Propofol Reduces Perioperative Remifentanil Requirements in a Synergistic Manner: Response Surface Modeling of Perioperative Remifentanil–Propofol Interactions

With local Medical Ethics Committee (Leiden, The Netherlands) approval and informed consent, 30 female patients with American Society of Anesthesiologists physical status I or II, aged 20–65 yr, who were scheduled to undergo lower abdominal surgery were asked to participate in the study. Patients with known cardiac, pulmonary, or renal disease and patients receiving medication or consuming more than 20 g alcohol daily were excluded from the study. The patients were randomly assigned to one of three study groups to receive, in a double-blind manner, a target propofol concentration of 2 μg/ml (group A), 4 μg/ml (group B), or 6 μg/ml (group C) in combination with remifentanil. The patients did not receive premedication.

An anesthesiologist who took no further part in the study prepared the solutions of propofol. For patients in group A, 40 ml glucose (5%) was added to 20 ml propofol (10 mg/ml) to obtain 60 ml propofol (3.3 mg/ml). For patients in group B, 20 ml glucose (5%) was added to 40 ml propofol to obtain 60 ml propofol (6.7 mg/ml). For patients in group C, the propofol solution was not diluted. The investigators were blinded to the propofol solution being used.

A palm-top computer was provided with three-compartment pharmacokinetic data of remifentanil 2to control 3an infusion pump for the infusion of remifentanil. The same computer was provided with three-compartment pharmacokinetic data of propofol 4and used to control another infusion pump for the infusion of propofol.

In the operating room, an intravenous cannula was inserted into a large forearm vein for infusion of remifentanil and propofol, and another cannula was inserted into a radial artery for continuous measurement of arterial blood pressure and collection of blood samples. The electrocardiogram, heart rate, arterial blood pressure, peripheral oxygen saturation, end-tidal carbon dioxide partial pressure, Bispectral Index (version A1000; Aspect Medical Systems Inc., Natick, MA), and the spectral edge frequency were monitored continuously throughout the study. Neuromuscular transmission was monitored by percutaneous stimulation of the ulnar nerve using the train-of-four method.

After breathing 100% oxygen for 3 min, 0.1 mg/kg atracurium was given intravenously, and anesthesia was induced by computer-controlled infusion of propofol with a target concentration set at 6 μg/ml. Depending on the propofol solution in the syringe, the actual target concentrations were 2, 4, or 6 μg/ml for the patients in groups A, B, and C, respectively. The target propofol concentration was maintained constant throughout the surgical procedure until the peritoneum was closed.

Five minutes after the start of the propofol infusion, the remifentanil infusion was started with a target concentration of 2 ng/ml. Ten minutes (i.e. , four to five times the blood-effect site equilibration half-time [T^1/2k^e0] of propofol) 5after the start of the propofol infusion, and provided that the patients had lost consciousness, 0.4 mg/kg atracurium was given intravenously. If a patient had not lost consciousness by 10 min after the start of the propofol infusion, the target remifentanil concentration was increased by 2–10 ng/ml to induce unconsciousness before the administration of atracurium.

Subsequently, laryngoscopy was performed. To optimally determine the remifentanil concentration–effect relation for this stimulus, a second and third laryngoscopy were performed with different target remifentanil concentrations, and the presence or absence of a response was recorded. If a patient did not respond to the first or second laryngoscopy, the target remifentanil concentration was decreased by 1 ng/ml. When patients did respond to the first or second laryngoscopy, the target remifentanil concentration was increased by 2–10 ng/ml, depending on the intensity of the response, for the following laryngoscopy. Five minutes (i.e. , six to seven times the T^1/2k^e0of remifentanil) 6after a new target remifentanil concentration was reached, the following laryngoscopy was performed. The aim was to achieve at least one response and at least one nonresponse to laryngoscopy in each patient. A response to laryngoscopy was defined using the same criteria as used to define inadequate anesthesia.

