PK-PD22
Research Paper
Pharmacokinetic–Pharmacodynamic Modeling of the Effectiveness and Safety of Buprenorphine and Fentanyl in Rats
Ashraf Yassen,1Erik Olofsen,2Jingmin Kan,1Albert Dahan,2and Meindert Danhof 1,3,4
Received February 27,2007;accepted August 20,2007;published online October 4,2007
Objective.Respiratory depression is a serious and potentially life-threatening side-effect of opioid therapy.The objective of this investigation was to characterize the relationship between buprenorphine or fentanyl exposure and the effectiveness and safety outcome in rats.
Methods.Data on the time course of the antinociceptive and respiratory depressant effect were analyzed on the basis of population logistic regression PK–PD models using non-linear mixed effects modeling software (NONMEM).The pharmacokinetics of buprenorphine and fentanyl were described by a three-and two-compartment model,respectively.A logistic regression model (linear logit model)was used to characterize the relationship between drug exposure and the binary effectiveness and safety outcome.Results.For buprenorphine,the odds ratios (OR)were 28.5(95%CI,6.9–50.1)and 2.10(95%CI,0.71–3.49)for the antinociceptive and respiratory depressant effect,respectively.For fentanyl these odds ratios were 3.03(95%CI,1.87–4.21)and 2.54(95%CI,1.26–3.82),respectively.
Conclusion.The calculated safety index (OR antinociception /OR respiratory depression )for fentanyl of 1.20suggests that fentanyl has a low safety margin,implicating that fentanyl needs to be titrated with caution.For buprenorphine the safety index is 13.54suggesting that buprenorphine is a relatively safe opioid.KEY WORDS:effectiveness;PK–PD;respiratory depression;safety;utility function.
INTRODUCTION
Worldwide millions of people suffer from severe (un-controlled)and sometimes incurable pain and are dependent on the daily intake of analgesic drugs to relief their pain.Opioid analgesics are among the most effective agents currently available for treating postoperative and chronic (malignant)pain.Apart from their analgesic actions,all opiates produce side-effects (1,2).Although most of these side effects are mild in nature and have little clinical relevance,respiratory depression is a potentially life-threatening complication of opiate therapy (3,4).Therefore,careful titration of the opioid dose to the desired analgesic effect is essential to avoid respiratory depression (5).This applies particularly to potent opioid analgesics.
Fentanyl is a m -opioid agonist which is frequently used both in anesthesia and for the treatment of acute and chronic pain (6–8).In pharmacological terms,fentanyl is a high-efficacy full agonist at the m -opioid receptor with steep concentration–response curves (9,10).Due to the relatively narrow therapeutic window of fentanyl the risk of severe fatal
respiratory depression is rather large.As a result fentanyl dosing needs to be carefully titrated to the optimal analgesic effect (11).To facilitate fentanyl dosing,advanced drug delivery systems,aiming at an improved selectivity of action have been introduced.Slow release preparations and trans-dermal patches for opiates are examples of drug delivery systems which have been developed with the aim to optimize opiate delivery and to reduced side-effects (12).
Another approach towards the reduction of side effects is the use of compounds with a more favorable effectiveness–safety balance.In this respect it is of interest that in theory,partial agonists can have a greater selectivity of action than full agonists (13).Considering the potential lethality of opioid-induced respiratory depression,partial agonists at the m -opioid receptor provide potential advantages over full agonists,in terms of the effectiveness–safety balance for the treatment of pain.Buprenorphine is a semi-synthetic opioid,which has been in clinical use for the treatment of acute and chronic pain since 1979(14).Recently,it has been demon-strated that buprenorphine behaves as a partial agonist with respect to respiratory depression both in rats (15)and in humans (16),consistent with its partial agonistic behavior in in vitro bio-assays (17).An important consequence of the observed F ceiling effect _is that an overdose of buprenorphine is less likely to cause severe and potentially life-threatening respiratory depression.Interestingly,for the antinociceptive effect,buprenorphine displays no ceiling effect in the same concentration range in which maximum respiratory depres-sion is elicited,indicating that within the therapeutic concen-tration range buprenorphine acts as a full agonist with regard
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0724-8741/08/0100-0183/0#2007Springer Science +Business Media,LLC
Pharmaceutical Research,Vol.25,No.1,January 2008(#2007)DOI:10.1007/s11095-007-9440-z
1
Division of Pharmacology,Gorlaeus Laboratories,Leiden/Amsterdam Center for Drug Research,P.O.Box 9502,2300RA,Leiden,The Netherlands.2
Department of Anesthesiology,Pain and Anesthesia Research Unit,Leiden University Medical Center,Leiden,The Netherlands.3
LAP&P Consultants BV,Leiden,The Netherlands.4
To whom correspondence should be addressed.(e-mail:m.danhof@lacdr.leidenuniv.nl)
to the antinociceptive effect(18,19).Differences in receptor expression in the distinct brain tissues can explain why buprenorphine behaves as partial agonist for one effect (respiratory depression,in brain tissue with no receptor reserve)and as a full agonist for another effect(antinocicep-tion,in brain tissue with receptor reserve;20).
