Abstract
The objective of this study was to develop a pharmacokinetic–pharmacodynamic (PKPD) model of the static allodynia response to pregabalin with and without sildenafil in a chronic constriction injury model of neuropathic pain. Six treatment groups were evaluated every 30 min for 6 h. Rats were treated with either 1) a saline infusion; 2) a 2h pregabalin infusion at 4 mg·kg^{−1}·h^{−1}; 3) a 2h pregabalin infusion at 10 mg·kg^{−1}·h^{−1}; 4) a 2.2mg loading dose + 12 mg·kg^{−1}·min^{−1} infusion of sildenafil; 5) a 2h pregabalin infusion at 1.6 mg·kg^{−1}·h^{−1} with sildenafil; and 6) a 2h infusion of pregabalin at 4 mg·kg^{−1}·h with sildenafil. The static allodynia endpoint was modeled by using three population PD approaches: 1) the behavior of the injured paw using a threecategory ordinal logistic regression model; 2) paw withdrawal threshold (PWT) (g) between the injured and uninjured paw using the Hill equation with a baseline function; and 3) the baseline normalized difference in PWT between the injured and uninjured paw. The categorical model showed a significant shift in the concentration–response relationship of pregabalin to lower concentrations with concomitant sildenafil. Likewise, the continuous PKPD models demonstrated a reduction in the EC_{50} of pregabalin necessary for PD response in the presence of sildenafil. The differencetransformed PD model resulted in a 54.4% (42.3–66.9%) decrease in EC_{50}, whereas the percentagetransformed PD model demonstrated a 53.5% (42.7–64.3%) shift. It is concluded from these studies that there is a synergistic PD interaction between pregabalin and sildenafil.
Neuropathic pain represents an area of largely unmet medical need with significant impact on healthrelated quality of life (Jensen et al., 2007). At present, neuropathic pain is treated by using a variety of different medications (e.g., antidepressants, gabapentin, pregabalin, opioids) with mechanisms of action that include inhibiting serotonin and norepinephrine uptake, altering ion channel transport, and occupying Nmethyldaspartate receptors (Nurmikko and Haanpää, 2005; Chong and Brandner, 2006; Francis et al., 2006; Gilron et al., 2006; Jackson 2006; Stillman, 2006). The current treatments for neuropathic pain achieve some relief; however, there remains significant room for improvement (Harden and Cohen, 2003). An intriguing question is whether increased relief can be obtained by using rational combinations of drugs (Gilron and Max, 2005; Backonja et al., 2006). The optimization of a rational drug combination represents a major challenge, because it involves not only the selection of the appropriate combination of drugs, each with a different mechanism of action, but also the optimal doses for using those drugs. The overall goal of this project was to develop a pharmacokinetic–pharmacodynamic (PKPD) model describing the interaction between pregabalin and sildenafil in rats.
Pregabalin is a ligand to the α_{2}δ subunit of the voltagegated calcium channel. Avid binding at this site reduces calcium influx at nerve terminals that reduces the release of several neurotransmitters including glutamate, norepinepherine, and substance P (Dooley et al., 2007). In addition to antiallodynic effects (Guay, 2005; Zareba, 2005), pregabalin has demonstrated anxiolytic activity (LauriaHorner and Pohl, 2003; Hitiris and Brodie, 2006) and anticonvulsant activity (Hamandi and Sander, 2006).
Sildenafil is a potent and selective phosphodiesterase type 5 (PDE5) inhibitor. PDE5 is an enzyme primarily responsible for the breakdown of cGMP, an intracellular second messenger. As the breakdown of cGMP is inhibited, increased intracellular concentrations of cGMP result and are thought to be primarily responsible for its therapeutic activity. Sildenafil was originally developed to treat angina, but its current therapeutic indication is in the treatment of male erectile dysfunction (Briganti et al., 2005). Because of the prevalence of PDE5 in many systems in the body, sildenafil has also been successfully applied for the treatment of other conditions including pulmonary hypertension (Jackson et al., 2005; Antoniu, 2006). Recently, it has been observed that sildenafil may enhance the effects of pregabalin in an animal model of neuropathic pain. The mechanism of interaction is currently unknown; however, it is hypothesized that sildenafil may exhibit a PD synergistic interaction with pregabalin by increasing intracellular concentrations of cGMP, leading to downstream regulation of the voltagegated calcium channel.