Inadequate anesthesia was defined by the following criteria 1:

1. An increase in systolic blood pressure by more than 15 mmHg above the preoperative mean systolic blood pressure, defined as the mean of three systolic blood pressures measured since admission

2. A heart rate exceeding 90 beats/min in the absence of hypovolemia

3. Other autonomic signs such as sweating or flushing

4. Somatic responses such as movements or swallowing

During the study, three persons observed each patient continuously for evidence of inadequate anesthesia: a resident in anesthesia, an anesthesiologist, and a trained medical student. If inadequate anesthesia was detected, it was only accepted if verified by all three observers. To facilitate identification of somatic responses, atracurium was given at the minimal dose necessary for surgery (train-of-four levels 1–3.

After the second or third laryngoscopy, the trachea of the patient was intubated, and the lungs were ventilated with 30% oxygen in air to an end-tidal carbon dioxide partial pressure of 29–34 mmHg.

The target propofol concentration was maintained constant until the peritoneum was closed and finally discontinued after skin closure. The remifentanil administration was changed in response to the presence or absence of signs of inadequate anesthesia. When signs of inadequate anesthesia developed, the target remifentanil concentration was increased by 1–10 ng/ml. When no signs of inadequate anesthesia were observed, the target remifentanil concentration was decreased by 1–10 ng/ml. If, at induction of anesthesia, patients had not lost consciousness in the absence of remifentanil, the target remifentanil concentration was not decreased below the remifentanil effect site concentration, as displayed on the target controlled infusion device at the time of loss of consciousness. After a new target concentration was reached (as judged from the computer display) this was maintained for 6 min.

Thirty minutes before skin closure, 0.2 mg/kg intravenous morphine was administered to provide postoperative pain relief.

After skin closure, neuromuscular blockade was antagonized by neostigmine, 1–2 mg intravenously, and atropine, 0.5–1 mg intravenously, and the remifentanil infusion was discontinued. The patients were tested every 2 min by verbal commands to evaluate return of consciousness. This was defined as a positive response to a verbal command. Once adequate spontaneous ventilation was established (i.e. , if the end-tidal carbon dioxide partial pressure was less than 46 mmHg, tidal volume was more than 7 ml/kg, and respiratory rate was more than 10 breaths/min), the trachea was extubated.

After the trachea had been extubated, the patient was transported to the recovery room. Twenty-four hours postoperatively, the patients were interviewed to evaluate possible side effects and any recall of intraoperative events.

Arterial blood samples for determination of propofol and remifentanil concentrations in whole blood were collected at laryngoscopy, intubation, skin incision, the opening of the peritoneum, awakening, and 6 min after a predicted target remifentanil concentration was reached during the intraoperative period. The total amount of blood sampled in each patient did not exceed 150 ml. Samples for the determination of blood propofol concentrations were transferred into test tubes containing potassium oxalate and stored at 4°C. Propofol concentrations in blood were measured at the Anesthesia Research laboratory of the Leiden University Medical Center by reverse-phase high-performance liquid chromatography. 7The limit of quantitation was 11.7 ng/ml. The coefficient of variation of this method was 3% or less in the concentration range encountered in this study. Propofol assays were performed within 12 weeks.

Samples for the determination of blood remifentanil concentrations were collected into tubes containing sodium heparin and immediately transferred to tubes containing 50% citric acid (to inactivate esterases) before freezing at −20°C. The assay method is based on tandem mass spectrometry detection with a quantitation limit of 0.1 ng/ml and an interassay coefficient of variation of less than 10% for concentrations greater than 0.1 ng/ml. The remifentanil analyses were performed in a commercial laboratory (Analytico, Breda, The Netherlands).

For each patient, one to three data points were available for laryngoscopy, intubation, skin incision, opening of the peritoneum, and return to consciousness. The interaction between propofol and remifentanil at these events was therefore determined over the group, for each event separately, using the response surface model described by Bol et al.  9: where π is the probability of no response, C^propis the blood propofol concentration, C^remis the blood remifentanil concentration, C^50,propand C^50,remare the steady state concentrations of propofol and remifentanil corresponding to a 50% probability of no response when either drug is administered alone, and γ and ε are the coefficients describing the shape of the response surface. The interaction parameter ε is equivalent to the Berenbaum interaction index 10(with ε= 0, equation 1describes an additive model; with ε≠ 0, a nonadditive model is described).

