Model effect of erythrocyte membrane on exchange of solutes between erythrocytes (red blood cells) and plasma water.
Model number: 0185
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 differential 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.
Preequilibrated injectionTracer 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
- at t = 0: Cp = 0 and CRBC = 0;
- at x = 0: Cp = (1 + β)/(1 + k1/k2 β) Cin and CRBC = k1/k2Cp
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") and the relative volume of plasma and erythrocytes:
The following tracers were injected into the portal vein of an anesthetized dog:
- Erythrocytes (Ery) labeled with 51Cr
- Labeled thiourea (NH2-14CS-NH2), a substance that penetrates easily into hepatocytes, and less easily into erythrocytes
- Tritiated water(3HOH)
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There are two parameter sets in this JSim model project file:
- HiHct: High hematocrit (0.42)
- LowHct: The hematocrit was lowered to 0.25 by bleeding and plasma substitution
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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
Author: Andreas J. Schwab (email@example.com)
- Flow limited model
- Simple elimination with flow-limited distribution
- Barrier limited model
- Linear flow coupling
- Two-barrier model
- Red cell model
indicator dilution, barrier-limited, liver, transport, vascular volume, organ, red blood cells, membrane, Goresky transport tutorial, tracer, Data, PDE
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[This page was last modified 30Jul13, 1:47 pm.]
Model development and archiving support at physiome.org provided by the following grants: NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.