Models Forced Expiratory Volume procedure using the Maxwell one chamber viscoelastic compartment model taken from Bates (ch. 7)

Description

	This model adapts the Maxwell single compartment viscoelastic lung as 
developed by Bates to the forced expiratory volume (FEV) procedure. The model 
includes a resistance term (represented by airway resistance) and a spring recoil 
term (spring resistance represented by 1 / lung compliance, 1/C) for the lung and 
lung wall. The combination of spring and dashpot in series, a Maxwell body, accounts 
for the viscoelastic behavior of this model. Several commonly used lung volumes have 
been calculated and reported. This model can be modified to add to a larger model or 
can be used alone as a simple model. Several data sets have been added and the model 
has been fit to each.
	This model has several problems. First, the driving pressure of the system is 
external, not from the chest wall, and therefore acts like a respirator pumping up 
the lung with positive pressure and sucking the air out with negative pressure, the 
reverse of normal ventilation. This is the opposite of the "forced expiration" 
compressing the chest and raising intrapleural pressure. However the mechanics of 
the lung are reasonably modeled, giving a 2-component outflow that can be fitted to 
actual data.
	The second problem is that the compliances, C1 and C2, are constant instead 
of being functions of the volume. In reality the FEV ends, at Vlung = Functional 
Reserve Capacity - Expiratory Reserve Volume = Residual Volume, when the force of 
chest muscle contraction cannot make the chest smaller (equivalent to compressing the 
spring further). The passive pressure-volumes curves should be concave upward for 
both chest and lungs at volumes above FRC, At FRC the chest recoil is toward 
enlargement and the lung recoil is toward shrinkage, so the combination produces a 
negative intrapleural pressure at rest.
	Thirdly, air is assumed to be incompressible. In reality air flow inward 
through the mouth is less than flow into the lungs because of the additional volume 
contributed by water vapor pressure rising to 47 mmHg. With an FEV the volume is 
compressed, often by 1/8th, i.e. 100 mmHg exhalation pressure added to 760 mmHg.
	This model differs from the FEV_simple model (insert model #) in its addition
of viscoelastic behavior created by the Maxwell body representing chest wall 
mechanics. By adding a second spring and resistor set, this model is capable of 
fitting well to FEV data curves. 

Figure

Equations

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.