Isometric growth of lung indices?
Body length and tidal volume
Consider a sleeping neonate in whom we record tidal volume. The breathing pattern is irregular, and tidal volume varies; on average it comes to slightly less than 20 mL in a neonate of 50 cm crown-heel length. Compare this to a tidal volume of about 600-700 mL in an adult of 185 cm standing height. The ratio between the two heights is 3.7. If tidal volume would increase proportional to length cubed, then in an adult it should come to 20·3.73 or about 1000 mL; in fact it is appreciably less.
Neonate versus adult
In a young adult male of 185 cm standing height the FRC is approximately 2500 mL. If all dimensions of lungs and airways increase proportionately from birth to adulthood (hence by a factor 3.7), then the FRC should have increased by a factor 50.65 (=3.73) and we would expect it to be 80·50.65 or about 4050 mL; this is almost 1½ times the actual volume. Similarly body weight (about 3 kg at birth, about 80 kg in a 25 yr old male) does not increase 50-fold.
The relationship between body length and the volumes that we looked into is not one of simple isometry.
This should not come as a surprise, as we shall see now.