SENSITIVITY ANALYSIS. The sensitivity of the model to changes in various variables was examined by introducing variability into one variable at a time: the ...
British Journal of Anaesthesia 1997; 79: 505–513
A physiological model of induction of anaesthesia with propofol in sheep. 2. Model analysis and implications for dose requirements
G. L. LUDBROOK AND R. N. UPTON
Summary The determinants of induction of anaesthesia with propofol, and their implications for dose requirements, were analysed using a physiological model of the process, validated previously using sheep data. The maximum depth of anaesthesia occurred 2–3 min after cessation of injection. Injection over 2 min minimized the induction dose. More rapid injection (:1 min) did not significantly hasten induction, but increased dose requirements and produced large peak arterial concentrations, potentially risking increased hypotension. Cardiac output and cerebral blood flow were important determinants of the induction process. Increased cardiac output decreased the duration of anaesthesia, while increased cerebral blood flow increased the depth but not duration of anaesthesia. The influence on dose requirements of propofol of factors such as anxiety, hyperventilation, age and co-induction with other drugs may be interpreted in terms of their effect on cardiac output and cerebral blood flow. (Br. J. Anaesth. 1997; 79: 505–513). Key words Anaesthetics i.v., propofol. Anaesthetic techniques, induction. Induction, anaesthesia. Pharmacokinetics, propofol. Pharmacodynamics. Model, physiological. Sheep.
In an accompanying article,1 we described and validated a physiological model of the kinetics and dynamics of induction of anaesthesia with propofol in sheep. In brief, the model included a small vascular mixing compartment, a lung compartment with nonlinear extraction, the brain represented as a two-compartment model with slight membrane limitation (cerebral effects, including feedback reduction in cerebral blood flow were related linearly to propofol concentrations in the second compartment of the brain), and two compartments nominally representing moderately and poorly perfused tissues, respectively. First-order hepatic clearance was included in the moderately perfused tissue pool. Each component of the model was validated1 against an extensive previously published in vivo data set collected in instrumented sheep,2–4 such that the model was shown to be capable of accurate de novo predictions.1 In this companion article, we analyse the structure
of the model in order to illustrate its fundamental properties and its implications for dose requirements of propofol in various circumstances. The properties of models of this complexity which represent convoluted physiological systems are not intuitively obvious, but become apparent by systematically examining the influence of each component or variables of the model.
Methods The detailed structure of the model and estimation of its variables have been published previously.1 5 The predictions of the model were examined by simulation of a variety of physiological states and dose regimens (elaborated below). The results of simulations were summarized by their influence on the time and magnitude of peak propofol concentrations in arterial blood and brain. The dynamic outcome was summarized by their effect on duration and depth of anaesthesia. We have shown previously that brain concentrations of propofol were related linearly to its major cerebral dynamic effects—reductions in cerebral blood flow and changes in depth of anaesthesia.1 3 Therefore, it was assumed that there was a threshold brain concentration of propofol for the onset and offset of loss of consciousness. While the magnitude of this threshold depends on the magnitude of the pharmacodynamic response to propofol in the brain, the level of surgical stimulus and other factors, this analysis is valid for comparison purposes. A value of 2 mg litre91 was chosen for the threshold, which was consistent with our previous observations.3 Note that as the brain was modelled as an apparent distribution volume, 2 mg litre91 is an apparent brain concentration which must be multiplied by the brain:blood partition coefficient to give the true brain concentration.6 The time of onset of anaesthesia (loss of consciousness) was the time the apparent brain concentrations first reached 2 mg litre91, the time of maximum depth of anaesthesia was the time of peak brain concentrations (expressed as percentage of normal for comparison purposes), while duration of anaesthesia was the length of time the brain concentrations remained greater than 2 mg litre91.
R. N. UPTON, BSC, PHD, G. L. LUDBROOK, MB, BS, FANZCA, Department of Anaesthesia and Intensive Care, Royal Adelaide Hospital, University of Adelaide, North Terrace, Adelaide, SA 5005, Australia. Accepted for publication: May 26, 1997. Correspondence to R. N. U.
