Passive Exhalation

Passive Exhalation
	There are two parts to respiration: inhalation and exhalation.
Unlike inhilation, exhalation is normally a passive event.  This is stated
as such because the act of normal exhalation requires no contraction of
muscle.  In this event, the muscles (i.e. the diaphragm) are resetting to
their normal relaxed state until the onset of inspiration.
	There are mathematical equations to interpret passive exhalation.
A list of variable used are:
	Pm = respiratory muscle pressure forcing
	R = respiratory system resistance
	C = respiratory system compliance
	VL = lung volume

		Pm = VL/C + R * dVL/dt
	For passive exhalation, the Pm = 0.  wazzu This is because all of
the muscles are in a passive nature (no contraction).  So your new
equation is:
		0 = VL/C + R * dVL/dt
or more specifically:
		dVL/dt = -VL/(R*C)
This becomes a first order differential equation.  After integrating both
sides of the equation, you are left with:
		VL(t) = VL(0) * EXP (-t/(R*C))
Since VL(t) at t=0 is equal to the tidal volume (VT), you can write this
equation like this:
		VL(t) = VT * EXP (-t/(R*C))
	This equation gives you the way to determine the lung volume over
time during the act of passive exhalation.  

Sample Problems:

QUESTION:
	A question that could show up on the test could be something like
this:
	1)	With an R=2cm H2O /Lps, a C=0.1 L/cm H2O, and a VT of 1 L,
		Please calculate the lung volume during passive exhalation
at time 
a) t = .005 seconds
b) t = .05 seconds
c) t = .25 seconds
d) t = .5 seconds
e) t = 1 second
2)	With the same conditions above, at what time will VL be one half
of VT? 

Answers:

1) a)VL(.005) = .9753 L
a) VL(.05) = .7788 L
b) VL(.25) = .2865 L
c) VL(.5) = .0821 L
d) VL(1) = .0067 L

2)   The answer is .1386 seconds

For more information on this topic, please refer to Dr. Y's Handout on the Mechanical Model of Respiration. The relevant portions are shown here:

Figure 6

Figure 7

Also, check out the following links that may be helpful:

• (No links)
• And, as always, if you have questions, or if you can suggest a helpful link, please e-mail me.

No!
Please don't make me go to any of those pages!
I want to go somewhere completely different!

This page was written by Matt Reaves, a student in this course.

BME 403 Pages maintained by the T.A., Douglas Miles.