For some end points, the obtained estimate of C⁵⁰was several orders of magnitude larger than the clinical concentration range and the concentrations encountered in this study. In these cases, estimates of ε were also extremely large, but the ratio of ε and C⁵⁰remained meaningful. Therefore, when estimates of C^50,remand ε were two or more orders of magnitude larger than the concentrations encountered in this study, the model was rewritten as: where ε″ is the ratio of ε and C^50,rem. In case the C⁵⁰s of both drugs were much higher than the actually achieved concentrations, the model was further simplified to: where ε′ is the ratio of ε and the product of C^50,propand C^50,rem.

The model parameters were estimated with the computer program NONMEM (version V, level 1.1; The NONMEM Project Group, University of California, San Francisco, CA), by minimizing the −2 × log likelihood (−2LL) for all observations:

where N is the number of adequate–nonadequate anesthesia or unconscious–awake data points, Rⁱis the observed response of the ith individual, being either 1 (i.e. , no response to any of the perioperative stimuli or no response to a verbal command after termination of the propofol and remifentanil target-controlled infusion) or 0 (i.e. , a response to any of the perioperative stimuli or a response to a verbal command after termination of the propofol and remifentanil target-controlled infusion), and P  is the probability of the response for each concentration combination. The interindividual variabilities of the model parameters C^50,prop, C^50,rem, and γ were modeled using a log-normal variance model: where θ^individualis the value in the individual, θ^typical,kis the typical value of the parameter in the population in patient k, and η^individualis a normally distributed random variable with a mean of zero and a variance of ω², which is estimated by NONMEM. The interindividual variability of ε was modeled using a normal variance model. The response surface models describe the probability of a dichotomous outcome (a response or no response during one of the above events) as a function of the measured blood propofol and remifentanil concentrations.

In contrast, for the intraabdominal part of surgery, multiple data were available per patient. The concentration–effect relation of the combination of remifentanil and propofol for suppression of responses to the intraabdominal part of surgery was therefore determined for each patient separately by logistic regression. The influence of the mean measured intraoperative blood propofol concentration on the C⁵⁰of remifentanil during the intraabdominal part of surgery was then determined by fitting a mechanistic model 10to the individual C⁵⁰s of remifentanil versus  the mean measured propofol concentrations data over all patients (see  Appendix).

Note that we initially explored the concentration–response surface of the combination of propofol and remifentanil for laryngoscopy, intubation, skin incision, opening of the peritoneum, suppression of responses to surgical stimuli, and probability of return to consciousness according to the recently described response surface modeling technique by Minto et al.  11(see Discussion). The response surface was obtained by modeling of adequate–nonadequate anesthesia data or the unconscious–awake data versus  the corresponding measured blood propofol and measured blood remifentanil concentration combinations (see  Appendix).

Patient characteristics and the mean measured blood propofol and blood remifentanil concentrations, Bispectral Index, spectral edge frequency, systolic and diastolic blood pressures, and heart rate as observed in the three study groups during the intraoperative period (between opening of the peritoneum and skin closure) were compared between groups using the Kruskal-Wallis test with a post hoc  Mann–Whitney U test for pairwise group comparison, if appropriate. To determine the nature of the interaction for suppression of responses to laryngoscopy, intubation, skin incision, the opening of the peritoneum, suppression of responses to intraabdominal surgical stimuli, and the probability of return to consciousness, the Akaike information-theoretic criterion 12(AIC =−2LL + 2p; where p is the number of parameters in the model) was used to assess the significance of incorporating an interaction term in the response surface model. The model with the lowest AIC was considered optimal.

Data are presented as mean ± SD unless stated otherwise. P < 0.05 was considered the minimum level of statistical significance except for multiple comparison tests when P < 0.02 was considered significant.

All but one of the patients were evaluable. One patient in group C had to be excluded from the study due to improper handling of the blood samples. Age, weight, height, and duration of anesthesia of the remaining patients (n = 29) did not differ among the three study groups (table 1). The mean measured blood propofol and blood remifentanil concentrations, Bispectral Index, spectral edge frequency, systolic and diastolic blood pressures, and heart rate during the intraoperative period (between opening of the peritoneum and skin closure) are shown in table 2. As intended, the mean measured blood propofol concentrations differed significantly between the three groups. Required mean measured plasma remifentanil concentrations were lower in groups B and C compared to group A (P < 0.02).

