RESEARCH PAPER

In Silico Modelling of Transdermal and Systemic Kineticsof Topically Applied Solutes: Model Development and InitialValidation for Transdermal Nicotine

Tao Chen1 & Guoping Lian1,2 & Panayiotis Kattou1

Received: 11 December 2015 /Accepted: 2 March 2016 /Published online: 8 March 2016# Springer Science+Business Media New York 2016

ABSTRACTPurpose The purpose was to develop a mechanistic mathe-matical model for predicting the pharmacokinetics of topicallyapplied solutes penetrating through the skin and into theblood circulation. The model could be used to support thedesign of transdermal drug delivery systems and skin careproducts, and risk assessment of occupational or consumerexposure.Methods A recently reported skin penetration model [PharmRes 32 (2015) 1779] was integrated with the kinetic equationsfor dermis-to-capillary transport and systemic circulation. Allmodel parameters were determined separately from the mo-lecular, microscopic and physiological bases, without fitting tothe in vivo data to be predicted. Published clinical studies ofnicotine were used for model demonstration.Results The predicted plasma kinetics is in good agreementwith observed clinical data. The simulated two-dimensionalconcentration profile in the stratum corneum vividly illustratesthe local sub-cellular disposition kinetics, including tortuouslipid pathway for diffusion and the “reservoir” effect of thecorneocytes.Conclusions A mechanistic model for predicting transdermaland systemic kinetics was developed and demonstrated withpublished clinical data. The integrated mechanistic approachhas significantly extended the applicability of a recently re-ported microscopic skin penetration model by providing pre-diction of solute concentration in the blood.

KEY WORDS diffusion . disposition . percutaneousabsorption . physiologically-based pharmacokinetic modelling .toxicokinetics

ABBREVIATIONS3Rs Replacement refinement and reductionCVODE C-language variable-coefficients ODE solverMW Molecular weightODE Ordinary differential equationPDE Partial differential equationQSPR Quantitative structure–property relationshipSUNDIALS SUite of nonlinear and differential/algebraic

equation solversSWIG Simplified wrapper and interface generator

INTRODUCTION

Transdermal permeation of chemicals is an important topic ina range of applications, such as transdermal delivery of drugs,design of skin care and cosmetic products, and safety assur-ance and risk assessment of exposure to hazardous chemicals.Due to its effective barrier properties, skin is of significantinterest to controlled release of pharmaceutical and otherproducts (1, 2). In the past, research in this field largely reliedon in vivo, ex vivo and in vitro tests (especially in early phasedevelopment), and clinical studies with human volunteers (typ-ically in late phase trials). This empirical approach is timeconsuming and expensive. In recent years, the research para-digm has undergone a significant change towards more mech-anistic and holistic understanding of various transdermal per-meation pathways, including the role of the physico-chemicalproperties of the solute of interest and its interaction with skin.Within this context, mathematical modelling, also referred toas in silico approach, has emerged as an important technologyto improve fundamental understanding of the transdermal

* Tao Chent.chen@surrey.ac.uk

1 Department of Chemical and Process Engineering, University ofSurrey, Guildford GU2 7XH, UK

2 Unilever Research Colworth, ColworthPark, Sharnbrook, Bedfordshire MK44 1LQ, UK

Pharm Res (2016) 33:1602–1614DOI 10.1007/s11095-016-1900-x

permeation kinetics. This in silico approach is also an impor-tant approach to the replacement, refinement and reductionof animal tests in research (the 3Rs).

In the literature, various modelling studies on transdermalpermeation have been reported. A frequently cited approachis the empirical quantitative structure–property relationship(QSPR) models, which intend to predict the steady-state per-meability coefficient based on experimental results of percu-taneous absorption (3, 4). Extension from steady-state to ki-netic modelling has been achieved by the compartmental ap-proach, which treats the skin layers as different compartmentseach having uniform concentration, e.g. (5, 6) and other studiesreviewed by Anissimov et al. (7). A major limitation of thecompartment model is that the model parameters often needto be fitted to experimental data, and thus the extrapolationcapability is limited. More recently, significant attention hasbeen given to the diffusion-based models that use the Fick’ssecond law of diffusion to describe time-dependant solute dif-fusion across skin layers. Early diffusion-based models ignoredthe heterogeneous structure of the stratum corneum and de-scribed the transdermal permeation as diffusion in homoge-neous media (8, 9); however the model parameters also need-ed to be fitted to experimental data in order to make satisfac-tory predictions. Since the heterogeneous “brick-and-mortar”structure of the stratum corneum was introduced to in silico

modelling, the main challenge has been to obtain the trans-port and disposition properties (diffusion and partition coeffi-cients). Some models chose to obtain these properties by data-fitting (10), limiting the applicability of the model. Wang et al.(11, 12) reported a more predictive two-dimensional model, inwhich the diffusion and partition coefficients were obtainedfrom fundamental principles, and only the trans-bilayer masstransfer coefficient was fitted to deduce a correlation with themolecular weight. A similar two-dimensional approach wastaken by Lian and co-workers (13, 14), where data-fittingwas only used to derive a correlation for calculating the diffu-sion coefficient in corneocytes, and the prediction accuracywas significantly improved when compared with the Wang’smodel in (11, 12). With consideration of the two-dimensionalmicroscopic skin structure, bothmodels (11–14) demonstratedthe importance of the trans-cellular diffusion pathway throughthe stratum corneum. In a later study, Lian and co-workersextended their model to include viable epidermis and dermiswhilst maintaining the predictive capability (15). Some excel-lent review articles have been published to summarise therecent progress in this area; see e.g. (7, 16, 17).

