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Abstract

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. References

Abstract:  Pharmacokinetic/pharmacodynamic (PK/PD) modelling can be used to characterize the relationship between dose regimen of opioids, plasma concentration and effect of opioids, which in turn can lead to more rational treatment regimens of pain. The aim of this study was to investigate the concentration–effect relationship for transdermal buprenorphine and fentanyl in experimentally induced pain. Twenty-two healthy volunteers were randomized to receive transdermal patches with fentanyl (25 μg/hr, 72 hr), buprenorphine (20 μg/hr, 144 hr) or placebo. The experimental pain tests were pressure at the tibial bone, cutaneous thermal stimulation, cold pressor test (conditioning stimulus (3 ± 0.3°C cold water), nerve growth factor–induced muscle soreness and intradermal capsaicin-induced hyperalgesia and allodynia. Experiments were carried out at baseline, 24, 48, 72 and 144 hr after application of patches. Time-course of placebo was described first and was afterwards added to the description of the time-courses of buprenorphine and fentanyl. This was either described by zero (no drug effect), linear or Emax model concentration–effect relationships. Time-dependent changes in pain measures in the placebo arm were described by linear or quadratic functions. The time-course of fentanyl and buprenorphine plasma concentrations was complex but could be represented by cubic spline interpolation in the models. Buprenorphine significantly attenuated bone-associated pain, heat pain, nerve growth factor–induced soreness and cold pressor pain. Fentanyl significantly attenuated cold pressor pain for the administered dose regimens. Although the PK/PD relationship for both drugs could be described with similar models, tissue-differentiated analgesic effects between buprenorphine and fentanyl was shown.

Pain is a frequently occurring symptom in patients; however, optimal treatment is often very complicated and difficult to achieve. Transdermal delivery of strong opioids has proven to be a valuable treatment option for chronic pain [1]. The opioids buprenorphine and fentanyl are substances that are suitable for transdermal delivery as they both have a low molecular weight (<500 DA), are very lipophilic and have high efficacy [2]. In addition, a pharmacokinetic and pharmacodynamic (PK/PD) study in rats showed similar equilibration constants (KD around 3.2–3.5 ng/ml) for the μ-receptor for buprenorphine and fentanyl [3]. Even though buprenorphine and fentanyl are similar regarding molecular weight and lipophilicity, their analgesic effect is mediated through different acting profiles. Buprenorphine is a semisynthetic opioid with partial agonistic effect at the μ-receptors and variable effect at the κ- and δ-receptors [4]. Buprenorphine is metabolized predominantly by cytochrome P450 3A4 in the liver, and its N-dealkylated metabolite norbuprenorphine is a δ-receptor agonist [1]. Fentanyl is a synthetic opioid, which on the other hand mediates its analgesic effect predominantly by interaction with the μ-receptors. It is also metabolized by cytochrome P450 3A4, but into two inactive and non-toxic metabolites [5].

Owing to the complex and differentiated actions of opioids, pain treatment is often based on a trial and error regimen. However, more rational and evidence-based approaches should be preferred to obtain effective dosing regimens in the clinic [6]. PK/PD modelling can be used to characterize the relationship between drug concentration and drug effect [6] and thus provide a base for a more rational therapy for the individual patient. However, in clinical trials, interpretation of results from PK/PD modelling may be problematic because of confounding factors such as sedation, nausea, general malaise and psychological factors interfering with the pain response [7]. Results from studies using human experimental pain models in which the investigator can control localization, intensity, frequency and duration of the painful stimulus may therefore be preferable because they provide less variable and confounded pain measures, which are more amenable for PK/PD modelling [8].

PK/PD modelling links effects to the blood concentrations of a drug substance [9]. Opioid receptors are mainly located in the central nervous system, and the effect of an opioid may be delayed relative to the plasma concentration profile, corresponding to time needed to pass the blood–brain barrier [9].

The aim of this study was to elucidate the PK/PD relationship of buprenorphine and fentanyl after transdermal administration applying superficial, deep and hyperalgesic experimental pain models and adjusting for the time-course of the placebo response. This provides a means for assessing the efficacy of transdermally administered fentanyl and buprenorphine in the various pain types.

Materials and methods

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. References

Study design, randomization and allocation.  The study was conducted accordingly to a randomized, placebo-controlled, double-blind (investigator and volunteers), double dummy, three-way cross-over design. It was approved by the local Ethical Committee (N-20070061) and the Danish Medicines Agency (EudraCT number: 2007-004524-21). Randomization was based on a list provided by the pharmacist, who was not otherwise involved in the project. The subjects were allocated to an identification number according to the randomization list.

Blinding procedure.  In each period, two patches were applied, as the buprenorphine and the fentanyl transdermal patches were not identical, i.e. buprenorphine active or placebo patch was placed on the right shoulder and fentanyl active or placebo patch was placed on the left shoulder (fig. 1). In the placebo arm, volunteers received two placebo patches. The patches were applied by either a nurse or a pharmacist, who was not otherwise involved in the project.

image

Figure 1.  Blinding of the study. To ensure blinding of the study, two patches (one being a placebo patch) were applied in each treatment period on the upper back of the healthy volunteers. A: Either active fentanyl or placebo fentanyl patch. B: Either active buprenorphine or placebo patch.

