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.     

Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model

A three-dimensional model with simplified geometry for the branched coronary artery is presented. The bifurcation is defined by an analytical intersection of two cylindrical tubes lying on a sphere that represents an idealized heart surface. The model takes into account the repetitive variation of curvature and motion to which the vessel is subject during each cardiac cycle, and also includes the phase difference between arterial motion and blood flowrate, which may be nonzero for patients with pathologies such as aortic regurgitation. An arbitrary Lagrangian Eulerian (ALE) formulation of the unsteady, incompressible, three-dimensional Navier-Stokes equations is employed to solve for the flow field, and numerical simulations are performed using the spectral/hp element method. The results indicate that the combined effect of pulsatile inflow and dynamic geometry depends strongly on the aforementioned phase difference. Specifically, the main findings of this work show that the time-variation of flowrate ratio between the two branches is minimal (less than 5%) for the simulation with phase difference angle equal to 90 degrees, and maximal (51%) for 270 degrees. In two flow pulsatile simulation cases for fixed geometry and dynamic geometry with phase angle 270 degrees, there is a local minimum of the normalized wall shear rate amplitude in the vicinity of the bifurcation, while in other simulations a local maximum is observed.     

Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model

The accumulation of low-density lipoprotein (LDL) is recognized as one of the main contributors in atherogenesis. Mathematical models have been constructed to simulate mass transport in large arteries and the consequent lipid accumulation in the arterial wall. The objective of this study was to investigate the influences of wall shear stress and transmural pressure on LDL accumulation in the arterial wall by a multilayered, coupled lumen-wall model. The model employs the Navier-Stokes equations and Darcy's Law for fluid dynamics, convection-diffusion-reaction equations for mass balance, and Kedem-Katchalsky equations for interfacial coupling. To determine physiologically realistic model parameters, an optimization approach that searches optimal parameters based on experimental data was developed. Two sets of model parameters corresponding to different transmural pressures were found by the optimization approach using experimental data in the literature. Furthermore, a shear-dependent hydraulic conductivity relation reported previously was adopted. The integrated multilayered model was applied to an axisymmetric stenosis simulating an idealized, mildly stenosed coronary artery. The results show that low wall shear stress leads to focal LDL accumulation by weakening the convective clearance effect of transmural flow, whereas high transmural pressure, associated with hypertension, leads to global elevation of LDL concentration in the arterial wall by facilitating the passage of LDL through wall layers.     

In-vivo coronary flow profiling based on biplane angiograms: influence of geometric simplifications on the three-dimensional reconstruction and wall shear stress calculation

Background  

Clinical studies suggest that local wall shear stress (WSS) patterns modulate the site and the progression of atherosclerotic lesions. Computational fluid dynamics (CFD) methods based on in-vivo three-dimensional vessel reconstructions have recently been shown to provide prognostically relevant WSS data. This approach is, however, complex and time-consuming. Methodological simplifications are desirable in porting this approach from bench to bedside. The impact of such simplifications on the accuracy of geometry and wall shear stress calculations has to be investigated.     

The effect of fluid shear stress on fibroblasts and stem cells on plane and groove topographies

ABSTRACT

In this study, we aimed to study the effect of fluid shear stress on fibroblasts and BMSCs on plane and groove topographies. The results showed that 0.6-Hz stress had the greatest influence on the alignment, polarity, migration and adhesion of fibroblasts on plane by increasing the expression of reoriented actin and vinculin; whereas 1.0-Hz stress promoted differentiation of fibroblasts into myofibroblasts by increasing Col-I and α-SMA expression. Interestingly, under the given frequency stress, the groove structure strengthened the above characteristics of fibroblasts beyond adhesion, and promoted differentiation of BMSCs into myofibroblasts. The above results indicate that 0.6 Hz may improve the implant-tissue sealing, while 1.0-Hz stress probably causes the disordered fiber deposition around implants.     

Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation

The oscillatory shear index (OSI) was developed based on the hypothesis that intimal hyperplasia was correlated with oscillatory shear stresses. However, the validity of the OSI was in question since the correlation between intimal thickness and the OSI at the side walls of the sinus in the Y-shaped model of the average human carotid bifurcation (Y-AHCB) was weak. The objectives of this paper are to examine whether the reason for the weak correlation lies in the deviation in geometry of Y-AHCB from real human carotid bifurcation, and whether this correlation is clearly improved in the tuning-fork-shaped model of the average human carotid bifurcation (TF-AHCB). The geometry of the TF-AHCB model was based on observation and statistical analysis of specimens from 74 cadavers. The flow fields in both models were studied and compared by using flow visualization methods under steady flow conditions and by using laser Doppler anemometer (LDA) under pulsatile flow conditions. The TF-shaped geometry leads to a more complex flow field than the Y-shaped geometry. This added complexity includes strengthened helical movements in the sinus, new flow separation zone, and directional changes in the secondary flow patterns. The results show that the OSI-values at the side walls of the sinus in the TF-shaped model were more than two times as large as those in the Y-shaped model. This study confirmed the stronger correlation between the OSI and intimal thickness in the tuning-fork geometry of human carotid bifurcation, and the TF-AHCB model is a significant improvement over the traditional Y-shaped model.     

