Population pharmacokinetic model of transdermal nicotine delivered from a matrix‐type patch

Abstract

Aims

Nicotine addiction is an issue faced by millions of individuals worldwide. As a result, nicotine replacement therapies, such as transdermal nicotine patches, have become widely distributed and used. While the pharmacokinetics of transdermal nicotine have been extensively described using noncompartmental methods, there are few data available describing the between‐subject variability in transdermal nicotine pharmacokinetics. The aim of this investigation was to use population pharmacokinetic techniques to describe this variability, particularly as it pertains to the absorption of nicotine from the transdermal patch.

Methods

A population pharmacokinetic parent‐metabolite model was developed using plasma concentrations from 25 participants treated with transdermal nicotine. Covariates tested in this model included: body weight, body mass index, body surface area (calculated using the Mosteller equation) and sex.

Results

Nicotine pharmacokinetics were best described with a one‐compartment model with absorption based on a Weibull distribution and first‐order elimination and a single compartment for the major metabolite, cotinine. Body weight was a significant covariate on apparent volume of distribution of nicotine (exponential scaling factor 1.42). After the inclusion of body weight in the model, no other covariates were significant.

Conclusions

This is the first population pharmacokinetic model to describe the absorption and disposition of transdermal nicotine and its metabolism to cotinine and the pharmacokinetic variability between individuals who were administered the patch.

What is Already Known about this Subject

• Transdermal nicotine is widely used as nicotine replacement therapy.

• Approximately 75% of nicotine in the body is metabolized to cotinine.

• Despite the prevalence of transdermal nicotine and the importance of its metabolism, population pharmacokinetic models that describe transdermal nicotine and cotinine in humans have not been described.

What this Study Adds

• This study provides a population pharmacokinetic model describing nicotine absorption from a transdermal patch, its disposition in the body, and its subsequent metabolism to cotinine, which have not previously been described in a single population model.

• It additionally describes between subject variability in the transdermal pharmacokinetics of nicotine.

Introduction

The World Health Organization estimated that in 2015, approximately 1.1 billion individuals worldwide smoked tobacco 1. Because of this widespread use, tobacco is thought to be responsible for about 6 million deaths annually worldwide 1, 2. The Centres for Disease Control suggest that nearly 17% of adults in the USA (~40 million) were cigarette smokers in 2014 and about 2100 youth and young adults become daily cigarette smokers each day 3. Smoking related illness costs approximately $300 billion each year in the USA, about $170 billion of which is direct medical care for adult smokers 4, and over $500 billion worldwide 5. For individuals who smoke, cessation has been associated with a number of short‐ and long‐term health benefits including lowered heart rate and blood pressure, improvement in blood circulation and reduced risks of lung diseases (including lung cancer), heart disease and stroke 6, 7. However, dependence on nicotine, the addictive agent in cigarettes and a number of other tobacco products, can make cessation difficult for many individuals.

Nicotine replacement therapy (NRT) is used each year by millions of Americans who are trying to quit smoking. It is estimated that the use of pharmacological treatment interventions, including NRT, can result in cost per life‐year savings of up to $1450 5. The aim of NRT is to gradually reduce an individual's exposure to nicotine in a controlled manner, ideally until the individual no longer has a physical dependence on nicotine. One of the most effective ways to do this is using the nicotine transdermal patch system. These systems target plasma nicotine concentrations in the lower range of what is expected after smoking one cigarette (10–20 ng ml^–1), while subsequent steps of lower doses result in corresponding lower concentrations 8, with the hope of slowly weaning users off of nicotine dependence completely.

Nicotine transdermal patches are available as both reservoir and matrix passive diffusion patches. Both patches provide control over the release rate of nicotine from the patch. However, the release profiles, and therefore the pharmacokinetics, may differ between patch types or brands, probably as a result of different formulations. This is exemplified by a study showing that one matrix nicotine patch exhibits Higuchi release kinetics (i.e. release proportional to the square root of time) while release from a different, reservoir patch may be better described with zero‐order drug release 9.

