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# BronchBronchiolAlv

This model represents airway with one bronchus, one bronchiole, and an alveolus.

Model number: 0006

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## Description

This model represents airway with one bronchus,one bronchiole, and one alveolus. The bronchus has largest resistance and smallest compliance. The bronchiole has smaller resistance and larger compliance than bronchus. The alveolus has the smallest resistance and largest compliance. Air flow is driven by a positive pressure ventilator.

## Equations

$\large {\it P}_{\text{\small{mouth}}}={\it P}_{\text{\small{scalar}}}\,{\it P}_{\text{\small{drive}}}$

$\large {\it P}_{\text{\small{mouth}}}-{\it P_{\text{\small{bronch}}}={\it F}_{\text{\small{mouth}}}\,{\it R}_{\text{\small{bronch}}}$

$\large {\it P}_{\text{\small{bronchi}}}={\frac {{{\it V}_{\text{\small{bronch}}}-{\it V}_{\text{\small{bronch0}}}}}{\it Com}_{\text{\small{Bronch}}}$

$\large {\it P_{bronch}}-{\it P_{bronchiol}}={\it F_{bronchiol}}\,{\it R_{bronchiol}}$

$\large {\it P_{bronchiol}}={\frac {{{\it V_{bronchiol}}-{\it V_{bronchiol0}}}}{\it Com_{Bronchiol}}$

$\large {\it P_{bronchiol}}-{\it P_{alv}}={\it F_{alv}}\,{\it R_{alv}}$

$\large {\it P_{alv}}={\frac {{{\it V_{alv}}-{\it V_{alv0}}}}{\it Com_{Alv}}$

$\large {\frac {d}{dt}}{\it V_{bronchi}}={\it F_{mouth}}-{\it F_{bronchiol}}$

$\large {\frac {d}{dt}}{\it V_{bronchiol}}={\it F_{bronchiol}}-{\it F_{alv}}$

$\large {\frac {d}{dt}}{\it V_{alv}}={\it F_{alv}}$

where Pmouth is the pressure at the mouth; P scalar multiplies Pdrive, a function representing inhalation pressure; Pbronch, Pbonchiol and Palv are the pressure in the bronchus, bronchiole, and alveolus; Fmouth, Fbronch,Fbronchiol,and Falv are the air flow at the mouth, bronchus, bronchiole, and alveolus; Rbronch, Rbonchiol and Ralv are the resistances of the bronchus, bronchiole, and alveolus to the air flow; Combronch, Combonchiol and Comalv are the compliances of the bronchus, bronchiole, and alveolus; and Vbronchi, Vbonchiol and Valv are the volumes of air in the the bronchus, bronchiole, and alveolus.

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

 M.G. Levitsky, Pulmonary Physiology, Sixth Edition, McGraw Hill, 2003.

V.C. Rideout, Mathematical and Computer Modeling of Physiological Systems,
Prentice Hall, 1991, p137-143



## Key Terms

lung compliance, resistance, RC circuit, lung mechanics, airflow in bronchus, tidal volume, positive pressure ventilation, airway, PV curves, bronchus, bronchiole, alveolus

## Model History

Get Model history in CVS.

Posted by: Feng Gao fg3-at-u.washington.edu

## 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.