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The predictions of the model were examined for two dose regimens of propofol—a bolus injection of 200 mg over 20 s (“bolus”) and an infusion of 40 mg min91 for 5 min (“infusion”). These correspond in general terms to the two major clinical methods used for induction of anaesthesia with this agent. STRUCTURAL ANALYSIS
The importance of various structural components of the model was analysed by systematically removing them from the model; these were drug-induced changes in cerebral blood flow, recirculation, hepatic clearance and vascular mixing. SENSITIVITY ANALYSIS
The sensitivity of the model to changes in various variables was examined by introducing variability into one variable at a time: the variables examined were cardiac output, cerebral blood flow, systemic distribution volumes, lung extraction and lung distribution volume. Simulations were performed with these variables set at their normal value, and at values 50% higher and 50% lower than normal (see tables 2 and 3 for actual values used). For lung extraction, simulations were performed with lung extraction at constant values of 15%, 30% and 60% rather than the usual non-linear extraction. IMPLICATIONS FOR DOSE REGIMENS
The model was used to examine the dose requirements of propofol to achieve a given level of
anaesthesia for two administration paradigms. First, the optimum duration of injection of propofol was determined by simulations for a range of durations of injections while varying the dose until a peak brain concentration of 2 mg litre91 was achieved in each case. The required dose, time to peak arterial and brain propofol concentrations, and magnitude of peak arterial propofol concentrations were related to duration of injection. Second, to mimic the clinical practice of infusion with titration to a given anaesthetic end-point, the model was used to simulate infusions of propofol at rates of 50, 100 and 200 mg min91 with administration stopped when a brain concentration of 2 mg litre91 (nominally loss of consciousness) was achieved. For each administration rate, the total dose administered at the time of the end-point, time that end-point was reached and resulting time course of brain concentrations predicted by the model were recorded. These data were also compared with data in humans of Peacock and colleagues7 8 and Stokes and Hutton.9
Results A TYPICAL OUTPUT OF THE MODEL
Arterial and brain concentrations of propofol expected after bolus and infusion regimens for the normal cardiac output state are shown in figure 1. It is apparent that arterial concentrations of propofol are relatively transient, particularly after bolus administration. For the same dose, the infusion regimen delayed the onset of anaesthesia rather than affecting its depth, compared with the bolus. Thus
Figure 1 Typical outputs of the model, also showing the sensitivity of the model to changes in cardiac output (CO). Data were simulated with CO at its normal baseline value (medium), and at a value 50% lower (low) or 50% higher (high) than normal.
Induction with propofol—model analysis
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Table 1 Structural analysis. Analysis of the effect of removing various components of the model on the peak concentration in arterial blood and brain, time of onset of anaesthesia, peak level of anaesthesia as a percent of normal and time of this peak, and total duration of anaesthesia. CBF:Cerebral blood flow
Analysis Bolus Normal No CBF changes No recirculation No hepatic clearance No vascular mixing Infusion Normal No CBF changes No recirculation No hepatic clearance No vascular mixing
Peak arterial (mg litre91)
Peak brain (mg litre91)
Onset time (min)
Peak effect (% normal)
Peak time (min)
Duration (min)
38.03 38.14 37.83 38.14 39.56
4.07 4.49 2.47 4.15 3.80
1.15 1.05 1.45 1.15 1.15
100 110 61 102 93
3.9 3.4 2.8 4.1 3.8
12.6 9.7 4.05 15.05 11.65
9.00 9.00 5.95 9.39 9.08
3.66 4.53 2.77 3.80 3.68
3.5 3.25 3.85 3.45 3.45
100 124 75 104 101
7.1 6.6 5.9 7.5 7.1
12.4 10.6 5.95 15.45 12.5
infusion of the same dose as used for the bolus caused a 10% decrease in the maximum depth of anaesthesia, but only a 1.5% reduction in duration of anaesthesia. However, the time of onset of anaesthesia was increased from 1.15 to 3.5 min, while the time of maximum depth of anaesthesia was increased from 3.9 to 7.1 min.
