Pulsatile flow of Casson's fluid through stenosed arteries with applications to blood flow

The effects of non-Newtonian nature of blood and pulsatility on flow through a stenosed tube have been investigated. A perturbation method is used to analyse the flow. It is of interest to note that the thickness of the viscous flow region is non-uniform (changing with axial distance). An analytic relation between viscous flow region thickness and red cell concentration has been obtained. It is important to mention that some researchers have obtained an approximate solution for the flow rate-pressure gradient equation (assuming the ratio between the yield stress and the wall shear to be very small in comparison to unity); in the present analysis, we have obtained an exact solution for this non-linear equation without making that assumption. The approximate and exact solutions compare well with one of the exact solutions. Another important result is that the mean and steady flow rates decrease as the yield stress theta increases. For the low values of the yield stress, the mean flow rate is higher than the steady flow rate, but for high values of the yield stress, the mean flow rate behaviour is of opposite nature. The critical value of the yield stress at which the flow rate behaviour changes from one type to another has been determined. Further, it seems that there exists a value of the yield stress at which flow stops for both the flows (steady and pulsatile). It is observed that the flow stop yield value for pulsatile flow is lower than the steady flow. The most notable result of pulsatility is the phase lag between the pressure gradient and flow rate, which is further influenced by the yield stress and stenosis. Another important result of pulsatility is the mean resistance to flow is greater than its steady flow value, whereas the mean value of the wall shear for pulsatile flow is equal to steady wall shear. Many standard results regarding Casson and Newtonian fluids flow, uniform tube flow and steady flow can be obtained as the special cases of the present analysis. Finally, some applications of this theoretical analysis have been cited.     

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.     

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.     

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.     

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.     

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.     

植物夜间液流的发生、生理意义及影响因素研究进展

植物夜间液流是指在夜间通过植物根、茎、叶的液流量。通过对不同物种、生境条件和生态系统的野外观测,发现植物普遍存在夜间液流现象。阐述了夜间液流的大小和组成,并从夜间液流的生理意义、影响因素以及生态水文效应方面对已有的研究进展进行了综述和分析。夜间液流占到全天液流量的比例一般为5%—20%。夜间液流包括夜间的茎干补水和夜间的蒸腾作用两个过程,但是目前没有确切的研究或技术将两个过程区分开来。虽然总体上夜间液流占全天液流量的比例较少,但是夜间液流的储水作用和蒸腾作用对植物生长有重要的生理意义:夜间储水作用提高了夜间茎干水势,减少了木质部栓塞化的形成,加强了植物对干旱环境的适应;而蒸腾作用在营养物质和氧气的运输,以及水力提升等方面有重要的作用。影响夜间液流的因素较多,气象因素是主要的环境驱动因子,而土壤水分对夜间液流的影响与生境有关;夜间液流还受到物种和生境条件的影响。由于夜间液流的发生,对不同尺度的生态水文过程产生了影响。未来的研究可进一步探索在全球气候变化条件下,夜间液流与植物生理过程的关系,定量评估夜间液流对生态水文过程的影响,深入研究夜间液流对环境变化的响应。     

Computational Fluid Dynamics (CFD) study of the 4th generation prototype of a continuous flow Ventricular Assist Device (VAD)

The continuous flow ventricular assist device (VAD) is a miniature centrifugal pump, fully suspended by magnetic bearings, which is being developed for implantation in humans. The CF4 model is the first actual prototype of the final design product. The overall performances of blood flow in CF4 have been simulated using computational fluid dynamics (CFD) software: CFX, which is commercially available from ANSYS Inc. The flow regions modeled in CF4 include the inlet elbow, the five-blade impeller, the clearance gap below the impeller, and the exit volute. According to different needs from patients, a wide range of flow rates and revolutions per minute (RPM) have been studied. The flow rate-pressure curves are given. The streamlines in the flow field are drawn to detect stagnation points and vortices that could lead to thrombosis. The stress is calculated in the fluid field to estimate potential hemolysis. The stress is elevated to the decreased size of the blood flow paths through the smaller pump, but is still within the safe range. The thermal study on the pump, the blood and the surrounding tissue shows the temperature rise due to magnetoelectric heat sources and thermal dissipation is insignificant. CFD simulation proved valuable to demonstrate and to improve the performance of fluid flow in the design of a small size pump.     

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.     

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.     