Nicotine is mainly metabolized to cotinine, which is in turn metabolized to trans‐3′‐hydroxycotinine and a number of other metabolites 8, 10. Several pharmacokinetic studies have been performed with transdermal nicotine, though the majority of them have employed noncompartmental methods 11, 12, 13, 14, 15, 16. In general, mixed‐effects population pharmacokinetic models for drugs delivered via transdermal patch are sparse 17, 18, 19, 20, 21, 22, particularly those describing transdermal nicotine 23. Some work has been done previously with the population pharmacokinetic modelling of transdermal nicotine in humans. However, in that study, the parameters used to describe the dose‐input function were not reported 23. As a result, drug absorption was not characterized. In addition, metabolism to cotinine was not considered in this model. Furthermore, there are no population pharmacokinetic models describing both transdermal absorption and the subsequent metabolism of nicotine to cotinine. We therefore used retrospective data from a previous adult clinical trial to construct a full population pharmacokinetic model for transdermal nicotine and its major metabolite. In addition, the population pharmacokinetic model is used to describe the between‐subject variability in transdermal nicotine pharmacokinetics.

Methods

Ethics approval and study registration

This was a retrospective study performed on data collected at the University of Utah in 2009–2010. The objective of this study was to determine the pharmacokinetics of transdermal nicotine, and its metabolite cotinine, in adults. This study was fully approved by the Institutional Review Board (IRB #21414 for initial study and IRB #74622 for secondary analysis) at the University of Utah (Salt Lake City, UT).

Study population

Healthy individuals aged 19–45 years who had a previous history of light smoking (<100 cigarettes in their lifetime) who had not smoked a cigarette or undergone treatment with any form of nicotine replacement therapy in the past year were included in the study. Individuals were excluded if there was a history of chronic cardiovascular or cerebrovascular disease, or if they were taking medication known to be contraindicated with nicotine. Patient height, weight, sex and race/ethnicity were collected. Nicotine abstinence was confirmed prior to the study via analysis of urine, plasma, and the first 3‐cm of hair growth closest to the scalp for the presence of either nicotine or cotinine.

Dosing and sampling schedule

Transdermal nicotine (7‐mg, Nicotine Transdermal System; Novartis, Basel, Switzerland) was administered for 4 h to each participant. After 4 h, the patch was removed. Blood samples were taken at baseline (prior to patch administration) and at 4.5, 4.75, 5, 6, 7, 8, 10, 12, 16, and 28 h after patch administration (equivalent to 0.5, 0.75, 1, 2, 3, 4, 6, 8, 12, and 24 h after patch removal). Blood was collected in sodium heparin Vacutainer tubes (BD, Franklin Lakes, NJ, USA) and refrigerated at 4°C until completion of the 24‐h blood draw. After this, the blood samples were centrifuged for 10–15 min at 1100 × g and the plasma was transferred to silanized 16 × 100 mm test tubes for storage at –80°C until analysis.

Analytical method

A previously published ultrahigh‐performance liquid chromatography–tandem mass spectrometry method was used to quantify nicotine plasma concentrations 24. Briefly, 1 ml of plasma was fortified with 50 μl of 1 μg ml^–1 of deuterated internal standard solution to achieve a concentration of 50 ng ml^–1. Solid phase extraction was performed using Oasis HLB and MCX mixed mode cartridges (Waters Corporation, Milford, MA, USA) conditioned with 2 ml methanol followed by 2 ml 10% aqueous trichloroacetic acid. The acidified plasma supernatants were loaded onto the cartridges and the target analytes were eluted with methanol containing 2% ammonium hydroxide. Following the addition of acid, the sample eluents were evaporated to dryness and reconstituted in 150 μl of initial mobile phase 10 mmol l^–1 ammonium acetate with 0.001% formic acid (pH 4.97) (A): methanol (B) (85:15; v/v). The assay was linear over the selected concentration ranges for both nicotine (2.5–50 ng ml^–1) and cotinine (2.5–100 ng ml^–1). Assay precision (as % relative standard deviation, %RSD) and accuracy (as % difference) were within ±7% for both compounds. Assay specificity was confirmed by the lack of a signal in blank samples.

