Ind. Eng. Chem. Res. 2008, 47, 6465–6472
6465
Use of “Bricks and Mortar” Model To Predict Transdermal Permeation: Model Development and Initial Validation Longjian Chen,† Guoping Lian,‡ and Lujia Han*,† China Agricultural UniVersity, P.O. Box 232, 17 Qing-Hua-Dong-Lu, Beijing 100083, P.R. China, and UnileVer Corporate Research, Sharnbrook, Bedford MK44 1LQ, U.K.
Presented in this paper is a general purpose computer model for predicting transdermal permeation of solutes in vivo. The “bricks and mortar” model is employed to represent the stratum corneum (SC), the main barrier to transdermal permeation. Transdermal permeation and absorption is modeled as a dynamic process of mass transfer in the heterogeneous stratum corneum including both the tortuous lipid pathway and the transcellular corneocytes pathway. The partition and diffusion properties of solutes in SC lipid matrix and corneocytes are calculated from the fundamental physical chemical properties of octanol-water partition coefficient, molecular size, and diffusion coefficients in water and lipid, using equations established elsewhere. To test the model, the in vivo tape striping data of 4-cyanophenol is simulated. Using the calculated partition and diffusion properties of 4-cyanophenol in SC lipids and corneocytes, the predicted dynamic profiles of 4-cyanophenol in the SC agreed very well with the experimental data. Results show that for a moderately hydrophobic solute like 4-cyanophenol, the transcellular pathway is also an important route of percutaneous absorption with about 2/3 of the absorbed 4-cyanophenol partitioned into the corneocytes. Introduction Understanding the permeation of molecules through human skin is of importance to a number of applications including transdermal delivery of drugs, formulation design of skin cream products, and risk assessment of hazardous chemical exposure. The process of transdermal permeation is affected by a number of factors. In particular, the partition properties of solutes between different phases (vehicle to skin, lipid to water, and keratin to water) are key factors for transdermal delivery. The cellular structure of the skin is also an important factor. As a result of the heterogeneous structure of human skin, transdermal permeation is normally envisaged as involving different stages including diffusion through stratum corneum (SC), penetration into the hydrophilic viable epidermis, and diffusion in the aqueous environment of living epidermis and dermis. It has been commonly accepted that the rate limiting step for the permeation of most solutes is the diffusion through the SC. This is primarily due to the composition and cellular structure of SC.1-4 The diffusion coefficient in the SC is found to be 2 to 4 orders of magnitude smaller than that in dermis and epidermis.5,6 There have been a number of modeling studies on transdermal permeation. Early studies modeled transdermal permeation as simple diffusion in homogeneous media and disregarded the heterogeneous structure of the SC. These models have limited use and rely on experimentally measured transdermal permeation data to fit the skin permeability or other model parameters.7-9 It was soon realized that the heterogeneous structure of the SC need to be considered and hence the “brick-and-mortar” model.1,3,10 The model was first proposed by Michaels et al.3 Tojo11 later extended the model by randomizing the packing order of the proteinaceous phase within the intercellular lipid phase. Albery and Hadgraft1 developed a nonsteady-state diffusion model based on an idealized geometry of the “brick and mortar” in which the cells are not stacked but rather are * To whom correspondence should be addressed. Telephone: 8610-62736313. Fax: 86-10-62736778. E-mail:
[email protected]. † China Agricultural University. ‡ Unilever Corporate Research.
diagonally packed continuously throughout SC. Heisig et al.10 presented a “brick-and-mortar” and solved the problem numerically. A challenge in applying many of the “brick-and-mortar” models is how the solute diffusion and partition properties in the SC lipids and corneocytes should be established.10,12,13 A few “brick-and-mortar” models obtained solute diffusion and partition properties in lipid matrix and corneocytes phase by fitting the same experimental data they modeled.14-17 As such, these “brick-and-mortar” models have limited use in predicting new molecules and new topical formulations and regimes. Recently, Wang and co-workers presented a multiphase microscopic diffusion model in which some of the solute diffusion and partition properties in SC lipids and corneocytes are established separately by relating to the fundamental physicochemical properties of solute.18,19 However, to apply their “brick-and-mortar” model to predict skin permeability of some molecules they still have to fit a model parameter (transbilayer mass transfer coefficient, ktrans) to the same skin permeability data. It appears that although some previous modeling studies have considered the heterogeneous