# Compliant_bifurcating_airway

Model number
0122

This model represents a bifurcating compliant airway that could be used as a building block for constructing a network of airways. You could use the model to simulate flow in rigid airway bifurcation.

## Description

```This model represents a bifurcating compliant airway that could be used as
a building block for constructing a network of airway. The resistance offered by
airway wall to the flow of air is represented by the resistor in the electrical
circuit.The compliance of the airway is represented by the capacitor. All the
three airway segment have separate compliances which are represented by three
individual capacitors.
```

## Equations

```Pa1 = (Va - Va_0)/Com_a
Pinlet = (Finlet * Ra1) + Pa1
Fa2 = Finlet - Fa1
d(Va)/dt = Fa2
d(Fa1)/dt = (Pa1 - Pa2 -(Fa1 * Ra2))/La
Pb1 = (Vb - Vb_0)/Com_b
Pa2 = (Fbin * Rb1) + Pb1
Fbin = Fa1 - Fcin
Fb2 = Fbin - Fb1
d(Fb1)/dt = (Pb1 - Pb2 -(Fb1 * Rb2))/Lb
d(Vb)/dt = Fb2
Pc1 = (Vc - Vc_0)/Com_c
Pa2 - Pc1 = Fcin * Rc1
Fc2 = Fcin - Fc1
d(Fc1)/dt = (Pc1 - Pc2 -(Fc1 * Rc2))/Lc
d(Vc)/dt = Fc2

Where: P is pressure, F is flow, R is resistance, Com is capacitance, L is inductance, V is the volume.
```
References
```K. R. Lutchen and G. M. Saidel, "Estimation of mechanical parameters in multicompartment
models applied to normal and obstructed lungs during tidal breathing,"
IEEE Trans. Biomed. Eng., vol. BME-33, no. 9, pp. 878-887, Sept. 1986.

Fung Y.C.; "Biomechanics" (Text Book)```
Key terms
Airway
Compliant airway
Bifurcating airway
Weibel
Lung
Respiratory system
respiratory mechanics
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.