Pharmacokinetic model development

Initial estimates for nicotine volume of distribution and clearance were generated with non‐compartmental methods using Phoenix WinNonlin v. 6.3 (Certara L.P., Princeton, NJ, USA). The nicotine population pharmacokinetic model was developed in NONMEM v. 7.2 interfaced with PDx‐Pop 5.0 (ICON Development Solutions, Ellicott City, MD, USA) and Pirana (http://pirana‐software.com). The model was developed using the first‐order conditional estimation with interaction (FOCE‐I) method. Data processing, checkout and visualization were performed in R v. 3.2.2 (CRAN.R‐project.org) interfaced with RStudio v. 0.99 (RStudio, Inc., Boston, MA, USA). During the model development process, standard diagnostic plots were generated and examined for model fit; including observed vs. population‐ and individual‐predicted concentrations and conditional weighted residuals (CWRES) vs. time and population‐predicted concentrations. All concentrations were expressed in nicotine equivalents (mg l^–1) based on molecular weights. While use of parent drug equivalents was not explicitly necessary for this model since cotinine concentrations were available, the conversion permits addition of other metabolites and analysis of minor metabolites by mass balance in potential future studies as demonstrated by Cook et al. 25 For a given patient, the first time a concentration value less than the assay's lower limit of quantitation was recorded, that value was entered as lower limit of quantitation/2 (0.5 ng ml^–1), and any subsequent concentration values for that patient were set to 0. Data points with |CWRES| > 4 were removed from the analysis.

Base model development

One‐ and two‐compartment models were considered for both nicotine and cotinine concentrations. Models were parameterized in terms of volume of distribution (V) and clearance (CL). Structural models also incorporated the rate of release from the transdermal patch, duration of patch administration, and documented bioavailability of nicotine (76.8%) 26. Calculation of the dose administered to each patient in this model is based on Higuchi release kinetics 9 from a 24 h patch that was worn for 4 h. The calculation of that dose is shown in Eq. (1) and (2) below:

$$M_{4h}=\frac{\left(M_{24h}\right)\left(\sqrt{t_{4h}}\right)}{\left(\sqrt{t_{24h}}\right)}=\frac{\left(7g\right)\left(\sqrt{4h}\right)}{\left(\sqrt{24h}\right)}=2.86g$$ (1)

$$\mathit{\text{Dose}}=M_{4h}*F=2.86g*0.768=2.20g$$ (2)

where M _4h is the mass of drug released at 4 h, M _24h is the mass released at 24 h, and F is bioavailability. The dose of 2.20 g calculated in Eq. (2) above was delivered with 0‐order kinetics into a depot compartment at 0.55 g/h over the span of 4 h.

Random effects were classified as either between‐subject variability (BSV) or residual unexplained variability (RUV). BSV was modelled with an exponential function (Eq. (3)):

$${\theta }_i={\theta }_{\mathit{pop}}\times e^{{\eta }_i}$$ (3)

where θ _i is the individual model‐predicted pharmacokinetic parameter, θ _pop is the population mean for that same parameter, and η _i is the between subject random effect for the i‐th individual. It should be noted that BSV was not estimated for the nicotine volume of distribution as no absorption phase data from when the patch was being worn were available. Therefore, any estimate of BSV for that parameter would not have sufficient data informing it.

Individual pharmacokinetic parameters were assumed to be normally distributed, whereas η _i is assumed to be log‐normally distributed with a mean of zero and a variance of ω ². Multiple error models were tested to describe the RUV including additive, proportional, exponential, and combined additive and proportional models. A number of absorption models describing drug absorption from the depot to the plasma were considered, including: first‐, zero‐, mixed first‐ and zero‐order absorption, Weibull absorption, Erlang absorption, and a transit compartment absorption model. The Weibull equation (Eq. (4)) is based on the Weibull statistical distribution where the Weibull absorption rate (WRATE) is described by the administered dose (DOSE), α and β rate constants, and time (T).

$$\mathit{\text{WRATE}}=\mathit{\text{DOSE}}*\left(\frac{\beta }{\alpha }\right)*\left({\left(\frac{T}{\alpha }\right)}^{\left(\beta –1\right)}\right)*e^{\left(–{\left(\frac{T}{\alpha }\right)}^{\beta }\right)}$$ (4)

