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Propofol Anesthesia and Rational Opioid Selection: Determination of Optimal EC50‐EC95 Propofol‐Opioid Concentrations that Assure Adequate Anesthesia and a Rapid Return of Consciousness

Vuyk, Jaap MD, PhD; Mertens, Martijn J. MD; Olofsen, Erik MSc; Burm, Anton G. L. MSc, PhD; Bovill, James G. MD, PhD, FFARCSI

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In clinical practice, propofol is usually combined with one of the currently available synthetic opioids to provide total intravenous anesthesia. [1–5] In the absence of adjuvant agents, the blood propofol concentration that is associated with loss of consciousness in 50% of patients is 3.4 micro gram/ml, whereas concentrations in excess of 10–15 micro gram/ml are needed to suppress responses to surgical stimuli. [1–3] Opioids decrease the required propofol concentrations and affect the propofol concentration associated with return of consciousness. [2,3] Recent studies on the interaction between propofol and alfentanil indicate that with blood propofol concentrations lower than 0.8–1.2 micro gram/ml, adequate anesthesia cannot be assured, thereby defining the lower limit of the intraoperative therapeutic window of propofol. [3,5] The upper limit of the therapeutic window of propofol has not yet been defined and probably is limited by the hemodynamic side effects of propofol. In the presence of surgical stimuli, patients have received blood propofol concentrations as high as 20 micro gram/ml without experiencing serious side effects. [2] The clinically used concentration range of propofol thus is substantial. This raises the question as to the clinical relevance of the intraoperative blood propofol concentration, provided that patients remain unconscious.
Recently, distinct propofol and alfentanil concentrations have been defined that are associated with a 50% probability of no response to surgical stimuli. [3] This study indicated that the speed of recovery varies with the intraoperative propofol and alfentanil concentrations, even when these were equipotent intraoperatively. By computer simulation, the time from termination of a 180‐min infusion of propofol and alfentanil to awakening was found to be shortest (10 min) after infusion of a constant target propofol concentration of 3.5 micro gram/ml combined with a constant target alfentanil concentration of 85 ng/ml3. On the basis of this model, [3] Stanski and Shafer [4]* determined the infusion rates to maintain optimal propofol concentrations when combined with alfentanil or remifentanil. Because the pharmacokinetics of propofol and the various opioids vary, it is conceivable that the optimal intraoperative propofol concentration varies with the selected opioid and the duration of infusion.
It is difficult to fully understand the implications of the differences in pharmacokinetics between the opioids on the magnitude and time frame of their clinical effects when given as sole agents. When opioids are combined with intravenous hypnotic agents, the pharmacokinetic implications of the selection of the opioid and of the duration of infusion on the rate of recovery become even more complex. Return of consciousness then is governed not only by the decrease in the effect site propofol concentration relative to the effect site opioid concentration, but also by the pharmacodynamic interaction between these agents, intraoperatively, relative to that for return of consciousness, postoperatively.
We evaluated the implications of opioid selection and duration of infusion on the rate of recovery for combinations of propofol with alfentanil, fentanyl, sufentanil, or remifentanil.
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Materials and Methods

Table 1
Table 1
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A pharmacokinetic‐pharmacodynamic (PK/PD) computer simulation program was constructed in a spreadsheet (Quattro Pro, Borland International Inc., Scotts Valley, CA) that was able to maintain a central compartment drug concentration stable for any length of time and that, after termination of the simulated infusion, could calculate the decreasing central compartment and effect compartment concentrations of propofol and one of the opioids fentanyl, alfentanil, sufentanil, and remifentanil simultaneously (see appendix [7,8]). These calculations were made using recently published pharmacokinetic parameters sets [9–13] and effect site equilibration half‐lives [11,14,15] (Table 1).