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Volunteers.  Criteria for inclusion were opioid-naive healthy men aged over 18 and able to understand the contents of the study including the assignment of informed consent. Criteria for exclusion were any known sensitivity to the opioids or patches, participation in other clinical studies within 14 days before screening, history of persistent pain conditions or other diseases, scheduled for hospitalization that would fall within the study period, use of any medication, use of any analgesics within 24 hr before study start, need to drive motor vehicles within the study period and any lesions at the testing sites.

Treatment.  Each subject received 20 μg/hr buprenorphine (transdermal patch, Norspan®; Norpharma A/S, Hørsholm, Denmark), 25 μg/hr fentanyl (transdermal patch, Durogesic®, Janssen-Cilag A/S, Birkerød, Denmark) or placebo (transdermal patch with no active compound) [10]. Duration of application for the buprenorphine patch was 144 hr, and for the fentanyl patch, it was 72 hr. Therefore, the patch placed on the right shoulder (buprenorphine active or placebo patch) was removed after 144 hr, and the patch placed on the left shoulder was removed after 72 hr (fentanyl active or placebo patch).

Pain assessment.  After enrolment in the study, pain measurements were taken before application [baseline (0)] and 24, 48, 72 and 144 hr after application of the patches.

Superficial and deep pain models. Bone pressure stimulation.  On the right tibia 15 cm below patella, a site was marked and used at every stimulation session. At this site, pressure stimulation was performed with a handheld algometer (Type 2, Somedic production AB, Sweden) with probe diameter of 2 mm. The force increase rate was 30 kPa/s adjusted to a probe size of 1 cm2. The subjects were instructed to press a button when they reached the pressure tolerance threshold and stimulation stopped. This stimulation has previously been demonstrated to be reproducible and to mimic bone pain evoked from the periost [11].

Heat stimulation.  Ten centimetres proximal from the wrist on the right volar forearm, an area (9 cm²) of the skin was heated with a computerized ‘Thermo Tester’ (TSA II NeuroSensory analyzer, Medoc Ltd., Ramat Yishai, Israel). The temperature increased from a baseline of 32°C to a maximum of 52°C with a rate of 1°C/sec. The subjects were told to press a button when the tolerance threshold was reached. Three successive stimulations were performed, and between each stimulation, the temperature returned to baseline. The average of the three stimulations was computed and used for the data analysis.

Cold pressor test.  The cold pressor test consisted of immersing the right hand into a circulating and refrigerated water bath (Thermostatic Bath, Model GD 120-R2, Grant Instruments Ltd, Cambridge, UK) with a temperature of 3 ± 0.3°C for 2 min. The subjects could remove their hand from the water bath if they reached their maximum pain threshold before 2 min. The perceived pain intensity was determined with an electronic visual analogue scoring (VAS) device and recorded during the test to assess area under the curve (AUC0–2 min) [12].

Inflammatory and hyperalgesic pain models Nerve growth factor.  Based on a previous study [13], a single dose of 2.5 μg nerve growth factor was given in 0.1 ml as a bolus injection (Product number: 800479, β-nerve growth factor, human 25 μg/ml; Aalborg Hospital Pharmacy, Denmark). The solution was injected into the extensor digitor longus muscle, 10 cm distal of patella on the lateral side of the left leg. Pressure tolerance threshold to pressure algometry was assessed before injection and 24, 48, 72 and 144 hr after injection.

Capsaicin.  Three sites were marked on the volar surface of the left forearm. They were marked 8 cm, 10 cm and 12 cm proximal from the wrist. Intradermal injection of 100 μg capsaicin in 0.1 ml (product number: 800644, Capsaicin 1 mg/ml, Aalborg Hospital Pharmacy, Denmark) was injected with a sterile syringe [14]. The first site was used before administration of the drug [baseline (0)], the second site 72 hr and the third site 144 hr after application of the patches. The area surrounding the injection site was defined as secondary hyperalgesic and allodynic area. Secondary hyperalgesic area was quantified with a von Frey filament (Touch Test Sensory Evaluator Kit, von Frey size 5.46; Stoelting Europe, Dublin, Ireland), and the area of allodynia was quantified with a soft brush. The areas were assessed immediately after injection. Stimulations with von Frey filament and brush started in normal skin away from the injection area and continued until the subjects reported a clear change in sensation. This was performed in eight radial directions. The borders from normal to sensitized skin were marked with a pen and drawn on a transparency film, and the area was calculated (Trust, 1200 wireless tablet; Trust International BV, Dordrecht, The Netherlands). The subjects remained supine during the injection and under the assessment of the areas of hyperalgesia and allodynia.

Blood samples.  Venous blood samples (K2 EDTA tube, 9 ml) were drawn at baseline and 6, 9, 12, 24, 36, 48, 60, 72, 78, 84, 96, 120, 144, 168, 192 and 216 hr after application of the patches. The samples were immediately centrifuged at 4°C at 3000 rpm for 15 min. Plasma was separated into two 2-ml polypropylene tubes – a ‘first sample’ and a ‘duplicate’. Both tubes were stored at −80°C until analysis.

Analysis of blood samples.  The analysis of the blood samples was carried out at Pharmaceutical Contract Research Group, Quotient Bioresearch Limited, Newmarket Road, Fordham, Cambridgeshire, UK. The concentration of buprenorphine, norbuprenorphine and fentanyl was determined by Ultra Pressure Liquid Chromatography (UPLC) (LC-MS/MS). The UPLC system was an Acquity UPLC binary solvent manager.

