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Published on January 3rd, 2013 | by Emma

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# Boom boxes, opera singers, blood pressure and a French revolutionary…

by Associate Professor Chris Wright, Monash University

Critically ill patients often need to have their blood pressure closely monitored, and we do this by putting a small tube into an artery, and measuring the pressure. However, there is a little complication…and it’s down to opera singers, and a French revolutionary!

The normal blood pressure waveform looks like this:

and when you feel your pulse (in your wrist or your neck), you’re feeling this waveform – you feed the “bump” at the top, and then a pause and then the next bump.

Now for the French revolutionary. John Baptiste Joseph Fourier was a mathematician and physicist who lead a pretty exciting life – he was a member of the local Revolutionary Committee, and went to Egypt with Napoleon. He’s remembered, though, for his contributions to physics and mathematics. Fourier showed that any waveform (like the arterial one shown above), can be constructed by adding up simple sine

and cosine

waves of varying frequencies. This is a really remarkable piece of mathematics, and has uses everywhere.

Even waveforms that don’t look smooth can be constructed this way. In this picture:

the really sharp line shown by the red dots in the upper image (called a “sawtooth” wave) can be very closely approximated by adding up all the smooth curves in the lower picture – the result of adding those up is the wavy green line in the top picture… adding even more curves makes the construction even more accurate.

Now, opera singers. You’ve all seen the video of a glass shattering when some opera singer sings “just the right note” – it’s a bit like pushing a child’s swing – if you push at just the right time, the swing moves in bigger and bigger arcs. This phenomenon is called resonance and is important and common. We say that the note is at the “resonant frequency” of the glass – the vibrations get bigger and bigger and eventually shatter the glass.

And it’s certainly important in measuring blood pressure with a small catheter or tube. It turns out that when you look at how to make up a blood pressure waveform from simple sine and cosine curves, you use one frequency that’s right near the resonant frequency of the tubing and measuring system. So that component of the blood pressure signal is magnified, resulting in a peak that shouldn’t be there; instead of seeing

we see

with the very high and narrow peak. The patient’s blood pressure isn’t that high, it’s just that the system is resonating at one frequency and this gives a false (or “artefactual”) reading. It might be a serious error to lower the patient’s blood pressure based on this waveform. Doctors and nurses have ways of correcting for (and identifying) this problem, but it’s a really good example of Fourier’s amazing discovery.

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

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