Recently, a theoretical framework for the design of rational drug combinations based on receptor theory has been proposed (Jonker et al., 2005). These operational models of agonism allow for the prediction of synergistic, additive, and antagonistic responses based on response data from the administration of multiple drugs (Van der Graaf and Danhof, 1997; Jonker et al., 2005; Danhof et al., 2007, 2008). Furthermore, these models predict that synergistic effects are more likely to occur when drug effects converge either later during signal transduction or when there is no substantial redundancy within the signal transduction pathway (Van der Graaf and Danhof, 1997; Danhof et al., 2007, 2008). The present article explores this system and the response to this drug combination. This work provides the framework for pursuing a receptor theorybased exploration of this interaction that can further the understanding of the mechanistic nature of the interaction between pregabalin and sildenafil.
The focus herein was to investigate static allodynia in a chronic constriction rat model after pregabalin administration at multiple dosing levels in the presence or absence of sildenafil. An optimal postPD sampling schedule developed previously was used to allow for accurate identification of individual rat PK while not interfering with PD measurements taken during the initial 6 h of the experiment (Field and Williams, 2008; Bender et al., 2009). These data then served as the basis for developing a population PKPD model to quantify the static allodynia response to pregabalin alone and then examine the influence of concomitant sildenafil on this response. Based on the measured PD responses and PK data, three different approaches to modeling the PD data were evaluated during this study: one categorical approach and two continuous approaches. The continuous models used either the difference in paw withdrawal threshold (PWT) between the injured and uninjured paw using the Hill equation with a baseline function or the baseline normalized difference in PWT between the injured and uninjured paw as the output measure.
Materials and Methods
Materials and Reagents (Chemicals and Standard Solutions).
Sildenafil, desmethylsildenafil, and pregabalin were obtained from the Compound Control Unit of Pfizer Global Research and Development, Pfizer, Sandwich, Kent, UK.
Study Design.
Male SpragueDawley rats (268–372 g), obtained from Charles River (Margate, Kent, UK), were housed under a 12:12 h light/dark cycle with food and water ad libitum. All experiments with animals were carried out in compliance with United Kingdom legislation and subject to ethical review. The experiments were conducted in a chronic constriction injury animal model of neuropathic pain. In brief, this surgical procedure involves tying four loose ligatures around the right sciatic nerve. After this procedure, the animal develops a peripheral mononeuropathy in the ipsilateral (right) paw that resembles the human condition in its response to static allodynia (Gilron and Max, 2005). Permanent jugular venous catheters for drug administration and coronary artery catheters for blood sample collection were implanted according to standard surgical procedures approximately 1 week before the experiments.
Static allodynia was evaluated on the basis of the PWT as assessed by the application of von Frey hairs in ascending order of force. The von Frey hair forces used in these experiments were 1.5, 2, 4, 6, 8, 10, 15, and 26 g. Each von Frey hair was applied to the paw for a maximum of 6 s or until a withdrawal response occurred. Once a withdrawal response to a von Frey hair was established, the paw was retested, starting with the filament below the one that produced a withdrawal, and subsequently with the remaining filaments in descending force sequence until no withdrawal occurred. Each animal had both hind paws tested in this manner. The lowest amount of force required to elicit a response was recorded as the PWT in grams.
