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Education  |   August 2003
Propofol Reduces Perioperative Remifentanil Requirements in a Synergistic Manner: Response Surface Modeling of Perioperative Remifentanil–Propofol Interactions
Author Affiliations & Notes
  • Martijn J. Mertens, M.D., Ph.D.
    *
  • Erik Olofsen, M.Sc.
  • Frank H. M. Engbers, M.D.
    *
  • Anton G. L. Burm, M.Sc., Ph.D.
  • James G. Bovill, M.D., Ph.D., F.F.A.R.C.S.I.
    §
  • Jaap Vuyk, M.D., Ph.D.
    *
  • *Staff Anesthesiologist, †Research Associate, ‡Professor of Anesthesiology and Head of the Anesthesia Research Laboratory, §Professor of Anesthesiology.
  • Received from the Department of Anesthesiology, Leiden University Medical Center, Leiden, The Netherlands.
Article Information
Education
Education   |   August 2003
Propofol Reduces Perioperative Remifentanil Requirements in a Synergistic Manner: Response Surface Modeling of Perioperative Remifentanil–Propofol Interactions
Anesthesiology 8 2003, Vol.99, 347-359. doi:
Anesthesiology 8 2003, Vol.99, 347-359. doi:
REMIFENTANIL is a new synthetic μ opioid that is characterized by a rapid onset of action due to a short blood–effect site equilibration half-time and a rapid offset of action due to its high clearance by nonspecific blood and tissue esterases. Propofol and remifentanil are both short-acting anesthetic agents that complement each other's pharmacodynamic profiles (i.e.  , hypnosis and analgesia). Remifentanil combined with propofol is therefore a promising combination for total intravenous anesthesia.
The pharmacodynamics of propofol and its interaction with alfentanil have been studied extensively. 1 The pharmacodynamics of remifentanil when given in combination with other intravenous agents have been less well described. In the current study, we investigated the pharmacodynamics of remifentanil and its interaction with propofol. To that end, various clinically relevant end points were studied in surgical patients when given remifentanil in combination with propofol.
Materials and Methods
Patients and Study Design
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.
Materials
A palm-top computer was provided with three-compartment pharmacokinetic data of remifentanil 2 to control 3 an infusion pump for the infusion of remifentanil. The same computer was provided with three-compartment pharmacokinetic data of propofol 4 and 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.
Study Protocol
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 [T1/2ke0] of propofol) 5 after 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 T1/2ke0of remifentanil) 6 after 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.
Blood Samples and Assays
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. 7 The 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).
Data Analysis
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, Cpropis the blood propofol concentration, Cremis the blood remifentanil concentration, C50,propand C50,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 C50,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 C50,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 C50,propand C50,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:MATHwhere 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 C50,prop, C50,rem, and γ were modeled using a log-normal variance model: where θindividualis the value in the individual, θtypical,kis the typical value of the parameter in the population in patient k, and ηindividualis 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 10 to the individual C50s of remifentanil versus  the mean measured propofol concentrations data over all patients (see 1).
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 1).
Statistical Analysis
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.
Results
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).
Table 1. Patient Characteristics
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Table 1. Patient Characteristics
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Table 2. Intraoperative Data of the Patients Available for Analysis*
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Table 2. Intraoperative Data of the Patients Available for Analysis*
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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.
Table 3. Additive and Nonadditive Interaction Models
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Table 3. Additive and Nonadditive Interaction Models
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Fig. 1. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to laryngoscopy. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 1. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to laryngoscopy. The curve (top 
	) was obtained by response surface modeling, according to equation 2, of the response (open squares 
	)–no response (closed squares 
	) data versus 
	the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom 
	) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 1. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to laryngoscopy. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
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Fig. 2. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to intubation. The curve (top  ) was obtained by response surface modeling, according to equation 3, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 3, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 2. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to intubation. The curve (top 
	) was obtained by response surface modeling, according to equation 3, of the response (open squares 
	)–no response (closed squares 
	) data versus 
	the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 3, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom 
	) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 2. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to intubation. The curve (top  ) was obtained by response surface modeling, according to equation 3, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 3, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
×
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 C50,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 C50,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).
Fig. 3. Measured blood propofol concentration versus  time in the individual patients of group A (▴= target propofol concentration 2 μg/ml), group B (○= target propofol concentration 4 μg/ml), and group C (▪= target propofol concentration 6 μg/ml).
