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Synergistic Interaction between Fentanyl and Bupivacaine Given Intrathecally for Labor Analgesia Warwick D. Ngan Kee, M.B., Ch.B., M.D., F.A.N.Z.C.A., F.H.K.A.M., Kim S. Khaw, M.B.B.S., M.D., F.R.C.A., F.H.K.A.M., Floria F. Ng, R.N., B.A.Sc., Karman K. L. Ng, M.B., Ch.B., F.A.N.Z.C.A., F.H.K.A.M., Rita So, M.B., Ch.B., F.A.N.Z.C.A., F.H.K.A.M., Anna Lee, M.P.H., Ph.D. ABSTRACT Background: Lipophilic opioids and local anesthetics are often given intrathecally in combination for labor analgesia. However, the nature of the pharmacologic interaction between these drugs has not been clearly elucidated in humans. Methods: Three hundred nulliparous women randomly received 1 of 30 different combinations of fentanyl and bupivacaine intrathecally using a combined spinal-epidural technique for analgesia in the first stage of labor. Visual analogue scale pain scores were recorded for 30 min. Response was defined by percentage decrease in pain score from baseline at 15 and 30 min. Dose–response curves for individual drugs were fitted to a hyperbolic dose–response model using nonlinear regression. The nature of the drug interaction was determined using dose equivalence methodology to compare observed effects of drug combinations with effects predicted by additivity. Results: The derived dose–response models for individual drugs (doses in micrograms) at 15 min were: Effect = 100 × dose / (13.82 + dose) for fentanyl, and Effect = 100 × dose / (1,590 + dose) for bupivacaine. Combinations of fentanyl and bupivacaine produced greater effects than those predicted by additivity at 15 min (P < 0.001) and 30 min (P = 0.015) (mean differences, 9.1 [95% CI, 4.1–14.1] and 6.4 [95% CI, 1.2–11.5] units of the normalized response, respectively), indicating a synergistic interaction. Conclusions: The pharmacologic interaction between intrathecal fentanyl and bupivacaine is synergistic. Characterization and quantification of this interaction provide a theoretical basis and support for the clinical practice of combining intrathecal opioids and local anesthetics. (Anesthesiology 2014; 120:1126-36) L IPOPHILIC opioids are commonly coadministered with local anesthetics for spinal and epidural analgesia in obstetrics and other subspecialties.1–3 Combining drugs has the advantage of reducing the dose that would be necessary if either drug were used alone, thus potentially decreasing the incidence and severity of associated side effects such as hypotension and motor block.1 However, the nature of the pharmacologic interaction between opioids and local anesthetics given neuraxially has not been clearly elucidated in a clinical context. Several studies in animals have reported a synergistic interaction.4,5 However, few experimental data examining the interaction of neuraxial drugs in humans are available. The aim of this randomized, double-blinded study was to describe the pharmacologic interaction between fentanyl and bupivacaine when administered intrathecally in combination for labor analgesia. We hypothesized that combinations of fentanyl and bupivacaine would produce greater analgesia than that predicted by simple additivity between drugs. Materials and Methods The study was approved by the Joint Chinese University of Hong Kong – New Territories East Cluster Clinical Research What We Already Know about This Topic • Quantitative analysis of drug interactions is commonplace for general anesthetics and sedatives, but has been little applied to intrathecal drugs in clinical practice • Addition of fentanyl enhances the analgesic effect of intrathecal bupivacaine for labor, but quantitative analysis of this interaction has not been adequately described What This Article Tells Us That Is New • In a study of 300 parturients receiving intrathecal fentanyl and bupivacaine for labor analgesia, these drugs interacted in a clearly synergistic fashion Ethics Committee, Shatin, Hong Kong, China, and the protocol was registered in the Centre of Clinical Trials Clinical Registry of the Chinese University of Hong Kong (reference no. CUHK_CCT00124). We recruited 300 women with American Society of Anesthesiologists physical status 1 to 2 who matched the following criteria: nulliparous, singleton pregnancy, gestation of 36 weeks or greater, in active labor with cervical dilatation Presented in part as a free article at Obstetric Anaesthesia 2013, Bournemouth, United Kingdom, May 23, 2013. Submitted for publication August 26, 2013. Accepted