Development and validation of a model to calculate anesthetic agent consumption from inspired and end-expired concentrations, minute ventilation, fresh gas flow and dead space ventilation

Anesthetic agent consumption is often calculated as the product of fresh gas flow (FGF) and vaporizer dial setting (F_VAP). Because F_VAP of conventional vaporizers is not registered in automated anesthesia records, retrospective agent consumption studies are hampered. The current study examines how F_VAP can be retrospectively calculated from the agent’s inspired (F_IN) and end-expired concentration (F_ET), FGF, and minute ventilation (MV). Theoretical analysis of agent mass balances in the circle breathing reveals F_VAP = [F_IN − (dead space fraction * F_IN + (1 − dead space fraction) * F_ET) * (1 − FGF/MV)]/(1-(1 − FGF/MV)). F_IN, F_ET, FGF and MV are routinely monitored, but dead space fraction is unknown. Dead space fraction for sevoflurane, desflurane, and isoflurane was therefore determined empirically from an unpublished data set of 161 patient containing F_VAP, F_IN, F_ET, MV and FGF ranging from 0.25 to 8 L/min delivered via an ADU® (GE, Madison, WI, USA). Dead space fraction for each agent was determined empirically by having Excel’s solver function calculate the value of dead space fraction that minimized the sum of the squared differences between dialed F_VAP and predicted F_VAP. With dead space fraction known, the model was then prospectively tested for sevoflurane in O₂/air using data collected over the course of two weeks with one FLOW-i (Getinge, Solna, Sweden) and one Zeus workstation (Dräger, Lübeck, Germany). Because both workstations use an electronically controlled vaporizer/injector, the dialed F_VAP were available to allow the calculation of median performance error (MDPE) and median absolute performance error (MDAPE). MDPE and MDAP are reported as median and interquartiles. The empirical dead space fraction for isoflurane, sevoflurane, and desflurane were 0.59, 0.49, and 0.66, respectively. For prospective testing, a total of 149.4 h of useful data were collected from 78 patient with the Zeus and Flow-i combined, with FGF ranging from 0.18 to 8 L/min. The model predicted dialed F_VAP well, with a MDPE of −1 (−11, 6) % and MDAPE of 8 (4, 17) %. F_VAP can be retrospectively calculated from F_IN, F_ET, FGF, and MV plus an agent specific dead space fraction factor with a degree of error that we believe suffices for retrospective sevoflurane consumption analyses. Performance with other agents and N₂O awaits further validation.