Cellular-level near-wall unsteadiness of high-hematocrit erythrocyte flow using confocal μPIV

In hemodynamics, the inherent intermittency of two-phase cellular-level flow has received little attention. Unsteadiness is reported and quantified for the first time in the literature using a combination of fluorescent dye labeling, time-resolved scanning confocal microscopy, and micro-particle image velocimetry (μPIV). The near-wall red blood cell (RBC) motion of physiologic high-hematocrit blood in a rectangular microchannel was investigated under pressure-driven flow. Intermittent flow was associated with (1) the stretching of RBCs as they passed through RBC clusters with twisting motions; (2) external flow through local obstacles; and (3) transitionary rouleaux formations. Velocity profiles are presented for these cases. Unsteady flow clustered in local regions. Extra-cellular fluid flow generated by individual RBCs was examined using submicron fluorescent microspheres. The capabilities of confocal μPIV post-processing were verified using synthetic raw PIV data for validation. Cellular interactions and oscillating velocity profiles are presented, and 3D data are made available for computational model validation.     

Electrical classification of single red blood cell deformability in high-shear microchannel flows

A sensor that can efficiently and sequentially measure the deformability of individual red blood cell (RBC) flowing along a microchannel is described. Counter-electrode-type microsensors are attached to the channel bottom wall, and as RBCs pass between the electrodes, the time series of the electric resistance is measured. An RBC is deformed by the high shear flow to a degree dependent upon its elastic modulus. Hence, the profile of the resistance, which is unique to the shape of the RBC, can be analyzed to obtain the deformability of each cell. First, theoretical and experimental analyses were conducted to identify the specific AC frequency at which the effect of the electric double layer formed on the electrode surface is minimized. Measurements were then conducted upon samples of normal human RBCs and glutaraldehyde-treated (rigidified) RBCs to evaluate the feasibility of the present method. In addition, simultaneous visualization of RBC deformation was performed using a high-speed camera. Normal RBCs were observed to have a degree of deformation index (DI) of around 0.57, whereas the rigidified RBCs was DI = 0 in the microchannel. The experimental measurements showed a strong correlation between the half-width of the maximum of the resistance distribution and the DI of the RBC.     

A lattice Boltzmann fictitious domain method for modeling red blood cell deformation and multiple‐cell hydrodynamic interactions in flow

To model red blood cell (RBC) deformation and multiple‐cell interactions in flow, the recently developed technique derived from the lattice Boltzmann method and the distributed Lagrange multiplier/fictitious domain method is extended to employ the mesoscopic network model for simulations of RBCs in flow. The flow is simulated by the lattice Boltzmann method with an external force, while the network model is used for modeling RBC deformation. The fluid–RBC interactions are enforced by the Lagrange multiplier. To validate parameters of the RBC network model, stretching tests on both coarse and fine meshes are performed and compared with the corresponding experimental data. Furthermore, RBC deformation in pipe and shear flows is simulated, revealing the capacity of the current method for modeling RBC deformation in various flows. Moreover, hydrodynamic interactions between two RBCs are studied in pipe flow. Numerical results illustrate that the leading cell always has a larger flow velocity and deformation, while the following cells move slower and deform less.Copyright © 2013 John Wiley & Sons, Ltd.     

A study on thrombus influenced red blood cell flow in microvasculature using moving particle semi-implicit method

Microvasculature plays a decisive role on the normal operation of the human body. Previous studies have shown that the causes of microvascular hemolytic anemia and other diseases are closely related to the interaction between micro-thrombi and RBCs. The movement and deformation of Red Blood Cells (RBCs) in microvasculature with hemicyclic micro-thrombi of different sizes on the wall are simulated based on the Moving Particle Semi-implicit method (MPS) and the spring network model of RBCs membrane. Simulation of a single RBC passing the straight blood vessel indicates the strong squeeze of the RBC caused by the thrombus, which leads to a 38.5% increasing of the RBC velocity and a greater deformation, and such squeeze effect is positively related with the size of the thrombus. When two RBCs pass through the straight blood vessel with two thrombi on the both sidewalls, the deformation of the RBCs first increases and then decreases. Results show that when the axial position between the two thrombi is 10 × d₀ different, the deformation of RBCs reaches the maximum of 3.10 (upper) and 2.79 (lower), respectively. When two side-by-side RBCs pass through a bifurcated blood vessel with a sidewall thrombus, the velocity and deformation of RBCs are greatly affected by the thrombus. When the thrombus radius changes from 0 × d₀ to 20 × d₀, the peak velocities of the two cells increase by 51.6% (upper) and 67.9% (lower), respectively.     