Fig. 3. Measured blood propofol concentration versus 
	time in the individual patients of group A (▴= target propofol concentration 2 μg/ml), group B (○= target propofol concentration 4 μg/ml), and group C (▪= target propofol concentration 6 μg/ml).
Fig. 3. Measured blood propofol concentration versus  time in the individual patients of group A (▴= target propofol concentration 2 μg/ml), group B (○= target propofol concentration 4 μg/ml), and group C (▪= target propofol concentration 6 μg/ml).
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Fig. 4. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 2 μg/ml. The mean measured blood propofol concentrations were 2.1, 2.3, 2.8, 2.0, 1.9, 2.2, 1.9, and 2.9 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 4. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 2 μg/ml. The mean measured blood propofol concentrations were 2.1, 2.3, 2.8, 2.0, 1.9, 2.2, 1.9, and 2.9 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus 
	the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots 
	= blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 4. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 2 μg/ml. The mean measured blood propofol concentrations were 2.1, 2.3, 2.8, 2.0, 1.9, 2.2, 1.9, and 2.9 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
×
Fig. 5. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 4 μg/ml. The mean measured blood propofol concentrations were 4.1, 3.7, 3.9, 4.6, 6.2, 4.5, 3.5, 5.1, 4.7, and 4.4 μg/ml in patients 1–10, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 5. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 4 μg/ml. The mean measured blood propofol concentrations were 4.1, 3.7, 3.9, 4.6, 6.2, 4.5, 3.5, 5.1, 4.7, and 4.4 μg/ml in patients 1–10, respectively (table 5). The curves were determined by logistic regression of response–no response data versus 
	the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots 
	= blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 5. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 4 μg/ml. The mean measured blood propofol concentrations were 4.1, 3.7, 3.9, 4.6, 6.2, 4.5, 3.5, 5.1, 4.7, and 4.4 μg/ml in patients 1–10, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
×
Fig. 6. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 6 μg/ml. The mean measured blood propofol concentrations were 5.8, 8.1, 8.6, 9.1, 4.6, 8.5, 8.7, and 9.1 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 6. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 6 μg/ml. The mean measured blood propofol concentrations were 5.8, 8.1, 8.6, 9.1, 4.6, 8.5, 8.7, and 9.1 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus 
	the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots 
	= blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 6. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 6 μg/ml. The mean measured blood propofol concentrations were 5.8, 8.1, 8.6, 9.1, 4.6, 8.5, 8.7, and 9.1 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
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Table 4. Blood Propofol and Blood Remifentanil Concentrations Associated with a 50% Probability of No Response to Intraabdominal Surgical Stimuli in the Individual Patients
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Table 4. Blood Propofol and Blood Remifentanil Concentrations Associated with a 50% Probability of No Response to Intraabdominal Surgical Stimuli in the Individual Patients
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Fig. 7. Blood remifentanil concentrations versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli. The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere Crem= the blood remifentanil concentration (ng/ml) associated with a 50% probability of no response to intraabdominal surgical stimuli; Cprop= the mean blood propofol concentration (μg/ml) calculated in each patient. Dots  = C50s of remifentanil at corresponding mean blood propofol concentrations for suppression of responses to intraabdominal surgical stimuli as determined in the individual patients by logistic regression (Figs. 4–6).
Fig. 7. Blood remifentanil concentrations versus 
	blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli. The curve represents a mechanistic function (see Appendix) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere Crem= the blood remifentanil concentration (ng/ml) associated with a 50% probability of no response to intraabdominal surgical stimuli; Cprop= the mean blood propofol concentration (μg/ml) calculated in each patient. Dots 
	= C50s of remifentanil at corresponding mean blood propofol concentrations for suppression of responses to intraabdominal surgical stimuli as determined in the individual patients by logistic regression (Figs. 4–6).
Fig. 7. Blood remifentanil concentrations versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli. The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere Crem= the blood remifentanil concentration (ng/ml) associated with a 50% probability of no response to intraabdominal surgical stimuli; Cprop= the mean blood propofol concentration (μg/ml) calculated in each patient. Dots  = C50s of remifentanil at corresponding mean blood propofol concentrations for suppression of responses to intraabdominal surgical stimuli as determined in the individual patients by logistic regression (Figs. 4–6).