structure of the SC using the “brick and mortar”, the partition and diffusion properties of the SC lipid matrix and corneocytes can not be established separately without fitting to the same experimental data. In addition, despite a number of recent studies on the influence of skin hydration on transdermal permeation,20 most models (apart from the model presented by Wang et al.18,19) did not include the effect of hydration on transdermal permeation. Generally, there is still a lack of models capable of directly predicting transdermal permeation of solutes without parameter fitting to the same data to be modeled. This paper presents a general purpose computer model for direct prediction of transdermal permeation. The “brick-and-mortar” model is used to represent the heterogeneous structure of the SC. Equations for calculating the partition and diffusion properties of the SC lipids and corneocytes are established separately by relating to the fundamental physical chemical properties of solutes. In addition, these equations are also functions of SC hydration. The general-purpose model has been coded in MATLAB. Validation of the model for predicting transdermal permeability
10.1021/ie701711v CCC: $40.75 2008 American Chemical Society Published on Web 07/31/2008
6466 Ind. Eng. Chem. Res., Vol. 47, No. 17, 2008
of both hydrophobic and hydrophilic solutes will be reported separately. Here, the model is applied to predict the in vivo tape striping data of 4-cyanophenol. The predicted 4-cyanophenol profile in the SC is compared with the experimental data and there is a good agreement. Methods Brick and Mortar Model. Like most previous studies, we consider the stratum corneum as the major barrier for transdermal permeation. First, consider the heterogeneous structure and biochemical composition of the stratum corneum. It is wellknown that stratum corneum is made of densely packed cells. Dead in their biological functions, cells in the stratum corneum serve to regulate water loss from the body and prevent the entry of foreign substances into the body. A number of experimental studies have been made on the cellular structure and biochemical composition of the stratum corneum.21-23 In particular, some imaging studies21,23 showed that the corneocytes phase creates elongated and tortuous pathways of intercellular lipid matrix. It is estimated that the tortuosity of the continuous lipid matrix is approximately 5-10.23,24 Typical human stratum corneum has a thickness of 10-20 µm on most areas of the body. There are 10-20 layers of tightly compacted cells discretely embedded in the lipid matrix. The main substance in the discrete cells of the stratum corneum is keratin. Keratin is a protein accumulated when the cells move up from the basal layer into the granular layer beneath the stratum corneum. The keratinized corneocyte represents of 85-90% of the dry mass of stratum corneum. Keratin is highly insoluble and is very resistant to the entry of foreign chemicals.25 It is the property and composition of keratinized corneocyte that plays an important role in acting as physical impediments and reducing the overall chemical transport through the SC.24 The continuous extra-cellular lipid matrix is believed to be the major pathways for transdermal permeation of hydrophobic solutes.24,26 Representing 10-15% of the dry mass, lipid matrix in stratum corneum generally consists of an equimolar mixture of ceramides, cholesterol, and free fatty acids. It has been proposed that lipids in the SC form crystalline lamellar phases surrounded by grain boundaries.27 Early studies have established the strong correlations of skin permeation with lipid content.22,28 Apart from lipid and protein, water is another major substance in the SC and is secondary to keratinized corneocytes in mass. At normal hydration level, water distribution along the SC is not homogeneous and changes from approximately 15% at the outer surface to approximately 50% at the most inner cells of the stratum corneum. Although the average water content of the SC in vivo under normal hydration level is approximately 30%,29,30 the water content of the SC in vivo can increase substantially under occlusion.31,32 The SC hydration level under an in vitro condition can vary widely and ranges from 45% to 70%.33 The level of hydration of the SC and in particular its distribution between lipid and corneocyte phases is also a key factor influencing the permeation properties of the SC.20,34,35 However, previous modeling studies on transdermal solute permeation have mostly ignored the effect of water content.3,10,12 In this study, the SC is considered as a heterogeneous material, using the widely accepted “bricks-and-mortar” model. The diffusion and partition properties of solutes in both the lipid matrix and the corneocytes are directly calculated from fundamental physical and chemical properties. First, consider the mathematical relationship between “brick-and-mortar” structure and the major biochemical compositions of the stratum corneum.