The majority of the transdermal permeation models devel-oped, especially those incorporating more realistic heteroge-neous skin physiology (11–13, 15), were intended to predictthe absorption kinetics in the skin only. When the chemicalreaches the dermis, it is cleared from the skin through bothdiffusion into deeper tissues and convection by the capillaryblood vessels. Although the dermis clearance pathways have

been modelled (18–21), the focus was still on improving themodelling accuracy within skin. The kinetics in systemic cir-culation has not been considered in these studies. Systemiccirculation was included in many compartment-based phar-macokinetic models (5, 6, 22), but they have limited predictivecapability due to the lack of sufficient microscopic details inskin. Therefore, there is a need to connect the microscopicskin penetration models with systemic circulation kinetics, sothat prediction capability can be extended to the concentra-tion profile in circulation. This capability is important becausethe plasma concentration profile is one of the primary param-eters from the efficacy and safety perspectives in many appli-cations. In addition, by validating the model against in vivo

plasma data, one can also infer detailed kinetic and bioavail-ability information in various skin layers from the model,which are not normally available in clinical studies.

Against this background, this study aims to integrate ourrecently reported skin penetration model with systemic circu-lation kinetics. Following the previous studies (13, 15), thebrick-and-mortar model is used to represent the heteroge-neous structure of the stratum corneum, while the viable epi-dermis and dermis are modelled as homogenised materialwith properties related to the main compositions of cellularlipid, protein and water. The transport of chemicals withinskin is governed by diffusion equations, and that into capillaryblood is modelled by using the assumption of equilibriumbetween dermis and blood, following the method in (5).Importantly, the partition and diffusion properties are calcu-lated by relating to the fundamental physico-chemical prop-erties of solutes, rather than fitting to the data to be predicted.The physiology in skin and blood circulation (e.g. depth of skinlayers, capillary blood flow rate, whole body blood volume,etc.) is also used. The model has been implemented in C++,which allowed fast computation using a much finer gridscheme in stratum corneum than reported previously (13,15). It should be noted that the coarse grids previouslyused (13, 15) were deemed numerically sufficient forpredicting one-dimensional pharmacokinetics, as furtherrefinement of the grids did not improve the resolution.However, for the purpose of simulating detailed two-dimensional local disposition, higher resolution is need-ed and this is the motivation of using finer grids in thepresent study. The model is applied to predict the pub-lished data from clinical studies of transdermal nicotinepatches (23, 24). The prediction is in good agreementwith the published data, showing excellent predictioncapability achieved with the integrated model of bothtransdermal permeation kinetics and systemic circulationkinetics. In addition, the simulated detailed two-dimensional concentration profile of nicotine in the stra-tum corneum vividly illustrates the tortuous lipid path-way for diffusion (the “fingering” effect) and the “reser-voir” effect of the corneocytes.

In Silico Modelling of Transdermal and Systemic Kinetics 1603

MATERIAL AND METHODS

This section describes the modelling method in general,followed by the particular details of reported clinical studiesof nicotine that were used for the initial validation and dem-onstration of the model.

The Mathematical Model

Figure 1 illustrates the modelling framework including a singlehomogenous vehicle layer, a two-dimensional heterogeneousbrick-and-mortar structure of the stratum corneum, one-dimensional (vertical diffusion) schemes for the viable epider-mis and dermis, the coupling of solute diffusion in dermis withtransport into the blood capillaries, and the solute clearance inthe circulation. The simulation scheme for stratum corneum,viable epidermis and dermis is the same as the previous study(15).

The Overall Simulation Approach

The simulation is based on solving the diffusion equation thatdescribes the transport of solute. The time- and space-dependent partial differential equation (PDE) of diffusion issolved by the method of lines. More specifically, the simula-tion domain is discretised into grids, which allow for the con-version of the PDE into a large number of ordinary differen-tial equations (ODEs). The grid scheme for the vehicle (onegrid), the viable epidermis (ten vertically and equally spacedgrids) and the dermis (ten vertically and equally spaced grids)is the same as in the previous study (15). However, to allow fordetailed simulation of the stratum corneum, the main

penetration barrier, much finer grids were used: in the verticaldirection, two grids were used for the lipid bi-layer and fourfor the corneocytes; in the lateral direction, two grids wereused for the inter-cellular lipid and 20 for the corneocytes.In total, this gives rise to 3189 grids in the skin, plus onecompartment for the blood (i.e. 3190 ODEs).

