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.

# Comp1FlowReactions2

Single Compartment with flow and irreversible conversion of C to D and D to E.

Model number: 0236

 Run Model: Help running a JSim model.
Java runtime required. (JSim model may take 10-20 seconds to load.)
MacOS: Adjust "System Preferences" -> "Security & Privacy" to allow Java JSim jnlp app to execute.
More info here.

## Description

This is a one compartment model. F is flow, Cin is inflow concentration, Cout, Dout, and Eout are outflow concentrations, V is volume, Gc2d is the rate at which substance C is converted to substance D, andGd2e is the rate at which substance D is converted to substance E. The reactions are irreversible. C0, D0, and E0 are the initial concentrations of C, D, and E respectively. The amount of material in the compartment is calculated by multiplying the volume by the sum of the concentrations and also by integrating the flow multiplying the difference of what flows in minus what flows out.

Further reading:

## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}C \left( t \right) ={\frac {F \cdot \left( {\it C_{in}} \left( t \right) -C \left( t \right) \right) }{V}}-{\frac {{\it G_{c2d}}\, \cdot C \left( t \right) }{V}}$

$\large {\frac {d}{dt}}{\it D} \left( t \right) =-{\frac {F \cdot {\it D} \left( t \right) }{V}}+{\frac {{\it G_{c2d}} \cdot C}{V}}-{\frac {{\it G_{d2e}} \cdot {\it D} \left( t \right) }{V}}$

$\large {\frac {d}{dt}}E \left( t \right) =-{\frac {F \cdot E \left( t \right) }{V}}+ {\frac {{\it G_{d2e}} \cdot {D} \left( t \right) }{V}}$

#### Initial Conditions

$\large {\it C} \left( 0 \right) ={\it C0}$
$\large {\it D} \left( 0 \right) ={\it D0}$
$\large {\it E} \left( 0 \right) ={\it E0}$

The equations for this model may 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


Jacquez JA. Compartmental Analysis in Biology
and Medicine. Ann Arbor: University of Michigan Press, 1996.



## Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

## Key Terms

Compartmental, one compartment, single compartment, flow, reactions, conversion, irreversible, Tutorial

## Model Feedback

We welcome comments and feedback for this model. Please use the button below to send comments:

## Model History

Get Model history in CVS.

## Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

[This page was last modified 14Mar18, 3:17 pm.]

Model development and archiving support at physiome.org provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.