Water Flow Through Vessel Perforation Plates--A Fluid Mechanical Approach

The effect of scalariform perforation plates on the flow ofwater through plant vessels remains poorly understood. In thisstudy, a new computational tool based on finite element methodsolutions to the Navier-Stokes equation was applied to modellingfluid flow through these structures in plant vessels. Modelsdeveloped for Liriodendron tulipifera vessel elements were solvedfor cells with and without the perforation plate to study effectsof the plate on the pressure drop along the cell. Results indicatethat the pressure gradient was 5-fold greater through the platethan for regions before and after the plate. However, the perforationplate in this species accounts for only about 8% of the resistanceto flow through typical vessels because the plate influencesflow for only a short distance along the cell relative to itslength. Details of the flow characteristics through pores ofthe perforation plate are also described. Key words: Conductance, finite element method, perforation plate, vessel, water flow     

Water flow through a 20-pore perforation plate in vessels of Liquidambar styraciflua

The flow of water through perforation plates of Liquidambar styraciflua vessels was studied through a computational fluid dynamics approach together with a large-scale physical model of the perforation plate. For the computational approach, a finite elements model was constructed of a 20-pore perforation plate and the region around the plate. Solutions of this model describe pressures and velocities for points within the model. The pressure gradient within the pores of the plate was about 40-fold greater than for regions away from the plate. However the influence of the plate on flow extends for only a very short distance before and after the plate. Overall, the perforation plate in this model was calculated to account for 23% of the total resistance to flow encountered along the vessel. Calculations from the physical model provided a similar estimate of 21% for the contribution of the perforation plate to flow resistance.      

Resistances to fluid flow of model xylem vessels with simple and scalariform perforation plates

The resistances of xylem vessel walls and perforation plates has been investigated using 18 large-scale physical models made of plastic tubing into which scale models of plates were inserted. Flow of water through vessels was modelled using glycerol instead of water to keep the Reynolds number below 0.1. The technique proved easy, cheap and reliable.Results showed that perforation plate resistance is low compared with the resistance of the walls, whatever the plate morphology; plates only provided 0.6-18.6% extra resistance. Simple plates provided less resistance than scalariform plates, but because they are arranged closer together in vessels, resistance values (1.7-5.1%) overlap with those of scalariform plates. The resistance of scalariform plates varied in a systematic way with their morphology. For a given plate angle, increasing the number of bars increased resistance. For a given bar number, increasing the angle of the plate to the vessel axis also increased the resistance. However, for a given gap between bars, increasing the angle of the plate to the vessel axis decreased resistance. These results are discussed in the light of theories about the function of perforation plates.Keywords: Flow, xylem vessel, perforation plate, models.      

Water Flow in Vessels with Simple or Compound Perforation Plates

Hydraulic conductance of vessels was studied in young stem internodesand petioles of five species of dicotyledons that have simpleor compound perforation plates. Measured conductances of Clematisdioscoreifolia, Hardenbergia violacea, and Olea europaea, whichhave simple perforation plates, ranged from 92 to 106% of predictedvalues based on Hagen-Poiseuille flow through ideal capillaries.Petioles of Liquidambar styraciflua and Liriodendron tulipifera,which have compound perforation plates, had measured hydraulicconductances in spring-collected material that matched predictedconductances, but values averaged 60% of predicted in materialfrom late summer, suggesting blockage of vessels with time.An analog model of a vessel with and without compound perforationplates was developed from tygon tubing and steel pins to determinethe effect of obstruction by bars, which produced little flowreduction. Likewise, calculations based on the observed geometryof a scalariform perforation plate suggested that the platetypically reduced flow by only 1%. These data suggest that flowrates in vessels with simple as well as compound perforationplates are essentially equal to flows in ideal capillaries ofthe appropriate diameters. Clematis dioscoreifolia, Hagen-Poiseuille, Hardenbergia violacea, hydraulic conductance, Liquidambar styraciflua, Liriodendron tulipifera, Olea europaea, xylem     

Dependence of red blood cell dynamics in microvessel bifurcations on the endothelial surface layer’s resistance to flow and compression

