Airway is one tank, alveolus a second. Both are elastic. Flow direction governs solute flux.
This model demonstrates two compartments with a pressure source and some initial amount of mass of compound C contained in the two tanks. The mass of compound C inside the two tanks decreases if we assume that the concentration of C in the incomming air is zero. Two mass balance equations and the periodic nature of flow driven by a pressure source cause the total mass of compound C to reach values close to zero after some time. We assume that pressure drops are proportional to the flow rate. Pressure-volume relationships are defined in a similar way as in one-tank-switched model. Rate of change of volume is equal to the difference of inflow and outflow (see Equations). We defined two switches to model the fact that the amount of compound C in the two flow streams depends on the directions of flows. The switch for flow direction has condition such that Switch = if (Flow > 0) 1 else 0. We applied a switch in the compound balance equation to change the concentration of inflow or outflow of each compartment based on the actual direction of flow.
The governing equations are:
where C is the concentration,
F is the flow rate,
P is the pressure,
Q is the number of moles,
R is the resistance, and
V is the volume.
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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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.