Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube

The effect of pulsatile flow on peristaltic transport in a circular cylindrical tube is analysed. The flow of a Newtonian viscous incompressible fluid in a flexible circular cylindrical tube on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The initial flow in the tube is induced by an arbitrary periodic pressure gradient. A perturbation solution with amplitude ratio (wave amplitude/tube radius) as a parameter is obtained when the frequency of the travelling wave and that of the imposed pressure gradient are equal. The interaction effects of periodic wall induced flow and periodic pressure imposed flow are visualized through the presence of substantially different components of steady and higher harmonic oscillating flow in the first order flow solution. Numerical results show a strong variation of steady state velocity profiles with boundary wave number and Reynolds number and a strong phase shift behaviour of the flow in the radial direction.     

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.     

Velocity field of pulsatile flow in a porous tube

This paper describes velocity fields for fully developed periodic laminar flow in a rigid tube with a porous wall. We obtained an analytical solution of the flow by the linear approximation of the Navier-Stokes equation. Unlike the previous works with a constant seepage rate along the axis, we used a wall velocity which contained hydraulic permeation constant Lp. The axial velocity profile shows a local maximum velocity near the wall at a large Womersley number alpha. This suggests that concentration polarization in porous tubular membrane may be reduced at high frequencies if a membrane device is operated under pulsatile flow conditions. The magnitude of wall permeation velocity decreases linearly along the tube axis because the damping of the pressure difference between the inside and the outside of the tube is very small.     

Two-equation turbulence modeling of pulsatile flow in a stenosed tube

The study of pulsatile flow in stenosed vessels is of particular importance because of its significance in relation to blood flow in human pathophysiology. To date, however, there have been few comprehensive publications detailing systematic numerical simulations of turbulent pulsatile flow through stenotic tubes evaluated against comparable experiments. In this paper, two-equation turbulence modeling has been explored for sinusoidally pulsatile flow in 75% and 90% area reduction stenosed vessels, which undergoes a transition from laminar to turbulent flow as well as relaminarization. Wilcox's standard k-omega model and a transitional variant of the same model are employed for the numerical simulations. Steady flow through the stenosed tubes was considered first to establish the grid resolution and the correct inlet conditions on the basis of comprehensive comparisons of the detailed velocity and turbulence fields to experimental data. Inlet conditions based on Womersley flow were imposed at the inlet for all pulsatile cases and the results were compared to experimental data from the literature. In general, the transitional version of the k-omega model is shown to give a better overall representation of both steady and pulsatile flow. The standard model consistently over predicts turbulence at and downstream of the stenosis, which leads to premature recovery of the flow. While the transitional model often under-predicts the magnitude of the turbulence, the trends are well-described and the velocity field is superior to that predicted using the standard model. On the basis of this study, there appears to be some promise for simulating physiological pulsatile flows using a relatively simple two-equation turbulence model.     

Analysis of non-linear pulsatile blood flow in arteries

Some aspects of the problem of computation of non-linear pulsatile blood flow in large arteries are investigated, in the context of the computational method developed by Ling and Atabek (1972). As examples, the following aspects are considered: stability of the computations; representation of higher-frequency components of the flow; effects of keeping or omitting non-linear terms in the equations; effects of varying the dimensionless parameters of the problem. The computational method is extended to include effects of viscoelasticity of arterial walls.     

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.     

The "black hole" phenomenon in ultrasonic backscattering measurement under pulsatile flow with porcine whole blood in a rigid tube

The "black hole" phenomenon was further investigated with porcine whole blood under pulsatile flow conditions in a straight rigid tube 120 cm long and of 0.95 cm diameter. A modified Aloka 280 commercial scanner with a 7.5 MHz linear array was used to collect the radio frequency (RF) signal of backscattering echoes from the blood inside the tube. The transducer was located downstream from the entrance and parallel to the longitudinal direction of the tube. The experimental results showed that higher hematocrits enhanced the black hole phenomenon, leading to a more apparent and larger diameter black hole. The black hole was not apparent at hematocrits below 23%. The highest hematocrit used in the experiment was 60%. Beat rates of 20, 40 and 60 beats per minute (bpm) were used, and the black hole became weaker in amplitude and smaller in diameter when the peak flow velocity was increased at each beat rate. These results are consistent with the suggestion in previous work that the black hole arises from insufficient aggregation of red blood cells (RBCs) at the center of the tube because of the low shear rate. At 20 and 40 bpm, the peak flow velocity ranges were 10 approximately 25 cm/s and 18 approximately 27 cm/s, respectively. The black hole was very clear at the minimal peak flow velocity but almost disappeared at the maximal velocities for each beat rate. At 60 bpm, experiments were only performed at one peak flow velocity of 31 cm/s and the black hole was clear. The results showed that the black hole was more pronounced at higher beat rates when the peak velocity was the same. This phenomenon cannot be explained by previous hypotheses. Acceleration seems to be the only flow parameter that varies at different beat rates when peak velocities are the same. Therefore, the influence of acceleration on the structural organization and orientation of RBC rouleaux might be another factor involved in the formation of the black hole in addition to the shear rate. As the entrance length was changed from 110 to 15 diameters (D) in seven steps at the hematocrit of 60%, it was found that a position farther downstream yielded a black hole with a greater contrast relative to the surrounding region, while the backscattering power at the central hypoechoic zone did not increase with increasing entrance length.     

