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Central Asian Problems of Modern Science and Education

Article Title

MATHEMATICAL MODELLING OF BLOOD FLOW

Abstract

The paper presents the two-phase model to describe blood flow in large and in small blood vessels. Based on this model the study gives an explanation for long known features (effects) of blood flow in the vessels: dependence of the hematocrit (packed cell volume) on the diameter of the vessel, existence of cell-free plasma layer near the vessel wall, obtuse (as compared with the profile of Poiseuille flow) velocity profile of a blood; dependence of the blood viscosity on the diameter of the vessel. The researcher determines dependences of the blood rate and viscosity on the diameter of a blood vessel. With the flow of blood in small vessels (less than 200 μm), the rheological properties of the blood depend on the size of the vessel - the apparent viscosity of the blood drops with a decrease in the diameter of the blood vessel. To describe the flow of blood in small vessels, it is necessary to create an equation of state that depends (apart from other parameters) on the diameter of the vessel

First Page

5

Last Page

14

References

[1]. Pries A.R., Secomb T.W. Blood flow in microvascular networks // Handbook of Physiology: Microcirculation / ed. R.F. Tuma, W.N. Dura, K. Ley. – Academ Press, 2008. [2].Sharan M., Popel A.S. A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall // Biorheology. – 2001. – Vol. 38. [3]. Long D.S., Smith M.L., Pries A.R. et al. Micro-viscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemo-dilution // Proc. Natl. – Acad. Sci. USA. 2004. – Vol. 101, ?27

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