The effect of pregabalin was determined in the presence of a steadystate infusion of sildenafil or placebo. Volumes and infusion rates were kept constant throughout all treatment groups. Specifically, to administer sildenafil or placebo, a bolus of 1 ml·kg^{−1} was administered over 10 min followed by an infusion at a rate of 2 ml·kg^{−1}·h^{−1} for the duration of the planned 6h PD experiment. When sildenafil was administered in addition to pregabalin, a 2.2mg sildenafil loading dose and 12 mg·kg^{−1}·h^{−1} continuous infusion was selected to achieve maximum target saturation. Pregabalin was administered as a 2h infusion. This infusion length allows characterization of the PD endpoints during both the upswing and downswing in concentration change throughout the course of the 6h sampling. To optimally characterize the PD interaction, pregabalin doses of 10 and 4 mg·kg^{−1}·h^{−1} were administered without sildenafil in two groups of rats, and two separate groups of rats received pregabalin at either 4 and 1.6 mg·kg^{−1}·h^{−1} with sildenafil dosing as described above. Table 1 outlines the dosages used during this study. Static allodynia sampling was conducted before dosing and every 30 min after dosing for 6 h. This resulted in a total of 13 paw withdrawal observations per animal over the 6h experiment.
Blood samples were obtained with an Accusampler automated blood sampling apparatus (DiLab Inc., Littleton, MA). The Accusampler sampler obtained blood samples of 200 μl through the coronary artery catheter into heparinized containers. After blood sampling, samples were centrifuged at 3000 rpm for 3 min, and plasma was separated and then stored at −20°C until analysis. PK sampling was determined by a preclinical trial simulation as described previously (Bender et al., 2009). Based on these simulations, three PK samples were obtained at 6, 8, and 24 h after the PD experiment.
Assay of Pregabalin and Sildenafil in Plasma.
Plasma samples were analyzed for quantification of pregabalin, sildenafil, and the major Nmethyl metabolite of sildenafil by liquid chromatographytandem mass spectrometry. The plasma samples, standard and quality control (50 μl), were extracted by using activated solidphase extraction sorbent (Oasis MCX; Waters, Milford, MA). Samples were analyzed on a PerkinElmerSciex Instruments (Boston, MA) API III+ mass spectrometer in positive ionspray mode. A fast gradient highperformance liquid chromatographer was used with a Chromolith Speed Rod RP18e (Merck, Darmstadt, Germany), 50 × 46 mm, 5 μm at 3 ml·min^{−1}. Detection was linear over the following concentration ranges for each analyte: pregabalin (100–10,000 ng·ml^{−1}), sildenafil (3–2000 ng·ml^{−1}), and UK103–320 (Nmethylsildenafil) (5–2000 ng·ml^{−1}). The limits of quantification (%CV) for pregabalin, sildenafil, and the Nmethyl metabolite of sildenafil assays were 70 ng/ml (10%), 1 ng/ml (14%), and 1 ng/ml (14%), respectively.
Data Analysis.
The population analysis includes the base model and final covariate model development. The base model defines the model parameters and describes the plasma concentration–time profile and the concentration–response relationship. The final model describes the influence of fixed effects (i.e., demographic factors) on the PK and PD parameters (Ette et al., 1995a,b). The population PK model used for this analysis was reported by Bender et al. (2009).
All PKPD modeling was accomplished with a standard nonlinear mixedeffects approach implemented within NONMEM software (double precision version 5, level 1.1; GloboMax, Hanover, MD) (Sheiner et al., 1977; Beal and Sheiner, 1992). The models consisted of a structural model that describes the drug concentrations and effects and a pharmacostatistical model that describes the betweensubject, betweenoccasion, and residual variability. Diagnostic graphics, exploratory analyses, and post processing of NONMEM outputs were performed by using R2.7.0 (http://www.rproject.org) and MATLAB 2007b (The MathWorks, Inc., Natick, MA). The firstorder conditional estimation method (FOCEINTER in NONMEM) was used for model building. The adequacy of each model was assessed by using standard goodnessoffit plots, the precision of the parameter estimates as calculated by using the covariance option in NONMEM, and the NONMEM objective function value (OFV). When discriminating between hierarchical models based on OFV, the likelihood ratio test was applied. This test is based on the property that the ratio of the NONMEM objective function values (−2 loglikelihood) were asymptotically χ^{2}distributed. An objective function decrease of 10.8 units was considered significant (χ^{2} p < 0.001, df = 1). Standard errors for all parameters were obtained by using the covariance option in NONMEM.
