Low Reynolds number equi-bifurcation flow in a two-dimensional channel

The fluid flow in some physiological vessels such as the blood flow in blood vessels and the air flow through bronchi and bronchioles in the lungs undergoes a large number of bifurcations. The understanding of the bifurcation flow is of importance for a better comprehension of its effect in the blood and the air circulatory systems of the living body. The Reynolds number of flow in large blood vessels and bronchi is high and fluid inertia plays a dominant role in the bifurcation flow in such vessels. In small caliber blood vessels such as arterioles and capillaries, and bronchioles, the Reynolds number of flow is quite low and the effect of fluid inertia is negligible compared to the pressure and shear forces. In order to have a quantitative understanding of the bifurcation flow at low Reynolds numbers, the low Reynolds number equi-bifurcation flow in a two-dimensional channel at zero bifurcation angle is studied based on the Stokes approximation. The solution of the problem is posed as an infinite series, where the truncated version is used in numerical calculations. The results of this analysis is discussed in connection with the bifurcation flow of blood in small caliber blood vessels and that of the air in bronchioles in the lung.     

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.     

Non-Newtonian effects of blood flow on hemodynamics in distal vascular graft anastomoses

Non-Newtonian fluid flow in a stenosed coronary bypass is investigated numerically using the Carreau-Yasuda model for the shear thinning behavior of the blood. End-to-side coronary bypass anastomosis is considered in a simplified model geometry where the host coronary artery has a 75% severity stenosis. Different locations of the bypass graft to the stenosis and different flow rates in the graft and in the host artery are studied. Particular attention is given to the non-Newtonian effect of the blood on the primary and secondary flow patterns in the host coronary artery and the wall shear stress (WSS) distribution there. Interaction between the jet flow from the stenosed artery and the flow from the graft is simulated by solving the three-dimensional Navier-Stokes equation coupled with the non-Newtonian constitutive model. Results for the non-Newtonian flow, the Newtonian flow and the rescaled Newtonian flow are presented. Significant differences in axial velocity profiles, secondary flow streamlines and WSS between the non-Newtonian and Newtonian fluid flows are revealed. However, reasonable agreement between the non-Newtonian and the rescaled Newtonian flows is found. Results from this study support the view that the residual flow in a partially occluded coronary artery interacts with flow in the bypass graft and may have significant hemodynamic effects in the host vessel downstream of the graft. Non-Newtonian property of the blood alters the flow pattern and WSS distribution and is an important factor to be considered in simulating hemodynamic effects of blood flow in arterial bypass grafts.     

Genomics of local adaptation with gene flow

Gene flow is a fundamental evolutionary force in adaptation that is especially important to understand as humans are rapidly changing both the natural environment and natural levels of gene flow. Theory proposes a multifaceted role for gene flow in adaptation, but it focuses mainly on the disruptive effect that gene flow has on adaptation when selection is not strong enough to prevent the loss of locally adapted alleles. The role of gene flow in adaptation is now better understood due to the recent development of both genomic models of adaptive evolution and genomic techniques, which both point to the importance of genetic architecture in the origin and maintenance of adaptation with gene flow. In this review, we discuss three main topics on the genomics of adaptation with gene flow. First, we investigate selection on migration and gene flow. Second, we discuss the three potential sources of adaptive variation in relation to the role of gene flow in the origin of adaptation. Third, we explain how local adaptation is maintained despite gene flow: we provide a synthesis of recent genomic models of adaptation, discuss the genomic mechanisms and review empirical studies on the genomics of adaptation with gene flow. Despite predictions on the disruptive effect of gene flow in adaptation, an increasing number of studies show that gene flow can promote adaptation, that local adaptations can be maintained despite high gene flow, and that genetic architecture plays a fundamental role in the origin and maintenance of local adaptation with gene flow.     

