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Errors in blood pressure measurements

As your heart beats, your blood pressure varies in a pattern that looks something like the figure below. The maximum values occur when your heart is contracting and is called the systolic pressure. The minimum values occur when your heart is dilating (expanding) and is called the diastolic pressure.

When your blood pressure is measured using an inflatable cuff, the pressure in the cuff is increased until it is greater than the systolic pressure. At that point, the pressure is not large enough to drive the blood through the cuff. The pressure on the cuff is lowered slowly. When the pressure of the cuff drops below the pressure of the blood, the blood begins to go through and it can be heard with a stethoscope placed on the artery just below the cuff. When it reaches the diastolic value, the sound changes again.

Blood pressure is typically measured in the (rather old-fashioned) units of "mm of Hg" or "millimeters of mercury" (left over from when mercury barometers were used). An average healthy value of the pressures in these units is 120/80. (The first number, 120 mm of Hg, is the systolic pressure, the second, 80 mm of Hg, is the diastolic. The pair are read "120 over 80" even though no division is implied.) Pressure of 150/90 is considered high and can be dangerous.

1. If the pressure of the cuff is lowered very slowly, an accurate reading is obtained. Illustrate this by sketching the cuff pressure on top of a copy of the graph shown above indicating at what instant the value of the measurement would be read for each of the two pressures measured.

2. If the pressure in the cuff if dropped quickly, an inaccurate value of the systolic pressure can be obtained. Explain why.

3. Suppose the pressure in the cuff is lowered at a rate f = ΔPt. If the time between heartbeats is τ, estimate the uncertainty in the reading. (Express your answer in terms of f and τ.) Explain your reasoning.

4. If the person measuring your blood pressure drops the cuff's pressure from 200 mm of Hg to 50 mm of Hg in 5 seconds, estimate the uncertainty in your systolic pressure reading.

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