Applying a physiological model to quantify the delay between changes in end-expired concentrations of sevoflurane and bispectral index  J.G.C. Lerou, J. Mourisse  British Journal of Anaesthesia  Volume 99, Issue 2, Pages 226-236 (August 2007) DOI: 10.1093/bja/aem148 Copyright © 2007 British Journal of Anaesthesia Terms and Conditions

Fig 1 Block diagram of the physiologically based model for sevoflurane. The brain has two compartments, each with its own perfusion (Q1 and Q2), volume (V1 and V2), and tissue/gas partition coefficient (λ1 and λ2). Ten data sets to quantify the two-compartment sub-model for the brain are given in the on-line supplement. The liver compartment includes the liver itself and the whole portal system. The blood pools serve to mimic circulation times in the body (c.v., central venous).29 Dashed lines represent the impact of arterial tensions of carbon dioxide, sevoflurane, and nitrous oxide on CBF and cardiac output. British Journal of Anaesthesia 2007 99, 226-236DOI: (10.1093/bja/aem148) Copyright © 2007 British Journal of Anaesthesia Terms and Conditions

Fig 2 Block diagram of two studies to quantify the ke0 under theoretical ideal conditions (study 1) and under practical conditions encountered in a clinical investigation (study 2). a, alveolar; a, arterial; BIS, bispectral index; c.v., central venous; d, dilution factor (the fraction of dead space gas in end-expired gas); E′, end-expired; e, effect-site; gm, grey matter; I, inspired; P, partial pressure. (a) Study 1: quantifying the theoretical ke0. The basic model (complete block diagram in Fig. 1) predicts sevoflurane partial pressures in a number of tissues, including grey matter. The physiological and pharmacological processes underlying the rate of equilibration between alveoli and grey matter may be lumped into an ‘effect-site equilibration rate constant’ ke0. Assuming that EEG changes caused by sevoflurane are directly related to its partial pressure in grey matter, one may estimate the unknown theoretical ke0 from the time courses of PA and Pgm (encircled variables) predicted by the basic model. (b) Study 2: sensitivity analysis. The extended model was used to study how sensitive experimental estimates for ke0 are to non-ideal conditions. Known values are first assigned to five parameters: ke0, E0, Emax, P50, and γ. Values assigned to ke0 are equal to the theoretical values obtained in study 1. Values for these five parameters are then recovered from the model-predicted time courses of end-expired partial pressures and BIS (encircled variables). A difference between a known assigned value for ke0 and a recovered value depends on the time delays in the monitoring devices and the dilution of alveolar gas by dead space gas. The partial pressure of sevoflurane in dead space gas equals that in inspired gas. British Journal of Anaesthesia 2007 99, 226-236DOI: (10.1093/bja/aem148) Copyright © 2007 British Journal of Anaesthesia Terms and Conditions

Fig 3 Comparison of internal jugular venous blood tensions of sevoflurane predicted by the model (lines) with corresponding measured values (symbols) and their 95% CI.14 The dashed line is for a uniform perfusion of the brain (data set #1 in Table 1). The solid line results from a data set recreating the experimental conditions of Nakamura and colleagues14 (details are in the on-line supplement). Time is on a logarithmic scale starting at 1 min. British Journal of Anaesthesia 2007 99, 226-236DOI: (10.1093/bja/aem148) Copyright © 2007 British Journal of Anaesthesia Terms and Conditions

Fig 4 Absolute values (right ordinates) for recovered ke0s and their percentage deviations (left ordinates) from ‘true’ ke0s are plotted vs Δt, that is, time delay in BIS monitor minus time delay in gas analysis monitor. Each of the four graphs refers to a specific alveolar ventilation with a matching ‘true’ value for ke0: (a) constant ventilation with arterial Pco2 of 4 kPa and ‘true’ ke0 = 0.2 min−1; (b) constant ventilation with arterial Pco2 of 5.33 kPa and ‘true’ ke0 = 0.35 min−1; (c) varying sevoflurane-depressed spontaneous ventilation and ‘true’ ke0 = 0.53 min−1; and (d) constant ventilation with arterial Pco2 of 6.67 kPa and ‘true’ ke0 = 0.53 min−1. Effects of dilution of alveolar gas by dead space gas (d = 0, 0.1, 0.2, and 0.5) and time delays in BIS processing (0, 15, 30, and 60 s) and in gas analysis (0, 5, 10, and 15 s) on the recovered values of ke0 were studied. Recovered values equalled ‘true’ values (squares) for d is zero and Δt is zero. British Journal of Anaesthesia 2007 99, 226-236DOI: (10.1093/bja/aem148) Copyright © 2007 British Journal of Anaesthesia Terms and Conditions