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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

# BronchTwoAlv

This model represents a bifurcating bronchiole with two alveolar compartments. The resistance to air flow is represented by resistors, and the compliance is repsented by a capacitor. It compares this model to Lutchen's model.

Model number: 0337

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## Description

This model represents a bifurcating bronchiole with two alveoli. This model is driven by external forcing
pressure (Ptp) as with positive pressure ventilation. There is no exchange between alveoli and blood,
and the fluid (air) is assumed to be incompressible. The pressure fluctuation at the mouth has a range
of 5 mmHg to 9 mmHg. It includes a comparison with Lutchen's model for two cases: Case 1 and Case 6sine.

Case 1 is for normal alveolar compartments that have synchronized flows and volume changes, and uses the
exponential pressure forcing function used in Lutchen's model. Case 6sine is for obstructive lung disease
affecting only one alveolar compartment, and uses a sinusoidal pressure forcing function.


Representative Electrical Circuit:

## Equations

The forcing pressure at the mouth for Case 1: Exponential forcing:

$\large {\it P_{tp}}={\it P_{0}}+A \{ \begin{array}{3 3} \left( 1-{e^{-{\frac {t-t_0(k)}{{\it tau_{R}}}}}} \right) & \quad {\it t_{0}(k)} \leq {\it t} \leq {\it t_1(k) }\\ \left( 1-{e^{-{\frac {t-t_1(k)}{{\it tau_{F}}}}}} \right) & \quad {\it t_{1}(k)} \leq {\it t} \leq {\it t_0(k+1) }\\ \end{array}$

The forcing pressure at the mouth for Case 6: Sinusoidal forcing:

$\large {\it P_{tp}}={\it P_{0}}+A \left( 1-\cos \left( 2 \cdot {\it PI}\cdot f\cdot t \right) \right)$

Governing Equations in the BronchTwoAlv model:

$\large {\it P_{tp}-P_1}={\it F_1\cdot R_1 }$

$\large {\it P_1 -P_2}={\it F_2\cdot R_2 }$

$\large {\it P_1 -P_3}={\it F_3\cdot R_3 }$

$\large {\frac {d}{dt}}{\it V_1}={\it F_1}$

$\large {\frac {d}{dt}}{\it V_2}={\it F_2}$

$\large {\frac {d}{dt}}{\it V_3}={\it F_3}$

$\large {\it F_1}={\it F_2 + F_3}$

$\large {\it P_1}={\it P_{ref} + (V_1-V_D)/Com_1}$

$\large {\it P_2}={\it P_{ref} + (V_2-V2_0)/Com_2}$

$\large {\it P_3}={\it P_{ref} + (V_3-V3_0)/Com_3}$

Governing Equations in Lutchen's model:

$\large {\it P_{tp}}={\it R_1\cdot \frac{d}{dt}V_L + (b_2/V_2)\cdot\frac{d}{dt}V_2+h_i\cdot e^{V_2/eps_2} }$

$\large {\it P_{tp}}={\it R_1\cdot \frac{d}{dt}V_L + (b_3/V_3)\cdot\frac{d}{dt}V_3+h_i\cdot e^{V_3/eps_3} }$

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.



Lung models

## Key Terms

lung compliance resistance RC circuit lung mechanics airflow in trachea tidal volume positive pressure ventilation

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## 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.

[This page was last modified 02Nov16, 2:21 pm.]

Model development and archiving support at physiome.org provided by the following grants: NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.