Mathematical analysis of the time course of alveolar CO₂

¹ Department of Physiology, School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania

Continuous respiratory CO₂ 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 CO₂ in the steady state, solutions for CO₂ as a time series are found to differ according to whether the site of entry of CO₂ is entirely by venous blood or is also by inspired CO₂. In the case of entry via the venous blood, increasing CO₂ is eliminated while keeping mean CO₂ constant with increasing fluctuations about this mean. In the case of entry via the lung, increasing CO₂ is eliminated by raising the mean and at the same time oscillations diminish.

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