for publication November 27, 2013. From the Department of Anaesthesia and Intensive Care, The Chinese University of Hong Kong, Prince of Wales Hospital, Shatin, Hong Kong, China (W.D.N.K., K.S.K., F.F.N., K.K.L.N., R.S., and A.L.). Copyright © 2014, the American Society of Anesthesiologists, Inc. Lippincott Williams & Wilkins. Anesthesiology 2014; 120:1126-36 Anesthesiology, V 120 • No 51126 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 May 2014 PERIOPERATIVE MEDICINE 5 cm or less, visual analogue scale pain score 50 mm or greater (scale, 0–100 mm), and requesting neuraxial analgesia. Patients were excluded if they had a known fetal abnormality, hypertension, a medical contraindication to regional anesthesia, or received parenteral opioid within the preceding 2 h. Informed consent was obtained from all participants in two stages. Initially, a research nurse approached patients who were potentially suitable soon after admission to the labor ward; an explanation of the study was given, and preliminary verbal consent was obtained. Subsequently, if the patient requested neuraxial analgesia, willingness to participate and patient eligibility were confirmed, written consent was obtained, and the patient was entered into the study. Patients were only recruited during office hours when members of the investigating team were available. Upon entering the study, patients were instructed on the use of a 100-mm visual analogue scale ruler (0 mm = no pain and 100 mm = worst pain imaginable) for assessment of pain scores, a baseline measurement of pain score was recorded, and intravenous prehydration of 500 ml lactated Ringer’s solution was given. Combined spinal-epidural (CSE) analgesia was then administered by using a needle-through-needle system. The anesthesiologist was free to choose the patient position. Under full aseptic precautions, an 18- or 16-gauge Tuohy needle was inserted into the epidural space at what was estimated to be the L3-4 or L4-5 vertebral interspace using a loss-of-resistance technique with either air or saline according to the anesthesiologist’s preference. A pencilpoint spinal needle was then inserted through the epidural needle with intrathecal placement confirmed by free-flow of cerebrospinal fluid. The study solution was then injected intrathecally followed by removal of the spinal needle and placement and fixation of an epidural catheter. The study solution was 1 of 30 different combinations of fentanyl and bupivacaine (table 1). Drug combinations were divided into five groups (n = 60 per group), each of which contained fentanyl and bupivacaine in a fixed ratio. Each group was subdivided into six subgroups (n = 10 per subgroup) in which the ratio of fentanyl to bupivacaine was constant, but the mass of drug varied on an approximately log-based scale. Randomization was performed in blocks of 30 (one code for each subgroup per block); a member of the secretarial staff who had no patient contact inserted coded instruction forms for each of the 30 different solutions into individual opaque envelopes and then sealed, thoroughly shuffled, and consecutively numbered them. An envelope was opened for each patient after confirmation of consent and participation but before commencement of the CSE procedure. The solutions were prepared by one of the investigators who was not involved with subsequent patient assessment. All drugs were freshly prepared by careful serial dilution with aseptic precautions, diluted to a total volume of 2.5 ml with saline in identical syringes, and maintained under sterile conditions until use. In the event that the CSE procedure was unsuccessful (failure to correctly place epidural needle, failure to correctly place spinal needle, or accidental dural puncture with epidural needle), the patient was withdrawn from the study, and the randomization envelope was reused for the subsequent patient recruited. After completion of the CSE procedure, visual analogue scale pain scores were assessed by a research nurse (F.F.N.), who was blinded to the patient’s group, at the peak of the uterine contraction nearest to consecutive 5-min intervals, for 30 min. At the same times, the upper level of sensory block was recorded by assessing changes in sensitivity to ice, and motor block was assessed using a modified Bromage scale (0 = able to lift extended leg at the hip, 1 = able to flex the knee but not lift extended leg, 2 = able to move the foot only, and 3 = unable to move even the foot). If the level