The objective of this study was to characterize the effec-tiveness and safety of buprenorphine and fentanyl in rats using non-linear mixed effects logistic regression analysis. Therapeutic utility functions(21–24)were constructed to assess the effectiveness/safety balances of buprenorphine and fentanyl.
MATERIALS AND METHODS
Animal data for the PK–PD analysis of the safety and effectiveness of buprenorphine and fentanyl were obtained from two previously published studies on the PK–PD relation-ships of buprenorphine and fentanyl for the antinociceptive (18)and respiratory depressant effect(15).The protocols of the investigations were approved by the Ethical Committee on Animal Experimentation of Leiden University.
Briefly,the experimental details of the investigations were as follows.Male Wistar rats(Charles River BV,Zeist, The Netherlands),weighting initially225–250g,were used in the studies.Two days before the start of the experiment, indwelling cannulae were implanted in the right femoral artery for the serial collection of blood samples and in the right jugular vein for drug administration.Surgical procedures were performed under anesthesia with an intramuscular injection of 0.1mg/kg medetomide hydrochloride(Domitor,1mg/ml, Pfizer,Capelle a/d IJssel,The Netherlands)and1mg/kg Ketamine base(Ketalar50mg/ml,Parke-Davis,Hoofddorp, The Netherlands).
Different doses of buprenorphine(0.025to0.1mg/kg) and fentanyl(0.015–0.04mg/kg)were tested to characterize the concentration–antinociceptive effect relationships.For respiratory depression,buprenorphine and fentanyl were tested in the dose ranges0.025–0.3mg/kg and0.03–0.085mg/kg, respectively.Buprenorphine and fentanyl were administered via a zero-order intravenous infusion(infusion duration20–40 min).Antinociception or respiratory depression was measured at pre-defined time points.Serial arterial blood samples were collected at fixed time-points.50m l plasma was separated from the blood by centrifugation and the plasma samples were stored at j20-C prior to analysis.
Measurement of Antinociception
A tail flick analgesia meter(Columbus Instruments, Columbus,Ohio,USA)was used to determine the pain sensitivity in the control and the drug-treated rats.Radiant heat was applied using a shutter-controlled lamp as a heat source focused on a spot located6.5to7.5cm from the tip of the tail.The intensity of the beam was set at a level producing basal latency times between 2.5and 3.5s.To prevent tissue injury,the cut-off time was fixed at10s.A digital response time indicator with a resolution of0.1s measured the time between activation of the light beam and the tail flick.Measurement of Respiratory Depression
Respiratory depression was determined in unrestrained,
conscious animals using whole-body plethysmography for the
quantification of ventilation(Model PLY3223,Buxco Elec-
tronics Inc.,UK).Briefly,the animals were placed in a
plethysmograph,consisting of a measurement chamber and
an integrated reference chamber to correct for atmospheric
disturbances.Both chambers were connected to a differential
pressure transducer(TRD5700,Buxco Electronics Inc.,UK).