One out of the 10 patients in group A, 6 out of the 10 patients in group B, and all but 1 of the patients in group C had lost consciousness 5 min after the start of the propofol infusion. In the 14 patients who remained conscious with the initial target remifentanil concentration, unconsciousness was induced when the target remifentanil concentration was increased to 4–15 ng/ml.

The C⁵⁰of remifentanil for laryngoscopy and intubation decreased with increasing propofol concentrations. For laryngoscopy and intubation, the data were best characterized by a synergistic model (table 3). The addition of the interaction term in the response surface model resulted in a reduction in the AIC (from 62.41 to 59.51 for laryngoscopy and from 39.21 to 34.95 for intubation). Introduction of intraindividual variability did not result in a further reduction in the AIC. As blood propofol concentrations increased from 2 to 7.3 μg/ml, the C⁵⁰of remifentanil decreased from 3.8 ng/ml to 0 ng/ml for laryngoscopy and from 4.7 ng/ml to 1.2 ng/ml for intubation (figs. 1 and 2). For skin incision and the opening of the peritoneum, the configuration of the data did not allow modeling.

In 3 of 29 patients, the data set for intraoperative stimuli did not allow modeling. The concentration–effect relation of remifentanil for intraabdominal stimuli could therefore not be determined in these 3 patients. In 17 patients, no overlap existed between response and nonresponse data. Because the lowest measured plasma remifentanil concentration at which no response occurred and the highest blood remifentanil concentration at which a response was noted differed only marginally in these patients, the C⁵⁰of remifentanil was determined as the midrange between the lowest measured blood remifentanil concentration at which no response occurred and the highest blood remifentanil concentration at which a response was noted. If in any patient no responses occurred, even when the actual measured blood remifentanil concentration was below the detection limit, the C⁵⁰of remifentanil was set to 0 ng/ml. The measured blood propofol concentration remained stable throughout the surgical procedure in most patients (fig. 3). The remifentanil concentration–effect relations for the intraabdominal part of the surgical procedure in the individual patients of the three groups are shown in figures 4–6. Results are presented in table 4. The C⁵⁰of remifentanil versus  mean blood propofol concentration relation for the intraabdominal part of surgery as determined over all patients is presented in figure 7. The C⁵⁰of remifentanil for suppression of responses to intraabdominal surgical stimuli decreased with increasing propofol concentrations. The data were best characterized by a synergistic model. The addition of the interaction term in the model resulted in a reduction in the AIC from 82.07 to 79.96. Because C^50,remand ε of the nonadditive model were very large, the model described in equation 9was fitted to the data. The parameters (± SE) describing the curve are C^50,prop= 9.02 ± 2.47 μg/ml and ε′= 0.557 ± 0.306. Introduction of intraindividual variability did not result in a further reduction in the AIC. As mean blood propofol concentrations increased from 2 to 9 μg/ml, the C⁵⁰of remifentanil for intraabdominal stimuli decreased from 6.3 to 0 ng/ml (fig. 7).

Remifentanil significantly affected the blood propofol concentration at which the patients regained consciousness. According to the response surface modeling technique described by Bol et al. , 9the interaction between propofol and remifentanil was judged to be synergistic for the probability of unconsciousness (table 3). Introduction of intraindividual variability did not result in a further reduction in the AIC. With blood remifentanil concentration increasing from 0 to 10 ng/ml, the C^50,propfor return of to consciousness decreased from 3.5 μg/ml to 0.4 μg/ml (fig. 8). For this unimodal end point, the response surface modeling technique described by Minto et al.  11proved also adequate. The additive model with the lowest AIC is a model in which γ^propand γ^remare identical. Introduction of intraindividual variability did not result in a further reduction in the AIC. Because the addition of the interaction term β^2,U50(see  Appendix) in the model resulted in a reduction in the AIC from 48.152 to 46.409, the interaction between propofol and remifentanil for the probability of unconsciousness based on the response surface modeling technique described by Minto et al.  11was also judged synergistic. The parameters (± SE) describing the response surface are E⁰= 0, E^max= 1, C^50,prop= 3.40 ± 0.75 μg/ml, C^50,rem= 8.91 ± 2.35 ng/ml, γ^prop= 4.29 ± 0.98, γ^rem= 4.29 ± 0.98, and β^2,U50= 1.69 ± 0.42. The C⁵⁰of propofol decreased from 3.4 μg/ml to 0.5 μg/ml as blood remifentanil concentrations increased from 0 to 8 ng/ml. The model described in equation 2was selected as the final model for the return to consciousness because its AIC was lower than that for the model described by Minto et al.  11(42.538 vs.  46.409). All patients breathed adequately on awakening. None of the patients reported awareness for any intraoperative event.

