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Anesthesiology 2003; 99:34759 2003 American Society of Anesthesiologists, Inc. Lippincott Williams & Wilkins, Inc.

Propofol Reduces Perioperative RemifentanilRequirements in a Synergistic Manner

Response Surface Modeling of Perioperative RemifentanilPropofol Interactions

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.*

Background: Remifentanil is often combined with propofol

for induction and maintenance of total intravenous anesthesia.

The authors studied the effect of propofol on remifentanil re-

quirements for suppression of responses to clinically relevant

stimuli and evaluated this in relation to previously published

data on propofol and alfentanil.

Methods:With ethics committee approval and informed con-

sent, 30 unpremedicated female patients with American Society

of Anesthesiologists physical status class I or II, aged 18 65 yr,

scheduled to undergo lower abdominal surgery, were randomly

assigned to receive a target-controlled infusion of propofol with

constant target concentrations of 2, 4, or 6 g/ml. The target

concentration of remifentanil was changed in response to signsof inadequate anesthesia. Arterial blood samples for the deter-

mination of remifentanil and propofol concentrations were

collected after blood effect site equilibration. The presence or

absence of responses to various perioperative stimuli were re-

lated to the propofol and remifentanil concentrations by re-

sponse surface modeling or logistic regression, followed by

regression analysis. Both additive and nonadditive interaction

models were explored.

Results:With blood propofol concentrations increasing from

2 to 7.3 g/ml, the C50of remifentanil decreased from 3.8 ng/ml

to 0 ng/ml for laryngoscopy, from 4.4 ng/ml to 1.2 ng/ml for

intubation, and from 6.3 ng/ml to 0.4 ng/ml for intraabdominal

surgery. With blood remifentanil concentrations increasing

from 0 to 7 ng/ml, the C50 of propofol for the return to con-

sciousness decreased from 3.5 g/ml to 0.6 g/ml.

Conclusions:Propofol reduces remifentanil requirements for

suppression of responses to laryngoscopy, intubation, and in-

traabdominal surgical stimulation in a synergistic manner. In

addition, remifentanil decreases propofol concentrations asso-

ciated with the return of consciousness in a synergistic manner.

REMIFENTANIL is a new synthetic opioid that is char-

acterized by a rapid onset of action due to a short

bloodeffect site equilibration half-time and a rapid off-

set 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 others pharmacodynamic profiles (i.e., hypnosisand 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 phar-macodynamics of remifentanil when given in combina-

tion with other intravenous agents have been less well

described. In the current study, we investigated the

pharmacodynamics of remifentanil and its interactionwith 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 femalepatients with American Society of Anesthesiologists

physical status I or II, aged 2065 yr, who were sched-

uled to undergo lower abdominal surgery were asked to

participate in the study. Patients with known cardiac,pulmonary, or renal disease and patients receiving med-

ication or consuming more than 20 g alcohol daily wereexcluded from the study. The patients were randomly

assigned to one of three study groups to receive, in adouble-blind manner, a target propofol concentration of

2 g/ml (group A), 4 g/ml (group B), or 6 g/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 propo-

fol (10 mg/ml) to obtain 60 ml propofol (3.3 mg/ml). Forpatients 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 propofolsolution being used.

Materials

A palm-top computer was provided with three-com-

partment pharmacokinetic data of remifentanil2 to con-trol3 an infusion pump for the infusion of remifentanil.

The same computer was provided with three-compart-

ment pharmacokinetic data of propofol4 and used to

control another infusion pump for the infusion ofpropofol.

* Staff Anesthesiologist, Research Associate, Professor of Anesthesiologyand Head of the Anesthesia Research Laboratory, Professor of Anesthesiology.

Received from the Department of Anesthesiology, Leiden University MedicalCenter, Leiden, The Netherlands. Submitted for publication December 3, 2001.Accepted for publication April 1, 2003. Supported by GlaxoSmithKline BV, Zeist,The Netherlands. Presented in part at the annual meeting of the European Societyof Anaesthesiologists, in Gothenburg, Sweden, October 4, 2001.

Address reprint requests to Dr. Mertens: Department of Anesthesiology, Lei-den University Medical Center, PO Box 9600, 2300 RC, Leiden, The Netherlands.Address electronic mail to: [email protected]. Individual article reprints maybe purchased through the Journal Web site, www.anesthesiology.org.

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In the operating room, an intravenous cannula wasinserted into a large forearm vein for infusion of remifen-tanil and propofol, and another cannula was insertedinto a radial artery for continuous measurement of arte-rial blood pressure and collection of blood samples. Theelectrocardiogram, heart rate, arterial blood pressure,

peripheral oxygen saturation, end-tidal carbon dioxidepartial pressure, Bispectral Index (version A1000; AspectMedical Systems Inc., Natick, MA), and the spectral edgefrequency were monitored continuously throughout thestudy. Neuromuscular transmission was monitored bypercutaneous stimulation of the ulnar nerve using thetrain-of-four method.

Study Protocol

After breathing 100% oxygen for 3 min, 0.1 mg/kgatracurium was given intravenously, and anesthesia wasinduced by computer-controlled infusion of propofol

with a target concentration set at 6 g/ml. Depending onthe propofol solution in the syringe, the actual targetconcentrations were 2, 4, or 6g/ml for the patients ingroups A, B, and C, respectively. The target propofolconcentration was maintained constant throughoutthe surgical procedure until the peritoneum wasclosed.

Five minutes after the start of the propofol infusion,the remifentanil infusion was started with a target con-centration of 2 ng/ml. Ten minutes (i.e., four to five timesthe 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. Ifa patient had not lost consciousness by 10 min afterthe start of the propofol infusion, the target remifen-tanil concentration was increased by 210 ng/ml toinduce unconsciousness before the administration ofatracurium.

Subsequently, laryngoscopy was performed. To opti-mally determine the remifentanil concentrationeffectrelation for this stimulus, a second and third laryngos-copy were performed with different target remifentanilconcentrations, and the presence or absence of a re-sponse was recorded. If a patient did not respond to thefirst or second laryngoscopy, the target remifentanil con-centration was decreased by 1 ng/ml. When patients didrespond to the first or second laryngoscopy, the targetremifentanil concentration was increased by 210 ng/ml,depending on the intensity of the response, for the follow-ing laryngoscopy. Five minutes (i.e., six to seven times theT1/2ke0 of remifentanil)

6 after a new target remifentanilconcentration was reached, the following laryngoscopy

was performed. The aim was to achieve at least oneresponse and at least one nonresponse to laryngoscopyin each patient. A response to laryngoscopy was definedusing the same criteria as used to define inadequate

anesthesia.