making the model show the first-pass passage of the injected peak of propofol, differed with the dose regimen. The peak arterial concentration was unaffected by the absence of recirculation for the bolus regimen, but was significantly lower for the infusion. Without recirculation peak brain concentrations of propofol were 61% and 75% of normal for the bolus and infusion, respectively, but duration of anaesthesia was substantially shorter than normal. Removing hepatic clearance from the model caused only a minor increase in peak arterial propofol concentrations, and its effect was similar for both dose regimens. Peak brain concentrations were altered by less than 4%, but the absence of hepatic clearance decreased the rate of elution of propofol from the brain and prolonged the duration of anaesthesia. Removing the vascular mixing component of the model resulted in only minor changes in the time course of anaesthesia, but was more important for the bolus regimen.
STRUCTURAL ANALYSIS
The structural analysis is summarized in table 1. Removing propofol-induced reductions in cerebral blood flow from the model caused insignificant changes in peak arterial concentrations for either dose regimen. This suggests that the contribution of recirculated propofol from the brain to arterial concentrations is low when cerebral blood flow is a small fraction of cardiac output (as in sheep). However, the peak brain concentration was 10–12% higher, onset of anaesthesia earlier and duration of anaesthesia 15–25% less in the absence of propofolinduced reductions in cerebral blood flow. This taller but narrower peak in brain concentrations is entirely consistent with, and characteristic of, the higher average flow in this situation.10 The effect of removing recirculation, effectively
SENSITIVITY ANALYSIS
Altering cardiac output had a profound effect on both arterial and brain concentrations of propofol
Table 2 Sensitivity analysis for bolus dose. Peak arterial and brain concentrations, time of onset of anaesthesia, peak level of anaesthesia as a percent of normal and time of this peak and total duration of anaesthesia after bolus administration for various values of the variables of the model. CBF:Cerebral blood flow
Variable
Value
Cardiac output Low (2.8 litre min91) Med (5.6 litre min91) High (8.4 litre min91) CBF Low (0.02 litre min91) Med (0.04 litre min91) High (0.06 litre min91) Tissue volumes Low (50%) Med (100%) High (150%) Lung ER Low (15%) Med (30%) High (60%) Lung volume Low (1.8 litre) Med (3.6 litre) High (5.4 litre)
Peak arterial (mg litre91)
Peak brain (mg litre91)
Onset time Peak effect (min) (% normal)
Peak time Duration (min) (min)
41.90 38.14 32.77 38.90 38.14 38.09 38.37 38.14 37.99 34.25 28.19 16.08 58.75 38.14 27.88
6.00 4.07 3.24 2.61 4.07 5.14 4.83 4.07 3.70 4.40 3.59 2.02 4.92 4.07 3.51
1.05 1.15 0.75 2.1 1.15 0.85 1.15 1.15 1.20 1.15 1.35 2.9 0.85 1.15 1.45
4.5 3.9 3.8 5.1 3.9 3.3 4.4 3.9 3.6 4.2 3.9 3.4 3.5 3.9 4.3
147 100 80 64 100 126 119 100 91 108 88 50 120 100 86
18.2 12.6 9.9 10.7 12.6 11.7 13.9 12.6 11.1 16.3 11.9 1 14.2 12.6 11.3
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British Journal of Anaesthesia Table 3 Sensitivity analysis for infusion dose. Peak arterial and brain concentrations, time of onset of anaesthesia, peak level of anaesthesia as a percent of normal and time of this peak, and total duration of anaesthesia after infusion administration for various values of the variables of the model. CBF:Cerebral blood flow
Variable
Value
Peak arterial Peak brain (mg litre91) (mg litre91)
Cardiac output Low (2.8 litre min91) 15.20 Med (5.6 litre min91) 9.00 91 High (8.4 litre min ) 6.53 CBF Low (0.02 litre min91) 8.98 Med (0.04 litre min91) 9.00 High (0.06 litre min91) 8.98 Tissue volumes Low (50%) 10.55 Med (100%) 9.00 High (150%) 8.19 Lung ER Low (15%) 8.65 Med (30%) 6.69 High (60 %) 3.37 Lung volume Low (1.8 litre) 9.53 Med (3.6 litre) 9.00 High (5.4 litre) 8.47
