Cell-free plasma layer in cerebral microvessels.

Two diameters of vessel and red cell column in cerebral microvessels (> 29.8 microns in diameter) of cat were measured together with red cell velocity, using a two fluorescent tracer method. A fluorescein isothiocyanate (FITC)-labeled red cell was adopted as a flow tracer to measure the cell velocity with a dual window technique. Based on the fluorescence image, the red cell column diameter was measured. Plasma was stained with rhodamine-B isothiocyanate (RITC)-labeled dextran to measure the vessel diameter. The thickness of the cell-free plasma layer could be determined from the difference of the two diameters. The obtained thickness of the cell-free layer was not described by a simple function of vessel diameter or red cell velocity; it was dependent on the pseudo shear rate defined by the ratio of cell velocity to vessel radius. The layer thickness increased with a decrease in the pseudo shear rate.     

Effects of wall shear stress and its gradient on tumor cell adhesion in curved microvessels

Tumor cell adhesion to vessel walls in the microcirculation is one critical step in cancer metastasis. In this paper, the hypothesis that tumor cells prefer to adhere at the microvessels with localized shear stresses and their gradients, such as in the curved microvessels, was examined both experimentally and computationally. Our in vivo experiments were performed on the microvessels (post-capillary venules, 30–50 μm diameter) of rat mesentery. A straight or curved microvessel was cannulated and perfused with tumor cells by a glass micropipette at a velocity of ~1mm/s. At less than 10 min after perfusion, there was a significant difference in cell adhesion to the straight and curved vessel walls. In 60 min, the averaged adhesion rate in the curved vessels (n = 14) was ~1.5-fold of that in the straight vessels (n = 19). In 51 curved segments, 45% of cell adhesion was initiated at the inner side, 25% at outer side, and 30% at both sides of the curved vessels. To investigate the mechanical mechanism by which tumor cells prefer adhering at curved sites, we performed a computational study, in which the fluid dynamics was carried out by the lattice Boltzmann method , and the tumor cell dynamics was governed by the Newton’s law of translation and rotation. A modified adhesive dynamics model that included the influence of wall shear stress/gradient on the association/dissociation rates of tumor cell adhesion was proposed, in which the positive wall shear stress/gradient jump would enhance tumor cell adhesion while the negative wall shear stress/gradient jump would weaken tumor cell adhesion. It was found that the wall shear stress/gradient, over a threshold, had significant contribution to tumor cell adhesion by activating or inactivating cell adhesion molecules. Our results elucidated why the tumor cell adhesion prefers to occur at the positive curvature of curved microvessels with very low Reynolds number (in the order of 10⁻²) laminar flow.     

A boundary layer model for wall shear stress in arterial stenosis

This paper proposes a model for wall shear stress in arterial stenosis based on boundary layer theory. Wall shear stress estimates are obtained by solving the momentum integral equation using the method proposed by Walz and applying this method to various stenosis geometries for Reynolds numbers (Re) of Re = 59-1000. Elevated wall shear stress may be of importance when considering thrombosis and vascular erosion in stenosis, as well as the potential for debris from the stenotic area to 'break away' and cause further pathology. The values of shear stress obtained using the model in this study agree well with published values of wall shear stress. When compared to a previously published boundary layer model utilizing the Thwaites method (Reese and Thompson, 1998), the model proposed herein performs better at higher Re while the model utilizing the Thwaites method performs better at lower Re. Wall shear stresses are shown to increase with increasing stenosis (increased area reduction) for a given stenosis length, increase with increasing Re for a given stenosis geometry, and increase for steeper stenosis of the same constriction. The boundary layer model proposed can be easily implemented by clinical researchers to provide in vivo estimates of wall shear stress through arterial stenoses.     

Unsteady wall shear stress in a distensible tube

An asymptotic expression of the wall shear stress (WSS) in an elastic tube is deduced for small values of the Womersley parameter. In the case of a rigid tube this asymptotic expression is shown to compare better with the exact solution than Poiseuille's or Lambossy's approximations. Its integration in a one-dimensional model of the internal carotid artery blood flow predicts more marked systolic and less marked diastolic WSS than those predicted by the commonly used Poiseuille's approximation.     

颈动脉血管壁切应力的分析

动脉中管壁的脉动低切应力在动脉粥样硬化形成中起始动和主要的决定作用。本文比较了几种计算血管壁切应力的方法,认为采用有约束的弹性管模型计算获得的动脉壁切应力更适合于临床应用。根据检测得到的正常人和动脉硬化性脑血管病患者的颈动脉血流速度、血管管径等数据,计算两者的颈动脉壁面切应力。研究发现动脉硬化性脑血管病患者的壁面切应力比正常人显著减小。这表明,颈动脉的壁面切应力可以作为动脉硬化性脑血管疾病的早期诊断的重要参考指标。     

Branching exponent heterogeneity and wall shear stress distribution in vascular trees

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent (z) = 3 [where z is defined by (D(1))(z) = (D(2))(z) + (D(3))(z); D(1) is the parent vessel diameter and D(2) and D(3) are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in z values, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.     