Numerical simulation of the transient shape of the red blood cell in microcapillary flow

The transient shape of a red blood cell (RBC) in a microcapillary flow is simulated under different initial conditions, including various axis orientations and centroid locations, using the LBM-DLM/FD method, which is derived from the lattice Boltzmann method and the distributed Lagrange multiplier/fictitious domain method. Although the terminal velocity is not sensitive to the initial configuration, the evolution of the velocity and the shape are determined by the initial conditions. The parachute and the slipper shape are the most probable shapes for a deformed RBC in the flow. An RBC with an initial axis orientation of 90 degrees exhibits a more complicated deformation. RBCs have a tendency to move to the centerline of a tube if an offset between the RBC centroid and the centerline exists. Our numerical results are validated by experiments, and some details beyond the experiment are provided.     

Efficient viscosity contrast calculation for blood flow simulations using the lattice Boltzmann method

The lattice Boltzmann method (LBM) combined with the immersed boundary method is a common tool to simulate the movement of red blood cel ls (RBCs) through blood vessels. With very few exceptions, such simulations neglect the difference in viscosities between the hemoglobin solution inside the cells and the blood plasma outside, although it is well known that this viscosity contrast can severely affect cell deformation. While it is easy to change the local viscosity in LBM, the challenge is to distinguish whether a given lattice point is inside or outside the RBC at each time step. Here, we present a fast algorithm to solve this issue by tracking the membrane motion and computing the scalar product between the local surface normal and the distance vector between the closest LBM lattice point and the surface. This approach is much faster than, for example, the ray-casting method. With the domain tracking applied, we investigate the shape transition of a RBC in a microchannel for different viscosity contrast and validate our method by comparing with boundary-integral simulations.     

基于微流体装置的微血管网内红细胞流动和分布特性的研究简

实体肿瘤血管具有扩张、扭曲、不规则分支以及分支间连接絮乱等特征. 为了考察这些特征对血液流动的影响,将肿瘤血管简化为垂直相互贯通的微血管网,借助微流体实验装置,以一定浓度的红细胞悬液作为流动介质,研究红细胞在微血管网中的流动和分布特性. 具体实验方案如下：首先,采用软刻蚀技术,在聚二甲基硅氧烷（polydimethylsiloxane, PDMS）上加工出微血管网;然后,采用微注射泵控制微血管网入口处的红细胞悬液流量,使用倒置显微镜和高速摄影系统观察并记录实验过程;最后,通过Matlab 软件包Piv-lab 及高速摄影配套软件对获得的视频图像进行处理,提取红细胞在微血管网中的流动和分布数据. 数据处理结果显示,红细胞在微血管网中的流动和分布特性受悬液内的红细胞压积（hematocit, Hct）的影响. 红细胞随悬液Hct 的不同呈现2 种运动轨迹：一种为仅沿着轴向微管道流动;另一种是从轴向微管道流入并穿过径向微管道,再进入另一侧的轴向微管道. 另外,入口流量相同时,红细胞在微血管网中的流动速度随Hct 变化呈现不同,Hct 为3% 和5% 的红细胞速度要明显高于Hct 为1% 的红细胞速度.     

