The Disappearance of K 42 from the Nonuniformly Mixed Circulation Pool in Dogs

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Abstract
The disappearance of injected labeled substances which disappear rapidly from the circulation is discussed theoretically and tested in experiments with injected K 42 in the dog. Comparing the inflow and outflow from a capillary bed, using semilogarithmic plots of label concentrations, events upstream are repeated downstream but displaced in time by the amount of the mean circulation time between the points of observation. Downward displacement occurs owing to the intervening loss of material, and smearing of the time relations is produced by the dispersing action of variable path lengths in the capillary labyrinth. For the circulation as a whole, the time relations consist of the sum of a periodic component and an aperiodic component. The periodic component is governed by the mixing relations in a virtual circulation whose architecture approximates that of the real circulation. Extrapolating the aperiodic component to zero time yields the volume of dilution of the injected material in the virtual circulation, providing that injection and sampling points are close together. When the points are separated, correction must be made for time delay and loss of label between. The initial slope is governed not only by the mean rate of exchange of injected substance with the tissues but also by the mean circulation time.