A model for unequal ventilation of the lungs assuming a common dead space and two separate dead spaces

This is a model for the time-variation of helium concentrations in lung wash-out curves. The helium (or other inert gas) is in a spirometer, which is connected by a common dead space to two separate dead spaces, each of which leads into a chamber. The chambers expand and contract, thus taking in some helium at each “breath.” Equations for the changes in helium concentration in each part of the system are set up; in this way difference equations are derived for the amount of helium in the spirometer after each breath, in and out, and complete solutions when the initial concentration is zero in all parts of the system except the spirometer. A simple solution when the chambers do not essentially differ (“equal ventilation”) is compared with the general case. The concept of “unequal lung ventilation” is discussed critically in relation to the model; some physiological interpretations are also mentioned. Numerical examples are given to show the effect of changes in various constants, in particular tidal volumes, end volumes, and the common dead space.