Model number
0332

  

Models a capillary consisting of N compartments. Explores sensitivity analysis and optimization. Includes curve statistics.

Description

diagram 1

N compartments in series simulate a partial differential equation with convection and diffusion. The relative dispersion of N compartments in series is 1/sqrt(N). There is not an exact relationship between the diffusion coefficient and the relative dispersion in the partial differential equation for diffusion and convection in a bounded domain with inflow and outflow at the ends. This model explores sensitivity analysis and optimization in a guided exercise.

Equations

 

     Ordinary Differential Equations

e0 ,   and for j=2..N: 

e1

 

     Initial Conditions

e2   for j=1..N.

 

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
CTEX
CTEX10
convection
diffusion
capillary
compartment
plasma
sensitivity
optimization
Tutorial
statistics
mean transit time
RD
relative dispersion
skewness
kurtosis
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.