Figure 1
Figure 1
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In addition, the PK/PD simulation program was provided with the pharmacodynamic model describing the interaction between propofol and alfentanil for suppression of responses to lower abdominal surgical stimuli in 50% of the patients (EC50) [3] and with the model describing the interaction between propofol and alfentanil for return of consciousness in 50% of patients postoperatively (Figure 1). [3]
For the combination of propofol and alfentanil, the decay in the effect site concentrations was observed after simulated infusions of 15, 60, 300, and 600 min that had been maintained constant at central compartment propofol and alfentanil concentrations equal to those required for suppression of responses to lower abdominal surgical stimuli in 50% [3] of the patients. Then, using the optimizer function, the concentration combination of propofol and alfentanil was determined that was associated with suppression of responses to lower abdominal surgical stimuli in 50% of the patients and with the shortest time to return of consciousness in 50% of patients. This concentration combination was considered the optimal intraoperative effect site EC50 propofol‐alfentanil concentration combination. In addition, the propofol‐alfentanil concentration combination was defined that is associated with suppression of responses to lower abdominal surgical stimuli in 95% of patients (EC95) and with the shortest time to return of consciousness in 50% of patients (Figure 1). This concentration combination was considered the optimal intraoperative propofol‐alfentanil combination in 95% of patients. In this way, for the combination of propofol and alfentanil, the optimal intraoperative effect site EC50 ‐EC95 therapeutic window was defined for infusions lasting 15, 60, 300, and 600 min.
In a similar manner, we defined the optimal intraoperative effect site EC50 ‐EC95 therapeutic window for the combinations of propofol‐fentanyl, propofol‐sufentanil, and propofol‐remifentanil for infusions lasting 15, 60, 300, and 600 min. We did this with the assumption, as based on the recent literature, [1–3,5,6,15–19] that the opioids alfentanil, fentanyl, sufentanil, and remifentanil all interact in a similar synergistic manner with propofol for the suppression of responses to surgical stimuli and for the return of consciousness postoperatively. The potency ratio of fentanyl‐to‐alfentanil‐to‐sufentanil‐to‐remifentanil is 1:1/70:630:1/2.3. [6,15] We thus defined the optimal intraoperative effect site EC50 ‐EC95 therapeutic window for the combinations of propofol‐alfentanil, propofol‐fentanyl, propofol‐sufentanil, and propofol‐remifentanil for infusions lasting 15, 60, 300, and 600 min.
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Results

Interaction Between Propofol and Alfentanil
Figure 2
Figure 2
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Table 2
Table 2
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Table 3
Table 3
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(Figure 2) shows the decrease (from bottom to top) in the effect site concentrations of propofol and alfentanil during the first 40 min after termination of infusions lasting 15, 60, 300, and 600 min, during which constant target propofol and alfentanil concentrations had been maintained at values associated with a 50% probability of no response to surgical stimulation as indicated by the curves in the x‐y planes (note that the curve in the x‐y plane is identical in all four diagrams in this figure). The bold line over the surface of each of the four diagrams represents the effect site propofol and alfentanil concentrations associated with a 50% probability of awakening and the corresponding times after termination of the infusions. The optimal intraoperative combination of propofol and alfentanil is defined as the combination that, while being associated with a 50% probability of no response to surgical stimuli intraoperatively, results in the fastest possible return of consciousness after termination of the infusion. This combination is represented in each diagram by the lowest point on the bold awakening line. The time to awakening is represented by the distance between this point and the nearest point on the curve in the x‐y plane (the bottom of the diagram). The optimal intraoperative effect site EC50 and EC95 propofol‐alfentanil combinations and the associated times to return of consciousness and the effect site concentrations at return of consciousness are presented in Table 2 and Table 3. For all infusion durations and for the optimal EC50 and EC95 propofol‐alfentanil combinations, the effect site propofol concentration decreases much more in the time span to return of consciousness (47–50%) compared with alfentanil (25–35%). From Figure 2, the clinical implications of the reduced steepness in the decay of the effect site alfentanil concentration relative to the effect site propofol concentration with increasing infusion duration become evident at the far ends of the diagrams displaying the simulations of high alfentanil‐low propofol or high propofol‐low alfentanil anesthesia. At these suboptimal concentration combinations, recovery is much more postponed with high effect site alfentanil concentrations of 200–373 ng/ml (it takes 45 and 50 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively) than with high effect site propofol concentrations of 11–12 micro gram/ml (it takes 32 and 39 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively).
