Institute for Anaesthesiology, University of Nijmegen, Geert Grooteplein 10, 6500 HB Nijmegen, The Netherlands *Corresponding author
Accepted for publication: August 9, 2000
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Abstract |
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Br J Anaesth 2001; 86: 2937
Keywords: anaesthetics volatile, isoflurane; anaesthetics volatile, desflurane; pharmacokinetics, models; equipment, breathing systems; anaesthetic techniques, inhalation
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Introduction |
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Here we explore the new model in more detail so as to confirm its credibility before it is applied in the clinical setting. Sets of specific circumstances are created and simulated to: (i) display the new capabilities of the model; (ii) test its sensitivity to variations in input data; and (iii) illustrate the use of the model.
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Methods |
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Variety of FGF
A desflurane anaesthetic was emulated using the variation in FGF encountered during clinical practice.
Simulation of bellows volume
A replenishment technique to automate closed-circuit anaesthesia (CCA) was simulated, i.e. the nitrous oxide and oxygen removed by a subject from the closed breathing system were replaced. A control algorithm based on simple decision rules was designed to add oxygen at a rate necessary to maintain a constant oxygen concentration, and nitrous oxide to maintain a constant bellows volume. Shortages in nitrous oxide and oxygen were assessed by calculating the volume of the standing bellows and the oxygen concentration therein. Feedback-controlled CCA began after pre-oxygenation and a period of high FGF (Table 2). A clinically important question to answer was: is it possible to build a stable control system if the shortages are only known at 10 s intervals? Such an interval reflects a realistic time window that is required in practice to detect the volume of the moving bellows.
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Blood/gas partition coefficient
The values chosen were: 0.42, 0.45, 0.48, 0.52, 0.548 and 0.576. Two scenarios were simulated. First, the tissue/gas partition coefficients were kept constant at values that are the products of the basic values in the model for the blood/gas (0.52) and tissue/blood partition coefficients (see reference 1, Table 5). For the second (less likely) scenario, the tissue/blood partition coefficients were kept constant (see reference 1, Table 5).
Cardiac output and ventilation
Simulations were performed with the cardiac output set at its baseline default value (5.345 litres min1) and at values 50% lower and 50% higher than normal. The cardiac output values other than default were obtained in two different ways. First, cardiac output was modified on its own, i.e. without any concomitant changes in other physiological variables, and the variation of the alveolar desflurane tension with time was studied. Second, the change in cardiac output was assumed to be the response to a change in oxygen requirement of the tissues. In view of the ensuing carbon dioxide production, the respiratory minute volume was adjusted to maintain the default target PACO2 (5.33 kPa) (see reference 1, Appendix 2). The variations of the alveolar oxygen, nitrous oxide and desflurane tensions with time were studied.
Use of the model
Clinical purposes
We addressed the clinically important issue of how to achieve rapid induction with minimum usage of a potent inhalational anaesthetic agent, in this case isoflurane. Two different dosing strategies that would be simple to implement clinically were investigated theoretically. The first was a sequence of a high initial FGF at a high inspired isoflurane tension followed by lower flows (Table 2). In the second, we simulated the combined use of a single bolus of liquid isoflurane injected into the expiratory limb of the circle system (see reference 1, Figure 2) and a vaporizer during minimal-flow anaesthesia, i.e. nitrous oxide 0.2 litres min1 in oxygen 0.3 litres min1 (Table 2). Both scenarios had been optimized so that they would increase as quickly as practicable the alveolar isoflurane tension to 1 ± 0.1% atm and maintain it for 20 min.
Research and development
We studied how the behaviour of the control system for CCA would be affected by 1% noise disturbing the oxygen signal.
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Results |
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Bellows volume
The rules designed to regulate FGF are shown in Figure 3. Figure 4 (left) shows the simulated behaviour of the rule-based control system in the absence of noise. At the start of CCA, oxygen FGF first stops until the bellows volume drops below its target, then reaches oxygen uptake within 2 min. After the change in set point for the oxygen concentration, oxygen inflow first decreases, then again tracks oxygen uptake. The mean (SD) undershoot of the bellows volume is 53.4 (2.3) ml (1328 min). For the oxygen concentration the undershoot is 0.46 (0.04) % atm (1320 min and 2128 min). Stable conditions are obtained, even though information on the actual volume of the bellows is sampled only once per 10 s. The right-hand half of Figure 4 shows the effect of 1% noise in oxygen measurement.