Red blood cells (RBCs) make up 40–45% of blood and play an important role in oxygen transport. That transport depends on the RBC distribution throughout the body, which is highly heterogeneous. That distribution, in turn, depends on how RBCs are distributed or partitioned at diverging vessel bifurcations where blood flows from one vessel into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. These studies, however, assume that the vessel wall is a flat impenetrable homogeneous surface. While this is a good first approximation, especially for larger vessels, the vessel wall is typically coated by a flexible, porous endothelial glycocalyx or endothelial surface layer (ESL) that is on the order of 0.5–1 µm thick. To better understand the possible effects of this layer on RBC partitioning, a diverging capillary bifurcation is analyzed using a flexible, two-dimensional model. In addition, the model is also used to investigate RBC deformation and RBC penetration of the ESL region when ESL properties are varied. The RBC is represented using interconnected viscoelastic elements. Stokes flow equations (viscous flow) model the surrounding fluid. The flow in the ESL is modeled using the Brinkman approximation for porous media with a corresponding hydraulic resistivity. The ESL’s resistance to compression is modeled using an osmotic pressure difference. One cell passes through the bifurcation at a time, so there are no cell–cell interactions. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. Decreasing hydraulic resistivity and/or decreasing osmotic pressure differences (ESL resistance to compression) produced four behaviors: (1) RBC partitioning nonuniformity increased slightly; (2) RBC deformation decreased; (3) RBC velocity decreased relative to blood flow velocity; and (4) RBCs penetrated more deeply into the ESL. Decreasing the ESL’s resistance to flow and/or compression to pathological levels could lead to more frequent cell adhesion and clotting as well as impaired vascular regulation due to weaker ATP and nitric oxide release. Potential mechanisms that can contribute to these behaviors are also discussed.

     

凹叶厚朴细弱枝与粗壮枝导管分子的比较研究

对凹叶厚朴粗壮枝和细弱枝的次生木质部进行离析研究,发现其导管穿孔板有两种类型,即单穿孔板和梯状穿孔板。在细弱枝中,具不同类型穿孔板的导管分子有八种类型,即一端为单穿孔板的导管分子,另一端为梯状穿孔板的导管分子;只有一端为单穿孔板的导管分子;只有一端为梯状穿孔板的导管分子;两端均为单穿孔板的导管分子;两端均为梯状穿孔板的导管分子;具三个单穿孔板的导管分子;两端具单穿孔板的导管分子,中间具多个梯状穿孔板的导管分子;具多个梯状穿孔板的导管分子。粗壮枝除了无具多个梯状穿孔板的导管分子外,其它细弱枝的导管分子的类型都具有。细弱枝的导管分子宽而长,粗壮枝导管分子窄而短。     

Single‐vessel flow measurements indicate scalariform perforation plates confer higher flow resistance than previously estimated

During vessel evolution in angiosperms, scalariform perforation plates with many slit‐like openings transformed into simple plates with a single circular opening. The transition is hypothesized to have resulted from selection for decreased hydraulic resistance. Previously, additional resistivity of scalariform plates was estimated to be small – generally 10% or less above lumen resistivity – based on numerical and physical models. Here, using the single‐vessel technique, we directly measured the hydraulic resistance of individual xylem vessels. The resistivity of simple‐plated lumens was not significantly different from the Hagen–Poiseuille (HP) prediction (+6 ± 3.3% mean deviation). In the 13 scalariform‐plated species measured, plate resistivity averaged 99 ± 13.7% higher than HP lumen resistivity. Scalariform species also showed higher resistivity than simple species at the whole vessel (+340%) and sapwood (+580%) levels. The strongest predictor of scalariform plate resistance was vessel diameter (r² = 0.84), followed by plate angle (r² = 0.60). An equation based on laminar flow through periodic slits predicted single‐vessel measurements reasonably well (r² = 0.79) and indicated that Baileyan trends in scalariform plate evolution maintain an approximate balance between lumen and plate resistances. In summary, we found scalariform plates of diverse morphology essentially double lumen flow resistance, impeding xylem flow much more than previously estimated.     

