Mathematical analysis of the time course of alveolar CO₂

Continuous respiratory CO 2 gas exchange is simulated theoretically by means of a suitably constructed dilution equation of the form (See PDF) where C is instantaneous concentration, Q quantity flow, and V volume flow. When such an equation is constrained in its numerical solutions to yield inflow-outflow equality for CO 2 in the steady state, solutions for CO 2 as a time series are found to differ according to whether the site of entry of CO 2 is entirely by venous blood or is also by inspired CO 2 . In the case of entry via the venous blood, increasing CO 2 is eliminated while keeping mean CO 2 constant with increasing fluctuations about this mean. In the case of entry via the lung, increasing CO 2 is eliminated by raising the mean and at the same time oscillations diminish. Submitted on August 13, 1959