Model-based administration of inhalation anaesthesia. 2 Model-based administration of inhalation anaesthesia. 2. Exploring the system model  J.G.C. Lerou, L.H.D.J. Booij  British Journal of Anaesthesia  Volume 86, Issue 1, Pages 29-37 (January 2001) DOI: 10.1093/bja/86.1.29 Copyright © 2001 British Journal of Anaesthesia Terms and Conditions

Fig 1 Simulation of the mechanisms governing concentration and second gas effects. At time zero, the inspired gas mixture is abruptly changed from air, which is composed of 79.1 vol% nitrogen and 20.9 vol% oxygen, to a mixture of 79.1 vol% nitrous oxide and 20.9 vol% oxygen. (a) Course of the inspiratory and alveolar partial pressures for nitrogen and nitrous oxide. The subject is denitrogenated as the induction with nitrous oxide proceeds. The mixed-venous partial pressure of nitrous oxide starts to increase after a lag time arising from successive equilibrations with blood pools and tissue compartments in the model (see reference 1, Figure 2). (b) Before zero time, the expiratory ventilation is marginally smaller than the inspiratory ventilation because the respiratory exchange ratio is 0.82. There is a net uptake of large volumes of gas as a result of the exchange between the key gases nitrous oxide and nitrogen. The maximum gas exchange occurs after about 1.5 min, i.e. just after the mixed-venous partial pressure of nitrous oxide starts to increase. The inspired ventilation is held constant, whereas the expiratory ventilation decreases. (c) As a result, in spite of the constant inspired oxygen partial pressure, the alveolar partial pressure of oxygen increases after the onset of the nitrous oxide inhalation. The same is true for carbon dioxide. However, the increase in alveolar carbon dioxide tension is probably exaggerated (see text). ATPD, ambient temperature pressure and dry conditions. British Journal of Anaesthesia 2001 86, 29-37DOI: (10.1093/bja/86.1.29) Copyright © 2001 British Journal of Anaesthesia Terms and Conditions

Fig 2 Simulated desflurane anaesthesia. Variation with time of the partial pressures for nitrogen (Pn2), oxygen (Po2), nitrous oxide (Pn2o), desflurane (Pdes) and carbon dioxide (Pco2). The FGFs indicated in the figure do not include the desflurane vapour and are expressed at ATPD. The increase in alveolar carbon dioxide tension is explained in Figure 1 and the reverse effect on carbon dioxide tension can be seen at wash-out. %atm=per centage of atmospheric pressure. British Journal of Anaesthesia 2001 86, 29-37DOI: (10.1093/bja/86.1.29) Copyright © 2001 British Journal of Anaesthesia Terms and Conditions

Fig 3 Rules for the automated supply of oxygen and nitrous oxide into the closed breathing system. Subtracting the actual volume (V) of the bellows from its target value (V*) yields a difference ΔV. If there is no volume shortage in the bellows (ΔV ≤0), no gases can be added. If there is volume shortage, indicated by a positive ΔV, the supply of fresh gases depends on ΔVo2. The latter is obtained by subtracting the actual volume of oxygen present in the bellows from the target volume of oxygen (Fo2=actual oxygen fractional concentration in the bellows; F*o2=set point oxygen fractional concentration). ΔVo2 can be positive, zero (oxygen volume is sufficient within the too small volume of the bellows) or negative. The supply of nitrous oxide is optional and equals the difference between ΔV and the calculated oxygen supply. The thick arrows relate to a numerical example. Suppose the bellows volume is smaller than its target and there is also a shortage of oxygen: e.g. ΔV=0.1 litre and ΔVo2=0.2 litre. Because ΔVo2 exceeds the shortage of the bellows volume, 0.1 litre of oxygen, but no nitrous oxide, must be supplied to the closed circuit. British Journal of Anaesthesia 2001 86, 29-37DOI: (10.1093/bja/86.1.29) Copyright © 2001 British Journal of Anaesthesia Terms and Conditions

