Differences In Shear Rate Research Articles

Characterizing Intracranial Hemodynamics in Sickle Cell Anemia: Impact of Patient-Specific Viscosity.

Pediatric and adult patients with sickle cell anemia (SCA) are at increased risk of stroke and cerebrovascular accident. In the general adult population, there is a relationship between arterial hemodynamics and pathology; however, this relationship in SCA patients remains to be elucidated. The aim of this work was to characterize circle of Willis hemodynamics in patients with SCA and quantify the impact of viscosity choice on pathophysiologically-relevant hemodynamics measures. Based on measured vascular geometries, time-varying flow rates, and blood parameters, detailed patient-specific simulations of the circle of Willis were conducted for SCA patients (n = 6). Simulations quantified the impact of patient-specific and standard blood viscosities on wall shear stress (WSS). These results demonstrated that use of a standard blood viscosity introduces large errors into the estimation of pathophysiologically-relevant hemodynamic parameters. Standard viscosity models overpredicted peak WSS by 55% and 49% for steady and pulsatile flow, respectively. Moreover, these results demonstrated non-uniform, spatial patterns of positive and negative WSS errors related to viscosity, and standard viscosity simulations overpredicted the time-averaged WSS by 32% (standard deviation = 7.1%). Finally, differences in shear rate demonstrated that the viscosity choice alters the simulated near-wall flow field, impacting hemodynamics measures. This work presents simulations of circle of Willis arterial flow in SCA patients and demonstrates the importance and feasibility of using a patient-specific viscosity in these simulations. Accurately characterizing cerebrovascular hemodynamics in SCA populations has potential for elucidating the pathophysiology of large-vessel occlusion, aneurysms, and tissue damage in these patients.

Shear-Induced Heterogeneity in Associating Polymer Gels: Role of Network Structure and Dilatancy.

We study associating polymer gels under steady shear using Brownian dynamics simulation to explore the interplay between the network structure, dynamics, and rheology. For a wide range of flow rates, we observe the formation of shear bands with a pronounced difference in shear rate, concentration, and structure. A striking increase in the polymer pressure in the gradient direction with shear, along with the inherently large compressibility of the gels, is shown to be a crucial factor in destabilizing homogeneous flow through shear-gradient concentration coupling. We find that shear has only a modest influence on the degree of association, but induces marked spatial heterogeneity in the network connectivity. We attribute the increase in the polymer pressure (and polymer mobility) to this structural reorganization.

Effect of prolonged sitting and breaks in sitting time on endothelial function.

Sitting time (ST) is associated with cardiovascular disease risk factors, whereas breaking ST has been reported to be beneficial for reducing cardiovascular risk. The objective of this study is to examine the effects of breaking ST on superficial femoral artery (SFA) endothelial function. 1) Prolonged sitting would induce endothelial dysfunction and changes in shear forces, and 2) breaking ST with brief periods of activity would prevent attenuation in endothelial function. Twelve nonobese men (24.2 ± 4.2 yr) participated in two randomized 3-h sitting trials. In the sitting (SIT) trial, subjects were seated on a firmly cushioned chair for 3 h without moving their lower extremities. In the breaking ST trial (ACT), subjects sat similar to the SIT trial but walked on a treadmill for 5 min at 2 mph at 30 min, 1 h 30 min, and 2 h 30 min during the sitting interval. SFA flow-mediated dilation (FMD) was assessed at baseline, 1 h, 2 h, and 3 h in each trial. Statistical analyses were performed using dependent variables SFA FMD and shear rates. Significance was set at P ≤ 0.05. In the SIT trial, there was a significant decline in SFA FMD from baseline to 3 h (baseline, 4.72% ± 3.78%; 1 h, 0.52% ± 0.85%; 2 h, 1.66% ± 1.11%; 3 h, 2.2% ± 2.15; P < 0.05 by ANOVA) accompanied by a decline in mean shear rate and antegrade shear rate but no difference in shear rate (area under the curve). By two-way repeated-measures ANOVA, ACT prevented the sitting-induced decline in FMD (baseline, 4.5% ± 2.3%; 1 h, 5.04% ± 2.85%; 2 h, 5.28% ± 5.05%; 3 h, 6.9% ± 4.5%) along with no decline in shear rates. Three hours of sitting resulted in a significant impairment in shear rate and SFA FMD. When light activity breaks were introduced hourly during sitting, the decline in FMD was prevented.

