Sets of multiple indicator dilution curves were obtained from working hearts of dogs with closed chests. A multiple capillary adaptation of a permeabilitylimited capillary model which assumes that exchanging material returns to the capillary at its site of escape was tested on these curves. The model has only two lumped parameters: a permeability surface product per accessible extravascular volume, and flow per extravascular volume. Labeled red cells and albumin were used as vascular indicators. The model provided close fits for the curves of diffusion-limited indicators (sucrose, inulin, sulfate, sodium, chloride, and urea), and unique values •were obtained for both parameters. The accessible extravascular volume obtained by this method was independent of flow whereas the permeability surface product per accessible extravascular volume (a relatively low value for these indicators) increased with flow. In this first group the outflow patterns varied with the size of the test molecule. For a second group of substances (water, ethanol and antipyrine), the outflow patterns were virtually identical and independent of molecular size (i.e., flowlimited). The modeling did not provide an appropriate description of these curves, and analysis indicated that the exchanging indicator may intercommunicate between capillaries in a random fashion, i.e., that the indicator may not return to each capillary at the same site at which it escaped.
More than 5035 of tracer rubidium entering the coronary circulation is actively taken up by the heart muscle cells during a single passage. Rubidium ions must traverse the capillary wall, the interstitial space, and the muscle cell membrane to enter the very large potential rubidium pool within the cells. The aim of this investigation was to determine which, if any, of these steps are rate limiting. The anterior descending branch of the left common coronary artery was perfused at its origin. Pulse injections containing 8n Rb + , 22 Na + or 14 C-sucrose, and 12B I-albumin were made into the perfusion line and timed serial samples of coronary sinus blood were collected and analyzed. A model was designed which incorporates rate constants describing both the exchange of 80 Rb + at the capillary wall and its entry at the muscle cell membrane. Labeled sucrose or 22 Na + was used to determine flow per interstitial fluid volume, a parameter necessary for the application of the model. It was assumed that the interstitial fluid volume available for labeled sucrose or 22 Na + was identical to that available for 86 Rb + . The rate constant describing exchange at the capillary wall (the permeability surface product per unit accessible interstitial fluid volume) increased with perfusion, whereas that for uptake by the myocardial cells was relatively constant and independent of flow. KEY WORDS indicators model analysis capillaries coronary microcirculationcapillary permeability diffusion working heart 8ti Rb + cardiac muscle membrane transport• At normal perfusion rates the heart actively removes more than 50* of labeled rubidium or potassium entering the coronary circulation. Both of these tracer ions are concentrated in cardiac muscle cells, and during the uptake process, traverse a multicomponent barrier consisting of capillary wall, interstitial fluid compartment, and sarcoplasmic membrane. Adrian (1) has shown that the effects of rubidium and potassium on muscle tissue are similar; and that rubidium can substitute to a large extent for potassium in living muscle cells. Indeed, 72 hours after
In the well-perfused visceral organs, active flow occurs in most capillaries, and they are packed closely. In this situation, lateral diffusion equilibration is relatively rapid and the distribution of exchanging materials is governed chiefly by the permeability of the capillary walls. We modeled extravascular distribution of exchanging substances from this kind of capillary and illustrated the changes expected in the outflow profile with increasing permeability, the evolution from the barrier-limited to the flow-limited case. We then examined the two extremes of the assemblies of such capillaries in an organ. In one, the large-vessel transit times are constant and the capillary transit times account for the outflow distribution of the vascular reference substance; in the other, the capillary transit times are constant but the large-vessel transit times vary. The barrier-limited and flow-limited cases corresponding to these are very different. In the case intermediate between these two extremes, the transit times in both the large vessels and the capillaries in the organs vary. If the organ is functionally homogeneous, the distribution of capillaries supplied by each large vessel is the same, and the situation may be described by a product distribution. The formulation for this intermediate case may then be used both to quantify capillary permeability and to describe the distributions of largevessel and capillary transit times.
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