# Rigid_bifurcating_bronchiole_compliant_alveolus

Model number
0188

This model represents a bifurcating rigid bronchiole with two compliant alveoli.

## Description

```   This model represents a bifurcating rigid bronchiole with two compliant alveoli.
The resistance offered by bronchial wall to the flow of air is represented by
the resistor in the model.The compliance of the bronchiole is represented by the capacitor.
The alveolar sac compliance is repsented by a capcitor. R4 and R5 represent the
resistance offered by the alveolar sacs to the airflow. The alveolar sac changes
its volume as a function of inlet flow or pressure.
```

Legend:
Finlet: Inlet Flow, P: Pressure, R: Resistance, F: Flow, Com: Compliance, V: Volume.

## Equations

```Pinlet - P12 = Finlet * R
P12 - P31 = F3 * R3
P12 - P21 = F2 * R2
F2 = Finlet - F3
P31 - P32 = F3 * R4
P32 - P33 = (V3 - V3_0)/Com3
P21 - P22 = F2 * R5
P22 - P23 = (V2 - V2_0)/Com2
d(V2)/dt = F2
d(V3)/dt = F3

Where: P is pressure, F is flow, R is resistance, Com is capacitance, and V is the volume. ```

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
```	Fung Y.C.; "Biomechanics" (Text Book)
```
Key terms
Bifurcating bronchiole
Alveolus
Bronchiole
Compliant alveolus
Respiratory system
respiratory mechanics
airway
Acknowledgements

Please cite https://www.imagwiki.nibib.nih.gov/physiome 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.

Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, 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.