The aims of this study were to determine the influence of propofol on remifentanil requirements for suppression of responses to perioperative stimuli and return of consciousness in female patients and to determine the nature of these interactions. The study demonstrated that propofol reduces remifentanil requirements for suppression of responses to laryngoscopy, intubation, and intraabdominal surgical stimulation in a synergistic manner in female patients. In addition, the study demonstrated that remifentanil decreases propofol concentrations associated with the return of consciousness in a synergistic manner.

Theoretically, a pharmacodynamic interaction between two agents is best defined if data are obtained by studying the effect of the agents separately and in combination. In our study, however, no data were obtained for remifentanil as a sole agent because this would have resulted in awareness. In this study, we intentionally chose a target of 2 μg/ml as the lowest target propofol concentration. Note that in the absence of premedication, a target propofol concentration of 2 μg/ml is below that at which patients may be unconscious. With these low blood propofol concentrations, remifentanil is needed to supplement the hypnotic effect of propofol. In retrospect, this target propofol concentration may have been conservative. In previously described interaction studies between propofol and opioids, the synergistic nature of the interaction became predominantly apparent at subhypnotic propofol concentrations (< 2–3 μg/ml). 13,14To further minimize the risk of awareness, the intraoperative target remifentanil concentration was never decreased below the predicted remifentanil effect site concentration at which patients had lost consciousness in the presence of propofol, if, at induction of anesthesia, patients had not lost consciousness in the absence of remifentanil. This may have led to the relatively large number of nonresponses compared to the number of responses to surgical stimuli during the intraabdominal part of surgery.

Recently, Minto et al.  11described a novel method for drug interaction analysis by means of response surface modeling. We explored the interaction between propofol and remifentanil for suppression of responses to various anesthetic end points (i.e. , laryngoscopy, intubation, skin incision, opening of the peritoneum, and intraabdominal surgical stimuli) using this new analytical instrument but found that the response–no response data could not be analyzed in this way. However, the anesthetic state is a bimodal phenomenon, consisting of both a hypnotic and an analgesic component, and may therefore not be considered as a single measure of drug effect. Because the studied perioperative pharmacodynamic end points of no response to nociceptive stimuli cannot be achieved by remifentanil alone in the absence of propofol, remifentanil has the pharmacodynamic characteristics of a partial agonist for these end points in the response surface modeling technique described by Minto et al.  11Because the basic concept in response surface modeling according to Minto et al.  11is that any given ratio of two drugs behaves as a “new drug” with its own sigmoidal concentration–response relation, this results in a model predicting that a maximal effect achieved by propofol alone (i.e. , a 100% probability of no response) is reduced by the addition of remifentanil (i.e. , the E^maxof the “new drug” is reduced). Based on our exploration of the data regarding the anesthetic state by response surface modeling, we conclude that although response surface modeling by Minto et al.  11is suitable for the analysis of unimodal end points such as loss of consciousness or the return to consciousness, it may not be suitable for the analysis of multimodal end points, such as adequacy of anesthesia. Pharmacodynamic end points of no response to nociceptive stimuli were therefore analyzed using the response surface model by Bol et al.  9as described in equation 1. The technique by Bol et al.  allows for a response surface modeling technique that respects the two agents as separate drugs and thereby allows for the modeling of bimodal effects.