Computing the direction of heading from affine image flow

Observers moving through a three-dimensional environment can use optic flow to determine their direction of heading. Existing heading algorithms use cartesian flow fields in which image flow is the displacement of image features over time. I explore a heading algorithm that uses affine flow instead. The affine flow at an image feature is its displacement modulo an affine transformation defined by its neighborhood. Modeling the observer's instantaneous motion by a translation and a rotation about an axis through its eye, affine flow is tangent to the translational field lines on the observer's viewing sphere. These field lines form a radial flow field whose center is the direction of heading. The affine flow heading algorithm has characteristics that can be used to determine whether the human visual system relies on it. The algorithm is immune to observer rotation and arbitrary affine transformations of its input images; its accuracy improves with increasing variation in environmental depth; and it cannot recover heading in an environment consisting of a single plane because affine flow vanishes in this case. Translational field lines can also be approximated through differential cartesian motion. I compare the performance of heading algorithms based on affine flow, differential cartesian flow, and least-squares search.     

The effect of a turbulent jet on gas transport during oscillatory flow

Axial mass transport due to the combined effects of flow oscillation and a turbulent jet was studied both experimentally and with a simple theoretical model. The experiments show that the distance over which turbulence enhances transport is greatly increased by flow oscillation, and is particularly sensitive to tidal volume. The jet flow rate and jet configuration are relatively less important. To analyze the results, the region influenced by the jet is divided into two zones: a near field in which the time-mean flow velocities are larger than the turbulent fluctuations, and a far field where the time-mean flow is essentially zero. In the far field, axial mass transport is increased due to the turbulence which decays in strength away from the jet. When oscillatory flow is superimposed upon the steady jet flow, the turbulence in the far field interacts with the flow oscillations to augment the transport of turbulence energy and of mass. This transport enhancement is modeled by introducing an effective axial diffusivity analogous to that used in laminar oscillatory flow.     

A numerical model of expired flow in a monoalveolar lung model subjected to pressure ramps

A numerical investigation of pulmonary flow properties was carried out in a monoalveolar model composed of a balloon and a compliant tube in series, subjected to pressure ramps. The flow is shown to become quickly limited by a wave-speed mechanism, occurring at the peak flow. The critical point then travels upstream, while the main part of the exit flow rate is provided by the tube collapse. After the critical flow period, the flow becomes subcritical and viscous effects are predominant in the deeply collapsed tube.     

A class of flow bifurcation models with lognormal distribution and fractal dispersion

We report a quantitative analysis of a simple dichotomous branching tree model for blood flow in vascular networks. Using the method of moment-generating function and geometric Brownian motion from stochastic mathematics, our analysis shows that a vascular network with asymmetric branching and random variation at each bifurcating point gives rise to an asymptotic lognormal flow distribution with a positive skewness. The model exhibits a fractal scaling in the dispersion of the regional flow in the branches. Experimentally measurable fractal dimension of the relative dispersion in regional flow is analytically calculated in terms of the asymmetry and the variance at local bifurcation; hence the model suggests a powerful method to obtain the physiological information on local flow bifurcation in terms of flow dispersion analysis. Both the fractal behavior and the lognormal distribution are intimately related to the fact that it is the logarithm of flow, rather than flow itself, which is the natural variable in the tree models. The kinetics of tracer washout is also discussed in terms of the lognormal distribution.     

Pulsatile flow and mass transport over an array of cylinders: gas transfer in a cardiac-driven artificial lung

The pulsatile flow and gas transport of a Newtonian passive fluid across an array of cylindrical microfibers are numerically investigated. It is related to an implantable, artificial lung where the blood flow is driven by the right heart. The fibers are modeled as either squared or staggered arrays. The pulsatile flow inputs considered in this study are a steady flow with a sinusoidal perturbation and a cardiac flow. The aims of this study are twofold: identifying favorable array geometry/spacing and system conditions that enhance gas transport; and providing pressure drop data that indicate the degree of flow resistance or the demand on the right heart in driving the flow through the fiber bundle. The results show that pulsatile flow improves the gas transfer to the fluid compared to steady flow. The degree of enhancement is found to be significant when the oscillation frequency is large, when the void fraction of the fiber bundle is decreased, and when the Reynolds number is increased; the use of a cardiac flow input can also improve gas transfer. In terms of array geometry, the staggered array gives both a better gas transfer per fiber (for relatively large void fraction) and a smaller pressure drop (for all cases). For most cases shown, an increase in gas transfer is accompanied by a higher pressure drop required to power the flow through the device.     

