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The washout of inert gas from tissues typically follows multiexponential curves rather than monoexponential curves as would be expected from homogeneous, well-mixed compartment. This implies that the ratio for the square root of the variance of the distribution of transit times to the mean (relative dispersion) must be greater than 1. Among the possible explanations offered for multiexponential curves are heterogeneous capillary flow, uneven capillary spacing, and countercurrent exchange in small veins and arteries. By means of computer simulations of the random walk of gas molecules across capillary beds with parameters of skeletal muscle, we find that heterogeneity involving adjacent capillaries does not suffice to give a relative dispersion greater than one. Neither heterogeneous flow, nor variations in spacing, nor countercurrent exchange between capillaries can account for the multiexponential character of experimental tissue washout curves or the large relative dispersions that have been measured. Simple diffusion calculations are used to show that many gas molecules can wander up to several millimeters away from their entry point during an average transit through a tissue bed. Analytical calculations indicate that an inert gas molecule in an arterial vessel will usually make its first vascular exit from a vessel larger than 20 micron and will wander in and out of tissue and microvessels many times before finally returning to the central circulation. The final exit from tissue will nearly always be into a vessel larger than 20 micron. We propose the hypothesis that the multiexponential character of skeletal muscle tissue inert gas washout curves must be almost entirely due to heterogeneity between tissue regions separated by 3 mm or more, or to countercurrent exchanges in vessels larger than 20 micron diam.

Morphometric data of the pulmonary veins in the cat right lung are presented. Silicone elastomer casts of the right lungs of five cats were made, measured, counted, and analyzed. The Strahler system is used to describe the branching pattern of the vascular tree. These data are needed for the physicomathematical approach to pulmonary circulation. For all the pulmonary blood vessels lying between the left atrium and the capillary beds, there are a total of 10 orders of vessels in the right upper lobe, 9 orders of vessels in the right middle lobe, and 11 orders of vessels in the right lower lobe. The ratios of the diameters, lengths, and the number of branches in successive orders of vessels are called the diameter, length, and branching ratios, respectively. For the cat pulmonary venous tree, the average branching ratio is 3.521, the average diameter ratio is 1.727, and the average length ratio is 2.402 for vessels of orders 1-3 and 1.532 for vessels of orders 4-10.