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Figure 6, depicts the more complex situation where, from the start of the simulation, cardiac output and minute ventilation have been adjusted to the oxygen requirement and carbon dioxide production, respectively.
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For time >0, low-flow conditions prevail (0.5 litres min1 each of oxygen and nitrous oxide). The greater the oxygen uptake (as well as cardiac output and ventilation), the greater the nitrous oxide tensions; the reverse is true for oxygen tensions. All nitrous oxide curves tend to rise after approximately 30 min, whereas all oxygen curves do the reverse. There is little spread in the three curves for desflurane. It appears that the effects of changes in ventilation cancel somewhat the effects of alterations in cardiac output. Concomitantly halving cardiac output and ventilation results in an initial average percentage difference for desflurane of about +7%, falling to less than +2% before 10 min (Figure 6). The difference curve is close to zero for time >20 min, i.e. approximately +1 and 1% at 30 and 60 min, respectively (Figure 6).
Uses of the model
Clinical purposes
The first dosing strategy (Table 2) causes the alveolar isoflurane tension to reach the target at approximately 1 min and to remain within the target window (1±0.1)% atm) thereafter, except for a tiny overshoot at 5 min (Figure 7; open squares). The success of the second regimen (Table 2) depends on the injection of 1.25 ml liquid isoflurane into the expiratory limb of the breathing system. This regimen causes the isoflurane tension to reach the target at 1.5 min with a small overshoot to 1.2% atm, then to drop a little below 1% atm, and to recover to the target. Without the priming dose, the target value would not be attained in the first 20 min (Figure 7). The accumulated usage of liquid isoflurane (and nitrous oxide gas) was 4.0 or 3.1 ml (18 or 4 litres) for the first or second dosing schedule, respectively.
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Discussion |
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Displaying the capabilities
Multiple-gas character
The uptake of large volumes of nitrous oxide may be associated with one or more of the following: an increase in inspired ventilation, a decrease in expired ventilation or a shrinkage in lung volume. The latter may be important during breath-holding manoeuvres.2 The three factors were analysed by Korman and Mapleson in a search for a comprehensive and improved explanation of the concentration and second gas effects.3 Their balanced view supports our assumption of a constant lung volume, a constant inflow and a decreased expiratory ventilation when using a constant volume ventilator. Our choice was made because we expected the new model to be used mostly for situations where artificial ventilation of the lungs with a pre-set inspiratory volume prevails.
Predictions for the first 3 min of the FA/FI curves for nitrous oxide are only qualitatively similar to those obtained by Poon, Wiberg and Ward.4 However, those workers used constant expired ventilation, not constant inspired ventilation. They excluded the effects of dead space ventilation, shunting and storage capacity of lung tissue. Recirculation of anaesthetic was excluded on the basis that their time span of interest was limited to 3 min. By contrast, our results include all these effects.
The increase in the oxygen partial pressure of 4.25 kPa occurring 2.83 min after the introduction of nitrous oxide (Figure 1) is greater than that predicted by Poon and co-workers (3.73 kPa after 3 min)4 and that experimentally assessed by Shah and colleagues (4.00 kPa).5 The accompanying increase in the carbon dioxide partial pressure was not predicted by Poon and co-workers, because they assumed constant expired ventilation and therefore maintained normal carbon dioxide eliminationa plausible hypothesis during spontaneous breathing. To the best of our knowledge, an increase in carbon dioxide has been experimentally confirmed in cats,6 but not in spontaneously breathing humans5 where normal carbon dioxide regulation would tend to maintain expired ventilation. The increase in carbon dioxide in Figure 1 is probably more than would occur in vivo because, in the first few minutes of reduced expired ventilation, the alveolar carbon dioxide partial pressure would not increase much above the mixed-venous level: an increase of about 0.8 kPa, not the 1.6 kPa in Figure 1.
