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# Pleural_vs_ExternalPress

Two different ways of expressing breathing, one as if using a ventilator at the mouth and the other one as human pleural muscle generating pressure gradient against external pressure. Three models used to compare differences.

Model number: 0180

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## Description

  These models compare three situations, each with two compartments having resistances,
compliances, switches and initial masses of specie in the two tanks. The first model
has a pressure source in external air as in the case of breathing support of patient
with a ventilator. The second model has a pressure source attached to the most inner
tank as in the case of regular human breathing, when the tension of pleural muscle
controls the generated pressure difference. Depending on the compliances and volumes
of the tanks, time elapsed to reach the stationary conditions may vary slightly.
However, the two cases show the same long time flow and concentration characteristics.
The last model shows the case when internal and external pressure sources are applied
simultaneously. It simulates the situation when a patient initially on a breathing
support starts to breath on his own, but the ventilator is still active.



## Equations

The governing equations are

External Pressure Source at the mouth

$\frac{\partial V2}{\partial t} = F2-F1$

$F2 = \frac{(Pair-P2)}{R2a}$

$P2= \{ \begin{array}{ll}\frac{(V2-Vr2)}{Com2}&& \text{for } V2>Vr2 \vspace{20} \\ \left[1-\left(\frac{Vr2}{V2}\right)^\beta\right] \frac{Vr2}{\beta Com2}&& \text{for } V2 \leq Vr2 \end{array}$

$\frac{\partial Q2}{\partial t} = (F1 \cdot (-C1 \cdot (1-switch1) - C2 \cdot switch1)+F2 \cdot (Cair \cdot switch2 + C2 \cdot (1-switch2)))$ $C2 = \frac{Q2}{V2}$

$\frac{\partial V1}{\partial t} = F1$

$F1 = \frac{(P2-P1)}{R12}$

$P1= \{ \begin{array}{ll}\frac{(V1-Vr1)}{Com1}&& \text{for } V1>Vr1 \vspace{20} \\ \left[1-\left(\frac{Vr1}{V1}\right)^\beta\right] \frac{Vr1}{\beta Com1}&& \text{for } V1 \leq Vr1 \end{array}$

$\frac{\partial Q1}{\partial t} = (F1 \cdot ((C2 \cdot switch1) + C1 \cdot (1- switch1)))$

$C1 = \frac{Q1}{V1}$

**Pleural Muscle as a Pressure Source** $\frac{\partial V1}{\partial t} = F1$

$F1 = \frac{(P2-P1)}{R12}$

$P1-Ppleural= \{ \begin{array}{ll}\frac{(V1-Vr1)}{Com1}&& \text{for } V1>Vr1 \vspace{20} \\ \left[1-\left(\frac{Vr1}{V1}\right)^\beta\right] \frac{Vr1}{\beta Com}&& \text{for } V1 \leq Vr1 \end{array}$

$\frac{\partial Q1}{\partial t} = (F1 \cdot ((C2 \cdot switch1) + C1 \cdot (1- switch1)))$

$C2 = \frac{Q1}{V1}$

$\frac{\partial V2}{\partial t} = F2-F1$

$F1 = \frac{(Pair-P2)}{R2a}$

$P2-Ppleural= \{ \begin{array}{ll}\frac{(V2-Vr2)}{Com2}&& \text{for } V2>Vr2 \vspace{20} \\ \left[1-\left(\frac{Vr2}{V2}\right)^\beta\right] \frac{Vr2}{\beta Com2}&& \text{for } V2 \leq Vr2 \end{array}$

$\frac{\partial Q2}{\partial t} = (F1 \cdot (-C1 \cdot (1-switch1) - C2 \cdot switch1)+F2 \cdot (Cair \cdot switch2 + C2 \cdot (1-switch2)))$

$C2 = \frac{Q2}{V2}$

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.

## Key Terms

Airway, Pleural, External, Respiratory mechanics,

## Model History

Get Model history in CVS.

Posted by: BEJ

## Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.