Effect of anatomical fine structure on the flow of cerebrospinal fluid in the spinal subarachnoid space

The lattice Boltzmann method is used to model oscillatory flow in the spinal subarachnoid space. The effect of obstacles such as trabeculae, nerve bundles, and ligaments on fluid velocity profiles appears to be small, when the flow is averaged over the length of a vertebra. Averaged fluid flow in complex models is little different from flow in corresponding elliptical annular cavities. However, the obstacles stir the flow locally and may be more significant in studies of tracer dispersion.     

Analysis of the flow field induced by the sessile peritrichous ciliate Opercularia asymmetrica

The feeding mechanism of the sessile protozoon Opercularia asymmetrica (Oligohymenophorea, Peritrichia) relies on the cilia beat generating a flow field that convectively transports suspended particles and dissolved substances to the oral cavity of the organism. By use of optical micro-flow measurement and theoretical methods the flow environment of two neighbouring peritrichous ciliate cells is studied. Both, yeast cells (Saccharomyces cerevisiae) and artificial flow tracers are used for the visualisation of the flow field. Artificial tracers are rejected by the protozoa and deviate from the fluid path lines, while yeast cells follow the flow almost perfectly. This is shown through a dimensional analysis of the involved hydrodynamic forces on the tracers. The measured flow field exhibits maximum velocities of 25 microm/s at around 20 microm distance ahead of an individual ciliate. The flow field extends 200 microm from the location of the ciliate. A nicking motion of the protozoon is observed and found not to obey any periodic law. Multiples of protozoa exhibit most commonly an alternating cilia beat regime generating a non-stationary flow field. It can be shown through theoretical methods that fluid exchange is enhanced in this alternating regime compared to a flow field generated by a single ciliate. Fluid exchange depends on the distance of the ciliates from each other and on the alteration frequency of the cilia beat. The comparison of an analytical Stokes' flow solution with the observed fluid flow serves to determine the force required to maintain the flow field against viscous dissipation. The force magnitude is in the order of magnitude of 10-100 pN.     

Sheared bioconvection in a horizontal tube

The recent interest in using microorganisms for biofuels is motivation enough to study bioconvection and cell dispersion in tubes subject to imposed flow. To optimize light and nutrient uptake, many microorganisms swim in directions biased by environmental cues (e.g. phototaxis in algae and chemotaxis in bacteria). Such taxes inevitably lead to accumulations of cells, which, as many microorganisms have a density different to the fluid, can induce hydrodynamic instabilites. The large-scale fluid flow and spectacular patterns that arise are termed bioconvection. However, the extent to which bioconvection is affected or suppressed by an imposed fluid flow and how bioconvection influences the mean flow profile and cell transport are open questions. This experimental study is the first to address these issues by quantifying the patterns due to suspensions of the gravitactic and gyrotactic green biflagellate alga Chlamydomonas in horizontal tubes subject to an imposed flow. With no flow, the dependence of the dominant pattern wavelength at pattern onset on cell concentration is established for three different tube diameters. For small imposed flows, the vertical plumes of cells are observed merely to bow in the direction of flow. For sufficiently high flow rates, the plumes progressively fragment into piecewise linear diagonal plumes, unexpectedly inclined at constant angles and translating at fixed speeds. The pattern wavelength generally grows with flow rate, with transitions at critical rates that depend on concentration. Even at high imposed flow rates, bioconvection is not wholly suppressed and perturbs the flow field.     

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.     

Relative contribution of bronchial flow to subpleural region in dog lung.

The bronchial flow is approximately 1% of the total pulmonary flow. Anastomosis between the bronchial and pulmonary vessels occurs primarily at the microcirculatory level. It is assumed that bronchopulmonary anastomoses are present in a homogeneous manner throughout lung parenchyma. To investigate this issue, an in situ blood-perfused left lower lung lobe (500 ml/min) was prepared in a live dog. The bronchial flow rate in the entire lobe was monitored using the rate of volume gain in the reservoir while the pulmonary and bronchial flow in the subpleural region was monitored using laser-Doppler flowmetry. The results were expressed as ratio of bronchial to pulmonary flow rate for the entire lobe and for the subpleural region. We found that, for the entire lobe, bronchial flow was 1.0% of pulmonary flow, while for the subpleural region this ratio was much higher, with an average of 12%. In two different experimental conditions that were imposed to affect the global bronchial flow, these ratios changed in the same direction as the global bronchial flow. After transfusion of blood into the animal, bronchial flow increased to 1.7%, while the subpleural bronchial flow increased to 18% of the subpleural pulmonary flow. During elevation of venous pressure, bronchial flow decreased to 0.6%, while the subpleural bronchial flow decreased to 10% of the subpleural pulmonary flow. The differences in the ratios between the global and subpleural region may be explained by having low pulmonary blood flow in the periphery compared with the interior regions of the lung.(ABSTRACT TRUNCATED AT 250 WORDS)     