×
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.  , 9 the 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 C50,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.  11 proved also adequate. The additive model with the lowest AIC is a model in which γpropand γremare identical. Introduction of intraindividual variability did not result in a further reduction in the AIC. Because the addition of the interaction term β2,U50(see 1) 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.  11 was also judged synergistic. The parameters (± SE) describing the response surface are E0= 0, Emax= 1, C50,prop= 3.40 ± 0.75 μg/ml, C50,rem= 8.91 ± 2.35 ng/ml, γprop= 4.29 ± 0.98, γrem= 4.29 ± 0.98, and β2,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.
Fig. 8. Concentration–effect relation of the combination of propofol and remifentanil for the probability of the return to consciousness. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the awake–unconscious data versus  the corresponding measured blood propofol concentrations and the corresponding measured blood remifentanil concentrations. Closed squares  = concentrations of propofol and remifentanil at skin closure, at which time the individual patients were still unconscious; open squares  = concentrations of propofol and remifentanil when the patients regained consciousness. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of the return to consciousness, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of return to consciousness are shown.
Fig. 8. Concentration–effect relation of the combination of propofol and remifentanil for the probability of the return to consciousness. The curve (top 
	) was obtained by response surface modeling, according to equation 2, of the awake–unconscious data versus 
	the corresponding measured blood propofol concentrations and the corresponding measured blood remifentanil concentrations. Closed squares 
	= concentrations of propofol and remifentanil at skin closure, at which time the individual patients were still unconscious; open squares 
	= concentrations of propofol and remifentanil when the patients regained consciousness. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of the return to consciousness, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom 
	) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of return to consciousness are shown.
Fig. 8. Concentration–effect relation of the combination of propofol and remifentanil for the probability of the return to consciousness. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the awake–unconscious data versus  the corresponding measured blood propofol concentrations and the corresponding measured blood remifentanil concentrations. Closed squares  = concentrations of propofol and remifentanil at skin closure, at which time the individual patients were still unconscious; open squares  = concentrations of propofol and remifentanil when the patients regained consciousness. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of the return to consciousness, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of return to consciousness are shown.
×
Discussion
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.
Critique on Methods
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). 13,14 To 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.  11 described 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.  11 Because the basic concept in response surface modeling according to Minto et al.  11 is 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 Emaxof 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.  11 is 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.  9 as 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.
Laryngoscopy and Intubation
In keeping with the observations of Vuyk et al.  1 on 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 C50,remand ε estimated with the model described by Bol et al.  9 were very large, whereas for intubation, C50,rem, C50,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.  1 have 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.  , 15 who determined the C50s of propofol for laryngoscopy and intubation at 9.8 and 17.4 μg/ml, respectively.
Intraoperative Interaction
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.  , 1 demonstrated 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 16–21 or intravenous 1,13 anesthetic agents to provide anesthesia (the so-called ceiling effect). Accordingly, when the model described by equation 8(see 1) was fitted to the data, the C50,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.
Return of Consciousness
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. 7 However, the C50,propfor return of consciousness determined in our study is lower than the C50,propfor return of consciousness of approximately 4 μg/ml determined in a similar study after total intravenous anesthesia with propofol and alfentanil. 1 It 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.
Remifentanil Potency in Relation to Alfentanil
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. 22 The 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). 6 For 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.  1 on 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 1). 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.  1 to remifentanil equivalents (C50,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 C50,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 C50,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).
Fig. 9. Remifentanil equivalents versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli, from this study (filled circles  ) and from the study by Vuyk et al.  1 (open circles  ). The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere C50,rem,eqis the remifentanil equivalent associated with a 50% probability of no response and Cpropis the mean blood propofol concentration calculated in each patient. The Calf,50s from the study by Vuyk et al.  1 were transformed to C50,rem,eq, by estimation of the potency of remifentanil relative to that of alfentanil for suppression of responses to lower abdominal surgery as an additional parameter (C50,rem,eq= C50,alf/31.1).
Fig. 9. Remifentanil equivalents versus 
	blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli, from this study (filled circles 
	) and from the study by Vuyk et al.  1(open circles 
	). The curve represents a mechanistic function (see Appendix) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere C50,rem,eqis the remifentanil equivalent associated with a 50% probability of no response and Cpropis the mean blood propofol concentration calculated in each patient. The Calf,50s from the study by Vuyk et al.  1were transformed to C50,rem,eq, by estimation of the potency of remifentanil relative to that of alfentanil for suppression of responses to lower abdominal surgery as an additional parameter (C50,rem,eq= C50,alf/31.1).