of sensory block differed between the left and right sides of the body, the highest level was recorded and used for analysis. During the study period, standard monitoring of Table 1. Combinations of Fentanyl and Bupivacaine in Study Groups Subgroup Group A (n = 60) Fentanyl dose, μg Bupivacaine dose, μg Group B (n = 60) Fentanyl dose, μg Bupivacaine dose, μg Group C (n = 60) Fentanyl dose, μg Bupivacaine dose μg Group D (n = 60) Fentanyl dose, μg Bupivacaine dose, μg Group E (n = 60) Fentanyl dose, μg Bupivacaine dose, μg A1 2 0 B1 1.5 50 C1 1 100 D1 0.5 150 E1 0 200 A2 5 0 B2 3.75 125 C2 2.5 250 D2 1.25 375 E2 0 500 A3 10 0 B3 7.5 250 C3 5 500 D3 2.5 750 E3 0 1,000 A4 15 0 B4 11.25 375 C4 7.5 750 D4 3.75 1,125 E4 0 1,500 A5 25 0 B5 18.75 625 C5 12.5 1,250 D5 6.25 1,875 E5 0 2,500 A6 40 0 B6 30 1,000 C6 20 2,000 D6 10 3,000 E6 0 4,000 All drug combinations were diluted to a total volume of 2.5 ml with saline. There were 10 patients in each subgroup. Anesthesiology 2014; 120:1126-361127 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. Intrathecal Fentanyl and Bupivacaine Synergism arterial pressure, pulse rate, oxyhemoglobin saturation, and cardiotocography was continued. Any occurrences of hypotension (defined by systolic arterial pressure <90 mmHg), nausea or vomiting, pruritus, and new nonreassuring fetal heart rate tracing were noted; these were managed according to the standard practice. After 30 min, the study was terminated, further analgesia was provided if required by epidural bolus, and patientcontrolled epidural analgesia was provided for maintenance of analgesia according to usual clinical practice. Statistical Analysis Sample size was determined using the previous recommendation by Tallarida et al.6 who suggested that for efficient design of studies designed to compare interactions of drug combinations, six doses be administered with a minimum of 10 subjects per dose; in our study, we regarded each of the five dose–ratio groups as equivalent to a single drug, therefore a total sample size of 300 patients were chosen. Univariate intergroup comparisons were made using ANOVA or the Kruskall–Wallis test. Categorical data were compared using the chi-square test and the chi-square test for trend. Data for pain scores were analyzed in several steps, repeated for the two main assessment times of 15 and 30 min: 1. Dose–response curves were first determined for the individual drugs using the data for patients who received fentanyl only (group A) or bupivacaine only (group E). As previously described,7 normalized response (effect) was calculated according to the following formula: Response = Initial VAS − Measured VAS pain score pain score Initial VAS pain score ×100% (1) Data were then fitted to a standard rectangular hyperbolic model according to the following formula: Y = E max × Dose (2) Dose + D50 where Y = normalized response, Emax = maximum response which was constrained to equal 100, and D50 = dose giving a half-maximal response. This analysis was performed using nonlinear regression using GraphPad Prism 5.01 (GraphPad Software, Inc., La Jolla, CA). 2. Using the dose–response models for fentanyl and bupivacaine determined above, the predicted additive effects of combinations of fentanyl and bupivacaine were calculated by using the principle of dose equivalence, using previously described methods.8–13 First, the predicted effect from the dose of fentanyl in each combination was calculated using the dose–response equation for fentanyl. This effect magnitude was then substituted into the dose–response equation for bupivacaine to determine the equivalent dose of bupivacaine. The sum of this equivalent dose and the actual dose of bupivacaine given in the combination was then substituted into the dose–response equation for bupivacaine to determine the predicted effect from the combination. This procedure is summarized by the following equation12: E( f + b ) = E max ( fD50 B + bD50 F ) fD50 B + bD50 F + D50 B D50 F (3) where E(f + b) is the predicted additive effect from a combined mixture of fentanyl and bupivacaine in doses f and b, respectively, and D50F and D50B are the respective doses of fentanyl and bupivacaine giving half-maximal effects, from equation (2). Because E(f+b) is derived from experimental data, it has a variance; this was estimated by the delta method,14 using the following equation, as described by Tallarida and Raffa12: ( ) Var E( f +b ) = (bE max ) 2 4 D50 F Var ( D50 B ) T 4 2 D + ( fE max ) 50 B Var ( D50 F ) T (4) where Var(E(f + b)) is the variance of E(f+b), Var(D50F) and Var(D50B) are the respective variances of the estimates of D50F and D50B derived from nonlinear regression, and T = fD50B + bD50F + D50FD50B. 3. Predicted additive effects for a full range of combinations of fentanyl and bupivacaine were calculated using equation (3) and a three-dimensional response surface plot was constructed with axes X = bupivacaine dose, Y = fentanyl dose, and Z = predicted additive effect, using Sigmaplot 2001 for Windows 7.0 (Systat Software Inc., Chicago, IL). 