Pulsatile non-Newtonian blood flow simulation through a bifurcation with an aneurysm

Blood flow is analysed by means of computer simulation in an idealized arterial bifurcation model which is pathologically altered by a saccular aneurysm. The theoretical study of the flow pattern and the paths of fluid particles is carried out under pulsatile Newtonian and non-Newtonian flow conditions. The governing equations are solved numerically with the use of the finite element method. The results show the disturbed blood flow in the bifurcation and the relatively low intra-aneurysmal flow circulation. In addition to the study of basic flow patterns in the segment, a comparison of non-Newtonian and Newtonian results is carried out. This comparison proves that for the considered large artery model under physiological flow conditions where the yield number is relatively low there is no essential difference in the results.     

Comparison of particle image velocimetry and phase contrast MRI in a patient-specific extracardiac total cavopulmonary connection

Particle image velocimetry (PIV) and phase contrast magnetic resonance imaging (PC-MRI) have not been compared in complex biofluid environments. Such analysis is particularly useful to investigate flow structures in the correction of single ventricle congenital heart defects, where fluid dynamic efficiency is essential. A stereolithographic replica of an extracardiac total cavopulmonary connection (TCPC) is studied using PIV and PC-MRI in a steady flow loop. Volumetric two-component PIV is compared to volumetric three-component PC-MRI at various flow conditions. Similar flow structures are observed in both PIV and PC-MRI, where smooth flow dominates the extracardiac TCPC, and superior vena cava flow is preferential to the right pulmonary artery, while inferior vena cava flow is preferential to the left pulmonary artery. Where three-component velocity is available in PC-MRI studies, some helical flow in the extracardiac TCPC is observed. Vessel cross sections provide an effective means of validation for both experiments, and velocity magnitudes are of the same order. The results highlight similarities to validate flow in a complex patient-specific extracardiac TCPC. Additional information obtained by velocity in three components further describes the complexity of the flow in anatomic structures.     

Computational and experimental investigation of flow and fluid mixing in the roller bottle bioreactor

The fully three-dimensional velocity field in a roller bottle bioreactor is simulated for two systems (creeping flow and inertial flow conditions) using a control volume-finite element method, and validated experimentally using particle imaging velocimetry. The velocity fields and flow patterns are described in detail using velocity contour plots and tracer particle pathline computations. Bulk fluid mixing in the roller bottle is then examined using a computational fluid tracer program and flow visualization experiments. It is shown that the velocity fields and flow patterns are substantially different for each of these flow cases. For creeping flow conditions the flow streamlines consist of symmetric, closed three-dimensional loops; and for inertial flow conditions, streamlines consist of asymmetric toroidal surfaces. Fluid tracers remain trapped on these streamlines and are unable to contact other regions of the flow domain. As a result, fluid mixing is greatly hindered, especially in the axial direction. The lack of efficient axial mixing is verified computationally and experimentally. Such mixing limitations, however, are readily overcome by introducing a small-amplitude vertical rocking motion that disrupts both symmetry and recirculation, leading to much faster and complete axial mixing. The frequency of such motion is shown to have a significant effect on mixing rate, which is a critical parameter in the overall performance of roller bottles.     

Pulmonary trunk, ductus arteriosus, and pulmonary arterial phasic blood flow interactions during systole and diastole in the fetus

Although the distribution of average fetal pulmonary trunk (PT) blood flow favors the ductus arteriosus (DA) over the lungs, the phasic aspects of this distribution during systole and diastole are not well understood. Accordingly, flow profile and wave intensity (WI) analyses were performed at baseline and during brief flow increases accompanying an extrasystole (ES) in 10 anesthetized late-gestation fetal sheep instrumented with PT, DA, and left pulmonary artery (PA) micromanometer catheters and transit-time flow probes. At baseline, 83% of mean PT flow crossed the DA and 17% entered the lungs. However, early systolic flow associated with a forward-running compression wave (FCW(is)) was higher in the PA and predominant DA flow only emerged in midsystole when a large PA backward-running compression wave (BCW(ms)), which reduced PA flow, was transmitted into the DA as a forward-running compression wave (FCW(ms)) that increased flow. Subsequent protodiastolic forward DA flow occurring during pulmonary valve closure was associated with substantial retrograde PA flow, but insignificant PT flow. Conversely, forward DA flow in the remainder of diastole occurred with forward PT but near-zero PA flow. These flow and WI patterns, in conjunction with the results of mathematical modeling, suggest that 1) fetal PT flow preferentially passes into the PA during early systole due to a lower PA-than-DA characteristic impedance, while DA flow predominates in mid- and late systole due to flow effects arising from the PA BCW(ms), and 2) forward DA flow is mainly sustained by reversal of PA flow in protodiastole but discharge of a more central reservoir in diastole.     

