Fluid particle diffusion through high-hematocrit blood flow within a capillary tube

Fluid particle diffusion through blood flow within a capillary tube is an important phenomenon to understand, especially for studies in mass transport in the microcirculation as well as in solving technical issues involved in mixing in biomedical microdevices. In this paper, the spreading of tracer particles through up to 20% hematocrit blood, flowing in a capillary tube, was studied using a confocal micro-PTV system. We tracked hundreds of particles in high-hematocrit blood and measured the radial dispersion coefficient. Results yielded significant enhancement of the particle diffusion, due to a micron-scale flow-field generated by red blood cell motions. By increasing the flow rate, the particle dispersion increased almost linearly under constant hematocrit levels. The particle dispersion also showed near linear dependency on hematocrit up to 20%. A scaling analysis of the results, on the assumption that the tracer trajectories were unbiased random walks, was shown to capture the main features of the results. The dispersion of tracer particles was about 0.7 times that of RBCs. These findings provide good insight into transport phenomena in the microcirculation and in biomedical microdevices.     

Estimation of viscosity from passage time of liquids flowing through a microchannel array

Recently, a microchannel flow analyzer (MC-FAN) has been used to study the flow properties of blood. However, the correlation between blood passage time measured by use of the MC-FAN and hemorheology has not been clarified. In this study, a simple model is proposed for estimation of liquid viscosity from the passage time t _p of liquids. The t _p data for physiological saline were well represented by the model. According to the model, the viscosity of Newtonian fluids was estimated reasonably well from the t _p data. For blood samples, although the viscosity $ \eta_{\text{mc}} $ estimated from t _p was shown to be smaller than the viscosity $ \eta_{{450{\text{s}}^{ - 1} }} $ measured by use of a rotatory viscometer at a shear rate of 450 s^?1, $ \eta_{\text{mc}} $ was correlated with $ \eta_{{450{\text{s}}^{ - 1} }} $ . An empirical equation for estimation of $ \eta_{{450{\text{s}}^{ - 1} }} $ from $ \eta_{\text{mc}} $ of blood samples is proposed.     

Microcontinuum model for pulsatile blood flow through a stenosed tube

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

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.     

Oscillatory flow of blood in a stenosed artery

In order to understand the abnormal flow conditions of blood in a locally constricted blood vessel, the analytical results are obtained for the oscillatory flow of blood which behaves as a Newtonian fluid. It is here assumed that the surface roughness is cosine-shaped and the maximum height of the roughness is very small compared with the radius of the unconstricted tube. Numerical solutions are presented for the instantaneous flow rate, resistive impedance, wall shear stress and phase lag.     

Red blood cell regulation of microvascular tone through adenosine triphosphate

The matching of blood flow with metabolic need requires a mechanism for sensing the needs of the tissue and communicating that need to the arterioles, the ultimate controllers of tissue perfusion. Despite significant strides in our understanding of blood flow regulation, the identity of the O(2) sensor has remained elusive. Recently, the red blood cell, the Hb-containing O(2) carrier, has been implicated as a potential O(2) sensor and contributor to this vascular control by virtue of its concomitant carriage of millimolar amounts of ATP, which it is able to release when exposed to a low-O(2) environment. To evaluate this possibility, we exposed perfused cerebral arterioles to low extraluminal O(2) in the absence and presence of red blood cells or 6% dextran and determined both vessel diameter and ATP in the vessel effluent. Only when the vessels were perfused with red blood cells did the vessels dilate in response to low extraluminal O(2). In addition, this response was accompanied by a significant increase in vessel effluent ATP. These findings support the hypothesis that the red blood cell itself serves a role in determining O(2) supply to tissue.     

Simulation of a tumor cell flowing through a symmetric bifurcated microvessel

Biomechanics and Modeling in Mechanobiology - Microvessel bifurcations serve as the major sites of tumor cell adhesion and further extravasation. In this study, the movement, deformation, and...     

Red blood cell magnetophoresis

The existence of unpaired electrons in the four heme groups of deoxy and methemoglobin (metHb) gives these species paramagnetic properties as contrasted to the diamagnetic character of oxyhemoglobin. Based on the measured magnetic moments of hemoglobin and its compounds, and on the relatively high hemoglobin concentration of human erythrocytes, we hypothesized that differential migration of these cells was possible if exposed to a high magnetic field. With the development of a new technology, cell tracking velocimetry, we were able to measure the migration velocity of deoxygenated and metHb-containing erythrocytes, exposed to a mean magnetic field of 1.40 T and a mean gradient of 0.131 T/mm, in a process we call cell magnetophoresis. Our results show a similar magnetophoretic mobility of 3.86 x 10(-6) mm(3) s/kg for erythrocytes with 100% deoxygenated hemoglobin and 3.66 x 10(-6) mm(3) s/kg for erythrocytes containing 100% metHb. Oxygenated erythrocytes had a magnetophoretic mobility of from -0.2 x 10(-6) mm(3) s/kg to +0.30 x 10(-6) mm(3) s/kg, indicating a significant diamagnetic component relative to the suspension medium, in agreement with previous studies on the hemoglobin magnetic susceptibility. Magnetophoresis may open up an approach to characterize and separate cells for biochemical analysis based on intrinsic and extrinsic magnetic properties of biological macromolecules.     

