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UBC Theses and Dissertations

Microvascular exchange in human tissue Gates, Ian


A transient, spatially distributed mathematical model is developed describing the exchange of materials (fluid and solute) across the capillary membrane into the interstitial space. The formulation includes a lymphatic sink which drains both fluid and solute from the tissue. This can be located anywhere within the tissue. The model is constructed in cylindrical coordinates and consist of the capillary lying along the z axis and the tissue envelope surrounding the capillary. The driving force for fluid motion is the fluid chemical potential. This is equal to the difference between the local fluid hydrostatic pressure and the local colloid osmotic pressure. Starling’s hypothesis governs fluid flow across the capillary wall. This states that the amount of fluid that crosses the capillary membrane is due to the transmembrane potential difference. The fact that solute may leak across the membrane promotes the use of a capillary membrane reflection coefficient. In the tissue, the fluid motion is found from a modified Darcy's law which makes use of the gradient in the fluid potential rather than the hydrostatic pressure. In addition, a tissue reflection coefficient is used. The study consists of an evaluation of the effect the physiological parameters have on the system. This is presented in the form of a sensitivity analysis for steady state results only. It is shown that the strength of the lymphatic sink is important in promoting fluid reabsorption back into the capillary and negative hydrostatic pressures (subatmospheric) throughout the tissue. Transient test are performed to evaluate the regulating mechanisms for capillary-tissue fluid balance. The capillary membrane, the colloid osmotic pressure, and the lymphatic sink are examined for their roles in maintaining fluid balance. It is found that the colloid osmotic pressure acts as a negative feedback signal regulating the cycle of solute concentrations and fluid hydrostatic pressures throughout the tissue. The lymphatic sink is important as it provides a mechanism for lowering tissue pressures and removing solute from the interstitial space, thus lowering the tissue colloid osmotic pressure. The trends indicated in the results compare well with results from Manning et al. (1983) and Taylor et al. (1973).

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