The flux due to diffusion between any two neighbouringgrids, either in the vertical or lateral direction, in the simulationdomain is described by the following mass transfer equation:

qi j ¼A

δiDi

þ K i jδ jD j

C i−K i jC j

� � ð1Þ

where qij is the rate of mass transfer (kg s−1) from grid i to grid j,A is the interfacial area between the two grids, δi and δj are thecorresponding diffusion lengths, Di and Dj are the diffusivity ofthe corresponding grids, Kij is the solute partition coefficientbetween grid i and j, and Ci and Cj are the concentration ingrid i and j, respectively. Since water is the reference used forpartition coefficients, Kij can be calculated as the ratio of Kiw(partition coefficient from grid i to water) to Kjw (partition co-efficient from grid j to water), which depend on the type ofmaterial of the grid and the calculation will be detailed inSection 2.1.2.

Building on the mass transfer rate described in Eq. (1), thelaw of mass conservation requires that the concentration ineach simulation grid in the vehicle, stratum corneum andviable epidermis follows the differential equation:

V i

dCi

dt¼ −

Xj

qi j ð2Þ

Fig. 1 Overview of the modelling framework.

1604 Chen, Lian and Kattou

where Vi is the volume of grid i, t is time, and the summation isfor all the grids that are neighbours of grid i.

In addition to diffusion, convection needs to be consid-ered when modelling the transport between dermis andcapillaries due to the blood flow. We follow Bookout Jr etal. (5) to model each grid in the dermis as a homogeneousvolume, and the solute in blood circulation has a uniformconcentration. Based on these assumptions, within eachdermis grid, the solute convection of the capillary intothe grid is given by Qb,iCb, where Qb,i is the blood flowinto the dermis grid i and Cb is the solute concentration inthe blood. When the capillary flow leaves the dermis grid,the capillary concentration is assumed to be in equilibri-um with the concentration in the dermis grid, and thusthe solute flux taken away by the capillary is given byQb,iCi/Kdb, where Kdb is the partition coefficient from der-mis to blood. Therefore, for a dermis grid i, the massbalance equation is

V i

dCi

dt¼ −

Xj

qi j þ Q b;i Cb−Ci

K db

� �ð3Þ

The above equilibrium assumption can be viewed asa simplification of the capillary clearance models re-ported in (18, 19), in which transient equations wereused to model the permeation of solute from dermisinto capillary. The transient equations are more com-plex since the permeability between dermis and capil-lary needs to be considered, in addition to the partitioncoefficient.

The volumetric blood flow, Qb,i, can be estimatedaccording to physiology. It is known that the averageresting cardiac output is ca. 5.6 L min−1 for a humanmale and 4.9 L min−1 for a female (25), and the overallblood flow to skin is estimated to be 5% of cardiacoutput (5). Therefore, the overall skin blood flow canbe estimated (0.05 × 5.6 = 0.28 L min−1 for male and0.05 × 4.9 = 0.245 L min−1). The blood flow is assumedto be distributed uniformly in the dermis; therefore theflow in each dermis grid (Qb,i) can be calculated basedon the volume of the grid and the volume of the der-mis. We used the average skin surface area (1.8 m2) andtypical dermis thickness of 1.2 mm (15) to calculate thevolume of the dermis, therefore the model representsthe absorption kinetics of a typical person.

The systemic circulation and clearance is descried by thefollowing equation:

V b

dCb

dt¼ N

Xi

Q b;i

C i

K db

−Cb

� �−kCb ð4Þ

where Vb is the volume of whole-body blood vessel, andkCb is the first-order clearance that may include

transport into other tissues and metabolism. The sum-mation is with respect to all dermis grids, and N is theratio of actual topical application area and the areabeing simulated. For computational efficiency, the later-al length being simulated usually covers a fewcorneocytes (one corneocyte in this study), and thusthe simulated area is much smaller than the actual ap-plication area. The whole-body blood volume, Vb, canbe calculated from the typical fraction of blood mass tothat of adult body weight (7%) and the blood density(1.06 of water density). The clearance rate, k, of manypharmaceutically or toxicologically important chemicalsis available from clinical pharmacokinetic studies of oraland/or intravenous delivery routes.

The simulation was performed by solving the ODEs on thegrids explained above. All initial concentration is set to zero,except that in the vehicle. The left and right boundaries in thestratum corneum are periodic conditions, to represent a largeapplication area.

The model was implemented in C++, where the dif-ferential equations are solved by calling the state-of-the-art CVODE solver as part of the SUNDIALS computa-t ional package (26) developed in the LawrenceLivermore National Laboratory (computation.llnl.gov/casc/sundials). The user interface was written in Python(www.python.org) with extensive use of Scipy (a scientificmodule of Python, www.scipy.org). Interfacing betweenC++ and Python was achieved by using the SWIG(Simplified Wrapper and Interface Generator, www.swig.org) tool. The hybrid programming method wasuseful to achieve sufficient computational efficiencywhen solving a large number (3190) of differential equa-tions, whilst limiting the developmental time. The sourcecode is publ ic ly avai lable at www.gi thub.com/anthonytchen/lck. All computation was conducted on alaptop computer with dualcore CPU (2.80 GHz) installedwith an Ubuntu (version 15.04) Linux operating system.

