A single chamber model of the lung pressure and volume with airway resistance and lung compliance.

Description

  Human lung pressure volume curves as influenced by serial 
  resistances of airways and chest wall and by compliance of chest 
  wall and lung.Volumes are driven by negative intrapleural pressure.

Equations

The model is represented by only two equations. The first equation:

V:t = - ( (1/Ccw + 1/Cl) * V + P) / (Rs + Rc + Ru);

equates the change in volume with respect to time with flow. The flow term on the right hand side is expressed by (the fluid equivalent of) Ohm's law as F = Plung/R and Plung is just the pressure attributed to vessel compliance, (1/Ccw + 1/Cl) * V, added to the negative pleural driving pressure P. The second equation:

P = PInit + PDelta * sin(2*PI*freq*t+PI/2) - PDelta;

represents the pleural pressure which is driving the lung ventilation here. The full set of parameters with the equations are shown below:

real FRC = 3.5 L,    // MIN LUNG VOLUME
     VT  = 0.5 L,    // TIDAL VOLUME
     RV  = 1.9 L,    // RESIDUAL VOLUME
     TLC = 7.3 L,    // TOTAL LUNG CAPACITY
     freq= 10 1/min, // BREATHING FREQUENCY (breaths/min)
     numCycles = 1;  // NUMBER OF BREATHS TO RUN

real PInit cmH2O;         // MEAN PRESSURE at initial volume
real PDelta  = 5 cmH2O;   // CHANGE IN PRESSURE over cycle

when (t=t.min) { V = FRC; PInit = -V/(1/(1/Cl + 1/Ccw));  }

V:t = - ( (1/Ccw + 1/Cl) * V + P) / (Rs + Rc + Ru);
P = PInit + PDelta * sin(2*PI*freq*t+PI/2) - PDelta;

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.