Relation of Femoral Diameter, Shear Rate, and Dilatory Response to Knee Extensor Exercise

Younger women typically exhibit marked dilation of the common femoral artery (CFA) during knee extensor exercise; this is in apparent contrast to subject groups with larger (men) and/or older (older women) vessels, which on average display much smaller exercise-induced increases in CFA diameter. To gain additional insight into this variation, the present study closely examined within- and between-group relationships among CFA diameter, shear rate, and the magnitude of exercise-induced CFA dilation. Healthy women (15 younger and 18 older) and men (15 younger and 13 older) performed graded single-leg knee extensor exercise while CFA diameter and blood velocity were measured using Doppler ultrasound. Resting CFA diameter was smaller (P < 0.05) in women (younger: 0.71 ± 0.02 cm; older: 0.72 ± 0.02 cm) compared with men (younger: 0.84 ± 0.01 cm; older: 0.97 ± 0.03 cm). Resting CFA diameter was inversely associated with peak shear rate (combined groups: r = -0.83, P < 0.001) and the magnitude of dilation in women (younger: r = -0.82; older: r = -0.73, P < 0.001) and younger men (r = -0.66, P < 0.01) but not in older men (r = -0.17, P = 0.56). The dilatory response of the CFA to graded increases in shear rate showed a continuum across groups best described by a quadratic function (r2 = 0.89). Using piecewise regression modeling, a threshold diameter of 0.79 cm was identified below which diameter is inversely related to the magnitude of CFA dilation but above which little to no dilation was present. The CFA dilates to knee extensor exercise in women and men, the magnitude of which varies because of differences in shear rate across CFA diameters.

Heterogeneity in conduit artery function in humans: impact of arterial size

To determine whether conduit artery size affects functional responses, we compared the magnitude, time course, and eliciting shear rate stimulus for flow-mediated dilation (FMD) in healthy men (n = 20; 31 +/- 7 yr). Upper limb (brachial and radial) and lower limb (common and superficial femoral) FMD responses were simultaneously assessed, whereas popliteal responses were measured in the same subjects during a separate visit. Glyceryl trinitrate (GTN)-mediated responses were similarly examined. Edge detection and wall tracking of high-resolution B-mode arterial ultrasound images, combined with synchronized Doppler waveform envelope analysis, were used to calculate conduit artery diameter, blood flow, and shear rate continuously across the cardiac cycle. Baseline artery size correlated inversely with the FMD response (r = -0.57, P < 0.001). Within-artery comparisons revealed a significant inverse correlation between artery size and FMD% for the radial (r = -0.66, P = 0.001), brachial (r = -0.55, P = 0.01), and popliteal artery (r = -0.48, P = 0.03), but not for the superficial and common femoral artery. Normalization of FMD responses for differences in eliciting shear rate did not abolish the between-artery relationship for artery function and size (r = -0.48, P < 0.001), suggesting that differences between artery function responses were not entirely due to size-related differences in shear rate. This was reinforced by a significant between-artery correlation for GTN responses and baseline artery size (r = -0.74, P < 0.001). In summary, systematic differences exist in vascular function responses of conduit arteries that differ in size. This raises the possibility that differences in artery size within or between individuals may influence functional responses.

Does Brachial Artery Flow Mediated Vasodilation Reflect Systemic Vascular Function?

