Model-based administration of inhalation anaesthesia. 3 Model-based administration of inhalation anaesthesia. 3. Validating the system model  J.G.C. Lerou, L.H.D.J. Booij  British Journal of Anaesthesia  Volume 88, Issue 1, Pages 24-37 (January 2002) DOI: 10.1093/bja/88.1.24 Copyright © 2002 British Journal of Anaesthesia Terms and Conditions

Fig 1 Measured and predicted (version 2) concentrations from a 44-yr-old female patient (weight 65 kg, height 1.58 m) for inspired oxygen, end-tidal nitrous oxide and nitrogen, and inspired and end-tidal desflurane. The following periods or events can be recognized: pre-oxygenation and denitrogenation; ventilation by face mask; intubation; period of 9 litres min−1 FGF, that is the period with 33% inspired oxygen. The ‘deviation spikes’ on the measured concentrations result from the three 40-s periods (encircled numbers 1, 2, and 3) during which fresh-gas is sampled by the respiratory mass spectrometer to measure the delivered desflurane concentrations. Note that the delivered desflurane concentration (11.81 vol%) goes off scale at the first sampling period. Stage 1 is the period of induction (vaporizer set to deliver 12 vol% desflurane in 0.5 litres min−1 of each of nitrous oxide and oxygen), and stage 2 is the maintenance period (vaporizer set to deliver 6 vol% desflurane in 0.5 litres min−1 of each of nitrous oxide and oxygen). British Journal of Anaesthesia 2002 88, 24-37DOI: (10.1093/bja/88.1.24) Copyright © 2002 British Journal of Anaesthesia Terms and Conditions

Fig 2 (a) Measured and predicted end-tidal desflurane concentrations obtained with version 2 in the same patient as in Figure 1. (b) Time course of the prediction errors: the y-axis extends from –25 to +25% with zero in the middle. The overall rmse, bias, and scatter for end-tidal desflurane in this patient were 6.9, 3.1, and 6.1%, respectively. For stage 1, rmse, bias, and scatter were 15.2, –12.4, and 8.7%, respectively; for stage 2, they were 5.1, 4.8, and 1.8%, respectively. British Journal of Anaesthesia 2002 88, 24-37DOI: (10.1093/bja/88.1.24) Copyright © 2002 British Journal of Anaesthesia Terms and Conditions

Fig 3 Cumulative uptakes of desflurane or isoflurane computed with three versions of the system model using different fractions of cardiac output redirected from the viscera to the adipose tissue: fR=0.0 (version 1), 0.03 (version 2) and 0.06. The calculated uptakes are compared with those reported (a square with bars represents mean with 95% CI) by Hendrickx and co-workers.12 They measured uptake of each anaesthetic, expressed in millilitres liquid, in 10 patients who received closed-circuit anaesthesia at 1.3 MAC with mechanical ventilation of the lungs. The simulation is for their average 42-yr-old female patient of 1.65 m height, and 74 (desflurane) or 66 kg (isoflurane) body weight. British Journal of Anaesthesia 2002 88, 24-37DOI: (10.1093/bja/88.1.24) Copyright © 2002 British Journal of Anaesthesia Terms and Conditions

Fig 4 A scatterplot of the bias for version 2 vs the bias for version 1 obtained for end-expired desflurane concentrations. Each patient (n=50) is represented by one symbol per stage. One diagonal of the square is the line of identity, the other is the line where the biases have identical magnitudes but opposite signs. Observations in shaded areas are closer to zero bias for version 1, whereas observations in blank areas are closer to zero bias for version 2. British Journal of Anaesthesia 2002 88, 24-37DOI: (10.1093/bja/88.1.24) Copyright © 2002 British Journal of Anaesthesia Terms and Conditions

Fig 5 A scatterplot of the bias for version 2 vs the bias for version 1 obtained for end-expired nitrous oxide and oxygen concentrations. Each patient (n=50) is represented by four symbols: one per stage and per gas. One diagonal of the square is the line of identity, the other is the line where the biases have identical magnitudes but opposite signs. Observations in shaded areas are closer to zero bias for version 1, whereas observations in blank areas are closer to zero bias for version 2. British Journal of Anaesthesia 2002 88, 24-37DOI: (10.1093/bja/88.1.24) Copyright © 2002 British Journal of Anaesthesia Terms and Conditions

Fig 6 Predictive performance measures obtained with version 2 for end-expired desflurane, nitrous oxide and oxygen concentrations. The individual scatters of the 50 patients (36 in group S and 14 in group F) are plotted against their individual biases. Ideally, all observations for one gas would coincide with the black dot at (0,0) representing the point of ideal performance (rmse=0%). The semicircles are the iso-rmse lines from 10 to 25%. The distance between the black dot and a symbol is the rmse representing the total error budget for an individual. The mathematical relationship between rmse, bias, and scatter (Table 1) is visualized in the graph for nitrous oxide. This relationship is the same as that of the sides of a right-angled triangle. If bias is the base of the triangle and scatter the perpendicular, then the rmse is the length of the hypotenuse. British Journal of Anaesthesia 2002 88, 24-37DOI: (10.1093/bja/88.1.24) Copyright © 2002 British Journal of Anaesthesia Terms and Conditions

Fig 7 Scattergram showing relationship between the individual biases obtained with version 2 for the end-expired nitrous oxide and oxygen concentrations. There is one symbol per stage for each of the 50 patients. Note that one unit of bias has the same length on both axes. The regression lines have intercepts not far from zero and slopes not far from minus one. British Journal of Anaesthesia 2002 88, 24-37DOI: (10.1093/bja/88.1.24) Copyright © 2002 British Journal of Anaesthesia Terms and Conditions