throughout the induction period for both dose regimens (fig. 1, tables 2 and 3). A four-fold increase in cardiac output (2.8 to 8.4 litre min91) produced a decrease in peak arterial and brain concentrations (to 78% and 54% of the low value for the bolus, and to 42% and 47% for the infusion, respectively). However, the time of these peak values were within 15% of each other, with the exception of the time to peak arterial concentrations after the bolus dose (from 0.5 to 0.3 min). Altering cerebral blood flow had a minimal effect on arterial concentrations and, in comparison with cardiac output, had an opposing effect on brain concentrations of propofol. A four-fold increase in cerebral blood flow produced an increase in brain concentrations after the bolus to 196% of the low value, and this increase was also substantial (172%) for the infusion. However, higher peak brain concentrations were not associated with longer durations of anaesthesia, as the decline in brain concentrations was also more rapid. The presence or absence of recirculation was found to substantially alter the time course of both arterial and brain propofol concentrations (table 1), but the model was less sensitive to the actual magnitude of the distribution volumes of the tissue pools that affected the extent of recirculation (tables 2 and 3). Larger tissue pools decreased peak arterial concentrations significantly for the infusion regimen, but the bolus was less affected. However, duration of anaesthesia was decreased to a similar extent for both regimens (15–20%). Of more importance to the propofol concentrations achieved after both dose regimens was the magnitude of lung extraction (tables 2 and 3). While this is markedly non-linear in sheep,1 this simulation showed what could be expected if extraction was set over a range of constant values. The extent of lung extraction greatly altered the magnitude of arterial concentrations. Peak arterial values decreased from 34.3 to 16.1 mg litre91 for the bolus, and from 8.65 to 3.37 mg litre91 for the infusion as lung extraction increased. Secondary to these altered arterial
5.85 3.66 2.77 2.56 3.66 4.42 4.20 3.66 3.40 3.73 3.01 1.70 3.87 3.66 3.45
Onset time Peak effect Peak time (min) (% normal) (min)
Duration (min)
2.75 3.5 4.35 5.1 3.5 2.85 3.3 3.5 3.6 3.5 4.05
19.8 12.4 7.8 10.4 12.4 12.1 13.4 12.4 11.4 15.4 10.4
3.1 3.5 3.85
160 7.6 100 7.1 75 6.9 69 8.32 100 7.1 121 6.7 115 7.5 100 7.1 93 6.8 102 7.5 82 7.1 Not anaesthetized 106 6.8 100 7.1 94 7.4
13 12.4 12.0
concentrations, brain concentrations also decreased with increasing lung extraction. At the highest value of lung extraction, brain concentrations were sufficiently low that propofol produced no anaesthesia. However, at anaesthetic concentrations, lung extraction of propofol is relatively low1 and it is unlikely that high values of lung extraction would be encountered when it is used as an induction agent. As the role of the lung in the metabolism of propofol is important, it may be expected that distribution of propofol into the lungs may also have a substantial effect on concentrations of propofol. However, the effect was relatively small for the infusion regimen, while more pronounced for the bolus (tables 2 and 3). In particular, the distribution volume of the lung had a clear role in attenuating peak arterial concentrations for this regimen. IMPLICATIONS FOR DOSE REGIMENS
Effect of rate of administration The effects of changes in the rate of injection on dose requirements to reach a peak brain concentration of 2 mg litre91 are shown in figure 2A. The dose was minimized when propofol was administered over approximately 2 min, with peak brain concentrations reached at approximately 4.5 min. More rapid injection had little effect on the time to achieve peak concentrations in the brain (fig. 2B) but was associated with a large increase in peak arterial concentrations (fig. 2C). In general, peak brain concentrations (and therefore maximum depth of anaesthesia) lagged behind the end of the injection by approximately 3 min for these rapid injections, but this was reduced to approximately 2 min for the slower injections. The effects of changing the rate of injection of a given dose (100 mg) are shown in figure 3. Decreasing the duration of injection to less than 1 min produced little effect on peak brain concentrations, but was accompanied by large increases in arterial concentrations. For infusion with titration to an end-point, the
Induction with propofol—model analysis
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Figure 4 Titration by infusion. Simulation of the time course of brain concentrations of propofol when administered at different infusion rates, with infusions ceased when a brain concentration of 2 mg litre91 was reached.
