Download Synergistic Interaction between Fentanyl and

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
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May 2014
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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.
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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
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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
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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 (%).
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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.
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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
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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
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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:
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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
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