Fig. 9. Remifentanil equivalents versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli, from this study (filled circles  ) and from the study by Vuyk et al.  1 (open circles  ). The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere C50,rem,eqis the remifentanil equivalent associated with a 50% probability of no response and Cpropis the mean blood propofol concentration calculated in each patient. The Calf,50s from the study by Vuyk et al.  1 were transformed to C50,rem,eq, by estimation of the potency of remifentanil relative to that of alfentanil for suppression of responses to lower abdominal surgery as an additional parameter (C50,rem,eq= C50,alf/31.1).
×
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 
Computer Simulations
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 Ceis 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 3 from the pharmacokinetic parameter sets for propofol 4 and remifentanil 2; ke0is the blood–effect site equilibration rate constant of propofol 5 or remifentanil 6; and Ce(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 Ce,prop(t) and Ce,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.
Fig. 10. Computer simulation of the effect site propofol 4,5 and remifentanil 2,6 concentrations versus  time during the first 40 min after termination of target-controlled infusions of propofol and remifentanil that had been maintained for 60 (top  ) or 180 min (bottom  ), respectively, at constant target blood concentrations combinations associated with a 50% probability of no response to surgical stimuli. These concentration combinations are represented by the line on the bottom of the figure in the x–y plane. The decrease in the concentrations following various intraoperative propofol-remifentanil combinations is represented by the curves running upward from the x–y plane. The curved lines  in parallel to the x–y plane represent consecutive 1-min time intervals. The bold line  represents the propofol–remifentanil–time relation at which the probability of regaining consciousness is 50%.
Fig. 10. Computer simulation of the effect site propofol 4,5and remifentanil 2,6concentrations versus 
	time during the first 40 min after termination of target-controlled infusions of propofol and remifentanil that had been maintained for 60 (top 
	) or 180 min (bottom 
	), respectively, at constant target blood concentrations combinations associated with a 50% probability of no response to surgical stimuli. These concentration combinations are represented by the line on the bottom of the figure in the x–y plane. The decrease in the concentrations following various intraoperative propofol-remifentanil combinations is represented by the curves running upward from the x–y plane. The curved lines 
	in parallel to the x–y plane represent consecutive 1-min time intervals. The bold line 
	represents the propofol–remifentanil–time relation at which the probability of regaining consciousness is 50%.
Fig. 10. Computer simulation of the effect site propofol 4,5 and remifentanil 2,6 concentrations versus  time during the first 40 min after termination of target-controlled infusions of propofol and remifentanil that had been maintained for 60 (top  ) or 180 min (bottom  ), respectively, at constant target blood concentrations combinations associated with a 50% probability of no response to surgical stimuli. These concentration combinations are represented by the line on the bottom of the figure in the x–y plane. The decrease in the concentrations following various intraoperative propofol-remifentanil combinations is represented by the curves running upward from the x–y plane. The curved lines  in parallel to the x–y plane represent consecutive 1-min time intervals. The bold line  represents the propofol–remifentanil–time relation at which the probability of regaining consciousness is 50%.
×
Similar computer simulations were performed using the pharmacodynamic interaction model for propofol and alfentanil described by Vuyk et al.  1 To allow comparison of the two studies, the results of the study by Vuyk et al.  1 were “translated” to remifentanil equivalents, as described elsewhere, 25 using the alfentanil/remifentanil potency ratio as described above. The results of these simulations are displayed in figure 11.
Fig. 11. Computer simulation of the time to return of consciousness after termination of target controlled infusions of propofol 4,5 and remifentanil 2,6 that had been maintained for 180 min at constant blood concentrations associated with a 50% probability of no response to surgical stimuli. The x-axis shows these blood concentration combinations associated with a 50% probability of no response to surgical stimuli. Bold line  = results of these simulations based on the models described in this study; dotted line  = results of the simulations based on the models described by Vuyk et al.  1 for the combination of alfentanil and propofol, whereby alfentanil concentrations were converted to remifentanil equivalents, assuming a potency ratio of 31.1. The difference between the two curves probably results from the fact that in the remifentanil study morphine for postoperative pain relief was given before the end of surgery.
