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CompNFlowDelay

Computes N compartment models in series, each with volume = Vp/N, and with an added delay.

Model number: 0250

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Description

N well stirred tanks (i.e. compartmental models with flow) are connected in series. A delay is imposed on the result. The total volume is kept constant. The transit time and the variances of the input to the first tank and the output of the last tank after the delay are computed. From this information, the transit time, and the variance of N stirred tanks plus delay is computed.

Further reading:     Understanding the CompNFlowDelay Model Download PDF file.

Equations

 

     Ordinary Differential Equations

,   and for j=2..N:  .

     Initial Conditions

  for j=1..N.

     Analytic Solution for Relative Dispersion

The equations for this model may also 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.

Download JSim project file

References

Bassingthwaighte, J.B. Plasma indicator dispersion in 
arteries of the human leg. Circ. Res. 19: 332-346, 1966.

Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

Key Terms

RD, Relative Dispersion, Compartmental, Compartment, Stirred Tanks, delay, transit time, Tutorial

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Acknowledgements

Please cite www.physiome.org 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.

[This page was last modified 29Jan20, 1:02 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.