A Simple Flow Indicator for Use in Perfusion Fixation

In perfusion fixation, we have preferred gravity flow rather than a peristaltic forced flow because the latter may cause rupture of small blood vessels. One difficulty encountered in the gravity flow method is detection of flow stoppage, often caused by the formation of a blood clot. If this is apparent soon enough, steps can be taken to re-establish the flow, Flow stoppage is not usually detected for several minutes—resulting in poor fixation of the organ involved. To allow immediate detection of stoppage, a glass flow indicator (figure 1) was manufactured     

A one-dimensional unsteady separable and reattachable flow model for collapsible tube-flow analysis

Taking into account both flow separation and reattachment observed in available experimental results on flows in a quasi-two-dimensional channel, we present a one-dimensional unsteady flow model, which is applicable to a flow in a collapsible tube. The flow model has been derived from the two-dimensional Navier-Stokes equations by introducing the concept of a dividing streamline, which divides a separated flow into a jet and a dead-water zone. We also present a criterion for the determination of a separation point. Numerical results show that the locations of the predicted separation points agree well with the experimental data. The predicted static pressure of the separated flow is almost constant downstream of the separation point and increases quickly just before the reattachment point as observed in the experiment. Finally, using the present flow model and the separation criterion, we examine the oscillatory behavior of an unsteady flow in a symmetric channel whose walls move sinusoidally.     

Pulsatile flow inside moderately elastic arteries,its modelling and effects of elasticity

Pulsatile flow inside a moderately elastic circular conduit with a smooth expansion is studied as a model to understand the influence of wall elasticity in artery flow. The solution of the simultaneous fluid-wall evolution is evaluated by a perturbative method, where the zeroth order solution is represented by the flow in a rigid vessel; the first order correction gives the wall motion and induced flow modification without the need to solve the difficult coupled problem. Such an approach essentially assumes a locally infinite celerity, therefore it represent a good approximation for the fluid-wall interaction in sites of limited extent (branches, stenosis, aneurism, etc.), which include typical situations associated with vascular diseases. The problem is solved numerically in the axisymmetric approximation; the influence of wall elasticity on the flow and on the unsteady wall shear stress is studied in correspondence of parameters taken from realistic artery flow. Attention is posed to the role of phase difference between the incoming pressure and flow pulses.     

Pressure drop and flow rate measurements in a human aortic bifurcation cast for steady and pulsatile flow

Pressure drop and flow rate measurements in a rigid cast of a human aortic bifurcation under both steady and physiological pulsatile flow conditions are reported. Integral momentum and mechanical energy balances are used to calculate impedance, spatially averaged wall shear stress and viscous dissipation rate from the data. In the daughter branches, steady flow impedance is within 30% of the Poiseuille flow prediction, while pulsatile flow impedance is within a factor of 2 of fully developed, oscillatory, straight tube flow theory (Womersley theory). Estimates of wall shear stress are in accord with measurements obtained from velocity profiles. Mean pressure drop and viscous dissipation rate are elevated in pulsatile flow relative to steady flow at the mean flow rate, and the exponents of their Reynolds number dependence are in accord with available theory.     

Oscillating fluid flow regulates cytosolic calcium concentration in bovine articular chondrocytes.