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Interaction Between Propofol and Fentanyl
Figure 3
Figure 3
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(Figure 3) shows the PK/PD interaction diagrams for the combination of propofol and fentanyl. The optimal effect site EC50 and EC95 propofol‐fentanyl concentration combinations and the associated times to awakening and the effect site concentrations at awakening are presented in Table 2 and Table 3. For all infusion durations, the effect site propofol concentration decreases much more (50–55%) in the time span to return of consciousness compared with the effect site fentanyl concentration (13–20%). More pronounced than for the combination of propofol and alfentanil, with suboptimal concentration combinations of propofol‐fentanyl, recovery is much more postponed with high effect site fentanyl concentrations of 3–5 ng/ml (it takes 127 and 190 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively) than with high effect site propofol concentrations of 11–12 micro gram/ml (it takes 36 and 42 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively).
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Interaction between Propofol and Sufentanil
Figure 4
Figure 4
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(Figure 4) shows the PK/PD interaction diagrams for the combination of propofol and sufentanil. The optimal effect site EC50 and EC95 propofol‐sufentanil concentration combinations and the associated times to return of consciousness and the effect site concentrations at awakening are presented in Table 2 and Table 3. For all infusion durations, although less obvious than for the combination of propofol and fentanyl, the effect site propofol concentration decreases more (48–49%) in the time span to return of consciousness compared with the effect site sufentanil concentration (27–29%). Although less evident than for the propofol‐fentanyl combination, at the extremes of the x and y axes of Figure 4 (displaying the simulations of high sufentanil‐low propofol or high propofol‐low sufentanil anesthesia), recovery is more postponed with high effect site sufentanil concentrations of 0.3–0.6 ng/ml (it takes 38 and 47 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively) than with high effect site propofol concentrations 11–12 micro gram/ml (it takes 30 and 38 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively).
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Interaction between Propofol and Remifentanil
Figure 5
Figure 5
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(Figure 5) shows the PK/PD interaction diagrams for the combination of propofol and remifentanil. The optimal effect site EC50 and EC95 propofol‐remifentanil combinations and the associated times to regaining consciousness and the effect site concentrations at awakening are presented in Table 2 and Table 3. In contrast to the other opioids, for all durations of infusion, the effect site propofol concentration decreases much less (by 25%) in the time span to return of consciousness compared with the effect site remifentanil concentration (by more than 60%). Figure 5 shows why remifentanil is considered to be a “forgiving” drug. The decay in the effect site remifentanil concentration is much steeper than that of the other opioids and that of propofol, especially with infusions in excess of 300 min. In contrast to the other opioids, at the extremes of the concentration axes displaying the simulations of high remifentanil‐low propofol or high propofol‐low remifentanil anesthesia, recovery is much less postponed with high effect site remifentanil concentrations of 7–12 ng/ml (it takes 9 and 10 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively) than with high effect site propofol concentrations of 11–12 micro gram/ml (it takes 18 and 21 min for 50% of patients to awaken after infusions of 300 and 600 min, respectively). For all concentration combinations of propofol and remifentanil associated with adequate intraoperative anesthesia in 50% and 95% of patients and for all durations of infusion, recovery after propofol‐remifentanil anesthesia is much faster than when propofol is combined with one of the other opioids at equipotent concentrations.