In each animal the effects of opiates and vehicle on
ventilation were assessed at an inhaled concentration of
6.5%carbon dioxide on a background of normoxia(20%
oxygen).The inhalation of the gas mixture lasted5min to
ensure that steady-state ventilation had been reached.Tidal
volume(V T),breathing frequency(RR)and minute ventila-
tion(V i,where V i=V T?RR)were obtained from changes in chamber pressure using a low-pressure differential transducer
connected to preamplifier modules(MAX2270,Buxco Elec-
tronics Inc.,UK).During the experiment body temperature
was maintained at37.5-C using heating pads.Body temper-
ature was monitored continuously by radiotelemetry(model
RPC-1,Data Sciences International,USA). Determination of Buprenorphine and Fentanyl Concentrations
Two different chemical assays were used for the deter-
mination of buprenorphine and fentanyl plasma concentra-
tion in rats.The details of these assays have been described
elsewhere(18).Briefly,for buprenorphine,to50m l plasma25m l
internal standard(4m g/100ml2H4-buprenorphine)was
added.Subsequently,25m l concentrated ammonia was
added and the samples were extracted by liquid/liquid
extraction with600m l tert.-butyl methyl ether(MTBE).The
chromatographic system consisted of an Agilent HP1100
HPLC system(Agilent,Waldbronn,Germany)coupled to an
API4000LC/MS/MS system(Applied Biosystems,Darmstadt,
Germany).Chroma-tography was performed on a precolumn
(Metaguard Polaris3m C18A2mm,Varian Darmstadt,
Germany)guarded Synergi4m Hydro-RP80A column75?2
mm(Phenomenex,Aschaffenburg,Germany).The lower limit
of quantification(LLOQ)was0.047ng/ml for buprenorphine.
The accuracy ranged from99.4to102.1%.The precision,
expressed as coefficient of variation,ranged from2.2to6.4%
for concentrations between0.14and8.9ng/ml.
For fentanyl,to50m l plasma25m l internal standard
(14.8ng/ml2H5-fentanyl)was added.After adding10m l
concentrated ammonia the samples were extracted by liquid/
liquid extraction with600m l tert.-butyl methyl ether(MTBE).
The chromatographic system consisted of an Agilent HP1100
HPLC system(Agilent,Waldbronn,Germany)coupled to an
API3000LC/MS/MS system(Applied Biosystems,
Darmstadt,Germany).Chromatography was performed on a
precolumn(Metaguard Polaris3m C18A2mm,Varian
Darmstadt,Germany)guarded Atlantis C18column3m
100mm?2.1mm(Waters,Eschborn,Germany).The lower
limit of quantification(LLOQ)was0.118ng/ml.The accuracy
ranged from87.0to96.1%and the precision from1.9to4.0%
for concentrations in the range from0.4to50.2ng/ml.
184Yassen et al.
PK–PD Modeling Procedure
The pharmacokinetic and pharmacodynamic parameters of fentanyl and buprenorphine were estimated using non-linear mixed-effects modeling as implemented in the NON-MEM software(version V,level1.1;25).For pharmacokinetic analysis,a population analysis approach using the first order conditional estimation method with h–(interaction(FOCE interaction)was undertaken.For logistic regression pharma-codynamic analysis,the maximum likelihood estimation algorithm in NONMEM with the Laplacian method(FOCE) and the likelihood option was used to estimate the probabil-ity of a certain event occurring.All fitting procedures were performed on an IBM-compatible computer(Pentium IV, 1,500MHz)running under Windows XP with the Fortran compiler Compaq Visual Fortan version6.1.An in-house available S-Plus6.0(Insightful Corp.,Seattle,WA,USA) interface to NONMEM was used for data processing and management(including tools to perform non-parametric bootstrap)and graphical data display.Model comparisons were based on the objective function values in NONMEM using the likelihood ratio test.The significance level was set at a=0.01,which corresponds to a reduction of 6.6U in objective function value(OFV;c2distribution)to discriminate between two nested structural models after inclusion of one additional parameter.Furthermore,the goodness-of-fit of the pharmacodynamic models was evaluated by simulating values of the effectiveness and safety outcome from the raw data. The simulations were repeated a total of a100times.The proportions of observed and simulated scores were plotted versus the25th,50th(median),75th quantiles of the pooled opioid biophase concentrations.
Pharmacokinetic Analysis
One,two and three-compartment linear models were evaluated to characterize the time course of buprenorphine and fentanyl concentration in plasma.The pharmacokinetic parameters were assumed to be log-normally distributed and therefore an exponential distribution model was used to account for inter-individual variability.Proportional error models were used to quantify residual error.Individual Bayesian pharmacokinetic parameter estimates obtained from the final population pharmacokinetic model served as input for pharmacodynamic model to predict fentanyl and bupre-norphine concentrations at observation scores time points (two-stage approach).The extent of Bayesian shrinkage was evaluated for each parameter in the final population pharma-cokinetic models of buprenorphine and fentanyl by(26):
Shrinkage?1àSD PK parameter
4PK parameter
e1T
in which the SD is the standard deviation of the individual estimates of h for each pharmacokinetic parameter and W PK parameter is the estimate of the standard deviation of the estimated population variance.
