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

# Comp1DecayPlus

One compartment model with decay of substance

Model number: 0281

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## Description

This is a one compartment model with a single substrate, C. C decays with rate constant G. Additionally, this model includes a tutorial on sensitivity analysis and optimization. Compartmental models are based on mass balance equations. The compartment has a volume, V, and a time-varying concentration of a substance, C(t). An underlying assumption of compartmental models is that the material in the compartment is instantaneously well mixed. The total amount of material, Q(t), is given by the equation Q(t)=V*C(t). The time rate of change of the amount of material is given by the derivative, dQ(t)/dt. If the volume is constant through time, then dQ(t)/dt=V*dC(t)/dt. The rate of change of the material in the volume equals the SUM OF THE SOURCES MINUS THE SINKS for the material. This is a model for exponential decay (and also growth). It provides a numeric solution and an analytic solution. The independent variable is named ?t? standing for time. The sink for the material is the exponential decay. It removes material from the system.

## Equations

#### Ordinary Differential Equation

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

#### Initial Condition

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

#### Analytic Solution

$\large {\it analyticC} \left( t \right) ={\it C0}\,{e^{-{\frac {G \cdot t}{V}}}}$

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

Transport physiology, compartment, compartmental, decay, one, single, sensitivity, optimization, tutorial