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# Comp3FlowExch

Three compartment model for plasma (p), interstitial fluid (ISF) and parenchymal cell (pc)

Model number: 0267

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## Description

Three Compartment model for exchange between plasma, ISF and parenchymal cell with flow in the plasma compartment. The flow transports an inflowing concentration, Cin, into the plasma compartment and transports the outflowing concentration, Cp, out of the plasma compartment.

## Equations

#### Ordinary Differential Equations

$\large {\frac {d}{dt}}{\it C_p} \left( t \right) ={\frac {{\it F_p}\cdot \left( { \it C_{in}} \left( t \right) -{\it C_p} \left( t \right) \right) }{{\it V_p}}} +{\frac {{\it PS_c}\cdot \left( {\it C_{isf}} \left( t \right) -{\it C_p} \left( t \right) \right) }{{\it V_p}}}$
$\large {\frac {d}{dt}}{\it C_{isf}} \left( t \right) ={\frac {{\it PS_{pc}}\cdot \left( {\it C_{pc}} \left( t \right) -{\it C_{isf}} \left( t \right) \right) }{{\it V_{isf}}}} +{\frac {{\it PS_c}\cdot \left( {\it C_p} \left( t \right) -{\it C_{isf}} \left( t \right) \right) }{{\it V_{isf}}}}$
$\large {\frac {d}{dt}}{\it C_{pc}} \left( t \right) = {\frac {{\it PS_{pc}}\cdot \left( {\it C_{isf}} \left( t \right) -{\it C_{pc}} \left( t \right) \right) }{{\it V_{pc}}}}$

#### Initial Conditions

$\large {\it C_p} \left( 0 \right) ={\it C_{p}{0}}$   ,   $\large {\it C_{isf}} \left( 0 \right) ={\it C_{isf}{0}}$   ,   $\large {\it C_{pc}} \left( 0 \right) ={\it C_{pc}{0}}$ .

#### Analytic Solutions when Cin is constant

$\large {\it C_p} \left( t \right) ={\it C_{in}}$   ,   $\large {\it C_{isf}} \left( t \right) ={\it C_{in}}$   and   $\large {\it C_{pc}} \left( t \right) ={\it C_{in}}$ .

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.

None.

## Related Models

Single Compartment Models:

Two Compartment Models:

N>2 Compartment Models:

Osmotic Exchange:

Pharmacology:

## Key Terms

compartment, compartmental, flow, exchange, mixing chamber, permeability, PS/F, washout, inflow-outflow operator, plasma, ISF, parenchymal cell, Tutorial