Flow-mediated vasodilation (FMD) has served as a noninvasive method to assess vascular health. However, recently both the importance of the FMD-induced shear stimuli and potential limb differences in terms of vascular function have come to light. PURPOSE: We sought to examine the FMD response in both the arm (brachial artery) and lower leg (popliteal artery). METHODS: To assess vessel diameter, blood velocity, and shear rate in six subjects, ultrasound Doppler measurements were made in the brachial artery and popliteal artery. Interestingly, preliminary studies revealed a large difference in the post-ischemic hyperemia in the leg following the standard 5 minute cuff occlusion. Thus, to more closely equate the shear stimulus an occlusion of 3 min and 5 min was adopted for the arm and leg, respectively. In both cases blood velocity was assessed at 0–15, 20–40, 50–70, 80–100 seconds post-occlusion while diameter was assessed at 80–100 seconds and compared to rest. RESULTS: Resting diameters were significantly larger in the popliteal artery than the brachial (0.59 ± .03 and 0.46 ± 0.01 cm, respectively) which also contributed to differences in post-cuff shear rate. A similar and significant FMD was observed both in the arm (5.4 ± 0.5%) and in the leg (5.2 ± 1%) while, despite experimental design, the mean change in shear rates were greater in the brachial (102 ± 9 s−1) than popliteal (68 ± 29 s−1) artery. To fully account for the remaining difference in shear rate, data were normalized (percent change in diameter/ average shear rate change) which revealed no difference between arm and leg vessels. CONCLUSIONS: These data reveal an attenuated post-ischemic hyperemia and larger vessel diameter in the popliteal artery which combine to reduce post-ischemic shear stimuli when compared to the brachial artery. However, when this difference in shear rate is normalized, the vessels of the arm and leg appear to respond in a similar fashion to a given shear stimulus.

A mesoscale model to predict the effect of microstructural heterogeneities on superplastic deformation

A two-dimensional approach is proposed to describe superplastic deformation at a mesoscopic scale in order to predict the effect on the mechanical behaviour of microstructural heterogeneities, like grain size distribution or spatial distribution of grains. The grains in the microstructure may slide and plastically deform, the extent of each mechanism depending on the applied conditions. The degree of homogeneity of deformation through the material is estimated by the predictions of differences in shear rates along bands specifically oriented in reference to the stress axis. It is shown that the superplastic behaviour not only depends on the grain size distribution but also on the degree of dispersion of the large grains through the microstructure, despite a same mean grain size. This dependence may concern the macroscopic behaviour as well as the extent of localisation of deformation through the sample.

On the deformation of star shaped polystyrenes in flowing solutions

The elongation of star shaped polystyrenes in flowing solutions depends on their number of branches and becomes lower when the number of branches increases. The deformation of these polymers, expressed by the change of the critical concentrations c** and c* , varies as (f/2)2 for a constant difference in shear rate (f is the number of branches). A simple theoretical model correlates the increase of the resistance to the deformation or the rigidity of the star shaped polymers to the factor (f/2)2.

Viscosity and elasticity during collagen assembly in vitro: relevance to matrix-driven translocation.

In order to better understand the gelation process associated with collagen assembly, and the mechanism of the in vitro morphogenetic phenomenon of "matrix-driven translocation" [S.A. Newman et al. (1985) Science, 228, 885-889], the viscosity and elastic modulus of assembling collagen matrices in the presence and absence of polystyrene latex beads was investigated. Viscosity measurements at very low shear rates (0.016-0.0549 s(-1)) were performed over a range of temperatures (6.9-11.5 degrees C) in a Couette viscometer. A magnetic levitation sphere rheometer was used to measure the shear elastic modulus of the assembling matrices during the late phase of the gelation process. Gelation was detected by the rapid increase in viscosity that occurred after a lag time tL that varied between O and approximately 500 s. After a rise in viscosity that occurred over an additional approximately 500 s, the collagen matrix was characterized by an elastic modulus of the order of several Pa. The lag time of the assembly process was relatively insensitive to differences in shear rate within the variability of the sample preparation, but was inversely proportional to the time the sample spent on ice before being raised to the test temperature, for test temperatures > 9 degrees C. This suggests that structures important for fibrillogenesis are capable of forming at 0 degrees C. The time dependence of the gelation process is well-described by an exponential law with a rate constant K approximately 0.1 s(-1). Significantly, K was consistently larger in collagen preparations that contained cell-sized polystyrene beads. From these results, along with prior information on effective surface tension differences of bead-containing and bead-lacking collagen matrices, we conclude that changes in matrix organization contributing to matrix-driven translocation are initiated during the lag phase of fibrillogenesis when the viscosity is < or = 0.1 Poise. The phenomenon may make use of small differentials in viscosity and/or elasticity, resulting from the interaction of the beads with the assembling matrix. These properties are well described by standard models of concentrated solutions.