Stent design properties and deployment ratio influence indexes of wall shear stress: a three-dimensional computational fluid dynamics investigation within a normal artery.

Restenosis limits the effectiveness of stents, but the mechanisms responsible for this phenomenon remain incompletely described. Stent geometry and expansion during deployment produce alterations in vascular anatomy that may adversely affect wall shear stress (WSS) and correlate with neointimal hyperplasia. These considerations have been neglected in previous computational fluid dynamics models of stent hemodynamics. Thus we tested the hypothesis that deployment diameter and stent strut properties (e.g., number, width, and thickness) influence indexes of WSS predicted with three-dimensional computational fluid dynamics. Simulations were based on canine coronary artery diameter measurements. Stent-to-artery ratios of 1.1 or 1.2:1 were modeled, and computational vessels containing four or eight struts of two widths (0.197 or 0.329 mm) and two thicknesses (0.096 or 0.056 mm) subjected to an inlet velocity of 0.105 m/s were examined. WSS and spatial WSS gradients were calculated and expressed as a percentage of the stent and vessel area. Reducing strut thickness caused regions subjected to low WSS (<5 dyn/cm(2)) to decrease by approximately 87%. Increasing the number of struts produced a 2.75-fold increase in exposure to low WSS. Reducing strut width also caused a modest increase in the area of the vessel experiencing low WSS. Use of a 1.2:1 deployment ratio increased exposure to low WSS by 12-fold compared with stents implanted in a 1.1:1 stent-to-vessel ratio. Thinner struts caused a modest reduction in the area of the vessel subjected to elevated WSS gradients, but values were similar for the other simulations. The results suggest that stent designs that reduce strut number and thickness are less likely to subject the vessel to distributions of WSS associated with neointimal hyperplasia.     

The role of the chemokines MCP-1, GRO-alpha, IL-8 and their receptors in the adhesion of monocytic cells to human atherosclerotic plaques

Monocyte adhesion to the arterial endothelium and subsequent migration into the intima are central events in the pathogenesis of atherosclerosis. Previous experimental models have shown that chemokines can enhance monocyte–endothelial adhesion by activating monocyte integrins. Our study assesses the role of chemokines IL-8, MCP-1 and GRO-α, together with their monocyte receptors CCR2 and CXCR2 in monocyte adhesion to human atherosclerotic plaques. In an adhesion assay, a suspension of monocytic U937 cells was incubated with human atherosclerotic artery sections and the levels of endothelial adhesion were quantified. Adhesion performed in the presence of a monoclonal antibody to a chemokine, chemokine receptor or of an isotype matched control immunoglobulin, shows that antibodies to all chemokines tested, as well as their receptors, inhibit adhesion compared to the control immunoglobulins. Immunohistochemistry demonstrated the expression of MCP-1, GRO-α and their receptors in the endothelial cells and intima of all atherosclerotic lesions. These results suggest that all these chemokines and their receptors can play a role in the adhesion of monocytes to human atherosclerotic plaques. Furthermore, they suggest that these chemokine interactions provide potential targets for the therapy of atherosclerosis.     

Simulation of Low Density Lipoprotein (LDL) permeation into multilayer coronary arterial wall: Interactive effects of wall shear stress and fluid-structure interaction in hypertension

Due to increased atherosclerosis-caused mortality, identification of its genesis and development is of great importance. Although, key factors of the origin of the disease is still unknown, it is widely believed that cholesterol particle penetration and accumulation in arterial wall is mainly responsible for further wall thickening and decreased rate of blood flow during a gradual progression. To date, various effective components are recognized whose simultaneous consideration would lead to a more accurate approximation of Low Density Lipoprotein (LDL) distribution within the wall. In this research, a multilayer Fluid-Structure Interaction (FSI) model is studied to simulate the penetration of LDL into the arterial wall. Distention impact on wall properties is taken into account by considering FSI and Wall Shear Stress (WSS) dependent endothelium properties. The results show intensified permeation of LDL whilst the FSI approach is applied. In addition, luminal distension prompted by FSI reduces WSS along lumen/wall interface, especially in hypertension. This effect leads to a lowered endothelial resistance against LDL permeation, comparing to the case in which WSS effect is overlooked. The results are in an acceptable consistency with the clinical researches on WSS effect on atherosclerosis development.     