In keeping with the observations of Vuyk et al.  1on the interactions between propofol and alfentanil, the interactions between propofol and remifentanil for suppression of responses to laryngoscopy and intubation were best described by a synergistic interaction model. For laryngoscopy, the C^50,remand ε estimated with the model described by Bol et al.  9were very large, whereas for intubation, C^50,rem, C^50,prop, and ε were several orders of magnitude larger than the concentrations encountered in this study. Therefore, these effects were modeled with the modified models (equations 2 and 3, respectively). Similarly, Vuyk et al.  1have demonstrated that propofol decreases alfentanil requirements for suppression of responses to laryngoscopy and intubation in a synergistic manner.

Remifentanil concentrations required to suppress responses to intubation are higher at any given propofol concentration compared to those required to suppress responses to laryngoscopy. This indicates that tracheal intubation is a stronger stimulus than laryngoscopy. The C⁵⁰of propofol for laryngoscopy in the absence of remifentanil, determined as the intercept of the interaction model with the x-axis (fig. 1), is 7.3 μg/ml. Because the interaction model for suppression of responses to intubation did not cross the x-axis in the concentration range studied (fig. 2), the C⁵⁰of propofol alone for intubation could not be determined. These findings are in accordance with the findings of Kazama et al. , 15who determined the C⁵⁰s of propofol for laryngoscopy and intubation at 9.8 and 17.4 μg/ml, respectively.

Intraoperatively, propofol reduced remifentanil requirements for suppression of responses to lower abdominal surgical stimuli in a synergistic manner. In a similar study, Vuyk et al. , 1demonstrated that propofol significantly reduced alfentanil requirements for suppression of responses to lower abdominal surgical stimuli in a synergistic manner. In previous interaction studies, opioids have been not to be able to replace completely inhalational 16–21or intravenous 1,13anesthetic agents to provide anesthesia (the so-called ceiling effect). Accordingly, when the model described by equation 8(see  Appendix) was fitted to the data, the C^50,remfor suppression of responses to lower abdominal surgical stimuli was six orders of magnitude higher than the maximum blood remifentanil concentration encountered in this study. Therefore, this effect was modeled with the modified model described in equation 9.

The propofol C⁵⁰for return of consciousness of 3.5 μg/ml corresponds well with the reported propofol concentrations at which consciousness was lost in 50% of the patients of 3.4 μg/ml. 7However, the C^50,propfor return of consciousness determined in our study is lower than the C^50,propfor return of consciousness of approximately 4 μg/ml determined in a similar study after total intravenous anesthesia with propofol and alfentanil. 1It is conceivable that 0.2 mg/kg morphine administered 30 min before the end of surgery to provide adequate initial postoperative pain control after remifentanil anesthesia may have lowered the concentration at which patients regained consciousness and delayed the return of consciousness in our study group.

The synthetic opioids fentanyl, alfentanil, sufentanil, and remifentanil can be considered a homogeneous group from a pharmacodynamic point of view because they act at similar receptor systems and have similar effects and similar side effects. 22The relative potencies of the synthetic opioids for several clinical end points were found to equal their relative potencies determined on the basis of their effect on the electroencephalogram 22(the potency ratio for alfentanil to remifentanil being 1:30). 6For this reason, the nature and the degree of the pharmacodynamic interaction between propofol and alfentanil probably will be similar to that for propofol and remifentanil.

The methodology, patient population, and type of surgery in this study were exactly the same as those in the study by Vuyk et al.  1on the pharmacodynamic interaction between propofol and alfentanil. Therefore, we could analyze the pooled intraoperative data from the two studies. The influence of the mean measured intraoperative blood propofol concentration on the C⁵⁰of an opioid during the intraabdominal part of surgery was determined using equation 8 or 9(see  Appendix). The potency of remifentanil relative to that of alfentanil for suppression of responses to lower abdominal surgery was estimated as an additional parameter, transforming the C⁵⁰s of alfentanil from the study by Vuyk et al.  1to remifentanil equivalents (C^50,alf/potency ratio).

Both the possibility of an additive and the possibility of a nonadditive interaction were explored. The AIC was lower for the nonadditive model than for the additive model (241.355 vs.  246.807, respectively). Because C^50,remand ε of the nonadditive model estimated with equation 8were very large, the model described in equation 9was fitted to the data. The results are presented in figure 9. The parameters (± SE) describing the response surface are C^50,prop= 12.1 ± 2.28 μg/ml, ε′= 0.830 ± 0.304, and potency ratio 31.1 ± 7.53. Introduction of intraindividual variability did not result in a further reduction in the AIC. The interaction between propofol and remifentanil was, therefore, judged to be synergistic. As the mean blood propofol concentrations increased from 2.0 to 9.0 μg/ml, the C⁵⁰of remifentanil (or remifentanil equivalents) for intraabdominal stimuli decreased from 6.1 ng/ml to 0.4 ng/ml (fig. 9).