PK Model Structures.
A twocompartment model based on previous analysis (Bender et al., 2009) was used as the structural model to describe the concentration time course of pregabalin. Although previous results demonstrated that the numerically superior PK model used a continuous covariate for the sildenafil metabolite, similar parameters were obtained if either a continuous sildenafil concentration or binary representation for sildenafil presence/absence was incorporated during the analysis. In the interest of simplicity, the binary covariate formulation for sildenafil PK interaction (SLDB = 1 if sildenafil was administered, SLDB = 0 otherwise) from the previous analysis was used, showing a reduction in pregabalin clearance by 23.8% when administered with sildenafil. Individual PK parameter estimates (empirical Bayes estimates) were generated with this model.
PD Model Structures.
A categorical PD model and two continuous models based on an E_{MAX} formulation (eq. 2) were evaluated to analyze the static allodynia endpoint. The first approach modeled the behavior of the injured paw by using a categorical modeling approach with logistic regression models with three categories (no response, partial response, and complete response). The second approach examined the difference in PWT between the injured and uninjured paw by using a continuous PD model applying the Hill equation for characterization of the concentration–effect relationship. The third approach examined the percentage of reduction in hypersensitivity relative to baseline (i.e., the difference between the two paws divided by the difference at baseline as a percentage). Each of these PD models was implemented by using the differential equation solver within ADVAN 6 (Globomax, Hanover, MD). The individual PK parameters derived from the population PK analysis were then used to calculate the concentration at each time point in the central compartment. All models incorporated the concept of “effect site concentration,” Ce(t), defined by Fuseau and Sheiner (1984) as:
Here k_{eo} is the equilibrium rate constant, and C(t) is the pregabalin concentration in the central compartment of the PK model.
Continuous Model.
The continuous PD models consisted of a sigmoid E_{MAX} model (eq. 2) to relate the concentration of drug available in the effect site [Ce(t)] to the observed response. In this model, E_{MAX} is the maximum change in response the drug can produce, EC_{50} is the value of Ce(t) producing 50% of the E_{MAX}, and Hill influences the steepness of the relationship:
Data from both the ipsilateral and contralateral paws were incorporated in this modeling approach via two separate transformations. In the first case, the data from the ipsilateral paw (IPSI) was subtracted from the contralateral paw (CONT) giving a difference transformation (DIFF) for the PWT. This difference transformation was then modeled by using the Hill equation with an E_{MAX} value set equal to the baseline (BL) difference in PWT at time 0. Alternatively, the data were transformed as percentage of hypersensitivity relief through a baseline normalization by using eq. 3:
Here, IPSI_{0} and CONT_{0} are the ipsilateral and contralateral PWT at time 0. The E_{MAX} model formulation used either the DIFF or percentage of relief as observations to fit and the baseline difference or 1 (100%) as the actual E_{MAX} value in these systems.
The stochastic variability was assumed to be lognormally distributed for the PD models. The relationship between a PD parameter (P) and its variance was expressed as in
Here, P_{i} is the value of PD parameter for the ith individual, PTV is the typical value of P for the population, and (η_{i}) denotes the difference between Pj and PTV, independently, which was identically distributed with a mean of zero and variance of ωP^{2}. The residual variability was examined by using additive, proportional, and combined error structures as described below:
Here y_{ij} was the jth observation in the ith individual, ȳ_{iy} was the corresponding model prediction, and ε_{ij} (or ε_{ij}′) was a normally distributed random error with mean zero and a variance of σ^{2}.