For fentanyl, the flow rate was set to 0.9 ml/min. and the analytical column was a 50 × 2.1 mm internal diameter Acquity BEH C18 with particle sizes of 1.7 μm. Column temperature was nominally 50°C, and the run time was 0.9 min. The mobile phase A was 0.1% (v/v) formic acid in acetonitrile, and mobile phase B was 0.1% (v/v) formic acid in water. The isocratic composition A:B was 25:75 (v/v). Mass spectrometer API 5000 (Applied Biosystems, Warrington, United Kingdom) was used, and the calibration range was 2–2000 pg/ml for all analyses.

For buprenorphine and norbuprenorphine, the flow rate was set to 0.6 ml/min. and the analytical column was a 100 × 2.1 mm internal diameter Acquity BEH C18 with particle sizes of 1.7 μm. Column temperature was nominally 60°C, and the run time was 4 min. The mobile phase A was acetonitrile, and mobile phase B was 10 mM ammonium formate pH 3. The gradient profile is shown in table 1. The mass spectrometer API 5000 (Applied biosystems, Warrington, United Kingdom) was used, and the calibration range was 25–2500 pg/ml for buprenorphine and norbuprenorphine.

Table 1.    Gradient profile of mobile phases A and B for analysis of buprenorphine and norbuprenorphine blood samples. Ultra Pressure Liquid Chromatography was used for the analysis.
Time (min)%A%B
Initial1090
3.005050
3.01955
3.4955
3.411090
4.001090

General modelling methods.  Data were analysed using non-linear mixed effect modelling (NONMEM) (Version VI, level 2; Icon Development Solutions, Maryland, USA). Models were fitted to population data with NONMEM using the first-order conditional estimation (FOCE) with interaction method [15]. The interindividual variability of parameters was assigned a log-normal distribution across the population as supported by the data. The residual error was assigned a combination of an additive and a proportional model, but was reduced to either proportional or additive if an error term was not supported by the data. Selection criteria for the final model were based on Bayesian Information Criteria (BIC) and goodness of fit assessed by visual inspection of observed and predicted values against time, residual plots and the distribution of the residual error. BIC adjust the objective function of NONMEM for the number of parameters and observations in the model. BIC do not describe whether two models are significantly different, but can be used as a robust method to describe a difference between models in a categorical way proposed by Kass & Raftery [16]. Differences in BIC between models were categorized as follows (compared to the model with lowest BIC): (1) BIC difference >10 was considered ‘very strong’ evidence in favour of the model with the smaller BIC; (2) BIC difference >6 to 10 as ‘strong’ evidence; (3) BIC difference of >2 to 6 as ‘positive’ evidence; (4) BIC difference of 0 to 2 as ‘weak’ evidence. Using the BIC for model selection counters the over-fitting of small data sets by favouring models with the least number of parameters [17].

A sequential PK/PD modelling approach was used, whereby the PK component of the model was developed first, with the PD model developed second with the PK parameters fixed at the previously determined values.

Pharmacokinetic models.  For both transdermal systems, the release is regulated by the concentration gradient across the skin and patch [1,5]. For buprenorphine, the matrix patch continuously delivers the drug for up to 144 hr, and for fentanyl, the delivery is up to 72 hr.

Initial investigations suggested that the complex course of release rates and concentrations produced by the patches could not be described using conventional first-order or zero-order dose regimens without systematic error. Modelling pharmacodynamic data require a description of the time-course of drug concentrations driving the pharmacodynamics effects. Usually, this is done with a pharmacokinetic model, but no suitable model of transdermal drug delivery was found in the literature. To minimize the contribution of this error to the PD component of the modelling, the concentrations were fitted to empirical cubic spline functions. By definition, cubic splines pass through every observed data point and interpolate the interval between points with a smooth curve. The coefficients for the spline were determined for each drug/subject data set using the ‘spline’ package of the R language, and these coefficients were copied to the NONMEM data file so that the spline describing the concentration–time-course could be reconstructed in NONMEM as used as the input for the PD models.

Pharmacodynamic models.  First models for the time-course of the placebo response for the six pain measurements were systematically examined for a range of linear, quadratic and Weibull models:

Linear model: Linear change in effect with time.

  • image

where BASE = baseline results and SLP = slope. This model was used to test whether time had an influence on effect for placebo and, furthermore, was tested with fixed (SLP = 0) or variable slopes, with or without population variability, with either proportional and/or additive error models or whether baseline results had an influence.

Quadratic model: Quadratic change in effect with time.

  • image

where SLP2 = slope 2. This model tested the assumption that there was a curvature in the effect–time relationship and was tested with or without population variability, with either proportional and/or additive error models or whether baseline results had an influence.

Weibull model: Exponential change in effect with time.

  • image

where SLP3 = slope 3 (SLP1 was kept >0 and SLP3 was kept >1). This model allows a delay in the onset of the effect and was tested with or without population variability with either additive or proportional effect corrected for baseline and whether baseline results had an influence. The models collapsed into a linear description and were therefore not used in the further analysis.

Each model was first used to investigate the placebo response. The model best describing the relationship for the placebo group for each of the pain measurements was then carried over to the investigation of the response of the pain measures to the drugs with the assumption that the drug effect was additive to the placebo response:

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or proportional to the placebo response:

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where the PD model represents the pharmacodynamic model (table 2).