岷江上游三种典型植被下土壤优势流现象的染色法研究

优势流是土壤中存在的一种普遍现象,对水分运动有重要的影响。为了进一步了解森林涵养水源的机理,用亮蓝野外染色示踪试验研究了岷江上游垂直梯度上的三种典型植被下土壤中的优势流。从染色结果来看,在三种植被下的土壤中均存在优势流现象,而这种优势流的产生由于植被、海拔高度、成土过程、根系及土壤动物活动的不同,复杂程度不一。染色面积的百分数反映了入渗水分在剖面的分布,即使在整体水分仅仅停留在表层10cm以上时,部分水分可通过优势流进入到土壤底层。三种植被下优势流染色的分形维数在1.59到1.85之间,分维数反映出优势流通道的复杂性,低海拔的原始暗针叶林土和高海拔的亚高山草甸土具有复杂的优势流通道。优势流的存在对坡面水文过程产生重要的影响,是今后进一步认识森林水文效应的基础。     

Physical properties of flowing blood

The changes of viscosity, optical reflection and electrical resistivity of blood due to flow are dependent on the orientation and deformation of red cells. From electrical point of view, it can be assumed that blood is suspension of small insulating particles (red cells) in conductive fluid (plasma) when the frequency of supplied voltage is lower than several hundreds KHz. When blood flows, red cells deform and orient in flow direction. Therefore, flowing blood shows anisotropic electrical and optical properties. In steady flow, blood resistivity longitudinal to flow decrease with flow rate, and transverse one increases. Blood flow in living body is not steady but pulsatile. We measured both longitudinal and transverse resistivity changes, optical reflection change and viscosity change of sinusoidally flowing blood in a rectangular conduit. The results are 1) during one period of sinusoidal flow the longitudinal resistivity change is opposite to that of transverse one, 2) the waveform of reflection light change is similar to that of resistance change, and 3) minimum points of both longitudinal resistivity and viscosity changes do not appear at the moment when flow is zero but are delayed. When the amplitude of sinusoidal flow is small and oscillation frequency is high, the phase difference between the zero crossing period of flow and the period of minimum change in resistivity, increases up to 90 degrees. Viscosity of blood decreases with increase of amplitude and frequency of sinusoidal flow.     

Investigating Pollen and Gene Flow of WYMV-Resistant Transgenic Wheat N12-1 Using a Dwarf Male-Sterile Line as the Pollen Receptor

Pollen-mediated gene flow (PMGF) is the main mode of transgene flow in flowering plants. The study of pollen and gene flow of transgenic wheat can help to establish the corresponding strategy for preventing transgene escape and contamination between compatible genotypes in wheat. To investigate the pollen dispersal and gene flow frequency in various directions and distances around the pollen source and detect the association between frequency of transgene flow and pollen density from transgenic wheat, a concentric circle design was adopted to conduct a field experiment using transgenic wheat with resistance to wheat yellow mosaic virus (WYMV) as the pollen donor and dwarf male-sterile wheat as the pollen receptor. The results showed that the pollen and gene flow of transgenic wheat varied significantly among the different compass sectors. A higher pollen density and gene flow frequency was observed in the downwind SW and W sectors, with average frequencies of transgene flow of 26.37 and 23.69% respectively. The pollen and gene flow of transgenic wheat declined dramatically with increasing distance from its source. Most of the pollen grains concentrated within 5 m and only a few pollen grains were detected beyond 30 m. The percentage of transgene flow was the highest where adjacent to the pollen source, with an average of 48.24% for all eight compass directions at 0 m distance. Transgene flow was reduced to 50% and 95% between 1.61 to 3.15 m, and 10.71 to 20.93 m, respectively. Our results suggest that climate conditions, especially wind direction, may significantly affect pollen dispersal and gene flow of wheat. The isolation-by-distance model is one of the most effective methods for achieving stringent transgene confinement in wheat. The frequency of transgene flow is directly correlated with the relative density of GM pollen grains in air currents, and pollen competition may be a major factor influencing transgene flow.     

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.