Bellows volume
The automated control system behaves well despite counteracting factors, such as the supply of gases being updated only once per 10 s, and the actual volume (V in Figure 3) being only part of the total volume to be controlled. The latter is, rather, the volume of the closed circuit plus the unknown volume of the patients lungs. As the system cannot calculate supply exactly and only makes a good guess, we classify it as a rule-based system. It may eliminate the labour-intensive manual control of CCA.7 Replacing nitrous oxide with xenon might support research into its use.8 A major drawback of feedback-controlled closed systems not using a form of forced circulation of gases and charcoal to absorb volatile agents is the slowness of response when changing set points.911
Sensitivity analysis
The complexity of the model arises from an attempt at physiological fidelity. However, increased complexity may introduce unexpected errors. Predictions deviating from clinical reality can result from errors in the enormous amount of a priori information fed to the model, e.g. incorrect blood/gas partition coefficients, or from errors propagating from one gas to another.
The value we chose for the blood/gas partition coefficient of desflurane may be subject to debate. The most cited value is 0.42, but 0.45 has been proposed as the most probable value. The latter is the average of the mean values obtained in two different studies.12 13 Recently, Lockwood and co-workers14 reported the values 0.52, 0.548 or 0.576 at a body temperature of 37°C, 36°C or 35°C, respectively. Being obliged to use one value for all simulations, we chose the value 0.52 because Lockwood and co-workers studied more individuals (both patients and volunteers) and we expected that the body temperature of most patients during clinical routine is <37°C. Thus a value of >0.45 seemed justified. The considerable impact of solubility, even at constant tissue/gas partition coefficients, may easily explain discrepancies between predicted and measured concentrations in patients (Figure 5).
Figure 6 illustrates that prediction errors may be generated by a model that does not have the correct inputs for cardiac output and ventilation. Therefore we assume that the curves obtained by using the default values are the ones computed by the model. These curves will differ from those observed in subjects who have other values, hidden from the observer. In addition, the behaviour of nitrous oxide affects the curves of other gaseous species (Figure 1). Errors made by the model in predicting the uptake of nitrous oxide will propagate, thus disturbing otherwise accurate prediction of concentrations of volatile agents and other gases administered concomitantly. On the other hand, Figure 6 also suggests that certain combinations of physiological variables present in a subject do not necessarily lead to grossly erroneous predictions for desflurane. These findings should not be extrapolated to other conditions of FGF, as the openness of a breathing system affects uptake.15
The effects of independent changes in cardiac output were broadly similar to those described by Conway.16 His model showed that these effects are enhanced by a lower FGF and, in terms of percentage change from control, are greater with a less soluble anaesthetic agent as well as a lower concentration. His results for 2 vol% nitrous oxide in an FGF of 1 litre min1 can thus be compared with ours for desflurane. Halving cardiac output resulted in 13% increase in alveolar concentration for nitrous oxide16 as compared with 14% for desflurane at the end of a 30 min administration.
Uses of the model
Clinical purposes
During the early stages of anaesthesia, the rate of isoflurane uptake is high and cannot be matched by the limited amount of anaesthetic delivered by a conventional out-of-circle vaporizer under low-flow conditions. The clinically important question, formulated by Mapleson, is then: How might the concentration and flow of fresh-gas best be varied during the first few minutes of anaesthesia in order to achieve rapid induction with minimum usage of volatile anaesthetic?17 Models are excellent tools to answer such questions, while satisfying the specific requirements of the individual clinician. The clinical use of model-based dosing strategies has yet to be reported.
The initial high flow and subsequent labour-intensive changes of flow and vaporizer settings (Table 2) can be omitted if one uses only one injection of liquid anaesthetic into the expiratory limb of the circle system. This technique7 achieves total independence of the near-basal FGF (0.5 litres min1), but the simulated rate of approach to the target is slower (Figure 7). Liquid is assumed to vaporize in the expiratory part of the breathing system over a period of 60 s, whereas the initial high vapour flow is directly introduced into the inspiratory subsystem (see reference 1, Figure 2).
Research and development
Figure 4 (right) suggests how the continuous assessment of oxygen consumption by a monitor based on the replenishment technique might be hampered by noise. A model can indeed aid in determination of the dynamic characteristics of an instrument under less ideal conditions and in testing possible solutions.18 Given the capabilities and credibility of the model, we can proceed to test and apply the model in the clinical setting.
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References |
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