A computational model for the transit of a cancer cell through a constricted microchannel

We propose a three-dimensional computational model to simulate the transient deformation of suspended cancer cells flowing through a constricted microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane, and its nucleus as a smaller stiffer capsule. The cell deformation and its interaction with the suspending fluid are solved through a well-tested immersed boundary lattice Boltzmann method. To identify a minimal mechanical model that can quantitatively predict the transient cell deformation in a constricted channel, we conduct extensive parametric studies of the effects of the rheology of the cell membrane, cytoplasm and nucleus and compare the results with a recent experiment conducted on human leukaemia cells. We find that excellent agreement with the experiment can be achieved by employing a viscoelastic cell membrane model with the membrane viscosity depending on its mode of deformation (shear versus elongation). The cell nucleus limits the overall deformation of the whole cell, and its effect increases with the nucleus size. The present computational model may be used to guide the design of microfluidic devices to sort cancer cells, or to inversely infer cell mechanical properties from their flow-induced deformation.

     

Pulsatile flow of blood through a stenosed tube: effect of periodic body acceleration and a magnetic field

A proper understanding of the interactions of body acceleration and a magnetic field with blood flow could be useful in the diagnosis and treatment of some health problems. In the work reported in this paper we studied the pulsatile flow of blood through stenosed arteries, including the effects of body acceleration and a magnetic field. Blood is regarded as an electrically conducting, incompressible, couple-stress fluid in the presence of a magnetic field along the radius of the tube. The effects of the body acceleration and the magnetic field on the axial velocity, flow rate, and fluid acceleration were obtained analytically by use of the Hankel transform and the Laplace transform. Velocity variations under different conditions are shown graphically. The results have been compared with those from other theoretical models, and are in good agreement. Finally, our mathematical model gives a simple velocity expression for blood flow so it will help not only in the field of physiological fluid dynamics but will also help medical practitioners with elementary knowledge of mathematics.     

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.     

Red blood cell membrane defects

We present an overview of the currently known molecular basis of red cell membrane disorders. A detailed discussion of the structure of the red cell membrane and the pathophysiology and clinical aspects of its disorders is reported. Generally speaking, hereditary spherocytosis (HS) results from a loss of erythrocyte surface area. The mutations of most cases of HS are located in the following genes: ANK1, SPTB, SLC4A1, EPB42 and SPTA1, which encode for ankyrin, spectrin beta-chain, the anion exchanger 1 (band 3), protein 4.2 and spectrin alpha-chain, respectively. Hereditary elliptocytosis (HE) reflects a diminished elasticity of the skeleton. Its aggravated form, hereditary pyropoikilocytosis (HPP), implies that the skeleton undergoes further destabilization. The mutations responsible for HE and HPP, lie in the SPTA1 and SPTB gene, and in the EPB41 gene encoding protein 4.1. Allele alpha LELY is a common polymorphic allele, which plays the role of an aggravating factor when it occurs in trans of an elliptocytogenic allele of the SPTA1 gene. Southeast Asian ovalocytosis derives from a change in band 3. The genetic disorders of membrane permeability to monovalent cations required a positional cloning approach. In this respect, channelopathies represent a new frontier in the field. Dehydrated hereditary stomatocytosis (DHS) was shown to belong to a pleiotropic syndrome: DHS + fetal edema + pseudohyperkalemia, which maps 16q23-24. Splenectomy is strictly contraindicated in DHS and another disease of the same class, overhydrated hereditary stomatocytosis, because it increases the risk of thromboembolic accidents.     

Red blood cell dielectrophoresis in axisymmetric fields

Dielectrophoretic velocities of human red blood cells in an axisymmetric field were measured as a function of the applied voltage and the distance from the axis of symmetry. The voltage of the alternating electric field (frequency 2 MHz), applied between two concentric cylindrical metal electrodes (outer and inner radii 0.24 and 1 mm, respectively), was varied up to 19 V. Two kinds of mediums were used: (a) 90% of 2.1% glycine solution and 10% of 5.5% glucose solution and (b) 5.4% sorbitol solution. The results have shown that in both mediums the cell velocities are proportional to the square of the applied voltage and inversely proportional to the cube of the distance from the axis of symmetry, as predicted by the theory. The coefficient of proportionality (dielectrophoretic coefficient) is on the order of 10(-25) A2S4kg-1. It depends on the donor of red blood cells and might be used for diagnostic purposes. These results will be used in future investigations of membrane adhesion, stability and fusion.     

Red blood cell dielectrophoresis in axisymmetric fields

Dielectrophoretic velocities of human red blood cells in an axisymmetric field were measured as a function of the applied voltage and the distance from the axis of symmetry. The voltage of the alternating electric field (frequency 2 MHz), applied between two concentric cylindrical metal electrodes (outer and inner radii 0.24 and 1 mm, respectively), was varied up to 19 V. Two kinds of mediums were used: (a) 90% of 2.1% glycine solution and 10% of 5.5% glucose solution and (b) 5.4% sorbitol solution. The results have shown that in both mediums the cell velocities are proportional to the square of the applied voltage and inversely proportional to the cube of the distance from the axis of symmetry, as predicted by the theory. The coefficient of proportionality (dielectrophoretic coefficient) is on the order of 10⁻²⁵ A²s⁴kg⁻¹. It depends on the donor of red blood cells and might be used for diagnostic purposes. These results will be used in future investigations of membrane adhesion, stability and fusion.     

Three-dimensional numerical simulations of flow through a stenosed coronary bypass

This work analyzes the flow patterns at the anastomosis of a stenosed coronary bypass. Three-dimensional numerical simulations are performed using a finite elements method. We consider a geometrical model of the host coronary artery with and without a 75% severity stenosis for three different locations from the anastomosis. The flow features - velocity profiles, secondary motions and wall shear stresses - are compared for different configurations of the flow rate and of the distance of the anastomosis from the site of occlusion (called distance of grafting). The combination of the junction flow effects - counter rotating vortices - with the stenosis effects - confined jet flow - is particularly important when the distance of grafting is short. Given that the residual flow issued from the pathologic stenosis being non-negligible after two weeks grafting, models without stenosis cannot predict the evolution of the wall shear stress in the vicinity of the anastomosis.