Fig. 11. Computer simulation of the time to return of consciousness after termination of target controlled infusions of propofol 4,5and remifentanil 2,6that had been maintained for 180 min at constant blood concentrations associated with a 50% probability of no response to surgical stimuli. The x-axis shows these blood concentration combinations associated with a 50% probability of no response to surgical stimuli. Bold line 
	= results of these simulations based on the models described in this study; dotted line 
	= results of the simulations based on the models described by Vuyk et al.  1for the combination of alfentanil and propofol, whereby alfentanil concentrations were converted to remifentanil equivalents, assuming a potency ratio of 31.1. The difference between the two curves probably results from the fact that in the remifentanil study morphine for postoperative pain relief was given before the end of surgery.
Fig. 11. Computer simulation of the time to return of consciousness after termination of target controlled infusions of propofol 4,5 and remifentanil 2,6 that had been maintained for 180 min at constant blood concentrations associated with a 50% probability of no response to surgical stimuli. The x-axis shows these blood concentration combinations associated with a 50% probability of no response to surgical stimuli. Bold line  = results of these simulations based on the models described in this study; dotted line  = results of the simulations based on the models described by Vuyk et al.  1 for the combination of alfentanil and propofol, whereby alfentanil concentrations were converted to remifentanil equivalents, assuming a potency ratio of 31.1. The difference between the two curves probably results from the fact that in the remifentanil study morphine for postoperative pain relief was given before the end of surgery.
×
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.  25 Infusion 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 
Table 5. Propofol and Remifentanil Infusion Schemes
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Table 5. Propofol and Remifentanil Infusion Schemes
×
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.
Conclusions
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.
Appendix
Data Analysis of the Interaction during the Intraabdominal Part of Surgery
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:MATHwhere π is the probability of no response, Cremis 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; Cremis the C50of remifentanil (ng/ml) for suppression of responses to intraabdominal surgical stimuli as determined in each patient by logistic regression; C50,propand C50,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 Cremas a dependent variable and O as an independent variable. When C50,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 Cremas a dependent variable and O as an independent variable.
Data Analysis of Interaction for Return of Consciousness
In the data analysis of the interaction for return of consciousness, according to Minto et al.  , 11 the 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; Emaxcorresponds with unconsciousness at the end of anesthesia just before termination of the target controlled infusions of propofol and remifentanil; Uprop= Cprop/C50,propand Urem/C50,rem; Cpropis the blood propofol and Cremis the blood remifentanil concentration; C50,propis the blood propofol and C50,propis the blood remifentanil concentration that results in 50% of maximal drug effect;MATHγ(θ) is the steepness of the concentration–response relation at ratio θ described by:γ(θ) =γprop+ (γrem−γprop−β2,γ) θ+β2,γθ2, where γpropand γremare the γ when propofol and remifentanil are given as sole agents, and β2,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 −β2,U50θ2,U50θ2, where β2,U50is a model parameter estimated from the data; and Emax(θ) is the maximum possible drug effect at ratio θ described by: Emax(θ) = Emax,prop+ (Emax,rem− Emax,prop)θ.
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Fig. 1. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to laryngoscopy. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 1. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to laryngoscopy. The curve (top 
	) was obtained by response surface modeling, according to equation 2, of the response (open squares 
	)–no response (closed squares 
	) data versus 
	the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom 
	) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 1. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to laryngoscopy. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
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Fig. 2. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to intubation. The curve (top  ) was obtained by response surface modeling, according to equation 3, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 3, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 2. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to intubation. The curve (top 
	) was obtained by response surface modeling, according to equation 3, of the response (open squares 
	)–no response (closed squares 
	) data versus 
	the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 3, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom 
	) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
Fig. 2. Concentration–effect relation of the combination of propofol and remifentanil for suppression of responses to intubation. The curve (top  ) was obtained by response surface modeling, according to equation 3, of the response (open squares  )–no response (closed squares  ) data versus  the corresponding measured blood propofol concentrations and blood remifentanil concentrations. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of no response, calculated using equation 3, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of no response are shown.
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Fig. 3. Measured blood propofol concentration versus  time in the individual patients of group A (▴= target propofol concentration 2 μg/ml), group B (○= target propofol concentration 4 μg/ml), and group C (▪= target propofol concentration 6 μg/ml).
Fig. 3. Measured blood propofol concentration versus 
	time in the individual patients of group A (▴= target propofol concentration 2 μg/ml), group B (○= target propofol concentration 4 μg/ml), and group C (▪= target propofol concentration 6 μg/ml).