Table 2.    Description of tested models for drug response. For each of the six experimental pain measurements, all models were tested to find the best fit for the drug response.
ModelDescriptionEquationPurpose
  1. SLPD, drug slope, F, hypothetical compartment concentration, Emax, maximum achievable effect, EC50, drug concentration at half the maximum effect, Ke0, equilibrium rate constant. The aforementioned models were also tested for the effect being proportional to the baseline value as follows: EFFECT = BASELINE *(1 + PD-Model), where PD-Model represents the linear and Emax pharmacodynamic functions above. The model best describing the relationship for the placebo group for each of the pain measurements was added (set in the control file) to the investigation of the response of the pain measures to the drugs. The drug response was assumed to be additive or proportional with any placebo response.

1No concentration–effect relationship. Fixed drug slope = 0, with no population variabilityEffect = BaselineAllows the baseline to vary between subjects
2No concentration–effect relationship. Fixed drug slope = 0 but with population variability.Effect = Baseline(pop)As above
3Linear direct drug effect with no population variabilityEffect = Baseline + SLPD*FAllows the baseline to vary between subjects. F is the hypothetical compartment concentration
3BLinear direct drug effect, with population variabilityEffect = Baseline + SLPD(pop)*FAs above
4Linear indirect effect with variable compartment rate. No population variabilityEffect = Baseline + SLPD*FAllows the baseline to vary between subjects where F is the hypothetical compartment concentration
4BLinear indirect effect with variable compartment rate. Population variabilityEffect = Baseline + SLPD(pop)*FAs above
5Direct Emax model with no population variabilityEffect = Baseline + (Emax*F)/(F + EC50)Test whether the effect–concentration relationship is non-linear in shape. Emax is maximum achievable effect. EC50 is drug concentration at half the maximum effect. F is the hypothetical compartment concentration
5BDirect Emax model with population variability.As aboveAs above
6Indirect Emax model with effect variable compartment rate constant. No population variability.As aboveAs above. Ke0 was set to 1.4.
6BIndirect Emax model with effect variable compartment rate constant with population variability.As aboveAs above

The models for the effect observed upon drug administration therefore include the change in PD measure because of placebo response. Hence, the true effect because of the drug alone can be estimated. Linear and Emax concentration–effect relationships were examined with models as described in table 2. Pain measurements were related either directly or indirectly [hypothetical compartment (F)] to the measured plasma concentration. The linear models described the concentration–effect relationship by the term “SLPD” (slope for the drug), where an indication of concentration-dependent analgesia could both be described by a positive and a negative value depending on the pain test. The Emax concentration–effect relationship described maximum effect (Emax) and concentration at which half the maximum effect was achieved (EC50). For both linear and Emax models, F described the hypothetical effect compartment. A delay in drug concentrations equilibrating with F relative to blood concentrations was described by a rate constant ke0. This is a classical ‘effect-compartment’ approach [18,19]. If there was no delay between pain measurement and plasma concentration, the data would support a PD model without the effect compartment F (t½ke0 = 0). If a delay was observed, then the data would support a PD model with an effect compartment where the larger the delay, the larger value of t½keo. The rate of equilibration of a drug between the plasma and the effect site is characterized by the parameter ke0. If a constant plasma concentration is maintained, then the time required for the effect site concentration to reach 50% of the plasma concentration is given by the t½ke0 = ln(2)/ke0.

Statistics.  Parameter estimates assessed by NONMEM are expressed as the typical population value. The variability across the population is expressed as the population variability parameter, which for a log-normal error model is an approximation of the coefficient of variation. The standard error of the parameter estimates (as returned by the $COVARIANCE step in NONMEM) was used to calculate the 95% confidence intervals of the parameter. If the interval did not include zero, the parameter was declared statistically significant.

Results

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. References

Volunteers.

Twenty-two healthy opioid-naïve male volunteers (mean age 23.1 ± 3.8) participated. They all gave written informed consent before inclusion. None of the subjects had any long-lasting pain complaints, and medical examination and routine blood samples were normal.

Analysis of blood samples.

Interday precision for fentanyl expressed as % coefficient of variation was <9.9% and intraday precision was <13.7% across the entire calibration range. Interday precision expressed as % coefficient of variation was <4.8% and intraday precision was <6.1% for buprenorphine. Interday precision was <9.5% and intraday precision was <10.8% for norbuprenorphine across the entire calibration range.

Pharmacokinetics.

Means of plasma concentrations for all 22 subjects for buprenorphine, norbuprenorphine and fentanyl are shown in fig. 2.

image

Figure 2.  Measured plasma concentration. Graph showing the measured plasma concentration for buprenorphine, fentanyl and norbuprenorphine (error bars: SD). Venous blood samples were drawn at baseline (0) and 6, 9, 12, 24, 36, 48, 60, 72, 78, 84, 96, 120, 144, 168, 192 and 216 hr after application of the transdermal patches.

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Pharmacodynamics.

An overview of the best models to describe the effect of the active drugs to the various experimental pain tests used in this study as well as the 95% confidential interval for the data is presented in table 3. The population estimates for the final models are represented in table 4. Between-subject variability at baseline (BSVBAS) and between-occasion variability at baseline (BOVBAS) were both highest for the inflammatory and hyperalgesic-induced pain models. A positive slope supports the analgesic effect (table 4). An overview of the objective values and the BIC differences from the different models that was used to investigate the relationship for the drug effect is given in table 5A and B.