Based on this analysis, remifentanil was 31 times more potent than alfentanil for suppression of responses to lower abdominal surgery in combination with propofol. This corresponds well with the potency ratio of alfentanil to remifentanil based on their effect on the electroencephalogram. Remifentanil was 41 times more potent than alfentanil for suppression of responses to lower abdominal surgery when given as a supplement to nitrous oxide anesthesia. 23,24 

To explore the time to return of consciousness after anesthesia with propofol and remifentanil C⁵⁰concentration combinations, we simulated, using an Excel (Excel 7.0; Microsoft Corp., Redmond, WA) spreadsheet, the decay in propofol and remifentanil effect site concentrations after termination of a target-controlled infusion of 60 and 180 min with equianesthetic C⁵⁰propofol–remifentanil combinations. Effect site concentrations of propofol and remifentanil were calculated using equation 6: where C^eis the decreasing effect site propofol or remifentanil concentration; t is the time elapsed after termination of infusion; A, B, D, α, β, and γ were derived according to Hull 3from the pharmacokinetic parameter sets for propofol 4and remifentanil 2; k^e0is the blood–effect site equilibration rate constant of propofol 5or remifentanil 6; and C^e(0) is the effect site propofol or remifentanil concentration when the infusion was terminated at t = 0. The time to the return of consciousness was calculated by substituting C^e,prop(t) and C^e,rem(t) along with the estimates of ε and γ as obtained in this study in equation 2. Using the Excel optimizer function, t was iterated until the probability of unconsciousness given by equation 2equaled 50%. The results of these simulations are displayed graphically in figure 10.

Similar computer simulations were performed using the pharmacodynamic interaction model for propofol and alfentanil described by Vuyk et al.  1To allow comparison of the two studies, the results of the study by Vuyk et al.  1were “translated” to remifentanil equivalents, as described elsewhere, 25using the alfentanil/remifentanil potency ratio as described above. The results of these simulations are displayed in figure 11.

The computer simulations showed that the decay of the remifentanil concentration after termination of the infusion is so much more rapid than that of propofol that the propofol–remifentanil concentration combination that provides both adequate anesthesia and the most rapid return of consciousness is the one with the lowest possible propofol concentration. The time from termination of a 180-min infusion of propofol and remifentanil to awakening was found to be shortest (6.5 min) after infusion of a constant target propofol concentration of 1.5 μg/ml combined with a constant target remifentanil concentration of 9.0 ng/ml. This “optimal” propofol–remifentanil concentration is not affected by the duration of anesthesia and corresponds well with that predicted on the basis of the interaction models determined by Vuyk et al.  25Infusion duration also has very little influence on the time to awakening at this “optimal” concentration combination. However, with “suboptimal” propofol–remifentanil concentration combinations (high propofol–low remifentanil), return of consciousness is rapidly postponed with increasing infusion duration. The time to return of consciousness in our study group was longer for all “suboptimal” propofol–remifentanil concentration combinations (fig. 11). As mentioned before, 0.2 mg/kg morphine administered intravenously 30 min before the end of surgery for postoperative pain control may have delayed the return of consciousness in our study group.

Based on the results of this study and our clinical experience, we recommend a minimum effect site propofol concentration of 2.0 μg/ml in combination with an effect site remifentanil concentration of 6.3 ng/ml in female patients with American Society of Anesthesiologists physical status I or II in the absence of premedication and significant muscle relaxation. These “optimal” effect site concentrations can be used as guidelines during target-controlled infusion. The actual target concentrations during anesthesia will have to be titrated to the desired effect. Dosing guidelines to rapidly achieve these adequate effect site concentrations without target controlled infusion are given in table 5. 5,6,26 

