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A mathematical model for the transport of oxygen in the systemic capillaries and the surrounding tissue in the presence of a magnetic field is presented in this paper. We have modeled the capillary by a circular cylinder surrounded by a tissue of uniform thickness. The model takes into account the transport mechanisms of molecular diffusion, convection and diffusion due to the presence of hemoglobin as a carrier of the gases (oxygen).The resulting system of differential equations is solved analytically by the method of separation of variable and Picard's method. The result for partial pressure of oxygen in the capillary and tissue region is obtained. The effect of the Hartmann number (H) and others parameters is obtained and discussed through graphs.
Rocznik
Tom
Strony
331--344
Opis fizyczny
Bibliogr. 24 poz., wykr.
Twórcy
autor
autor
autor
- Harcourt Butler Technological Institute Kanpur -208 002, INDIA, sharmasunil43@gmail.com
Bibliografia
- Chandrasekhara B.C. and Rudraih N. (1980): MHD flow through a channel of varying capillary. - Indian J. Pure Appl. Math., vol.11, No.8, pp.1105-1123.
- Deshikachar K.S. and Ramachandra A. Rao (1985): Effect of a static magnetic field on the flow and blood oxygenation in channels of cross-section. - Int. J. Engng. Sci., vol.23, No.10, pp.1121-1133.
- Drew D.A. (1974): Low concentration of two phase flow near a stagnant point. - Physics Fluid, vol.17, pp.1688-1691.
- Ellis C.G., Jagger J. and Michael S. (2005): The microcirculation as a functional system. - Critical Care, vol.9, (Suppl.4), S3-S8.
- Elsworth M.L. and Pittman R.N. (1990): Arterioles supply oxygen to capillary by diffusion as well as by convection. - Am J. Physiol., vol.258, H1240-H1243.
- Ellsworth M.L., Ellis C.G., Popel A.S. and Pittman R.N. (1994): Role of microvessels in oxygen supply to tissue. - New Physiol Sci., vol.9, pp.119-123.
- Krogh A. (1919): The number and distribution of capillaries in muscle with the calculation of the oxygen pressure necessary for supplying tissue. - J. Physiol (Lond), vol.52, pp.409-515.
- Lih M.M. (1974): Transport phenomena in medicine and biology. - John Wiley and Sons, Inc.
- Popel A.S., Charky C.K. and Divinsky A.S. (1986): Effect of heterogeneous oxygen delivery on the oxygen distribution in skeletal muscle. - Math. Bio. Sci., vol.81, pp.91-113.
- Reneau D.D., Bruley D.F. and Knisely M.H. (1967): A mathematical simulation of oxygen release diffusion and consumption in the capillaries and tissue of the human brain. - Chemical Engineering in Medicine and Biology, Plenum Press, New York, 135.
- Salathe E.P. and K.N. (1976): A mathematical analysis of fluid movement across capillary walls. - Microvasc. Res., vol.11, pp.1-23.
- Salathe E.P., Wang T.C. and Gross J.F. (1980): A mathematical analysis of oxygen transport to tissue. - Math. BioSci., vol.57, pp.89-115.
- Salathe E.P. and Wang T.C. (1980): Substrate concentrations in tissue surrounding single capillaries. - Math. BioSci., vol.49, pp.239-247.
- Salathe E.P. (2003): Mathematical analysis of oxygen concentration in a two dimensional array of capillaries. - J. Math. Biol., vol.46, pp.287-308.
- Secomb T.M. and Hsu R. (1994): Simulation of oxygen transport in skeletal muscle: diffusive and exchange between arterioles and capillaries. - Am. J. Physiol., vol.267, H1214-H1221.
- Sharan M. and Popel A.S. (1988): A mathematical model of counter current exchange of oxygen between paired arterioles and venules. - Math. Bio. Sci., vol.91, pp.17.
- Sharan M., Singh M.P., Saxena R.K. and Sud I. (1989): Numerical simulation of systemic oxygen and exchange in hyperbaric environment. - Biosystems, vol.23, pp.21.
- Sharan M., Singh B. and Kumar P. (1997): A two layer model for studying the effect of plasma layer on the delivery of oxygen to tissue using a finite element method. - Appl. Math. Modelling, vol.21, pp.419-426.
- Sharan M., Singh M.P. and Singh B. (1995): An analytical model for oxygen transport in tissue capillaries in a hyperbaric environment with first order metabolic consumption. - Math. Comput. Modelling, vol.22, pp.99-111.
- Srivastava V.P. (2007): A theoretical model for blood flow in small vessels. - Application and Applied Mathematics: An International Journal, vol.2, No.1, pp.51-65.
- Sud V.K., Suri P.K. and Mishra R.K. (1974): Effect of magnetic field on oscillating blood flow in arteries. - Studia Biophysica, vol.46, pp.163.
- Suri P.K. and Suri P.R. (1981): Effect of static magnetic field on blood flow in a branch. - Indian J. Pure and Appl. Math., vol.12, No.7, pp.907-918.
- Vardanyan V.A. (1973): Biophysics. - Vol.18, pp515.
- Whiteley J.P., Gavaghan D.J. and Hahn C.W. (2002): Mathematical modelling of oxygen transport to tissue. - J. Math. Biol., vol.44, pp.503-522.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ5-0017-0001