Table 3.    Schematic overview of the models best describing the data for each pain test as well as the 95% confidential interval (CI).
Buprenorphine95% CIAnalgesic effectModel–drug
  1. BP, bone-associated pain, HP, heat pain, CPA, cold pressor pain, NP, NGF muscle soreness, CAPV, area assessed with von Frey filament to capsaicin-induced hyperalgesia, CAPB,  area assessed with brush to capsaicin-induced allodynia. 1 = slope fixed to 0 as this was the default no drug effect model, 3B = linear direct additive or proportional effect–concentration model. CI for parameter estimates were obtained from the covariance step of NONMEM. However, this does not always reach a solution even for well-structured models. A bootstrap estimate of CI is sometimes used as an alternative, but was not feasible in this case because of the large number of models and the long run time of individual models.

BP0.119–0.891Yes3B
HP0.056–0.156Yes3B
CPA−35.337 to −412.667Yes3B
NP126.257–494.598Yes3B
CAPV  1
CAPB  1
Fentanyl
BP−0.068–0.150No3B
HP0–0.048No3B
CPA−37.386 to −170.614Yes3B
NP  1
CAPV  1
CAPB  1
Table 4.    Population pharmacodynamic estimates and intra- and interindividual variability of the preferred models for each of the pain measurements.
 Population estimateParameter estimate (%SE)BSVBAS (%)BOVBAS (%)
BUPFENBUPFENBUPFENBUPFEN
  1. BP, bone-associated pain, SLOPD, slope of the graph for the drug, HP, heat pain, CPA, cold pressor pain (SLOPD is expected to be negative for this measurement as the result is the area under the curve and thereby should get smaller with analgesic effect), NP, NGF muscle soreness, CAPV, area assessed with von Frey to capsaicin-induced hyperalgesia, CAPB, area assessed with brush to capsaicin-induced allodynia, BSVBAS, between-subject variability at baseline, BOVBAS, between-occasion variability at baseline, BUP, buprenorphine, FEN, fentanyl, VAS, visual analogue scoring.

BP, model 3B
 Baseline (kPa/s)604060006.78.224261815
 SLOPD0.5050.07536.8127.4    
Proportional and additive error model for both drugs        
HP, model 3B
 Baseline (°C)46.446.310.93.63.71.81.7
 SLOPD0.1060.023622.647.9    
Proportional and additive error model for both drugs        
CPA, model 3B
 Baseline (VAS*sec)8508402.215.614126.910
 SLOPD−224−10440.530.8    
Additive error model for both drugs        
NP, model 3B (BUP), 1(FEN)
 Baseline (kPa/s)8218266.836291820
 SLOPD270Fixed (0)25.6Fixed (0)    
Proportional error model for both drugs        
CAPV, model 1        
 Baseline (cm2)49.141.954593828
 SLOPDFixed (0)Fixed (0)Fixed (0)Fixed (0)    
Additive error model for both drugs        
CAPB, model 1
 Baseline (cm2)16.71554623533
 SLOPDFixed (0)Fixed (0)Fixed (0)Fixed (0)    

Placeboresponse.

The placebo response for the various experimental tests was best described by quadratic models except for the allodynic area assessed with a brush (capsaicin model), where a linear fit was more suitable to describe the placebo response.

Superficial and deep pain models.

Bone pressure stimulation.  A linear direct effect model with population variability (model 3B) was the best fit to describe the drug effect of buprenorphine and fentanyl to pressure at the tibia. However, only buprenorphine showed significant analgesic effect to bone-associated pain assessed by the confidence interval (CI) not including zero (table 3). For fentanyl model 2, no concentration–effect relationship with population variability was equal to model 3B as assessed by the BIC (BIC < 2). However, there was a clear advantage of model 3B over model 2 regarding the objective function, and hence, model 3B was chosen (table 5A). Other models, e.g. 6 and 6B, showed ‘very strong’ (BIC > 10) evidence in favour of the model with smaller BIC.

