A compliant 1 compartment lung with resistance to air flow, driven by intrapleural negative pressure (chest or diaphragmatic breathing) or by a positive pressure ventilator or both together, even competing, interfering..

Description

The equations governing airflow in and out of a one compartment lung are
given by the following analogy to electrical circuits:

      Airway pressure is analogous to voltage.
      Air flow is analogous to current flow.
      Volume is analogous to charge.
      Resistance to air flow is analogous to electrical resistance.
      Compliance, the relationship between pressure and volume, is
        analogous to capacitance, the relationship between charge 
        and voltage.

The response to a  negative step input in Pintrapl is an exponentially decaying 
flow with time constant tau=R*Com. 
 
The main assumption is that the human lungs can be approximated as a single 
compartment modeled by an RC circuit where the quantities of interest, air 
flow, volume of air, pressure, compliance, and resistance are analogous to 
current, charge, voltage, capacitance, and resistance respectively.

GENERAL RESULTS: Normally breathing is simulated when the driving force
is provided by expansion of the chest, creating a negative pressure in the 
intrapleural space, just the oppposite of a positive pressure ventilator.  
Using Pmusc = 2-second pulse of negative driving pressure of -20 mmHg pressure 
intrapleural gives an approximately normal tidal volume.
Both sources of driving the system can be used at once, mimicking the patient 
struggling to breath on his own when still being ventilated by a purely periodic
ventilatory cycle. (The ventilator should be replaced with a "ventilatory assist"
device, i.e. one that is triggered to provide at assisting positive pressure 
ventilation to augment flow when the patient initiates inflow by chest 
or diaphragmatic breathing.

Aplying the Ideal Gas Law to Vintrapl shows that the error in assuming air to be
incompressible air is small:

               Boyle's Law for Ideal gas in intrapleural space
***********************************************************************************
* Boyle's Law: P*V = n*R*T    STP =standard temp pressure is 0 deg C, 1 atm       *
*   with P mmHg, V ml, n moles of gas where 1 mole at STP occupies 22,414 ml      *
*   R = Boltzmann const or Gas Const =  0.082 l * atm * mol^(-1) * K^(-1)         *
*   T = deg K = 273.16 + deg C                                                    *
* so that nRT at 37C and 760 mmHg (1 atmos)                                       *
*                 (volume of gas in ml)* 0.082 l * atm * mol^(-1) *K^(-1) * 310 K *
*          P*V  = --------------------------------------------------------------- *
*                 (volume of 1 mole of gas, 22.4 * 310/273 l)                     *
*                                                                                 *
* PV(for 100 ml)= (100/(22400*310/273))moles * 0.082 mole^(-1) * 760mmHg * 310    *
*                                                                                 *
*               =  0.082 * 760 * 273 / 224 = 75.95 mmHg *100ml = 0.7595 mmHg * ml *
*                                                                                 *
* Using P*V= Const, then with a const amount of gas in intrapleural space there is*
* a small volume change with each breath, the direction depending on the driver.  *
*         V2 = V1 * P1/P2     See Eqn for Plung                                   *
***********************************************************************************

Equations

The equations for this model may be viewed by running the JSim model 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.