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Discussion

Clinical Interpretation of the Simulations
Interpretation of the optimal propofol‐opioid concentrations. The aim of this study was to identify the EC50 ‐EC95 effect site propofol‐opioid concentrations that assure adequate anesthesia intraoperatively and allow patients to return to consciousness in the shortest possible time. These optimal concentrations are the result of the pharmacokinetics of propofol relative to those of the opioid and of the position of the interaction curves associated with a 50% or 95% probability of no response to surgical stimuli relative to the position of the interaction curve associated with a 50% probability of return of consciousness postoperatively. The decay in the effect site propofol concentration relative to the decay in the opioid concentration to achieve return of consciousness is affected to a great extent by the selection of the opioid and only marginally by the duration of infusion. For infusion durations of 15–600 min, the context‐sensitive half‐times [20] of the opioids decrease in the order of fentanyl > alfentanil > sufentanil much > remifentanil. The longer the context‐sensitive half‐time of the opioid relative to propofol, the more the opioid delays the return of consciousness and the more the propofol‐opioid combination shifts to higher propofol concentrations and correspondingly lower opioid concentrations. As a result, the optimal propofol concentration decreases in the order of fentanyl > alfentanil > sufentanil much > remifentanil. The duration of infusion is the second factor of influence on the decay of the two agents and thereby on the optimal propofol‐opioid concentrations. Within the time studied (15–600 min), the context‐sensitive half‐time [20] of fentanyl still increases relative to that of propofol; the half‐times of sufentanil and alfentanil run parallel to that of propofol after 30–60 min of infusion, whereas the half‐time of remifentanil decreases relative to that of propofol. Consequently, one would expect that with increasing duration of infusion, the optimal propofol concentration would increase when combined with fentanyl, would remain constant when combined with alfentanil and sufentanil, and would decrease when combined with remifentanil. However, with increasing duration of infusion, the optimal effect site propofol‐opioid concentrations change only marginally. This discrepancy is explained by the fact that for return of consciousness, the concentrations of fentanyl, alfentanil, and sufentanil do not have to decrease by 50% but only by 15–25%, whereas the concentration of remifentanil decreases by approximately 60%. Because the effect site propofol concentration decreases more rapidly than that of alfentanil, fentanyl, and sufentanil, return of consciousness is mainly caused by a reduction in the effect site propofol concentration (by 50%) and less by alfentanil, fentanyl, or sufentanil (15–25%). In contrast, after propofol‐remifentanil anesthesia, the effect site propofol concentration decreases much slower than that of remifentanil. As a result, return of consciousness after propofol‐remifentanil anesthesia is caused more by a decrease in the effect site concentration of the opioid (by 60%) than by that of propofol (by 25%). The 15% decrement curve of fentanyl and the 25% decrement curve of alfentanil and sufentanil run almost parallel to the 50% context‐sensitive half‐time curve of propofol. Further, the 60% decrement curve of remifentanil runs more or less parallel to the 25% decay curve of propofol. Consequently, infusion duration has little effect on the value of optimal concentrations. Although the concept of the context‐sensitive half‐time [20] has improved our understanding of the clinical implications of the pharmacokinetics of anesthetic agents more than the elimination half‐life, it should be kept in mind that concentrations not always need to decrease by as much as 50% to achieve return of consciousness or spontaneous breathing. Next to the relative pharmacokinetics of propofol and the opioids, the other factor determining the values of the optimal propofol‐opioid concentrations is the position of the interaction curve associated with a 50% or 95% probability of no response to surgical stimuli relative to the position of the interaction curve associated with a 50% probability of return of consciousness. These interaction curves do not lie parallel to one another (Figure 1), making it extremely difficult to predict intuitively at which propofol and opioid concentrations return of consciousness will occur.