Inadequate anesthesia was defined by the followingcriteria1:

1. An increase in systolic blood pressure by more than15 mmHg above the preoperative mean systolic bloodpressure, defined as the mean of three systolic bloodpressures measured since admission

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

3. Other autonomic signs such as sweating or flushing4. Somatic responses such as movements or

swallowingDuring the study, three persons observed each patient

continuously for evidence of inadequate anesthesia: aresident in anesthesia, an anesthesiologist, and a trainedmedical student. If inadequate anesthesia was detected,it was only accepted if verified by all three observers. Tofacilitate identification of somatic responses, atracurium

was given at the minimal dose necessary for surgery

(train-of-four levels 13.After the second or third laryngoscopy, the trachea of

the patient was intubated, and the lungs were ventilatedwith 30% oxygen in air to an end-tidal carbon dioxidepartial pressure of 2934 mmHg.

The target propofol concentration was maintainedconstant until the peritoneum was closed and finallydiscontinued after skin closure. The remifentanil admin-istration was changed in response to the presence orabsence of signs of inadequate anesthesia. When signs ofinadequate anesthesia developed, the target remifentanilconcentration was increased by 110 ng/ml. When no

signs of inadequate anesthesia were observed, the targetremifentanil concentration was decreased by 110 ng/ml.If, at induction of anesthesia, patients had not lost con-sciousness in the absence of remifentanil, the targetremifentanil concentration was not decreased below theremifentanil effect site concentration, as displayed on thetarget controlled infusion device at the time of loss ofconsciousness. After a new target concentration wasreached (as judged from the computer display) this wasmaintained for 6 min.

Thirty minutes before skin closure, 0.2 mg/kg intrave-nous morphine was administered to provide postopera-tive pain relief.

After skin closure, neuromuscular blockade was antag-onized by neostigmine, 12 mg intravenously, and atro-pine, 0.51 mg intravenously, and the remifentanil infu-sion was discontinued. The patients were tested every 2min by verbal commands to evaluate return of con-sciousness. This was defined as a positive response to a

verbal command. Once adequate spontaneous ventila-tion was established (i.e., if the end-tidal carbon dioxidepartial pressure was less than 46 mmHg, tidal volume

was more than 7 ml/kg, and respiratory rate was morethan 10 breaths/min), the trachea was extubated.

After the trachea had been extubated, the patient was

transported to the recovery room. Twenty-four hours

348 MERTENS ET AL.

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postoperatively, the patients were interviewed to evalu-ate possible side effects and any recall of intraoperativeevents.

Blood Samples and Assays

Arterial blood samples for determination of propofol

and remifentanil concentrations in whole blood werecollected at laryngoscopy, intubation, skin incision, theopening of the peritoneum, awakening, and 6 min aftera predicted target remifentanil concentration wasreached during the intraoperative period. The totalamount of blood sampled in each patient did not exceed150 ml. Samples for the determination of blood propofolconcentrations were transferred into test tubes contain-ing potassium oxalate and stored at 4C. Propofol con-centrations in blood were measured at the AnesthesiaResearch laboratory of the Leiden University MedicalCenter by reverse-phase high-performance liquid chro-

matography.7

The limit of quantitation was 11.7 ng/ml.The coefficient of variation of this method was 3% or lessin the concentration range encountered in this study.Propofol assays were performed within 12 weeks.

Samples for the determination of blood remifentanilconcentrations were collected into tubes containing so-dium heparin and immediately transferred to tubes con-taining 50% citric acid (to inactivate esterases) beforefreezing at 20C. The assay method is based on tandemmass spectrometry detection with a quantitation limit of0.1 ng/ml and an interassay coefficient of variation of lessthan 10% for concentrations greater than 0.1 ng/ml. The

remifentanil analyses were performed in a commerciallaboratory (Analytico, Breda, The Netherlands).

Data Analysis

For each patient, one to three data points were avail-able for laryngoscopy, intubation, skin incision, openingof the peritoneum, and return to consciousness. Theinteraction between propofol and remifentanil at theseevents was therefore determined over the group, foreach event separately, using the response surface modeldescribed by Bol et al.9:

Cprop

C50,prop

Crem

C50,rem

Cprop

C50,prop Crem

C50,rem

1 CpropC50,prop

Crem

C50,rem

Cprop

C50,prop

Crem

C50,rem (1)

where is the probability of no response, Cprop is theblood propofol concentration, Cremis the blood remifen-tanil concentration, C50,prop and C50,rem are the steadystate concentrations of propofol and remifentanil corre-sponding to a 50% probability of no response wheneither drug is administered alone, and and are thecoefficients describing the shape of the response sur-face. The interaction parameter is equivalent to the

Berenbaum interaction index10 (with 0, equation 1

describes an additive model; with 0, a nonadditivemodel is described).

For some end points, the obtained estimate of C50wasseveral orders of magnitude larger than the clinical con-centration range and the concentrations encountered inthis study. In these cases, estimates of were also ex-

tremely large, but the ratio of and C50remained mean-ingful. Therefore, when estimates of C50,remand weretwo or more orders of magnitude larger than the con-centrations encountered in this study, the model wasrewritten as:

CpropC50,prop

Cprop

C50,propC rem

1 CpropC50,prop Cprop

C50,propC rem

(2)

where is the ratio of and C50,rem. In case the C50s ofboth drugs were much higher than the actually achievedconcentrations, the model was further simplified to:

C prop C rem

1 Cprop C rem (3)

where' is the ratio of and the product of C50,propandC50,rem.

