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The purpose of this symposium is to summarize recent developments in approaches to measuring the rates of exchange of substances between the parenchymal cells of the individual organ and the blood. The emphasis is on new techniques that offer good probabilities for measuring unidirectional rates of flux into cells, and that also have some possibility for measuring unidirectional effluxes from cells. The approaches to making such studies relatively noninvasive is being brought closer to reality with the development of techniques for labeling substrates with short-lived tracers.
Historically, much information on the clearances of substrates from the blood into the tissues was gained from observations on the disappearance of tracers from the plasma. When the substances were removed by an identified single organ, organ function could be assessed from the rates of disappearance or, alternatively, by the rate of infusion necessary to keep the plasma concentration at a constant level. Particular examples are hepatic anq renal clearances of substances excreted into the bile and urine where there is a net flux from the body. The clearance by an individual organ is defined as the blood flow through that organ times the fractional arteriovenous extraction; the extraction is the steady-state arteriovenous concentration difference divided by the arterial concentration. For a metabolized substance this net uptake was a direct measure of utilization. However, neither of the Clearance techniques, although good for measuring overall net transport, gave much information on the mechanisms of transport into cells.
The emphasis in this symposium will be on the use of the multiple indicator dilution technique for measuring uptake rates. Although there are variations on the technique, the usual approach requires sampling from the venous outflow from the organ and, therefore, in that mode of usage it is somewhat invasive. The general idea of how the system is considered in these studies is given in Fig. 1. Some set of tracers or nontracer substrates is injected into the inflow giving concentration time curves Cin(t) that change as a function of time, but that are all identical. The resultant outflow concentration-time curves differ by virtue of their behavior within the organ. Thus one uses a reference intravascular tracer that represents what would happen to any tracers for which there is no transcapillary exchange. Other tracers traverse the capillary membrane to enter the interstitial space, a process usually of passive diffusional transport, but that also may occur by a facilitated transport mechanism like that shown by Crone (4) for glucose uptake across the blood-brain barrier. Certain tracers may go beyond the interstitial space to enter the cells and may also return. The form of the outflow tracer dilution curve is influenced by each of these processes of exchange and by the volumes of distribution for the tracer within the interstitial fluid space and the cells. Accordingly, the governing parameters for the mathematical descriptions of the events are the permeability-surface area for the capillary PScap; the permeability-surface area product for the cells PScell; the volumes of distribution in the capillary Vcap, in the interstitial space VISF, and within the cell Vcell; and the rate of consumption within the cell.
The key to the approach is the idea that at any moment there is a distribution of concentrations as a function of distance x along the length of the capillary, Ccap(x, t). It has been recognized since Renkin's 1959 study that accounting for the change in concentration along the length of the capillary is critical to the evaluation of the transport parameters. Lumped compartmental analysis does not suffice for parameter estimation except under a very limited circumstance, that is, when the conductances PScap and PScell are so low and the net uptake so small relative to the flow that the arteriovenous difference is exceedingly small. The definition of so low differs in different organs. The governing parameter for the trans capillary exchange is PScap/Fs, where Fs is the flow of the mother fluid containing the solute; Fs is the plasma flow through the prgan whenever the solute does not enter the red cells.
The power of the approach of using multiple indicator dilution techniques, either outflow detection techniques or organ residue detection techniques by external detection, is the use of reference tracers. Although the intravascular reference serves well against which to estimate the capillary permeability-surface product PScap other references are useful for sharpening the estimates of PScell Thus, for example, Bassingthwaighte (2) uses l-glucose as a reference tracer for d-glucose because the l-glucose permeates the capillary membrane with identical kinetics to d-glucose but remains confined to the interstitial and capillary spaces and does not enter the cells. Similarly, Yudilevich and Mann (8) use small extracellular solutes as reference tracers that have the same extracellular volume of distribution as the solutes interest that enter the cells.
Mathematical models have been developed for defining both the mechanisms and the kinetics of the exchange processes. When one uses tracer techniques so that there is no change in the chemical concentration of the test substance during the transcapillary passage of the tracer, the values of PS are governed by the chemical concentration levels and appear first order as far as tracer is concerned (3). Thus a single experiment cannot distinguish passive transport from facilitated or active transport. But a series of experiments done at different levels of chemical concentration leads to a distinction because the transport rates differ at different concentrations. The apparent PS for a saturable transport mechanism having first-order Michaelis-Menton kinetics is shown in Fig. 2, which gives an idea of the large range of concentrations over which one must work to estimate the maximum transport rate Vmax, and the apparent Michaelis constant for binding at the transport site Km. Such kinetics might apply at either the capillary or cell membranes.
Goresky (5) has concentrated on the development of analytical models with closed-form solutions that account completely for mass balance. Closed-form solutions are a vehicle for providing mathematical exactness, but it is important to remember that computer solutions for such equations are not exact, and in addition to having possibly large errors may actually be slower than the numerical forms preferred by Bassingthwaighte (1) or by Harris and co-workers (6). When numerically correct, the closed-form solution also provides a baseline against which one can check limiting cases of numerical solutions.
Not all of the mathematics is developed. For example, Goresky (unpubished) is extending the blood-tissue exchange models to handle the complicated cases where, in the steady state for a consumed substance, the concentration is diminishing as a function of distance along the length of the capillary. As another example, the method of Yudilevich and Mann (8) of calculating an uptake relative to an extracellular reference tracer has not had a formal mathematical development that has demonstrated both the degree of precision and the limitations of the approach. Silverman and Trainor (7) are tackling the problem of capillary beds in series and. attempting to differentiate the events occurring at the two types of capillary exchange regions and to obtain measures of the cellular uptake or exchange as well. Their approaches are logical, but their quantitative accuracy is not yet demonstrated. Silverman and Trainor's approach has the additional merit of providing data from an extravascular region, namely the urine, as well as from the venous outflow; it illustrates the power of obtaining multiple sets of data of different types simultaneously.
In summary, each of the studies emphasizes one or more fundamental aspects of the approach to measuring cellular uptake rates; each demonstrates that to obtain the greatest accuracy in the characterization of the system under study, one must obtain multiple sets of data simultaneously.
Preparation of the manuscript by Geraldine Crooker and of the illustrations by Hedi Nurk is greatly appreciated.
*MEASURING CELLULAR TRANSPORT IN VIVO–Symposium presented at the 32nd Annual Fall Meeting of The American Physiological Society, Cincinnati, Ohio, October 13, 1981. Chaired by J. B. Bassingthwaighte.