profile of brain concentrations at different infusion rates is shown in figure 4. Note that the peak brain concentrations occurred approximately 3 min after cessation of the infusion, and that the highest infusion rate was associated with peak brain concentrations 2–3 times higher than those chosen as the end-point. The corresponding total doses administered and the time of onset of anaesthesia are shown Figure 2 Effects of duration of administration on: (A) dose required to reach a peak brain concentration of propofol of 2 mg litre91; (B) concurrent times to reach peak concentrations in arterial blood (!) and brain ("); and (C) concurrent peak arterial concentrations achieved.
Figure 3 Simulation of administration of propofol 100 mg at different rates of injection on the time course of concentrations in the brain (A) and arterial blood (B).
Figure 5 Comparison of the predictions of the model with data from humans on the influence of decreasing the infusion rate of propofol when titrating to a given anaesthetic end-point. Total administered dose (A) and time of onset of the anaesthetic endpoint (B) are shown for the model based on data in sheep (solid line) and for the data in humans of Stokes and Hutton (),9 Peacock and colleagues 1990 (")7 and the young patient group of Peacock and colleagues 1992 (!).8 As different anaesthetic end-points were used in each study, the total dose and time to end-point are expressed as a percentage of the fastest infusion rate. Data for the old patient group from the latter study could therefore not be presented in this format, as no 200 mg min91 dose was given.
510 in figure 5. Lower infusion rates were associated with a slower onset of anaesthesia, lower total doses at the point of onset of anaesthesia and lower peak brain concentrations after cessation of administration.
Discussion The principal purpose of this model was to consolidate experimental data from a chronically instrumented sheep preparation.2 3 It is important to remember that the model has therefore been validated extensively against a comprehensive in vivo data set1 comprising measurements of blood flows and propofol concentrations in several sites, rather than the more traditional single set of arterial or venous blood concentrations. This greatly increases the physiological “fidelity” of the model. MODEL ANALYSIS
Most features of the model had a significant influence on the output of the model, and their inclusion would seem reasonable on more than theoretical grounds. Interestingly, the value of some features depended on the administration regimen. In particular, the bolus regimen was influenced by the vascular mixing and lung kinetic components, highlighting the crucial role of these systems as “capacitors” or stores of drug after rapid injection.11 12 Two of the features of the model were analysed for mechanistic reasons only. Recirculation of drug is clearly unavoidable, and is an integral part of the induction process (table 1). However, it is surprising to what extent first-pass passage of the injected peak contributes to induction of anaesthesia (approximately 60% of the peak anaesthesia and 33% of its duration). Recirculation of drug is often thought to occur rapidly (seconds rather than minutes), a situation that is not consistent with drugs such as propofol with high distribution volumes in tissues. The vascular mixing component of the model is compatible with our previous experimental observations of injection site to pulmonary artery transit13 and contributes to the accurate description of kinetics after very rapid injections. The remaining features of the model have more physiological significance, and will be discussed in turn. DOSE AND INJECTION RATE
Rapid rates of injection of a dose of propofol achieved little in terms of increased depth of anaesthesia, but hastened its onset at the expense of markedly increased peak concentrations in the arterial system (fig. 2). While the significance of high initial concentrations in arterial blood vessels is not clear, arterial and venous dilatation are major contributors to hypotension during induction with propofol and may relate to direct exposure to vascular smooth muscle.14–16 It is probably this effect that produces an increased incidence of hypotension with propofol compared with thiopentone, as both agents have a similar effect on myocardial contractility.17
