MATHEMATICAL MODELLING OF FLUID EXCHANGE THROUGH BLOOD CAPILLARIES

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dc.contributor.authorSALEH, AISHATU
dc.date.accessioned2014-02-11T10:05:50Z
dc.date.available2014-02-11T10:05:50Z
dc.date.issued1986-10
dc.descriptionA THESIS SUBMITTED TO THE POSTGRADUATE SCHOOL AHMAOU BELLO UNIVERSITY IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE (MATHEMATICS) Department of Mathematics, Faculty of Science, Ahmadu Bello University, Zaria - Nigeria,en_US
dc.description.abstractFlow properties of blood play an increasing role in the diagnostic and therapy of many diseases as well as in different artificial organs. The vessels of human circulatory system range in internal diameter from approximately 2.5 cm to 3μ (μ=10-4 cm). The vessels with an internal dimension less than about 500μ are commonly reffered to as the microvessels. Microcirculatory vessels are small artries (70-500μ), arterioless (l0-70μ); capillaries (4-10μ), venules (10-100μ) and small viens (110-500μ). The first interest in mathematical modelling of the microcirculation developed from experimental investigations to determine the arrangement of blood vessels in tissue. These experiments were being conducted as a result of interest in the mechanism by which oxygen was transported from blood to tissue and how this transfer could be controlled. The first theoretical study on the exchange of oxygen across the capillary walls and the tissue surrounding them was made by Krogh (1919) for which he won his Nobel prize. He observed in detail the distribution of capillaries in muscle, and proposed a functional unit of capillary beds. Krogh's model in composed of a long straight cylindrical capillary and a concentric cylinder of homogeneous tissue surrounding it. The present thesis, which is concerned with the mathematical modelling of fluid exchange through blood capillaries, comprises of four chapters. The first chapter introduces the subject 'Biomechanics' and outlines the historical background of the subject and its applications to clinical problems in the cardiovascular system, quantitative physiology, orthopedics, artifical limb and etc. The second chapter describes the various aspects of the microcirculation. The factors, Starting hypothesis, capillary filtration coefficient, capillary and tissue hydrostatic pressures, plasma and tissue osmotic pressures are discussed. Finally this chapter discusses a variety of approaches and formulations for the mathematical modelling of the microcirculation. In the third chapter a mathematical model is developed to see the effects of the variable filtration coefficient, lymph flow and reflection coefficient on the fluid exchange between blood capillary and the tissue space. It is assumed that the exchange of fluid across the capillary wall obey Starling's law and that the filtration coefficient and the reflection coefficient of the capillary wall are not uniform along the length of capillary but is a linear function of the distance from the arterial end. It is further assumed that the flow of fluid through the tissue region is governed by a generalized Darey's equation. Under these assumptions the velocity and pressure distributions in the capillary and tissue regions are obtained. We also obtain the average interstitial fluid pressure and the average effective pressure difference between the blood and interstitial fluid. While chapter three is concerned about the uniform capillary radius, chapter four is devoted to fluid exchange between blood capillary of slowly but arbitrary varying cross section and the tissue space. An analytical solution in the general case is obtained by perturbation technique.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/1113
dc.language.isoenen_US
dc.subjectMATHEMATICALen_US
dc.subjectMODELLINGen_US
dc.subjectFLUIDen_US
dc.subjectEXCHANGEen_US
dc.subjectTHROUGHen_US
dc.subjectBLOODen_US
dc.subjectCAPILLARIESen_US
dc.titleMATHEMATICAL MODELLING OF FLUID EXCHANGE THROUGH BLOOD CAPILLARIESen_US
dc.typeThesisen_US
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