Formation of a boundary layer in steady-state blood flow

This paper is devoted to a study of boundary layer formation in the steady flow of blood through the human aorta. Blood is treated as an incompressible fluid. Consideration is given to a flat-top velocity profile which combines the potential flow with the boundary layer; expressions for the displacement thickness, skin-friction and pressure in the entry region are derived.     

Mathematical model of movement of asymmetrical erythrocyte along the capillary

The proposed 3-dimensional mathematical model describes the motion of asymmetrical erythrocytes through capillaries of different sections. The lubrication theory is used to describe the flow of the suspending fluid in the gaps between the cell and the vessel wall. It is shown that the cell velocity and diameter of the capillary defines the value of the resistance of erythrocyte motion.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

洋蒲桃次生木质部中导管分子的解剖学

运用细胞图像分析系统和显微照相的方法对洋蒲桃(Syzygium samarangense)次生木质部导管分子进行了观察研究。次生木质部导管分子类型有: 两端具尾导管、一端具尾导管和无尾导管。导管分子穿孔板存在着4种类型: 两端均为具2个单穿孔的复穿孔板;一端为1个单穿孔板, 另1端为具2个单穿孔的复穿孔板;两端均为单穿孔板;两单穿孔板位于同一端壁两侧相互对应以及一些过渡类型穿孔板。根据观察结果, 分析了各类型穿孔板之间的演化关系。     

洋蒲桃次生木质部中导管分子的解剖学

运用细胞图像分析系统和显微照相的方法对洋蒲桃（Syzygium samarangense）次生木质部导管分子进行了观察研究。次生木质部导管分子类型有：两端具尾导管、一端具尾导管和无尾导管。导管分子穿孔板存在着4种类型：两端均为具2个单穿孔的复穿孔板;一端为1个单穿孔板,另1端为具2个单穿孔的复穿孔板;两端均为单穿孔板：两单穿孔板位于同一端壁两侧相互对应以及一些过渡类型穿孔板。根据观察结果,分析了各类型穿孔板之间的演化关系。     

Momentum integral method for studying flow characteristics of blood through a stenosed vessel

Taking into consideration the slip velocity at the wall of a blood vessel, a mathematical model is developed in the paper for the study of blood flow through a mammalian blood vessel in the presence of a stenosis. By employing the momentum integral technique, analytical expressions for the velocity profile, pressure gradient and skin-friction are derived. The condition for an adverse pressure gradient is also deduced. It is observed that the slip velocity bears the potential to influence the velocity distribution of blood to a remarkable extent and to reduce considerably the pressure-gradient as well as the skin-friction.     

A circle of Willis simulation using distensible vessels and pulsatile flow

The development of a one-dimensional numerical (finite-difference) model of the arterial network surrounding the circle of Willis is described based on the full Navier-Stokes and conservation of mass equations generalized for distensible vessels. The present model assumes an elastic wall defined by a logarithmic pressure-area relation obtained from the literature. The viscous term in the momentum equation is evaluated using the slope of a Karman-Pohlhausen velocity profile at the vessel boundary. The afferent vessels (two carotids and two vertebrals) are forced with a canine physiologic pressure signature corresponding to an aortic site. The network associated with each main efferent artery of the circle is represented by a single vessel containing an appropriate amount of resistance so that the mean flow through the system is distributed in accordance with the weight of brain irrigated by each vessel as determined from a steady flow model of the same network. This resistance is placed a quarter wave-length downstream from the heart to insure proper reflection from the terminations, where the quarter wavelength is determined using the frequency corresponding to the first minimum on an input impedance-frequency diagram obtained at the heart. Computer results are given as time histories of pressure and flow at any model nodal point starting from initial conditions of null flow and constant pressure throughout the model. Variations in these pressure and flow distributions caused by the introduction of pathologic situations into the model illustrate the efficacy of the simulation and of the circle in equalizing and redistributing flows in abnormal situations.     

On Vessel Member Differentiation in the Bean (Phaseolus vulgaris L.)