Fig. 3. Measured blood propofol concentration versus  time in the individual patients of group A (▴= target propofol concentration 2 μg/ml), group B (○= target propofol concentration 4 μg/ml), and group C (▪= target propofol concentration 6 μg/ml).
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Fig. 4. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 2 μg/ml. The mean measured blood propofol concentrations were 2.1, 2.3, 2.8, 2.0, 1.9, 2.2, 1.9, and 2.9 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 4. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 2 μg/ml. The mean measured blood propofol concentrations were 2.1, 2.3, 2.8, 2.0, 1.9, 2.2, 1.9, and 2.9 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus 
	the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots 
	= blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 4. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 2 μg/ml. The mean measured blood propofol concentrations were 2.1, 2.3, 2.8, 2.0, 1.9, 2.2, 1.9, and 2.9 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
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Fig. 5. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 4 μg/ml. The mean measured blood propofol concentrations were 4.1, 3.7, 3.9, 4.6, 6.2, 4.5, 3.5, 5.1, 4.7, and 4.4 μg/ml in patients 1–10, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 5. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 4 μg/ml. The mean measured blood propofol concentrations were 4.1, 3.7, 3.9, 4.6, 6.2, 4.5, 3.5, 5.1, 4.7, and 4.4 μg/ml in patients 1–10, respectively (table 5). The curves were determined by logistic regression of response–no response data versus 
	the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots 
	= blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 5. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 4 μg/ml. The mean measured blood propofol concentrations were 4.1, 3.7, 3.9, 4.6, 6.2, 4.5, 3.5, 5.1, 4.7, and 4.4 μg/ml in patients 1–10, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
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Fig. 6. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 6 μg/ml. The mean measured blood propofol concentrations were 5.8, 8.1, 8.6, 9.1, 4.6, 8.5, 8.7, and 9.1 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 6. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 6 μg/ml. The mean measured blood propofol concentrations were 5.8, 8.1, 8.6, 9.1, 4.6, 8.5, 8.7, and 9.1 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus 
	the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots 
	= blood remifentanil concentrations associated with a 50% probability of no response.
Fig. 6. Remifentanil concentration–effect relations in the individual patients for the intraabdominal part of surgery when remifentanil was given as a supplement to a target propofol concentration of 6 μg/ml. The mean measured blood propofol concentrations were 5.8, 8.1, 8.6, 9.1, 4.6, 8.5, 8.7, and 9.1 μg/ml in patients 1–8, respectively (table 5). The curves were determined by logistic regression of response–no response data versus  the corresponding measured blood remifentanil concentrations of remifentanil, as shown beneath the curves. Dots  = blood remifentanil concentrations associated with a 50% probability of no response.
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Fig. 7. Blood remifentanil concentrations versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli. The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere Crem= the blood remifentanil concentration (ng/ml) associated with a 50% probability of no response to intraabdominal surgical stimuli; Cprop= the mean blood propofol concentration (μg/ml) calculated in each patient. Dots  = C50s of remifentanil at corresponding mean blood propofol concentrations for suppression of responses to intraabdominal surgical stimuli as determined in the individual patients by logistic regression (Figs. 4–6).
Fig. 7. Blood remifentanil concentrations versus 
	blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli. The curve represents a mechanistic function (see Appendix) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere Crem= the blood remifentanil concentration (ng/ml) associated with a 50% probability of no response to intraabdominal surgical stimuli; Cprop= the mean blood propofol concentration (μg/ml) calculated in each patient. Dots 
	= C50s of remifentanil at corresponding mean blood propofol concentrations for suppression of responses to intraabdominal surgical stimuli as determined in the individual patients by logistic regression (Figs. 4–6).
Fig. 7. Blood remifentanil concentrations versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli. The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere Crem= the blood remifentanil concentration (ng/ml) associated with a 50% probability of no response to intraabdominal surgical stimuli; Cprop= the mean blood propofol concentration (μg/ml) calculated in each patient. Dots  = C50s of remifentanil at corresponding mean blood propofol concentrations for suppression of responses to intraabdominal surgical stimuli as determined in the individual patients by logistic regression (Figs. 4–6).