Table 5.    Schematic overview of differences in the Bayesian Information Criteria as well as the objective values achieved with the models used to investigate the concentration–effect relationship of the drug response against the different pain tests (see table 2). The upper table A shows the results from the bone, heat and cold pressor pain test, and the lower table B shows the results from the nerve growth factor test and capsaicin-induced hyperalgesia and allodynia.
Bone painHeat painCold pressor test
ModelObj.BIC diff.ModelObj.BIC diff.ModelObj.BIC diff.
A Superficial and deep pain models: bone pain, heat pain and cold pressor test
Buprenorphine
BUPBP_3B3152.0760BUPHP_4B348.2620BUPCPA_3B12050.4390
BUPBP_3B13152.0760BUPHP_5B349.8251.6BUPCPA_3B2096.79957
BUPBP_23154.4772.4BUPHP_3350.131.9BUPCPA_32096.79962.3
BUPBP_13161.5984.2BUPHP_3B350.1411.9BUPCPA_12107.86762.7
BUPBP_4B3152.0095.3BUPHP_6B347.6944.8BUPCPA_22107.86762.7
BUPBP_5B3152.0765.3BUPHP_4348.2635.3BUPCPA_42096.79767.6
BUPBP_53151.87810.4BUPHP_5349.8256.9   
BUPBP_6B3152.00910.6BUPHP_1369.53210.1   
BUPBP_5_13152.07610.6BUPHP_6347.69510.1   
BUPBP_63151.79615.7BUPHP_2368.02514.4   
BUPBP_33269.736123      
BUPBP_43269.172128      
Fentanyl
FENBP_2_23394.7980FENHP_3B348.2620FENCPA_3B12172.9810
FENBP_3B_0B13389.8090.35FENHP_5B349.8251.2FENCPA_3B2172.98310.7
FENBP_3B3388.2294.1FENHP_1350.131.3FENCPA_22176.84614.5
FENBP_23388.6544.6FENHP_4B350.1411.4FENCPA_12182.60815
FENBP_4B3387.3898.6   FENCPA_4B2172.84816
FENBP_33389.80211FENHP_3347.6944.8FENCPA_32172.98316
FENBP_43389.69616.3FENHP_6B348.2635.2FENCPA_42172.84821.2
FENBP_3B_03407.66423.6FENHP_2349.8255.7FENCPA_5B2182.39725.4
FENBP_3B_0B1A3440.27645.5FENHP_5369.2566.6FENCPA_6B2182.39530.8
FENBP_3BA13440.27645.5FENHP_4347.69568FENCPA_52182.60831
FENBP_13440.42751FENHP_6368.02510.6FENCPA_62182.60836.3
FENBP_2_13440.42751      
FENBP_3B_0B3440.34156      
FENBP_3B13450.49661      
NGFCapsaicin(HA)Capsaicin(allodynia)
ModelObj.BIC diff.ModelObj.BIC diff.ModelObj.BIC diff.
  1. Obj., objective value; BIC diff., differences in Bayesian Information Criteria; NGF, nerve growth factor. Selection criteria for the final model were based on BIC and goodness of fit assessed by visual inspection of observed and predicted values against time, residual plots and the distribution of the residual error. BIC adjust the objective function of NONMEM for the number of parameters and observations in the model. BIC do not describe whether two models are significantly different, but can be used as a robust method to describe a difference between models in a categorical way proposed by Kass & Raftery [16]. All models were investigated further (e.g. 1 referring to no variation at all) if the covariance step could not be finalized.

B Pain models inducing inflammation/hyperalgesia: Nerve growth factor–induced muscle soreness and capsaicin-induced hyperalgesia and allodynia
Buprenorphine
BUPNP_12411.7770BUPCPA_3B12050.4390BUPCAPB_1876.2340
BUPNP_3B2407.9191.5BUPCPA_3B2096.79957BUPCAPB_2874.0542.6
BUPNP_22411.7775.3BUPCPA_32096.79962.3BUPCAPB_3B876.2334.8
BUPNP_4B2407.4346.3BUPCPA_12107.86762.7BUPCAPB_4B873.5886.9
BUPNP_32407.9196.8BUPCPA_22107.86762.7BUPCAPB_3874.0527
BUPNP_5B2407.9196.8BUPCPA_42096.79767.6BUPCAPB_5B876.2339.5
BUPNP_6B2407.43411.6   BUPCAPB_4872.81510.9
BUPNP_42407.43411.6   BUPCAPB_5876.23314.3
BUPNP_62407.43416.9   BUPCAPB_6B876.23414.3
BUPNP_52420.35224.5   BUPCAPB_6876.23419
Fentanyl
FENNP_12450.3270FENCAPV_1941.9320FENCAPB_1880.0860
FENNP_3B2448.2083.2FENCAPV_3B940.9823.8FENCAPB_3B879.2523.9
FENNP_22450.3275.3FENCAPV_2941.9324.8FENCAPB_2880.0864.8
FENNP_32448.2088.6FENCAPV_5B940.0237.7FENCAPB_4B879.1948.7
FENNP_4B2450.32710.7FENCAPV_4B940.8058.5FENCAPB_3879.2528.7
FENNP_5B2450.32710.7FENCAPV_3940.9828.6FENCAPB_5B879.7689.2
FENNP_6B2450.32716FENCAPV_6B940.00212.5FENCAPB_4879.19413.4
FENNP_42450.32716FENCAPV_5940.02312.5FENCAPB_6B879.76714
FENNP_52450.32716FENCAPV_4940.80513.3FENCAPB_5879.76814
FENNP_62450.32721.3FENCAPV_6940.00217.3FENCAPB_6879.76718.8

Heat stimulation.  For heat-induced pain, a linear direct effect model with no population variability (model 3B) was the best fit to describe the drug effect for buprenorphine and fentanyl (fig. 3). The parameter CI revealed that buprenorphine had a significant analgesic effect against heat stimulation which was not the case for fentanyl (table 3). The linear indirect effect model with compartment (keo) and no population variability (model 4B) as well as the Emax model with no population variability (model 5B) were both equal to model 3B regarding differences in BIC (BIC < 2) (table 5A). However, the value for keo in model 4B was low for both drugs (<0.2 hr−1), indicating that this parameter did not have a marked influence on the time-course of the analgesic effect of the active drugs. The values for EC50 achieved with model 5B tended to be low for both drugs. This mimics an ‘additive’ effect, meaning that a linear direct concentration–effect relationship would be sufficient to describe the effect of the drugs to heat pain. Model 6B showed for both drugs a BIC > 4.8 and the models with the smaller BIC were therefore considered as more ‘positive’ evidence to describe the drug effect. Hence, model 3B was chosen as it was the simplest model to adequately describe the data.

image

Figure 3.  Pharmacokinetic/pharmadynamic for cutaneous heat pain. The graph illustrates effect of buprenorphine (black) and fentanyl (grey) against cutaneous heat pain [measured in degrees Celsius and represented as population mean predicted values (PRED)]. Confidential intervals obtained from the covariance step of NONMEM revealed that buprenorphine had a significant analgesic effect to cutaneous heat-induced pain, which was not the case for fentanyl.

