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# DiffusionLimitedProfiles

Concentration profiles in capillary and tissue when exchange is diffusion limited. Includes axial and radial diffusion in a 2-D (x,r,t) partial differential equation problem.

Model number: 0325

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## Description

This is a modified version of a BTEX20 model where the cell
has been divided into 20 sub-compartments. The exchange
coefficients between the sub-compartments are calculated to
solve the radial diffusion equation. This is a two-dimensional
partial differential equation.

Solutions are displayed in 3 formats:
Contours,
Wire Mesh (RUN LOOPS), and
Vertically Exaggerated Wire Mesh (RUN LOOPS).

NOTA BENE: To construct the wire mesh plots requires 21*21=441
solutions. The program takes significant time to run.

The vertically exaggerated wire mesh shows that the low
tissue diffusion coefficient results in a "trailing wave"
of concentration in the tissue. This model was generated
by MPC (the Modular Program Constructor).

The wire mesh concentration profiles in capillary and tissue when exchange is diffusion limited.

## Equations

#### Advection-diffusion partial differential equation in cylindrical coordinates without angular dependence

$\large {\frac {\partial}{\partial t}}C= -U \left( r \right) {\frac {\partial }{\partial x}}C + D \cdot \left( {\frac {1}{r}} \cdot {{\frac {\partial }{\partial r}} \left( r{\frac {d}{dr}}C \right) }} +{\frac {\partial ^{2}}{\partial {x}^{2}}}C \right)$

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

## References

Bassingthwaighte JB, Knopp TJ, and Hazelrig JB.
A concurrent flow model for capillary-tissue exchanges.
In: Capillary Permeability (Alfred Benzon Symp. II), edited
by Crone C and Lassen NA. Copenhagen: Munksgaard, 1970, pp 60-80.

## Related Models

Blood Tissue Exchange (BTEX) models

MPC: This model was initially created using the Modular Program Constructor (MPC). For more information:

## Key Terms

diffusion limited, btex20, radial diffusion, wire mesh, contour, 2-d, 2D, partial differential equation, PDE, Modular Program Constructor, MPC, publication

## Model Feedback

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## Model History

Get Model history in CVS.

Posted by: G.M. Raymond

## Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 14Mar18, 3:17 pm.]

Model development and archiving support at physiome.org provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, 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.