Extended theory of the early diffusion of multiple indicators: bounds on permeability ratios, with applications to...

The determination of ratios of capillary permeabilities to multiple indicators is secured by constructing upper bounds on effects of early back-diffusion following a single arterial injection. The analysis does not exclude highly extracted indicators, and it allows for effects of asymmetric blood-tissue exchange and of tissue concentration gradients. The concept of flow limitation of uptake is delimited operationally. It is shown how to identify effects of heterogeneity of uptake for data sets extended over large ranges of rate of blood flow. These new methods are used to show, for several sets of previously published data from muscle, that back-diffusion cannot change appreciably the permeability ratios determined previously without any quantification of back-diffusion. The main application is to data published by Perry and Granger (1981) on the permeability of cat intestinal capillaries to raffinose and inulin. The permeability ratios deduced from these data imply paradoxically restricted diffusion; it is shown that this cannot be attributed to effects of back-diffusion, heterogeneity of extraction, or of solvent drag. It is shown that the paradox is removed if tissue-to-blood permeability to raffinose is at least double the blood-to-tissue permeability, possibly as part of the active transport of sugars from the intestinal lumen. It is shown that corresponding results on permeability ratios in dog gastric capillaries are not paradoxical (against the standard of unrestricted diffusion) under symmetric permeability to raffinose.