The Erlang absorption (Eq. (5)) is a particular case of the γ distribution function describing a number of transit compartments which must be manually optimized, where a is an integer number of compartments, b is the identical exit rate between compartments, and Γ(a) is the γ distribution function with respect to a.(19)

$$f\left(t\right)=\frac{b^a}{\Gamma \left(a\right)}*t^{a–1}*e^{\left(–b*t\right)}$$ (5)

Covariate evaluation

A number of covariates were considered for the model including: body weight, body mass index, body surface area (BSA), and sex. BSA was calculated using the Mosteller 27 equation (Eq. (6)):

$$\mathit{BSA}=\sqrt{\frac{\mathit{\text{Height}}\left(\mathit{cm}\right)*\mathit{\text{Weight}}\left(\mathit{kg}\right)}{3600}}$$ (6)

Race was not considered during covariate analysis because only one patient was non‐Caucasian. Forward addition and backward elimination were used to determine covariate significance. Changes in the objective function value (OFV) of >3.84 were considered significant (p < 0.05 based on a Chi‐square distribution with 1 df) during forward addition, while an OFV change of >6.63 was required to retain the covariate during backward elimination (p < 0.01). Continuous covariates were tested with linear, power and exponential models, with no normalization, normalization to the population mean or normalization to the population median. For categorical covariates (i.e. sex), inclusion was tested using a power model (Eq. (7)):

$${\theta }_i={\theta }_{\mathit{pop}}{}^{*}{{\theta }_{\mathit{cov}}}^{{\mathit{COV}}_i}$$ (7)

where θ _i is the individual pharmacokinetic parameter, θ _pop is the population value for that parameter when COV _i is 0, and θ _cov represents the change in θ _pop when COV _i is 1.

Model evaluation

Base and final models were evaluated using goodness of fit plots. CWRES plots were evaluated for their fit between –2 and +2 for both the nicotine and cotinine concentrations. To test the stability of the model, a nonparametric bootstrap was performed using PDx‐Pop to generate 1000 bootstrap datasets by random sampling with replacement. Visual (VPC) and numerical (NPC) predictive checks were also run in Pirana (using Perl speaks NONMEM) with 1000 simulated datasets in order to determine if the developed model appropriately characterized the data 28.

Results

There were 31 patients enrolled with 620 concentrations. Six patients were removed from the analysis for lacking either viable concentration and/or time data, or for lacking all covariate data. Demographic information for the study population (n = 25) is summarized in Table 1. The median age was 26 years (range: 19–43 years), with a median body weight of 72.8 kg (range: 54–129.3 kg). The median body mass index was 23.4 kg/m² (range: 18.6–46.0 kg/m²), and the median body surface area calculated from the Mosteller equation was 1.85 m² (range: 1.60–2.45 m²). There were an approximately equal number of men and women included in the analysis.

Table 1.

Demographic information of patients included in analysis

Demographic	Value (n = 25)
Sex, male (%)	13 (52%)
Age, y (median, range)	26 (19–43)
Weight, kg (median, range)	72.8 (54.0–129.3)
Body mass index, kg m –2 (median, range)	23.4 (18.6–46.0)
Body surface area, m 2 (median, range)	1.85 (1.60–2.45)

An additional six concentrations (three nicotine, three cotinine) were removed from the analysis due to lack of time information and another four concentrations (two nicotine, two cotinine) were removed because |CWRES| > 4. Finally, one patient's cotinine concentrations were removed from the development of the final model, due to the significant impact of patient's concentrations on the model fit (Jacknife ΔOFV = 241.2), leaving a total of 25 patients and 482 concentrations included in the model. Demographic information for the study population are summarized in Table 1.

The data were best fit by a one‐compartment model with first order elimination for nicotine and cotinine and a first‐order process describing nicotine conversion to cotinine (Figure 1). A Weibull model (Eq. (5)) was chosen to describe the absorption of nicotine from the transdermal patch based on model convergence, goodness‐of‐fit plots, and reduction of Akaike information criterion. An additive error model (Eq. (8)) was used to describe the RUV for both nicotine and cotinine, where Y is an individual drug concentration, F is individually predicted drug concentration, and ERR(i) is the additive residual error for nicotine (i = 1) or cotinine (i = 2).

$$\mathrm{Y}=\mathrm{F}+\mathrm{ERR}\left(\mathrm{i}\right)$$ (8)

Figure 1.