Understanding the fluid mechanics behind transverse wall shear stress

The patchy distribution of atherosclerosis within arteries is widely attributed to local variation in haemodynamic wall shear stress (WSS). A recently-introduced metric, the transverse wall shear stress (transWSS), which is the average over the cardiac cycle of WSS components perpendicular to the temporal mean WSS vector, correlates particularly well with the pattern of lesions around aortic branch ostia. Here we use numerical methods to investigate the nature of the arterial flows captured by transWSS and the sensitivity of transWSS to inflow waveform and aortic geometry. TransWSS developed chiefly in the acceleration, peak systolic and deceleration phases of the cardiac cycle; the reverse flow phase was too short, and WSS in diastole was too low, for these periods to have a significant influence. Most of the spatial variation in transWSS arose from variation in the angle by which instantaneous WSS vectors deviated from the mean WSS vector rather than from variation in the magnitude of the vectors. The pattern of transWSS was insensitive to inflow waveform; only unphysiologically high Womersley numbers produced substantial changes. However, transWSS was sensitive to changes in geometry. The curvature of the arch and proximal descending aorta were responsible for the principal features, the non-planar nature of the aorta produced asymmetries in the location and position of streaks of high transWSS, and taper determined the persistence of the streaks down the aorta. These results reflect the importance of the fluctuating strength of Dean vortices in generating transWSS.     

Twenty-fold difference in hemodynamic wall shear stress between murine and human aortas

Endothelial cells regulate vascular tone and mural remodelling in a shear-dependent manner that is commonly assumed to keep wall shear stress constant across arteries and species. Allometric arguments show that aortic flow velocity is constant across species, a deduction that is consistent with much experimental data, but the same arguments also show that the shear stress experienced by aortic endothelium will depend inversely on body mass to the 3/8th power, and hence will be 20-fold higher in mice than in men. This conclusion is robust and has important implications for the study of shear-dependent vascular biology and pathology.     

Modeling of mechanosensitive channel gating in response to wall shear stress

The accurate biological function of mechanosensitive (MS) channels is crucial for maintaining the viability of living cells. For instance, in vascular endothelial cells, calcium influx from the extracellular environment into cytoplasm is regulated by stretch-activated channels. However, the mechanism by which cells sense force remains unclear. For this study, we hypothesized that gating of ion channels is simply regulated by the direct mechanical stress induced in a membrane. We modeled a membrane channel using crystallographic data of the bacteria Mycobacterium tuberculosis (Tb-MscL) because MscL homologs are integral membrane proteins with sequence similarity to most known ion channels. Molecular dynamics (MD) simulations were performed to elucidate the gating mechanism of the channel protein in response to the fluid shear stress. Results suggest that the stretched membrane drives the interfacial part of the protein–membrane complex to expand and maintains the stability of the constricted part of the transmembrane pore. Moreover, structural similarities between Tb-MscL and the family of ligand-gated ion channels suggest that the conformational change of this model in response to fluid shear stress is useful for modeling the gating mechanism in a broad class of gated channels.     

Adaptive regulation of wall shear stress optimizing vascular tree function

The branching structure of the mammalian arterial tree has been known to be close to that of an optimal conduit system of the minimum work model characterized as the branch system of constant wall shear rate. The physiological mechanism producing such construction was considered to be based on the local response of arterial caliber induced by the wall shear stress (shear rate × blood viscosity) and thereby maintaining this stress constant, which was previously observed at the canine common carotid artery shunted to the external jugular vein. The stress levels at various parts of the arterial system estimated from available data fell within ±50% of the mean (15 dyn/cm²), which was consistent with the value predicted from the model. Theoretical analyses on the cost function of the model indicated that the suspected variation of shear rate levels in the arterial tree due to the anomalous changes in blood viscosity which might bring about 3- to 4-fold differences between the minimum and maximum shear rates would cause less than 10% increase in the total energy cost. It was concluded that a local adaptive response to wall shear stress is the mechanism which effectively optimizes the design of the arterial tree.     

Design of cellular porous biomaterials for wall shear stress criterion

The microfluidic environment provided by implanted prostheses has a decisive influence on the viability, proliferation and differentiation of cells. In bone tissue engineering, for instance, experiments have confirmed that a certain level of wall shear stress (WSS) is more advantageous to osteoblastic differentiation. This paper proposes a level‐set‐based topology optimization method to regulate fluidic WSS distribution for design of cellular biomaterials. The topological boundary of fluid phase is represented by a level‐set model embedded in a higher‐dimensional scalar function. WSS is determined by the computational fluid dynamics analysis in the scale of cellular base cells. To achieve a uniform WSS distribution at the solid–fluid interface, the difference between local and target WSS is taken as the design criterion, which determines the speed of the boundary evolution in the level‐set model. The examples demonstrate the effectiveness of the presented method and exhibit a considerable potential in the design optimization and fabrication of new prosthetic cellular materials for bioengineering applications. Biotechnol. Bioeng. 2010;107:737–746. © 2010 Wiley Periodicals, Inc.     