Diffusion and Partition Coefficients of Skin and Vehicle

The diffusion and partition coefficients of skin and ve-hicle depend on the physicochemical properties of thesolute, including the molecular weight (MW, Da), thehydrophobicity in terms of octanol/water partition co-efficient (Kow), the dissociation constant (pKa), as wellas the composition of the skin. A range of QSPRmodels have been reported for calculating the diffusionand partition parameters. In this section, the QSPRmethods implemented in our model is outlined forcompleteness. More details can be found in the originalarticles (13, 15, 27).

In the vehicle, the diffusion and partition coefficients de-pend on the formulation. If a simple aqueous solution is used,

In Silico Modelling of Transdermal and Systemic Kinetics 1605

the partition coefficient between vehicle and water, Kfw, isunity, and the diffusion coefficient can be calculated usingthe Stokes-Einstein equation:

Dw ¼ KT

6πηrsð5Þ

where K is the Boltzmann constant, T is the temperature, η isthe viscosity of water and rs is the solute radius (Å) calculated

as: rs ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3=4� 0:0987MW3

p(28).

In the stratum corneum, the partition coefficient betweenthe “mortar” (the lipid bilayer) and water is determined by thefollowing relationship:

K mw ¼ ρlρw

K 0:69ow ð6Þ

where ρl and ρw are the bulk density of lipid and water, re-spectively. The solute diffusion coefficient, Dm (m2 s−1) in thelipid is related to solute radius as described in (1, 13):

Dm ¼ 2� 10−9exp −0:46 r2s� �

; MW ≤ 380Da3 � 10−13 ; MW > 380Da

�ð7Þ

The partition coefficient between corneocytes (i.e. the“brick”) and water (Kbw) is estimated from the volume fractionof water in corneocytes (ϕb is the fraction at saturation and θbis the actual fraction), and the solute binding constant to ker-atin in stratum corneum (Kkw):

K bw ¼ 1−ϕbð ÞK kw þ θb ð8Þ

where Kkw = ρk/ρw × 4.2Kow0.31 and ρk is the bulk density of

keratin (29, 30). The diffusion coefficient in the corneocyte(Db) is estimated according to the following equation of hin-dered diffusion (13):

Db ¼exp −αSλ

� �1þ rsffiffiffi

kp þ r2s

3k

� Dw ð9Þ

where k= βrf2(1− θb)

γ, S= (1− θb)[(rs+ rf)/rf]2, and rf is the ra-

dius of keratin microfibril (35 Å). The others are parametersfitted to experimental data: λ = 1.09, γ = − 1.17, α = 9.47,β= 9.32 × 10− 8.

The partition coefficient (Kvw) in the viable epidermis anddermis is assumed to be the same, and so is the diffusioncoefficient (Dv, m

2 s−1), because of the similar multiphase com-positions in the two skin layers (20, 31). This approach wasalso used in other modelling studies (15, 31, 32). We follow themethod presented in (15, 20) to relate the partition and

diffusion coefficients to solute ionisation and binding to albu-min as follows:

K vw ¼ 0:7� 0:68þ 0:32f u

þ 0:025 f nonK mw

� �ð10Þ

Dv ¼ 10−8:15−0:655logMW

0:68þ 0:32f u

þ 0:025 f nonK mw

ð11Þ

where fnon is the non-ionised fraction of solute in the aqueousphase; fnon depends on the chemical dissociation constant andthe pH of the solution, and it can be calculated by using theformulate given in (33, p.72) or more sophisticated softwaretools (e.g. ACD/Labs). The fraction of unbound (to albumin)solute (fu) may be estimated by using the QSPR model devel-oped in (34).

Finally, the dermis to blood partition coefficient, Kdb, needsto be estimated. In the literature, various QSPR models havebeen reported for volatile organic compounds, where Kdb canbe related to experimentally measured oil-to-air and/orsaline-to-air partition coefficients (35). Alternatively it can alsobe estimated by using the Abraham descriptors and accord-ingly the QSPR model reported in (27).

Model Demonstration: Clinical Studies of Nicotine

A published clinical study of transdermal delivery of nicotine(23) was used to support model development and demonstra-tion. The model was also applied to predict another clinicalstudy of nicotine (24), which was not considered during modeldevelopment, to test the prediction performance.

Nicotine replacement therapy has been widely used for thepurpose of smoking cessation, and its transdermal delivery hasbeen popular. One important advantage of the transdermalroute is that it provides continuous and controlled release ofthe drug, which has contributed to the reduction of cravingand withdrawal symptoms during smoking cessation. As aresult, various nicotine transdermal systems have been devel-oped, with many clinical studies reported in the literature (e.g.,23, 36). A brief description of the study by Bannon et al. (23),which was used to support model development, is givenbelow.