Compartmental representation of the pharmacokinetic model. Drug release from the patch was represented as an “infusion” into a theoretical depot compartment. Drug absorption was then modeled from the depot using a Weibull model

This error model structure was chosen based on convergence of the model and reduced parameter % coefficient of variation compared to the other error models tested.

Available covariates were tested on nicotine and cotinine volume of distribution and clearance parameters. The only significant covariate during forward addition was the effect of population‐mean normalized weight (population mean WT = 76.0 kg) on V_NIC. The same covariate was significant at the ΔOFV > 6.63 level (P < 0.01) on backward elimination, and so was included in the final model (Table 2).

Table 2.

Parent‐metabolite (nicotine‐cotinine) model population pharmacokinetic parameter estimates

Parameter	Estimate	RSE (%)	Bootstrap median(95% CI)(n = 906/1000)
θ‐Structural model
α	3.72	13	3.79 (3.02–4.92)
β	1.53	8	1.60 (1.34–1.88)
V 2 (l)	104	33	103 (3.25–154)
(WT/76.0) θ	1.42	28	1.51 (0.490–12.9)
CL 2 (l h –1 )	90.4	12	91.0 (70.7–117)
V 3 (l)	112	12	110 (87.9–140)
CL 3 (l h –1 )	4.07	8	4.06 (3.52–4.81)
ω 2 ‐BSV
IIV V 2	Not estimated	NA	NA
IIV CL 2 (%CV)	52	16	52 (35–73)
ω 1,2	0.26	NA	0.25 (0.12–0.39)
IIV V 3 (%CV)	68	11	65 (47–84)
IIV CL 3 (%CV)	35	17	33 (19–45)
σ 2 ‐RUV
Add. error NIC (mg l –1 )	0.202	16	0.192 (0.134–0.258)
Add. error COT (mg l –1 )	0.945	20	0.905 (0.590–1.32)

RSE, relative standard error; CI, confidence interval; BSV, between subject variability (calculated ${\sqrt{e^{{\omega }^2}–1}}^{*}100$ for IIV); RUV, residual unexplained variability; α, Weibull scale parameter; β, Weibull shape parameter; V₂, nicotine volume of distribution; WT, patient weight (kg); CL₂, nicotine clearance; V₃, cotinine volume of distribution; CL₃, cotinine clearance; IIV, Inter‐individual variability; ω_1,2, covariance of ω² values for CL₂ and V₃; Add. Error NIC, additive residual variability for nicotine concentrations; Add. Error COT, additive residual variability for cotinine concentrations;

Model evaluation

A number of metrics and visual methods for determination of model fit were performed and presented. Goodness‐of‐fit plots demonstrated that there was no evident bias in the model fit. Population predicted concentration values (PRED) were relatively evenly spread above and below observed concentrations (Figure 2A), and individual predicted concentrations (which additionally consider between‐subject variability) showed good agreement with observed values (Figure 2B). There was additionally no trend in the data over time‐ or population‐predicted concentrations, as indicated by the spline of the CWRES vs. time and PRED plots (Figure 2C, D). Visual predictive checks for nicotine (Figure 3A) and cotinine (Figure 3B) demonstrated expected concentration vs. time profiles. Additionally, with the exception of the 28‐h nicotine time point (for which all concentrations were 0), the median and the 5% and 95% confidence interval lines stayed with their 90% confidence limits. Numerical predictive check showed 4.5% of nicotine observations and 8.9% of cotinine concentrations were outside the 90% confidence interval. Finally, mean parameter values from a bootstrap analysis (n = 1000 datasets) were similar to those of the original dataset (Table 2), supporting model stability. Taken together, these measures of model validity suggest that the constructed model generates a good and stable fit for the data.

Figure 2.

Goodness of fit plots displaying: A) Observed concentrations (DV) vs. population predicted concentrations (PRED), B) Observed concentrations (DV) vs. individual model‐predicted concentrations (IPRED), C) CWRES vs. Time, and D) CWRES vs. population predicted concentrations (PRED) for both nicotine and cotinine. For plots A and B, solid grey lines are lines of identity while dotted black lines show the spline of the data. For plots C and D, solid grey lines represent a CWRES of 0 while dotted black lines show the spline of the data. Model fits were not significantly different for nicotine and cotinine, and they were therefore plotted together in each plot

Figure 3.