4. Observed (measured) effects were graphically compared with predicted effects by superimposing the means of the observed effects from each experimental fentanyl– bupivacaine combination group upon the predictive additive response surface graph. Points above the surface indicate responses that are greater than that predicted by simple additivity and are indicative of synergism. 5. Observed and predicted effects were compared statistically. For this analysis, because predicted values were derived from curve-fitting procedures rather than enumerated data, simulated datasets for comparison were generated based on the derived parameters. This was achieved by programming syntax using the RV.NORMAL function in IBM SPSS Statistics version 20 (IBM SPSS Inc., Chicago, IL);15 for each fentanyl–bupivacaine combination group, a dataset of 10 was generated from a normal distribution based on the individual parameters (mean and SD) for that group. Observed effect data were then compared with Anesthesiology 2014; 120:1126-361128 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. PERIOPERATIVE MEDICINE predicted effect data using two-way ANOVA. For the latter analysis, the dependent variable was effect and the independent variables included were (1) dose group, (2) observed or predicted, and (3) the interaction of factors (1) and (2). If the interaction between independent variables was not significant on initial analysis, the analysis was repeated with interactions excluded. Bootstrapping was applied with 1,000 replications to derive two-way ANOVA final results. 6. For illustrative purposes, response surfaces for the observed effects were derived by modeling using methods described in appendix. Analyses were performed using Microsoft Excel 2010 (Microsoft Corporation, Redmond, WA), GraphPad Prism 5.01 (GraphPad Software, Inc.), IBM SPSS Statistics version 20 (IBM SPSS Inc.), and Stata 12.1 (STATA; StataCorp LP, College Station, TX). P values less than 0.05 were considered significant. Results Patient recruitment and flow are summarized in figure 1. Twenty-one patients were excluded after entry into the study (unsuccessful CSE procedure [n = 19], protocol violation [n = 2]) and were replaced. Patient characteristics were similar among groups (table 2). The derived dose–response models for individual drugs were: 15 min: 100 × Dose Y = (5) Fentanyl: Dose × 13.82 D50: 13.82 μg Standard error of D50: 3.10 95% CI of D50: 7.61 to 20.00 μg Bupivacaine: 30 min: Fentanyl: Y = 100 × Dose (6) Dose + 1590 D50: 1,590 μg Standard error of D50: 299 95% CI of D50: 993 to 2,188 μg Y = 100 × Dose (7) Dose × 19.83 D50: 9.83 μg Standard error of D50: 2.11 95% CI of D50: 5.61 to 14.10 μg Bupivacaine: 100 × Dose (8) Dose + 2184 D50: 2,184 μg Standard error of D50: 421 μg 95% CI of D50: 95% CI 1,341 to 3,026 μg Y = The dose–response curves are shown in figures 2 and 3. The predicted effect surfaces as functions of fentanyl– bupivacaine combinations, with superimposed mean values of observed experimental effects for 15- and 30-min data, are shown in figures 4 and 5, respectively. Analysis of 15-min data showed that the observed effects were greater than the predicted effects (P < 0.001), with a mean difference averaged across all dose combination groups of 9.1 units (95% CI, 4.1–14.1) of the normalized response. The interaction between the independent variables was not significant (P = 0.74). Analysis of 30-min data also showed that the observed effects were greater than the predicted effects (P = 0.015), with a mean difference averaged across all dose combination groups of 6.4 units (95% CI, 1.2–11.5) of the normalized response. The interaction between the independent variables was not significant (P = 0.15). These results indicate that the interaction between fentanyl and bupivacaine is synergistic. The response surface derived from modeling of observed effect data is shown in figure 6. Details of the