The model parameters were estimated with the com-puter program NONMEM (version V, level 1.1; TheNONMEM Project Group, University of California, SanFrancisco, CA), by minimizing the 2 log likelihood(2LL) for all observations:

2LL 2 i1

N

Ri lnP 1 Ri ln1 P (4)

where N is the number of adequatenonadequate anes-thesia or unconsciousawake data points, Ri is the ob-served response of the ith individual, being either 1 (i.e.,no response to any of the perioperative stimuli or noresponse to a verbal command after termination of thepropofol and remifentanil target-controlled infusion) or0 (i.e., a response to any of the perioperative stimuli ora response to a verbal command after termination of thepropofol and remifentanil target-controlled infusion),andPis the probability of the response for each concen-tration combination. The interindividual variabilities ofthe model parameters C50,prop, C50,rem, andwere mod-eled using a log-normal variance model:

individual typical,k eindividual (5)

whereindividual is the value in the individual, typical,kisthe typical value of the parameter in the population inpatient k, andindividualis a normally distributed random

variable with a mean of zero and a variance of2, whichis estimated by NONMEM. The interindividual variabilityof was modeled using a normal variance model. The

response surface models describe the probability of a

349PROPOFOLREMIFENTANIL PHARMACODYNAMIC INTERACTION



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dichotomous outcome (a response or no response dur-ing one of the above events) as a function of the mea-sured blood propofol and remifentanil concentrations.

In contrast, for the intraabdominal part of surgery,multiple data were available per patient. The concentra-tioneffect relation of the combination of remifentaniland propofol for suppression of responses to the intra-abdominal part of surgery was therefore determined for

each patient separately by logistic regression. The influ-ence of the mean measured intraoperative blood propo-fol concentration on the C50 of remifentanil during theintraabdominal part of surgery was then determined byfitting a mechanistic model10 to the individual C50s ofremifentanil versus the mean measured propofol con-centrations data over all patients (see Appendix).

Note that we initially explored the concentrationresponse surface of the combination of propofol andremifentanil for laryngoscopy, intubation, skin incision,opening of the peritoneum, suppression of responses tosurgical stimuli, and probability of return to conscious-

ness according to the recently described response sur-face modeling technique by Minto et al.11 (see Discus-sion). The response surface was obtained by modeling ofadequatenonadequate anesthesia data or the uncon-sciousawake data versus the corresponding measuredblood propofol and measured blood remifentanil con-centration combinations (see Appendix).

Statistical Analysis

Patient characteristics and the mean measured bloodpropofol and blood remifentanil concentrations, Bispec-tral Index, spectral edge frequency, systolic and diastolicblood pressures, and heart rate as observed in the threestudy groups during the intraoperative period (betweenopening of the peritoneum and skin closure) were com-pared between groups using the Kruskal-Wallis test witha post hoc MannWhitney U test for pairwise groupcomparison, if appropriate. To determine the nature ofthe interaction for suppression of responses to laryngos-copy, intubation, skin incision, the opening of the peri-toneum, suppression of responses to intraabdominal sur-gical stimuli, and the probability of return toconsciousness, the Akaike information-theoretic criteri-on12 (AIC 2LL 2p; where p is the number ofparameters in the model) was used to assess the signifi-

cance of incorporating an interaction term in the re-

sponse surface model. The model with the lowest AICwas considered optimal.

Data are presented as mean SD unless stated other-wise. P 0.05 was considered the minimum level ofstatistical significance except for multiple comparisontests when P 0.02 was considered significant.

Results

All but one of the patients were evaluable. One patientin group C had to be excluded from the study due toimproper handling of the blood samples. Age, weight,height, and duration of anesthesia of the remaining pa-tients (n 29) did not differ among the three studygroups (table 1). The mean measured blood propofoland blood remifentanil concentrations, Bispectral Index,spectral edge frequency, systolic and diastolic bloodpressures, and heart rate during the intraoperative pe-riod (between opening of the peritoneum and skin clo-sure) are shown in table 2. As intended, the mean mea-

sured blood propofol concentrations differed significantlybetween the three groups. Required mean measuredplasma remifentanil concentrations were lower in groups Band C compared to group A (P 0.02).

One out of the 10 patients in group A, 6 out of the 10patients in group B, and all but 1 of the patients in groupC had lost consciousness 5 min after the start of thepropofol infusion. In the 14 patients who remained con-scious with the initial target remifentanil concentration,unconsciousness was induced when the target remifen-tanil concentration was increased to 415 ng/ml.

The C50 of remifentanil for laryngoscopy and intuba-tion decreased with increasing propofol concentrations.For laryngoscopy and intubation, the data were bestcharacterized by a synergistic model (table 3). The addi-tion of the interaction term in the response surfacemodel resulted in a reduction in the AIC (from 62.41 to59.51 for laryngoscopy and from 39.21 to 34.95 forintubation). Introduction of intraindividual variability didnot result in a further reduction in the AIC. As bloodpropofol concentrations increased from 2 to 7.3 g/ml,the C50 of remifentanil decreased from 3.8 ng/ml to0 ng/ml for laryngoscopy and from 4.7 ng/ml to 1.2ng/ml for intubation (figs. 1 and 2). For skin incision andthe opening of the peritoneum, the configuration of the

data did not allow modeling.

Table 1. Patient Characteristics

ParameterGroup A

(2 g/ml Propofol)Group B

(4 g/ml Propofol)Group C

(6 g/ml Propofol)

n 10 10 9Age, yr 35 4 39 10 39 9

Height, cm 165 12 168 8 166 9

Weight, kg 68 13 65 10 67 11Duration of anesthesia, min 210 67 185 67 182 40

Data are mean SD. All patients were female.

