Abstract
In this study we use the multiple indicator dilution technique to outline the kinetic mechanisms underlying the uptake of rubidium, a cation which, in the steady state, is concentrated by hepatic parenchymal cells. We inject a mixture of 51Cr-labeled red blood cells (a vascular reference substance), 22Na (which is confined to the extracellular space, the expected extravascular distribution space for rubidium, in the absence of cellular uptake), and 86Rb into the portal vein and obtain normalized outflow patterns, expressed as outflowing fractions of each injected mass per milliliter vs. time. The labeled red cell curve rises to the highest and earliest peak and decays rapidly. That for labeled sodium rises to a later and lower peak, and decays less rapidly. Its extrapolated recovery is equal to that for the red cells. The observed 86Rb curve consists of two parts: an early clearly defined peak of reduced area, related to the 22Na peak in timing; and a later tailing, obscured by recirculation, so that total outflow recovery cannot be defined (even though it would be expected to be the same). We model the concentrative uptake of 86Rb and find two corresponding outflow fractions: throughput material, which sweeps past the cell surface as a wave delayed with respect to the vascular reference (tracer which has not entered cells); and exchanging material (tracer which has entered cells and later returns to the circulation). We find that the outflow form of the rubidium curve, the presence of both a relatively clearly defined throughput component and a relatively prolonged low-in-magnitude tailing, is consequent to the concentrative character of the transport mechanism, to the presence of an influx rate constant many times the efflux rate constant. The modeling which we develop is general, and has potential application in situations where transport is nonconcentrative.
Full text
PDF















Images in this article
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- BRAUER R. W. Liver circulation and function. Physiol Rev. 1963 Jan;43:115–213. doi: 10.1152/physrev.1963.43.1.115. [DOI] [PubMed] [Google Scholar]
- BURCH G. E., THREEFOOT S. A., RAY C. T. The rate of disappearance of Rb86 from the plasma, the biologic decay rates of Rb86, and the applicability of Rb86 as a tracer of potassium in man with and without chronic congestive heart failure. J Lab Clin Med. 1955 Mar;45(3):371–394. [PubMed] [Google Scholar]
- Bassingthwaighte J. B., Ackerman F. H., Wood E. H. Applications of the lagged normal density curve as a model for arterial dilution curves. Circ Res. 1966 Apr;18(4):398–415. doi: 10.1161/01.res.18.4.398. [DOI] [PMC free article] [PubMed] [Google Scholar]
- CHINARD F. P., VOSBURGH G. J., ENNS T. Transcapillary exchange of water and of other substances in certain organs of the dog. Am J Physiol. 1955 Nov;183(2):221–234. doi: 10.1152/ajplegacy.1955.183.2.221. [DOI] [PubMed] [Google Scholar]
- CRONE C. THE PERMEABILITY OF CAPILLARIES IN VARIOUS ORGANS AS DETERMINED BY USE OF THE 'INDICATOR DIFFUSION' METHOD. Acta Physiol Scand. 1963 Aug;58:292–305. doi: 10.1111/j.1748-1716.1963.tb02652.x. [DOI] [PubMed] [Google Scholar]
- Friedman J. J. Muscle blood flow and 86Rb extraction: 86Rb as a capillary flow indicator. Am J Physiol. 1968 Mar;214(3):488–493. doi: 10.1152/ajplegacy.1968.214.3.488. [DOI] [PubMed] [Google Scholar]
- GORESKY C. A. A linear method for determining liver sinusoidal and extravascular volumes. Am J Physiol. 1963 Apr;204:626–640. doi: 10.1152/ajplegacy.1963.204.4.626. [DOI] [PubMed] [Google Scholar]
- GORESKY C. A. INITIAL DISTRIBUTION AND RATE OF UPTAKE OF SULFOBROMOPHTHALEIN IN THE LIVER. Am J Physiol. 1964 Jul;207:13–26. doi: 10.1152/ajplegacy.1964.207.1.13. [DOI] [PubMed] [Google Scholar]
