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

# Comp1Flow

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

Model number: 0241

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## Description

(See Comp1FlowPlus for more detailed treatment.)

In a single compartment with flow, there is a source term, (Flow/Volume)*Cin, which adds material to the compartment, and a sink term, -(Flow/Volume)*C, the washout term, which removes material from the compartment. These two terms are usually combined as a single term in the mass balance ordinary differential equation after dividing left and right hand sides by the volume:

dC/dt = (Flow/Volume)*(Cin-C).

The compartment is instantaneously well mixed.

Various methods for checking the calculations in a model are illustrated: (1) two methods of calculating the amount of material in a compartment with flow, (2) comparison of the running integrals of inflow and outflow concentrations, and (3) calculation of the system transit time of a compartment model with flow by two different methods.

## Equations

#### Ordinary Differential Equation

$\large {\frac {d}{dt}}C \left( t \right) ={\frac {{\it Flow} \cdot \, \left( {\it C_{in}} \left( t \right) -{\it C_{p}} \left( t \right) \right) }{{\it Volume}}}$

#### Initial Condition

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

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

compartment, compartmental, flow, first order process, Tutorial