Certain ultrastructural features of vessel member differentiationwere examined in the primary xylem of petiole of bean (Phaseolusvulgaris L.). The cells used had helical secondary wall thickeningsand simple perforation plates. The primary cell wall increasesin thickness before the helices of secondary wall develop. Ina common wall between two vessel members of different ages,theprimary thickening occurs first in the older cell so thatfor a time the middle lamella is located closer to the youngercell rather than medianly. Apparently the helix is depositedafter the primary wall of a given cell reaches maximum thickness.The perforation of the end wall is preceded by primary thickeningof the part of the wall that is later removed. The marginalregion remains relatively thin and becomes covered with a rimof secondary wall. Vesicles with fibrous content appear nearthe surface within the end wall shortly before the perforationoccurs. A highly vacuolated protoplast with a much enlargednucleus and numerous organdIes is present during cell wall differentiation.After that process is completed, the protoplast disintegratesand the primary wall bearing the helix is hydrolysed where itis exposed to the cell lumen and, under certain conditions,also under the secondary wall.     

Cell-free plasma layer in cerebral microvessels.

Two diameters of vessel and red cell column in cerebral microvessels (> 29.8 microns in diameter) of cat were measured together with red cell velocity, using a two fluorescent tracer method. A fluorescein isothiocyanate (FITC)-labeled red cell was adopted as a flow tracer to measure the cell velocity with a dual window technique. Based on the fluorescence image, the red cell column diameter was measured. Plasma was stained with rhodamine-B isothiocyanate (RITC)-labeled dextran to measure the vessel diameter. The thickness of the cell-free plasma layer could be determined from the difference of the two diameters. The obtained thickness of the cell-free layer was not described by a simple function of vessel diameter or red cell velocity; it was dependent on the pseudo shear rate defined by the ratio of cell velocity to vessel radius. The layer thickness increased with a decrease in the pseudo shear rate.     

The effect of vessel element structure on element conductivity

Summary A number of structural variables influence the conductivity of simple and scalariform perforation plates, and of vessel lumina. Using a previously developed computer model, the effects on conductivity of over 8,000 permutations of different lumen radii, perforation plate angles, perforation plate rim widths, scalariform slit pore heights, and scalariform bar thicknesses are considered. By taking advantage of basic patterns of similarity in the data, and by using scaling techniques, it has proved possible to calculate a series of factors which may be used to predict the conductivity of a vessel element or perforation plate of known dimensions. A number of previous workers have sought relationships between element structure and evolutionary or adaptive trends. Some important variables have been ignored in these studies in the past.     

Computational fluid dynamic studies of leukocyte adhesion effects on non-Newtonian blood flow through microvessels

The study of the effect of leukocyte adhesion on blood flow in small vessels is of primary interest to understand the resistance changes in venular microcirculation. Available computational fluid dynamic studies provide information on the effect of leukocyte adhesion when blood is considered as a homogeneous Newtonian fluid. In the present work we aim to understand the effect of leukocyte adhesion on the non-Newtonian Casson fluid flow of blood in small venules; the Casson model represents the effect of red blood cell aggregation. In our model the blood vessel is considered as a circular cylinder and the leukocyte is considered as a truncated spherical protrusion in the inner side of the blood vessel. The cases of single leukocyte adhesion and leukocyte pairs in positions aligned along the same side, and opposite sides of the vessel wall are considered. The Casson fluid parameters are chosen for cat blood and human blood and comparisons are made for the effects of leukocyte adhesion in both species. Numerical simulations demonstrated that for a Casson fluid with hematocrit of 0.4 and flow rate Q = 0.072 nl/s, a single leukocyte increases flow resistance by 5% in a 32 microns diameter and 100 microns long vessel. For a smaller vessel of 18 microns, the flow resistance increases by 15%.     

细枝木麻黄导管分子及穿孔板解剖学研究

运用细胞图象分析系统和显微照相的方法对细枝木麻黄(CasuarinacunninghamianaMiq.)次生木质部导管分子进行了观察研究。细枝木麻黄次生木质部导管分子有3种类型,即两端具尾导管、一端具尾导管和无尾导管。导管分子穿孔板有4种类型:两端均为梯状穿孔板、一端为单穿孔板,另一端为梯状穿孔板、两端均为单穿孔板、一梯状穿孔板与一单穿孔板位于同一端壁两侧相互对应以及一些过渡类型穿孔板。根据观察结果,分析了各类型穿孔板之间的演化关系。