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# Comp2FlowExchange

Two compartments, plasma and interstitial fluid (ISF), with flow and exchange using physiological names and units for parameters and variables. The model is

Model number: 0247

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## Description

A flow, Fp, carries an inflow concentration, Cin, into a plasma compartment with volume Vp. The substance is instantaneously well mixed. The material undergoes a passive exchange with an interstitial fluid (ISF) space with volume Visf. No reactions occur in this system. For a constant concentration of inflowing material the analytic steady state solution is Cp=Cin and Cisf=Cin if Psc is positive. Various methods for checking the calculations in a model are illustrated: (1) comparison with an analytic solution, (2) two methods of calculating the amount of material in a compartment with flow, (3) comparison of the running integrals of inflow and outflow concentrations, and (4) calculation of the system transit time of a compartment model with flow by two different methods. The model parameters are optimized to fit a data set.

## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}{\it C_p} \left( t \right) ={\frac {{\it F_p}\, \left( { \it C_{in}}-{\it C_p}\left( t \right) \right) }{{\it V_p}}}+{\frac {{\it PS_c}\, \left( { \it C_{isf}} \left( t \right) -{\it C_p} \left( t \right) \right) }{{\it V_p}}}$
$\large {\frac {d}{dt}}{\it C_{isf}} \left( t \right) ={\frac {{\it PS_c}\, \left( {\it C_p} \left( t \right) -{\it C_{isf}} \left( t \right) \right) }{{\it V_{isf}}}}$

#### Initial Conditions

$\large {\it C_p} \left( 0 \right) ={\it C_{p}{0}}$   and   $\large {\it C_{isf}} \left( 0 \right) ={\it C_{isf}{0}}$ .

#### Analytic Steady State Solutions when Cin is constant

$\large {\it C_p} \left( t \right) ={\it C_{in}}$   and   $\large {\it C_{isf}} \left( t \right) ={\it C_{in}}$ .

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, flow, exchange, multi-compartments, two compartments, data