Common carotid wall shear stress and carotid atherosclerosis in end-stage renal disease patients

Decrease of arterial wall shear stress (WSS) is associated with higher probability of atherosclerotic plaque development in many disease conditions. End-stage renal diseases (ESRD) patients suffer from vascular disease frequently, but its nature differs from general population. This study was aimed at proving an association between common carotid wall shear stress and the presence of carotid bifurcation plaques in a group of ESRD patients. ESRD subjects, planned for the creation of a dialysis access and therapy were included. Wall shear rate (WSR) was used as a surrogate of WSS and was analyzed in the common carotid arteries by duplex ultrasonography. Intima media thickness (IMT) was measured at the same site. The presence/absence of carotid bifurcation plaques was recorded. The endothelial function was estimated by the levels of von Willebrand factor (vWf). 35 ESRD patients were included (19 females, 17 diabetics). Atherosclerotic plaque was present in 53 % of bifurcations. Wall shear rate was lower in arteries with plaques (349+/-148 vs. 506+/-206 s(-1), p=0.005) and was directly related to the height of IMT and inversely to the activity of vWf (r= -0.65, p=0.016). Lower wall shear rate in the common carotid arteries is linked to the endothelial dysfunction and to the presence of atherosclerotic plaques in carotid bifurcations in ESRD subjects. Faster arterial dilatation may facilitate this process in ESRD subjects.     

Dynamic response of wall shear stress on the stenosed artery

The present study deals with an appropriate mathematical model of an artery in the presence of constriction in which the generated wall shear stress due to blood flow is analysed. The geometry of the stenosed arterial segment in the diseased state, causing malfunction of the cardiovascular system, is formed mathematically. The flowing blood contained in the stenosed artery is treated as non-Newtonian and the flow is considered to be two-dimensional. The motion of the arterial wall and its effect on local fluid mechanics is not ruled out from the present pursuit. The flow analysis applies the time-dependent, two-dimensional incompressible nonlinear Navier–Stokes equations for non-Newtonian fluids. The flow-field can be obtained primarily following the radial coordinate transformation, using the appropriate boundary conditions and finally adopting a suitable finite difference scheme numerically. The influences of flow unsteadiness, the arterial wall distensibility and the presence of stenosis on the flow-field and the wall shear stresses are quantified in order to indicate the susceptibility to atherosclerotic lesions and thereby to validate the applicability of the present theoretical model.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

Velocity and wall shear stress patterns in the human right coronary artery.

Blood flow dynamics in the human right coronary artery have not been adequately quantified despite the clinical significance of coronary atherosclerosis. In this study, a technique was developed to construct a rigid flow model from a cast of a human right coronary artery. A laser photochromic method was used to characterize the velocity and wall shear stress patterns. The flow conditions include steady flow at Reynolds numbers of 500 and 1000 as well as unsteady flow with Womersley parameter and peak Reynolds number of 1.82 and 750, respectively. Characterization of the three-dimensional geometry of the artery revealed that the largest spatial variation in curvature occurred within the almost branch-free proximal region, with the greatest curvature existing along the acute margin of the heart. In the proximal segment, high shear stresses were observed on the outer wall and lower, but not negative, stresses along the inner wall. Low shear stress on the inner wall may be related to the preferential localization of atherosclerosis in the proximal segment of the right coronary artery. However, it is possible that the large difference between the outer and inner wall shear stresses may also be involved.     

Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability

A better understanding of how hemodynamic factors affect the integrity and function of the vascular endothelium is necessary to appreciate more fully how atherosclerosis is initiated and promoted. A novel technique is presented to assess the relation between fluid dynamic variables and the permeability of the endothelium to macromolecules. Fully anesthetized, domestic swine were intravenously injected with the albumin marker Evans blue dye, which was allowed to circulate for 90 min. After the animals were euthanized, silicone casts were made of the abdominal aorta and its iliac branches. Pulsatile flow calculations were subsequently made in computational regions derived from the casts. The distribution of the calculated time-dependent wall shear stress in the external iliac branches was directly compared on a point-by-point basis with the spatially varying in vivo uptake of Evans blue dye in the same arteries. The results indicate that in vivo endothelial permeability to albumin decreases with increasing time-average shear stress over the normal range. Additionally, endothelial permeability increases slightly with oscillatory shear index.     

Modelling of peak-flow wall shear stress in major airways of the lung

Some respiratory diseases result in the inflammation of the lung airway epithelium. An associated chronic cough, as found in many cases of asthma and in long-term smokers, can exacerbate damage to the epithelial layer. It has been proposed that wall shear stresses, created by peak expiratory flow-rates during a coughing episode, are responsible. The work here uses a computational fluid dynamics technique to model peak expiratory flow in the trachea and major lung bronchi. Calculated wall shear stress values are compared to a limited set of published measurements taken from a physical model. The measurements are discussed in the context of a flow study of a complex bronchial network. A more complete picture is achieved by the calculation method, indicating, in some cases, higher maximum wall shear stresses than measured, confirming the original findings of the experimental work. Recommendations are made as to where further work would be beneficial to medical applications.