Shear stress gradient over endothelial cells in a curved microchannel system.

Our purpose was to test a scale model of the microcirculation by measuring the shear forces to which endothelial cells were exposed, and comparing this to computer simulations. In vitro experiments were performed to measure the 2-dimensional projected velocity profile along endothelial cell lined microchannels (D-shaped, 10-30 microns radius, n = 15), or in microchannels without endothelial cells (n = 18). Microchannels were perfused with fluorescently labeled microspheres (0.5 micron dia., < 1%) suspended in cell culture media. The velocity of individual microspheres was obtained off-line (videorecording), using an interactive software program; velocity was determined as the distance traveled in one video field (1/60 s). Mass balance was verified in the microchannels by comparing the microsphere velocities to the perfusion pump rate. In confluent endothelial cell lined microchannels, a velocity profile was obtained as microspheres passed an endothelial cell nucleus (identified by fluorescent dye), and again, for a paired region 100 microns away without nuclei (cytoplasm region). The velocity profile was significantly shifted and sharpened by the endothelial cell nucleus, as anticipated. Over the nucleus, data are consistent with a normal sized nucleus extending into the lumen, further confirming that this scale model can be used to determine the wall shear stress to which endothelial cells are exposed. Using the experimental bulk phase fluid parameters as boundary conditions, we used computational fluid dynamics (CFD) to predict the expected wall shear stress gradient along an endothelial cell lined D-shaped tube. The wall shear stress gradient over the nucleus was 2-fold greater in the radial versus axial directions, and was sensitive to lateral versus midline positioned nuclei.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

Microcontinuum model for pulsatile blood flow through a stenosed tube

The effects of polar nature of blood and pulsatility on flow through a stenosed tube have been analysed by assuming blood as a micropolar fluid. Linearized solutions of basic equations are obtained through consecutive applications of finite Hankel and Laplace transforms. The analytical expressions for axial and particle angular velocities, wall shear stress, resistance to flow and apparent viscosity have been obtained. The axial velocity profiles for Newtonian and micropolar fluids have been compared. The interesting observation of this analysis is velocity, in certain parts of cycle, for micropolar fluid is higher than Newtonain fluid. Variation of apparent viscosity eta a with tube radius shows both inverse Fahraeus-Lindqvist and Fahraeus-Lindqvist effects. Finally, the resistance to flow and wall shear stress for normal and diseased blood have been computed and compared.     

The fluid shear stress distribution on the membrane of leukocytes in the microcirculation

Recent in-vivo and in-vitro evidence indicates that fluid shear stress on the membrane of leukocytes has a powerful control over several aspects of their cell function. This evidence raises a question about the magnitude of the fluid shear stress on leukocytes in the circulation. The flow of plasma on the surface of a leukocyte at a very low Reynolds number is governed by the Stokes equation for the motion of a Newtonian fluid. We numerically estimated the distribution of fluid shear stress on a leukocyte membrane in a microvessel for the cases when the leukocyte is freely suspended, as well as rolling along or attached to a microvessel wall. The results indicate that the fluid shear stress distribution on the leukocyte membrane is nonuniform with a sharp increase when the leukocyte makes membrane attachment to the microvessel wall. In a microvessel (10 microns diameter), the fluid shear stress on the membrane of a freely suspended leukocyte (8 microns diameter) is estimated to be several times larger than the wall shear stress exerted by the undisturbed Poiseuille flow, and increases on an adherent leukocyte up to ten times. High temporal stress gradients are present in freely suspended leukocytes in shear flow due to cell rotation, which are proportional to the local shear rate. In comparison, the temporal stress gradients are reduced on the membrane of leukocytes that are rolling or firmly adhered to the endothelium. High temporal gradients of shear stress are also present on the endothelial wall. At a plasma viscosity of 1 cPoise, the peak shear stresses for suspended and adherent leukocytes are of the order of 10 dyn/cm2 and 100 dyn/cm2, respectively.     

