Institute for Anaesthesiology, University of Nijmegen, Geert Grooteplein 10, NL-6500 HB Nijmegen, The Netherlands*Corresponding author
Accepted for publication: August 31, 2001
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Abstract |
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Methods. In 50 patients, desflurane anaesthesia was maintained with a fresh-gas flow (FGF) of 0.5 litres min1 of both nitrous oxide and oxygen, preceded by fast (n=14) or slow (n=36) induction: FGF greater than total ventilation, Group F; FGF equal to 1.0 litres min1, Group S. The two versions of the model studied differed in the size of their inter-tissue diffusion, as 0 (version 1) and 3% (version 2) of the cardiac output was shifted from the viscera to adipose tissue. Model performance was judged by comparing measured and predicted gas concentrations in terms of three variables for each gas concentration in each patient: root mean squared error (rmse=total error), bias (mean predicted measured) (systematic error), and scatter (error around bias). These variables were then averaged over all patients. These measures were calculated overall, and separately for each group and each stage (1=induction or 2=maintenance).
Results. Model predictions were in reasonable to very good agreement with clinically obtained data. Version 2 performed better than version 1. Differences between groups were not demonstrated. The model performed better for stage 2, but only for desflurane. In group S, results (mean (SD); as percentages of the measured values for nitrous oxide, oxygen and desflurane) in the order rmse, bias, and scatter were for end-tidal concentrations of nitrous oxide: 8 (4), 8 (5), 2 (1)%; oxygen: 11 (4), 10 (6), 2 (1.1)%; nitrogen: 0.9 (0.6), 0.8 (0.6), 0.2 (0.1) vol%; carbon dioxide: 1.8 (0.6), 1.8 (0.6), 0.2 (0.1) vol%; desflurane, stage 2: 8 (4), 4 (7), 4 (2)%, vs 15 (6), 10 (8), 9 (4)% for stage 1.
Conclusion. Administration of inhalation anaesthesia can be based on version 2 of this model, but must be guided by active monitoring.
Br J Anaesth 2002; 88: 2437
Keywords: anaesthetics volatile, desflurane; pharmacokinetics, models; equipment, breathing systems; anaesthetic techniques, inhalation
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Introduction |
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This paper presents a prospective comparison with clinical data and aims to quantify the predictive performance of the model. General anaesthesia with desflurane and nitrous oxide in oxygen was administered to 50 patients under low-flow conditions. We retrospectively compared the predicted inspired and end-tidal concentrations of desflurane, nitrous oxide, oxygen, carbon dioxide, and nitrogen with those measured in each patient. Two versions of the model were formulated. One version (1) is the basic model;1 another (2) accounts for large-scale diffusion between body compartments.3
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Patients and methods |
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The anaesthetic breathing system (Fig. 1 in reference 1) was filled with air by flushing it with 9 litres min1 medical air for 3 min. When the mask was applied to the face of the patient, fresh gas was switched from air to oxygen to perform denitrogenation and pre-oxygenation. Fentanyl 3 µg kg1 i.v. was given. Two minutes later, anaesthesia was induced with an i.v. dose of propofol sufficient to obtund the eyelash reflex and rocuronium 0.5 mg kg1 i.v.. The patients lungs were ventilated manually by mask for 2 min, using a FGF of 12 litres min1 (nitrous oxide:oxygen, 1:1); an increment of propofol of 2040 mg i.v. was then given, according to body mass, and changes in the NIBP as a result of inducing anaesthesia. After a further 30 s, topical anaesthesia of the larynx with 24 ml of lidocaine 4.3% spray was performed, the patients trachea was intubated with a cuffed tube, and the cuff was inflated.
The patient was reconnected to the breathing system and the ventilator, and the lungs were artificially ventilated with a FGF of 9 litres min1 (nitrous oxide:oxygen, 2:1) until the end-expiratory nitrogen concentration was less than 2 vol% (vol% is used for concentrations to avoid confusion with the per cent unit for the performance measures), or for a maximum of 10 min. Subsequent treatment depended on allocation to group S (slow scheme) or group F (fast scheme). Patients were not deliberately placed in one or the other group, but an increased proportion of patients (5:2, eventually) were assigned to group S (to achieve greater clinical experience with low-flow conditions).