Viscosity and elasticity during collagen assembly in vitro: Relevance to matrix-driven translocation

In order to better understand the gelation process associated with collagen assembly, and the mechanism of the in vitro morphogenetic phenomenon of "matrix-driven translocation" [S.A. Newman et al. (1985) Science, 228, 885-889], the viscosity and elastic modulus of assembling collagen matrices in the presence and absence of polystyrene latex beads was investigated. Viscosity measurements at very low shear rates (0.016-0.0549 s(-1)) were performed over a range of temperatures (6.9-11.5 degrees C) in a Couette viscometer. A magnetic levitation sphere rheometer was used to measure the shear elastic modulus of the assembling matrices during the late phase of the gelation process. Gelation was detected by the rapid increase in viscosity that occurred after a lag time tL that varied between O and approximately 500 s. After a rise in viscosity that occurred over an additional approximately 500 s, the collagen matrix was characterized by an elastic modulus of the order of several Pa. The lag time of the assembly process was relatively insensitive to differences in shear rate within the variability of the sample preparation, but was inversely proportional to the time the sample spent on ice before being raised to the test temperature, for test temperatures > 9 degrees C. This suggests that structures important for fibrillogenesis are capable of forming at 0 degrees C. The time dependence of the gelation process is well-described by an exponential law with a rate constant K approximately 0.1 s(-1). Significantly, K was consistently larger in collagen preparations that contained cell-sized polystyrene beads. From these results, along with prior information on effective surface tension differences of bead-containing and bead-lacking collagen matrices, we conclude that changes in matrix organization contributing to matrix-driven translocation are initiated during the lag phase of fibrillogenesis when the viscosity is < or = 0.1 Poise. The phenomenon may make use of small differentials in viscosity and/or elasticity, resulting from the interaction of the beads with the assembling matrix. These properties are well described by standard models of concentrated solutions.

Relationship between arterial thrombosis and neutralization of a polyethylene ionomer.

The influence of three levels of sodium neutralization of an ethylene/methacrylic acid copolymer on in vivo blood compatibility was studied in a canine arterial model. Effects due to sample fabrication methods (thermal pressing versus solution casting) were also monitored. Sodium content, sodium release, hydrogen dissociation, and localization of anionic groups were noted. Polymer surface energy, surface morphology, water uptake, and thermal properties were characterized. Material characterization and in vivo implantation disclose the following: 1) Thermal pressing generated oxidation degradation products that decreased in vivo blood compatibility. Solution-cast samples adhered and activated fewer blood elements. 2) Platelets and leukocytes were sensitive to differences in shear rate in the carotid and femoral arteries, with the femoral site tending toward higher shear, more platelet deposition and fewer leukocytes. 3) The surface properties of the polyethylene control, 0% Na, and 50% Na samples tended to be similar. These properties were different from the 100% Na sample. The 100% Na ionomer was more hydrophilic, had a higher polar component for its surface energy, and was unique in exhibiting discrete ionic clusters 1-10 microns in diameter on its surface. 4) These differences were manifested in vivo by platelet activation and thrombus development on the polyethylene, 0% Na, and 50% Na implants, while the 100% Na implant surfaces were predominantly covered by singly adherent, unactivated platelets. 5) It is proposed that the improvement in biocompatibility for the 100% Na ionomer is due to the cluster development in the neutralized methacrylic component and that either directly, or through appropriate protein adsorption and/or conformational adjustment to the cluster regions, platelets are not activated and do not initiate the coagulation mechanism.

