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# Comp2x2Recirc

Dual comp2 flow-exchange models in series with recirculation and clearance.

Model number: 0285

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## Description

A two organ two comparmental model with recirculation for exchange between plasma and ISF in both organs, with an input function, Cin, defined at run time using the function generator. Set Clear to 0 for no clearance, Clear to 1 for complete clearance (no recirculation).

 DIAGRAM:
__________________         __________________
|V1p      C1p(t) | C1p(t)  |V2p      C2p(t) | C2p(t)
Cin->--(+)->|                |--->---->|                |--->|
^   |     ^ PS1c     |  Flow   |      ^  PS2c   |    |
|   ------|----------|         -------|=--------|    |
|   |     v  C1isf(t)|         |      v C2isf(t)|    |
|   |                |         |                |    v
Clear \_   |V1isf           |         |V2isf           |    |
|   -----------------|         ------------------    |
|                       Flow                         |
-------------------------<----------------------------


## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}{\it C_{1p}}={\frac {{\it Flow}\cdot \left( {\it C_{in}} +{\it C_{2p}}\cdot \left( 1-{\it Clear} \right) -{\it C_{1p}} \right) } {{\it V_{1p}}}} -{ \frac {{\it PS_{1c}}\cdot \left( {\it C_{1p}}-{\it C_{1isf}} \right) }{{\it V_{1p}}}}$
$\large {\frac {d}{dt}}{\it C_{1isf}}={\frac {{\it PS_{1c}}\cdot \left( {\it C_{1p}} -{\it C_{1isf}} \right) }{{\it V_{1isf}}}}$
$\large {\frac {d}{dt}}{\it C_{2p}}={\frac {{\it Flow}\cdot \left( {\it C_{1p}} -{\it C_{2p}} \right) }{{\it V_{2p}}}}-{\frac {{\it PS_{2c}}\cdot \left( {\it C_{2p}} -{\it C_{2isf}} \right) }{{\it V_{2p}}}}$
$\large {\frac {d}{dt}}{\it C_{2isf}}={\frac {{\it PS_{2cP}}\cdot \left( {\it C_{2p}} -{\it C_{2isf}} \right) }{{\it V_{2isf}}}}$

#### Initial Conditions

$\large {\it C_{1p}} \left( 0 \right) ={\it C_{1p0}}$ ,   $\large {\it C_{1isf}} \left( 0 \right) ={\it C_{1isf0}}$ ,   $\large {\it C_{2p}} \left( 0 \right) ={\it C_{2p0}}$ ,   $\large {\it C_{2isf}} \left( 0 \right) ={\it C_{2isf0}}$ ,

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

  Jacquez JA. Compartmental analysis in biology and medicine.
3rd ed.. Ann Arbor, MI: BioMedware, 1996, 514 pp.



## Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

## Key Terms

compartment, compartmental, flow and exchange, mixing chamber, permeability, PS/F, washout, organ, multi-organ, Comp2x2Recirc, Tutorial