Visual predictive check for A) nicotine and B) cotinine concentrations over time. Bold black lines represent the median predicted concentrations with a 90% confidence interval denoted by the upper and lower thin black lines. Shaded area around each line represents the 95% confidence interval of the simulated predictions

Discussion

This model represents the first population pharmacokinetic model to describe the absorption of transdermal nicotine and its subsequent conversion to cotinine. Since the 24‐h patch was only worn for 4 h, the actual dose delivered per unit time was estimated using known bioavailability and patch release characteristics. The dose per unit time was considered to be infused via zero‐order kinetics into a depot compartment, from which drug was absorbed into a central compartment using a Weibull absorption model. Transdermal nicotine has been demonstrated to have a physiological depot in the skin where some residual amount of nicotine will reside even after patch removal 29. We used a depot compartment as a mathematical construct to allow differentiation in describing drug release from the patch and drug absorption into systemic circulation. The Weibull absorption model contains α and β values to represent a scale parameter and a shape parameter, respectively, which can describe complex drug absorption 30. Accounting for weight on the nicotine volume of distribution provided a significant improvement in model fit. Model diagnostic and validation techniques demonstrated that the model accurately and robustly described the observed data.

Previous pharmacokinetic models for transdermal patch drugs have used a number of different absorption models. While zero‐ and first‐order absorption models have been used for patches such as fentanyl 19 and donepezil 20, it is not uncommon for more complicated models such as transit or Weibull models to be used. The benefit of the latter models is that they provide the mathematical structure to describe the controlled release nature of transdermal patch delivery that may better reflect the complexity of transdermal drug absorption. In fact, this transdermal model demonstrates the utility of the Weibull absorption model, as it provided a good model fit (evidenced by reduction of Akaike information criterion, goodness‐of‐fit plots, and VPCs) despite absorption phase data being unavailable. Future studies could consider the use of known physiological parameters for nicotine diffusion across the skin to describe absorption for the included patients in a semiphysiological model with physiologically‐based absorption and population‐based disposition.

One patient [removed from the model due to significantly affecting the model fit (Jackknife)] had cotinine concentrations that were much higher than other patients', although those concentrations may have been reasonable given other factors and covariates that were not captured. One possible explanation for this patient's exceedingly high cotinine concentrations may be related to either increased metabolism of nicotine, or, more likely given the relatively high nicotine concentrations (C_peak > 7 mg l^–1), decreased metabolism and/or clearance of cotinine. Indeed, a number of CYP2A6 mutations (a major metabolizing enzyme for both nicotine and cotinine) result in a poor metabolizer phenotype, which could potentially explain the relatively high concentrations of both nicotine and cotinine seen in this patient 10, 31. The overall prevalence of phenotypes demonstrating less than normal CYP2A6 activity is approximately 20% in Caucasians, although <1% of these are categorized as poor metabolizers 31. Unfortunately, data were not available to know if that patient had any phenotypic reduction in CYP metabolism, and therefore the patient was removed from the analysis.

A number of pharmacokinetic models, detailed below, have previously been performed for nicotine delivered via various routes of administration. Hukkanen et al. have compiled a number of pharmacokinetic studies detailing nicotine and/or cotinine disposition 8. These prior studies have used both one‐ 32, 33 and two‐compartment 23 models to describe nicotine pharmacokinetics. The present data was best described using a one‐compartment model for both nicotine and its major metabolite, cotinine, with first‐order elimination in both cases. Previous IV studies that have used one‐compartment or noncompartmental methods to describe nicotine PK have reported volume of distribution and clearance values of 154–231 l and 66.6–90.0 l h^–1 8, 11, 12, 13, 14, 15, 34. The nicotine volume of distribution reported for this model (104 l) is somewhat lower than the published range, while the nicotine clearance for this model (90.4 l h^–1) is at the higher end of the range suggested by previous models. For the proposed model, it was also determined that body weight significantly affected volume of distribution of nicotine which is consistent with previous study by Benowitz et al. that demonstrated a correlation between nicotine volume of distribution and total body weight 13.

