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# Comp1Decay

One compartment with decay of substance, a first order process.

Model number: 0240

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## Description

(See Comp1DecayPlus for more detailed treatment.)

A compartment model has a volume and a concentration of a substance. The product of the volume and the concentration is a quantity of material. The change in the quantity is described by mass balance equations.

The volume is usually designated as V, the concentration as C, and the amount of material as Q. The change in concentration, dQ/dt is governed by sources (which add material to Q) and sinks which subtract material from Q. A source will be a positive quantity. A sink will be a negative quantity. The change in Q can be written as

   dQ/dt = d(V*C)/dt = C*dV/dt+V*dC/dt.
Assuming V is constant,
   dQ/dt = V*dC/dt.
The ODE equation describing the first order decay process is given as
   V*dC/dt = -G*C
which is usually rewritten as
 dC/dt = -(G/V)*C,
after dividing both sides by the volume. The term on the right hand side is a sink term. It is negative and removes material from the compartment.

## Equations

#### Ordinary Differential Equation

$\large {\frac {d}{dt}}C \left( t \right) =-{\frac {G \cdot C \left( t \right) }{V}}$

#### 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

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N>2 Compartment Models:

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## Key Terms

compartment, compartmental, decay, first order process, Tutorial