BTEX20radialDiffusion

A two region model of capillary and cell with cell subdivided into 20 subregions with axial and radial diffusion. Time-dependent plots of contours and center-of-mass of material are calculated using MATLAB.

Model number: 0327

Run Model:

Help running a JSim model.

Description

   This is a modification of the BTEX20 model. Radial diffusion
has been included by subdividing the tissue region into 20
layers and solving the 2-D time dependent problem. The model
includes a java interface to Matlab(TM) to make a movie (avi file)
of the concentration contours in the capillary and tissue as
a function of time. In order to use this feature, the user
must have the Matlab(TM) routines and this JSim project file in
the user's directory, along with the Matlab(TM) path set to that
directory. The two lines of code at the end of this model
which call the java interface to Matlab(TM) have been commented out
(see code above). The Matlab routines are contained in a
tar file which can be downloaded from this page along with
the project file.

These graphs are snapshots at different times of contours of the Concentration in the capillary and surrounding tissue.
Panel Bottom Center shows the center of Mass of the substance (red tissue only, blue tissue+capillary).
Panel Bottom Left shows the corresponding components as functions of time.

Parameters are
L=1000 um (capillary length),
Fp=3 ml/(g*min) (flow),
PS = 10 ml/(g*min) (membrane permeability surface area product),
Dcap=1E-6 cm^2/sec (capillary axial diffusion coefficient),
Dx=1E-6 cm^2/sec (tissue axial diffusion coefficient),
Dr=1E-7 cm^2/sec (tissue radial diffusion coefficient).

Download P1Dm7.avi Movie (below) to see time lapse movie of contours generated with these parameters.

Equations

The equations for this model may be viewed by running the 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). To make the avi Movies, you must have Matlab installed, and the path set to the directory where the JSim project and Matlab files are stored. 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.

Download matlab files and project in tar archive.

Download PSdivFeq10.avi Movie

Blue-white curve is the center of mass including the capillary.
Red-white curve is the center of mass excluding the capillary.

Fp = 1 ml/(g*min)
PS = 10 ml/(g*min)
Dcap = 1e-4 cm^2/sec
Dx = 6e-5 cm^2/sec
Dr = 2e-7 cm^2/sec;

Download FlowLimited.avi Movie

Blue-white curve is the center of mass including the capillary.
Red-white curve is the center of mass excluding the capillary.

Fp = 3 ml/(g*min)
PS = 10 ml/(g*min)
Dcap = 1e-6 cm^2/sec
Dx = 1e-6 cm^2/sec
Dr = 1e-7 cm^2/sec;

Download BarrierLimited.avi Movie

PS = 0.1
Dr = 1e-7 cm^2/sec

Download MixedCase.avi Movie

PS = 1 ml/(g*min)
Dr = 1e-7 cm^2/sec

Download hiPS_lowDr.avi Movie

PS = 10 ml/(g*min)
Dr = 1e-8

References


W.C. Sangren and C.W. Sheppard.  A mathematical derivation of the
exchange of a labelled substance between a liquid flowing in a
vessel and an external compartment.  Bull Math BioPhys, 15, 387-394,
1953.

C.A. Goresky, W.H. Ziegler, and G.G. Bach. Capillary exchange modeling:  
Barrier-limited and flow-limited distribution. Circ Res 27: 739-764, 1970.

J.B. Bassingthwaighte. A concurrent flow model for extraction
during transcapillary passage.  Circ Res 35:483-503, 1974.

B. Guller, T. Yipintsoi, A.L. Orvis, and J.B. Bassingthwaighte. Myocardial 
sodium extraction at varied coronary flows in the dog: Estimation of 
capillary permeability by residue and outflow detection. Circ Res 37: 359-378, 1975.

C.P. Rose, C.A. Goresky, and G.G. Bach.  The capillary and
sarcolemmal barriers in the heart--an exploration of labelled water
permeability.  Circ Res 41: 515, 1977.

J.B. Bassingthwaighte, C.Y. Wang, and I.S. Chan.  Blood-tissue
exchange via transport and transformation by endothelial cells.
Circ. Res. 65:997-1020, 1989.

Poulain CA, Finlayson BA, Bassingthwaighte JB.,Efficient numerical methods 
for nonlinear-facilitated transport and exchange in a blood-tissue exchange 
unit, Ann Biomed Eng. 1997 May-Jun;25(3):547-64.

Related Models

Key Terms

plasma,cell,2-d, radial diffusion, axial diffusion, center of mass, Java interface, Matlab movie, avi, statistics

Model Feedback

We welcome comments and feedback for this model. Please use the button below to send comments:

Model History

Get Model history in CVS.

Posted by: Name

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 15May12, 11:24 am.]

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.