Equation for inert gas exchange which treats ventilation as cyclic

¹ Departments of Pharmacology, University of Buffalo School of Medicine, Buffalo, New York, and Stanford University School of Medicine, Palo Alto, California

When a constant concentration of an inert gas is inhaled, the rate at which the equilibrium quantity of the gas in blood and tissues is approached depends upon many factors. In previous mathematical descriptions of this process, ventilation has been assumed to be continuous. In the present analysis, respiration is treated as cyclic, and an equation for the time needed to achieve any given proportion of equilibrium is derived. This equation is a complex function of eight variables. However, two of these, the functional residual capacity and the volume of lung tissue, are of negligible importance. Furthermore, an n-fold increase in rate of respiration has almost the same effect upon the calculated rate of approach to equilibrium as an n-fold increase in alveolar ventilation per breath. The assumption that ventilation is continuous is therefore a legitimate simplification, and the complex equation has no practical advantage over a much less intricate formulation.