model are provided in appendix. Upper levels of sensory changes and side effects that occurred during the study period are summarized in table 3. Two patients had hypotension, both of whom were in group E6 (largest dose of bupivacaine: 4,000 μg, without fentanyl); both patients responded to standard treatment without sequelae. Two patients (one in group B1 and one in group E6) had nausea or vomiting. Four patients had motor block, all of whom were in group E6 (three with Bromage scale 1 and one with Bromage scale 2); one of these patients also had hypotension. Pruritus occurred in 46 patients (15.3%) and was significantly associated with increasing dose of fentanyl in the combination (P < 0.0001, chi-square test for trend). New nonreassuring fetal heart rate tracings occurred in three patients (one in group B2, one in group B4, and one in group E5); these were all transient decreases in fetal heart rate of duration of 1 min or less that resolved spontaneously without sequelae. Discussion The results of our study provide evidence for a synergistic interaction between fentanyl and bupivacaine given intrathecally in combination for labor analgesia. These findings are consistent with the results of previous studies in animals. For example, Maves et al.16 used isobolographic analysis to demonstrate antinociceptive synergism between morphine and lidocaine given as intrathecal boluses to rats that were tested with both somatic and visceral noxious stimuli. Saito et al.5 also confirmed synergism when the same drugs were given intrathecally by infusion to rats over 6 days. Synergism has also been shown for epidural coadministration of opioids and local anesthetics in animals. Kaneko et al.4 administered morphine and lidocaine Anesthesiology 2014; 120:1126-361129 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. Intrathecal Fentanyl and Bupivacaine Synergism Fig. 1. Patient recruitment and flow. Table 2. Patient Characteristics Group A (n = 60) Age, yr Weight, kg Height, cm Cervical dilatation, cm Induction of labor, n Oxytocin use, n 29.3 (4.7) 68.4 (4.7) 156 (12) 2 [1–2] 37 (62%) 27 (45%) Group B (n = 60) 28.9 (4.6) 66.8 (8.1) 159 (6) 2 [1–2] 42 (70%) 27 (45%) Group C (n = 60) 30.1 (4.3) 67.4 (7.5) 157 (5) 2 [1–2.8] 42 (70%) 25 (42%) Group D (n = 60) Group E (n = 60) P Value 29.5 (4.8) 70.0 (14.8) 157 (14) 2 [1.2] 36 (60%) 26(43%) 29.2 (4.2) 66.4 (12.3) 159 (6) 2 [1–2] 42 (70%) 25 (42%) 0.70 0.49 0.32 0.90 0.60 0.99 Values are mean (SD), median [interquartile range], or number (%). Anesthesiology 2014; 120:1126-361130 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. PERIOPERATIVE MEDICINE Fig. 2. Dose–response curves at 15 min for (A) fentanyl and (B) bupivacaine derived by nonlinear regression using a hyperbolic model. The derived dose–response models for individual drugs (doses in micrograms) were: Effect = 100 × dose / (13.82 + dose) for fentanyl, and Effect = 100 × dose / (1,590 + dose) for bupivacaine. epidurally to rats and, also using isobolographic analysis, showed a synergistic interaction for both visceral and somatic antinociception. Several previous studies have reported on the interaction of neuraxial opioids and local anesthetics in humans with equivocal results. Some studies have suggested the presence of a synergistic interaction but without supporting experimental evidence.17,18 In obstetrics, Camann et al.19 investigated the combination of intrathecal sufentanil and epidural bupivacaine given together for labor analgesia. Isobolographic analysis based on ED50 doses was performed, and although this was suggestive of synergism, the 95% CIs for the estimate of ED50 of the combined dose overlapped the line of additivity, and therefore an additive interaction could not be excluded. McLeod et al.20 used up–down sequential methodology to determine the median effective concentrations of levobupivacaine and diamorphine given epidurally for labor analgesia followed by investigation of the interaction of combinations of the drugs. By using isobolographic analysis, they concluded that the interaction was additive. The reason for difference between the findings of the latter study and our results Fig. 3. Dose–response curves at 30 min for (A) fentanyl and (B) bupivacaine derived by nonlinear regression using a hyperbolic model. The derived dose–response models for individual drugs (doses in micrograms) were: Effect = 100 × dose / (19.83 + dose) for fentanyl, and Effect = 100 × dose / (2,184 + dose) for bupivacaine. is