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In 3 of 29 patients, the data set for intraoperativestimuli did not allow modeling. The concentrationeffect relation of remifentanil for intraabdominal stimulicould therefore not be determined in these 3 patients. In17 patients, no overlap existed between response andnonresponse data. Because the lowest measured plasmaremifentanil concentration at which no response oc-curred and the highest blood remifentanil concentrationat which a response was noted differed only marginallyin these patients, the C50of remifentanil was determinedas the midrange between the lowest measured bloodremifentanil concentration at which no response oc-curred and the highest blood remifentanil concentrationat which a response was noted. If in any patient noresponses occurred, even when the actual measured

blood remifentanil concentration was below the detec-tion limit, the C50of remifentanil was set to 0 ng/ml. Themeasured blood propofol concentration remained stablethroughout the surgical procedure in most patients (fig.3). The remifentanil concentrationeffect relations forthe intraabdominal part of the surgical procedure in theindividual patients of the three groups are shown infigures 46. Results are presented in table 4. The C50ofremifentanilversusmean blood propofol concentrationrelation for the intraabdominal part of surgery as deter-

mined over all patients is presented in figure 7. The C50of remifentanil for suppression of responses to intraab-dominal surgical stimuli decreased with increasingpropofol concentrations. The data were best character-ized by a synergistic model. The addition of the interac-tion term in the model resulted in a reduction in the AICfrom 82.07 to 79.96. Because C50,rem and of the non-additive model were very large, the model described inequation 9 was fitted to the data. The parameters ( SE)describing the curve are C50,prop 9.02 2.47 g/mland ' 0.557 0.306. Introduction of intraindividual

variability did not result in a further reduction in the AIC.As mean blood propofol concentrations increased from2 to 9 g/ml, the C50of remifentanil for intraabdominalstimuli decreased from 6.3 to 0 ng/ml (fig. 7).

Remifentanil significantly affected the blood propofolconcentration at which the patients regained conscious-ness. According to the response surface modeling tech-nique described by Bol et al.,9 the interaction betweenpropofol and remifentanil was judged to be synergisticfor the probability of unconsciousness (table 3). Intro-duction of intraindividual variability did not result in afurther reduction in the AIC. With blood remifentanilconcentration increasing from 0 to 10 ng/ml, the C50,propfor return of to consciousness decreased from 3.5 g/ml

Table 2. Intraoperative Data of the Patients Available for Analysis*

ParameterGroup A

(2 g/ml Propofol)Group B

(4 g/ml Propofol)Group C

(6 g/ml Propofol)

Patients, No. 8 10 8Propofol concentration,g/ml 2.2 0.4 4.5 0.8 7.8 1.7

Remifentanil concentration, ng/ml 7.3 3.8 2.2 2.2 1.1 2.2

Bispectral Index 59 15 56 20 43 23Spectral edge, Hz 14.6 3.5 13.9 5.6 11.4 4.1Systolic blood pressure, mmHg 116 8 119 10 107 12

Diastolic blood pressure, mmHg 67 7 69 7 61 8Heart rate, beats/min 67 9 67 6 68 10

Data are mean SD. Data are mean intraoperative measured blood propofol and blood remifentanil concentration, Bispectral Index, spectral edge frequency,

systolic and diastolic blood pressures and heart rate. Data were compared between groups using the Kruskal-Wallis test with a post hocMann Whitney U test

for pairwise group comparison, if appropriate.

* In 3 of 29 patients, the data set for intraoperative stimuli did not allow modeling. These patients are therefore not included in this table. P 0.02, group

Avs. group B. P 0.02, group Avs. group C. P 0.02, group B vs. group C.

Table 3. Additive and Nonadditive Interaction Models

Stimulus C50, prop SE C50, rem SE SE (, ) SE AIC

Laryngoscopy 5.63 0.96 4.82 1.50 4.39 1.5 62.413

Laryngoscopy 7.32 1.83 3.82 1.18 0.69 0.32 59.511*Intubation 8.69 3.26 4.95 2.33 3.22 1.79 39.213Intubation 2.25 4.41 0.11 0.03 34.950*

Awakening 2.92 0.51 5.15 2.80 3.88 1.09 48.152Awakening 3.49 0.64 3.52 1.01 0.72 0.31 42.538*

Models are determined by response surface modeling according to equations 1, 2, or 3 and describe the influence of the blood propofol and the blood

remifentanil concentration on the probability of no response to laryngoscopy or intubation and on the probability of unconsciousness. Shown are the fitted values

of C 50, propC50, rem, , and SE, describing the shape of the response surface of the two response surfaces that were determined to explore the possibilities

of an additive and of a nonadditive interaction between propofol and remifentanil for the suppression of responses to laryngoscopy, intubation, and for the

probability of unconsciousness, and theAIC of these models. For some end points, C50,propor C50,remestimated with equation 1 were greater than 3 orders of

magnitude higher than the maximum concentrations encountered in this study. In these cases, the coefficients describing the shape of the response surface

correspond to those used in either equation 2 or 3. AIC is the Akaikes information-theoretic criterion.12 The model with the lowestAIC was considered to be

optimal and is marked by an asterisk.




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to 0.4 g/ml (fig. 8). For this unimodal end point, theresponse surface modeling technique described byMintoet al.11 proved also adequate. The additive model

with the lowest AIC is a model in whichpropand remare identical. Introduction of intraindividual variabilitydid not result in a further reduction in the AIC. Becausethe addition of the interaction term 2,U50 (see Appen-dix) in the model resulted in a reduction in the AIC from48.152 to 46.409, the interaction between propofol andremifentanil for the probability of unconsciousnessbased on the response surface modeling technique de-scribed by Mintoet al.11was also judged synergistic. Theparameters ( SE) describing the response surface areE0 0, Emax 1, C50,prop 3.40 0.75g/ml, C50,rem 8.91 2.35 ng/ml, prop 4.29 0.98, rem 4.29 0.98, and 2,U50 1.69 0.42. The C50 of propofoldecreased from 3.4 g/ml to 0.5 g/ml as blood remifen-tanil concentrations increased from 0 to 8 ng/ml. The

model described in equation 2 was selected as the final

Fig. 2. Concentration effect relation of the combination ofpropofol and remifentanil for suppression of responses to in-tubation. The curve (top) was obtained by response surfacemodeling, according to equation 3, of the response (opensquares)no response (closed squares) dataversus the corre-sponding measured blood propofol concentrations and bloodremifentanil concentrations. The displayed curve representsremifentanil and propofol concentrations associated with a50% probability of no response, calculated using equation 3,and the fitted values of the coefficients from table 3, describingthe synergistic interaction model. In the concentrationresponse surface (bottom) for the combination of propofol andremifentanil, the isoboles for 25, 50, and 75% probability of noresponse are shown.

Fig. 3. Measured blood propofol concentrationversus time inthe individual patients of group A ( target propofol concen-tration 2 g/ml), group B ( target propofol concentration4 g/ml), and group C ( target propofol concentration6 g/ml).