In group S (n=36), the initial total FGF was set to 1 litre min1 (i.e. 0.5 litres min1 each of nitrous oxide and oxygen). Reducing the FGF from 9 to 1 litre min1 necessitated adjustment of tidal volume because delivered tidal volume depended on the rate of FGF into the standing bellows ventilator.4 5 Once the total ventilation was stable, the vaporizer was set to deliver 12 vol% desflurane until its end-expired concentration was appropriate as judged by the attending anaesthetist (J.L.). Then, for the second stage, the vaporizer setting was reduced to 1 vol% above the target end-expired concentration, while the FGF was kept unchanged.
In group F (n=14), the initial total FGF exceeded at least the assumed alveolar ventilation, or was even greater than total ventilation, and the vaporizer was initially set to deliver 6 vol% desflurane until its end-expired concentration was appropriate as judged by the attending anaesthetist (J.L.). The second stage was the same as in group S. Each of the schemes reflected one out of two dosing strategies commonly used in the clinical environment.
During maintenance, we modified desflurane administration to provide adequate anaesthesia. We therefore carefully monitored the patients response to surgery by assessment of NIBP, heart rate, and heart rate variability judged by ear with the aid of pulse oximetry, and also end-tidal desflurane concentration. Extra fentanyl (0.050.1 mg) was given according to clinical needs. The end-tidal carbon dioxide concentration was maintained at 3.64.6 vol%. Desflurane was purchased from Pharmacia Nederland B.V. (Woerden).
Instrumentation
The anaesthetic equipment consisted of a Modulus CD anaesthesia system (Ohmeda, Madison, USA), which is routinely used in the operating theatres for ophthalmic surgery. The anaesthetic breathing system comprised a soda-lime canister (part of the Ohmeda GMS (Gas Management System) Absorber), two 1-m corrugated tubes in each limb, a water trap in each limb, and a Y-piece. The switch in the GMS allowed swift alternation between reservoir bag and ventilator: (i) a 2-litre bag at the end of 1-m length of corrugated tubing was used for spontaneous breathing and manual ventilation by mask; and (ii) a standing bellows ventilator (Ohmeda 7850) supported artificial ventilation of the lungs. A scheme of the breathing system with an internal volume of 6.6 litres, as used during artificial ventilation, was given in Figure 1 of reference 1. Leaks in the circuit were detected by plugging the Y-piece, pressurizing the breathing system to 4 kPa, and observing the volume and pressure gauge; a gas leak up to 60 ml min1 was accepted. Desflurane was delivered in all patients by the same Ohmeda Tec 6 vaporizer. The accuracy of the Rotameters (oxygen, nitrous oxide, air) was checked against a bubble flow meter. The expiratory volumes were measured with an Ohmeda volume monitor; the turbine vane transducer sensor has an accuracy of ±5%.6
A respiratory mass spectrometer (QP 9000) was located in a nearby room. One of its two inlet ports was connected to a 2-m inlet probe, the other to a valve box which sampled via 30-m nylon probes,7 8 at 60 ml min1, either at the Y-piece or from the FGF. Switching between the two inlet ports was done by pinch valves incorporated in the mass spectrometer, and between the long probes by a pair of electromagnetic valves. The hospital vacuum was used to draw continuously a matching 60 ml min1 from whichever 30-m probe was not connected to the mass spectrometer. Normally the mass spectrometer continuously sampled gas from the Y-piece but, each time the setting of the vaporizer was changed, it was switched to sample fresh gas for 40 s.
The mass spectrometer was calibrated once or twice per day (morning and afternoon list) with just the 2-m inlet probe according to a procedure recommended by the manufacturer (CaSE, Gillingham, UK) using two gas mixtures of known composition. In addition, before starting each list we verified the mass spectrometers calibration with one of the long probes (both had same geometry) using room air and the same two calibration gas mixtures: (i) 1 vol% argon, 5 vol% carbon dioxide, 44 vol% oxygen in nitrous oxide; and (ii) 4 vol% desflurane, 44 vol% oxygen in nitrogen (AGA Gas, Amsterdam, The Netherlands). Six channels were tuned to the mass-charge ratios required to measure nitrogen (28), oxygen (32), carbon dioxide (12), nitrous oxide (30), argon (40), and desflurane (51). An eight-channel thermal array recorder (Nihon Kohden RTA 1300) running at 10 mm min1 recorded the mass spectrometer signals.