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Fig. 8. Concentration–effect relation of the combination of propofol and remifentanil for the probability of the return to consciousness. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the awake–unconscious data versus  the corresponding measured blood propofol concentrations and the corresponding measured blood remifentanil concentrations. Closed squares  = concentrations of propofol and remifentanil at skin closure, at which time the individual patients were still unconscious; open squares  = concentrations of propofol and remifentanil when the patients regained consciousness. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of the return to consciousness, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of return to consciousness are shown.
Fig. 8. Concentration–effect relation of the combination of propofol and remifentanil for the probability of the return to consciousness. The curve (top 
	) was obtained by response surface modeling, according to equation 2, of the awake–unconscious data versus 
	the corresponding measured blood propofol concentrations and the corresponding measured blood remifentanil concentrations. Closed squares 
	= concentrations of propofol and remifentanil at skin closure, at which time the individual patients were still unconscious; open squares 
	= concentrations of propofol and remifentanil when the patients regained consciousness. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of the return to consciousness, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom 
	) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of return to consciousness are shown.
Fig. 8. Concentration–effect relation of the combination of propofol and remifentanil for the probability of the return to consciousness. The curve (top  ) was obtained by response surface modeling, according to equation 2, of the awake–unconscious data versus  the corresponding measured blood propofol concentrations and the corresponding measured blood remifentanil concentrations. Closed squares  = concentrations of propofol and remifentanil at skin closure, at which time the individual patients were still unconscious; open squares  = concentrations of propofol and remifentanil when the patients regained consciousness. The displayed curve represents remifentanil and propofol concentrations associated with a 50% probability of the return to consciousness, calculated using equation 2, and the fitted values of the coefficients from table 3, describing the synergistic interaction model. In the concentration–response surface (bottom  ) for the combination of propofol and remifentanil, the isoboles for 25, 50, and 75% probability of return to consciousness are shown.
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Fig. 9. Remifentanil equivalents versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli, from this study (filled circles  ) and from the study by Vuyk et al.  1 (open circles  ). The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere C50,rem,eqis the remifentanil equivalent associated with a 50% probability of no response and Cpropis the mean blood propofol concentration calculated in each patient. The Calf,50s from the study by Vuyk et al.  1 were transformed to C50,rem,eq, by estimation of the potency of remifentanil relative to that of alfentanil for suppression of responses to lower abdominal surgery as an additional parameter (C50,rem,eq= C50,alf/31.1).
Fig. 9. Remifentanil equivalents versus 
	blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli, from this study (filled circles 
	) and from the study by Vuyk et al.  1(open circles 
	). The curve represents a mechanistic function (see Appendix) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere C50,rem,eqis the remifentanil equivalent associated with a 50% probability of no response and Cpropis the mean blood propofol concentration calculated in each patient. The Calf,50s from the study by Vuyk et al.  1were transformed to C50,rem,eq, by estimation of the potency of remifentanil relative to that of alfentanil for suppression of responses to lower abdominal surgery as an additional parameter (C50,rem,eq= C50,alf/31.1).
Fig. 9. Remifentanil equivalents versus  blood propofol concentrations associated with a 50% probability of no response to intraabdominal surgical stimuli, from this study (filled circles  ) and from the study by Vuyk et al.  1 (open circles  ). The curve represents a mechanistic function (see 1) fitted to the data by unweighted least-squares nonlinear analysis described by the equation:MATHwhere C50,rem,eqis the remifentanil equivalent associated with a 50% probability of no response and Cpropis the mean blood propofol concentration calculated in each patient. The Calf,50s from the study by Vuyk et al.  1 were transformed to C50,rem,eq, by estimation of the potency of remifentanil relative to that of alfentanil for suppression of responses to lower abdominal surgery as an additional parameter (C50,rem,eq= C50,alf/31.1).
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Fig. 10. Computer simulation of the effect site propofol 4,5 and remifentanil 2,6 concentrations versus  time during the first 40 min after termination of target-controlled infusions of propofol and remifentanil that had been maintained for 60 (top  ) or 180 min (bottom  ), respectively, at constant target blood concentrations combinations associated with a 50% probability of no response to surgical stimuli. These concentration combinations are represented by the line on the bottom of the figure in the x–y plane. The decrease in the concentrations following various intraoperative propofol-remifentanil combinations is represented by the curves running upward from the x–y plane. The curved lines  in parallel to the x–y plane represent consecutive 1-min time intervals. The bold line  represents the propofol–remifentanil–time relation at which the probability of regaining consciousness is 50%.