To quantify the precision of the pharmacokinetic param-eters estimates a non-parametric bootstrap was performed.Briefly,one thousand bootstrap replicates were generated by sampling randomly from the original data set with replace-ment.Subsequently,the data sets were fitted one at the time to the final population PK model.The mean,standard error, coefficient of variation and the lower and upper95% confidence intervals of the model parameter values were calculated and compared to the typical model parameter values from the original study.
Pharmacodynamic Data Analysis
The effectiveness(antinociception)and safety(respira-tory depression)variable were modeled as dichotomous category variables.The following transformation statements were applied to convert the continuous data into logical two-valued data:
–If antinociceptive effect Q10s,then observation score is1(a yes response;complete antinociception)else0(a no response;no antinociception)
–If respiratory depressant effect Q50%,then observa-tion score is1(a yes response;severe respiratory depression) else0(a no response;no respiratory depression)
Logistic regression analysis was performed to determine the relationship between opioid concentration at the biophase (C e)and its respective antinociceptive or respiratory depres-sant effect in rats.The opioid biophase concentration was predicted using a standard effect–compartment model(27):
dC e
dt
?k e0áC pàC e
àá
e2T
in which C p represents the opioid plasma concentration,C e the opioid concentration at the biophase and k e0the first-order rate constant for biophase distribution.
A linear logit model was fitted to relate the probability of having complete antinociception or respiratory depression to drug exposure at the biophase:
P
Y ij?1
eT?
1
1teàf C eeT
eT
e3T
The logit transformation ensures that the probability P will fall between0and1,f(C e)is a linear function of drug exposure at the biophase:
f C e
eT?!t C e
eTe4T
in which a and b are the intercept and slope of the regression equation and C e is the drug biophase concentration.Incor-poration of individual random effects,h with mean zero and variance w2,was tried by assuming exponential distributions for the regression parameters(a and b).For each concentration–effect relationship,the odds ratio was calculated using the exponent of the estimated slope b(e b).The odds ratio is defined as the change in the estimated odds of the outcome when the biophase concentration increases by1U.Bootstrap analysis was performed with the final logistic regression pharmacodynamic models to construct the95%confidence intervals of the calculated odds ratios.
185
Effectiveness and Safety of Buprenorphine and Fentanyl
Finally,an overall ordinal utility function was constructed to evaluate the effectiveness/safety balance of buprenorphine and fentanyl as a function of drug exposure.The utility function was determined by the sum of the weighted probabilities of an efficacious and safe outcome.The effectiveness and safety variables were weighted equally.For the desirable antinoci-ceptive effect the weight factor was positive and for respiratory depression the factor was negative.The effectiveness/safety balance,characterized by the utility function was thus expressed as Pr{effectiveness}–Pr{safety},where Pr{x}is the probability of outcome x(28).A negative value of the utility function indicates that the respiratory depressant effect dominates and a positive value suggests that the desired antinociceptive effect dominates.
