UBC Theses and Dissertations
A compartmental model of microvascular exchange in humans Chapple, Clive
A mathematical model describing the transport and distribution of fluid and plasma proteins between the circulation, the interstitium, and the lymphatics, is formulated for the human. The formulation parallels that adopted by Bert et al. in their model of microvascular exchange in the rat. The human microvascular exchange system is subdivided into two distinct compartments: the circulation and the interstitium. Both compartments are treated as homogeneous and well-mixed. Two alternative descriptions of transcapillary exchange are investigated: a homoporous "Starling Model" and a heteroporous "Plasma Leak Model". Parameters which characterize fluid and protein transport within the two models are determined by a comparison (quantified statistically) of the model predictions with selected experimental data. These data consist of interstitial fluid volumes and colloid osmotic pressures measured as a function of plasma colloid osmotic pressure for subjects suffering from hypoproteinemia. The relationship between this fitting data and the model transport parameters is investigated using a visual "graphical optimization technique" and additionally, in the case of the Starling Model, by use of a non-linear optimization technique. Both the Starling Model and the Plasma Leak Model provide good representations of the fitting data for several alternative sets of parameter values. The ranges of parameter values obtained generally agree well with those available in literature. The fully determined model is used to simulate the transient behaviour of the system when subjected to an intravenous infusion of albumin. All alternative "best-fit" parameter sets determined for both models produce simulations which compare reasonably well with the experimental infusion data of Koomans et al.. The predictions of both models compare favourably not only with the available experimental data but also with the known behavioural characteristics of the human microvascular exchange system. However, no conclusions may be drawn regarding which of the alternative transcapillary transport mechanisms investigated provides the better description of human microvascular exchange, although it appears likely that diffusion of proteins plays a significant role in both. Final model selection and choice of fitting parameters await the availability of more and better microvascular exchange data for humans. Analysis of both the Starling Model and Plasma Leak Model indicates that the microvascular system is capable of regulating the interstitial fluid volume over a fairly wide range of transport parameter values. The important model-predicted passive regulatory mechanisms are tissue "protein washout", which reduces its colloid osmotic pressure,and a low tissue compliance which increases the hydrostatic pressure of the interstitium as it becomes hydrated. It would therefore seem that the human microvascular system can be regarded as a fairly "robust" system when considering its ability to regulate interstitial fluid volume (i.e., small changes in the values of transport parameters, such as the capillary wall permeability, have little effect on the conditions and operation of the system).
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