British Journal of Anaesthesia, 2001, Vol. 86, No. 1 29-37
© 2001 The Board of Management and Trustees of the British Journal of Anaesthesia
Model-based administration of inhalation anaesthesia. 2. Exploring the system model
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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We explored our model by displaying its new capabilities, testing its sensitivity to variations in input data and illustrating its use. Its multiple-gas character allows simulation of the mechanisms governing concentration and second gas effects. Simulating the volume of a standing bellows makes it possible to test algorithms for automated closed-circuit anaesthesia. Using desflurane, the model’s sensitivity to changes in blood/gas partition coefficient (range 0.42–0.576), cardiac output and minute ventilation was analysed. The model was very sensitive to changes in blood solubility; other results agreed with those reported previously. An alveolar isoflurane tension of 1% atm was rapidly attained and maintained, even using 0.5 litres min–1 of fresh gas, when isoflurane was ‘co-administered’ through a vaporizer set to 3.5 vol% and a single aliquot (1.25 ml liquid) injected into the expiratory limb. As a result of its credibility and capabilities, the model is to be tested in the clinical setting.
Br J Anaesth 2001; 86: 29–37
Keywords: anaesthetics volatile, isoflurane; anaesthetics volatile, desflurane; pharmacokinetics, models; equipment, breathing systems; anaesthetic techniques, inhalation
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Introduction |
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We have described the development of a physiological system model for the kinetics of respiratory and inert gases, including the potent inhalational anaesthetic agents.1 It incorporates a multi-compartment model of the circulation and body tissues, a three-compartment lung and a three-compartment anaesthetic breathing system (when referring to an anaesthetic breathing system, we imply a circle breathing system with carbon dioxide absorption). Circulation and ventilation are treated as continuous processes.
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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Except where otherwise stated, input data to the model were those described in our previous paper.1 Features of the model patient are outlined in Table 1.
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Displaying the capabilities of the model
Multiple-gas character
The model subject breathed air (79.1 vol% nitrogen and 20.9 vol% oxygen) from the anaesthetic breathing system, followed by a mixture of 79.1 or 39.1 vol% nitrous oxide, 20.9 vol% oxygen and balance nitrogen. Total fresh-gas flow (FGF) was 9 litres min–1 (ATPD), which was more than total ventilation (Table 1).
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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Sensitivity analysis
Using desflurane, we examined the sensitivity of the model to changes in blood/gas partition coefficient, cardiac output and minute ventilation. Essentially, 12 vol% desflurane was administered for 5 min and 6 vol% thereafter in 0.5 litres min–1 each of nitrous oxide and oxygen (Table 2).
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 min–1) 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 min–1 in oxygen 0.3 litres min–1 (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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Displaying the capabilities of the model
Multiple-gas character
After the sudden introduction of 79.1% nitrous oxide in the breathing mixture, nitrogen is exchanged for the more soluble nitrous oxide (Figure 1A). Large volumes of nitrous oxide are transferred from alveoli to blood and removed by solution in lung tissue, whereas relatively small volumes of nitrogen are excreted. Since the inspired ventilation and alveolar volume are held constant, the expired ventilation decreases by the amount of the net uptake of gas molecules (Figure 1B). Consequently, there is an increase in the partial pressures of all gases (except nitrogen) present in the alveoli. As this increase depends on the net uptake, the alveolar nitrous oxide fractional concentration (FA) approaches its inspired fractional concentration (FI) more quickly when the latter is greater (concentration effect). The difference in FA/FI at 3 min is 0.081 for 79.1% compared with 39.1% inspired nitrous oxide. The alveolar oxygen tension increases from 13.61 to 17.86 kPa, despite its constant inspiratory tension, and carbon dioxide tension increases from 5.33 to 6.93 kPa (Figure 1C).
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Variety of FGF
The various epochs of a typical desflurane anaesthesia show the wide variety of FGF handled by the model (Figure 2). The initial conditions reflect those of air breathing. The pre-oxygenation (and denitrogenation) process then begins. Since the breathing system is not pre-filled with oxygen, it takes about 1 min for the inspiratory oxygen tension to reach the intended value. Denitrogenation is 95% complete within 3 min.
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Administration of 4, 5 and 6 vol% desflurane in an FGF of 6 litres min–1 (ATPD; 10–15 min) rapidly achieves the desired alveolar tension. The inspiratory tension does not attain the delivered tension because there is some rebreathing. The chosen FGF is indeed smaller than the minute ventilation of 7.60 litres min–1 (ATPD) required to attain the initial target alveolar carbon dioxide tension of 4.50 kPa. Reduction of FGF to 0.5 litres min–1, to which 5% desflurane is added, yields virtually constant desflurane tensions in the period 15–75 min. Nitrous oxide and oxygen partial pressures evolve as dictated by the ratio of the delivery and the uptake of each of the two substances. Ending the delivery of desflurane without increasing FGF causes its tensions to decrease slowly (75–90 min). Nitrous oxide and desflurane are washed out with oxygen (90– 95 min). After 5 min of air breathing, oxygen and nitrogen are not far from resuming their initial partial pressures.
