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# Comp2ExchangeReaction

Two comparment model with two substances, irreversibly converting A to B.

Model number: 0246

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## Description

This is a two compartment model for two substances, A and B. Both substances can passively move from one compartment to the other. A is irreversibly converted to B in either or both compartments.

Further reading:

## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}{\it A_1} \left( t \right) ={\frac {{\it PS_a}\, \left( { \it A_2} \left( t \right) -{\it A_1} \left( t \right) \right) }{{\it V_1 }}}-{\frac {{\it G_1}\,{\it A_1} \left( t \right) }{{\it V_1}}}$
$\large {\frac {d}{dt}}{\it B_1} \left( t \right) ={\frac {{\it PS_b}\, \left( { \it B_2} \left( t \right) -{\it B_1} \left( t \right) \right) }{{\it V_1 }}}+{\frac {{\it G_1}\,{\it A_1} \left( t \right) }{{\it V_1}}}$
$\large {\frac {d}{dt}}{\it A_2} \left( t \right) ={\frac {{\it PS_a}\, \left( { \it A_1} \left( t \right) -{\it A2} \left( t \right) \right) }{{\it V_2 }}}-{\frac {{\it G_2}\,{\it A_2} \left( t \right) }{{\it V_2}}}$
$\large {\frac {d}{dt}}{\it B_2} \left( t \right) ={\frac {{\it PS_b}\, \left( { \it B_1} \left( t \right) -{\it B_2} \left( t \right) \right) }{{\it V_2 }}}+{\frac {{\it G_2}\,{\it A_2} \left( t \right) }{{\it V_2}}}$

#### Initial Conditions

$\large {\it A_1} \left( 0 \right) ={\it A_10}$$\large {\it A_2} \left( 0 \right) ={\it A_20}$$\large {\it B_1} \left( 0 \right) ={\it B_10}$ ,  and   $\large {\it B_2} \left( 0 \right) ={\it B_20}$ .

#### Analytic Solutions exist but are very long.

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.

## References

 None.



## Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

## Key Terms

Course, compartment, compartmental, tutorial, exchange, multiple compartments, flux, steady state, reaction, conversion

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## Model History

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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 14Mar18, 3:17 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.