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Math Awareness Month 1999

Measuring Blood Pressure

When you come into the hospital and the nurse puts that fancy inflatable doo-dad (called a blood pressure cuff) on your arm, how does it measure your blood pressure? In order to measure it directly, one would have to put a pressure gauge in an artery, and it would be no fun. Instead, a method was devised that is not invasive, and has a little bit of mathematics up its sleeve.

The cuff is there to put pressure on the artery in your arm. At first, it is inflated so that the pressure from the outside is greater than the blood pressure - so the blood flow is cut off! Then the air is slowly let out, and the pressure in the cuff drops gradually. At the same time, the nurse puts a stethoscope on your arm and listens for the blood to start flowing. At the moment when the nurse can hear the blood gushing, the blood pressure in the blood pressure cuff (outside pressure) is equal to the blood pressure in the artery, or as you can see on the picture, the two graphs intersect.

This story is incomplete, however. Remember that the heart pumps blood by contracting periodically. Blood gushes through the body in waves (see page 7) , and blood pressure also varies like a wave. Therefore, by listening for the first time blood pressure exceeds the outside pressure, we only find the highest value of the blood pressure, also known as the systolic pressure. After that, blood pressure will fluctuate - sometimes going above the outside pressure, and sometimes dipping below it, until finally the blood pressure cuff will lose so much pressure that the blood pressure fluctuations will remain above it, and blood will flow continuously (in the figure, the line intersects with the lowest part of the wave). At this moment we have reached the lowest blood pressure, also known as the diastolic pressure. This is why blood pressure is always given as two numbers, say 120/60 - the first is the peak blood pressure, and the second is the lowest blood pressure.

M & B Exhibits | intro | pg 2 | pg 3 | pg 4 | pg 5 | pg 6 | pg 7 | pg 8