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Published on April 4th, 2013 | by Jo

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# Asthma and mechanical ventilators…

Chris Wright is a Melbourne Intensive Care Specialist doctor who’s just finished studying Physics at Monash University. He’s of the general view that http://xkcd.com/435

When patients with asthma are having a worsening of their condition, they find it “harder” to breathe, and when their disease is really severe, they may need assistance from a mechanical ventilator to breathe. The ventilator helps push the air in, but what about getting the air out?

If we draw a (very!) simple picture of the normal lung, it looks like this:

Air goes in and out (through the airways) and the lung expands and contracts like a balloon – it’s got some “elasticity”.

With asthma, things look different:

The air doesn’t find it so easy to flow, because there’s a blockage in the airways that increases the resistance to the flow of air. Again, this is a pretty simple depiction of the process, but it’s OK for our purposes.

We can do some maths and write down an equation for the situation. If we pump air into the lung, and then turn the pumping pressure off, we can wait for the lung to deflate – like a balloon being emptied through a straw.

The equation[1] looks like this:

$V(t) = V_0 e^{\frac{-t}{RC}}$

$V(t)$ is how much air is left in the lung  seconds after we stopped pumping air in

$V_0$ is how much air we pumped into the lungs

$e^$ is one of the wonders of the world – it’s a number like π , turns up everywhere; its value is about 2.71

$t$ is the number of seconds since we stopped pumping air in

$R$ is the resistance of the tube and $C$ is “elasticity” of  the lungs

So we can draw a graph of how much air is left in the lung after we’ve pumped air in, and now letting the lung deflate:

At first, the air rushes out (because the pressure in the lung is much higher than the atmospheric pressure), but then the flow out slows.

What happens if we double the resistance (give the equation asthma!)

It takes longer for the air to get out…

If we make the asthma really bad (increase the resistance three times)

then the air takes a loooooong time get out of the lungs.

All this explains why patients with asthma take a long time to breathe OUT – it’s not just hard to breathe IN, and also makes us very careful when we mechanically assist the breathing of patients with severe asthma, we have to give them enough time to breathe out – otherwise we can “blow up” the lungs and really bad things can happen!

[1] This derivation shows how we get that equation. It’s high school calculus…

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