Comp1FlowReaction

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# Comp1FlowReaction

In a single compartment with flow, substrates C and D convert to each other using an equilibrium constraint.

Model number: 0237

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## Description

This is a one compartment model. F is flow, Cin is inflow concentration, Cout and Dout are outflow concentrations, V is volume, kc2d is the rate at which substance C is converted to substance D, and kd2c is the rate at which substance D is converted to substance C. C0 and D0 are the initial concentrations of C and D 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. Statistics about this system can be calculated on either the sum of Cout plus Dout, or on either substance separately.

## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}C \left( t \right) ={\frac {F \cdot \left( {\it C_{in}} -C \left( t \right) \right) }{V}}-{\it k_{c2d}}\cdot C \left( t \right) +{\it k_{d2c}}\cdot D \left( t \right)$

$\large {\frac {d}{dt}}D \left( t \right) =-{\frac {F \cdot D \left( t \right) }{V}}+ {\it k_{c2d}}\cdot C \left( t \right) -{\it k_{d2c}}\cdot D \left( t \right)$

#### Initial Conditions

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

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

single compartment, flow, reaction, conversion, Tutorial