The final model structure was developed by testing the effect of the following subjectspecific covariates: 1) body weight; 2) age; 3) time after surgery; 4) time after catheterization surgery; 5) sildenafil concentration; and 6) sildenafil metabolite concentration. Sildenafil metabolite concentration was included as a covariate for thoroughness as it was identified previously as a significant PK model covariate when included as a continuous measure (Bender et al., 2009). All of the above covariates were initially modeled as continuous. In addition, sildenafil was modeled as a discrete covariate because the steadystate infusions resulted in a relatively stable concentration of sildenafil at a level that saturates PDE5 enzymes throughout the experiment. Stepwise covariate selection was used for the covariate model building (Mandema et al., 1992; Wade et al., 1994; Wählby et al., 2001, 2002; Beal, 2002). First, exploratory covariate selection was performed by examination of the normalized eta deviation between individual post hoc parameter estimates and candidate covariates. Subsequently, various parameterizations of the selected covariates were added to the base model and evaluated for significance by observing ΔOFV and diagnostic plots. The covariate parameterization resulting in the largest reduction in the objective function value without evidence of misspecification from the goodnessoffit plots then moved on to the next stage. This continued until no significant improvements in model fit were achieved through further covariate inclusion. Equations 6 and 7 demonstrate an example of including a continuous covariate on EC_{50}:
TVEC_{50} was the typical value for the population; η_{i} was the random effect representing the difference of the ith subject from the population mean. The random effects of betweensubject variability were assumed to be lognormally distributed, with a mean of zero and standard deviation of ω. Cov was the continuous covariate that affected CL; and Med_{Cov} was the median Cov. Equation 8 describes an example for the effect of a discrete covariate sildenafil presence (SLDB) on EC_{50}:
Here SLDB denotes either the presence (SLDB = 1) or absence (SLDB = 0) of sildenafil. When SLDB is 0, TVEC_{50} equals θ_{EC50}; likewise, when SLDB is 1 the θ_{Cov} term is the percentage of the reduction in the typical population estimate of EC_{50}.
Model Evaluation.
The final model was evaluated by using bootstrapping with resampling to examine the stability of the final model and estimate the confidence intervals for the parameters. This technique consisted of repeatedly fitting the model to 1000 replicates of the data set by using the bootstrap option in Wings for NONMEM version 412. Parameter estimates for each of the replicate data sets were obtained. The results from 500 successful runs were obtained, and the mean and 5th and 95th percentiles (denoting the 90% confidence interval) for the population parameters were determined and compared with the estimates of the original data (Ette et al., 1997, 2003; Parke et al., 1999),. In addition, as a final check, a visual predictive check was performed by using the simulation option within NONMEM to create a 90% prediction interval. These were obtained by simulating 1000 replications using the final model and a data set including identical experimental design. For each observation, the value of the 51st highest and 51st lowest prediction became the edges of the 90% prediction band. Observed values were then plotted on the same scale as these bands to help visualize the adequacy of the model fit (Yano et al., 2001). After completion of these steps, the final descriptive PKPD model was proposed.
Categorical Model.
The categorical model used a threecategory ordinal scale to represent the degree of relief obtained from the static allodynia endpoint to obtain sufficient observations within each response category. This categorical approach incorporated only measures from the ipsilateral paw. The ipsilateral paw response was arbitrarily subdivided into three categories representing no (≤2 g), partial (2 g > 8 g), and complete (≥8 g) elimination of hypersensitivity. A logistic regression model was used to model the probability of achieving a static allodynia response. Given the assumption that p is the probability of achieving response, the general structure for this model can be described by using eqs. 9 and 10:
Here, i is an index denoting the category, p_{i} is the probability of response at a predicted Ce(t), and η_{j} is interindividual variability for the jth individual. For i > 1, the probability of response is calculated by using p_{i} − p_{i}_{−1}. The logit transformation assures that the probability, p_{i}, remains between 0 and 1. Functional structures [f(Ce(t),η_{j}] evaluated were limited to a linear relationship [slope × Ce(t) + intercept_{i} + η_{j}], power law [α × Ce(t)^{β} + intercept_{i} + η_{j}], or the Hill equation specified in eq. 2. Administered sildenafil was incorporated within the categorical models as a discrete covariate effect on the slope [slope × (1 − θ_{Cov} × SLDB)], where SLDB denotes the presence (SLDB = 1) or absence (SLDB = 0) of sildenafil and θ_{Cov} is the covariate coefficient. The administered sildenafil was evaluated as either a discrete covariate effect on EC_{50} or the Hill coefficient of eq. 2 [EC_{50} × (1 − θ_{Cov} × Cov) or n × (1 + θ_{Cov} × Cov), respectively]. Likewise, the sildenafil effect was incorporated as a binary covariate affecting either α or β in the power law equation.
