TranspMM.2sided.Distrib2F

Model number: 0019

An axially distributed two region two-sided Michaelis-Menten transporter model, with permeation across the capillary wall via clefts (PS_g) and cell transporters (PS_c).

Detailed Description

A two-dimensional convection-permeation-diffusion-reaction model consisting of two concentric cylinders separated by a membrane. The capillary plasma region, volume V_p, has flow F_p, first order consumption G_p, and axial diffusion (dispersion) D_p. Units are physiological per gram of tissue so that a single unit can model a homogenously perfused organ. Radial diffusion is assumed instantaneous (short radial distances).

The interstitial fluid region, ISF, with volume V_ISF, is axially distributed. The gradients axially are dissipated by a concentration-independent axial diffusion or dispersion. Radial diffusion within this space is considered instantaneous, and consumption, G_ISF, is first order. Capillary-tissue exchange occurs by way of two parallel routes.

1. PS_g: Passive exchange between plasma and surrounding non-flowing interstitial fluid is through interendothelial clefts. PS_g is Permeability Surface area product.

2. PS_c: Facilitated transport occurs via a transporter on the capillary membrane, with PS_cmax as maximal conductance at low concentrations. Transporter is modified from TranspMM.1sided.Distrib2F, in that facilitated transport can go either way.

This model is used in multicapillary models as one of a set of units in parallel.

Relevant Equations

${ PS_{\text{\small{c}}}(t) = \frac {PS_{\text{\small{cMAX}}}}{1 + \frac {C_{\text{\small{p}}}}{K_{\text{\small{mc}}}} + \frac {C_{\text{\small{ISF}}}}{K_{\text{\small{mc}}}}}$

${ \frac {d}{dt}C_{\text{\small{p}}}(t) = - \frac {F_{\text{\small{p}}}L}{hV_{\text{\small{p}}} \frac {dC_{\text{\small{p}}}}{dx}} - \frac {(PS_{\text{\small{g}}} + PS_{\text{\small{c}}})(C_{\text{\small{p}}} - C_{\text{\small{ISF}}})}{hV_{\text{\small{p}}}} - \frac {G_{\text{\small{p}}}C_{\text{\small{p}}}}{hV_{\text{\small{p}}}} + D_{\text{\small{p}}} \frac {d^2C_{\text{\small{p}}}}{dx^2}$

${ \frac {d}{dt}C_{\text{\small{ISF}}}(t) = \frac {(PS_{\text{\small{g}}} + PS_{\text{\small{c}}})(C_{\text{\small{p}}} - C_{\text{\small{ISF}}})}{hV_{\text{\small{ISF}}}} - \frac {G_{\text{\small{ISF}}}C_{\text{\small{ISF}}}}{hV_{\text{\small{ISF}}}} + D_{\text{\small{ISF}}} \frac {d^2C_{\text{\small{ISF}}}}{dx^2}$

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References

Bassingthwaighte JB. A concurrent flow model for extraction during transcapillary passage. Circ Res 35: 483-503, 1974. (This gives numerical solutions, which are faster than the analytic solutions, and imbeds the model in an organ with tissue volums conserved, and with arteries and veins. The original Lagrangian sliding fluid element model with diffusion.)

Klingenberg M. Membrane protein oligomeric structure and transport function. Nature 290: 449-454, 1981.

Stein WD. The Movement of Molecules across Cell Membranes. New York: Academic Press, 1967.

Stein WD. Transport and Diffusion across Cell Membranes. Orlando, Florida: Academic Press Inc., 1986.

Wilbrandt W and Rosenberg T. The concept of carrier transport and its corollaries in pharmacology. Pharmacol Rev 13: 109-183, 1961.

Schwartz LM, Bukowski TR, Ploger JD, and Bassingthwaighte JB. Endothelial adenosin transporter characterization in perfused guinea pig hearts. Am J Physiol Heart Circ Physiol 279: H1502-H1511, 2000.

Dawson CA, Linehan JH, Rickaby DA, and Roerig DL. Inﬂuence of plasma protein on the inhibitory effects of indocyanine green and bromcresol green on pulmonary prostaglandin E1 extraction. Br J Pharmac 81: 449-455, 1984.

Related Models

Return to Transporter

Key Terms

Axially Distributed, two region, capillary-tissue exchange, facilitated transport, plasma, interstitial fluid region, radial diffusion.

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Copyright (C) 1999-2009 University of Washington. From the National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061. Academic use is unrestricted. Software may be copied so long as this copyright notice is included. This software was developed with support from NIH grant HL073598. Please cite this grant in any publication for which this software is used and send one reprint to the address given above.

Model development and archiving support at physiome.org provided by the following grants: 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.