A personal computer system located in the operating theatre processed the signals from the mass spectrometer (12-bit analogue-to-digital board (Keithley Metrabyte, USA)), was allowed to operate the switching mechanism for the valves, and recorded all variables acquired by the Modulus CD anaesthesia system (e.g. expiratory ventilation) from its RS232 output port. The data acquisition software was developed with the aid of ASYSTTM (Keithley Metrabyte). On-line analysis of the respiratory waveforms allowed continuous monitoring of the actual inspiratory and end-expired concentrations of nitrogen, oxygen, carbon dioxide, nitrous oxide, argon, and desflurane. Every 10-s the last inspiratory and end-expired concentrations of these gases were saved on hard disk for further data processing.
The model
Versions
Version 1 is the basic model that was quantified earlier.1 For desflurane it uses the tissue/gas partition coefficients reported by Yasuda and colleagues,9 and a bloodgas partition coefficient of 0.52 as reported by Lockwood and co-workers.10 Version 2 uses one of the amendments that Allott and colleagues11 made to their basic model as a simple means of mimicking inter-tissue diffusion. Part of the cardiac output was, therefore, redirected from the viscera, i.e. kidneys, heart, brain, and liver, to the adipose tissue. In successive simulation runs, the total fraction redirected cardiac output (fR) was increased, with steps of 0.01, until the cumulative uptakes of desflurane and isoflurane predicted by our model agreed closely with those reported by Hendrickx and co-workers.12 Their experimental conditions were mimicked in the way already described.1 As the sum of the fractions of cardiac output to the viscera in version 1 is 0.76, the fractions for version 2 were obtained by multiplying those in version 1 by (0.76fR)/0.76.
Adapting the model to experimental conditions
Clinically important details were incorporated into the original model with the aim of performing this validation study. During the process of intubation there is a period of apnoea that may be short but also rather lengthy in case of a more difficult intubation. It is virtually impossible to fully describe the impact of removing the facemask and intubating the trachea on the composition of the gas mixture in the lungs and the anaesthetic breathing system. The model therefore assumed that, during apnoea, alveolar ventilation was zero and gas exchange continued across the alveolo-capillary membrane.
With a leak measured to be 60 ml min1 at a continuous breathing-system pressure of 4 kPa, plus a sample flow of 60 ml min1, careful consideration of detail led us to conclude that, in use, a net loss as 75 ml min1 of inspired mixture would be a good estimate of the effective loss. (Accuracy is minimally influenced by this legitimate assumption.)
The model also accounted for the sample flow drawn off continuously by the hospital vacuum at the common gas outlet (V·sf). If V·Fi was the FGF for each component i (nitrogen, oxygen, nitrous oxide, or desflurane), then its effective FGF entering the circle system was given as:
The ventilation in the model was matched to that measured for each patient as follows. A target value for the ideal alveolar carbon dioxide tension (PAco2, assumed equal to PaCO2) was obtained from: (i) the ventilation measured (averaged over the period of administration of desflurane); (ii) a chosen value of 50% for wasted ventilation;1 and (iii) a specific, rearranged form of equation (24) in Appendix 2 of reference 1. The value obtained was used by the model to calculate alveolar ventilation (see below).
Simulated end-expired tensions were calculated according to Landon and co-workers13 from the ideal alveolar (PA) and dead space (=inspired; PI) tensions predicted by our model: PE'=(1d)PA+dPI. For each patient, the dilution factor d (the fraction of dead space gas in end-expiratory gas)13 was deduced from the arterial and end-expired carbon dioxide tensions: d=(PaCO2PE'CO2)/PaCO2. Assuming that PaCO2PE'CO2=0.533 kPa (see discussion) and as PaCO2=PAco2, it follows that d=0.533/PAco2.
