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# CTEX20

Computes N compartmental two region CTEX20.

Model number: 0234

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## Description

N well stirred tanks (i.e. compartmental models with flow) representing the capillary region are connected in series and exchange with N additional tanks in parallel representing the interstitial fluid region.

## Equations

#### Ordinary Differential Equations

$\large {\frac {{\it V_p}}{N}} \cdot {\frac {d}{dt}}{\it C_{p,1}} \left( t \right) ={\it F_p}\cdot \left( {\it C_{in}} \left( t \right) - {\it C_{p,1}} \left( t \right) \right) + {\it PS_g}\cdot \left( {\it C_{isf,1}} \left( t \right) -{\it C_{p,1}} \left( t \right) \right) - {\it Gp}\cdot \left( {\it C_{p,1}} \left( t \right) \right)$ ,

for j=2..N:
$\large {\frac {{\it V_p}}{N}} \cdot {\frac {d}{dt}}{\it C_{p,j}} \left( t \right) ={\it F_p}\cdot \left( {\it C_{p,j-1}} \left( t \right) -{\it C_{p,j}} \left( t \right) \right) + {\it PS_g}\cdot \left( {\it C_{isf,j}} \left( t \right) -{\it C_{p,j}} \left( t \right) \right) - {\it Gp}\cdot \left( {\it C_{p,j}} \left( t \right) \right)$ ,

for j=1..N:
$\large {\frac {{\it V_{isf}}}{N}} \cdot {\frac {d}{dt}}{\it C_{isf,j}} \left( t \right) = {\it PS_g}\cdot \left( {\it C_{p,j}} \left( t \right) -{\it C_{isf,j}} \left( t \right) \right) - {\it Gisf}\cdot \left( {\it C_{isf,j}} \left( t \right) \right)$ .

#### Initial Conditions

for j=1..N:
$\large {\it C_{p,j}} \left( 0 \right) ={\it C_{p,j}{0}}$ , and   $\large {\it C_{isf,j}} \left( 0 \right) ={\it C_{isf,j}{0}}$ .

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

CTEX20, BTEX20, Compartmental, Stirred Tanks, Tutorial