Results
Pregabalin and Sildenafil Effects on Static Allodynia.
Differencetransformed results from the PD experiment for the six treatment groups are shown in Fig. 1. Sildenafil administration alone had no effect on the paw withdrawal threshold. A dosedependent increase in static allodynia hypersensitivity was observed after administration weight pregabalin without and with sildenafil (Fig. 1, A and B, respectively). A complete response was not observed at either of the highest dosing levels, and the treatment effect did not return to baseline by the end of the PD experiment. Less pregabalin was necessary to achieve the same reduction in static allodynia when sildenafil was administered. In this respect it is important that different doses of pregabalin were administered in the experiments with sildenafil versus without sildenafil. Specifically, similar maximum responses for 10 mg·kg^{−1}·h^{−1} pregabalin alone and 4 mg·kg^{−1}·h^{−1} pregabalin with sildenafil (1.6 ± 1.6 versus 1.3 ± 1.8 g) and for 4 mg·kg^{−1}·h^{−1} pregabalin alone and 1.6 mg·kg^{−1}·h^{−1} pregabalin with sildenafil (4.0 ± 0.9 versus 4.2 ± 1.5 g) were observed, respectively. Likewise, ends of experiment responses were similar for 10 mg/kg pregabalin alone and 4 mg·kg^{−1}·h^{−1} pregabalin with sildenafil (4.3 ± 1.6 versus 4.4 ± 1.7 g) and 4 mg·kg^{−1}·h^{−1} pregabalin alone and 1.6 mg·kg^{−1}·h^{−1} pregabalin with sildenafil (5.1 ± 1.6 versus 4.6 ± 1.0 g). This decrease in hypersensitivity was not an additive effect of sildenafil because no response was observed over the experimental time course when it was administered to rats as a single agent at doses that saturate the target (Fig. 1B; maximum response of 5.6 ± 0.8 g) compared with control (Fig. 1A; maximum response of 5.6 ± 0.9 g).
PD Model Development: Continuous Models.
The first continuous model used to describe the static allodynia response used eq. 2 and a differencetransformed metric with baseline and maximum response defined by eq. 3. Final model parameters are listed in Table 2. An additive error model was selected to account for the residual variability. For comparison, plasma and effect compartment predictions for two different pregabalin doses are shown in Fig. 2. These correspond to the low and highdose pregabalin treatment arms (groups 2 and 3 from Table 1). Over the study duration, peak plasma and effect compartment concentrations were reached at 2 and 2.3 h, respectively. The ratio of mean peak to end of study (6 h) concentrations in the central and effect compartments were likewise 3 and 2.3, respectively, for both dosing groups. With the addition of sildenafil time to peak was unchanged; however, peak/end of study ratios for the plasma and effect compartments decreased to 2.4 and 1.9, respectively. Mean peak concentrations predictions from groups 2 and 6 (4 mg/kg/h pregabalin with and without sildenafil, respectively; Table 1) were similar for the central compartment [mean (90% prediction interval), 8.1 (3.5; 16.5) group 2; 8.1 (3.3; 17.2) group 6]. In contrast, end of study values differed by approximately 24% because of the inclusion of sildenafil inhibition on pregabalin clearance [mean (90% prediction interval): 2.7 (0.4; 5.5) group 2; 3.4 (0.9; 6.5) group 6].
Of all the covariates investigated, only sildenafil had a significant impact on the PD model. A binary model implemented by examining the presence or absence of sildenafil in the experiment as a continuous model for sildenafil interaction could not be justified given the time until sildenafil reached saturable plasma concentrations and the PD sampling interval. The sildenafil effect resulted in a 54.4% (42.3–66.9%) decrease in the EC_{50} estimated for the impact of pregabalin on static allodynic response. A plot of individual predictions versus observations and a visual predictive check of the model predictions of the time course of all treatment responses are shown in Fig. 3. Model predictions were centered on the line of unity except for difference PWT values near values of zero (representative of a complete response). This bias results from the shift in the error distribution as a complete response is approached and was not accounted for during model development. Additional distributions were tested including exponential, inflated Poisson, and a truncated maximum; none of them showed an improvement over the original model approach (data not shown). Furthermore, the model predicted responses clearly demonstrate a leftward shift in EC_{50} in the presence of sildenafil.