Mechanical loading is a well-known regulator of cartilage metabolism. This suggests that a loading-induced physical signal regulates chondrocyte behavior. Previous studies have focused on the effects of steady fluid flow on chondrocytes. In contrast to steady flow, loading induced fluid flow occurs in an oscillatory pattern and includes a reversal of flow direction with each loading event. In this study we examined the hypothesis that oscillating fluid flow increases cytosolic Ca2+ concentration ([Ca2+]i) in bovine articular chondrocytes (BAC) in a frequency-dependent manner and that the presence of serum affects this response. The aims of our study were to examine (1) whether BAC respond to physiologic oscillating fluid flow in vitro and compare these results to steady fluid flow, (2) the effect of fetal bovine serum on fluid flow responsiveness of BAC and (3) whether the response of BAC to fluid flow is flow rate and/or frequency dependent. [Ca2+]i was quantified using the fluorescent dye fura-2. BAC were exposed to steady, 0.5, 1, or 5 Hz sinusoidal oscillating fluid flow at five different flow rates in a parallel plate flow chamber. Our findings demonstrate that BAC respond to oscillating fluid flow with an increase in [Ca2+]i (p > 0.05), and furthermore, chondrocyte responsiveness to fluid flow increases with peak flow rate (p < 0.0001) and decreases with increasing frequencies (p < 0.0001). Finally, the presence of serum in the media potentiated the responsiveness of BAC to fluid flow (p < 0.0001). Our results suggest an important role for mechanical load-induced oscillating fluid flow in chondrocyte mechanotransduction.     

Periodic hemodynamics in skeletal muscle during local arterial pressure reduction.

The time-dependent features of red blood cell flow were evaluated with laser-Doppler flowmetry (LDF) in the left gastrocnemius muscle of 31 anesthetized New Zealand White rabbits during stepwise arterial occlusion. During the control period with a median femoral pressure of 72 mmHg, 29 animals showed minor irregular fluctuations in LDF blood flow, and only two animals displayed periodic variations of blood flow. Lowering femoral arterial pressure induced maximal periodic blood flow variations at a median pressure of 35 mmHg in all animals with a median frequency of 1.5 cycles/min (termed "slow-wave flow motion"). The median amplitude was 48% of the corresponding average flow. These slow waves disappeared at a median femoral pressure of 20 mmHg. The median LDF flow value was 4.00 arbitrary units (AU) at control pressure and 2.05 AU at maximum slow-wave flow motion. When slow-wave flow motion was seen at several pressure levels, their frequency was identical, which supports the local pacemaker concept. This study promotes a novel concept for the role and physiological significance of periodic hemodynamics in that it is a condition not characteristic for normal control situations but is activated below a specific local arterial blood pressure and flow threshold, which is known to be the lower end of autoregulation in the microcirculation of rabbit skeletal muscle. This also suggests that slow-wave flow motion is primarily under local control mechanisms.     

Analysis of cortical flow models in vivo

Cortical flow, the directed movement of cortical F-actin and cortical organelles, is a basic cellular motility process. Microtubules are thought to somehow direct cortical flow, but whether they do so by stimulating or inhibiting contraction of the cortical actin cytoskeleton is the subject of debate. Treatment of Xenopus oocytes with phorbol 12-myristate 13-acetate (PMA) triggers cortical flow toward the animal pole of the oocyte; this flow is suppressed by microtubules. To determine how this suppression occurs and whether it can control the direction of cortical flow, oocytes were subjected to localized manipulation of either the contractile stimulus (PMA) or microtubules. Localized PMA application resulted in redirection of cortical flow toward the site of application, as judged by movement of cortical pigment granules, cortical F-actin, and cortical myosin-2A. Such redirected flow was accelerated by microtubule depolymerization, showing that the suppression of cortical flow by microtubules is independent of the direction of flow. Direct observation of cortical F-actin by time-lapse confocal analysis in combination with photobleaching showed that cortical flow is driven by contraction of the cortical F-actin network and that microtubules suppress this contraction. The oocyte germinal vesicle serves as a microtubule organizing center in Xenopus oocytes; experimental displacement of the germinal vesicle toward the animal pole resulted in localized flow away from the animal pole. The results show that 1) cortical flow is directed toward areas of localized contraction of the cortical F-actin cytoskeleton; 2) microtubules suppress cortical flow by inhibiting contraction of the cortical F-actin cytoskeleton; and 3) localized, microtubule-dependent suppression of actomyosin-based contraction can control the direction of cortical flow. We discuss these findings in light of current models of cortical flow.