian arteries in regions of enhanced cell turnover as indicated by 3H-thymidine although these cells were less than 1% of the population and the open junctions occupied less than 10(-5) of the endothelial surface. The time-dependent models described herein have been used to identify a time window and size of probe molecule wherein this hypothesis could be tested experimentally in the larger blood vessels. The first stages of these experiments have now been completed and provide convincing evidence that the junctions of virtually all endothelial cells in the M phase of the cell cycle are leaky to macromolecules (Lin et al., 1988). The statistical frequency of such leakage sites has also been determined. The time-dependent models developed herein contain two important refinements that were not contained in the earlier steady state model. First the finite resistance of the open cleft as a function of molecular size is accounted for by introducing a diffusion coefficient ratio Dj/Dz describing the relative resistance of the open cleft compared to the subendothelial tissue in the direction normal to the endothelial surface. Second the non-isotropy of the vessel wall due to the elastic lamina is considered by introducing a second diffusion coefficient ratio Dx/Dz describing the relative resistance in the lateral as compared to the normal direction. This second ratio can be as large as 100 for the arterial intima, but is of order unity for capillaries. In Part I a short time model is presented to describe the initial labeling of the open cleft and the subendothelial space in the vicinity of the cleft exit following the introduction of a tracer macromolecule. This model is valid for both larger vessels and capillaries since wall thickness and curvature and the interaction between leakage sites does not enter into the model description. In Part II (Wen et al., 1988) a long-time model is developed for larger vessels only which is valid for greater times including steady-state labeling.

The three-dimensional hydrodynamic interaction of a finite sphere with a circular orifice at low Reynolds number

This paper proposes a combined multipole-series representation and integral-equation method for solving the low-Reynolds-number hydrodynamic interaction of a finite sphere at the entrance of a circular orifice. This method combines the flexibility of the intergral-equation method in treating complicated geometries and the accuracy and computational efficiency of the multipole-series-representation technique. For the axisymmetric case, the hydrodynamic force has been solved for the difficult case where the sphere intersects the plane of the orifice opening, which could not be treated by previous methods. For the three-dimensional case, the first numerical solutions have been obtained for the spatial variation of the twelve force and torque correction factors describing the translation or rotation of the sphere in a quiescent fluid at a pore entrance or the Sampson flow past a fixed sphere. Restricted by excessive computation time, accurate three-dimensional solutions are presented only for a sphere which is one-half the orifice diameter. However, based on an analysis of the behaviour of the force and torque correction factors for this case, approximate interpolation formulas utilizing the results on or near the orifice axis and in the far field are proposed for other diameter ratios, thus greatly extending the usefulness of the present solution.

On the time dependent diffusion of macromolecules through transient open junctions and their subendothelial spread. 2. Long time model for interaction between leakage sites.

In Part 1 of this study (Weinbaum et al., 1988) a short time model has been proposed to describe the initial time dependent leakage of macromolecules at short distances (5 microns or less) from the exit of a transient open junction which the authors have hypothesized as a characteristic feature of endothelial cells in the process of turnover (Weinbaum et al., 1985). This open junction pathway has also been proposed (Weinbaum et al., 1988) to be the primary ultrastructural correlate of the 20 nm diameter large pore suggested by Renkin et al. (1977) using the predictions of cylindrical pore theory. The short time model in (Weinbaum et al., 1988), however, has major limitations in that it neglects the interaction between leakage sites, macromolecular entry through other pathways, the finite thickness of the vessel wall and the curvature of the cell perimeter. The longer time model developed herein will attempt to describe each of these features and also present an improved model and analytic solution for the steady state flux and uptake. In the previous steady state model developed by Weinbaum et al. (1985) the effect of the resistance of the transient open junctions and the non-isotropic diffusion in the underlying tissue due to the internal elastic lamina (IEL) were both neglected. New solutions are first presented which describe the effect of these important model refinements on the steady state macromolecular permeability of the major arteries. Time dependent solutions are then presented to predict the transient longer time labeling following the introduction of tracer macromolecules of varying size. These solutions and the corresponding short time solutions in Weinbaum et al. (1988) are the first solutions to our knowledge to describe the difficult time-dependent boundary value problem to determine how the channel exit concentration and flux at a leaky junction vary with time. This is accomplished by casting the boundary value problem in the form of an integral equation for the unknown flux at the cleft exit and then solving this problem using a specially designed numerical technique. The theoretical predictions are used to interpret the behavior of the localized leaks to HRP and albumin that have been reported in Stemerman et al. (1986) and our own recent experiments (Lin et al., 1988).

Transmission of steady and oscillatory fluid shear stress across epithelial and endothelial surface structures

The glycocalyx on the apical surface of vascular endothelial cells and the microvilli and cilia on kidney epithelial cells have been modeled as surface layers with a hexagonal arrangement of structural elements. These elements have been proposed to serve a mechanosensory function in the initiation of intracellular signaling by fluid shear stress. In this paper we examine the response of these surface layers when steady or oscillating shear is applied at their outer edge. In the case of steady shear, our results show that the deflection of the structural elements is proportional to the product of the applied shear stress and their length L and inversely proportional to the natural damped vibration frequency of the structural element ωc. A fluid velocity boundary layer develops at the outer edge of the surface layers when the dimensionless Brinkman parameter α=L∕KP, where KP is the Darcy permeability, is asymptotically large. In the case of oscillating shear, we find that the motions of both the fluid and s...

Behavior of multiple spheres in shear and poiseuille flow fields at low Reynolds number

Abstract The multipole truncation technique developed previously by the authors for describing the hydrodynamic interaction of three-dimensional finite clusters of spherical particles at low Reynolds number is used to obtain solutions for the motion of freely suspended particles in planar shear and/or Poiseuille flow fields. Instantaneous configurations containing up to 13 particles are studied and quasi-steady trajectories are obtained for time-varying configurations of two or three particles. Interesting applications of the theory presented in this paper include the time-dependent motion of a chain of spheres with fixed interparticle spacings in shear flow which may serve as a model to study the deformation of a polymer chain and the motion of neutrally buoyant configurations in planar Poiseuille flow to study the lateral migration of particles. The motion of a neutrally buoyant sphere in the presence of a rigidly held sphere in shear flow is also examined. This study reveals a very intriguing behavior in which the free sphere rolls along the fixed sphere but an adverse pressure gradient forces a retrograde motion of its center.