Mathematical Model Explaining the Sources of Error in Certain Estimates of the Gas Exchange Constants for the Middle Ear

Abstract

Mover-Lev and colleagues reported a carbon dioxide-oxygen time-constant ratio of 3.9 for transmucosal gas exchange in guinea pigs under conditions of a large positive oxygen pressure gradient and a negative carbon dioxide gradient. That ratio is much less than the value of 19 reported previously for monkeys and used in predictive models of middle ear pressure regulation. In this report, the mathematics that underlie models of transmucosal gas exchange are developed and the conditions that allow accurate estimation of time constants are defined. The results demonstrate that the experimental and analytic methods used by Mover-Lev et al do not control for certain confounding effects or concurrently measure all required system parameters. Under the most realistic conditions, their ratio of 3.9 represents a significant underestimation of a true value on the order of 10. Also, their expectation of nonvarying, transmucosal time constant ratios for pairings that include reactive gases is simplistic and true only for identical experimental contexts.