British Journal of Anaesthesia For a given dose of propofol, very rapid injections appear to produce a peak in arterial concentrations that is too transient to fully load the brain with propofol (fig. 2), while for very slow injections peak brain concentration can be attenuated by metabolism and redistribution of the dose before the time of the peak (fig. 3). Consequently, there appears to be an optimal duration of injection of a given dose of propofol (2 min) for maximum depth of anaesthesia. Thus the model predicts that there are two possible benefits of administration of propofol over 2 min rather than the more traditional bolus—a direct dose-sparing effect and reduced peak arterial concentrations which may have a haemodynamic advantage. When titrating to an anaesthetic end-point, it has been shown previously that slower rates of infusion of propofol reduce the total dose administered.7–9 It has been speculated that this may be because of more propofol being “in transit” between the injection site and brain at higher infusion rates,18 and this is confirmed in figure 4. For higher infusion rates, brain concentrations increased rapidly and continued to increase prodigiously after cessation of infusion, because of the greater mass of propofol stored in venous blood and lungs that had yet to reach the brain. Slower infusion rates were associated with slower increases in brain concentrations with better titration against the end-point, and minimized this “overshoot” in brain concentrations. The dose-sparing effect of the slower infusion is an illusion in the sense that although less propofol was used to reach the end-point, the total amount of anaesthesia produced (the AUC of the brain concentrations), particularly after cessation of infusion, was also significantly less. Regardless, there are considerable benefits in using the slower rate in that it reduces the profound increase in depth of anaesthesia after the desired end-point. CARDIAC OUTPUT
Cardiac output was an important factor affecting induction of anaesthesia, with increased cardiac output decreasing depth and duration of anaesthesia. While the initial effect of cardiac output would be expected on the basis of indicator dilution principles before recirculation,13 it is surprising that it persisted throughout the study. This is likely to be a result of the influence of cardiac output on tissue distribution in the model, which is reinforced by an increasing number of studies,19–22 and is a feature of other physiological models.23 24 Indeed, this growing evidence suggests that cardiac output may be a clinically significant determinant of the induction process, and a widely neglected pharmacokinetic variable. Cardiac output can be subject to large changes in vivo because of factors such as age, anxiety or co-administration of other drugs, and the model predicted that these changes would also influence induction of anaesthesia with propofol. This is confirmed to some extent by the recent work suggesting that co-administration of esmolol, a beta blocker, provided a large dose-sparing effect on propofol
Induction with propofol—model analysis requirements during induction of anaesthesia,25 a phenomenon consistent with the cardiac output lowering effect of esmolol. The contribution of this process to the dose-sparing effect observed with other co-induction agents is as yet unknown.
511 in rats, however,31 32 and provides support for such a mechanism underlying the observed extraction of the phenol, propofol, after rapid administration to sheep. CLEARANCE
CEREBRAL BLOOD FLOW
Cerebral blood flow was also a substantial determinant of the induction process, with increased cerebral blood flow increasing depth of anaesthesia, but causing relatively small changes in its duration. The fact that propofol reduces cerebral blood flow by up to 50%, thereby altering its own kinetics in the brain, was a significant feature of the induction process resulting in a lower mean cerebral blood flow and prolongation of the duration of anaesthesia by almost 3 min. There have been few experimental studies to confirm the role of cerebral blood flow in the induction process, although we have confirmed the cerebral kinetic implications of altered cerebral blood flow for propofol.26 Cerebral blood flow would be expected to change in vivo, particularly in response to changes in carbon dioxide tension in the blood (e.g. after hyperventilation and by states such as anxiety), and the model predicts that these changes would also influence induction of anaesthesia with propofol. TISSUE DISTRIBUTION VOLUMES
As for thiopentone,27 distribution into systemic tissues contributed to the decline in arterial concentrations of propofol (tables 2 and 3), although clearance by the lung was also a significant factor for lower doses of propofol in this species. As expected, smaller tissue volumes increased the rate of recirculation of propofol, but the model was relatively insensitive to changes in the magnitude of the tissue distribution volumes. These volumes are a composite term incorporating the physical volumes of these tissues, their lipid content, extent of blood and tissue protein binding, and partitioning of ions across pH gradients.28 The changes simulated were relatively large—it is not clear to what extent these changes can be accounted for in vivo by alterations in factors such as protein binding of propofol within and between individuals. For example, a four-fold increase in apparent tissue volume would require a decrease in the fraction bound in blood from 90% to 22.5%. LUNG KINETICS