Bannon et al. (23) investigated the absorption of nicotinedelivered from a hydrogel based matrix-type transdermalpatch (Nicolan™). Three dose levels were studied by varyingthe surface areas of the patch: 3.5 cm2 for 15, 7.0 cm2 for 30,and 14.0 cm2 for 60 mg. Healthy smokers were recruited forthe study, and they agreed to abstain from smoking prior toand during the study which was verified by monitoring thecarbon monoxide levels. In the first study, the transdermalpatches were applied to the volar forearm of nine subjectsfor 24 h and the plasma nicotine concentration was measured

1606 Chen, Lian and Kattou

at several time points up to 30 h. The aim was to examine theimpact of dose level on absorption kinetics. In the multipledose study, the subjects were given one fresh 30-mg patchevery 24 h for 7 days and blood samples were taken at varioustime points. The total delivered dose was approximately 85%of the nicotine content in the patches, as calculated frommea-suring the residual nicotine in the patch after removal.

To simulate the above scenarios, various skin physiologyand solute physicochemical parameters are needed; thesewere largely taken from the literature and summarised inTable I. We adjusted the number of cell layers in thestratum corneum according to the reported thickness atvolar forearm, which has significant variability within onestudy and between different studies. The thickness of thestratum corneum was set to 20.5 μm, which is the averagemeasured by Egawa et al. (37) (22.6 μm) and Sandby-Molleret al. (38) (18.3 μm). This thickness corresponds to 23corneocyte-lipid layers (assuming 0.875 μm for each layer(15)). The thickness of the patch was not given; hence thenicotine concentration in the vehicle has to be estimated.We followed similar modelling studies (e.g. 22) to assume avehicle depth of 100 μm, from which and the given surfacearea the concentration can be determined.

The partition and diffusion coefficients of nicotine in thehydrogel-based vehicle depend on the properties of the hydro-gel. Solute partitioning and diffusion in hydrogel has beenwidely studied both theoretically and experimentally (39,40). Hydrodynamic hindrance of hydrogel on the diffusioncoefficient is rather limited for small molecules, often less than10% reduction of that in water (39, 41). For this reason, the

diffusion coefficient of nicotine in the hydrogel vehicle wasfixed to the same value as in water (calculated in Eq. (5)).The partition coefficient between hydrogel and water wastypically reported to be between 0.5 and 1, depending onthe volume fraction of dispersed polymers (40). In this study,the partition coefficient of nicotine between vehicle and waterwas set to 0.7. Due to the lack of precise information about thevehicle, sensitivity analysis was conducted to investigate theimpact of vehicle properties (partition and diffusioncoefficients).

The diffusion and partition properties of nicotine instratum corneum were calculated in the same way aspreviously verified (14). The fraction of nonionised nico-tine at pH 7.4 and binding to plasma protein, which areneeded for these calculations, were set to the experimen-tally reported values: fnon = 0.31 and fu = 0.95 (42, 43).The partition coefficient of nicotine between dermisand blood is also set to the experimental value: logKdb = − 0.04 (27). The nicotine clearance in systemic cir-culation was set to 1.40 L min−1 as reported (43).

The other clinical study reported the systemic kinetics ofthe Nicorette® Invisi 25 mg Patch™ (McNeil Products Ltd.,Maidenhead, UK) (24). The patch was designed to be wornfor 16 h and plasma concentration data were available for 32h. The vehicle concentration was calculated based on the re-ported loading dose (1.75 mg/cm2), patch size (22.5 cm2) andthe assumed vehicle thickness of 100 μm. All other input pa-rameters are the same as the Nicolan case described above.The intention was to further test the prediction performanceof the model.

Table I The Input Parameters ofthe Model for Simulating theNicotine Study

Part name Parameter Value

Nicotine Molecular weight (MW) 162.23 Da

Octanol-water partition coefficient (logKow) 1.17

Fraction of non-ionised solute (fnon) 0.31

Fraction of unbound solute (fu) 0.95

Vehicle Thickness 100 μmInitial nicotine concentration 428.57 mg mL−1

Stratum corneum Number of corneocyte layers 23 (volar forearm)

Width of corneocytes 40 μmHeight of corneocytes 0.8 μmThickness of inter-cellular lipid 0.075 μmThe lateral spacing between corneocytes 0.075 μm

Viable epidermis Thickness 100 μmDermis Thickness 1200 μm

Dermis-blood partition coefficient of nicotine (logKdb) −0.04

Blood Cardiac output 5.6 L min−1

Skin blood flow as fraction of cardiac output 5%

Nicotine clearance in blood (k) 1.40 L min−1

In Silico Modelling of Transdermal and Systemic Kinetics 1607

RESULTS

For the Nicolan patch, the predicted plasma concentration fordifferent dose levels is illustrated in Fig. 2, in comparison withthe clinical data. It appears that the model is capable of re-producing the main trend of the kinetics in plasma. This isespecially the case for the intermediate dose level of 30 mg.For 60mg, themodel slightly over-predicts the rate of increasein concentration at the beginning, whilst for 15 mg, the peakconcentration is slightly over-predicted. It should be notedthat in the original report (23), only the mean concentrationvalues of nine subjects were given but not the standard devi-ation, and thus it is not possible to fully consider the inter-subject variability in comparison. However, for 30 mg, thedata from both the single dose study and the first 24 h of themultiple dose study were augmented in Fig. 2, and even thesetwo sets of average data exhibit significant differences.Therefore, the difference between the model prediction andclinical data is well within the variability of such clinicalstudies.

