The simple model in Example 3.3.5 of the textbook is widely used by physicians to predict the steady state concentration of CO2 in the lungs C as a function of the ventilation rate V. Its importance stems, in part, from its prediction about how a change in ventilation rate V affects the steady state CO2 level C. In particular, Example 3.3.5 of the textbook demonstrates that the rate of change of C with respect to V is given by
This shows that, as we might expect, an increase in ventilation rate decreases the steady state concentration of CO2 (because the derivative is negative). Perhaps surprisingly, however, it also shows that the magnitude of the effect of increasing the ventilation rate depends on the current ventilation rate. Specifically, the decrease in steady state CO2 is smaller in magnitude in circumstances where the ventilation rate is already high (because the derivative decreases in magnitude as V increases). Put another way, the effect of increasing the ventilation rate gets progressively smaller as the ventilation rate increases. This has important implications since changes in ventilation rate will be relatively ineffective if a patient is already being ventilated at a high rate.
For more information about this model see Example 1.2.5 of the textbook and its associated ‘Biology Background’ material on this website.