Use of the optimal concentrations in practice. The data in Table 2 and Table 3 can be used as guidelines during target‐controlled infusion. From these data, the impression may be made that it does not really matter whether propofol is combined with alfentanil, fentanyl, or sufentanil. However, from observing Figure 2, Figure 3, Figure 4, it is clear that at suboptimal concentrations, as often will occur in clinical practice because of the interindividual variability in pharmacokinetics, recovery is more postponed after propofol‐fentanyl anesthesia than when propofol is combined with alfentanil and sufentanil. From observing Figure 5, it also is clear that the optimal propofol‐remifentanil concentrations are less important than the other propofol‐opioid combinations because even at suboptimal propofol‐remifentanil concentrations, recovery after prolonged infusion still is rapid. To avoid delayed return of consciousness, these data suggest that intraoperative responses can be best counteracted by additional propofol when combined with fentanyl, alfentanil, or sufentanil and by additional remifentanil during propofol‐remifentanil anesthesia. A note of caution should be made for the application of propofol‐remifentanil anesthesia with the effect site concentrations as described in Table 2 and Table 3. The optimal effect site propofol concentrations described in these tables are below those that assure hypnosis in the absence of remifentanil. These propofol concentrations can only be given in the presence of the described effect site remifentanil concentrations in anticipation of signs of awareness and events that may cause an interruption of the infusion of one of the agents.
Interindividual variability and the application of suboptimal propofol‐opioid concentrations. The EC50 and EC95 values displayed in Table 2 and Table 3 are population‐naive and validated for American Society of Anesthesiologists (ASA) I or II patients scheduled for abdominal surgery. A huge interindividual variability exists in the pharmacokinetics and pharmacodynamics between patients. The reported EC sub 50 and EC95 values should be used as guidelines, and adjustments should be made to factors such as age, sex, or stimulus intensity. Further, when spontaneous breathing is desired, lower than optimal effect site opioid concentrations (e.g., effect site alfentanil concentrations <50 ng/ml) in the presence of correspondingly higher than optimal effect site propofol concentrations should be given. Whereas, in contrast, in the cardiovascular‐compromised patient, the hemodynamic function may become less depressed in the presence of higher than optimal effect site alfentanil and correspondingly lower than optimal effect site propofol concentrations. In spontaneously breathing and cardiovascularly compromised patients, suboptimal propofol‐opioid concentrations are indicated intraoperatively at the expense of a prolonged recovery.
Table 4
Table 4
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Translation of EC50 and EC95 values to infusion rates. With the use of the described pharmacokinetic parameter sets and the optimal intraoperative effect site EC50 ‐EC95 concentrations, infusion schemes for manually controlled infusion can de defined that maintain the effect site propofol‐opioid concentrations within +/‐ 15% of the optimal (Table 4). Again, these infusion schemes should be used as guidelines, and adjustments should be made to the individual needs of the patient and in anticipation of factors such as age, sex, and stimulus intensity related to the type of surgery.
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Critique of Methods
Validation of the simulations. The data displayed in this manuscript are the result of computer simulations. Ideally, these data should be confirmed in clinical studies in the near future. At least five patients are needed to evaluate each data point in the diagrams of Figure 2, Figure 3, Figure 4, Figure 5. Consequently, 3,200 patients are needed to validate each diagram. Approximately 51,200 patients are then needed to validate the entire study. Hence, only fragments of the data shown here will actually be checked in a scientific manner, whereas for most data, only the simulations will be available.