基于微流体装置的微血管网内红细胞流动和分布特性的研究

实体肿瘤血管具有扩张、扭曲、不规则分支以及分支间连接絮乱等特征. 为了考察这些特征对血液流动的影响,将肿瘤血管简化为垂直相互贯通的微血管网,借助微流体实验装置,以一定浓度的红细胞悬液作为流动介质,研究红细胞在微血管网中的流动和分布特性. 具体实验方案如下:首先,采用软刻蚀技术,在聚二甲基硅氧烷（polydimethylsiloxane, PDMS）上加工出微血管网;然后,采用微注射泵控制微血管网入口处的红细胞悬液流量,使用倒置显微镜和高速摄影系统观察并记录实验过程;最后,通过Matlab 软件包Piv-lab 及高速摄影配套软件对获得的视频图像进行处理,提取红细胞在微血管网中的流动和分布数据. 数据处理结果显示,红细胞在微血管网中的流动和分布特性受悬液内的红细胞压积（hematocit, Hct）的影响. 红细胞随悬液Hct 的不同呈现2 种运动轨迹:一种为仅沿着轴向微管道流动;另一种是从轴向微管道流入并穿过径向微管道,再进入另一侧的轴向微管道. 另外,入口流量相同时,红细胞在微血管网中的流动速度随Hct 变化呈现不同,Hct 为3% 和5% 的红细胞速度要明显高于Hct 为1% 的红细胞速度.      

Multiphase non‐Newtonian effects on pulsatile hemodynamics in a coronary artery

Hemodynamic stresses are involved in the development and progression of vascular diseases. This study investigates the influence of mechanical factors on the hemodynamics of the curved coronary artery in an attempt to identify critical factors of non‐Newtonian models. Multiphase non‐Newtonian fluid simulations of pulsatile flow were performed and compared with the standard Newtonian fluid models. Different inlet hematocrit levels were used with the simulations to analyze the relationship that hematocrit levels have with red blood cell (RBC) viscosity, shear stress, velocity, and secondary flow. Our results demonstrated that high hematocrit levels induce secondary flow on the inside curvature of the vessel. In addition, RBC viscosity and wall shear stress (WSS) vary as a function of hematocrit level. Low WSS was found to be associated with areas of high hematocrit. These results describe how RBCs interact with the curvature of artery walls. It is concluded that although all models have a good approximation in blood behavior, the multiphase non‐Newtonian viscosity model is optimal to demonstrate effects of changes in hematocrit. They provide a better stimulation of realistic blood flow analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

Study on the packed volume and the void ratio of idealized human red blood cells using a ?nite-discrete element method

Numerical simulations are performed to examine the packing behavior of human red blood cells(RBCs). A combined ?nite-discrete element method(FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The packed volume and the void ratio of a large number of randomly packed RBCs are clari?ed,and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the ?at or thick cells used in this study. Such information is bene?cial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.     

Thermal transport and performance analysis of pressure- and electroosmotically-driven liquid flow microchannel heat sink with wavy wall

The present study investigates the microchannel heat sinks (MCHSs) with smooth and wavy wall for pure electroosmotic flow (EOF), pressure-driven flow (PDF) and combined electroosmotic and pressure-driven flow (PDF + EOF). A three-dimensional numerical analysis was performed for EOF, PDF and combined flow (PDF + EOF) through finite volume analysis. The EOF was combined with the PDF to enhance the flow rate and to reduce the thermal resistance of the MCHS. The effect of wall waviness on electroosmosis and thermal performance of the MCHS was critically investigated for flow rate, friction factor, Nusselt number, thermal resistance and pumping power. The design variables related to the wavelength and amplitude and width of microchannel were investigated for their effect on the overall thermal performance and pumping power. The electroosmosis not only increases the flow rate but also suppresses the secondary flow developed due to the topology of the microchannel walls. The non-uniformity of the velocity and temperature is reduced due to the application of the EOF in a PDF and combined flow (PDF + EOF).     

