A. The typical diameter of an alveolus is about 0.3 mm. If there are 300 x 106al

Question

A. The typical diameter of an alveolus is about 0.3 mm. If there are 300 x 106alveoli in thelungs calculate the approximate area for gas exchange, assuming that the alveoli are spheres

B. Based on this number and size of alveoli, calculate the total volume of gas in the alveoli. Howdoes this compare to typical values for FRC? Differences between these two ought to be dueto errors or rounding in either the size or number of alveoli. If the number of alveoli is correct,what would the diameter have to be to make this volume equal to the FRC? If the diameteris correct, what would the number of alveoli have to be to make this volume equal to theFRC?

Explanation / Answer

Answer A. Surface area of the sphere is equal to 4?r2. Where r is radius of the sphere. Since diameter of one alveoli is given as 0.3 mm thus radius r = 0.3/2= 0.15

Thus surface area of one alveoli A = 4x 3.14x (0.15)2 , A = 0.283 mm2.

Since there are 300x 106 alveoli in the lungs. So the total surface area of the lungs= 300x 106x 0.283 = 8999.4 mm2.

So by this calculation, the total surface area of the lungs is around 9000 mm2.

Answer B. Volume of sphere= 4/3?r3. By putting the values, volume of one alveoli is equal to 4/3x 3.14x (0.15)3.

Thus volume of one alveoli= 0.014 mm3. Thus total volume of lungs= total volume of gas in the lungs= 300x106x0.014= 445.2 mm3.

The FRC or fractional residual capacity of the lungs is equal to the addition of expiratory reserve volume and residual volumes. In normal healthy individuals it is around 2.3 litres. Thus by using this knowledge, one can calculate size and diameter of the alveoli by simple mathematics.

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