Propofol interacts in a similar manner with all opioids. Is this assumption justified? According to Shafer et al., [6] alfentanil, fentanyl, and sufentanil, considering their differences in potency, all depress the respiratory drive and cerebral activity, suppress responses to intubation and surgical stimuli during opioid‐oxygen anesthesia, to a similar degree, and interact with nitrous oxide in a similar manner. The potency ratio of the four opioids for all these pharmacologic endpoints is the same, which suggests that the opioids in the presence and absence of other agents behave pharmacodynamically in a similar manner and only differ from a pharmacokinetic point of view. Similarly, it also is clear that the opioids interact in a similar manner with various inhalational anesthetic agents. [16–19] Further, the interaction between the opioids alfentanil and fentanyl with propofol has been found to be similar [2,3,5] with respect to sedative endpoints (loss of consciousness) and for analgesic endpoints (suppression of responses to skin incision and intraabdominal surgery). In summary, the interaction between the opioids and other agents is similar for combinations of opioids with nitrous oxide, [6] with volatile anesthetic agents, [16–19] and with propofol. [1–3,5] Although fentanyl and alfentanil interact in a similar manner with propofol for loss of consciousness, [1,5] the interaction between propofol and alfentanil for return of consciousness, which is equal to that for loss of consciousness, has not been described for other propofol‐opioid combinations. Based on the previously described studies, the assumption is justified that all opioids interact in a similar manner with propofol for various endpoints, just as they do combined with nitrous oxide and with volatile anesthetic agents.
Relation between EC50 and EC95 values. Increasing the optimal intraoperative effect site concentrations from the EC50 up to the EC95 values for the combination of propofol with alfentanil, fentanyl, or sufentanil is accomplished by an increase in the effect site opioid (by 30%) and the propofol concentration (by 25%), whereas for the combination with remifentanil this is accomplished solely by an increase in the effect site remifentanil concentration (up by 100%). Again, this can be explained on the basis of the pharmacokinetics of propofol relative to that of the opioids. At intraoperative effect site EC95 concentrations, return of consciousness is less postponed by relatively high propofol concentrations than by high alfentanil, fentanyl, or sufentanil concentrations because the decay in the propofol concentrations is steeper compared with these three opioids. In contrast, combined with remifentanil, return of consciousness is less postponed by high remifentanil concentrations because remifentanil concentrations decrease more rapidly than those of propofol.
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Conclusions

We have determined the optimal effect site propofol‐opioid concentration window that assures adequate anesthesia in 50% and 95% of patients for combinations of propofol with alfentanil, fentanyl, sufentanil, and remifentanil for durations of infusion lasting 15–600 min. The time to return of consciousness after propofol‐opioid anesthesia depends predominantly on the selected opioid and only marginally on the duration of infusion. Optimal effect site propofol concentrations that allow the most rapid return of consciousness are lower when propofol is combined with remifentanil than when combined with either alfentanil, fentanyl, or sufentanil. The target concentrations or the infusion rates of propofol and of the opioid with which propofol is combined should be adjusted in relation to the selected opioid and the duration of the infusion to allow an optimal rapid return of consciousness.
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Appendix

PK/PD Simulation Program
Pharmacokinetic and pharmacodynamic models were implemented in a spreadsheet (Quattro Pro, Borland International Inc.) Simulations were performed in two stages. In the first stage, a central compartment target drug concentration was maintained constant for any desired length of time (15, 60, 300, or 600 min). In stage 2, after termination of the simulated infusion, the decreasing effect compartment concentrations of propofol and one of the opioids fentanyl, alfentanil, sufentanil, or remifentanil were determined simultaneously. In a stepwise manner, the simulation program is described as follows.
Equation 1
Equation 1
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Equation 2
Equation 2
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Equation 3
Equation 3
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Equation 4
Equation 4
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1. The concentrations in the various compartments of the three‐compartment model and the effect compartment at time t were calculated using Equation 1, Equation 2, Equation 3, Equation 4.
2. With the use of recently published pharmacokinetic parameter sets [9–13] and effect site equilibration constants [11,14,15] and with Equation 1, Equation 2, Equation 3, Equation 4, the central compartment concentrations (C1) of propofol and the opioids alfentanil, fentanyl, sufentanil, and remifentanil could be maintained constant for any desired duration of infusion, and after termination of the simulated infusion, the decay in the effect compartment concentration of these agents could subsequently be studied.
