A Mathematical Model of Mean Airway Pressure Based Upon Positive End-Expiratory Pressure, I:E Ratio, and Plateau Pressure

A mathematical model of mean airway pressure (P_mean) has been derived which is based upon positive end-expiratory pressure (P_peep) and I:E ratio (I:E). Plateau pressure (P_PL) is also utilized: $$ P_{rm mean}/P_{rm PL} = [(I{:}E) + {bf R}]/[(I{:}E) + 1] $$ where R is defined as: R = P_peep/P_PL. Based upon this model, it can be shown that (1) increasing I:E ratio will increase P_mean/P_PL in a self-limiting logarithmic manner; (2) P_mean/P_PL is a linear function with respect to R; (3) increases in R are associated with a diminished effect of I:E ratio on P_mean/P_PL; (4) similarly, increases in I:E ratio are associated with a diminished effect of R on P_mean/P_PL; (5) overall, changes in P_mean/P_PL will consistently be effected more by changes in R than by changes in I:E ratio. This model illustrates the interrelationship between plateau pressure, PEEP, and I:E ratio as they affect mean airway pressure. Furthermore, it appears to be useful in explaining the clinically reported discrepancies regarding the efficacy of inverse ratio ventilation (IRV), especially when simultaneously applied with varying levels of PEEP. In addition, for a given plateau pressure, it is also possible to mathematically optimize PEEP and I:E ratio combinations so as to avoid excessive amounts of either.