Comparing measurements with predicted values
This was a three-step process. During step one, the model input was generated. The model input consisted of the anthropometric data (age, sex, body weight, and height), the FGF rates (air, oxygen, and nitrous oxide), the desflurane concentration in the FGF (the measured signal averaged over 5 s), the target value for the ideal alveolar carbon dioxide tension, and the period of apnoea during intubation. Throughout step two, our model generated the predicted time courses of the inspired and end-expired concentrations of desflurane, nitrous oxide, oxygen, carbon dioxide, and nitrogen by running the model in a TutsimTM simulation program (Meerman Automation, Neede, The Netherlands). In the final step three, the differences between predicted and measured concentrations (the predictive performance measures, vide infra) were analysed in a Mathcad (version 7) worksheet (Mathsoft, Bagshot, Surrey, UK).
Predictive performance measures
Definitions
The summary measures that served to determine the predictive performance of the model are defined in Table 1. The prediction error (pe) is the difference between a predicted and a measured concentration; pe can be expressed as a vol% difference (nitrogen and carbon dioxide) or as a percentage of the measured value (N2O, O2, desflurane). Prediction error and squared prediction error (pe2) are calculated for each time period of 10 s. These two quantities are used to provide the following three predictive performance measures.
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2. Bias (me), that is the average of the prediction errors for an individual patient, is a measure of the systematic component of error. It can be either positive or negative, thus indicating over- or under-prediction, respectively. It does not provide information about the typical size of the prediction error if there are both under- and over-predictions in an individual patient.
3. Scatter is a measure of the variation of the prediction errors for an individual patient around the mean (or bias) for that patient.
These three measures were calculated for the inspired and end-tidal concentrations of desflurane, nitrous oxide, oxygen, and nitrogen, and for the end-tidal concentration of carbon dioxidea total of 3x9=27 performance measures for each patient, or 54 when calculated separately for stages 1 and 2.
Overall performance measures
Overall measures evaluate the whole period including stages 1 and 2, which ends at the moment when artificial ventilation was stopped. Each of 27 performance measures per patient were averaged over all patients to yield the three group overall performance measures for each of the nine gas concentrations.
Performance measures per stage and group
Each of the performance measures was also assessed separately for each stage (1 or 2) and group (S or F). Calculating the numerical averages of the 36 (group S) or 14 (group F) performance measuresone per patient and per gas concentrationyielded the group performance measures for a gas concentration for each stage.
Performance measures per version
Performance measures were calculated once for version 1 and once for version 2 of the model. Figures 013F1 and 013F2 serve to illustrate the predictive performance measures. Figure 013F1 shows a selection of measured and predicted concentration time profiles in a patient who was considered representative because she belonged to the largest group S, had average physical characteristics, and showed individual results in agreement with group results. Figure 013F2 illustrates the biases and scatters of end-tidal desflurane in the same patient.
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Results for each of the 27 (or 54) performance indicators, per version, were expressed as mean of all patients and SD between patients, except where otherwise stated.
The sign test was used to compare the predictive performance of version 1 with that of version 2. We therefore tested the hypothesis of whether the rmse for version 2 was closer to zero. The same hypothesis was tested for bias and scatter.
Performance indicators were tested for differences between the means of stage 1 vs 2 (for each group) with a t-test for paired data, and group S vs F (for each stage) with a t-test for unpaired data. A P<0.001 (correction for multiple comparisons) was considered statistically significant; n denotes number of patients.
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Results |
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Table 6 shows that total error budgets for inspired concentrations are similar to those for end-expiratory concentrations. For desflurane, nitrous oxide, and oxygen, values of rmse are less than 12%. For carbon dioxide, there is an important total error budget of approximately 1.75 vol%. Performance measures are further reported only for end-expiratory concentrations, as their group rmse values tend to be slightly higher for most gases.
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Version 2: performance per stage and group
Each of the performance measures was calculated four times, that is once for each group (S or F) and stage (1 or 2). In Figure 013F6, each patient is represented by two symbols on each of the xy plots, that is one symbol per stage. The iso-rmse semicircles allow a visual impression of the predictive performance of version 2.