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 (13–28 min). For the oxygen concentration the undershoot is 0.46 (0.04) % atm (13–20 min and 21–28 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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V. If there is no volume shortage in the bellows (
0), no gases can be added. If there is volume shortage, indicated by a positive
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Sensitivity analysis
The value chosen for the blood/gas partition coefficient has considerable impact on the speed of build-up of desflurane in the alveoli (Figure 5). When tissue/gas partition coefficients are kept constant, concentrations are in the range 4.72–5.21% at 20 min, and the slowest wash-in curve intersects the 5% atm line 16 min later than the fastest curve. On the assumption of constant tissue/blood partition coefficients, the range is 4.67–5.32%, and the difference in time is 21 min.
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When only the cardiac output was changed, to 50% greater or 50% less than normal, the rate of build up of alveolar desflurane tension was decreased or increased, respectively. The average percentage differences between wash-in curves were –9 (1) % and +13 (1) %, respectively.
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, the FGF is 12 litres min–1 (ATPD; nitrous oxide:oxygen 2:1; Table 2) to guarantee non-rebreathing conditions even with increased ventilation. The oxygen tensions decline from the high values obtained through the preceding pre-oxygenation. Nitrous oxide tensions rapidly increase to the tension in the fresh gas. The rate of increase is slowest for the case with concomitant halving of cardiac output and ventilation (closed circles).
For time >0, low-flow conditions prevail (0.5 litres min–1 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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Research and development
Figure 4 (right) shows that the presence of noise in the oxygen signal does not alter the behaviour of the bellows, but the inflow of oxygen is chaotic around oxygen uptake.
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Discussion |
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The new system model meets the essential criteria that were the basis of its development.1 The model handles FGFs from basal to more than total ventilation. It describes all gases present in an anaesthetic breathing system with a standing bellows. Simulating the bellows volume is a unique feature.
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 elimination—a 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 patient’s 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.9–11
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 min–1 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 min–1), 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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1 Lerou JG, Booij LH. Model-based administration of inhalation anaesthesia. 1. Developing a system model. Br J Anaesth 2000; 86: 12–28
2 Johnson TS, Swanson GD, Sodal IE, Reeves JT, Virtue RW. A closed lung system study of inert gas absorption. J Appl Physiol 1979; 47: 240–4
3 Korman B, Mapleson WW. Concentration and second gas effects: can the accepted explanation be improved? Br J Anaesth 1997; 78: 618–25
4 Poon CS, Wiberg DM, Ward SA. Dynamics of gaseous uptake in the lungs: the concentration and second gas effects. IEEE Trans Biomed Eng 1981; 28: 823–31[Web of Science][Medline]
5 Shah J, Jones JG, Galvin J, Tomlin PJ. Pulmonary gas exchange during induction of anaesthesia with nitrous oxide in seated subjects. Br J Anaesth 1971; 43: 1013–21
6 Kitahata LM, Taub A, Conte AJ. The effect of nitrous oxide on alveolar carbon dioxide tension: a second-gas effect. Anesthesiology 1971; 35: 607–11[Web of Science][Medline]
7 Booij LH, Lerou JG. The differences between closed-circuit, low-flow, and high-flow breathing systems: controllability, monitoring, and engineering aspects. In: Schwilden H, Stoeckel H, eds. Control and Automation in Anaesthesia. Berlin: Springer, 1995; 60–75
8 Dingley J, Ivanova-Stoilova TM, Grundler S, Wall T. Xenon: recent developments. Anaesthesia 1999; 54: 335–46[Web of Science][Medline]
9 Westenskow DR, Zbinden AM, Thomson DA, Kohler B. Control of end-tidal halothane concentration. Part A: Anaesthesia breathing system and feedback control of gas delivery. Br J Anaesth 1986; 58: 555–62
10 Zbinden AM, Frei F, Westenskow DR, Thomson DA. Control of end-tidal halothane concentration. Part B: Verification in dogs. Br J Anaesth 1986; 58: 563–71
11 Ritchie RG, Ernst EA, Pate BL, Pearson JD, Sheppard LC. Closed-loop control of an anesthesia delivery system: development and animal testing. IEEE Trans Biomed Eng 1987; 34: 437–43[Web of Science][Medline]
12 Eger EI, II. Partition coefficients of I-653 in human blood, saline, and olive oil. Anesth Analg 1987; 66: 971–3
13 Yasuda N, Eger EI, II, Weiskopf RB, Tanifuji Y, Kobayashi K. Solubility of desflurane (I-653), sevoflurane, isoflurane, and halothane in human blood. Masui 1991; 40: 1059–62[Medline]
14 Lockwood GG, Sapsed-Byrne S, Smith MA. Effect of temperature on the solubility of desflurane, sevoflurane, enflurane and halothane in blood. Br J Anaesth 1997; 79: 517–20
15 Lockwood GG, White DC. Effect of ventilation and cardiac output on the uptake of anaesthetic agents from different breathing systems: a theoretical study. Br J Anaesth 1991; 66: 519–26
16 Conway CM. Gaseous homeostasis and the circle system. Factors influencing anaesthetic gas exchange. Br J Anaesth 1986; 58: 1167–80
17 Mapleson WW. The theoretical ideal fresh-gas flow sequence at the start of low-flow anaesthesia. Anaesthesia 1998; 53: 264–72[Web of Science][Medline]
18 Westenskow DR, Johnson CC, Jordan WS, Gehmlich DK. Instrumentation for measuring continuous oxygen consumption of surgical patients. IEEE Trans Biomed Eng 1977; 24: 331–7[Web of Science][Medline]
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