RESULTS
Pharmacokinetics
A three-compartment model adequately described the time course of the concentration profiles of buprenorphine after intravenous administration in rats.Inter-individual vari-ability was estimated for all pharmacokinetic parameters except for Q3.The parameter estimates with their corresponding standard error(SE)are summarized in Table I.For fentanyl,a two-compartment pharmacokinetic model with inter-animal variability on all pharmacokinetic parameters best described the disposition in plasma.The parameter estimates with their corresponding standard error(SE)are summarized in Table II. Estimates of shrinkage were low and ranged from0.02(Cl)to 0.19(V1)for buprenorphine and from0.03(Cl)to0.12(V2)for fentanyl,suggesting that the individual pharmacokinetic parameter estimates of buprenorphine and fentanyl are robust. For comparison,values of shrinkage close to1indicate poor individual estimates of the pharmacokinetic parameters.The goodness-of-fit plots(predicted/individual predicted versus observed concentrations,population predicted concentrations versus weighted residuals for population predictions(WRES) and time versus weighted residuals for population predictions (Figs.1and2)indicated that the pharmacokinetic models adequately described the concentrations of buprenorphine and fentanyl.Finally,bootstrap analysis showed that the95%CI of the pharmacokinetic parameter estimates and their random effect variables,except for w2V2of buprenorphine,did not overlap their respective null values(Tables I and II). Pharmacodynamics
After transformation of the continuous data into cate-gories,615(35animals)and444(32animals)observations of response/no response scores to complete antinociception and severe respiratory depression,respectively,were available for analysis of the pharmacodynamic effect of buprenorphine in rats.For fentanyl,486(40animals)and216(32animals) observations were included for pharmacodynamic analysis for the antinociceptive and respiratory depressant effect,respec-tively.For the antinociceptive effect of buprenorphine,the values of parameters characterizing the linear logistic re-gression model were j13.3(95%CI,j16.08to j10.52)for the intercept a and3.35(95%CI,2.59–4.11)for the slope b of the regression equation.The odds ratio of complete anti-nociception occurring is equal to e3.35,corresponding to an odds ratio of28.5(95%CI, 6.9–50.1).The odds ratio is statistically different from1,indicating that the probability of complete antinociception occurring is dependent on the buprenorphine plasma concentration.Inter-animal variability, w2was estimated for b and was0.130(95%CI,0.08–0.181). For respiratory depression,the typical values estimates for
Table I.Parameter Estimates(95%CI)for the Final Population Pharmacokinetic Model of Buprenorphine
Original Data1,000Bootstrap Replicates
Typical Estimate Inter-Animal Variability w2Typical Estimate Inter-Animal Variability w2 Cl(ml/min)18(16.3–19.7)0.128(0.108–0.148)18(16.1–19.9)0.125(0.086–0.164)
V1(ml)110(77–142)0.936(0.348–1.52)108(65–150)0.914(0.267–1.56)
V2(ml)370(312–428)0.274(0.117–0.431)400(320–480)0.353(j0.041–0.745)
V3(ml)1,200(1,009–1,391)0.337(0.200–0.474)1,181(907–1,455)0.239(0.063–0.415)
Q2(ml/min)30(26–34)–30.3(26–35)–
Q3(ml/min)11(9.6–12.4)0.172(0.094–0.250)10.2(7.8–12.6)0.128(j0.048–0.304) Proportional error(%)0.032(0.022–0.042)0.033(0.021–0.045)
Table II.Parameter Estimates(95%CI)for the Final Population Pharmacokinetic Model of Fentanyl
Original Data1,000Bootstrap Replicates
Typical Estimate Inter-Animal Variability w2Typical Estimate Inter-Animal Variability w2 Cl(ml/min)17.0(16.9–18.1)0.060(0.040–0.080)16.6(15.7–17.4)0.058(0.038–0.078)
V1(ml)250(218–282)0.227(0.129–0.325)255(222–287)0.224(0.126–0.322)
V2(ml)440(404–476)0.080(0.041–0.119)444(409–479)0.077(0.039–0.116)
Q(ml/min)9.7(8.3–11.1)0.224(0.126–0.312)9.7(8.3–11.1)0.216(0.118–0.314) Proportional error(%)0.034(0.0240.044)0.034(0.024–0.044) 186Yassen et al.
the intercept(a)and slope(b)of the regression equation were j5.22(95%CI,j6.54to j3.90)and0.744(95%CI, 0.083–1.405),respectively.The odds ratio of severe respiratory depression occurring is equal to e0.774,corresponding to an odds ratio of 2.10(95%CI,0.71–3.49).The odds ratio is not statistically different from1,indicating that the probability of observing severe respiratory depression does not change within the studied buprenorphine biophase concentration range.Inter-animal variability,w2was estimated for b and was1.82(95%CI,0.57–3.07).The odds ratio estimates of buprenorphine obtained from the logistic regression analysis are shown in Table III.Goodness-of-fit was evaluated by the objective function value(OFV)and by simulating the raw data from the final pharmacodynamic logistic regression model. The proportion of the simulated values of the outcome scores for buprenorphine agreed well with the observed scores as can be seen in Fig.3.For fentanyl,the values of the parameters a and b were j8.77(95%CI,j11.49to j6.05)and1.11(95% CI,0.726–1.494),respectively.The odds ratio for the antinociceptive effect was3.03(95%CI,1.87–4.21)and was significantly different from1(p<0.05).Inter-animal variability, w2was estimated for b and was0.0839(95%CI,j0.01–0.177). For the respiratory depressant effect the values of the logistic regression parameters a and b were j5.86(95%CI,j8.17 to j3.55)and0.930(95%CI,0.430–1.430).The odds ratio for the occurrence of severe respiratory depression was2.54(95% CI,1.26to3.82).Inter-animal variability,w2was estimated for b and was0.193(95%CI,0.085to0.300).The odds ratio estimates of fentanyl obtained from the logistic regression analysis are shown in Table III.The goodness-of-fit plots for fentanyl are shown in Fig.4.In the final analysis,the half-time of biophase distribution was included in the final
model.
