Model number
0292

A model for triple-labeled indicator dilution experiments in a four region tissue exchange model.

Further reading:     Distributed Blood Tissue Exchange Models Explained 

Description

fig 1


This is a model for triple-labeled indicator dilution experiments in a four region tissue exchange model. A BTEX10 model is used for the vascular tracer (plasma), a BTEX20 model is used for the extracellular tracer (plasma and interstitial fluid region), and a BTEX40 model is used for the permeant tracer (plasma ,interstitial fluid region, and endothelial and parenchymal cell regions. Extraction is calculated and used to calculate estimated permeability-surface area factors between various regions. See MID4ode for a version using compartment models

 

 

 

 

 

 

 

 

 

 

Equations

  Vascular Equations

 

     Differential Equation

e0

     Left Boundary Condition

e1

    Right Boundary Conditions

e2 , e3

     Initial Conditions

e4  or  e5

  Extracellular Equations

 

     Differential Equations

e6

e7

    Left Boundary Conditions

e8 , e9

    Right Boundary Conditions

e10  ,  e11  ,  e12

     Initial Conditions

e13  ,  e14   or   e15

  Permeant Equations

 

     Differential Equations

e16

e17

e18

e19

    Left Boundary Conditions

e20 , e21 , e22 , e23 .

    Right Boundary Conditions

e24 , e25 , e26 , e27 , e28 .

     Initial Conditions

e29 , e30 , e31 , e32  or  e33 ,   ,   ,   .

 

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.

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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. 
Key terms
reaction
distributed
capillary
plasma
isf
interstitial fluid
endothelial
parenchymal
cell blood
tissue
exchange
extraction
crone-renkin
PS
BTEX10
BTEX20
BTEX40
optimization
confidence limits
vascular
extracellular
permeant
MID4
multi-tracer
albumin
sucrose
tritiated water
Acknowledgements

Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome 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.