Model number

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..


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                                   *


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.

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M.G. Levitsky, Pulmonary Physiology, Sixth Edition, McGraw Hill, 2003.
Key terms
lung compliance
RC circuit
lung mechanics
airflow in trachea
tidal volume
positive pressure ventilation
chest or diaphragmatic breathing

Please cite 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: 
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.

Model development and archiving support at 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.