Plots:
P_V_F_vs_t
Plot 1
Pinlet  inlet pressure in the bronchiole
Finlet  flow in the bronchiole
P2  pressure in the bronchiole
V1  volume of the bronchiole
Note that hte volume of the bronchiole (V1) is scaled
Plot 2
P4  pressure in the alveolus
V2  volume of the alveolus
// MODEL NUMBER: 0125
// MODEL NAME: Compliant_bronchiole_compliant_alveolus
// SHORT DESCRIPTION: This model represents a compliant bronchiole with a compliant alveolar sac.
// The driving force for this model is a pressure gradient which represents the difference in the alveolar and the pleural pressures.
/*
************************************************************************************
C O M P L I A N T B R O N C H I O L E W I T H C O M P L I A N T A L V E O L U S
************************************************************************************
************************************************************************************
*/
import nsrunit;
unit conversion on;
math comp_bron_comp_alv{
// *****************************************************************************
// I N P U T P A R A M E T E R S
// *****************************************************************************
realDomain t s; t.min=0; t.max=25; t.delta= 0.1;
real
R1 = 0.045 mmHg*sec/ml, // Resistance of the bronchiole
R2 = 0.045 mmHg*sec/ml, // Resistance of the bronchiole
Com1 = 5 ml/mmHg, // Compliance of the bronchiole
V1_0 = 0 ml, // Initial volume of the bronchiole
Com2 = 5 ml/mmHg, // Compliance of the alveolus
R3 = 0.045 mmHg*sec/ml, // Resistance in the alveolus
V2_0 = 0 ml; // Initial volume of the alveolus
// *****************************************************************************
// S T A T E V A R I A B L E S
// *****************************************************************************
real
Finlet(t) ml/sec, // Inlet flow
P2(t) mmHg, // Intermediate pressure in the bronchiole
P3(t) mmHg, // Pressure at the end of the bronciole
P4(t) mmHg, // Pressure in the alveolus
F1(t) ml/sec, // flow in the bronchiole due to complaiance
F2(t) ml/sec, // flow into the alveolus
V1(t) ml, // Volume of the bronchiole
V2(t) ml; // Volume of the alveolus
// *****************************************************************************
// I N I T I A L C O N D I T I O N S
// *****************************************************************************
extern real Pinlet(t); // Pressure at the beginning of the bronchiole
when(t=t.min)
{
V1 = V1_0; // Initial volume of the bronchiole
V2 = V2_0; // Initial volume of the alveolar sac
}
// *****************************************************************************
// S Y S T E M O F E Q U A T I O N S
// *****************************************************************************
Pinlet  P2 = Finlet * R1;
F1 = Finlet  F2;
P2 = (V1V1_0)/Com1;
P2  P3 = F1 * R2;
P3  P4 = F1 * R3;
P4 = (V2V2_0)/Com2;
V1:t = F2;
V2:t = F1;
}
/*
SCHEMATIC:

Finlet R1 P2 R2 F1 P3 R3 P4  
/\/\/\/\o/\/\/\/\o/\/\/\/\o
Pinlet   
 
 Com1 Com2
F2  V1 V2





LEGEND:

 or  = Compliance
 
o = Junction < or > = flow  = Ground


DETAILED DESCRIPTION:
This model represents a compliant bronchiole with a compliant alveolar sac.
The resistance offered by bronchial wall to the flow of air is represented by
the resistor in the model. The total resistance of the bronchiole is split into
two resistors in series to fecilitate smooth coupling of downstream circuits.
The compliance of the bronchiole is represented by the capacitor. The alveolar sac
compliance is repsented by a capcitor. The alveolar sac changes its volume as a
function of inlet flow or pressure. The driving force for this model is the pressure
gradient which represents the pressure difference between the alveolar sac and the
pleural pressure. Since this model lacks a pleural cavity, a positive pressure
gradient is imposed to drive the flow into the alveolar sac. The important difference
between this model and the rigid_bronchiole_compliant_alveolus model is the shape of
alveolar volume curve.
SHORTCOMINGS/GENERAL COMMENTS:
 Specific inadequacies or next level steps
KEY WORDS: Compliant Bronchiole, Bronchiolus, Alveolus, Alveolar sac,
Respiratory system, respiratory mechanics, airway
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. BME33, no. 9, pp. 878887, Sept. 1986.
Fung Y.C.; Biomechanics (Text Book)
REVISION HISTORY:
Original Author : S Kabilan Date: 05/12/08
Revised by : BEJ Date: 10/19/09
Revision: 1) Update comment formating
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 19992009 University of Washington. From the National Simulation Resource,
Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 981955061.
Academic use is unrestricted. Software may be copied so long as this copyright notice is included.
This software was developed with support from NIH grant HL073598.
Please cite this grant in any publication for which this software is used and send one reprint
to the address given above.
*/