Numerical simulations of pulsatile blood flow using a new constitutive model

In the present paper we use a new constitutive equation for whole human blood [R.G. Owens, A new microstructure-based constitutive model for human blood, J. Non-Newtonian Fluid Mech. (2006), to appear] to investigate the steady, oscillatory and pulsatile flow of blood in a straight, rigid walled tube at modest Womersley numbers. Comparisons are made with the experimental results of Thurston [Elastic effects in pulsatile blood flow, Microvasc. Res. 9 (1975), 145-157] for the pressure drop per unit length against volume flow rate and oscillatory flow rate amplitude. Agreement in all cases is very good. In the presentation of the numerical and experimental results we discuss the microstructural changes in the blood that account for its rheological behaviour in this simple class of flows. In this context, the concept of an apparent complex viscosity proves to be useful.     

Stress analysis in a layered aortic arch model under pulsatile blood flow

Background  

Many cardiovascular diseases, such as aortic dissection, frequently occur on the aortic arch and fluid-structure interactions play an important role in the cardiovascular system. Mechanical stress is crucial in the functioning of the cardiovascular system; therefore, stress analysis is a useful tool for understanding vascular pathophysiology. The present study is concerned with the stress distribution in a layered aortic arch model with interaction between pulsatile flow and the wall of the blood vessel.     

Heat transfer to blood flow in a small tube

Blood flow in a small tube (30-1000 mum) can be successfully modeled by the two-fluid model. The fully developed, constant heat flux convective heat transfer problem is studied. The velocity and temperature profiles are determined in closed form. Formulas for friction-factor-Reynolds number product, axial temperature gradient, and Nusselt number are found.     

Pulsatile blood flow and gas exchange across a cylindrical fiber array

The pulsatile blood flow and gas transport of oxygen and carbon dioxide through a cylindrical array of microfibers are numerically simulated. Blood is modeled as a homogeneous Casson fluid, and hemoglobin molecules in blood are assumed to be in local equilibrium with oxygen and carbon dioxide. It is shown that flow pulsatility enhances gas transport and the amount of gas exchange is sensitive to the blood flow field across the fibers. The steady Sherwood number dependence on Reynolds number was shown to have a linear relation consistent with experimental findings. For most cases, an enhancement in gas transport is accompanied with an increase in flow resistance. Maximum local shear stress is provided as a possible indicator of thrombosis, and the computed shear stress is shown to be below the threshold value for thrombosis formation for all cases evaluated.     

Periodic pulsatile stimulation of a nonlinear oscillator

We consider pulsatile periodic stimulation of an integrate-and-fire oscillator, and investigate the possible phase-locked patterns between the intrinsic rhythm and the forcing system. These stimulations are varied according to their period and intensity, corresponding to controllable experimental parameters. Phase transition curves are derived and analyzed under functional iteration. Two different perturbative mechanisms are considered, leading to significant differences in possible behaviors. Bistability can be obtained in one case.The analysis is reduced to the investigation of two-parameter families of discontinuous maps of the circle into itself.     

Ventilatory effects of high and pulsatile blood flow in the pulmonary circulation

The mechanism of ventilatory stimulation that accompanies increases in cardiac output is unknown. Previous studies addressing this issue have been inconclusive. However, only steady pulmonary blood flow was used. The effect of flow pulsatility merits consideration, because increasing cardiac output raises not only mean pulmonary arterial pressure but also pulse pressure; mechanoreceptors with an important dynamic component to their responses may cause a response to pulsatile, but not steady, flow. Studies were done on anesthetized cats (n = 4) and dogs (n = 4). The right pulmonary artery was cannulated within the pericardium, and systemic blood was pumped from the left atrium to the right pulmonary artery. The right pulmonary circulation was perfused at different levels of flow, which was either steady or pulsatile. Steady-state flow of up to 150 ml.kg-1.min-1 (270 ml.kg-1.min-1 when corrected for the proportion of lung tissue perfused) did not affect breathing pattern. When high pulmonary flow was made pulsatile (pulse pressure approximately 23 mmHg), breath duration decreased from 3.7 +/- 0.72 to 3.4 +/- 0.81 (SD) s (P less than 0.01), representing a change in frequency of only 9%. There was no change in peak inspiratory activity. It was concluded that pulmonary vascular mechanoreceptors are not likely to contribute significantly to the increase in ventilation in association with increases in cardiac output.     

A model for blood flow through a stenotic tube

This article deals with the introduction of the modified Casson's fluid model as the true representation for the blood for the steady laminar flow through a small diameter artery with axi-symmetric identical double stenoses in series. The governing equations are solved by using the finite element method. The results for the velocity profiles, the pressure and the wall shear stress distributions in addition to the location and length of the flow reversal zones have been brought out and discussed in reference to the severity of the disease. It has been observed that the non-Newtonian nature of the blood helps in reducing the magnitude of the peak wall shear stress at the throat and the length of the reversed flow regions in the post stenotic dilatation.     

Analysis of pulsatile blood flow: A carotid siphon model

Numerical results for axial and secondary flow velocity and pressure in a three-dimensional model of the human carotid siphon have been calculated; the investigations were carried out under physiologically relevant pulsatile flow conditoins. Time-dependent, three-dimensional Navier-Stokes equations were solved numerically by using a special finite element method. The results of the computer simulation presented here concentrate on the secondary motion effect during the pulsatile flow cycle in multiple three-dimensional curvatures.