While the lung kinetics of propofol were shown to be important factors in the induction process, the significant kinetic process was not distribution, but metabolism, particularly for lower doses. Both processes have been demonstrated to occur in the lungs for a variety of drugs.29 Unfortunately, current double indicator methods for studying lung kinetics after bolus administration12 30 are poor at differentiating between metabolism and distribution. Extensive, saturable conjugation of phenol by the lungs after bolus administration has been identified
In this study, clearance via the lungs was the only significant route of elimination for propofol during induction. Although hepatic clearance of propofol is sheep is large (approximately 87% extraction4), it had a relatively small effect on the induction process. By removing hepatic clearance, onset time and peak depths of anaesthesia were changed little, although duration of anaesthesia was increased by 2.5–3 min. This is consistent with reports of declines in propofol blood concentrations in anhepatic individuals.33 Thus even large variations in hepatic enzyme efficiency caused by processes such as enzyme induction or inhibition would be expected to have minimal effects on the induction process. IMPLICATIONS FOR HUMANS
Clearly, the basic mechanisms of kinetics and dynamics discussed in this article can be studied only in animals. The mechanisms described are valid for sheep, for which the variables of the model were estimated from an extensive in vivo data set. The technique of examining arterio-jugular gradients of drugs may be used to re-parameterize the model for humans,34 particularly if cerebral blood flow is measured concurrently.35 There is some evidence that the changes needed are not great with respect to initial bolus kinetics. The general size of the heart–lung system and cardiac output of a 50-kg sheep are similar to those of a 70-kg human, although the fraction of cardiac output reaching the brain is much reduced.36 However, as relative perfusion of the brain is comparable with humans and cerebral blood flow responses to drugs in sheep have been found to be similar to those in humans,2 37 the time course of the brain concentrations is also similar. The evidence for substantial lung extraction of propofol in humans is ambiguous, although it should be noted that clearance of propofol in humans often exceeds the expected liver blood flow. The data of Major and colleagues38 showed large gradients across the lung, while Gray and colleagues33 reported no gradient in anhepatic individuals. It is evident, however, that this extraction is relatively low at blood concentrations of propofol used clinically to induce anaesthesia, and so inter-species differences are likely to be relatively insignificant. Despite these considerations of species differences, it is worth noting the very close agreement between the effects of the rate of propofol administration on induction dose and time to onset of anaesthesia between the current model and data in humans by different investigators (fig. 5). This suggests that the fundamental principles of distribution after bolus administration of propofol are similar between sheep and humans, and that the model, as presented, provides a valuable tool for designing
512 further studies of induction of anaesthesia with propofol in sheep and humans. We advance the following hypotheses arising out of this work. (1) There is little benefit in injecting propofol more rapidly than over 2 min. More rapid administration does not greatly increase the rate of induction, and potentially may increase the risk of hypotension because of high arterial concentrations. (2) For titration of depth of anaesthesia with small bolus doses or infusion, a period of 2–3 min should be allowed between cessation of the dose and assessment of the level of anaesthesia in order to ensure the maximum depth of anaesthesia has been achieved. (3) The effect of many clinical scenarios on propofol dose requirements (such as anxiety, hyperventilation, extremes of body weight and coadministration of other drugs) can be interpreted in terms of their primary effect on cardiac output and cerebral blood flow. Thus selection of a dose regimen for propofol may be best determined by consideration of these two factors.
Acknowledgements This project was funded by the National Health and Medical Research Foundation of Australia, the Royal Adelaide Hospital and the Faculty of Medicine, University of Adelaide. We acknowledge the experimental contributions of our co-workers Mr Cliff Grant, Ms Elke Gray and Ms Allison Martinez.
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