Equation 5
Equation 5
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3. For the combination of propofol and alfentanil, the central compartment concentrations in equilibrium with the effect site that are associated with a 50% probability of no response to surgical stimuli are defined by the Equation 5 [3]: Equation 5 where PropEffect (I) is the mean blood propofol concentration in the ith individual, Alf sub Effect (I) is the EC50 of alfentanil in the ith individual, the Effect is no response to surgical stimuli, and EC50Prop and EC50 sub Alf are the blood propofol and plasma alfentanil concentrations in equilibrium with the effect site at which 50% of patients do not respond to surgical stimuli when these agents are given as sole agents (for alfentanil this parameter is required in the analysis but has no clinical value because alfentanil is known to be incapable of assuring anesthesia as sole agent), and epsilon is a dimensionless parameter characterizing the shape of the curve (with epsilon = 0 the result is a straight line suggesting additivity, with epsilon [not =] 0 the result is a curved line suggesting nonadditivity). EC50Alf = ‐329.971, EC50Prop = 21,794.8, and epsilon = 26.5. [3]
Equation 6
Equation 6
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4. For the combination of propofol and alfentanil, the central compartment concentrations associated with a 50% probability of return of consciousness are defined by the equation [3]: Equation 6 where the EC50 propofol is the blood propofol concentration associated with a 50% probability of return of consciousness postoperatively, CAlf is the measured plasma alfentanil concentration, and beta0, beta1, and beta2 are the coefficients describing the shape of the curves (beta0 = 17.1923, beta1 ‐3.0289, and beta2 = ‐2.6782). [3]
5. For propofol and alfentanil, multiple concentration combinations (increasing with a step size in the propofol concentration of 0.01 micro gram/ml from 1.5 micro gram/ml up to 12 micro gram/ml) associated with a 50% probability of no response to surgical stimuli (Equation 5) were maintained constant for 15, 60, 300, and 600 min, and the decay in the effect site concentrations after termination of these infusions was then studied. To shorten the blood‐effect site disequilibrium for the infusion of 15 min of propofol, fentanyl, and sufentanil, an overshoot in the central compartment concentration was allowed such that the effect site concentrations of these agents associated with a 50% probability of no response to surgical stimuli were reached within 15 min.
Equation 7
Equation 7
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6. After termination of the target‐controlled infusion of propofol and alfentanil, effect site concentrations of propofol and alfentanil decreased according to Equation 7: Equation 7 where t is the time elapsed after termination of infusion and A1, B1, D1, alpha, beta, and gamma were derived according to Hull. [21]
With the optimizer function, t was iterated until Ce,prop (t) (Equation 7) equaled the EC50 of propofol for return of consciousness given by Equation 6.
7. For each infusion duration, the concentration combination of propofol and alfentanil associated with a 50% probability of no response to surgical stimuli and the most rapid possible return of consciousness was considered the optimal intraoperative effect site propofol‐alfentanil concentration combination for that duration of infusion.
8. After determination of the propofol‐alfentanil concentrations associated with a 95% probability of no response to surgical stimuli (see below), we determined in a similar manner the optimal intraoperative effect site propofol‐alfentanil concentrations associated with a 95% probability of no response to surgical stimuli and the most rapid possible return of consciousness for infusion durations of 15, 60, 300, and 600 min. In this way, for the combination of propofol and alfentanil, the optimal intraoperative effect site EC50 ‐EC95 therapeutic window was defined for infusions lasting 15, 60, 300, and 600 min.
