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# Comp1FlowReactions2

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

Model number: 0236

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## 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.

## 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.



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## Key Terms

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