This page will look better in a graphical browser that supports web standards, but is accessible to any browser or internet device.

Served by Samwise.

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

# Comp1FlowDecay

Models single compartment with inflowing and outflowing concentration of a single substance which undergoes decay. Does not use physiological units.

Model number: 0242

 Run Model: Help running a JSim model.
Java runtime required. Web browser must support Java Applets.
(JSim model applet may take 10-20 seconds to load.)

## 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

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

#### Initial Condition

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

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

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

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.



## Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

## Key Terms

Course, compartment, compartmental, tutorial, flow, decay, clearance, Comp1FlowDecay