Abstract
A mathematical theory of the process of the exchange of substances between the blood in the capillaries of a homogeneous tissue and the extracellular space, and between the extracellular space and the cells is developed. An ideal geometry of the tissue is assumed, based to some extent on recent anatomical work concerning the functional distinction between two types of capillaries, the arteriolo-venular and the true capillaries. Equations are developed relating the concentration in the arterial blood to the mean capillary concentration, the concentration at the wall of the capillary in the extracellular space, and the average concentration in the extracellular space, and also relating the cellular concentration to the average extracellular concentration. The solutions of the equations are given for certain special cases and numerical results obtained. It is shown that the average extracellular concentration is a sensitive function of the permeability of the capillary wall and also is strongly influenced by the diffusion coefficient of the extracellular space. Furthermore, it is shown that the speed with which the average extracellular concentration approaches the steady state is largely a function of the permeability of the capillary wall.
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Schmidt, G.W. A mathematical theory of capillary exchange as a function of tissue structure. Bulletin of Mathematical Biophysics 14, 229–263 (1952). https://doi.org/10.1007/BF02477816
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DOI: https://doi.org/10.1007/BF02477816