Fig. 1. Concentration effect relation of the combination ofpropofol and remifentanil for suppression of responses to la-ryngoscopy. The curve (top) was obtained by response surfacemodeling, according to equation 2, of the response (opensquares)no response (closed squares) dataversus the corre-sponding measured blood propofol concentrations and blood

remifentanil concentrations. The displayed curve representsremifentanil and propofol concentrations associated with a50% probability of no response, calculated using equation 2,and the fitted values of the coefficients from table 3, describingthe synergistic interaction model. In the concentrationresponse surface (bottom) for the combination of propofol andremifentanil, the isoboles for 25, 50, and 75% probability of noresponse are shown.

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model for the return to consciousness because its AIC waslower than that for the model described by Minto et al.11

(42.538 vs. 46.409). All patients breathed adequately onawakening. None of the patients reported awareness forany intraoperative event.

Discussion

The aims of this study were to determine the influenceof propofol on remifentanil requirements for suppres-sion of responses to perioperative stimuli and return ofconsciousness in female patients and to determine thenature of these interactions. The study demonstratedthat propofol reduces remifentanil requirements for sup-pression of responses to laryngoscopy, intubation, andintraabdominal surgical stimulation in a synergistic man-ner in female patients. In addition, the study demon-strated that remifentanil decreases propofol concentra-tions associated with the return of consciousness in asynergistic manner.

Critique on Methods

Theoretically, a pharmacodynamic interaction be-tween two agents is best defined if data are obtained bystudying the effect of the agents separately and in com-bination. 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 intentionallychose a target of 2 g/ml as the lowest target propofolconcentration. Note that in the absence of premedica-tion, a target propofol concentration of 2 g/ml is belowthat at which patients may be unconscious. With theselow blood propofol concentrations, remifentanil isneeded to supplement the hypnotic effect of propofol.In retrospect, this target propofol concentration mayhave been conservative. In previously described interac-tion studies between propofol and opioids, the synergis-tic nature of the interaction became predominantly ap-parent at subhypnotic propofol concentrations ( 23g/ml).13,14 To further minimize the risk of awareness,the intraoperative target remifentanil concentration wasnever decreased below the predicted remifentanil effectsite concentration at which patients had lost conscious-ness in the presence of propofol, if, at induction ofanesthesia, patients had not lost consciousness in theabsence of remifentanil. This may have led to the rela-tively large number of nonresponses compared to thenumber of responses to surgical stimuli during the intra-abdominal part of surgery.

Recently, Minto et al.11 described a novel method fordrug interaction analysis by means of response surfacemodeling. We explored the interaction between propo-

fol and remifentanil for suppression of responses to

Fig. 4. Remifentanil concentrationeffect relations in the indi-vidual patients for the intraabdominal part of surgery whenremifentanil was given as a supplement to a target propofolconcentration of 2 g/ml. The mean measured blood propofolconcentrations were 2.1, 2.3, 2.8, 2.0, 1.9, 2.2, 1.9, and 2.9 g/mlin patients 18, respectively (table 5). The curves were deter-mined by logistic regression of responseno response dataver-susthe corresponding measured blood remifentanil concentra-tions of remifentanil, as shown beneath the curves. Dots blood remifentanil concentrations associated with a 50% prob-ability of no response.

Fig. 5. Remifentanil concentrationeffect relations in the indi-vidual patients for the intraabdominal part of surgery whenremifentanil was given as a supplement to a target propofolconcentration of 4 g/ml. The mean measured blood propofolconcentrations were 4.1, 3.7, 3.9, 4.6, 6.2, 4.5, 3.5, 5.1, 4.7, and4.4 g/ml in patients 110, respectively (table 5). The curveswere determined by logistic regression of responseno re-sponse dataversus the corresponding measured blood remifen-tanil concentrations of remifentanil, as shown beneath thecurves. Dots blood remifentanil concentrations associatedwith a 50% probability of no response.




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various anesthetic end points (i.e., laryngoscopy, intuba-tion, skin incision, opening of the peritoneum, and in-

traabdominal surgical stimuli) using this new analyticalinstrument but found that the responseno responsedata could not be analyzed in this way. However, theanesthetic state is a bimodal phenomenon, consisting ofboth a hypnotic and an analgesic component, and maytherefore not be considered as a single measure of drugeffect. Because the studied perioperative pharmacody-

namic end points of no response to nociceptive stimulicannot be achieved by remifentanil alone in the absenceof propofol, remifentanil has the pharmacodynamic

characteristics of a partial agonist for these end points inthe response surface modeling technique described byMinto et al.11 Because the basic concept in responsesurface modeling according to Minto et al.11 is that anygiven ratio of two drugs behaves as a new drug with itsown sigmoidal concentrationresponse relation, this re-sults in a model predicting that a maximal effect

Fig. 6. Remifentanil concentrationeffect relations in the indi-vidual patients for the intraabdominal part of surgery whenremifentanil was given as a supplement to a target propofolconcentration of 6 g/ml. The mean measured blood propofolconcentrations were 5.8, 8.1, 8.6, 9.1, 4.6, 8.5, 8.7, and 9.1 g/mlin patients 18, respectively (table 5). The curves were deter-mined by logistic regression of responseno response dataver-susthe corresponding measured blood remifentanil concentra-tions of remifentanil, as shown beneath the curves. Dots blood remifentanil concentrations associated with a 50% prob-ability of no response.