9. In a similar manner, we defined the optimal intraoperative effect site EC50 ‐EC95 therapeutic window for the combinations of propofol‐fentanyl, propofol‐sufentanil, and propofol‐remifentanil for infusions lasting 15, 60, 300, and 600 min. This was possible under the assumption, as based on the recent literature, [1–3,5,6,15–19] that the opioids alfentanil, fentanyl, sufentanil, and remifentanil all interact in a similar synergistic manner with propofol for the suppression of responses to surgical stimuli and for the return of consciousness postoperatively. The potency ratio being fentanyl‐to‐alfentanil‐to‐sufentanil‐to‐remifentanil = 1:1/70:630:1/2.3. [6,15] On the basis of this potency ratio, Equation 5 and Equation 6 were converted to obtain the propofol‐fentanyl, propofol‐sufentanil, and propofol‐remifentanil concentration combinations that are associated with a 50% and 95% probability of no response to surgical stimuli and a 50% probability of return of consciousness. With the use of the corresponding pharmacokinetic parameter sets [9,11–13] and Equation 1, Equation 2, Equation 3, Equation 4, and Equation 7, the optimal effect site propofol‐fentanyl, propofol‐sufentanil, and propofol‐remifentanil concentrations were defined for infusion durations of 15, 60, 300, and 600 min.
In the end, we thus defined the optimal intraoperative effect site EC50 ‐EC95 therapeutic window for the combinations of propofol‐alfentanil, propofol‐fentanyl, propofol‐sufentanil, and propofol‐remifentanil for infusions lasting 15, 60, 300, and 600 min.
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Intraoperative EC sub 95 Propofol‐Alfentanil Interaction
Figure 6
Figure 6
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The original publication on which the simulations are based only describes the intraoperative propofol‐alfentanil EC50 values for suppression of responses to surgical stimuli. [3] Because in clinical practice we are not interested in anesthetizing only 50% but rather all of our patients, we reevaluated the data of the original manuscript and determined the intraoperative propofol‐alfentanil EC95 values for suppression of responses to surgical stimuli. [3] With the individual EC50 and gamma values as displayed in Table 4 of the original manuscript [3] (characterizing the concentration‐effect curve in each individual), and by changing pi in the logistic function from 0.5 to 0.95, we calculated the plasma alfentanil concentrations in the patients associated with a 95% probability of no response to surgical stimuli. These individual EC95 values were then related to the mean measured blood propofol concentrations in the patients with the use of the interaction model as described by Equation 5 (but then with AlfEffect (I) is the EC95 of alfentanil in the ith individual, the Effect is no response to surgical stimuli, and EC95Prop and EC95Alf are the blood propofol and plasma alfentanil concentrations in equilibrium with the effect site at which 95% of patients do not respond to surgical stimuli when these agents are given as sole agents). The data were best fitted using the model exploring the possibility of a nonadditive interaction. For alfentanil EC95Opioid = ‐1000.66, EC95 sub Prop = 22000 and epsilon = 39.05. [3] Accordingly, the plasma alfentanil concentration versus blood propofol concentrations associated with no response to lower abdominal surgery in 95% of patients is characterized by the equation: AlfEffect (I) = (‐1000.66 x [22000 ‐ PropEffect (I)]/(22000 ‐ 39.05 x PropEffect (I)), R2 = 0.74 (Figure 6).
*Shafer SL. New intravenous anesthetic agents. Refresher course 226, in the 46th annual refresher course lectures and clinical updata program. American Society of Anesthesiologists.
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References

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Cited By:

This article has been cited 1 time(s).

Biomedical Engineering-Biomedizinische Technik
Design and implementation of a control system reflecting the level of analgesia during general anesthesia
Janda, M; Schubert, A; Bajorat, J; Hofmockel, R; Noldge-Schomburg, GFE; Lampe, BP; Simanski, O
Biomedical Engineering-Biomedizinische Technik, 58(1): 1-11.
10.1515/bmt-2012-0090
CrossRef
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Keywords:
Anesthetics, intravenous: alfentanil; fentanyl; sufentanil; remifentanil; propofol; Anesthetic techniques, intravenous: computer‐controlled infusion: target‐controlled infusion; computer simulation; Pharmacodynamics: alfentanil; fentanyl; sufentanil; remifentanil; propofol; drug‐drug interactions; Pharmacokinetics: alfentanil; fentanyl; sufentanil; remifentanil; propofol; drug‐drug interactions.

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