Reconsidering the effect of local plasma convection in a classical model of oxygen transport in capillaries.

In 1970, Aroesty and Gross investigated the influence of local plasma convection in between two successive red blood cells (RBC) in a capillary on the local oxygen transfer into tissue by combining convectional and diffusional oxygen transport. They concluded that the effect of local plasma convection on oxygen transport in the capillaries was insignificant. Here it is shown that this result was due to their choice of flat oxygen concentration profiles as boundary conditions. In fact, the plasma motion can be of importance when more realistic oxygen concentrations are used as boundary conditions. The fluxes of oxygen through the capillary wall could be up to 50% larger as compared to those of Aroesty and Gross, especially for low hematocrit values and for maximally working muscle. Since the boundary concentrations in the model of the current paper are fixed, chosen not to be influenced by the transport processes, calculations will not show to what extent motion really enhances the oxygen transport, and should be considered as rough indications of the effect of plasma motion. The results in this investigation indicate that in capillaries motion has to be taken into account under conditions of low hematocrit or high RBC velocity.

[1]  C. Bos,et al.  Mathematical model of erythrocytes as point-like sources. , 1995, Mathematical biosciences.

[2]  A. Popel,et al.  Effect of red blood cell shape on oxygen transport in capillaries. , 1993, Mathematical biosciences.

[3]  J F Gross,et al.  Analysis of oxygen transport to tumor tissue by microvascular networks. , 1993, International journal of radiation oncology, biology, physics.

[4]  M Intaglietta,et al.  Evidence of flowmotion induced changes in local tissue oxygenation. , 1993, International journal of microcirculation, clinical and experimental.

[5]  M Sugihara-Seki,et al.  Motion of a doublet of two cylinders in contact in a narrow channel flow. , 1992, Journal of biomechanical engineering.

[6]  K. Tyml,et al.  Distribution of red blood cell velocity in capillary network, and endothelial ultrastructure, in aged rat skeletal muscle. , 1992, Microvascular research.

[7]  B. Klitzman,et al.  Effects of chronic hypoxia on capillary flow and hematocrit in rat skeletal muscle. , 1992, The American journal of physiology.

[8]  K. Tyml.  Heterogeneity of microvascular flow in rat skeletal muscle is reduced by contraction and by hemodilution. , 1991, International journal of microcirculation, clinical and experimental.

[9]  J. Olson,et al.  A simple model for prediction of oxygen transport rates by flowing blood in large capillaries. , 1990, Microvascular research.

[10]  K. Groebe.  A versatile model of steady state O2 supply to tissue. Application to skeletal muscle. , 1990, Biophysical journal.

[11]  B. Surawicz.  Modern Cardiovascular Physiology , 1989 .

[12]  R. Skalak,et al.  Numerical study of asymmetric flows of red blood cells in capillaries. , 1988, Microvascular research.

[13]  K. Rakušan,et al.  Cardiac output distribution in rats measured by injection of radioactive microspheres via cardiac puncture. , 1974, Canadian journal of physiology and pharmacology.

[14]  J F Gross,et al.  Mathematical models of capillary flow: a critical review. , 1972, Biorheology.

[15]  H. K. Huang.  Theoretical analysis of flow patterns in single-file capillaries. , 1971, Journal of biomechanics.

[16]  J. S. Vrentas,et al.  Steady flow in the region of closed streamlines in a cylindrical cavity , 1971, Journal of Fluid Mechanics.

[17]  G. Hsiao,et al.  A mathematical model of the flow in the axial plasmatic gaps of the smaller vessels. , 1970, Biorheology.

[18]  J. Aroesty,et al.  Convection and diffusion in the microcirculation. , 1970, Microvascular research.

[19]  H. S. Lew,et al.  The motion of the plasma between the red cells in the bolus flow. , 1969, Biorheology.

[20]  Henry Wang,et al.  Viscous flow in a cylindrical tube containing a line of spherical particles , 1969, Journal of Fluid Mechanics.

[21]  D. Franklin,et al.  Cardiovascular Performance of Alaska Sled Dogs during Exercise , 1969, Circulation research.

[22]  A. C. Burton,et al.  The physics of blood flow in capillaries. III. The pressure required to deform erythrocytes in acid-citrate-dextrose. , 1962, Biophysical journal.

[23]  A C BURTON,et al.  The physics of blood flow in capillaries. I. The nature of the motion. , 1961, Biophysical journal.

[24]  Richard J. Lowell,et al.  Handbook of Respiration , 1958 .

[25]  A Krogh,et al.  The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary for supplying the tissue , 1919, The Journal of physiology.

[26]  M. Singh,et al.  Finite-element analysis of oxygen transport in the systemic capillaries. , 1991, IMA journal of mathematics applied in medicine and biology.

[27]  L. Hoofd,et al.  Oxygen pressures calculated in a tissue volume with parallel capillaries. , 1990, Advances in experimental medicine and biology.

[28]  K. Groebe,et al.  Effects of red cell spacing and red cell movement upon oxygen release under conditions of maximally working skeletal muscle. , 1989, Advances in experimental medicine and biology.

[29]  E. Leonard,et al.  The analysis of convection and diffusion in capillary beds. , 1974, Annual review of biophysics and bioengineering.