uncertain. It is possible that the interaction between opioids and local anesthetic may differ between intrathecal and epidural administration. Alternatively, the difference could be explained by methodological dissimilarity between studies or by differences between the specific opioids and local anesthetics studied. The underlying mechanism by which intrathecally administered fentanyl and bupivacaine interact to produce synergism remains to be determined. Previously, it has been suggested that the interaction between drugs that are agonists at the same receptor is expected to be additive, whereas drugs that act at different receptors are more likely to show a synergistic interaction.21 Our results are consistent with this, because the primary site and mode of action of intrathecally administered opioids and local anesthetics are different. It is also possible that pharmacokinetic factors might also have contributed to our observed results.4 For example, changes to pH or other characteristics of cerebrospinal fluid induced by intrathecal injection of one drug might influence the disposition of the other drug. Further investigation is required to determine whether this possible mechanism is important in the context of our study. Anesthesiology 2014; 120:1126-361131 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. Intrathecal Fentanyl and Bupivacaine Synergism Fig. 4. Predicted and observed effects at 15 min for combinations of fentanyl and bupivacaine. The surface plot shows predicted effect as a function of drug combinations when the interaction between drugs is additive. Superimposed points show mean values of observed effects for experimental drug combinations. Points above the surface are shown as black circles. (A) Standard representation. (B) Graph rotated 80° counterclockwise to reveal points under the surface. Fig. 5. Predicted and observed effects at 30 min for combinations of fentanyl and bupivacaine. The surface plot shows predicted effect as a function of drug combinations when the interaction between drugs is additive. Superimposed points show mean values of observed effects for experimental drug combinations. Points above the surface are shown as black circles. (A) Standard representation. (B) Graph rotated 80° counterclockwise to reveal points under the surface. In our study, we investigated the interaction between drugs by comparing observed experimental effect magnitude with predicted additive effect magnitude. This method of analysis based on comparisons on the effect scale is an alternative to traditional isobolographic analysis and has been described previously in the pharmacology literature.8–13 The method is based on the same principle of dose equivalence which is used with isobolographic analysis. However, it has the added advantage of allowing analysis at multiple effect levels, it provides a useful visual representation, and it is more suited to statistical analysis than isobolographic analysis. When using the principle of dose equivalence, a number of assumptions are made, for example that both drugs are full agonists; modification of the analysis is required if one drug is a partial agonist.12 In our study, we considered both drugs to be full agonists, as evidenced by the observation that some patients who received either drug alone achieved a complete relief of pain (normalized response of 100%). However, it should be noted that fentanyl may not capable of producing a full response in other clinical circumstances, for example, when given for analgesia in advanced or second-stage labor or when given as part of spinal anesthesia for surgery. In these circumstances, the nature of the interaction between opioids and local anesthetics remains to be determined. Our study specifically examined the interaction of fentanyl and bupivacaine given in combination as single boluses Anesthesiology 2014; 120:1126-361132 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. PERIOPERATIVE MEDICINE with the largest dose of bupivacaine and the dose-related incidence of pruritus with fentanyl. Together, reduction of side effects and improvement in analgesic effect seem compelling reasons to recommend combining the drugs in routine clinical practice. Of note, this advantage would also be present if the interaction between fentanyl and bupivacaine were simply additive. Nonetheless, our demonstration of a synergistic interaction reinforces the practice and provides quantitative information and a theoretic basis that informs the