Fig. 10. Computer simulation of the effect site propofol 4,5and remifentanil 2,6concentrations versus 
	time during the first 40 min after termination of target-controlled infusions of propofol and remifentanil that had been maintained for 60 (top 
	) or 180 min (bottom 
	), respectively, at constant target blood concentrations combinations associated with a 50% probability of no response to surgical stimuli. These concentration combinations are represented by the line on the bottom of the figure in the x–y plane. The decrease in the concentrations following various intraoperative propofol-remifentanil combinations is represented by the curves running upward from the x–y plane. The curved lines 
	in parallel to the x–y plane represent consecutive 1-min time intervals. The bold line 
	represents the propofol–remifentanil–time relation at which the probability of regaining consciousness is 50%.
Fig. 10. Computer simulation of the effect site propofol 4,5 and remifentanil 2,6 concentrations versus  time during the first 40 min after termination of target-controlled infusions of propofol and remifentanil that had been maintained for 60 (top  ) or 180 min (bottom  ), respectively, at constant target blood concentrations combinations associated with a 50% probability of no response to surgical stimuli. These concentration combinations are represented by the line on the bottom of the figure in the x–y plane. The decrease in the concentrations following various intraoperative propofol-remifentanil combinations is represented by the curves running upward from the x–y plane. The curved lines  in parallel to the x–y plane represent consecutive 1-min time intervals. The bold line  represents the propofol–remifentanil–time relation at which the probability of regaining consciousness is 50%.
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Fig. 11. Computer simulation of the time to return of consciousness after termination of target controlled infusions of propofol 4,5 and remifentanil 2,6 that had been maintained for 180 min at constant blood concentrations associated with a 50% probability of no response to surgical stimuli. The x-axis shows these blood concentration combinations associated with a 50% probability of no response to surgical stimuli. Bold line  = results of these simulations based on the models described in this study; dotted line  = results of the simulations based on the models described by Vuyk et al.  1 for the combination of alfentanil and propofol, whereby alfentanil concentrations were converted to remifentanil equivalents, assuming a potency ratio of 31.1. The difference between the two curves probably results from the fact that in the remifentanil study morphine for postoperative pain relief was given before the end of surgery.
Fig. 11. Computer simulation of the time to return of consciousness after termination of target controlled infusions of propofol 4,5and remifentanil 2,6that had been maintained for 180 min at constant blood concentrations associated with a 50% probability of no response to surgical stimuli. The x-axis shows these blood concentration combinations associated with a 50% probability of no response to surgical stimuli. Bold line 
	= results of these simulations based on the models described in this study; dotted line 
	= results of the simulations based on the models described by Vuyk et al.  1for the combination of alfentanil and propofol, whereby alfentanil concentrations were converted to remifentanil equivalents, assuming a potency ratio of 31.1. The difference between the two curves probably results from the fact that in the remifentanil study morphine for postoperative pain relief was given before the end of surgery.
Fig. 11. Computer simulation of the time to return of consciousness after termination of target controlled infusions of propofol 4,5 and remifentanil 2,6 that had been maintained for 180 min at constant blood concentrations associated with a 50% probability of no response to surgical stimuli. The x-axis shows these blood concentration combinations associated with a 50% probability of no response to surgical stimuli. Bold line  = results of these simulations based on the models described in this study; dotted line  = results of the simulations based on the models described by Vuyk et al.  1 for the combination of alfentanil and propofol, whereby alfentanil concentrations were converted to remifentanil equivalents, assuming a potency ratio of 31.1. The difference between the two curves probably results from the fact that in the remifentanil study morphine for postoperative pain relief was given before the end of surgery.
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Table 1. Patient Characteristics
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Table 1. Patient Characteristics
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Table 2. Intraoperative Data of the Patients Available for Analysis*
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Table 2. Intraoperative Data of the Patients Available for Analysis*
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Table 3. Additive and Nonadditive Interaction Models
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Table 3. Additive and Nonadditive Interaction Models
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Table 4. Blood Propofol and Blood Remifentanil Concentrations Associated with a 50% Probability of No Response to Intraabdominal Surgical Stimuli in the Individual Patients
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Table 4. Blood Propofol and Blood Remifentanil Concentrations Associated with a 50% Probability of No Response to Intraabdominal Surgical Stimuli in the Individual Patients
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Table 5. Propofol and Remifentanil Infusion Schemes
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Table 5. Propofol and Remifentanil Infusion Schemes
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