Vascular endothelial cells (ECs) are exposed to hemodynamic forces, which modulate EC functions and vascular biology/pathobiology in health and disease. The flow patterns and hemodynamic forces are not uniform in the vascular system. In straight parts of the arterial tree, blood flow is generally laminar and wall shear stress is high and directed; in branches and curvatures, blood flow is disturbed with nonuniform and irregular distribution of low wall shear stress. Sustained laminar flow with high shear stress upregulates expressions of EC genes and proteins that are protective against atherosclerosis, whereas disturbed flow with associated reciprocating, low shear stress generally upregulates the EC genes and proteins that promote atherogenesis. These findings have led to the concept that the disturbed flow pattern in branch points and curvatures causes the preferential localization of atherosclerotic lesions. Disturbed flow also results in postsurgical neointimal hyperplasia and contributes to pathophysiology of clinical conditions such as in-stent restenosis, vein bypass graft failure, and transplant vasculopathy, as well as aortic valve calcification. In the venous system, disturbed flow resulting from reflux, outflow obstruction, and/or stasis leads to venous inflammation and thrombosis, and hence the development of chronic venous diseases. Understanding of the effects of disturbed flow on ECs can provide mechanistic insights into the role of complex flow patterns in pathogenesis of vascular diseases and can help to elucidate the phenotypic and functional differences between quiescent (nonatherogenic/nonthrombogenic) and activated (atherogenic/thrombogenic) ECs. This review summarizes the current knowledge on the role of disturbed flow in EC physiology and pathophysiology, as well as its clinical implications. Such information can contribute to our understanding of the etiology of lesion development in vascular niches with disturbed flow and help to generate new approaches for therapeutic interventions.

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Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives

Today's concept of vulnerable plaque has evolved primarily from the early pioneering work uncovering the pivotal role of plaque rupture and coronary thrombosis as the major cause of acute myocardial infarction and sudden cardiac death. Since the first historical description of plaque rupture in 1844, several key studies by leading researchers and clinicians have lead to the current accepted views on lesion instability. Important to the complex paradigm of plaque destabilization and thrombosis are many discoveries beginning with the earliest descriptions of advanced plaques, reminiscent of abscesses encapsulated by fibrous tissue capable of rupture. It was not until the late 1980s that studies of remodeling provided keen insight into the growth of advanced plaques, beyond the simple accumulation of lipid. The emphasis in the next decade, however, was on a focused shift toward the mechanisms of lesion vulnerability based on the contribution of tissue proteolysis by matrix metalloproteinases as an essential factor responsible for thinning and rupture of the fibrous cap. In an attempt to unify the understanding of what constitutes a vulnerable plaque, morphological studies, mostly from autopsy, suggest the importance of necrotic core size, inflammation, and fibrous cap thickness. Definitive proof of the vulnerable plaque, however, remains elusive because animal or human data supporting a cause-and-effect relationship are lacking. Although emerging imagining technologies involving optical coherence tomography, high-resolution MRI, molecular biomarkers, and other techniques have far surpassed the limits of the early days of angiography, advancing the field will require establishing relevant translational animal models that produce vulnerable plaques at risk for rupture and further testing of these modalities in large prospective clinical trials.

Concept of Vulnerable/Unstable Plaque

Over the past decade, since it was first observed in vivo, there has been an explosion in interest in the thin (∼500 nm), gel-like endothelial glycocalyx layer (EGL) that coats the luminal surface of blood vessels. In this review, we examine the mechanical and biochemical properties of the EGL and the latest studies on the interactions of this layer with red and white blood cells. This includes its deformation owing to fluid shear stress, its penetration by leukocyte microvilli, and its restorative response after the passage of a white cell in a tightly fitting capillary. We also examine recently discovered functions of the EGL in modulating the oncotic forces that regulate the exchange of water in microvessels and the role of the EGL in transducing fluid shear stress into the intracellular cytoskeleton of endothelial cells, in the initiation of intracellular signaling, and in the inflammatory response.

https://www.annualreviews.org/doi/pdf/10.1146/annurev.bioeng.9.060906.151959

The Structure and Function of the Endothelial Glycocalyx Layer

The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined.

https://msvlab.hre.ntou.edu.tw/grades/meshless/MFS98.pdf

The method of fundamental solutions for elliptic boundary value problems

Clinically, vascular calcification is now accepted as a valuable predictor of coronary heart disease.151 Achieving control over this process requires understanding mechanisms in the context of a tightly-controlled regulatory network, with multiple, nested feedback loops and cross-talk between organ systems, in the realm of control theory. Thus, treatments for osteoporosis such as calcitriol, estradiol, bisphosphonates, calcium supplements, and intermittent parathyroid hormone are likely to affect vascular calcification, and, conversely, many treatments for cardiovascular disease such as statins, antioxidants, hormone replacement therapy, ACE inhibitors, fish oils, and calcium channel blockers may affect bone health. As we develop and use treatments for cardiovascular and skeletal diseases, we must give serious consideration to the implications for the organ at the other end of the bone-vascular axis.

Vascular Calcification Pathobiology of a Multifaceted Disease

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

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.

A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion

A new quantitative model is presented to explore the changes in vascular permeability that would result if the intercellular clefts around widely scattered endothelial cells were to become leaky to...

Effect of cell turnover and leaky junctions on arterial macromolecular transport

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.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112078000051

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

The study of bounded and unbounded flows in the Stokes-flow regime, sometimes referred to as micro hydrodynamics (Batchelor 1976), has been the subject of greatly renewed interest since the early 1970s due in large measure to the development of three important new numerical techniques for solving more complicated boundary-value problems in viscosity-domi­ nated flows. These flows have general application in such diverse areas as microvascular fluid mechanics, cellular biophysics, suspension rheology, colloids, aerosols, and polymers. The three techniques are generally referred to as (a) the multipole collocation method, (b) the boundary integral equation technique, and (c) the multipole-moment method. In this review we briefly explain the conceptual origin of each technique, show the important relationships between the three methods, and illustrate the diversity of boundary-value problems that are best suited for each

Peter Ganatos

Papers

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

A strong interaction theory for the creeping motion of a sphere between plane parallel boundaries. Part 1. Perpendicular motion

Effect of cell turnover and leaky junctions on arterial macromolecular transport

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

Numerical Multipole and Boundary Integral Equation Techniques in Stokes Flow