Physics + Medicine = The Bends

About a fortnight ago I was in the unusual position of teaching human biology to medical physicists and physics to medical students. Interestingly, during this overlapping week a disease came up in both tutes, a physics based medical condition.

Arguably many diseases can be based in physics including heart disease, atherosclerosis and pretty much anything else to do with the pipes in your body but a disease known as ‘the bends’ or ‘decompression sickness’ invokes a bunch of physics laws and principles and then also requires a physics based treatment to deal with it.

The bends gets its name, like Jumping Frenchman of Maine Syndrome, because it literally causes the patient to bend over. This is because the condition is so excruciatingly painful that almost everyone who gets it doubles over in pain.

The bends is caused by rapid decompression resulting in painful phase transitions of solubilised gas into bubbles occurring in the blood, muscles, bones and fatally in the brain. But first it’s a question of how decompression can cause these problems.

The other name for the bends is ‘divers disease’ as it is only divers who really have the ability to increase the external pressure of their environment. As they diver deeper they effectively increase the atmospheric pressure which has important consequences for the composition of air in their lungs.

Now for a little physics. The concept of partial pressure is very important when talking about the bends. So, partial pressure (or pp) is defined as the pressure exerted by one gas in a mixture of gases. Another way of thinking about it is that in a mixture of gases the sum of all the pp of all the individual gases will equal the total pressure of the mixed gas. The air we breathe is a perfect example. Air is made up of approximately 80% nitrogen and 20% oxygen and the rounding errors are a bunch of other trace gases. So the pp of nitrogen at sea level is 80% of atmospheric pressure, which is defined as 1 atmosphere (or 1 atm), therefore 0.80 atm and oxygen has a pp at sea level of 0.20 atm.

Divers however are not at sea level, they are lower and therefore experience higher pressures (and for the purpose of the diagram I have made lets say divers are at a pressure 4 times normal or 4 atm).

Still with me? Well here’s a little more physics.

A guy named Boyle has a law and his law states that pressure is inversely proportional to volume, as you increase the pressure on a gas you decrease the volume that gas occupies. Pretty self-explanatory. Essentially you concentrate the molecules of the gas but don’t change the composition of the gas. So the pp of nitrogen will be 80% of 4 atm or 3.2 atm and the pp of oxygen will be 20% of 4 atm or 0.8 atm. So when you are a diver breathing compressed air at depth you inhale more molecules of gas per breath into your lungs.

So here’s the next bit of physics. The concentrated air in your lungs now needs to get into your blood so that the oxygen can be used. Oxygen moves into the blood based on the pp gradient, there is some oxygen in the lungs, less in the blood and so the oxygen moves in. By the same principle nitrogen dissolves into the blood too, but how much? Henry’s law (the only other law we need here) states that at a gas/liquid interface the amount of gas solubilised into that liquid is determined by the pp of the gas, or, the more gas molecules in a space (lungs) the more gas molecules dissolved into the liquid (blood).

So at this point we have described how the diver would have more nitrogen dissolved in the blood but the pathology develops, as I have said above, when and how it comes back out of the blood.

If the diver ascends to the surface too quickly the solubilised nitrogen is no longer under the increased pressure and so the pp of nitrogen in the blood is 3.2 atm and outside in the air the pp of nitrogen is still 0.80 atm. Moving along the pp gradient nitrogen does its best to rejoin the air as quickly as possible, a problem when it is separated from the rest of the air by your body.

The bends is something that divers all know about but is interesting in so much as it is reasonably medicine free for a disease. Normally the medical conditions we discuss with the medical students are complex matters of biology, anatomy and physiology but this pathology can be understood without knowing much about the body as long as the physics foundations are sound.

Next week I will talk about how the bends get straightened out.

See what I did there?

Reference

Vann RD, Butler FK, Mitchell SJ, & Moon RE (2011). Decompression illness. Lancet, 377 (9760), 153-64 PMID: 21215883