The second model used to describe the static allodynia response was a continuous PD model (Hill equation) using a percentagetransformed metric. Final model parameters are listed in Table 2. An additive error model was selected to account for the residual variability. Of all the covariates investigated, only sildenafil had a significant impact on the model. As before, a binary model was implemented examining the presence or absence of sildenafil in the experiment. The sildenafil effect resulted in a 53.5% (42.7–64.3%) decrease in the estimated EC_{50} of pregabalin associated with hypersensitivity response. Overall, diagnostic plots demonstrated a reasonable model fit (Fig. 4A). Observed values versus individual predicted values are centered on the line of identity with the exception of some bias at either extreme (0 or 100%) of the percentagetransformed response. The bias observed at these regions results from the same truncated distribution described above. A visual predictive check (Fig. 4B) revealed a majority of the observations contained within the 90% confidence bands.
PD Model Development: Categorical Model.
When the data from the ipsilateral paw are broken down into three categories as described under Materials and Methods and plotted, a clear difference between the individuals treated with pregabalin alone and those treated with pregabalin and sildenafil can be visualized (Fig. 5). At the highest dosing level, a complete response was observed in 50 to 60% of the measurements when the effect compartment concentration was >14.5 μg·ml^{−1}. In contrast, in the presence of sildenafil a complete response was observed in all measurements where the effect compartment concentration exceeded 8.0 μg·ml^{−1}.
This difference in response was then accounted for by using a logistic regression model with the parameters shown in Table 3. The effect of pregabalin concentration was modeled by using a linear relationship in addition to the cut points. Sildenafil was modeled as a binary additive covariate with a negative shift on the slope parameters in the logit model. The final parameters for this model are listed in Table 3. The probability for no, partial, or complete response versus concentration in the effect compartment for the model is shown as mean ± 90% confidence intervals in Fig. 5. These response were consistent with the experimental results, predicting ∼50% response in rats with a pregabalin effect compartment concentration of 16.6 μg·ml^{−1} and a complete response in rats administered pregabalin and sildenafil when the effect compartment concentration was >8.5 μg·ml^{−1}. The evaluation of both a power law and Hill equation nested in the logit relating drug concentration to response resulted in nonsignificant improvements in the OFV. Furthermore, EC_{50} parameter values were in excess of pregabalin effect compartment concentration prediction, implying that a categorical model formulation with saturation was not necessary.
Discussion
The primary objective of this study was to identify and quantify the PKPD relationship of pregabalin for static allodynia in the presence and absence of sildenafil. Pregabalin by itself demonstrated an ability to reduce static allodynia. These results were similar to those obtained by Field et al. (1999) where a dosedependent reduction in static allodynia was observed after administration of 3–30 mg per kg body weight pregabalin by mouth. Results from the present study demonstrated that an equivalent reduction in static allodynia in a rat chronic constriction injury model could be achieved with less pregabalin when administered intravenously. Furthermore, coadministration with sildenafil allowed for an equivalent PD response with even less pregabalin (i.e., 4 mg·kg^{−1}·h^{−1} pregabalin over a 2h infusion with sildenafil was equivalent to 10 mg·kg^{−1}·h^{−1} pregabalin administered over a 2h infusion). As such, it may be possible to achieve dose reduction in pregabalin administered by mouth as well as by coadministering sildenafil. Finally, the increased effect with coadministered sildenafil was not additive because no reduction in hypersensitivity to static allodynia was observed when sildenafil was administered by itself (Fig. 1B ).
