Airway is one tank, alveolus a second. Both are elastic. Flow direction governs solute flux.

Description

 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.	

Equations

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.