- GORESKY C. A., SILVERMAN M. EFFECT OF CORRECTION OF CATHETER DISTORTION ON CALCULATED LIVER SINUSOIDAL VOLUMES. Am J Physiol. 1964 Oct;207:883–892. doi: 10.1152/ajplegacy.1964.207.4.883. [DOI] [PubMed] [Google Scholar]
- Goresky C. A., Cronin R. F., Wangel B. E. Indicator dilution measurements of extravascular water in the lungs. J Clin Invest. 1969 Mar;48(3):487–501. doi: 10.1172/JCI106006. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Goresky C. A., Ziegler W. H., Bach G. G. Capillary exchange modeling. Barrier-limited and flow-limited distribution. Circ Res. 1970 Nov;27(5):739–764. doi: 10.1161/01.res.27.5.739. [DOI] [PubMed] [Google Scholar]
- Griffen W. O., Jr, Levitt D. G., Ellis C. J., Lifson N. Intrahepatic distribution of hepatic blood flow: single-input studies. Am J Physiol. 1970 May;218(5):1474–1479. doi: 10.1152/ajplegacy.1970.218.5.1474. [DOI] [PubMed] [Google Scholar]
- LOVE W. D., ROMNEY R. B., BURCH G. E. A comparison of the distribution of potassium and exchangeable rubidium in the organs of the dog, using rubidium. Circ Res. 1954 Mar;2(2):112–122. doi: 10.1161/01.res.2.2.112. [DOI] [PubMed] [Google Scholar]
- Levi A. J., Gatmaitan Z., Arias I. M. Two hepatic cytoplasmic protein fractions, Y and Z, and their possible role in the hepatic uptake of bilirubin, sulfobromophthalein, and other anions. J Clin Invest. 1969 Nov;48(11):2156–2167. doi: 10.1172/JCI106182. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Levitt D. G. Theoretical model of capillary exchange incorporating interactions between capillaries. Am J Physiol. 1971 Jan;220(1):250–255. doi: 10.1152/ajplegacy.1971.220.1.250. [DOI] [PubMed] [Google Scholar]
- Lifson N., Levitt D. G., Griffen W. O., Jr, Ellis C. J. Intrahepatic distribution of hepatic blood flow: double-input studies. Am J Physiol. 1970 May;218(5):1480–1488. doi: 10.1152/ajplegacy.1970.218.5.1480. [DOI] [PubMed] [Google Scholar]
- PROTHERO J., BURTON A. C. The physics of blood flow in capillaries. I. The nature of the motion. Biophys J. 1961 Sep;1:565–579. doi: 10.1016/s0006-3495(61)86909-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Perl W., Chinard F. P. A convection-diffusion model of indicator transport through an organ. Circ Res. 1968 Feb;22(2):273–298. doi: 10.1161/01.res.22.2.273. [DOI] [PubMed] [Google Scholar]
- RELMAN A. S., LAMBIE A. T., BURROWS B. A., ROY A. M. Cation accumulation by muscle tissue: the displacement of potassium by rubidium and cesium in the living animal. J Clin Invest. 1957 Aug;36(8):1249–1256. doi: 10.1172/JCI103522. [DOI] [PMC free article] [PubMed] [Google Scholar]
- RENKIN E. M. Transport of potassium-42 from blood to tissue in isolated mammalian skeletal muscles. Am J Physiol. 1959 Dec;197:1205–1210. doi: 10.1152/ajplegacy.1959.197.6.1205. [DOI] [PubMed] [Google Scholar]
- SHEPPARD C. W. Mathematical considerations of indicator dilution techniques. Minn Med. 1954 Feb;37(2):93–104. [PubMed] [Google Scholar]
- SHOEMAKER W. C., WALKER W. F., VAN ITALLIE T. B., MOORE F. D. A method for simultaneous catheterization of major hepatic vessels in a chronic canine preparation. Am J Physiol. 1959 Feb;196(2):311–314. doi: 10.1152/ajplegacy.1959.196.2.311. [DOI] [PubMed] [Google Scholar]
- Sheehan R. M., Renkin E. M. Capillary, interstitial, and cell membrane barriers to blood-tissue transport of potassium and rubidium in mammalian skeletal muscle. Circ Res. 1972 May;30(5):588–607. doi: 10.1161/01.res.30.5.588. [DOI] [PubMed] [Google Scholar]
- THOMPSON H. K., Jr, STARMER C. F., WHALEN R. E., MCINTOSH H. D. INDICATOR TRANSIT TIME CONSIDERED AS A GAMMA VARIATE. Circ Res. 1964 Jun;14:502–515. doi: 10.1161/01.res.14.6.502. [DOI] [PubMed] [Google Scholar]
- TYOR M. P., ELDRIDGE J. S. A comparison of the metabolism of rubidium 86 and potassium 42 following simultaneous injection into man. Am J Med Sci. 1956 Aug;232(2):186–193. doi: 10.1097/00000441-195608000-00009. [DOI] [PubMed] [Google Scholar]