Table 4. Blood Propofol and Blood Remifentanil Concentrations Associated with a 50% Probability of No Response to

Intraabdominal Surgical Stimuli in the Individual Patients

Group A(2 g/ml)

Group B(4 g/ml)

Group C(6 g/ml)

No.Cprop SD,

g/mlC50,rem SE,

ng/ml No.Cprop SD,

g/mlC50,rem SE,

ng/ml No.Cprop SD,

g/mlC50,rem SE,

ng/ml

1 2.1 0.1 15.9 1 4.1 0.4 0.0 1 5.8 0.4 0.0

2 2.3 0.2 3.4 2 3.7 0.2 1.0 2 8.1 0.5 0.0 3 2.8 0.2 5.8 0.2 36.4 3 3.9 0.3 5.6 3 8.6 0.5 0.1 4 2.0 0.2 5.5 1.8 2.0 4 4.6 0.5 0.4 4 9.1 0.6 0.0 5 1.9 0.2 3.8 0.8 5.4 5 2.9 0.6 0.0 5 4.6 0.7 5.7 0.8 6.96 2.2 0.2 3.4 0.4 8.7 6 4.5 0.4 2.4 1.3 2.3 6 8.5 0.9 0.0

7 1.9 0.3 3.5 7 3.5 0.4 4.1 1.1 2.6 7 8.7 0.5 0.0 8 2.9 0.2 5.3 0.6 8.0 8 5.1 0.9 0.0 8 9.1 1.0 0.0 9 2.1 0.1 9 4.7 0.4 0.3 0.1 2.5 9 10 1.7 0.5 10 4.4 0.6 0.9 10

Cprop; mean ( SD) measured blood propofol concentrations. Fitted C50( SE) and , for remifentanil characterizing the probability of no response to surgical

stimuli observed during the intraabdominal period of surgery in patients receiving remifentanil as a supplement to propofol at target concentrations of 2 g/ml

(group A), 4 g/ml (group B), or 6 g/ml (group C).

Fig. 7. Blood remifentanil concentrations versus blood propofolconcentrations associated with a 50% probability of no responseto intraabdominal surgical stimuli. The curve represents a mech-anistic function (see Appendix) fitted to the data by unweightedleast-squares nonlinear analysis described by the equation:

Crem 1 (Cprop/9.02)

0.55 (Cprop/9.02)

where Crem the blood remifentanil concentration (ng/ml)associated with a 50% probability of no response to intraab-dominal surgical stimuli; Cprop the mean blood propofolconcentration (g/ml) calculated in each patient. Dots C50s ofremifentanil at corresponding mean blood propofol concentra-tions for suppression of responses to intraabdominal surgicalstimuli as determined in the individual patients by logistic re-gression (Figs. 46).

354 MERTENS ET AL.



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achieved by propofol alone (i.e., a 100% probability ofno response) is reduced by the addition of remifentanil

(i.e., the Emax of the new drug is reduced). Based onour exploration of the data regarding the anesthetic state

by response surface modeling, we conclude that al-

though 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. Pharmacody-

namic end points of no response to nociceptive stimuliwere 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 Vuyket al.1 on the

interactions between propofol and alfentanil, the inter-

actions between propofol and remifentanil for suppres-sion of responses to laryngoscopy and intubation were

best described by a synergistic interaction model. For

laryngoscopy, the C50,rem and estimated with the

model described by Bol et al.9 were very large, whereas

for intubation, C50,rem, C50,prop, and were several or-

ders of magnitude larger than the concentrations en-

countered in this study. Therefore, these effects were

modeled with the modified models (equations 2 and 3,

respectively). Similarly, Vuyket al.1 have demonstrated

that propofol decreases alfentanil requirements for sup-

pression of responses to laryngoscopy and intubation in

a synergistic manner.Remifentanil concentrations required to suppress re-

sponses 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

C50 of propofol for laryngoscopy in the absence of

remifentanil, determined as the intercept of the interac-

tion model with the x-axis (fig. 1), is 7.3 g/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 C50 of propofol alone for

intubation could not be determined. These findings arein accordance with the findings of Kazama et al.,15 who

Fig. 8. Concentration effect relation of the combination ofpropofol and remifentanil for the probability of the return toconsciousness. The curve (top) was obtained by response sur-face modeling, according to equation 2, of the awakeuncon-scious dataversusthe corresponding measured blood propofolconcentrations and the corresponding measured blood

remifentanil concentrations. Closed squares

concentrationsof propofol and remifentanil at skin closure, at which time theindividual patients were still unconscious; open squares con-centrations of propofol and remifentanil when the patientsregained consciousness. The displayed curve representsremifentanil and propofol concentrations associated with a50% probability of the return to consciousness, calculated usingequation 2, and the fitted values of the coefficients from table 3,describing the synergistic interaction model. In the concentra-tionresponse surface (bottom) for the combination of propofoland remifentanil, the isoboles for 25, 50, and 75% probability ofreturn to consciousness are shown.

Table 5. Propofol and Remifentanil Infusion Schemes

Infusion scheme Propofol C50 (2.0 g/ml) Remifentanil C50 (6.3 ng/ml) Remifentanil C50 (6.3 ng/ml)

Bolus 1 mg/kg 1 g/kg Infusion 1 6 mg kg1 h1 for 20 min 24g kg1 h1 for 5 min 50 g kg1 h1 for 3 minInfusion 2 5 mg kg1 h1 for 60 min 18g kg1 h1 thereafter 18g kg1 h1 thereafter

Infusion 3 4 mg kg1 h1 thereafter

Propofol and remifentanil infusion schemes required to maintain effect site concentrations of these agents at a level associated with a 50% probability of no

response to surgical stimuli and the most rapid possible return of consciousness after termination of the infusions. For remifentanil, infusion schemes are given

with or without the use of a bolus dose. Based on a 40-yr-old female patient with a height of 165 cm, a weight of 65 kg, and a lean body mass of 46.6 kg.

Pharmacokinetic parameters for propofol and remifentanil by Marshet al.26 and Eganet al.,6 respectively. T1/2ke0for propofol and remifentanil by Kazama et al.5

and Egan et al.,6 respectively.




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determined the C50s of propofol for laryngoscopy andintubation at 9.8 and 17.4 g/ml, respectively.

Intraoperative Interaction

Intraoperatively, propofol reduced remifentanil re-quirements for suppression of responses to lower ab-

dominal surgical stimuli in a synergistic manner. In asimilar study, Vuyk et al.,1 demonstrated that propofolsignificantly reduced alfentanil requirements for sup-pression of responses to lower abdominal surgical stim-uli in a synergistic manner. In previous interaction stud-ies, opioids have been not to be able to replacecompletely inhalational1621 or intravenous1,13 anes-thetic agents to provide anesthesia (the so-called ceilingeffect). Accordingly, when the model described by equa-tion 8 (see Appendix) was fitted to the data, the C50,remfor suppression of responses to lower abdominal surgicalstimuli was six orders of magnitude higher than the

maximum blood remifentanil concentration encoun-tered in this study. Therefore, this effect was modeled

with the modified model described in equation 9.

