Models four different viscoelastic compartments with one or two chambers for modeling lungs.
These equations model various configurations of a viscoelestic lung compartment as developed by Bates. Each model includes a resistance term (represented by lung resistance) and a spring recoil term (spring resistance represented by 1 / lung compliance). Each configuration of either one (simple or Maxwell) or two (parallel or series) compartment can be modified to add to a larger model or can be used alone as a simple model. While these models were developed for positive pressure ventilation, they can also be adapted for passive exhalation. If possitive pressure ventilation is used, the difference in compartment behavior is much clearer than for the passive exhalation.
Images adapted from Bates
Simple One Compartment Model
Maxwell One Compartment Model
Parallel Two Compartment Model
Series Two Compartment Model
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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J.H.T. Bates. Lung Mechanics: An Inverse Modeling Approach. Cambridge University Press, (2009) Chapter 3: 37-44, Chapter 7: 108-118.
Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome 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.