ERK5/KLF2 activation is involved in the reducing effects of puerarin on monocyte adhesion to endothelial cells and atherosclerotic lesion in apolipoprotein E-deficient mice

Puerarin has properties of anti-oxidation and anti-inflammation, which has been demonstrated protective effects in atherosclerosis and other cardiovascular diseases. However, the detail molecular mechanism still remains unclear. Here, we determined whether the atheroprotective effect of puerarin was by reducing monocyte adhesion and explored the underlying mechanism. The results showed that puerarin dose- and time-dependently reduced oxLDL-induced monocyte THP-1 adhesion to HUVECs and the expression of adhesion-related genes such as VCAM-1, ICAM-1, MCP-1 and IL-8 in HUVECs. Puerarin activated ERK5 phosphorylation and up-regulated expressions of downstream KLF2 and its targeted genes endothelial nitric oxide synthase and thrombomodulin. However, the protective effects were reversed by ERK5/KLF2 pathway inhibitor XDM8-92, BIX02189 or KLF2 siRNA suggesting the pathway involved in the function. The ex vivo assay, in which THP-1 adhesion to endothelium isolated from apoE?/? mice received various treatments further confirmed the results from HUVECs. Finally, we found that the atherosclerotic lesions in both cross sections at aortic root and whole aorta were significantly reduced in high fat-diet (HFD) mice with puerarin treatment compared with the HFD-only mice, but were increased respectively by 76% and 71% in XMD8-92 group, and 82% and 73% in BIX02189 group. Altogether, the data revealed that puerarin inhibited the monocyte adhesion in vitro and in vivo and thus reduced atherosclerotic lesions in apoE?/? mice; the protective effects were mediated by activation of ERK5/KLF2 signaling pathway. Our findings advance the understanding of puerarin function in atherosclerosis and point out a way to prevent the disease.     

Modulation of anti-inflammatory response in lipopolysaccharide stimulated human THP-1 cell line and mouse model at gene expression level with indigenous putative probiotic lactobacilli

The anti-inflammatory potential of eight indigenous probiotic Lactobacillus isolates was evaluated in vitro in terms of modulating the expression of tumor necrosis factor-alpha (TNF-α) and interleukin-6 (IL-6) in human acute monocytic leukemia (THP-1) cells under inflammatory conditions. Amongst these, Lactobacillus plantarum Lp91 was the most potent anti-inflammatory strain as it evoked a significant (P < 0.001) down-regulation of TNF-α by −1.45-fold relative to the control in THP-1 cells. However, in terms of IL-6 expression, all the strains could up-regulate its expression considerably at different levels. Hence, based on in vitro expression of TNF-α, Lp91 was selected for in vivo study in lipopolysaccharide (LPS)-induced mouse model to look at the expression of TNF-α, IL-6, monocyte chemotactic protein-1 (MCP-1), vascular cell adhesion molecule-1 (VCAM-1), intercellular adhesion molecule (ICAM-1) and E-selectin in mouse aorta. In LPS challenged (2 h) mice group fed with Lp91 for 10 days, TNF-α, IL-6, MCP-1, VCAM-1, ICAM-1 and E-selectin expressions were significantly down-regulated by 3.10-, 10.02-, 4.22-, −3.14-, 2.28- and 5.71-fold relative to control conditions. In conclusion, Lp91 could serve as a candidate probiotic strain to explore it as a possible biotherapeutic anti-inflammatory agent against inflammatory diseases including cardiovascular disease.

Electronic supplementary material

The online version of this article (doi:10.1007/s12263-013-0347-5) contains supplementary material, which is available to authorized users.     

Regulation of flow and wall shear stress in arteriolar networks of the hamster cheek pouch.

Our purpose was to define arteriolar network hemodynamics during moderate increases in interstitial adenosine or nitric oxide in the hamster (n = 34, pentobarbital sodium 70 mg/kg) cheek pouch tissue. The network consists of a feed arteriole (approximately 12-microm diameter, approximately 800-microm length) with three to six branches. Observations of diameter, red blood cell flux, and velocity were obtained at the feed before the branch and within the branch. A comparison of baseline with suffused adenosine or sodium nitroprusside (SNP) 10(-9) to 10(-5) M showed the following. First, diameter change was heterogeneous by agonist, did not reflect the expected dilatory response, and was related to location within the network. With adenosine, upstream branch points constricted and those downstream dilated, even at 10(-5) M. With SNP, upstream branch points dilated, whereas those downstream constricted. Second, with adenosine, changes in diameter, flux, and velocity together resulted in no change in wall shear stress until 10(-5) M. Wall shear stress was not maintained at a constant level with Nomega-nitro-L-arginine (10(-5) M), suggesting a role for flow-dependent diameter changes with adenosine. With SNP, diameter change correlated with the baseline (before SNP) shear stress conditions.     

Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation.

To analyse the pulsatile flow field and the mechanical stresses in a three-dimensional carotid artery bifurcation model, computer simulation is applied. The approximation of the Navier-Stokes equations uses a pressure correction finite element method. Numerical results are presented for axial and secondary flow velocity and wall shear stresses with special emphasis on the fluid dynamics in the carotid sinus. This region is of major interest because it is affected preferentially by lesions. Detailed local flow studies as carried out here should lead to a further insight into the mechanisms of atherogenesis. The flow conditions used in the study were chosen according to Ku et al. (Arteriosclerosis 5, 293-302, 1985). The results of this numerical analysis agree in the essential features with their experimental results.     

The influence of aortic dimensions on calculated wall shear stress in the mouse aortic arch

In this paper, the influence of the aortic dimensions of an investigated mouse on its resulting wall shear stress (WSS) was studied. A numerical model of a mouse aortic arch was created based on a micro-CT scan of a vascular corrosion cast of an 8-week-old wild type mouse. This model was then rescaled to obtain five models with aortic root diameters corresponding to five different stages in the mouse life cycle varying from late fetal (0.7 mm) to old adult (1.5 mm). Consistent with literature, WSS values much higher than those normally encountered in humans were found. WSS was found to decrease rapidly in early life stages and to reach a plateau in adulthood, thus supporting a mediating role for WSS in arterial growth. Our results show that WSS values for mice should be interpreted very cautiously, and if possible an animal-specific geometry with animal-specific boundary conditions should be used.     

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.     

Evaluation of the surface-averaged load exerted on a blood element by the Reynolds shear stress field provided by artificial cardiovascular devices

Implantable prosthetic devices can often affect the recipient's hemostasis, with possible hemolysis and thrombus formation. Since such devices can produce turbulent flow, it is important to characterize it as accurately as possible, by means of the Reynolds stress tensor. Some parameters related to the latter have been often used to provide a quantity related to the possible damage to blood constituents: the TSS_max, for instance, has been associated with hemolysis. It can be expressed as TSS_max=(σ₁−σ₃)/2, σ₁ and σ₃ being the highest and lowest principal normal stresses (PNSs) in each point of the flow.

In the present work, the average value of the shear stress over a spherical surface, representative of a blood component, is derived. All three PNSs (σ₁, σ₂ and σ₃) are found to have an equal role in the determination of this parameter, since the relative formula shows a marked symmetry with respect to the PNSs. The average shear stress level, for a given (σ₁, σ₃) pair (hence, for a given TSS_max), has a minimum and maximum value, depending on the particular σ₂ value yielded by the local structure of the turbulent flow field. A numerical investigation on more complex geometries shows similar results. The role of the intermediate PNS is thus shown for the first time to have a physical relevance. The presented results can be useful whenever a spatial averaging of the shear field is important to be assessed, such as in the case of platelet activation. A new parameter is thus proposed, which can be correlated with prosthetic devices complications.     

Effects of elastic compression stockings on wall shear stress in deep and superficial veins of the calf

The purpose of this study was to estimate wall shear stress (WSS) in individual vessels of the venous circulation of the calf and quantify the effects of elastic compression based on change of vessel geometry and velocity waveform. The great saphenous vein and either a peroneal or posterior tibial vein have been imaged in four healthy subjects using magnetic resonance imaging, with and without the presence of a grade 1 medical stocking. Flow through image-based reconstructed geometries was numerically simulated for both a range of steady flow rates and ultrasound-derived transient velocity waveforms, scaled to give a standardized time averaged flow rate. For steady flow, the stocking produced an average percentage increase in mean WSS of approximately 100% in the great saphenous vein across a range of 0.125-1.25 ml/s. The percentage increase in the peroneal/posterior tibial veins varied from 490 to 650% across a range of 0.5-5 ml/s. In addition, application of the stocking eliminated periods of very low or zero flow from the transient waveforms. The average minimum value of WSS in all vessels without the stocking was <0.1 Pa. With the stocking, this was increased to 0.7 Pa in the great saphenous and 0.9 Pa in the peroneal/posterior tibial veins. The pathophysiological effects of these changes are discussed. In conclusion, the flight stocking was effective in raising venous WSS levels in prone subjects, and this effect was much more pronounced in the deep vessels. The stocking also tended to prevent cessation of flow during periods of increased downstream pressure produced by respiration.