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Cold pressor test.  For both drug substances, a linear direct effect model with no population variability (model 3B) was the best fit for the effect to cold pressor-induced pain (fig. 4) (table 5A). For fentanyl, model 3B was further better described with no population variability. It was only possible to finalize the run for model 6 and 6B for buprenorphine, however, for fentanyl BIC was >30 (table 5A), leading to a ‘very strong’ evidence for models with smaller BIC (model 3B). Both drugs showed significant analgesic effect to the cold pressor test (table 3).

image

Figure 4.  Pharmacokinetic/pharmadynamic for the cold pressor test. The graph illustrates the effect of buprenorphine (black) and fentanyl (grey) against cold-induced pain using the cold pressor test [pain measured as area under curve (AUC (visual analogue scoring (VAS)*time)) and represented as population mean predicted values (PRED)]. Confidential intervals obtained from the covariance step of NONMEM revealed that both buprenorphine and fentanyl had significant analgesic effect against cold-induced pain.

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Hyperalgesic pain models.

Nerve growth factor.  A linear direct effect model with no population variability (model 3B) best described the effect of buprenorphine to nerve growth factor–induced muscle soreness. On the contrary, no concentration–effect relationship with no random variability in the measure (model 1) best described the effect of fentanyl. Model 1 showed a clear advantage over model 3B as well as the other models – the BIC difference was >3 (table 5B) and the slope was negative for model 3B. Buprenorphine had a significant analgesic influence on muscle soreness. For fentanyl, it was impossible to determine the CI because the slope was fixed to 0 (the default of no effect model) (table 3).

Capsaicin.  There was a high variability observed between-subject variability at baseline (BSVBAS > 50%, table 4) for intradermal capsaicin. For both drug substances, the analgesic effect to allodynic area assessed with brush and the analgesic effect to hyperalgesic area assessed with the von Frey filament were best described with model 1 – no effect–concentration relationship and not allowing random variability in the measure (table 5B). It is not possible to determine the CI for these models, as the slope was fixed to 0 (the default of no effect model) (table 3).

Discussion

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. References

To our knowledge, this study is the first to describe the PK/PD relationships for transdermal buprenorphine and fentanyl in human beings. The drug response could be described either by a direct relationship between plasma concentration and pain measurement (model 3B) or by models showing no relation between plasma concentration and pain measurement (model 1 and 2). Buprenorphine significantly attenuated bone-associated pain, heat pain, nerve growth factor–induced soreness and cold pressor pain compared to placebo. Fentanyl significantly attenuated cold pressor pain compared to placebo. Even though similar models described the PK/PD relationship for both drugs, the present study stressed the point that opioids with various receptor affinity can lead to tissue-differentiated effect.

Methodological considerations.

The experimental pain models used in the present study are renowned methods, which have previously been demonstrated to be both reproducible and robust. Superficial and deep pain models as well as models inducing hyperalgesia have revealed sensitivity towards opioids [20]. As the main focus of this study was to describe the concentration–effect relationship for buprenorphine and fentanyl in tissue-differentiated experimentally induced pain, the pharmacokinetic characteristics were not investigated in detail. For further detailed kinetic characteristics of the two drugs, see Kress 2008 and Nelson & Schwaner 2009 [1,5].

In the present study, it was considered essential to use equipotent doses. A study by Koltzenburg et al. (2006) showed analgesic effect with transdermal patches of 25 μg/hr fentanyl and 35 μg/hr buprenorphine [21]. The analgesic potency ratio to morphine would be 1:110 to 1:115 for buprenorphine and 1:100 for fentanyl [10]. To obtain equipotent doses between the two drugs, fentanyl was chosen as a 72-hr treatment patch (25 μg/hr) and buprenorphine as a 144-hr treatment patch (20 μg/hr).

Opioids exert their main effects in the central nervous system. Hence, after administration of opioids, a delay in the time-course of the PD effect with respect to the time-course of the drug concentration in the blood has been observed [9,22]. Contradictory, Gourlay et al. (1988) found a direct relationship between blood concentration and analgesic effect for fentanyl when administered as an intravenous infusion [23], suggesting fast onset of the analgesic effect. Similarly, in the present study, no delay was observed for the induced experimental pain for either of the drugs. This could indicate a peripheral analgesic effect followed by a central effect or may be a consequence of the long time scale of the study relative to the typical delay for opioids (<30 min).

It is important when assessing concentration–effect relationships to have several samples over a range of concentrations, for example during the absorption phase. Blood samples were taken 6, 9, 12 hr (followed by every 12 hr) after application of the patches. This should be sufficient to describe the initial absorption phase as the release from the patches is regulated by the concentration across the skin and patch [5,10]. Even though PK/PD modelling would have benefited from more frequent dynamic measurements, this was not achievable in the present study.

Cubic splines were used to represent the blood concentrations in this study to maximize the information contained in the PD data. This empirical approach is suitable for defining the concentration–effect relationship (as here) but does not produce a model that can be used to predict the consequences of altered dose regimens. As studies on PK modelling of transdermal patches are still sparse, it is considered a fruitful area for future investigation.

