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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

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.

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