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.     

Peristaltic flow of a couple stress fluid in an asymmetric channel

This paper presents an analysis of the peristaltic flow of a couple stress fluid in an asymmetric channel. The asymmetric nature of the flow is introduced through the peristaltic waves of different amplitudes and phases on the channel walls. Mathematical modelling corresponding to a two-dimensional flow has been carried out. The flow analysis is presented under long wavelength and low Reynolds number approximations. Closed form solutions for the axial velocity, stream function and the axial pressure gradient are given. Numerical computations have been carried out for the pressure rise per wavelength, friction forces and trapping. It is noted that there is a decrease in the pressure when the couple stress fluid parameter increases. The variation of the couple stress fluid parameter with the size of the trapped bolus is also similar to that of pressure. Furthermore, the friction force on the lower channel wall is greater than that on the upper channel wall.     

High efficiency Hall effect micro-biosensor platform for detection of magnetically labeled biomolecules

Detection of magnetically labeled biomolecules using micro-Hall biosensors is a promising method for monitoring biomolecular recognition processes. The measurement efficiency of standard systems is limited by the time taken for magnetic beads to reach the sensing area of the Hall devices. Here, micro-current lines were integrated with Hall effect structures to manipulate the position of magnetic beads via field gradients generated by localized currents flowing in the current lines. Beads were accumulated onto the sensor surface within seconds of passing currents through the current lines. Real-time detection of magnetic beads using current lines integrated with Hall biosensors was achieved. These results are promising in establishing Hall biosensor platforms as efficient and inexpensive means of monitoring biomolecular reactions for medical applications.     

Peristaltic motion of Phan–Thien–Tanner fluid in the presence of slip condition

This investigation considers the peristaltic flow of a Phan–Thien–Tanner fluid in the presence of slip condition and induced magnetic field. By use of the long wavelength and low Reynolds number approximations, closed form series solutions for stream function, pressure gradient, magnetic force function, axial induced magnetic field, and current density were obtained. The pressure gradient and frictional forces per wavelength were computed by numerical integration. The velocity slip condition in terms of shear stress is taken into account. Graphical results show the comparison between no-slip and viscous fluid cases. Pumping and trapping phenomena are discussed.     

Two-layered blood flow in stenosed tubes for different diseases

A two-fluid model for blood flow through a stenosed tube has been developed. The model consists of a core (suspension of RBCs) and peripheral plasma layer. The core is assumed to be represented by a polar fluid and the plasma layer by a Newtonian fluid. The flow is assumed to be steady and laminar, and the fluids incompressible. The flow variables are computed for normal blood and for the cases of polycythemia, plasma cell dyscrasias and for Hb SS diseases. Resistance to flow has been computed for different stenosis length and for different stenosis height. Shear stress distribution along the axial distance has been computed for different stenosis height. The impact of size effects (particle size to tube diameter) on blood diseases is discussed.     

Microcontinuum approach to the pulsatile flow in tubes with and without longitudinal vibration

A fully developed pulsatile flow in a circular rigid tube is analysed by a microcontinuum approach. Solutions for radial variation of axial velocity and cell rotational velocity across the tube are obtained using the momentum integral method. Simplified forms of the solutions are presented for the relevant physiological data. Marked deviations in the results are observed when compared to a Newtonian fluid model. It is interesting to see that there is sufficient reduction in the mass flow rate, phase lag and friction due to the micropolar character of the fluid.     

Axial flow velocity patterns in a pulmonary artery model with varying degrees of valvular pulmonic stenosis: pulsatile in vitro studies

With the advent of noninvasive clinical techniques which can measure blood flow velocities (Doppler ultrasound), it is suggested that a fundamental knowledge of the axial flow velocity patterns in the pulmonary artery, and the changes caused by stenosis, may be used to support accurate diagnosis of valvular pulmonic stenosis. The present study was designed to characterize the axial flow velocity patterns in an in vitro model of a human adult pulmonary artery with varying degrees of valvular pulmonic stenosis. A two-dimensional laser Doppler anemometer (LDA) system was used to map the flow fields in the main (MPA), left (LPA), and right (RPA) branches of the pulmonary artery model. The study was conducted in the Georgia Tech. right heart pulse duplicator system. It was observed that the axial flow velocity patterns in the MPA and the LPA change dramatically with increasing degree of valvular stenosis. This indicates that the axial flow velocity patterns in these two branches are strongly influenced by the degree of valvular stenosis. The axial flow velocity patterns in the RPA, however, do not change much with varying degrees of valvular stenosis, indicating that the axial flow fields in the RPA are mainly influenced by the geometry of the bifurcation. It may be concluded therefore, that the changes in the axial flow velocity patterns in the MPA and LPA (rather than in the RPA) could be sensitive and reliable indicators of the severity of the defect.     