Although its value is not significantly different from zero,its inclusion significantly improved the fits as judged by a significant drop(>6.6points)in objective function value.
Finally,a therapeutic overall utility function was con-structed for the effectiveness/safety balance of buprenor-phine and fentanyl.In Fig.5,it is shown that in the measured concentration range,the utility function of buprenorphine is positive.This indicates that the antinociceptive effectiveness of buprenorphine exceeds the risk of the occurrence of respiratory depression.For fentanyl,the utility function is negative in the measured concentration range,indicating that fentanyl produced more respiratory depression than bupre-norphine.At relatively high concentrations the utility func-tion is close to zero for fentanyl and buprenorphine, suggesting that the probability of a desired and side-effect are equal.DISCUSSION
Population PK–PD models of buprenorphine and fen-tanyl,administered intravenously with plasma concentration as the exposure variable and the response to complete antinociception or severe respiratory depression as a binary outcome variable were developed to evaluate the effective-ness and safety of these opiates in rats.
The assignment of observation scores0and1to the pharmacodynamic safety outcome to indicate B no^or B severe^respiratory depression,respectively,was arbitrarily chosen and is a matter of discussion.Despite its severity, there is no clear and unifying definition for respiratory depression in the literature(29).Partly this is related to the difficulty of measuring opiate-induced respiratory depression in a reliable and strictly quantitative manner.
Although
various biomarkers for respiratory depression have been proposed,including the measurement of respiratory rate (30)and arterial P a CO 2values (31),many of these biomarkers are rather subjective and only provide a qualitative assessment of respiratory depression (32).Furthermore,many of the tech-niques used to characterize respiratory depression,may well underestimate the respiratory depressant effect of opiates (11).In contrast,minute ventilation measured by whole-body plethysmography or the dynamic end-tidal forcing technique has been shown to be an objective,reproducible and sensitive measure of the respiratory effects of opiates (33).
More
Fig.3.Goodness-of-fit plots of the logistic regression model for buprenorphine.Observed (left panels )and simulated (right panels )values of the buprenorphine _s effectiveness (upper panels )and safety (lower panels )outcome for the different concentration categories.Simulations were repeated in total a 100times.The concentrations were divided in the following categories (scores at C e =0,between 0and 25th quantiles,25th–50th quantiles,50th–75th quantiles,>75th quantiles;h score=0and v score=1).
Table III.Odds Ratio and Half-Time of Biophase Distribution (T 1/2,ke0)Estimates (95%CI)Obtained From the Logistic Regression
Pharmacodynamic Analysis for Buprenorphine and Fentanyl T 1/2,ke0(min)
Buprenorphine Fentanyl Antinociception
86.4(71.3–101.5) 6.08(4.43–7.73)Respiratory depression 109(49–169) 1.97(j 0.32–4.26)Odds ratio
Antinociception
28.5(6.9–50.1) 3.03(1.87–4.21)Respiratory depression
2.10(0.71–
3.49)
2.54(1.26–
3.82)
189
Effectiveness and Safety of Buprenorphine and Fentanyl
importantly,minute ventilation as a biomarker of respiratory depression has been shown to reflect the functioning of various opiates at the m -opioid receptor in a strictly quantitative manner (15,16,34).Since measurement of minute ventilation allows for a quantitative assessment of respiratory depression,we defined respiratory depression as a decrease in ventilation of more than 50%relative to baseline.For the antinociceptive effect,reaching the cut-off tail flick latency time is frequently used to indicate that complete antinociception is reached (35).In the present investigation,therefore,the same definition was used to indicate complete antinociception.PK–PD analysis revealed marked difference in the kinetics of onset and offset for buprenorphine versus fentanyl.The biophase distribution of buprenorphine was significantly slower than for fentanyl.On the basis of the physico-chemical properties (buprenorphine being more lipophilic than fentanyl;16)it can be expected that bupre-norphine displays slower biophase distribution.Furthermore,buprenorphine _s slow receptor association/dissociation kinet-ics contributes to the delay in the onset of buprenorphine _s analgesic and respiratory depressant effect.Previously it was shown that the delay in buprenorphine _s antinociceptive
and
Fig.4.Goodness-of-fit plots of the logistic regression model for fentanyl.Observed (left panels )and simulated (right panels )values of the buprenorphine _s effectiveness (upper panels )and safety (lower panels )outcome for the different concentration categories.Simulations were repeated in total a 100times.The concentrations were divided in the following categories (scores at C e =0,between 0and 25th quantiles,25th–50th quantiles,50th–75th quantiles,>75th quantiles;h score=0and v score=1).
