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# Comp1FlowDecayPhysiologicalVersion

Models single compartment with inflowing and outflowing concentration of a single substance which undergoes decay.

Model number: 0244

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## Description

A Flow carries an inflow concentration, Cin, into a one compartment model with a given Volume. Cin is constantly and instantaneously well mixed becoming C, the concentration in the compartment. C empties out of the compartment and is designated Cout. G is a clearance rate. For a constant concentration of inflowing material the analytic solution is given.

## Equations

#### Ordinary Differential Equation

$\large {\frac {d}{dt}}C \left( t \right) ={\frac {F \cdot \left( {\it C_{in}} \left( t \right) -{\it C_{out}} \left( t \right) \right) } {V}}-{\frac {G \cdot C \left( t \right) }{V}}$

#### Initial Condition

$\large {\it C} \left( 0 \right) ={\it C0}$

#### Analytic Solution when Cin(t) is constant

$\large {\it C_{analytic}}=\frac {\left( F \cdot {\it C_{in}}- \left( F \cdot \left( {\it C_{in}}-{\it C_0} \right) -G \cdot {\it C_0} \right) {e^{-{\frac { \left( F+ G \right) t}{V}}}} \right)}{ \left( F+ G \right) }$

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.



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## Key Terms

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