Table II compares the predicted pharmacokinetic param-eters for the single dose study with the experimentally deriveddata. As observed from Fig. 2, the model tends to predict thetime to reach maximum concentration (tmax) earlier than thatindicated by the data, though still within 1.0 ~ 1.5 standarddeviation from the average of the data. The prediction of theremaining pharmacokinetic parameters, such as AUCs, Cmax

and the fraction of absorbed dose ( f ), is in good agreementwith the data.

Figure 3 compares the model prediction and clinical datafor the 30 mg multiple dose study. Apparently the predictedend-of-day plasma concentration, when the old patch is re-placed by a new one, is higher than the actual data. In thecollected data, the value at 24 h for the multiple dose study

(4.58 ng mL−1) was also reported to be substantially lowerthan the value for the single dose study (7.90 ng mL−1).Therefore the model prediction is in reasonably good agree-ment with the data. Another observation is that from day 2,the model predicted plasma concentration cycles quite stablywith negligible day-to-day variation, whereas the reportedclinical data showed variation at 24, 48, 96, 144 and 168 h.

Figure 4 illustrates the simulated disposition of nicotine atdifferent skin layers, in the blood compartment and the cumu-lative amount cleared from the blood. The simulation was ex-tended to 50 h (i.e. 26 h after the patch is removed) to allow forsufficient clearance of nicotine from the system. It can be seenthat within the skin, themajority of the applied dose is absorbedin the stratum corneum, whilst the viable epidermis and dermiscontain very small proportions. The concentration of nicotinein the stratum corneum is significantly higher than that in theunderlying viable epidermis and dermis. There is a large par-tition coefficient of nicotine between the stratum corneum(lipid) to viable epidermis (K= 7.73). The diffusion of nicotinein the viable epidermis and dermis (2.36 × 10−10 m2 s−1) is alsomuch faster than that in lipid bilayer (1.43 × 10−11 m2 s−1) andcorneocyte (2.67 × 10−15 m2 s−1) in the stratum corneum.Physiologically, the viable epidermis and dermis contain up to70% aqueous phase (20), which has important impact on thepartition and diffusion coefficients of the lipophilic nicotine. Inaddition, the concentration of solute in systemic circulation alsoappears to be much lower than in the stratum corneum, whichis likely due to the rapid clearance as a result of metabolism intocotinine (23). The detailed modelling of various plasma clear-ance pathways, e.g.metabolism and transport into other tissues,is outside the scope of this study.

From the simulation results, the relative ratio of nicotinedeposition in skin can be obtained. Figure 5 gives the relativepercentage nicotine disposition within the stratum corneum; it

Fig. 2 Comparison of modellingresults with the published clinicaldata of Bannon et al. (23) followingthe application of nicotine transder-mal patches with different doses(patch removed after 24 h ofapplication).

1608 Chen, Lian and Kattou

shows that more solute stays in the corneocyte (the “brick”)than in the lipid (the “mortar”). Although the concentration inthe lipid is much higher than that in the corneocyte (c.f. Fig. 6),the total volume fraction of lipid in the stratum corneum isonly about 8.7% (calculated by using the geometricparameters in Table I), and thus the total solute amount inlipid is less. In addition, the peak amount in the lipid isachieved more quickly than in the corneocyte; this is expectedbecause the diffusion coefficient in the lipid is much higherthan that in the corneocyte.

Figure 6 gives detailed disposition of nicotine in the stratumcorneum at different time points using two-dimensional con-centration surface plots. The profiles vividly illustrate thedominant role of lipid pathway in skin penetration for thislipophilic compound, though the effect of corneocyte is notnegligible. At the early stage of permeation, the diffusionalong the lipid creates a clear “fingering” effect as seen inthe figure. It is also interesting to observe that at the beginning,when solute diffuses along the lipid layer, it may “back-dif-fuse” from a lower lipid layer to upper corneocytes due tothe gradient in chemical potential (considering gradient inconcentration and the effect of partitioning). This back-diffusion may slow down the initial penetration rate ascorneocytes serve as “reservoirs” and need to be filled with

the solute from the lipid. In a later stage, these reservoirs firstreach equilibrium with surrounding lipid and then release thesolute as the chemical potential in the lipid is further lowereddue to diffusion into the dermis and viable dermis. This cor-responds to the point when a significant amount of solute hasbeen consumed in the patch. Release from corneocyte reser-voirs can be clearly seen when the patch is removed (i.e. after24 h). For example in Fig. 6e and f, the concentration in thecentre of the topmost corneocyte layer is even higher than thatin the surrounding lipid layer, and when combined with theeffect of partitioning the chemical potential gradient createssignificant driving force to release the solute.