A “low” target propofol concentration of 2.0 μg/ml in combination with a relatively higher remifentanil concentration of 6.3 ng/ml should only be used in the absence of significant muscle relaxation. When maximum muscle relaxation is required for surgery, we advise use of a target propofol concentration of 3 μg/ml or greater to reduce the risk of awareness. To avoid unrecognized awareness, premedication will further increase the margin of safety. None of the patients in our study had recall of any perioperative event. Patients in group A (the lowest target propofol concentration of 2.0 μg/ml) were hemodynamically stable, and the mean intraoperative Bispectral Index value was 59 (table 2). Because the level of intraoperative neuromuscular blockade was maintained at a train-of-four level of 1–3, patients were able to move in response to inadequate anesthesia at all times.

In conclusion, this study shows that propofol reduces remifentanil requirements for suppression of responses to laryngoscopy, intubation, and intraabdominal surgical stimulation in a synergistic manner. In addition, remifentanil decreases propofol concentrations associated with the return of consciousness in a synergistic manner. Computer simulations revealed that the optimal blood propofol and blood remifentanil concentrations with respect to satisfactory intraoperative anesthetic conditions and speed of recovery are 2.0 μg/ml and 6.3 ng/ml, respectively.

Multiple response and nonresponse data were available for each patient for the intraabdominal part of surgery. Therefore, the concentration–effect relation of remifentanil for suppression of responses to intraabdominal surgical stimuli could be determined in each patient individually. This was performed by means of logistic regression. The logistic function is described by equation 5:

where π is the probability of no response, C^remis the blood remifentanil concentration, and β⁰are the coefficients describing the shape of the curve. The remifentanil concentrations associated with a 50% probability of no response to lower abdominal surgery (C⁵⁰), determined in each patient by logistic regression, were related to the corresponding mean intraoperative propofol concentrations with a mechanistic model over all patients by nonlinear regression analysis. The mechanistic function is described by equation 810: where O is the mean intraoperative blood propofol concentration (μg/ml) calculated in each patient; C^remis the C⁵⁰of remifentanil (ng/ml) for suppression of responses to intraabdominal surgical stimuli as determined in each patient by logistic regression; C^50,propand C^50,remare the blood propofol (μg/ml) and remifentanil (ng/ml) concentrations that are associated with a 50% probability of no response if each drug would be administered as a single agent; and ε is a dimensionless parameter characterizing the shape of the curve (with ε= 0, the result is a straight line suggesting additivity; with ε≠ 0, the result is a curved line suggesting nonadditivity). Both the possibilities of an additive and nonadditive interaction were explored. The model was fitted to the data with C^remas a dependent variable and O as an independent variable. When C^50,remwas more than three orders of magnitude higher than the maximum concentration encountered in this study, equation 8was rewritten as: The model was fitted to the data with C^remas a dependent variable and O as an independent variable.

In the data analysis of the interaction for return of consciousness, according to Minto et al. , 11the response surface was obtained by modeling of the unconscious–awake data versus  the corresponding measured blood propofol concentrations and the corresponding measured blood remifentanil concentrations. The response surface is described by equation 1011: where E is the combined drug effect; E⁰corresponds with the return of consciousness; E^maxcorresponds with unconsciousness at the end of anesthesia just before termination of the target controlled infusions of propofol and remifentanil; U^prop= C^prop/C^50,propand U^rem/C^50,rem; C^propis the blood propofol and C^remis the blood remifentanil concentration; C^50,propis the blood propofol and C^50,propis the blood remifentanil concentration that results in 50% of maximal drug effect;

γ(θ) is the steepness of the concentration–response relation at ratio θ described by:γ(θ) =γ^prop+ (γ^rem−γ^prop−β^2,γ) θ+β^2,γθ2, where γ^propand γ^remare the γ when propofol and remifentanil are given as sole agents, and β^2,γis a model parameter estimated from the data; C⁵⁰(θ) is the number of units (U) associated with 50% of maximum effect at ratio θ described by: U⁵⁰(θ) = 1 −β^2,U50θ+β^2,U50θ2, where β^2,U50is a model parameter estimated from the data; and E^max(θ) is the maximum possible drug effect at ratio θ described by: E^max(θ) = E^max,prop+ (E^max,rem− E^max,prop)θ.