Return of Consciousness

The propofol C50 for return of consciousness of3.5 g/ml corresponds well with the reported propofolconcentrations at which consciousness was lost in 50%of the patients of 3.4 g/ml.7 However, the C50,propforreturn of consciousness determined in our study is lowerthan the C50,prop for return of consciousness of approx-imately 4 g/ml determined in a similar study after total

intravenous anesthesia with propofol and alfentanil.

1

Itis conceivable that 0.2 mg/kg morphine administered 30min before the end of surgery to provide adequate initialpostoperative pain control after remifentanil anesthesiamay have lowered the concentration at which patientsregained consciousness and delayed the return of con-sciousness in our study group.

Remifentanil Potency in Relation to Alfentanil

The synthetic opioids fentanyl, alfentanil, sufentanil,and remifentanil can be considered a homogeneousgroup from a pharmacodynamic point of view becausethey act at similar receptor systems and have similareffects and similar side effects.22 The relative potenciesof the synthetic opioids for several clinical end points

were found to equal their relative potencies determinedon the basis of their effect on the electroencephalo-gram22 (the potency ratio for alfentanil to remifentanilbeing 1:30).6 For this reason, the nature and the degreeof the pharmacodynamic interaction between propofoland alfentanil probably will be similar to that for propo-fol and remifentanil.

The methodology, patient population, and type of sur-gery in this study were exactly the same as those in thestudy by Vuyket al.1 on the pharmacodynamic interac-

tion between propofol and alfentanil. Therefore, we

could analyze the pooled intraoperative data from thetwo studies. The influence of the mean measured intra-

operative blood propofol concentration on the C50of anopioid during the intraabdominal part of surgery wasdetermined using equation 8 or 9 (see Appendix). Thepotency of remifentanil relative to that of alfentanil forsuppression of responses to lower abdominal surgery

was estimated as an additional parameter, transformingthe C50s of alfentanil from the study by Vuyket al.

1 toremifentanil equivalents (C50,alf/potency ratio).

Both the possibility of an additive and the possibility ofa nonadditive interaction were explored. The AIC waslower for the nonadditive model than for the additivemodel (241.355 vs. 246.807, respectively). BecauseC

50,rem

and of the nonadditive model estimated withequation 8 were very large, the model described inequation 9 was fitted to the data. The results are pre-sented in figure 9. The parameters ( SE) describing theresponse surface are C50,prop 12.1 2.28g/ml,' 0.830 0.304, and potency ratio 31.1 7.53. Introduc-tion of intraindividual variability did not result in a fur-ther reduction in the AIC. The interaction betweenpropofol and remifentanil was, therefore, judged to besynergistic. As the mean blood propofol concentrationsincreased from 2.0 to 9.0 g/ml, the C50of remifentanil(or remifentanil equivalents) for intraabdominal stimulidecreased from 6.1 ng/ml to 0.4 ng/ml (fig. 9).

Based on this analysis, remifentanil was 31 times more

Fig. 9. Remifentanil equivalents versusblood propofol concen-trations associated with a 50% probability of no response tointraabdominal surgical stimuli, from this study (filled circles)and from the study by Vuyk et al.1 (open circles). The curverepresents a mechanistic function (see Appendix) fitted to thedata by unweighted least-squares nonlinear analysis described

by the equation:

C50,rem,eq1 (Cprop/9.97)

0.68 (Cprop/9.97)

where C50,rem,eqis the remifentanil equivalent associated with a50% probability of no response and Cprop is the mean bloodpropofol concentration calculated in each patient. The Calf,50sfrom the study by Vuyket al.1were transformed to C50,rem,eq, byestimation of the potency of remifentanil relative to that ofalfentanil for suppression of responses to lower abdominalsurgery as an additional parameter (C50,rem,eq C50,alf/31.1).

356 MERTENS ET AL.



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potent than alfentanil for suppression of responses tolower abdominal surgery in combination with propofol.This corresponds well with the potency ratio of alfen-tanil to remifentanil based on their effect on the electro-encephalogram. Remifentanil was 41 times more potentthan alfentanil for suppression of responses to lower

abdominal surgery when given as a supplement to ni-trous oxide anesthesia.23,24

Computer Simulations

To explore the time to return of consciousness afteranesthesia with propofol and remifentanil C50 concen-tration combinations, we simulated, using an Excel (Ex-cel 7.0; Microsoft Corp., Redmond, WA) spreadsheet,the decay in propofol and remifentanil effect site con-centrations after termination of a target-controlled infu-sion of 60 and 180 min with equianesthetic C50 propo-folremifentanil combinations. Effect site concentrations

of propofol and remifentanil were calculated using equa-tion 6:

Cet A ke0

ke0 et

B ke0

ke0 et

D ke0

ke0 et

A ke0 ke0

B ke0

ke0

D ke0

ke0 Ce0eke0t (6)

where Ce is the decreasing effect site propofol orremifentanil concentration; t is the time elapsed aftertermination of infusion; A, B, D, , , and were derivedaccording to Hull3 from the pharmacokinetic parameter

sets for propofol

4

and remifentanil

2

; ke0 is the bloodeffect site equilibration rate constant of propofol5 orremifentanil6; and Ce(0) is the effect site propofol orremifentanil concentration when the infusion was termi-nated 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 and as obtained in thisstudy in equation 2. Using the Excel optimizer function,t was iterated until the probability of unconsciousnessgiven by equation 2 equaled 50%. The results of thesesimulations are displayed graphically in figure 10.

Similar computer simulations were performed usingthe pharmacodynamic interaction model for propofoland alfentanil described by Vuyket al.1 To allow com-parison of the two studies, the results of the study by

Vuyk et al.1 were translated to remifentanil equiva-lents, as described elsewhere,25 using the alfentanil/remifentanil potency ratio as described above. The re-sults of these simulations are displayed in figure 11.