Figure 7 shows the sensitivity analysis with respect to themodel input parameters in the vehicle of the Nicolan study.We first examine the likely effect of varying the partition co-efficient between vehicle and water from 1/10 to 10 times ofits nominal value (Kfw= 0.7). Increasing the partition coeffi-cient represents the use of a more hydrophobic vehicle formu-lation. Conversely, decreasing the partition coefficient mimicsthe use of a more hydrophilic formulation. Clearly, changingvehicle partition property has a significant impact on the de-livered plasma concentration (Fig. 7a). Using a more hydro-philic vehicle of lower partition coefficient results in fasterincrease of plasma concentration, shorter tmax, and higher

Table II Plasma NicotinePharmacokinetic Parameters for theSingle Dose Study. StandardDeviation is Given in theParentheses. In the Clinical Study,the Fraction of Solute Absorbed (f)was Calculated from ResidualNicotine in the Patch After Removal

Dose level 15 mg Model 30 mg Model 60 mg ModelData Data Data

AUC0–30 (ng hr mL−1) 152 (34.6) 153 294 (53.1) 273 509 (88.9) 494

AUCinf (ng hr mL−1) 170 (36.5) 165 310 (56.4) 294 541 (99.7) 533

tmax (hr) 7.78 (4.27) 5.53 7.78 (1.86) 5.53 8.22 (3.07) 5.53

Cmax (ng mL−1) 8.02 (1.96) 8.62 17.1 (5.03) 15.4 28.9 (9.14) 27.9

f 0.85 (0.084) 0.82 0.87 (0.024) 0.82 0.83 (0.072) 0.82

Fig. 3 Comparison of modellingresults with clinical data of Bannonet al. (23) following the applicationof nicotine transdermal patches thatwere replaced every 24 h.

In Silico Modelling of Transdermal and Systemic Kinetics 1609

Cmax of nicotine. The plasma concentration of nicotine at laterstage is also more rapidly depleted. In contrast, by using amore hydrophobic vehicle of higher partition coefficient, nic-otine is predicted to favour staying in the vehicle, leading tosustained slower release into skin and blood circulation. For agiven vehicle formulation, different solutes also have differentvehicle:water partition coefficients but the effect is more com-plicated, as the partition and diffusion properties in the skinwill also vary.

We also examine the effect of nicotine mobility in the ve-hicle. The diffusion coefficient of nicotine in vehicle was re-duced to 1/10, 1/100, 1/1000 and 1/10000. This essentiallymodels the effect of controlled releases. Figure 7b shows thatreducing the diffusion coefficient of the vehicle by two ordersof magnitude has negligible impact on the pharmacokineticsof nicotine delivery – its plasma concentration appears to be

not distinguishable. The diffusivity of nicotine in vehicle onlystarts to reduce the plasma concentration when this parameteris reduced by more than 100-fold. Further reduction of thediffusion in vehicle makes this parameter comparable withthat in skin, and thus it slows down the penetration, leadingto sustained slow release and lower plasma concentration.

Finally, Fig. 8 illustrates the results for the separateNicorette data set reported by DeVeaugh-Geiss et al. (24).Good agreement between model prediction and clinical datais also achieved. The predicted kinetics is appreciably fasterthan the actual data (experimentally derived tmax is 12.0 h,while the prediction gives 6.0 h). Nevertheless, the modelwas able to describe the main pattern of the profile, with goodprediction of AUC0–32 (model: 262.9 ng hr mL−1; data:238.51 ng hr mL−1) and Cmax (model: 14.50 ng mL−1; data:16.56 ng mL−1).

Fig. 4 Simulated disposition ofnicotine in different skin layers andthe circulation. The patch isremoved after 24 h of application.

Fig. 5 Simulated disposition ofnicotine in lipid and corneocytes,and their relative amount(percentage) with respect to thetotal nicotine in the stratumcorneum. The initial dose in thevehicle is 30 mg, and the patch isremoved after 24 h of application.

1610 Chen, Lian and Kattou

DISCUSSIONS

The primary intention of this paper is to present an integratedmechanistic model that captures the important molecular andmicroscopic principles involved in skin penetration andsystemic bioavailability. To demonstrate the use of theintegrative mechanistic model, two sets of published clinicaldata of nicotine patches (23, 24) have been simulated. Thepredicted nicotine concentration in systemic circulation is ingood agreement with the reported clinical data. Furthermore,after validation with plasma concentration, such a bottom-upmodel can predict the microscopic kinetic and bioavailabilityinformation in various skin layers, which may not be easily

measured in clinical studies but are of particular importancefor intended topical delivery. From the simulation, the dispo-sition of nicotine in different skin layers is also obtained (Figs.4, 5 and 6).

