A pharmacodynamic model of respiratory rate and end-tidal carbon dioxide values during anesthesia in children

It is essential to monitor the end-tidal carbon dioxide (ETCO₂) during general anesthesia and adjust the tidal volume and respiratory rate (RR). For the purpose of this study, we used a population pharmacodynamic modeling approach to establish the relationship between RR versus ETCO₂ data during general anesthesia in children, and to identify the clinical variables affecting this relationship. A prospective observational study was designed to include 51 patients (aged ≤ 12 years), including users of antiepileptic drugs (levetiracetam, valproic, or phenobarbital (n = 21)) and non-users (n = 30), scheduled to receive general anesthesia during elective surgery. When the ETCO₂ was at 40 mmHg, the RR was adjusted 1 breath per every 2 min until the ETCO₂ was 30 mmHg and recovered to 40 mmHg. Pharmacodynamic analysis using a sigmoid E_max model was performed to assess the RR-ETCO₂ relationship. As RR varied from 3 to 37 breaths per minute, the ETCO₂ changed from 40 to 30 mmHg. Hysteresis between the RR and ETCO₂ was observed and accounted for when the model was developed. The C_e50 (RR to achieve 50% of maximum decrease in ETCO₂; i.e. 35 mmHg) was 20.5 in non-users of antiepileptic drugs and 14.9 in those on antiepileptic drug medication. The values of γ (the steepness of the concentration-response relation curve) and k_eo (the first-order rate constant determining the equilibration between the RR and ETCO₂) were 7.53 and 0.467 min^-1, respectively. The C_e50 and ETCO₂ data fit to a sigmoid E_max model. In conclusion, the RR required to get the target ETCO₂ was much lower in children patients taking antiepileptic drugs than that of non-user children patients during the general anesthesia.