Ideally, concentrations of a drug should be measured at the effect site, where the interaction with the respective biological receptor system takes place. Unfortunately, this is impossible in most cases, as opioid receptors are mainly located in the central nervous system. Hence, concentrations in easily accessible body fluids like plasma are used for PK/PD modelling [24]. Using PK/PD modelling in experimental pain makes it possible to characterize the time-dependent contribution of the concentration of a drug as well as account for several factors e.g. weight, height. In addition, experimental pain in healthy volunteers comes around confounding factors in the clinic e.g. sedation, nausea, general malaise and psychological factors that interfere with the pain response [7].

A linear direct concentration–effect relationship (i.e. no ke0 term) is often a simplification of an observed phenomenon as a plot of plasma concentration versus effect may show a hysteresis loop because of delayed drug response, e.g. time-lag required for the drug to transit from plasma to the actual effect site, from the time necessary for conversion of the drug–receptor binding, a rate-limiting receptor dissociation process [22]. Nevertheless, in the present study, the best descriptions of the concentration–effect relationship for the two drugs were direct linear models.

Superficial and deep pain models.

For all superficial and deep pain measurements, linear direct effect models provided the best description of the data for both drug substances, suggesting that analgesic effects could directly be related to plasma concentrations for these pain tests. These results imply that there is no upper limit for the analgesic effect of the drugs, at least in these experimental pain models. However, it is important to keep in mind that our study investigated a single dose and thus a limited concentration range.

Even though animal studies indicate an inverse U-shaped dose–response relationship for buprenorphine, it has become clear that the concentration–effect relation is dependent on the applied pain model [25]. This is in accordance with what was observed in the present study as well as in previous work in both animal and human models, where full analgesic effect and no ceiling effect of buprenorphine have been observed [25–27].

Both drugs are very lipophilic, meaning that they cross the blood–brain barrier easily, suggesting a fast onset of analgesic effect. However, previous studies have shown that slow biophase equilibration kinetics is a major determinant of the time-course of the analgesic effect of buprenorphine [25,28]. The study by Jensen et al. assessed a ke0 (min−1) = 0.00803–0.0104, and the study by Yassen et al. assessed a ke0 (min−1) of 0.00447, corresponding to the ke0 (hr−1) of 0.223 assessed in our study [25,28]. This might explain the differences observed between the two drugs to bone-associated pain and thermal stimulation. On the other hand, a study in rats showed similar equilibration constants (KD around 3.2–3.5 ng/ml) for the μ-receptor for buprenorphine and fentanyl [3]. This could explain the results in the present study, where both drugs showed analgesic effects in the cold pressor pain, which is a tonic conditioning stimuli that evoke the endogenous central pain inhibiting system involving an opioidergic link [29–31].

Hyperalgesic pain models.

The current experimental approach using superficial and deep pain models gives the possibility to investigate tissue- and modality-differentiated effects of opioids. On the other hand, experimental hyperalgesic models can act as proxies for clinical manifestations and hence are more clinically relevant than superficial pain models [32,33]. Nevertheless, in the present study, the variability in the measurements of the hyperalgesic models was higher than in the acute and deep pain models. This variability can complicate PK/PD modelling.

For the hyperalgesic pain models, no relationship between effect, time and concentration was provided, meaning that the slope could not be determined. It was only for the effect of buprenorphine to nerve growth factor–induced muscle soreness that a linear direct effect–concentration relation was seen.

Intradermal injection of capsaicin has shown to be reproducible [34,35]. However, in the present study, a high variability was observed between subjects for the baseline measurements (BSVBAS > 50%). This could have influenced the power of the PK/PD modelling to distinguish the effects of buprenorphine and fentanyl. This might also be the reason why it was impossible to determine the slope, and therefore, models with a fixed slope set to zero were the best models, also evidenced with the objective function as well as BIC.

Active metabolite – norbuprenorphine.

Approximately one-third of buprenorphine is metabolized predominantly by cytochrome P450 3A4 in the liver, yielding the active metabolite norbuprenorphine – about 40 times less potent [1]. It is known from animal studies that norbuprenorphine possesses an analgesic effect and has high affinity for δ-receptors [36,37]. Nevertheless, the contribution of norbuprenorphine to the central clinical effect of burprenorphine is questionable as norbuprenorphine is less lipophilic and thereby does not readily cross the blood–brain barrier, at least after acute administration [38,39]. On the other hand, a study in sheep demonstrated that norbuprenorphine might contribute to the central effect of buprenorphine. In that study, significant respiratory depression was demonstrated after administration of norbuprenorphine [40]. In the present study, norbuprenorphine was measurable in the plasma after 24 hr and stayed stable over the treatment period. Nevertheless, the measured plasma concentration of norbuprenorphine was three times lower than the measured plasma concentration of buprenorphine. Both drugs were detectable over the period of time where blood samples were collected. The contribution of norbuprenorphine to the analgesic effect after transdermal administration of buprenorphine could not be distinguished in the present study and might not be of importance in the present study.

Conclusion

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. References

It was possible to reveal tissue-differentiated differences between the two drugs even though similar PK/PD models used to describe the concentration–effect relationship for buprenorphine and fentanyl and equipotent doses were used. This may reflect observations in the clinic, where treatment with opioids can lead to different effectiveness in individual patients.

Acknowledgement

  1. Top of page
  2. Abstract
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. References

Mundipharma Research GmbH & Co is acknowledged for supporting this study with an unrestricted grant. There are no conflicts of interests for all authors.

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  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusion
  7. Acknowledgement
  8. References
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