Wall Shear Stress Rather Than Shear Rate Regulates Cytoplasmic Ca ++ Responses to Flow in Vascular Endothelial Cells

Recent evidence suggests that the vascular endothelial cell (EC) can sense the flow-rate over its surface and according to the information, regulates not only its own morphology and functions but also those of the surrounding smooth muscle and other tissues. There is now a discussion over which of the following mechanisms actually initiates the signal-transacting response of EC against flow: the mechanical shear deformation of the cell due to flow-oriented wall shear stress (τ), or the diffusional accumulation of vasoactive agonists on the cell surface modulated by wall shear rate (γ) or both. To identify the relative importance of each mechanism, we examined quantitative changes in the cytoplasmic free Ca ++ concentration ([Ca ++] i) in cultured EC in the presence of the Ca ++ mobilizing agonist ATP, i.e., a second messenger response of the internal signalling system, following the perfusion of two buffers with different viscosities (μ), which relates these factors as τ = μγ. The results of in vitro fluorescence photometry in EC with Fura-2 showed that the [Ca ++ i] level was enhanced with increase in the shear rate but to a greater extent with higher viscosity, and that the [Ca ++] i levels at the same calculated level of shear stress were virtually identical, regardless of difference in shear rate and viscosity. This quantitative one-to-one relationship between the shear stress and the second messenger response suggests that wall shear stress rather than wall shear rate is the principal physical factor eliciting EC responses to flow.

Role of CD11/CD18 in shear rate-dependent leukocyte-endothelial cell interactions in cat mesenteric venules.

In vivo microscopy was used to assess the relationships among shear rate (and shear stress), leukocyte rolling velocity, and leukocyte adherence in a cat mesentery preparation. Shear rate in individual venules and arterioles of 25-35 microns diameter were varied over a wide range by graded occlusion of an arterial loop. There was a linear decline in leukocyte rolling velocity (Vwbc) as red cell velocity (Vrbc) was reduced. The ratio Vwbc/Vrbc remained constant despite variations in shear stress from 5-25 dyn/cm2. A reduction in shear stress was associated with an increased leukocyte adherence, particularly when Vwbc was reduced below 50 microns/s. Reduction in wall shear rate below 500 s-1 in arterioles allowed 1-3 leukocytes to adhere per 100 microns length of vessel, while venules exposed to the same shear rates had 5-16 adherent leukocytes. In arterioles, leukocyte rolling was only observed at low shear rates. At shear rates less than 250 s-1 leukocyte rolling velocity was faster in arterioles than venules, and the ratio Vwbc/Vrbc for arterioles was 0.08 +/- 0.02, which was fourfold higher than the ratio obtained in venules at similar shear rates. Pretreatment with the CD18-specific antibody (mAb) IB4 increased leukocyte rolling velocity in venules by approximately 20 microns/s at red cell velocities below 2,000 microns/s. mAb IB4 largely prevented the leukocyte adherence to arterioles and venules, and increased the ratio Vwbc/Vrbc observed in venules at low shear elicit a CD18-dependent adhesive interaction between leukocytes and microvascular endothelium, and that differences in shear rates cannot explain the greater propensity for leukocyte rolling and adhesion in venules than arterioles.

Structure of Thixotropic Suspensions in Shear Flow. III. Time-Dependent Behavior

The time-dependent viscosity of bentonite-water suspensions was studied experimentally in Couette flow for various transitions between constant shear rates. It was found that after a sudden change in the shear rate the time dependence of the viscosity can be described by η(t)=A exp[−(t/τ1)4.0]+B exp(−t/τ2)+C, with τ2&amp;gt;τ1. In general, the characteristic times: 1) become longer as the differences in shear rates become smaller; 2) decrease with increasing concentration; 3) show little temperature effect for a 20°C temperature change. A theory for the time-dependent behavior is given which can reproduce the essential features of the experimental results.

Time-dependent behavior of thixotropic suspensions

The time-dependent behavior of the viscosity of bentonite-water suspensions was studied experimentally inCouette flow for various transitions between constant shear rates. It was found that, in general, the characteristic times become longer as the final shear rate becomes smaller and, for the same final shear rate, as the differences in shear rates become smaller. The characteristic time increases with increasing temperature and decreasing concentration. A discussion of the kinetics of the time dependence is given.