Developing steady laminar flow through uniform straight tubes with varying wall cross curvature

Numerical calculations are used to determine not only the wall shear stress but also the entry length in a laminar steady flow of an incompressible Newtonian fluid. The fluid is conveyed through rigid straight tubes with axially uniform cross sections, which mimic collapsed vessels. For each tube configuration, the "Navier-Stokes" equations are solved using the finite element method. The numerical tests are performed with the same value of the volume flow-rate whatever the tube configuration for three "Reynolds numbers". The wall shear stress is computed and determined along the axis of the tube, then the entry length is estimated by introducing two indexes by using: (i) the axial fluid velocity, and (ii) the wall shear stress. The results are analysed in order to exhibit the mechanical environment of cultured endothelial cells in the flow chamber for which the test conditions will be well-defined. For example, in a tube configuration where the opposite walls are in contact for which the inner perimeter and the area of the cross section are respectively given by 45 mm and 37.02 mm(2), the computed entry lengths with the criteria defined by (i) and (ii) are equals to about 118 and 126 mm, respectively for R(e0) = 500.     

The effect of viscosity of semen diluents on motility of bull spermatozoa

The effect of egg yolk extender on semen viscosity and bull sperm motility of fresh and cooled or deep frozen semen was determined by a computer-assisted system. Viscosity of the extender was determined by flow time. Based on the sperm velocity (velocity of the average path), individual spermatozoon were classified into groups of progressively motile (>==30 microm/sec) and immotile (<10 microm/sec) spermatozoa. The average velocity of progressively motile spermatozoa (VPM), the velocity of linear progressively motile spermatozoa (VLP) and the percentage of linear swimming spermatozoa (LIN) were evaluated. The addition of 10, 20 or 30% egg yolk to Tris buffer (pH 6.5) resulted in a linear decrease of VPM and a decrease in the percentage of progressively motile spermatozoa, but it increased the relative rate of LIN in fresh diluted semen. Increasing the levels of egg yolk in the diluent resulted in higher viscosity. The VLP was significantly higher than the VPM. In refrigerated or frozen semen samples, extender with 30 and 20% egg yolk had a similar effect on the VPM but not on the percentage of progressively motile sperm cells. Freezing of egg yolk (30%) extender to -20 degrees C resulted in a significant increased flow time and higher viscosity. Dilution of semen samples with high viscosity extender decreased the VPM in fresh and chilled semen. Freezing semen of high viscosity extender with glycerol had no apparent effect on the percentage of progressively motile spermatozoa compared with that of non-glycerinated egg yolk extender. The results suggest that different concentrations of egg yolk in the extender can influence the parameters of semen viscosity and sperm motility evaluated by a computer-assisted system.     

Effects of pH on the reactivation of human spermatozoa demembranated with Triton X-100

The aim of this work was to study the role of different parameters involved in the motility of human spermatozoa. Human spermatozoa were totally demembranated with 0.05% Triton X-100, and the demembranation was checked using electron microscopy. We have shown that, with a concentration of ATP-Mg lower than 2 mM, a pH effect was observed with a dose-dependent motility reactivation at pH 7.1, with 14% +/- 2.0% motile cells at 1 mM ATP-Mg and a straight line velocity (VSL) of 12.0 +/- 1.4 microns/sec. However, at pH 7.8, more than 65% of the spermatozoa were reactivated with as low as 0.02 mM ATP-Mg and 77.8% +/- 2.5% of them were motile at 1 mM ATP-Mg and had a VSL of 23.4 +/- 3.9 microns/sec. The depletion of free calcium by the addition of 0.5 mM EGTA in the reactivation medium (RM) improved the percentage of motile cells and the VSL most markedly at low ATP-Mg and low pH. If no MgSO4 was added in RM, cells were not motile at pH 7.8, but 30-40% reactivated at pH 7.1. If 5 mM Ca2+ was added to the RM, up to 88% of the cells became reactivated at both pHs, but the beat frequencies were very low, suggesting different mechanisms of reactivation when Mg2+ or when Ca2+ is present in the RM.     

Effects of osmolality, morphology perturbations and intracellular nucleotide content during the movement of sea bass (Dicentrarchus labrax) spermatozoa.

