Gas transport in serpentine microporous tubes under steady and pulsatile blood flow conditions

A serpentine gas exchange unit was built with cylindrical tubular microporous membranes featuring periodic arcs with a fixed curvature ratio (ratio of tube radius to radius of curvature) of 1/14 and circular angles between 30 and 360 deg. Oxygen transfer was measured under steady and pulsatile blood flow conditions in vitro and ex vivo to assess the design features which most effectively augment gas transfer. Under steady blood flow conditions, oxygen transfer increased with circular angles beyond 70 deg. Under pulsatile conditions, a wide range of geometrical and fluid mechanical parameters could be combined to enhance gas transfer performance, which eventually depended upon the secondary Reynolds number and the Womersley parameter.     

The hemodynamic and embolizing forces acting on thrombi--II. The effect of pulsatile blood flow

A previous analysis (Basmadjian, J. Biomechanics 17, 287-298, 1984) of the embolizing forces acting on thrombi in steady Poiseuille flow has been extended to pulsatile blood flow conditions in the major blood vessels. We show that for incipient and small compact thrombi up to 0.1 mm height, the maximum embolizing stresses can be calculated from the corresponding 'quasi-steady' viscous drag forces and measured maximum wall shear. Their magnitude is from 5 to 30 times (tau w)Max, the maximum wall shear stress during the cardiac cycle in the absence of thrombi. For larger thrombi, inertial and 'history' effects have to be taken into account, leading to embolizing stresses in excess of 100 Pa (1000 dyn cm-2).     

The inverse Womersley problem for pulsatile flow in straight rigid tubes

In this study a numerical solution for the problem of pulsating flow in rigid tubes is described. The method applies to the case of known flow rate waveform, as opposed to Womersley solution where the pressure gradient was the known quantity. The solution provides the pressure gradient and wall shear stress waveforms as well as the instantaneous velocity profiles. Results show that the method can be used to study the blood flow characteristics in large arteries.     

Calculations of pulsatile flow across bifurcations in distensible tubes

A simple method is given for extending across junctions the numerical methods previously used to study fluid flow in nonuniform, nonbranching, distensible tubes. Calculations with this method suggest that the ratio of downstream to upstream cross-sectional areas and the pressure wave velocity ratio in mammals are optimal for energy transfer across the junction.     

Effects of flow geometry on blood viscoelasticity

The viscoelastic properties of blood are dominated by microstructures formed by red cells. The microstructures are of several types such as irregular aggregates, rouleaux, and layers of aligned cells. The dynamic deformability of the red cells, aggregation tendency, cell concentration, size of confining vessel and rate of flow are determining factors in the microstructure. Viscoelastic properties, viscosity and elasticity, relate to energy loss and storage in flowing blood while relaxation time and Weissenberg number play a role in assessing the importance of the elasticity relative to the viscosity. These effects are shown herein for flow in a large straight cylindrical tube, a small tube, and a porous medium. These cases approximate the geometries of the arterial system: large vessels, small vessels and vessels with many branches and bifurcations. In each case the viscosity, elasticity, relaxation time and Weissenberg number for normal human blood as well as blood with enhanced cell aggregation tendency and diminished cell deformability are given. In the smaller spaces of the microtubes and porous media, the diminished viscosity shows the possible influence of the F?hraeus-Lindqvist effect and at high shear rates, the viscoelasticity of blood shows dilatancy. This is true for normal, aggregation enhanced and hardened cells.     

Platelet near-wall excess in porcine whole blood in artery-sized tubes under steady and pulsatile flow conditions

Platelet margination (enhanced platelet concentration in the near wall region of a blood vessel) has been well documented in small vessels. In artery-sized vessels margination has only been demonstrated in one study, using ghost cell suspensions and under relatively non-physiologic conditions of steady flow and 50 cm development length. Local sampling experiments were performed to confirm platelet margination in artery-sized stainless steel tubes, for a typical anatomical length and under pulsatile flow, using fresh EDTA-anticoagulated porcine whole blood (N=21). Experiments were designed using three-dimensional Computational Fluid Dynamics (CFD) to model the sample region with greater fidelity. Steady flow experiments in 50 cm long tubes verify published laser Doppler measurements of platelet margination in 3 mm ID tubes at normal arterial shear rate (500 s(-1). Margination persists under pulsatile flow conditions (63.8 pulses/min), but in steady flow at length of 10 cm, margination is reduced. Platelet margination ratio (the ratio of the platelet concentration near the wall to bulk average platelet count) ranges from 1.21 to 2.48. No significant effects of calculated sampling thickness (20 microm and 50 microm) or pulsatility were detected. Hematocrit margination ratio is 0.68 to 0.90. Two model platelet concentration profiles are fit to the experimental results.     

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.     

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.     

Arthropump with peristaltic effect and pulsatile flow

This paper describes a pump of novel design, with peristaltic effect and pulsatile flow. Special features are the facility for occlusive or non-occlusive pumping, and the absence of moving parts in the flow section. A compressible drive medium allows ‘individual’ transport of big particles in the pumped fluid. Pumping of a relatively high proportion of solids in liquid is possible. This pump is suitable for handling living structures in cell and tissue separating systems. Pumping of fluids with increased viscosity and abrasives in liquid is also feasible.     

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.     

A note on the flow of blood in capillary tubes

It is demonstrated that an explanation of the small radius effect or the so-called sigma phenomenon may be obtained by noting that one of the effects of the presence of suspended particles in a flowing fluid is to increase the velocity of flow near the wall over that existing in the absence of particles. This effect may be considered equivalent to relaxing the boundary conditions at the wall. An expression for the viscosity is compared with data and fit is found to be good.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.