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.     

Effect of nonaxisymmetric hematocrit distribution on non-Newtonian blood flow in small tubes

Hematocrit distribution and red blood cell aggregation are the major determinants of blood flow in narrow tubes at low flow rates. It has been observed experimentally that in microcirculation the hematocrit distribution is not uniform. This nonuniformity may result from plasma skimming and cell screening effects and also from red cell sedimentation. The goal of the present study is to understand the effect of nonaxisymmetric hematocrit distribution on the flow of human and cat blood in small blood vessels of the microcirculation. Blood vessels are modeled as circular cylindrical tubes. Human blood is described by Quemada's rheological model, in which local viscosity is a function of both the local hematocrit and a structural parameter that is related to the size of red blood cell aggregates. Cat blood is described by Casson's model. Eccentric hematocrit distribution is considered such that the axis of the cylindrical core region of red cell suspension is parallel to the axis of the blood vessel but not coincident. The problem is solved numerically by using finite element method. The calculations predict nonaxisymmetric distribution of velocity and shear stress in the blood vessel and the increase of apparent viscosity with increasing eccentricity of the core.     

Effect of blood flow on gas transport in a pulmonary capillary

The effects of blood velocity on gas transport within the alveolar region of lungs, and on the lung diffusing capacity DL have for many years been regarded as negligible. The present work reports on a preliminary, two-dimensional investigation of CO convection-diffusion phenomenon within a pulmonary capillary. Numerical simulations were performed using realistic clinical and morphological parameter values, with discrete circular red blood cells (RBCs) moving with plasma in a single capillary. Steady-state simulations with stationary blood (RBCs and plasma) were performed to validate the model by comparison with published data. Results for RBCs moving at speeds varying from 1.0 mm/s to 10 mm/s, and for capillary hematocrit (Ht) from 5% to 55%, revealed an increase of up to 60% in DL, as compared to the stationary blood case. The increase in DL is more pronounced at low Ht (less than 25%) and high RBC speed and it seems to be caused primarily by the presence of plasma. The results also indicate that capillary blood convection affects DL not only by improving the plasma mixing in the capillary bed but also by replenishing the capillary with fresh (zero concentration) plasma, providing an additional reservoir for the consumption of CO. Our findings cast doubt on the current belief that an increase in the lung diffusing capacity of humans (for instance, during exercising), with fixed hematocrit, can only be accomplished by an increase in the lung volume effectively active in the respiration process.     

Effects of sedimentation of small red blood cell aggregates on blood flow in narrow horizontal tubes

The flow properties of aggregating red cell suspensions flowing at low flow rates through horizontal tubes are analyzed using a theoretical model. The effects of sedimentation of small aggregates, which will be formed at comparatively high flow rates, on the relative apparent viscosity are considered. In the case in which a large number of small aggregates are formed in a suspension flowing through a horizontal tube, it seems that red cells are transported as a concentrated suspension through the bottom part of the tube because of sedimentation of aggregates. A two-layer flow model is used for the distribution of red cells. It consists of plasma in the upper part and a concentrated red cell suspension in the bottom part of the tube divided by a smooth and horizontal interface. It is assumed that the suspension is a Newtonian fluid whose viscosity increases exponentially with hematocrit. The velocity distribution, the relative apparent viscosity and the flux of red cells are calculated as functions of width of plasma layer for a different discharge hematocrit. The theoretical results are compared with the results obtained from experimental data. The relative apparent viscosity increases rapidly with an increasing degree of sedimentation over a wide range of plasma layer widths.     

A note on a theoretical study of erythrocyte sedimentation in inclined tubes

The expression for the sedimentation rate in inclined tubes given by Nakamura et al (Nakamura, H. and Kuroda, K. Keijo J. Med. 8, 256-296, 1937) is improved to be applicable to the problem that the falling velocity of a particle from the top wall of the tube v' differs from the one from the interface between the particle free layer and the suspended layer v. The effects of the shape at the bottom of the tube and the increase in height of the layer closely packed with particles are taken into account.