Sea bass spermatozoa are maintained immotile in the seminal fluid, but initiate swimming for 45 s at 20 degrees C, immediately after dispersion in a hyperosmotic medium (1100 mOsm kg-1). The duration of this motile period could be extended by a reduction of the amplitude of the hyperosmotic shock. Five seconds after the initiation of motility, 94.4 +/- 1.8% of spermatozoa were motile with a swimming velocity of 141.8 +/- 1.2 microns s-1, a flagellar beat frequency of 60 Hz and a symmetric type of flagellar swimming, resulting in linear tracks. Velocity, flagellar beat frequency, percentage of motile cells and trajectory diameter decreased concomitantly throughout the swimming phase. After 30 s of motility, the flagellar beat became asymmetric, leading to circular trajectories. Ca2+ modulated the swimming pattern of demembranated spermatozoa, suggesting that the asymmetric waves produced by intact spermatozoa after 30 s of motility were induced by an accumulation of intracellular Ca2+. Moreover, increased ionic strength in the reactivation medium induced a dampening of waves in the distal portion of the flagellum and, at high values, resulted in an arrest of wave generation in demembranated spermatozoa. In non-demembranated cells, the intracellular ATP concentration fell immediately after transfer to sea water. In contrast, the AMP content increased during the same period, while the ADP content increased slightly. In addition, several morphological changes affected the mitochondria, chromatin and midpiece. These results indicate that the short swimming period of sea bass spermatozoa is controlled by energetic and cytoplasmic ionic conditions and that it is limited by osmotic stress, which induces marked changes in cell morphology.     

Time-dependent rheological behaviour of blood flow at low shear in narrow horizontal tubes

Magnitude and time-dependence of the effects of red cell aggregation and sedimentation on the rheology of human blood were studied during low shear (tau W 2.5 to 92 mPa) flow through horizontal tubes (ID 25 to 105 microns). Immediately following reduction of perfusion pressure to a low value the red cell concentration near the tube walls decreases as a result of red cell aggregation. This is associated with a transient increase of centerline velocity. Simultaneously, sedimentation begins to occur and eventually leads to the formation of a cell-free supernatant plasma layer. Time-course and extent of this sedimentation process are strongly affected by wall shear stress variation, particularly in the larger tubes. At the lower shear stresses, centerline velocity decreases (flow resistance increases) with time following the initial acceleration period, due to sedimentation of red cells. This is followed by a further increase of resistance caused by the elevation of hematocrit occurring because of the reduction of cell/plasma velocity ratio. The time dependence of blood rheological behaviour under these flow conditions is interpreted to reflect the net effect of the partially counteracting phenomena of sedimentation and red cell aggregation.     

Large eddy simulation of LDL surface concentration in a subject specific human aorta

The development of atherosclerosis is correlated to the accumulation of lipids in the arterial wall, which, in turn, may be caused by the build-up of low-density lipoproteins (LDL) on the arterial surface. The goal of this study was to model blood flow within a subject specific human aorta, and to study how the LDL surface concentration changed during a cardiac cycle. With measured velocity profiles as boundary conditions, a scale-resolving technique (large eddy simulation, LES) was used to compute the pulsatile blood flow that was in the transitional regime. The relationship between wall shear stress (WSS) and LDL surface concentration was investigated, and it was found that the accumulation of LDL correlated well with WSS. In general, regions of low WSS corresponded to regions of increased LDL concentration and vice versa. The instantaneous LDL values changed significantly during a cardiac cycle; during systole the surface concentration was low due to increased convective fluid transport, while in diastole there was an increased accumulation of LDL on the surface. Therefore, the near-wall velocity was investigated at four representative locations, and it was concluded that in regions with disturbed flow the LDL concentration had significant temporal changes, indicating that LDL accumulation is sensitive to not only the WSS but also near-wall flow.     

