Model number
0288

  

A model for triple-labeled indicator dilution experiments in a four compartment 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 compartment model. A one compartment model is used for the vascular tracer (plasma), a two compartment model is used for the extracellular tracer (plasma and interstitial fluid region), and a 4 compartment 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 MID4pde for a distributed model using partial differential equations instead of ordinary differential equations.

Equations

     Differential Equation

e0

     Initial Condition

e1

  

 

 

 

 

Extracellular Equations

     Differential Equations

e2

e3

     Initial Conditions

e4

  Permeant Equations

     Differential Equations

e5

e6

e7

e8

     Initial Conditions

e9 , e10 , e11 , e12 .

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
4 region
albumin
blood
BTEX10
BTEX20
BTEX40
capillary
cell
compartment
confidence limits
convection
Crone-Renkin
diffusion
dilution
endothelial
exchange
extracellular
extraction
indicator
interstitial fluid
isf
MID4ode
MID4pde
multiple
multi-tracer
optimization
parenchymal
permeant
permeation
plasma
PS
reaction
sucrose
tissue
tritiated water
vascular
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.