The computer simulations showed that the decay ofthe remifentanil concentration after termination of theinfusion is so much more rapid than that of propofol thatthe propofolremifentanil concentration combinationthat provides both adequate anesthesia and the mostrapid return of consciousness is the one with the lowest

possible propofol concentration. The time from termi-

Fig. 10. Computer simulation of the effect site propofol4,5 andremifentanil2,6 concentrationsversus time during the first 40 minafter termination of target-controlled infusions of propofol andremifentanil that had been maintained for 60 (top) or 180 min(bottom), respectively, at constant target blood concentrationscombinations associated with a 50% probability of no response tosurgical stimuli. These concentration combinations are repre-sented by the line on the bottom of the figure in the xy plane. Thedecrease in the concentrations following various intraoperativepropofol-remifentanil combinations is represented by the curvesrunning upward from the xy plane. The curved linesin parallelto the xy plane represent consecutive 1-min time intervals. Thebold line represents the propofolremifentaniltime relation atwhich the probability of regaining consciousness is 50%.




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nation of a 180-min infusion of propofol and remifentanilto awakening was found to be shortest (6.5 min) afterinfusion of a constant target propofol concentration of

1.5g/ml combined with a constant target remifentanilconcentration of 9.0 ng/ml. This optimal propofolremifentanil concentration is not affected by the dura-tion of anesthesia and corresponds well with that pre-dicted on the basis of the interaction models determinedby Vuyk et al.25 Infusion duration also has very littleinfluence on the time to awakening at this optimalconcentration combination. However, with subopti-mal propofolremifentanil concentration combinations(high propofollow remifentanil), return of conscious-ness is rapidly postponed with increasing infusion dura-tion. The time to return of consciousness in our studygroup was longer for all suboptimal propofolremifen-tanil concentration combinations (fig. 11). As mentionedbefore, 0.2 mg/kg morphine administered intravenously30 min before the end of surgery for postoperative paincontrol may have delayed the return of consciousness inour study group.

Based on the results of this study and our clinicalexperience, we recommend a minimum effect sitepropofol concentration of 2.0 g/ml in combination

with an effect site remifentanil concentration of6.3 ng/ml in female patients with American Society of

Anesthesiologists physical status I or II in the absence ofpremedication 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 with-

out target controlled infusion are given in table 5. 5,6,26

A low target propofol concentration of 2.0g/ml in

combination with a relatively higher remifentanil con-centration of 6.3 ng/ml should only be used in the

absence of significant muscle relaxation. When maxi-

mum muscle relaxation is required for surgery, we ad-

vise use of a target propofol concentration of 3 g/ml or

greater to reduce the risk of awareness. To avoid unrec-

ognized 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 g/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 13, 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, remifen-

tanil decreases propofol concentrations associated with thereturn of consciousness in a synergistic manner. Computer

simulations revealed that the optimal blood propofol and

blood remifentanil concentrations with respect to satisfac-

tory intraoperative anesthetic conditions and speed of re-

covery are 2.0 g/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 eachpatient for the intraabdominal part of surgery. Therefore, the concen-

trationeffect 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:

e01lnCrem

1 e01lnCrem (7)

whereis the probability of no response, Crem is the blood remifen-

tanil concentration, and0are the coefficients describing the shape of

the curve. The remifentanil concentrations associated with a 50%

probability of no response to lower abdominal surgery (C50), deter-

mined in each patient by logistic regression, were related to the

corresponding mean intraoperative propofol concentrations with a

Fig. 11. Computer simulation of the time to return of conscious-ness after termination of target controlled infusions of propo-fol4,5 and remifentanil2,6 that had been maintained for 180 minat constant blood concentrations associated with a 50% proba-bility of no response to surgical stimuli. The x-axis shows theseblood concentration combinations associated with a 50% prob-ability of no response to surgical stimuli. Bold line results ofthese simulations based on the models described in this study;dotted line results of the simulations based on the modelsdescribed by Vuyket al.1 for the combination of alfentanil andpropofol, whereby alfentanil concentrations were converted toremifentanil equivalents, assuming a potency ratio of 31.1. Thedifference between the two curves probably results from thefact that in the remifentanil study morphine for postoperativepain relief was given before the end of surgery.

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mechanistic model over all patients by nonlinear regression analysis.

The mechanistic function is described by equation 810:

Cprop

C50prop

Crem

C50rem

Cprop

C50prop

Crem

C50rem 1 (8)

where Cprop is the mean intraoperative blood propofol concentration

(g/ml) calculated in each patient; Crem is the C50 of remifentanil

(ng/ml) for suppression of responses to intraabdominal surgical stimulias determined in each patient by logistic regression; C50,prop and

C50,rem are the blood propofol (g/ml) and remifentanil (ng/ml) con-

centrations that are associated with a 50% probability of no response if

each drug would be administered as a single agent; and is a dimen-

sionless parameter characterizing the shape of the curve (with 0,

the result is a straight line suggesting additivity; with 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 Crem as a dependent variable and Cprop as an

independent variable.

When C50,remwas more than three orders of magnitude higher than

the maximum concentration encountered in this study, equation 8 was

rewritten as:

Cprop

C50,prop

Cprop

C50,propC rem 1 (9)

The model was fitted to the data with Cremas a dependent variable and

Cprop as an independent variable.

Data Analysis of Interaction for Return of

ConsciousnessIn 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 unconsciousawake data versus the corresponding

measured blood propofol concentrations and the corresponding mea-

sured blood remifentanil concentrations. The response surface is de-

scribed by equation 1011:

E E0 Emax E0

Uprop UremU50

1 Uprop UremU50

(10)

where E is the combined drug effect; E 0corresponds with the return

of consciousness; Emax corresponds with unconsciousness at the end

of anesthesia just before termination of the target controlled infusions

of propofol and remifentanil; Uprop Cprop/C50,prop and Urem/C50,rem;

Cpropis the blood propofol and Cremis the blood remifentanil concen-

tration; C50,propis the blood propofol and C50,propis the blood remifen-

tanil concentration that results in 50% of maximal drug effect;

Urem

Uprop Urem; (11)

() is the steepness of the concentrationresponse relation at ratio

described by:() prop (rem prop 2,) 2,2, where

prop and rem are the when propofol and remifentanil are given as

sole agents, and 2, is a model parameter estimated from the data;

C50() is the number of units (U) associated with 50% of maximum

effect at ratio described by: U50() 1 2,U50 2,U502, where

2,U50is a model parameter estimated from the data; and Emax() is the

maximum possible drug effect at ratio described by: Emax ()

Emax,prop (Emax,rem Emax,prop).

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