Analysis of the Velocity Distribution in Partially-Filled Circular Pipe Employing the Principle of Maximum Entropy

The flow velocity distribution in partially-filled circular pipe was investigated in this paper. The velocity profile is different from full-filled pipe flow, since the flow is driven by gravity, not by pressure. The research findings show that the position of maximum flow is below the water surface, and varies with the water depth. In the region of near tube wall, the fluid velocity is mainly influenced by the friction of the wall and the pipe bottom slope, and the variation of velocity is similar to full-filled pipe. But near the free water surface, the velocity distribution is mainly affected by the contractive tube wall and the secondary flow, and the variation of the velocity is relatively small. Literature retrieval results show relatively less research has been shown on the practical expression to describe the velocity distribution of partially-filled circular pipe. An expression of two-dimensional (2D) velocity distribution in partially-filled circular pipe flow was derived based on the principle of maximum entropy (POME). Different entropies were compared according to fluid knowledge, and non-extensive entropy was chosen. A new cumulative distribution function (CDF) of partially-filled circular pipe velocity in terms of flow depth was hypothesized. Combined with the CDF hypothesis, the 2D velocity distribution was derived, and the position of maximum velocity distribution was analyzed. The experimental results show that the estimated velocity values based on the principle of maximum Tsallis wavelet entropy are in good agreement with measured values.     

Particle flow behavior in models of branching vessels. II. Effects of branching angle and diameter ratio on flow patterns

To further elucidate the role of fluid mechanical factors in the localization of atherogenesis and thrombogenesis, we have studied the 3-dimensional flow patterns in square T-junctions with branching angles theta from 30 degrees to 150 degrees and diameter ratios d/D (side: main tube) from 1.05/3.0 to 1.0. Cine films of the motions of tracer microspheres in dilute suspensions were taken at inflow Reynolds numbers from 15 to 400 and flow ratios (main: side tube) from 0.1 to 4.0. Flow patterns with suspension entering through the main tube were similar to those previously described in uniform 3 mm diameter T-junctions: paired vortices (spiral secondary flows) symmetrical about the common median plane formed at the entrances of the main and side daughter tubes. Particles circulated through the main vortex, some crossing above and below the mainstream into and through the side vortex. At the geometrical flow ratio, the main vortex became smaller and smaller as the branching angle (theta less than 90 degrees) and diameter ratio decreased, and was confined to a thin side tube was a minimum. In obtuse angle T-junctions the stagnation point shifted from the flow divider into the side tube, enhancing the flow disturbance there. The velocity distributions in main and side tubes were skewed towards the inner walls close to the flow divider. When flow entered through the side tube, a pair of recirculation zones formed in the main tube at the inner wall of the bend with a sharper angle.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models

Pulsatile flow was studied in physiologically realistic models of a normal and a moderately stenosed (30% diameter reduction) human carotid bifurcation. Time-resolved velocity measurements were made using magnetic resonance imaging, from which wall shear stress (WSS) vectors were calculated. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for a computational fluid dynamics (CFD) model. Experimental flow patterns and derived WSS vectors were compared qualitatively with the corresponding CFD predictions. In the stenosed phantom, flow in the bulb region of the "internal carotid artery" was concentrated along the outer wall, with a region of low and recirculating flow near the inner wall. In the normal phantom, the converse was found, with a low flow region near the outer wall of the bulb. Time-averaged WSS and oscillatory shear index were also markedly different for the two phantoms.     

Effect of caffeine and of pentoxifylline on the motility and metabolism of human spermatozoa

Human spermatozoa were washed and incubated with 6 mM-caffeine or 0.15-1.2 mM-pentoxifylline. Sperm motility was measured by time-lapse photography, the rate of glycolysis by the release of tritiated water from 1 mM-[3-3H]D-glucose and the rate of mitochondrial respiration by the release of 14CO2 from 1 mM-[U-14C]-L-lactate or 1 mM-[2-14C]pyruvate. Caffeine stimulated the majority of spermatozoa to convert from the 'rolling' to the 'yawing' mode of progression with a concomitant increase in lateral head displacement from 4.1 +/- 0.09 microns (343) to 6.7 +/- 0.25 microns (105) (mean +/- s.e.m. (number of spermatozoa)). There was a 45% decline in the percentage of progressively motile spermatozoa and a very small decrease in their velocity. Pentoxifylline had only a slight effect on lateral head displacement or percentage motility but produced a significant increase in velocity. Both compounds increased the rate of glycolysis by greater than 40% but elevated the rate of 14CO2 production to a smaller extent. The concentrations of ATP and ADP changed very little. We conclude that the glycolytic pathway in human spermatozoa can respond efficiently to changes in energy demand.     

Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube

The effect of pulsatile flow on peristaltic transport in a circular cylindrical tube is analysed. The flow of a Newtonian viscous incompressible fluid in a flexible circular cylindrical tube on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The initial flow in the tube is induced by an arbitrary periodic pressure gradient. A perturbation solution with amplitude ratio (wave amplitude/tube radius) as a parameter is obtained when the frequency of the travelling wave and that of the imposed pressure gradient are equal. The interaction effects of periodic wall induced flow and periodic pressure imposed flow are visualized through the presence of substantially different components of steady and higher harmonic oscillating flow in the first order flow solution. Numerical results show a strong variation of steady state velocity profiles with boundary wave number and Reynolds number and a strong phase shift behaviour of the flow in the radial direction.     

An apparatus to study the response of cultured endothelium to shear stress

An apparatus which has been developed to study the response of cultured endothelial cells to a wide range of shear stress levels is described. Controlled laminar flow through a rectangular tube was used to generate fluid shear stress over a cell-lined coverslip comprising part of one wall of the tube. A finite element method was used to calculate shear stresses corresponding to cell position on the coverslip. Validity of the finite element analysis was demonstrated first by its ability to generate correctly velocity profiles and wall shear stresses for laminar flow in the entrance region between infinitely wide parallel plates (two-dimensional flow). The computer analysis also correctly predicted values for pressure difference between two points in the test region of the apparatus for the range of flow rates used in these experiments. These predictions thus supported the use of such an analysis for three-dimensional flow. This apparatus has been used in a series of experiments to confirm its utility for testing applications. In these studies, endothelial cells were exposed to shear stresses of 60 and 128 dynes/cm2. After 12 hr at 60 dynes/cm2, cells became aligned with their longitudinal axes parallel to the direction of flow. In contrast, cells exposed to 128 dynes/cm2 required 36 hr to achieve a similar reorientation. Interestingly, after 6 hr at 128 dynes/cm2, specimens passed through an intermediate phase in which cells were aligned perpendicular to flow direction. Because of its ease and use and the provided documentation of wall shear stress, this flow chamber should prove to be a valuable tool in endothelial research related to atherosclerosis.     

Relationship between human sperm motility characteristics and sperm penetration into human cervical mucus in vitro

A series of 100 modified Kremer tests of human sperm penetration into human cervical mucus was carried out as part of the routine investigation of couples presenting with infertility. The outcome of these tests was significantly correlated with the concentration and progressive motility of the spermatozoa in the semen sample used for the test. Other semen characteristics significantly correlated with the test result were the mean velocity of progression (VP) and the amplitude of lateral head displacement about the axis of progression (AH) of the progressive spermatozoa. Normal sperm morphology was also correlated with the outcome. Using these semen characteristics as the independent variables to predict the test outcome in a discriminant analysis (normal vs abnormal tests), 34.2% of the variance was accounted for. From the discriminant function equation 75.0% of the test results could be predicted correctly. In the 30 cases in which the semen samples used for the tests showed greater than or equal to 25 X 10(6) progressively motile spermatozoa per ml, mean VP of greater than or equal to 25 microns/sec and mean AH of greater than or equal to 7.5 microns, 83.3% had normal test results. Conversely, all 13 cases for which the semen characteristics were below these limits had abnormal test results. Therefore, both the concentration of progressively motile spermatozoa and their movement characteristics are significant factors determining the outcome of homologous tests of human sperm-cervical mucus interaction.     

Numerical 3D-simulation of pulsatile wall shear stress in an arterial T-bifurcation model

The structure of pulsatile blood flow and wall shear stress in a 90° T-bifurcation model is analysed numerically. The nonlinear Navier-Stokes equations for time-dependent incompressible Newtonian fluid flow are approximated using a newly developed pressure correction, finite element method. The wall shear stress is calculated from the finite element velocity field. The investigation shows viscous flow phenomena such as flow separation and stagnation and the distribution of high and low wall shear stress during the pulse cycle. Furthermore, the effect of a sharp corner the bifurcation edge on the wall shear stress is analysed. Detailed local flow investigation is required to examine fluid dynamic contribution to the development of arterial diseases such as atherosclerosis and thrombosis.