common practice of combining opioids and local anesthetics for neuraxial administration. In theory, the optimal combination dose of fentanyl and bupivacaine would balance the relative risks of side effects from the local anesthetic and opioid components; this is likely to vary according to clinical circumstances and patient population and is not addressed by our study. Finally, we modeled the observed effects to generate response surfaces for the data at 15 and 30 min. These were superimposed on the predictive additive surfaces for illustrative purposes as previously described.11,13 Of note, the modeled response surfaces were irregular and not positioned uniformly above the additive surfaces as shown in previous examples of superimposed synergistic and additive response surfaces.11,13 However, the latter depictions were made with the assumption of a constant value of the interaction index between experimental drugs. This may not be a valid assumption, and furthermore, experimental and individual variation in the clinical setting may explain the irregularity of our modeled surfaces. Fig 6. Modeled response surfaces for observed data, superimposed on predicted additive response surface, for data at 15 min (A) and 30 min (B). The modeled surfaces are shown in color to differentiate them from the predicted additive surfaces, with color of shading changing according to vertical height above horizontal plane. using the CSE technique for labor analgesia. Although we have demonstrated a synergistic interaction in this clinical context, further investigation is required to delineate the interaction in other circumstances, for example, when the drugs are given in repeated doses, by infusion, by the epidural route, and for other acute and chronic pain indications. In our study, the magnitude of the mean difference between the observed and predicted effects was modest (<10 units of the normalized response), and the clinical significance of this might be questioned. However, our results (figs. 1 and 2) show that the doses of fentanyl and bupivacaine required to provide complete or near-complete analgesia in this clinical context are relatively large. Large doses of individual drugs are likely to be associated with a greater risk of adverse effects, as evidenced in our study by hypotension and motor block that was observed Acknowledgments The authors thank the midwives of the Labour Ward, Prince of Wales Hospital, Shatin, Hong Kong, China, for their assistance and cooperation. The modeling of the response surfaces detailed in appendix was performed by Jack Lee, Ph.D., Division of Biostatistics, Jockey Club School of Public Health and Primary Care, The Chinese University of Hong Kong, Shatin, Hong Kong, China. The work described in this article was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. 473409). Competing Interests The authors declare no competing interests. Correspondence Address correspondence to Dr. Ngan Kee: Department of Anaesthesia and Intensive Care, The Chinese University of Hong Kong, Prince of Wales Hospital, Shatin, Hong Kong, China. [email protected]. Information on purchasing reprints may be found at www.anesthesiology.org or on the masthead page at the beginning of this issue. Anesthesiology’s articles are made freely accessible to all readers, for personal use only, 6 months from the cover date of the issue. Anesthesiology 2014; 120:1126-361133 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. Intrathecal Fentanyl and Bupivacaine Synergism Table 3. Sensory Levels and Side Effects Group A1 A2 A3 A4 A5 A6 B1 B2 B3 B4 B5 B6 C1 C2 C3 C4 C5 C6 D1 D2 D3 D4 D5 D6 E1 E2 E3 E4 E5 E6 Fentanyl Dose (μg) 2 5 10 15 25 40 1.5 3.75 7.5 11.25 18.75 30 1 2.5 5 7.5 12.5 20 0.5 1.25 2.5 3.75 6.25 10 0 0 0 0 0 0 Bupivacaine Dose (μg) 0 0 0 0 0 0 50 125 250 375 625 1,000 100 250 500 750 1,250 2,000 150 375 750 1,125 1,875 3,000 200 500 1,000 1,500 2,500 4,000 Upper Sensory Level at 15 min (Dermatome) Upper Sensory Level at 30 min (Dermatome L2.5 [L5 to T10] T11.5 [L5 to T6] T7 [L4 to T6] T9 [T11.5 to T9] T8 [T10 to T7] T9 [L4 to T3.5] T10 [L5 to T8] L2 [L2 to T10] T12 [L4 to T8] T11 [L2 to T8] T6.5 [T8 to T4] T7 [T11 to T4] T12.5 [L3 to T8] T10 [L3 to T6] T10.5 [L3 to T7.5] T7 [L2 to T5] T8 [T10 to T5.5] T7 [T10 to T4] T10 [L1 to T6] T12.5 [L3 to T12.5] T12.5 [L2 to T6.5] T9 [L2 to T5] T7 [T10 to T5] T6.6 [T11 to T5] L3 [L3 to T10] L1 [L5 to T9] L2 [L3 to T10.5] T8.5 [T11.5 to T7] T7.5 [T12 to T4.5] T4.5 [T10 to T2] L2 [L4 to T10] T9 [L4 to T6] T7 [L4 to T4.5] T8 [T11 to T4.5] T7.5 [T11 to T5] T6.5 [T11 to T1] T10 [L5 to T7] L2 [L3 to T11] T10 [L3 to T7] T10.5 [L2 to T7.5] T4.5 [T8 to T4] T6 [T12 to T4] T12 [L3.5 to T8] T10.5 [L3 to T6] T11 [L3 to T7.5] T8 [L1 to T5] T6.5 [T11 to T4] T6 [T9 to T2] T10 [L2 to T6.5] T11 [L3 to T9] T11.5 [L1 to T6.5] T10 [L5 to T5] T6 [T10 to T4] T6 [T10 to T5] L1 [L3 to T10] L2 [L4 to T9] T12 [L2 to T10] T8 [T12.5 to T7] T6.5 [T10 to T4] T4.5 [T9 to T2] Hypotension Nausea or Vomiting Motor Block Pruritus New Fetal Heart Rate Changes 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 (20%) 0 0 0 0 0 0 1 (10%) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 (10%) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 (40%) 0 0 3 (30%) 3 (30%) 3 (30%) 4 (40%) 0 1 (10%) 1 (10%) 1 (10%) 5 (50%) 5 (50%) 2 (20%) 0 1 (10%) 4 (40%) 3 (30%) 5 (50%) 0 0 1 (10%) 3 (30%) 0 1 (10%) 0 0 0 0 0 0 0 0 0 0 0 0 0 1 (10%) 0 1 (10%) 0 0 0 0 0 1 (10%) 0 0 0 0 0 0 0 0 0 0 0 0 1 (10%) 0 Data are presented as median (interquartile range) or number (%). Patients classified as having motor block are those with modified Bromage scale ≥1. Appendix To obtain estimated response surfaces for the observed data, models were derived from the data using regression analysis.22 Mathematical equations were fitted to the data, and by substituting the full range of drug doses as independent variables, the response surfaces were generated. The response surfaces are represented by the generic second-order polynomial equation as follows23: Y = b0 + ∑ j =1 b j X j + ∑ ∑ i < j bij X i X j + ∑ j =1 b jj X 2j + ε (1) m m For the current particular data, equation (1) transforms to generic equation (2) below: Y = b0 + b1 X 1 + b2 X 2 + b12 X 1 X 2 + b11 X 12 + b22 X 22(2) Where Y is the predicted response (normalized reduction in visual analogue scale pain score), b0, b1, b2, b12, b11, and b22 are estimated coefficients, X1 and X2 are the coded independent factors (bupivacaine dose and fentanyl dose, respectively), and ε is the random error (noise). The coefficients of the equation were estimated from quadratic model fitting techniques with a generalized linear model using the software Matlab R2013a (The MathWorks, Inc., Natick, MA). ANOVA was used to determine the interactions between the process variables and the responses. The quality of the fit of the polynomial model was expressed by the coefficient of determination R2, and its statistical significance/model adequacy was checked by Fisher F test. Model terms were evaluated by the P value (probability) with 95% confidence level. Homogeneity of the variance and significance of the polynomial coefficients were tested by the G-test and coefficient significance index-test, respectively. The estimated coefficients of the models are detailed below: Anesthesiology 2014; 120:1126-361134 Downloaded From: http://anesthesiology.pubs.asahq.org/pdfaccess.ashx?url=/data/journals/jasa/930982/ on 06/18/2017 Ngan Kee et al. PERIOPERATIVE MEDICINE A. 5-min Data b0 (intercept) b1 b2 b12 b11 b22 Estimate Standard Error tStat P Value 7.6237 0.03324 3.6766 −0.00094189 −4.3561e-06 −0.050864 0.9618 0.0015483 0.15483 7.0323e-05 4.0016e-07 0.0040016 7.9265 21.469 23.745 −13.394 −10.886 −12.711 3.7146e-08 3.5663e-17 3.5238e-18 1.2441e-12 9.1356e-11 3.7634e-12 Number of observations: 30, error degrees of freedom: 24. Root mean squared error: 2.22. R-squared: 0.991, adjusted R-squared: 0.989. F-statistic vs. constant model: 528, P value = 1.03e-23. ANOVA Results for Model Total Model Linear Nonlinear Residual SumSq DF MeanSq 13,169 13,050 11,688 1,362.1 118.74 29 5 2 3 24 454.11 2,610.1 5,844.2 454.04 4.9475 F 527.56 1,181.2 91.772 P Value 1.034e-23 1.0702e-24 2.7385e-13 B. 30-min Data b0 (intercept) b1 b2 b12 b11 b22 Estimate Standard Error tStat P Value 8.6429 0.025376 4.5188 −0.00090739 −2.8519e-06 −0.069667 1.2736 0.0020503 0.20503 9.3122e-05 5.299e-07 0.005299 6.7861 12.377 22.04 −9.7441 −5.3821 −13.147 5.1005e-07 6.576e-12 1.9551e-17 8.1356e-10 1.5846e-05 1.8456e-12 Number of observations: 30, error degrees of freedom: 24. Root mean squared error: 2.95. R-squared: 0.985, adjusted R-squared: 0.982. F-statistic vs. constant model: 319, P value = 4.04e-21. ANOVA Results for Model Total Model Linear Nonlinear Residual SumSq DF MeanSq F P Value 14,033 13,825 12,123 1,701.9 208.21 29 5 2 3 24 483.9 2,765 6,061.5 567.32 8.6755 318.71 698.69 65.393 4.0434e-21 5.3708e-22 1.0752e-11 References 1. 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