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.     

An evaluation of a micropolar model for blood flow through an idealized stenosis

In this paper, the behavior of a viscous fluid described by Newtonian constitutive theory is compared with that predicted by a model based on micropolar continuum theory. The geometry chosen for this comparative analysis is a stenosis in which gradient effects should be pronounced. A range of boundary conditions for fluid microspin are considered. Although velocities and streamlines are found to be similar for the two continuum models, striking differences in shear stresses are revealed. These differences may be as high as 50% for vanishing microspin boundary conditions. Such significant discrepancies highlight the need for further study of higher order modeling of blood flow.     

The accuracy of magnetic resonance phase velocity measurements in stenotic flow

Nuclear magnetic resonance (MR) can be used to measure velocities in fluid flow using the technique of phase velocity mapping. Advantages of MR velocimetry include the simultaneous mapping of the entire flow field through a non-contacting, magnetic window. The phase velocity mapping technique assumes that velocity is constant over the measurement time (typically around 10 ms). For many fluid flows, this assumption is not valid. The current study showed that MR phase velocity measurements of velocity through stenotic flow can be in error by over 100% immediately upstream and downstream of the stenosis throat and by 20% far downstream of the throat in comparison with laser Doppler anemometer measurements taken at the same location. Highly turbulent flow also led to significant errors in velocity measurement. These errors can be attributed to several sources including low signal-to-noise ratio, additional phase shifts due to non-constant velocities, and non-stationary transit-time effects. Velocity measurement errors could be reduced to under 30% at all measurement locations through the use of MR sequences with high signal-to-noise ratios, low echo times, and thick slices.     

Blood flow through a stenosis in microcirculation

A theoretical and experimental study concerning two-component fluid pulsating flow through cylindrical ducts having a slight constriction is presented. The model corresponds to blood flows through small diameter vessels (smaller than 400 micron) affected by a singular stenosis. The theoretical approach is based on a asymptotical expansion of the stream function. The physical hypotheses used were based on findings from simultaneous visualization methods. The influence of geometrical, hydrodynamical and structural parameters is systematically examined and related to velocity profiles, hydrostatic pressure, surface stresses.     

Velocity field studies at surgically imposed arterial stenoses on the abdominal aorta in pigs

In order to describe velocity profiles and the size of deterministic and non-deterministic velocity disturbances at arterial stenoses, symmetrical and asymmetrical stenoses with intended area reductions of 50% (‘moderate’) and 85% (‘severe’) were applied on the abdominal aorta in six pigs. Blood velocities were registered by hot-film anemometry in 21 measuring points distributed across the vessel cross-sectional area in one pre-stenotic and three post-stenotic positions. Signal analysis included ensemble averaging, the high-pass filtering technique, and three-dimensional visualization. None of the stenoses affected the pre-stenotic velocity field. Downstream moderate stenoses flow separation and vortex formation were present. Moderate asymmetric stenoses induced turbulence in the post-stenotic velocity field. Immediately downstream of severe stenoses a prominent post-stenotic jet was present. Farther downstream, a multitude of coherent vortices and turbulence dominated the flow field. The transverse distribution of turbulence intensity parallelled with the peak systolic velocity profile, whereas transverse profiles of the relative turbulence intensity (turbulence intensity/mean velocity) revealed peak values in flow field locations with high velocity gradients. Velocity parameters for symmetric and asymmetric severe stenoses were highly comparable. However, the exact degree of stenosis was significantly higher for symmetrical (85%) than for asymmetrical (76%) stenoses. Therefore, recalling that stenosis severity strongly influences the development of velocity disturbances, this indicates that asymmetry of a stenosis is a predictor for blood velocity disturbances.     