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Version 2: differences in performance between stages
Figure 013F6 and Table 8 show that notable differences between stages only exist for desflurane (plus signs vs circles; crosses vs squares). Figure 013F6A shows that only a minority of the observations (24%) for stage 1, but a majority (74%) for stage 2 is found in the semicircular area where rmse is less than 10%. Most observations for stage 1 are in the under-prediction zone, whereas observations for stage 2 appear to be evenly dispersed either side of the +2% bias line (Fig. 013F6A).
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Version 2: differences in performance between groups
The study failed to demonstrate differences in model performance between groups (Table 8).
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Discussion |
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Structure of the model
Despite these findings we cannot conclude that the complete structure of the model is correct. This is a general problem of complex physiological models.14 Validating each and every variable in such a model may present insurmountable difficulties.15
The value for fR in version 2 was found on the basis of data from an other institution.12 The results in Figure 013F3 lend credence to the broad validity of the model, but do not prove that version 2 is entirely correct. Our results even do not indicate that direct diffusion of desflurane from well-perfused organs into adjacent fat is an indispensable part of a physiological model. Nonetheless, large-scale diffusion between body compartments is a well-known physical process.3 11 1618 The over-prediction we reported earlier, especially during longer anaesthetics,19 might have been minimized by adopting inter-tissue diffusion.
Diverting 3% of the cardiac output from viscera to fat (Table 5) represents inter-compartment diffusion only indirectly. Furthermore, an fR in the range from 0.01 to 0.05 would also have been a legitimate choice as the uptake curves obtained with these values were within the 95% CIs shown in Figure 013F3.
Our results also do not prove that we are right in using a bloodgas partition coefficient for desflurane of 0.52.10 This value is different from the most cited value2 (0.42), but lies within the range of measured values. Even a value of 0.58 (SD 0.06) has been reported.20 Illustrations of the impact of various values on desflurane wash-in and reasons for using 0.52 were given elsewhere.2 It is noteworthy that our model uses the tissuegas partition coefficients reported by Yasuda and co-workers.9 Tissueblood partition coefficients were obtained by dividing the latter coefficients by 0.52 (Table 5 in reference 1).
Accuracy for different gas species
There are some basic criteria to judge the accuracy of the model. First, valid models should not under-predict or over-predict reality in a systematic way. It is reasonable to expect a certain degree of bias for each patient. Nonetheless, the group bias should approximate zero. A value within ±10% can be defended as an acceptable approximation on the grounds that this is within the limits that can be achieved for control of concentrations clinically. Second, if the group bias approximates zero, the total error budget (rmse) should be acceptable for a majority (90%) of the patients. A 010% group bias can indeed coexist with a significant dispersion of the individual results for bias and scatter. The accuracy of the model becomes unacceptable when the individual rmses are greater than can be reasonably expected on the basis of the biological variability found in a general human population. Although we arrived at defining objective criteria to determine whether a physiological model has acceptable accuracy for the special case of closed-circuit anaesthesia,19 further research is needed to define such rules for low-flow conditions, if at all possible.
For desflurane, nitrous oxide and oxygen, group biases are 10% (Tables 7 and 8). For desflurane, rmse values are less than 25% (stage 1) and less than 17% (stage 2) for
93% of the patients (Fig. 013F6). For nitrous oxide and oxygen, rmse values are less than 15% for 92100% of the individuals.
The accurate performance of the model for nitrogen (rmse1 vol%) is not totally surprising. The largest stores of nitrogen are in the lungs and are washed out almost completely during the first minutes of an anaesthetic. The discrepancies between theory and experiment might have been greater during these very early stages, but they were omitted for reasons discussed further.
The mass balance model of Beams and co-workers21based on the same specific breathing systemseems to represent clinical low-flow anaesthesia better than ours. In their study, however, actual patient exchanges for isoflurane, oxygen, nitrous oxide, and nitrogen were measured and used as input for the model. This points out that the predictive performance of a model heavily depends on variability in exchange rates of gases and vapours.
Can the cause of the systematic errors be elucidated?
In this study we could exclude errors induced by departures from the settings of the vaporizer as we measured the actual delivered concentration at each setting. Although deviations between checks of the Rotameters cannot be excluded, it is very unlikely that temporary deviations would always occur in the same direction.
