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UBC Theses and Dissertations

A mathematical model of interstitial transport and microvascular exchange Taylor, David G.


A generalized mathematical model is developed to describe the transport of fluid and plasma proteins or other macromolecules within the interstitium. To account for the effects of plasma protein exclusion and interstitial swelling, the interstitium is treated as a multiphase deformable porous medium. Fluid flow is assumed proportional to the gradient in fluid chemical potential and therefore depends not only on the local hydrostatic pressure but also on the local plasma protein concentrations through appropriate colloid osmotic pressure relationships. Plasma protein transport is assumed to occur by restricted convection, molecular diffusion, and convective dispersion. A simplified version of the model is used to investigate microvascular exchange of fluid and a single 'aggregate' plasma protein species in mesenteric tissue. The interstitium is approximated by a rigid, rectangular, porous slab displaying two fluid pathways, only one of which is available to plasma proteins. The model is first used to explore the effects the interstitial plasma protein diffusivity, the tissue hydraulic conductivity, the restricted convection of plasma proteins, and the mesothelial transport characteristics have on the steady-state distribution and transport of plasma proteins and flow of fluid in the tissue. The simulations predict significant convective plasma protein transport and complex fluid flow patterns within the interstitium. These flow patterns can produce local regions of high fluid and plasma protein exchange along the mesothelium which might be erroneously identified as 'leaky sites'. Further, the model predicts significant interstitial osmotic gradients in some instances, suggesting that the Darcy expression invoked in a number of previous models appearing in the literature, in which fluid flow is assumed to be driven by hydrostatic pressure gradients alone, may be inadequate. Subsequent transient simulations of hypoproteinemia within the model tissue indicate that the interstitial plasma protein content decreases following this upset. The simulations therefore support (qualitatively, at least) clinical observations of hypoproteinemia. Simulations of venous congestion, however, demonstrate that changes in the interstitial plasma protein content following this upset depends, in part, on the relative sieving properties of the filtering and draining vessels. For example, when the reflection coefficients of these two sets of boundaries are similar, the interstitial plasma protein content increases with time due to an increased plasma protein exchange rate across the filtering boundaries and sieving of interstitial plasma proteins at the draining boundaries. (This effect is supported by the clinical observation that interstitial plasma protein content in liver increases during venous congestion.) As the reflection coefficient of the draining boundaries decreases relative to that of the filtering boundaries, there is a net loss of plasma proteins from the interstitium, resulting in a decrease in the total interstitial plasma protein content over time (i.e., the familiar 'plasma protein washout'). Further, the model predicts increased fluid transfer from the interstitium to the peritoneum during venous congestion, supporting the clinical observation of ascites. Finally, the model is used to study the effects of interstitial plasma protein convection and diffusion, plasma protein exclusion, and the capillary transport properties on the transit times of two macromolecular tracers representative of albumin and γ-globulin within a hypothetical, one-dimensional tissue. As was expected, the transit times of each of the tracers through the model tissue varied inversely with the degree of convective transport. Increasing the interstitial diffusivity of the albumin tracer also led to a moderate decrease in the transit time for that tracer. The capillary wall transport properties, meanwhile, had only a marginal effect on the transit time for the range of capillary permeabilities and reflection coefficients considered. However, these properties (and, in particular, the reflection coefficient) had a more pronounced effect on the ultimate steady-state concentration of the tracer in the outlet stream. It was the interstitial distribution volume of a given tracer that had the greatest impact on the time required for the outlet tracer concentration to reach 50 % of its steady-state value. This was attributed to the increased filling times associated with larger interstitial distribution volumes. These findings suggest that the 'gel chromatographic effect' observed in some tissues could possibly be explained on the basis of varying distribution volumes.

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