Numerical study on the flow of a non-Newtonian fluid through an axisymmetric stenosis

The laminar steady flow of non-Newtonian fluid (biviscosity fluid) through an axisymmetric stenosis is calculated using the finite element methods. The flow pattern, the separation and reattachment points, and the distributions of pressure and shear stress at the wall are obtained. Then, the axial force acting on the stenosis is evaluated. It is suggested by the authors that this force can become one of the causes of post-stenotic dilatation. Calculated results show that the non-Newtonian property of blood weakens the distortion of flow pattern, pressure and shear stress at the wall associated with the stenosis and that the non-Newtonian property of blood decreases the axial force acting on the stenosis.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.     

The effects of slip velocity on a micropolar fluid through a porous channel with expanding or contracting walls

In this paper, a simple mathematical model depicting blood flow in the deforming porous channel is developed with an emphasis on the permeability property of the blood vessel and slip boundary based on Beavers and Joseph slip condition. In this study, the blood is represented by a micropolar fluid. With such an ideal model, the governing equations are reduced to ordinary ones by introducing suitable similar transformations. Homotopy analysis method is employed to obtain the expressions for velocity and microrotation fields. Graphs are sketched for some values of parameters such as slip coefficient and expansion ratio, and the associated dynamic characteristics are analysed in detail.     

Formation of a cylindrical ion beam in the field of an axisymmetric system of ring currents at a low Hall current

A study is made of the structure of an accelerating layer with a closed Hall current and the geometry of an ion beam in an external magnetic field created by an arbitrary axisymmetric system of ring currents under conditions such that the Hall current can be ignored. It is shown that the ion trajectories are perpendicular to the magnetron cutoff surface for electrons and that the cathode plasma boundary coincides with a magnetic field line. A magnetic field configuration is found in which the cutoff surface is a plane surface perpendicular to the axis of the system. It is shown that, for a small ratio of the gyroradius of the electrons (in terms of the maximum energy acquired by them in the layer) to the characteristic size of the structure, such a configuration provides sufficient means to ensure the formation of slightly converging ion beams or those that are essentially parallel to the system axis.     

Double-diffusion convective biomimetic flow of nanofluid in a complex divergent porous wavy medium under magnetic effects

We explore the physical influence of magnetic field on double-diffusive convection in complex biomimetic (peristaltic) propulsion of nanofluid through a two-dimensional divergent channel. Additionally, porosity effects along with rheological properties of the fluid are also retained in the analysis. The mathematical model is developed by equations of continuity, momentum, energy, and mass concentration. First, scaling analysis is introduced to simplify the rheological equations in the wave frame of reference and then get the final form of equations after applying the low Reynolds number and lubrication approach. The obtained equations are solved analytically by using integration method. Physical interpretation of velocity, pressure gradient, pumping phenomena, trapping phenomena, heat, and mass transfer mechanisms are discussed in detail under magnetic and porous environment. The magnitude of velocity profile is reduced by increasing Grashof parameter. The bolus circulations disappeared from trapping phenomena for larger strength of magnetic and porosity medium. The magnitude of temperature profile and mass concentration are increasing by enhancing the Brownian motion parameter. This study can be productive in manufacturing non-uniform and divergent shapes of micro-lab-chip devices for thermal engineering, industrial, and medical technologies.

     

Secondary flow mixing due to biofilm growth in capillaries of varying dimensions

Using a magnetic resonance microscopy (MRM) technique, velocity perturbations due to biofouling in capillaries were detected in 3D velocity maps. The velocity images in each of the three square capillary sizes (2, 0.9, and 0.5 mm i.d.) tested indicate secondary flow in both the x‐ and y‐directions for the biofouled capillaries. Similar flow maps generated in a clean square capillary show only an axial component. Investigation of these secondary flows and their geometric and dynamic similarity is the focus of this study. The results showed significant secondary flows present in the 0.9 mm i.d. capillary, on the scale of 20% of the bulk fluid flow. Since this is the “standard 1 mm” size capillary used in confocal microscopy laboratory bioreactors to investigate biofilm properties, it is important to understand how these enhanced flows impact bioreactor transport. Biotechnol. Bioeng. 2009;103: 353–360. © 2009 Wiley Periodicals, Inc.     

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.     

Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall features observed in nature also provide efficient mechanisms which can be utilized in biomimetic designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in this paper, we discussed a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generates a two-dimensional velocity profile. This mechanism is imposed by a periodic boundary condition which generates propulsion in the channel flow. Under the classical lubrication approximation, the boundary value problem is non-dimensionalized and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic parameters on velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.