The erythrocyte membrane potentially limits the exchange of solutes between erythrocytes (red blodd cells) and plasma water. The multiple indicator dilution technique can be used to investigate the effect of this barrier on the exchange of tracer substances.
The concentrations in plasma, Cp and in erythrocytes, CRBC are discribed by the following system of partial differenctial equations in time t and space x: where Cp and CRBC are concentrations in plasma and in erythrocytes, W is the linear velocity of erythrocytes within the sinusoidal lumen, k1 and k2 are transfer coefficients or rate constants, defining the transfer of tracer between plasma and the cytoplasm of perythrocytes, β is the ratio of the red cell water space to the plasma water space in the blood, t0 is the large vessel transit time, and γ is the ratio of the extravascular water space to the sinusoidal plasma water space.
Tracer to be injected are added to a blood sample or the same hematocrit as in systemic blood some time before injection. In this case, the tracer will equilibrate between plasma and erythrocytes, and the boundary conditions are
where Cin is the tracer concentration at the inflow of the organ. In order to make calculations easier, concentrations are normalized by dividing through the injected amount, and distances are normalized by dividung through the linear velocity W, thus assuiming W = 1.
The concentration in the blood leaving the organ through the portal vein is calculated as the average weighted according to the flow in all sinusoidal paths (analogous to the case of “barrier-limited transport”:Barrier_limited_LSFEA and the relative volume of plasma and erythrocytes:
The following tracers were injected into the portal vein of an anesthetized dog:
Samples from a hepatic vein were analyzed for beta radioactivity, and the various isotopes where distinguished by scintillation spectrometry. In the following applet o click on “Run” to calculate the curves o click on plotpage_1 to see the data and the calculated curves
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CA Goresky, GG Bach and BE Nadeau. Red cell carriage of label: its limiting effect on the exchange of materials in the liver. Circulation Research:36, 328-351, 1975
Key Terms: indicator dilution, barrier-limited, liver, transport, vascular volume, organ
Andreas J. Schwab email@example.com
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