In the simulation, all input parameters for the vehicle, stra-tum corneum, viable dermis, dermis and systemic circulationwere derived separately from their molecular, microscopicand physiology bases. The nicotine partition and diffusioncoefficients in the hydrogel-based vehicle were estimated byreferring to “typical” hydrogel properties and the impact onsolute diffusion/partition reported in the literature (39, 40).Reducing the diffusion coefficient in vehicle within 3 ordersof magnitude was found to have negligible impact on the

Fig. 6 Microscopic disposition ofnicotine in the stratum corneum.The initial dose in the vehicle is30 mg, and the patch is removedafter 24 h of application. The unit inall colour maps is mg mL-1. Theboundary between lipid andcorneocytes are marked with solidline. Note that because of the verysmall lipid size relative to that ofcorneocytes, the 2D simulationdomain is illustrated in terms of gridpoints and thus is not to scale. (a)0.5 h; (b) 1 h; (c) 2 h (d) 24 h; (e)25 h; (f) 25 h with adjusted colourmap. The same, fixed colour mapwas used for (a)-(e), but to illustratethe detailed concentration profile at25 h, the colour map in (e) wasadjusted to produce (f).

In Silico Modelling of Transdermal and Systemic Kinetics 1611

Fig. 7 Sensitivity analysis of theimpact of vehicle properties onsystemic kinetics of nicotine. (a) Theimpact of vehicle:water partitioncoefficient; (b) The impact ofdiffusion coefficient in vehicle. Thelegend B×0.1^ denotes that theinput parameter in the base modelwas multiplied by 0.1 to obtain theresult. Experimental data is fromBannon et al. (23).

Fig. 8 Comparison of modelprediction with the published clinicaldata of Nicorette patch fromDeVeaugh-Geiss et al. (24).

1612 Chen, Lian and Kattou

simulation results. The partition coefficient between vehicleand water however does have a significant effect. The chosenvalue (0.7) was derived by mainly considering the exclusioneffect. Mathematically, vehicle partition coefficient can be fur-ther refined by optimisation so that the fit to the clinical datacould be further improved. Nevertheless, that vehicle partitioncoefficient has significant effect on the simulation results, asshown in the sensitivity analysis, is a valuable insight for con-trolling the delivery of topically applied nicotine.Experimental and theoretical insight for designing vehicle par-tition property is an area of active research (39–41). Here weperformed a systematic sensitivity analysis of the vehicle.Increasing the hydrophobicity of the vehicle leads to slowerrelease and sustained delivery of nicotine to systemic circula-tion. Using more hydrophilic vehicle formulation leads tofaster delivery depletion of nicotine in the plasma circulation.Reducing the diffusion coefficient of the vehicle by 3 orders ofmagnitude has negligible effect on the pharmacokinetics ofnicotine release, absorption and bioavailability. For controlledrelease formulations to be effective, the equivalent diffusioncoefficient of nicotine in the vehicle has to be reduced bymorethan two orders of magnitude.

In the clinical studies only the area of the patch is given, butnot the depth. For the simulation, the thickness of the vehicle isestimated from the dose. Varying the depth of the vehiclerequires the corresponding adjustment of nicotine concentra-tion and hence can impact on pharmacokinetics of plasmaconcentration of nicotine but the shape of curve will remain.This feature enabled us to estimate the thickness of the vehicleto be ca. 100 μm. The corresponding initial nicotine concen-tration in the vehicle (Nicolan) is 428.57 mg mL−1, or 42.67%w/w, (assuming the vehicle as an ideal aqueous solution). Thisvalue is close to the nicotine concentration (48% w/w)achieved for the maximum steady-state flux across skin (44).

CONCLUSION

This paper reports the development of a detailed mechanisticmodel that integrates the skin penetrationmodel with systemiccirculation kinetics. To validate the model, the published clin-ical data of transdermal pharmacokinetics of nicotine wassimulated. All input parameters for the model, including thesolute (nicotine), the vehicle, the stratum corneum, the dermis,the viable dermis and systemic circulation, were determinedindependent of the in vivo pharmacokinetics being predicted.The integrated mechanistic modelling has significantly ex-tended the applicability of the current microscopic skin pene-tration model by providing prediction of solute concentrationin the blood. In addition, by using advanced computationaltechniques, we report the simulation of detailed two-dimensional concentration profile in the stratum corneum,which provides useful information of the local sub-cellular

disposition kinetics in skin. The future work will be focusedon more comprehensive validation of the model with a widerange of chemicals, and further assessment of the usability ofthis model in the design and safety assessment of pharmaceu-tical, personal care and other chemical products to which thetransdermal route is relevant.

ACKNOWLEDGMENTS AND DISCLOSURES

This work was supported by the UK Royal Academy ofEngineering (grant number: ISS1415\7\46), theBiotechnology and Biological Sciences Research Council(grant number: BB/L502042/1), and Unilever ResearchColworth, UK. We would like to thank Drs Stephen Glavinand Ian Sorrell at the Safety and Environmental AssuranceCentre, Unilever, for useful discussions on dermal pharmaco-kinetic modelling and safety assessment.

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