The under-prediction for oxygen could be simply explained by assuming that actual oxygen uptake was lower than predicted. This would conflict with prior notions that reported values were greater than those predicted by our model.1 In addition, this single factor governed explanation might be too simplistic. There are many factors influencing the kinetics of the various gases, and their kinetics are inter-dependent.2 22 This leads to propagation of errors and thus presents nearly insuperable difficulties in tracing the exact sources of error. As oxygen plus nitrous oxide make up about 90% of the gas mixture, it is almost certain that a negative bias in one will be associated with a positive bias in the other.
Assuming that the actual uptake of nitrous oxide was greater than that predicted would not only explain the over-prediction found for nitrous oxide, but also the under-prediction found for oxygen. Figure 013F7 confirms this by re-plotting data from Figure 013F6B and C to show a strong link between the individual biases for nitrous oxide and oxygen: r2=0.58 and r2=0.70 for stages 1 and 2, respectively. Others23 also observed an actual uptake of nitrous oxide greater than predicted.
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The systematic over-prediction for carbon dioxide (bias1.8 vol%) may be partially related to systematic measurement errors, despite the use of mass-charge ratio 12. Error-free assessment of relatively low carbon dioxide levels in gas mixtures containing high concentrations of nitrous oxide is a well-known problem in respiratory mass spectrometry. Carbon dioxide readings lower than expected have been reported.24 We found that carbon dioxide levels, as measured by the mass spectrometer, were invariably lower than those assessed by the infrared analyser incorporated in the anaesthesia system, at least during controlled ventilation. It is puzzling, however, why calibration mixtures showed no error. Notably, two infrared analysers may differ up to 0.4 vol%.25
Research design
Early stages of the anaesthetic
A reservoir bag at the end of a 1-m length of corrugated tubing was used for spontaneous breathing and manual ventilation by mask with high flows of fresh gas. This was not mimicked in the simulation as the volume of tubing and bag (2 litres when full, but much <2 litres when squeezed) averaged over a respiratory cycle closely matches the volume of the standing bellows (1.5 litres when full). Future research might be improved by using the standing bellows for both spontaneous breathing and artificial ventilation of the lungs by maskas advocated for two-handed mask ventilation of the difficult airway by a single individual.26
Early stages, such as pre-oxygenation and manual ventilation of the lungs, were omitted from calculations of performance measures because the values obtained for inspired and end-tidal concentrations were too inaccurate before intubation.
Nitrous oxide
As the present study may suffer from some error as a result of the use of nitrous oxide (as described above), further research would preferably also include a group of subjects breathing oxygen in air. This would allow studying the impact of nitrous oxide and (better) assessing the behaviour of nitrogen and carbon dioxide.
Alveolar ventilation
The value for arterialend-expired PCO2 difference, 0.533 kPa, was chosen to yield a 10% dilution factor for all patients. Others found a similar difference.25 27 Future research will need to include the invasive sampling of arterial blood for bloodgas analysis if one would want to assess individual alveolar ventilation. This would help to investigate the sources for a bias for carbon dioxide.
Clinical implications
The target end-expired desflurane concentration was rapidly attained, that is within 6.1 min on average, with both FGF regimens. The average difference between the fast and slow scheme, 3.6 min, would probably be clinically unimportant in many cases (Table 4). The low solubility of desflurane thus allows the use of a low FGF even during induction.
Although our results are based on a limited array of FGF and anaesthetics lasting 1 h, we are confident that the model can be safely used to develop drug-dosing regimens for various purposes.28 It is a unique feature of a physiological model to conceive such regimens for maintaining steady concentrations under different physiological conditions.29 Obviously, model-based predictions must be validated and are no substitute for actual monitoring of gases and vapours.
Our results suggest that version 2 of the new system model is an adequate representation of desflurane anaesthesia in the clinical setting. It allows, with a known uncertainty, prediction of the behaviour of most gases present in the anaesthetic breathing system. Nonetheless, administration of inhalation anaesthesia based on this model must be guided by active monitoring.
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Acknowledgement |
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References |
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