In previous investigations, a reduction in PWT has been observed after relatively high doses of sildenafil (10–30 mg·kg^{−1} s.c.). In contrast, no such effect was observed in the present investigation despite administered doses that resulted in concentrations well above the EC_{50} for binding to PDE5. Alternatively, the previous investigations showing an effect of sildenafil on PWT did not monitor plasma concentrations, and it cannot be excluded that the doses in these investigations led to higher plasma concentrations. The results of the present investigation demonstrate that a synergistic antiallodynic effect with pregabalin is achievable under conditions of maximum PDE5 activation.
All of the PKPD models examined in this work identified a significant synergistic interaction between pregabalin and sildenafil demonstrated by a significant shift left in the concentration–response relationship for pregabalin in the presence of sildenafil. This effect was present even after accounting for the minor PK interaction described previously (Bender et al., 2009). The mechanism for this effect is unknown; however, it is hypothesized that sildenafil may exhibit a PD synergistic interaction with pregabalin by increasing intracellular concentrations of cGMP. In turn, this increase in intracellular cGMP may modify important downstream regulation of the voltagegated calcium channel and alter nociception. This work described the interaction by using empirical modeling approaches.
The analysis of static allodynia data presented herein represented a challenge because of its nature and the manner in which hypersensitivity response was quantified. The underlying PWT for an individual animal can be considered continuous; however, the Von Frey hairs represent an ordinal categorical measuring system for this underlying state. We propose several continuous and one categorical method for analyzing this type of data with advantages and disadvantages depending on the model type.
The categorical approach was more statistically valid, reducing the complexity of the data by dividing it into three categories. Results from the categorical model as a probability of response are also easier to interpret for someone not familiar with the scales incorporated within this work. Attempts to incorporate a Hilltype or power law relationship into the logit resulted in significant model instability. As a result, only linear relationships were used to affect the elements of the logit.
The continuous models were better suited to a mechanistic modeling approach because they both incorporate the Hill equation to describe the system. Both continuous models demonstrated a reduction in the EC_{50} of pregabalin in the presence of sildenafil. The differencetransformed model resulted in a 39.4% (24.7–54.1%) decrease in the EC_{50}, whereas the percentagetransformed model demonstrated a 43.9% (29.8–57.9%) shift. Although the different approaches resulted in a slightly different magnitude of effect, the shift was significant in both cases, demonstrating a PD interaction between the two compounds. This difference was also seen in the categorical model with significant shifts in the probabilities at lower concentrations of pregabalin. In addition, with the categorical model, the presence of sildenafil had a greater effect on the transition from partial to complete response than it did on the transition from no response to partial response.
Although all of the models described a significant shift in the static allodynia response to lower concentrations of pregabalin in the presence of sildenafil, they each possess certain advantages and disadvantages. With ordinal categorical data of this type (only six potential categories), the most statistically correct model is the ordinal categorical model. However, as discussed above, attempts to apply this approach to a categorical model with an EC_{50} were not successful. Therefore, mechanistic interpretation of the results obtained from the categorical model in the context of an operational model of agonism (Jonker et al., 2005) is made more complex. The continuous models both used EC_{50} parameters. The differencetransformed model estimates individual baselines for each individual, whereas the percentagetransformed model baseline normalizes the data. This makes the differencetransformed model better able to deal with a subject with a variable baseline. However, the percentagetransformed model's conversion of the von Frey hair scores into a percentage change makes it more easily interpretable from a clinical standpoint. This makes it an ideal candidate for use in a clinical trial simulation with interspecies scaling techniques.
Footnotes

This work was supported by Pfizer, Global Research and Development, Sandwich, United Kingdom.
Article, publication date, and citation information can be found at http://jpet.aspetjournals.org.
doi:10.1124/jpet.110.166074.

ABBREVIATIONS:
 PK
 pharmacokinetic
 PD
 pharmacodynamic
 OFV
 objective function value
 PWT
 paw withdrawal threshold
 PDE5
 phosphodiesterase type 5
 CV
 coefficient of variation
 UK103–320
 Nmethylsildenafil
 Received January 17, 2010.
 Accepted May 4, 2010.
 Copyright © 2010 by The American Society for Pharmacology and Experimental Therapeutics