Background: The delay between changes in end-expired sevoflurane concentrations and bispectral index (BIS) may be characterized by a 'rate constant' (ke0). A smaller ke0 reflects a longer delay. Values for ke0 vary substantially among studies. The question arises how ke0 depends on experimental conditions, including ventilation and apparatus.
Methods: Increasing and decreasing sevoflurane concentrations were cyclically delivered to our validated model. First, we quantified theoretical ke0 values for distinct alveolar ventilations, estimating ke0 from sevoflurane tensions in alveolar space and grey matter. Secondly, we investigated the impact of experimental conditions. To predict BIS, the model was extended with a pharmacodynamic section, including ke0. Known values, matching theoretical values, were assigned to this ke0. These were recovered from end-expired concentrations and BIS. Possible determinants of error (difference between assigned and recovered ke0) were varied, that is fraction of dead space gas in end-expired gas (d), and time delays in measuring BIS (tBIS) and end-expired concentrations (tEE).
Results: Theoretical ke0s were 0.7, 0.53, 0.35, and 0.2 min(-1) for an arterial Pco2 of 8, 6.67, 5.33 (normocapnia), and 4 kPa, respectively. For spontaneous ventilation, ke0 = 0.53 min(-1). Recovered ke0s depended on d and Deltat (= tBIS - tEE) and were smaller than assigned values (if Deltat > 0). Errors increased with increasing d and Deltat. For normocapnia, ke0 was between 0.32 and 0.23 min(-1) (d = 0.1; any Deltat = 0-60 s). For spontaneous ventilation, ke0 was between 0.51 and 0.40 min(-1) (d = 0-0.1; Deltat = 5-20 s).
Conclusions: Published ke0s (0.22-0.53 min(-1)), including our own for sevoflurane-depressed spontaneous ventilation (0.48 min(-1)), are in the ranges dictated by investigation-specific conditions.