190Yassen et al.
respiratory depressant effect is mainly caused by biophase distribution rather than slow receptor association/dissociation kinetics(15,18).
Beside the kinetics of the opioid action,PK–PD analysis yielded important information on the effectiveness and safety outcome of fentanyl and buprenorphine.The odds ratios which had been calculated for the estimated probability of a complete antinociceptive or severe respiratory depressant event can be used as a measure of pharmacological effect size. For fentanyl,the calculated odds ratios for the antinociceptive and respiratory depressant effect were3.03(95%CI,1.87–4.21) and2.54(95%CI,1.26–3.82),respectively,suggesting that increasing the fentanyl concentration with1ng/ml,there is a 3.03and2.54greater chance of having complete antinociception or respiratory depression,respectively.In terms of probabilities rather than changes in odds,the estimated risk of severe respiratory depression increased from10.5to22.9%when the concentration was increased from4to5ng/ml.In addition,the probability of achieving complete antinociception increased from0.4to1.2%.The estimated values of the odds ratio for antinociception(3.03)and respiratory depression(2.54)are nearly identical and suggest that fentanyl displays almost no in vivo tissue selectivity.Accordingly,the ratio of the two OR_s (antinociception/respiratory depression)is equal to 1.20 (3.03:2.54)for fentanyl.This ratio can be used as a safety index and suggests that fentanyl displays no selectivity of action.
For buprenorphine,the odds ratios were28.5(95%CI, 6.9–50.1)and2.10(95%CI,0.71–3.49)for the antinociceptive and respiratory depressant effect,respectively.The large difference in calculated odds ratio_s for the antinociceptive and respiratory depressant effect indicates that buprenorphine_s displays a varying degree of tissue selectivity.The safety index is equal to13.54(28.5:2.10)and suggests a favorable selectivity of action.This provides further evidence,in contrast to fentanyl,for the relative safety of buprenorphine when administered in therapeutic analgesic doses.In various receptor binding studies, buprenorphine has been shown to act as a partial agonist at the m-opioid receptor(17).Partial agonists typically require complete receptor occupancy for maximal response(36).For the respiratory depressant effect,the in vitro partial agonist activity correlates well its in vivo respiratory depressant effect, characterized by ceiling at higher concentrations(37,38).
Buprenorphine and fentanyl are m-opioid agonists with distinct pharmacological properties.Since fentanyl behaves as full agonist its in vivo potency for respiratory depression and antinociception are determined by both the affinity and the intrinsic efficacy at the m-opioid receptor In contrast,for the partial agonist buprenorphine the in vivo potency is deter-mined solely by its affinity for the m-opioid receptor(39). These differences between efficacy-and affinity-driven ago-nism may have major implications for the therapeutic utility of opioids.Therapeutic utility is a measure of the effectiveness of drugs.Given this measure,one can speak of increasing or decreasing utility and thereby explain pharmacological behav-ior of a drug in terms of attempts to optimize pharmacother-apy.As recently discussed by Cullberg et al.(2005;28)the most adequate representation of drug_s effectiveness/safety balances with a utility function remains a matter of debate.In the present study,the therapeutic utility function is equal to the sum of the weighted probabilities of an effective(anti-nociception)and a safety(respiratory depression)outcome. The effect measures,antinociception and respiratory depres-sion,were weighted equally and this seems justified,given that respiratory depression is a potentially life-threatening side-effect with an acute time course.Furthermore,for the construction of the utility function the continuous antinoci-ceptive and respiratory depressant continuous effect variables were transformed into dichotomous data.This type of data transformation will entail loss of pharmacodynamic informa-tion.Especially the kinetics of onset and offset of the opioids effect can be estimated less accurately.However,the kinetics of onset and offset of buprenorphine_s antinociceptive and respiratory depressant effect have been characterized previous-ly(15,18).Using a continuous measure of respiratory depres-sion and antinociception one can still construct utility functions. However,using this approach it requires a clear definition of an E max value for respiratory depression and antinociception.For antinociception no E max could be identified in the studied dose range.As a consequence the therapeutic utility of buprenor-phine can be overestimated when the continuous variables were used for the construction of a utility function.Therefore, the continuous data were transformed into dichotomous data enabling the definition of clear cut-offs.