RESISTANCE EFFECT OF ELECTRIC DOUBLE LAYER ON LIQUID FLOW IN MICROCHANNEL

Poisson-Boltzrnann equation for EDL (electric double layer) and Navier-Stokes equation for liquid flows were numerically solved to investigate resistance effect of electric double layer on liquid flow in microchannel. The dimension analysis indicates that the resistance effect of electric double layer can be estimated by an electric resistance number, which is proportional to the square of the liquid dielectric constant and the solid surface zeta potential, and inverse-proportional to the liquid dynamic viscosity, electric conductivity and the square of the channel width. An "electric current density balancing" (ECDB) condition was proposed to evaluate the flow-induced streaming potential, instead of conventional "electric current balancing" (ECB) condition which may induce spurious local backflow in neighborhood of the solid wall of the microchannel. The numerical results of the flow rate loss ratio and velocity profile are also given to demonstrate the resistance effect of electric double layer in microchannel.     

Effects of deformability of RBCs on their dynamics and blood flow passing through a stenosed microvessel: an immersed boundary-lattice Boltzmann approach

In this paper, the motion of high deformable (healthy) and low deformable (sick) red blood cells in a microvessel with and without stenosis is simulated using a combined lattice Boltzmann-immersed boundary method. The RBC is considered as neo-Hookean elastic membrane with bending resistance. The motion and deformation of the RBC under different values of the Reynolds number are evaluated. In addition, the variations of blood flow resistance and time-averaged pressure due to the motion and deformation of the RBC are assessed. It was found that a healthy RBC moves faster than a sick one. The apparent viscosity and blood flow resistance are greater for the case involving the sick RBC. Blood pressure at the presence of stenosis and low deformable RBC increases, which is thought of as the reason of many serious diseases including cardiovascular diseases. As the Re number increases, the RBC deforms further and moves easier and faster through the stenosis. The results of this study were compared to the available experimental and numerical results, and good agreements were observed.     

Transient rheology in a new type of couette apparatus. Application to blood

By using our new air-bearing viscometer different types of transient flow can be studied; in the present work this viscometer was specifically applied to non-Newtonian blood suspensions. To observe the influence of both the aggregation and the deformation of red blood cells (RBCs), different concentrations of fibrinogen and dextran were used: the suspended RBCs were simply washed or rigidified with diamide. From the data three rheological parameters were determined, two of which are relative to the behavior at low and at high shear gradients, respectively. Their values were related to the theory of Taylor, and the internal viscosity of RBCs was estimated to be around 3 cp.     

A novel interface‐tracking method based on Lagrangian particles for deformation analysis of a red blood cell in a capillary

A novel efficient interface‐tracking method is developed to gain an insight into the interface in a multiphase or multifluid system, called the modified particle binary level set (MPBLS) method, in which the binary level set function is defined to distinguish the different phases or fluids and further modified by Lagrangian particles scattered along the interface for achieving higher accuracy. The validation of the MPBLS method is carried out first by simulating the free motion of a red blood cell (RBC) in the rotating, shear and Poiseuille flows, respectively. Subsequently, further validations are performed by comparing with the experimental and numerical results published previously. As one of important applications, the MPBLS method is employed to investigate the deformation behaviors of RBCs with different shapes in a capillary. The simulations show that the healthy RBC gradually changes the geometric shape from a biconcave to a steady parachute shape. It is thus guaranteed that the RBC successfully traverses through the smaller capillaries compared with undeformed RBC. However, the unhealthy RBC with the circular or elliptical shape has different deformation behaviors, in which the steady parachute shape is much less concave at the rear and more convex in the front. Copyright © 2011 John Wiley & Sons, Ltd.     