Similar to nicotine, population PK models for cotinine have been described using one‐ 33, 2‐ 32, and three‐compartment 35 model structures. Previous one‐compartment/noncompartmental estimates for cotinine volume range from 48.3–65.1 l while clearance estimates range from 2.4–3.3 l h^–1 8, 12, 13, 14, 15, 34. Volume of distribution for cotinine determined in this model was higher than previously published values. This discrepancy could be a result of lack of concentrations available from when the patch was still being worn, which might bias the model towards a higher volume of distribution for cotinine. However, despite the unavailability of these data, diagnostic plots and visual and numerical predictive checks support the model fit and in turn support the pharmacokinetic parameters estimated in this model.

There were several assumptions that had to be made during the development of this model. First, the exact dosing information was not available. The transdermal patches used in this study were intended for delivery of 7 mg over the course of 24 h. However, because the patches were only worn for 4 h, the actual delivered dose had to be estimated as discussed in the methods. The estimated dose delivered was based on literature describing Higuchi release kinetics from the matrix‐type nicotine patch 9 and 76.8% bioavailability 8, 16, 26, 36. Additionally, the first plasma concentration was taken 30 min following the removal of the patch, meaning that there were no data describing the absorption kinetics of nicotine from the transdermal patch, which is a primary limitation of this work. To account for this limitation, we tested a variety of models that have been used in previous literature to describe transdermal patch absorption. We selected the Weibull statistical absorption model based not only on standard modelling criteria, but also because it is a descriptive empirical model of atypical or complex drug absorption that is often observed in transdermal drug delivery 37. It follows that the limitations caused by having insufficient data to characterize transdermal patch absorption fully are minimized by our use of the Weibull model. The BSV in V_NIC was also fixed to zero since there was not enough data to estimate that variability accurately. Finally, it was assumed that 72% of the delivered nicotine dose was converted into cotinine 34 in order to give an identifiable model, which would allow estimation of V_COT 38. This assumption has a solid basis in several studies that were compiled in the review by Hukkanen et al. 8 and appears to be appropriate for this model.

Despite the limitations, there are a number of potential applications of the model in future studies. First, the model could be applied to other adult transdermal nicotine studies for which patches were worn for the full 24‐h period and data were collected during drug absorption. Importantly, while the model structure would not change, the Weibull α and β parameters would need to be re‐estimated based on the differences in length of absorption (e.g. 4 h vs. 24 h). An additional benefit from the described model is to give a template for future planned studies in adolescents and paediatrics. Use of passive diffusion patches in those populations may require reduced doses and/or shortened wear times, and this model could be adjusted for application to these scenarios.

The proposed model successfully describes the available nicotine and cotinine concentration data. Nicotine volume of distribution varied linearly with population mean‐normalized to weight. While additional work is necessary to better describe the absorption of nicotine from the transdermal patch, this model is the first to use population techniques to describe the pharmacokinetics and the variability associated with transdermal delivery of nicotine and subsequent metabolism to cotinine.

Competing Interests

There are no competing interests to declare.

The authors would like to acknowledge Dr Douglas Rollins for his involvement in the original trial, and they would like to thank Drs Chris Stockmann, Sarah Cook and Xiaoxi Liu for their guidance and advice in the development of the model. M.L. is supported by a Pre‐doctoral Fellowship from the American Foundation for Pharmaceutical Education.

Contributors

M.W.L. performed the data analysis and modelling and drafted the manuscript. J.E.R. and J.K.R. provided input and advice into the data analysis and modelling process. E.I.M. developed the bioanalytical assay and ran samples in which nicotine and cotinine were quantified. D.G.W. oversaw the initial human study including sample and data acquisition and was involved in study design. C.M.T.S. designed and oversaw the modelling and data analysis process and provided feedback with regards to that process. All authors provided critical revision during the drafting process and approve the final submitted manuscript.

Linakis, M. W. , Rower, J. E. , Roberts, J. K. , Miller, E. I. , Wilkins, D. G. , and Sherwin, C. M. T. (2017) Population pharmacokinetic model of transdermal nicotine delivered from a matrix‐type patch. Br J Clin Pharmacol, 83: 2709–2717. doi: 10.1111/bcp.13393.