An intriguing question remains whether the calculated safety margins and therapeutic utilities of buprenorphine and fentanyl are similar in rats and humans.The calculated therapeutic utility is determined by the opioid_s affinity and intrinsic effectiveness at the m-opioid receptor.In theory,these two pharmacological terms are drug-specific parameters,both of which are expected to be similar between man and rat for the m-opioid receptor(high degree of receptor homology). Recently,it was shown that indeed the drug-specific param-eters of buprenorphine are similar in rats and humans for both the antinociceptive and respiratory depressant effect(40).It is therefore advocated that the calculated therapeutic utility
for
buprenorphine,in line with its clinical experience,is similar in rats and humans.Since fentanyl is a full m-opioid agonist for both antinociception and respiratory depression,produc-ing maximal pharmacological responses in rats and humans, it is expected that the therapeutic utility of fentanyl is not significantly different between these two species.On the basis of the calculated therapeutic utility of fentanyl in rats it can be concluded that fentanyl has a narrow therapeutic window in man(low safety index)requiring fentanyl to be administered cautiously to patients.In fact,a series of recent case-reports on fentanyl-induced severe respiratory depres-sion and death in patients confirm fentanyl_s low safety margin underscoring the importance of careful dose titration of high-effectiveness opioids like fentanyl(41).For bupre-norphine,the utility function also approaches zero at relatively high concentration upon acute exposure.It should be noted, however,that this is inherent to the definition of the occurrence of respiratory depression in the present study.Previously it has been shown that the maximum respiratory depressant effect of buprenorphine is approximately48to55%versus90to100% for fentanyl,suggesting that although the utility function becomes zero,the absolute degree of respiratory depression is less for buprenorphine than for fentanyl.Furthermore,the calculated safety index indicates that buprenorphine has a wider therapeutic window,allowing for the administration of relatively high doses of buprenorphine.Reported safety incidences related to buprenorphine are low and deaths due to buprenorphine misuse are rare.This makes buprenorphine a particularly safe opioid with an increased margin of safety(42).
As evaluation of drug safety becomes increasingly more important in contemporary drug development,there will be a clear shift towards the application of PK/PD modeling to predict drug safety outcomes.As more mechanistic bio-markers become available to assess drug safety,this gives rise to the development of more sophisticated and mechanistic PK/PD models to assess drug effectiveness/safety balances. Clearly,this also influences the selection and structure of therapeutic utility functions to assess the effectiveness/safety balances of drugs under development.To this end,utility function will become less descriptive and more predictive.Also, the potential utility of mechanistic biomarkers to facilitate drug development may lead to better techniques to assess the safety in humans more in line with those used in animals,yielding more accurate animal to human effectiveness/safety extrapola-tion in an early stage of drug development.
CONCLUSION
Logistic regression pharmacodynamic models were de-veloped to predict the safety and effectiveness outcome of buprenorphine and fentanyl in rats.Buprenorphine has been shown to display ceiling in respiratory effects but not in analgesia upon acute administration.This explains the relatively high safety index and indicates that the ceiling respiratory effect contributes to the safety profile of bupre-norphine.For fentanyl a narrow therapeutic window has been observed,complicating fentanyl dose titration to the optimum analgesic effect without the occurrence of severe respiratory depression.The modeling of the effectiveness/safety balances is a first quantitative assessment of the effectiveness/safety of opiates and these results are in good agreement with the general perception on the safety issues of buprenorphine and fentanyl,underscoring the importance of the development of PK–PD models to quantitatively assess the rationality of pharmacotherapeutic utilities.
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Effectiveness and Safety of Buprenorphine and Fentanyl