This page will look better in a graphical browser that supports web standards, but is accessible to any browser or internet device.

Served by Samwise.

Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

TranspMM.2sided.Distrib3F.2Ch

Model number: 0020

A capillary-ISF-cell convection diffusion model, modified BTEX30 with a Michaelis-Menten saturable transporter on the pc membrane. It is represented by two separated and independent unidirectional transporters, each governed by the fractional saturation in the source compartment, i.e. by the concentration in the ISF to define PSISF2pc, and in the pc, Cpc, to define PSpc2ISF, the conductance via the carrier from pc to ISF. A three region two-side Michaelis-Menten transporter model.

Detailed Description

This model is almost the same as TranspMM.2sided.Distrib2F.proj but differs in the form of the transporter. In this program the two opposite fluxes are independent. In the .Distrib2F.proj model the conductances are identical for the two directions.

BTEX stands for blood-tissue exchange, 3 denotes 3 regions, 0 indicates a basic model. The 3 regions are the convecting plasma, p, and stagnant ISF and parenchymal cell, pc. Axial gradients exist in all three regions. Each region is considered radially uniform on the basis that radial diffusion distances are so short that diffusional relaxation times are at most a few miolliseconds and can be considered instantaneous. The endothelial cell is considered as a passive barrier without capacitance and has permeability-surface area product, PSg, where the subscript g indicates the interendothelial clefts. The organ parenchymal cells, pc, here has a saturable PSpc.

Consumption in all regions is by simple first order reactions with rate constant G. Axial diffusion occurs in all regions, Dp, DISF, and Dpc. Capillary mean transit time is Vp/Fp, physical velocity is L/(Vp/Fp).

Relevant Equations

$\large { PS_{\text{\small{ISF2pc}}}(t,x) = \frac {PS_{\text{\small{pcmax}}}}{1 + \frac {C_{\text{\small{ISF}}}}{K_{\text{\small{mISF}}}}}$

$\large { PS_{\text{\small{pc2ISF}}}(t,x) = \frac {PS_{\text{\small{pcmax}}}}{1 + \frac {C_{\text{\small{pc}}}}{K_{\text{\small{mpc}}}}}$

$\large { h V_{\text{\small{p}}} \frac {d C_{\text{\small{p}}}(t,x)}{dt} = -F_{\text{\small{p}}} L_{\text{\small{cap}}} \frac {d C_{\text{\small{p}}}}{dx} - G_{\text{\small{p}}}C_{\text{\small{p}}} + h V_{\text{\small{p}}} D_{\text{\small{p}}} \frac {d^2 C_{\text{\small{p}}}}{dx^2} - PS_{\text{\small{g}}} (C_{\text{\small{p}}} - C_{\text{\small{ISF}}})$

$\large { h V_{\text{\small{ISF}}} \frac {d C_{\text{\small{ISF}}}(t,x)}{dt} = -G_{\text{\small{ISF}}} C_{\text{\small{ISF}}} + h V_{\text{\small{ISF}}} D_{\text{\small{ISF}}} \frac {d^2 C_{\text{\small{ISF}}}}{dx^2} + PS_{\text{\small{g}}}(C_{\text{\small{p}}} - C_{\text{\small{ISF}}}) + PS_{\text{\small{pc2ISF}}} C_{\text{\small{pc}}} - PS_{\text{\small{ISF2pc}}} C_{\text{\small{ISF}}}$

$\large { h V_{\text{\small{pc}}} \frac {d C_{\text{\small{pc}}}(t,x)}{dt} = -G_{\text{\small{pc}}} C_{\text{\small{pc}}} + h V_{\text{\small{pc}}} D_{\text{\small{pc}}} \frac {d^2 C_{\text{\small{pc}}}}{dx^2} + PS_{\text{\small{ISF2pc}}} C_{\text{\small{ISF}}} - PS_{\text{\small{pc2ISF}}} C_{\text{\small{pc}}}$

Run JSim Model

Press the "Run Applet" button to bring up the model in a separate window.

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.

Crone C. Facilitated transfer of glucose from blood into brain tissue. J Physiol 181: 103-113, 1965.

Key Terms

Michaelis-Menten, BTEX30, Blood tissue exchange, 3 region, interstitial fluid, parenchymal cell, axial diffusion, passive barrier, interendothelial clefts, capillary mean transit time

JSim Tutorial

Click here to go to a JSim tutorial webpage, with an introduction to the JSim GUI, detailed usage instructions, and an accompaying video.