Fig 4 Simulated behaviour of the rule-based system controlling the volume of a standing bellows and the oxygen concentration in the presence of a noise-free signal (left) and a noisy oxygen signal (right). The input to the circle system is as in Table 2. Left: (a) The bellows volume drops from its maximum volume (1.5 litres) after the start of automated CCA, then stabilizes below its target value (– · · · –). (b) The oxygen concentrations are the inspired (open circles), alveolar (closed circles) and bellows (no symbols) concentrations. Bellows oxygen concentration and bellows volume are the two input signals to the rule-based control system (Figure 3). The set point for the oxygen concentration is 32% until 20 min and 31% thereafter. (c) Oxygen FGF rapidly tracks down the oxygen uptake (0.217 litres min−1 ATPD; Table 1) (– • –). The ‘steps’ in the FGF result from the adjustments in oxygen supply which can be made only at 10 s intervals. FGFs are calculated by dividing the volume shortages (litres ATPD) obtained from the flow chart (Figure 3) by 0.125 min. Right: Labelling of the curves is the same as on the left. As a result of the noisy signal of bellows oxygen concentration, oxygen FGF does not track oxygen uptake properly. British Journal of Anaesthesia 2001 86, 29-37DOI: (10.1093/bja/86.1.29) Copyright © 2001 British Journal of Anaesthesia Terms and Conditions

Fig 5 Simulated impact on the alveolar tension of various blood/gas partition coefficients (range 0.42–0.576) for desflurane. The input to the circle system is as in Table 2 (sensitivity analysis with the lower flows for oxygen and nitrous oxide). Time zero is the start of the administration of desflurane. The six continuous lines refer to the assumption of constant tissue/gas partition coefficients. The worst-case, but less likely, scenario of constant tissue/blood partition coefficients is illustrated by the two non-continuous lines obtained with the lowest and highest value for the blood/gas partition coefficient. Obviously, the curves obtained with a blood gas partition coefficient of 0.52 are equal for both scenarios. The horizontal dotted lines are reference lines. British Journal of Anaesthesia 2001 86, 29-37DOI: (10.1093/bja/86.1.29) Copyright © 2001 British Journal of Anaesthesia Terms and Conditions

Fig 6 Simulated impact of concomitant changes in oxygen requirement, cardiac output and ventilation on oxygen, nitrous oxide and desflurane kinetics under low-flow conditions. The input to the circle system is as in Table 2 (sensitivity analysis with the higher flows for oxygen and nitrous oxide). Time zero is the start of the administration of desflurane. Squares indicate curves obtained with baseline values for oxygen requirement (201 ml min−1 STPD), cardiac output (5.35 litres min−1) and inspired alveolar ventilation (3.60 litres min−1 BTPS). Circles indicate a 50% reduction (100.5 mL min−1 STPD, 2.67 litres min−1, 1.8 litres min−1 BTPS) and triangles a 50% increase (301.5 ml min−1 STPD, 8.02 litres min−1, 5.4 litres min−1 BTPS) from baseline values. Lower portion: the horizontal dotted lines are reference lines; the line without symbols refers to the percentage differences between baseline circumstances and those with a concomitant reduction in cardiac output and ventilation (squares and circles, respectively). British Journal of Anaesthesia 2001 86, 29-37DOI: (10.1093/bja/86.1.29) Copyright © 2001 British Journal of Anaesthesia Terms and Conditions

Fig 7 Simulated variation with time of the alveolar isoflurane tension (target window 1 ± 0.1%) resulting from two different dosing strategies (see Table 2) for rapid induction with minimum usage. First strategy: the out-of-circle vaporizer setting is 3.5 vol% (0–5 min) and 2 vol% (5–20 min) in an FGF of 7.5 litres min−1 (0–1 min), 1.5 litres min−1 (1–5 min) and 1 litres min−1 (5–20 min). Second strategy: isoflurane is ‘co-administered’ through the vaporizer set at 3.5 vol% and a single bolus of 1.25 ml liquid isoflurane injected in the expiratory limb of the circle system (see reference 1, Figure 2) at time zero, using an FGF of 0.5 litres min−1. The two other curves illustrate the effects of using only the vaporizer or only the single injection of liquid isoflurane with 0.5 litres min−1 FGF. British Journal of Anaesthesia 2001 86, 29-37DOI: (10.1093/bja/86.1.29) Copyright © 2001 British Journal of Anaesthesia Terms and Conditions