Ethanol–CO2 two-phase flow in diverging and converging microchannels

The present study investigates experimentally two-phase flow patterns and pressure drop of ethanol and CO₂ in a converging or diverging rectangular microchannel. The two-phase flow pattern visualization is made possible using a high speed video camera. The increased superficial gas velocity due to the acceleration effect and the large pressure drop in a converging channel may result in the elongation of bubbles in slug flow, while the decreased superficial velocity owing to the deceleration effect and the possible pressure rise in the diverging channel may cause shortening of bubbles in slug flow significantly. For both types of channel, the collision and merger of two consecutive bubbles may take place and result in necking of bubbles. Two-phase flow pressure drop in the converging microchannel increases approximately linearly with the increasing liquid or gas flow rate with the frictional pressure drop being the major contributor to the channel pressure drop. In the diverging microchannel, the deceleration effect results in the pressure rise and counteracts the frictional pressure drop. Consequently, for low liquid flow rates the channel pressure drop increases only slightly with the gas flow rate while it is low and a reversed trend appears while it is high. For high liquid flow rates the effect of increasing gas flow rate on channel pressure drop is much more significant; a more significant reverse trend of the effect of gas flow rate is present in the region of high gas flow rates. The two-phase frictional multiplier in the converging or diverging microchannel is quite insensitive to the liquid flow rate and can be fitted very well within ±15% based on the Lockhart–Martinelli equation with a modified Chisholm parameter for the diverging microchannel and together with a modified coefficient for the X⁻² term for the converging microchannel.     

Modeling of micropipette aspiration and optical tweezers stretching of erythrocytes with or without Malaria parasite

The erythrocytes play an important role in the human body. The healthy erythrocytes can undergo extremely large deformation while passing through small capillaries. Their infection by Malaria Plasmodium falcipurum (P.f.) will lead to capillary blockage and blood flow obstruction. Many experimental and computational methods have been applied to study the increase in stickiness and decrease in deformability of the Malaria (P.f.) infected erythrocytes. The novelty of this paper lies in the establishment of an multi-component model for investigating mechanical properties of Malaria (P.f.) infected erythrocytes, especially of their enclosed parasites. Finite element method was applied to simulate the erythrocytes’ deformation in micropipette aspiration and optical tweezers stretching using the computational software ABAQUS. The comparisons between simulations and experiments were able to quantitatively conclude the effects of stiffness and stickiness of the parasitophorous vacuole membrane on the cells’ deformation, which could not be obtained from experiments directly.     

Hybrid continuum–coarse-grained modeling of erythrocytes

The red blood cell (RBC) membrane is a composite structure, consisting of a phospholipid bilayer and an underlying membrane-associated cytoskeleton. Both continuum and particle-based coarse-grained RBC models make use of a set of vertices connected by edges to represent the RBC membrane, which can be seen as a triangular surface mesh for the former and a spring network for the latter. Here, we present a modeling approach combining an existing continuum vesicle model with a coarse-grained model for the cytoskeleton. Compared to other two-component approaches, our method relies on only one mesh, representing the cytoskeleton, whose velocity in the tangential direction of the membrane may be different from that of the lipid bilayer. The finitely extensible nonlinear elastic (FENE) spring force law in combination with a repulsive force defined as a power function (POW), called FENE–POW, is used to describe the elastic properties of the RBC membrane. The mechanical interaction between the lipid bilayer and the cytoskeleton is explicitly computed and incorporated into the vesicle model. Our model includes the fundamental mechanical properties of the RBC membrane, namely fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. We present three simulation examples to demonstrate the effectiveness of this hybrid continuum–coarse-grained model for the study of RBCs in fluid flows.     

Numerical simulation of lateral migration of red blood cells in Poiseuille flows

A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the RBC rheology in two‐dimensional Poiseuille flows using an immersed boundary method. The lateral migration properties of the cells in Poiseuille flows have been investigated. The simulation results show that the rate of migration toward the center of the channel depends on the swelling ratio and the deformability of the cells. We have also combined the above methodology with a fictitious domain method to study the motion of RBCs in a two‐dimensional micro‐channel with a constriction with an application to blood plasma separation. Copyright © 2010 John Wiley & Sons, Ltd.     

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

A mathematical study is developed for the electro-osmotic flow of a nonNewtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer(EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelength parameter, the plug flow width, the Helmholtz-Smoluchowski velocity, and the Joule heating on the normalized temperature, the velocity, the pressure gradient, the volumetric flow rate, and the Nusselt number for heat transfer are evaluated in detail using graphs. The analysis provides important findings regarding heat transfer in electroosmotic flows through a wavy microchannel.