// MODEL NUMBER: 0182
// MODEL NAME: PulmonMech_andGasConc
// SHORT DESCRIPTION: This model is based on Lutchen et al. A nonlinear model
// combining pulmonary mechanics and gas concentration dynamics. IEEE Trans.
// Biomed. Eng. 29: 629-641, 1982
import nsrunit;
unit conversion on;
math Lung {
realDomain t sec;t.min = 0;t.max = 28;t.delta = 0.01;
real R_taw = 1.6 cmH2O/(liter/s); // A total airway resistance
real R_c = 1.36 cmH2O/(liter/s); //resistance associated with conducting airways(85% of R_taw)
real R_1 = 1.36 cmH2O/(liter/s) ; //R_c is for typical R_1 (ressistance for conducting airways)
real b_2 = 1.62 cmH2O*sec; // specific resistance for compartment 2
real b_3 = 1.62 cmH2O*sec; // specific resistance for compartment 3
real epsilon_2 = 0.68 liter; //volume cofficient for compartment 2
real epsilon_3 = 0.68 liter; //volume cofficient for compartment 3
real h_2 = 0.552 cmH2O; // pressure coefficient for compartment 2
real h_3 = 0.552 cmH2O; // pressure coefficient for compartment 3
real V_L(t) liter; // volume of the lung
real V_D = 0.15 liter; // volume of dead space
real V_2(t) liter; // volume of compartment 2
real V_3(t) liter; // volume of compartment 3
real F_2(t) liter/sec; //flow of compartment 2
real F_3(t) liter/sec; // flow of compartment 3
real F_L(t) liter/sec; // flow of the lung
real F_1(t) liter/sec; // flow of compartment 1 (dead space)
//Pressure forcing function
real P_tp(t) cmH2O; // the tranpulmonary pressure
real P_0= 5 cmH2O; // parameter in transpulmonary forcing funciton
real A =4 cmH2O; // parameter in transpulmonary forcing function
real tau_R = 0.11 sec; // parameter in transpulmonary forcing function
real tau_F = 0.22 sec; // parameter in transpulmonary forcing function
real tmod(t) sec; // periodic
real t_1 = 1.33 sec; // rise time
real cycle = 4 sec; // breathing cycle
tmod = rem(t, cycle);
P_tp=if(tmod<=t_1) P_0+A*(1-exp((-tmod)/tau_R))
else P_0+A*exp((t_1-tmod)/tau_F); // transpulmonary forcing funciton
//Equations for pulmonary mechanics
when (t=t.min) { V_2 = 1.5; V_3 = 1.5;}
R_1*F_L+(b_2/V_2)*F_2+h_2*exp(V_2/epsilon_2)=P_tp; // Eq. 15
R_1*F_L+(b_3/V_3)*F_3+h_3*exp(V_3/epsilon_3)=P_tp; // the second and third item is related with compliance
V_L= V_D+V_2+V_3; // Eq. 5
V_2:t=F_2; // Eq. 7
V_3:t=F_3; // Eq. 7
F_L=F_2+F_3; // Eq. 6
F_1=F_L;
// Gas transport
real C_in= 0 mmol/ml; // input concentration
real C_0 = 1 mmol/ml; // initial concentraion throughout the lung
real C_2(t) mmol/ml; // concentration in compartment 2
real C_3(t) mmol/ml; // concentration in compartment 3
real C_m(t) mmol/ml; // concentration of the gas in the mixing node m
real C_ao(t) mmol/ml; // output concentration at the airway opening
real X_1(t) dimensionless; // switch for flow in compartment 1
real X_2(t) dimensionless; // switch for flow in compartment 2
real X_3(t) dimensionless; // switch for flow in compartment 3
X_1 = if (F_1>0) 1 else 0;
X_2 = if (F_2>0) 1 else 0;
X_3 = if (F_3>0) 1 else 0;
when (t=t.min) { C_2=C_0; C_3=C_0;}
real v_Lin(t) = integral(t=t.min to t, F_1);
real v_Lex(t) liter;
v_Lex = V_L-V_L(1.33);
C_m = if(v_Lin>0.15 and F_1>0) C_in else (C_2+C_3)/2; // this is assuming Piston or plug flow
C_ao = if(abs(v_Lex)>0.15 and F_1<0) C_m else C_in;
V_2*(C_2:t)=F_2*(C_m-C_2)*X_2; // Eq. 19
V_3*(C_3:t)=F_3*(C_m-C_3)*X_3; // Eq. 19
}
/*
DETAILED DESCRIPTION:
The model equations derived from mass and force balances describe the intrabreath
dynamics of pressure, flow, volume, and gas species concentration after a step change
in gas composition at the airway opening.
This model has two parallel, perfectly mixed alveolar compartments connected to a single,
constant-volume airway (dead space) in which no mixing occurs. There is a mixing point m
at the junction of the two alveolar compartments and the conducting airway. The
gas that enters the airway opening during inspiration will reach the mixing point after
the dead space is cleared. During expiration, until the dead space is cleared, the output
concentration at the airway opening is the input concentration.
SHORTCOMINGS/GENERAL COMMENTS:
- Specific inadequacies or next level steps
KEY WORDS: Pulmonary mechanics, Gas concentration, Alveolar compartment, Dead space,
Lutchen, Respiratory System, Airway mechanics
REFERENCES:
Lutchen KR, Primiano FP Jr, Saidel GM; Nonlinear model combining pulmonary mechanics
and gas concentration dynamics. IEEE Trans Biomed Eng. 29(9):629-41, 1982.
REVISION HISTORY:
Original Author : fgao Date: 08/12/08
Revised by: bej Date:01nov11 : Update comment format
COPYRIGHT AND REQUEST FOR ACKNOWLEDGMENT OF USE:
Copyright (C) 1999-2011 University of Washington. From the National Simulation Resource,
Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
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 an email
with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
*/