Assume the stratum corneum as consisting of N layers of corneocytes (bricks) of width d and height t, imbedded in a continuous lipid matrix (mortar) of thickness g. The lateral spacing between neighboring keratinocytes is denoted as s. The SC is considered to consist of lipids, keratin, and water only. Both the lipid matrix and the corneocytes contain water. The volume fraction of water at saturation is φm for lipid matrix (mortar) and φb for corneocytes (brick). Changes in water content result in swelling and shrinking of the SC. Like many previous modeling studies,24,26 swelling and shrinking of stratum corneum is ignored in this study for simplicity. The underlying implication is that the porosities of both SC lipids and corneocytes are considered to be constant. Here the porosity is defined as the volume fraction of the SC pores at fully dehydrated state. For this reason, the use of volume fraction of water at saturation and porosity is exchangeable. The volume fraction of water in the SC at saturation (φSC) is related to the volume of lipid (Vl), keratin (Vk), and saturated water (Vw) by φSC ) Vw/(Vw + Vl + Vk). The water phase is distributed into the SC lipids and corneocytes (Vw ) Vwl + Vwk) with the corresponding saturated volume fraction of water (or porosity) in SC lipids and corneocytes as φm ) Vwl/(Vwl + Vl) and φb ) Vwk/(Vwk + Vk). Since Vw + Vl + Vk ) Vwl + Vl + Vwk + Vk, it follows that Vw/φSC ) Vwl/φm + Vwk/φb. Using the relationship Vw ) mw/Fw, Vl ) ml/Fl, and Vk ) mk/Fk (where m is mass, F is density, and the subscripts w, l, and k represent water, lipids, and keratin), it follows that porosity of the SC is related to the porosities of SC lipids and corneocytes by fl/Fl fk/Fk fl/Fl + fk/Fk ) + 1 - φSC 1 - φm 1 - φb
(1)
where fl (≈ 12.5%) and fk (≈ 87.5%) are the dry mass fractions of SC lipid and keratin. The bulk densities of lipid, water, and keratin are set to Fl (≈ 1000 kg/m3), Fw (≈ 1000 kg/m3), and Fk (≈ 1200 kg/m3).36 The overall porosity of the SC can be also related to its saturated water content (mass fraction) by the following equation φSC )
fSC Fw(1 - fSC)(fl/Fl + fk/Fk) + fSC
(2)
where fSC is the saturated water content of the SC expressed in mass fraction. The geometrical dimensions of the “brick-and-mortar” model have to be consistent with the compositions of the stratum corneum in terms of the dry mass of lipid matrix and corneocytes. The relationship can be written as for lipid matrix Fl[g(d + t + g)(1 - φm)] ) 12.5% Flg(d + t + g)(1 - φm) + Fkdt(1 - φb)
(3)
and for keratin Fkdt(1 - φb) ) 87.5% Flg(d + t + g)(1 - φm) + Fkdt(1 - φb)
(4)
Typical geometrical parameters of the stratum corneum are given as d ) 40 µm, t ) 0.8 µm, s ) 0.075 µm, and g ) 0.075 µm.24 The other important parameter of the “brick-and mortar” model is the offset ratio, w, which is expressed as the ratio to the path lengths from the interkeratinocyte lipid slit of one layer to the two closest slits in the next lower layer, as shown in Figure 1. For rodent skin, the typical value of the off-set ratio is 8. Talreja and co-workers showed that for the human SC, the off-set ratio is approximately 3, which leads to twice the
Ind. Eng. Chem. Res., Vol. 47, No. 17, 2008 6467
This relationship fits measured SC lipid partition data well, although reported values of n varied. In this study the power index is set to n ) 0.7. This is the fitted value of Mitragotri38 who combined the data set of Raykar et al.42 with that of Johnson et al.41 and some other later experimental data.43 Mass Transfer in Corneocytes. Mass transfer in the discrete “bricks” of SC corneocytes is also described by two parameters, the effective diffusion coefficient and partition coefficient between corneocytes and water, both dependent on the water content. The equation of mass transfer in the corneocytes may be expressed as ∂Cb ) ∇ (Db ∇ Cb) ∂t
Figure 1. Schematic diagram of the “brick-and-mortar” model of human stratum corneum (SC). Corneocyte width (d), corneocyte thickness (t), number of corneocyte layers (N), the vertical gap between corneocytes (g), the lateral spacing between corneocytes (s), and the offset ratio (w ) dm/ dn).
tortuosity.23 The off-set ratio of 8 is frequently used in many modeling studies.24,26 In this study, the off-set ratio is also set to 8. Mass Transfer in Lipid Matrix. In this study the mass transfer properties of the SC lipids and corneocytes are established separately. The mass transfer equation in the continuous “mortar” of lipid matrix may be written as ∂Cm ) ∇ (Dm ∇ Cm) ∂t
(5)
where Cm is the apparent concentration of solute in the continuous “mortar” of lipid matrix and Dm is the diffusivity of solute in lipid matrix. There are two mass transfer parameters for the SC lipids, the diffusion coefficient and the partition coefficient. Few models considered the anisotropic diffusion in the SC lipids, characterized by lateral diffusion and transverse lipid bilayer transfer.19 However, the majority of “brick and mortar” models regarded diffusion in the SC lipids as isotropic. Considering that the SC has complex lipid organizations with crystalline and liquid domains coexist,37 the current paper assumes that at continuum media level, the diffusion in the SC lipid matrix is also isotropic. A model for predicting solute diffusion and partitioning in SC lipids was proposed by Mitragotri.38 Using the scaled particle diffusion theory, the equation of solute diffusion in lipid matrix was derived as follows: Dm )
{
2 × 10-9 exp(-0.46rs2) if MW e 380 Da if MW > 380 Da 3 × 10-13
(6)
2
where Dm is expressed in m /s and rs is the solute radius which can be calculated using the method described by Bondi39 or the empirical equation 4/3r3 ) 0.9087MW.40 Based on the linear free energy theory, many studies suggest that the solute partition coefficient between lipid matrix and water can be related to the octanol/water partition coefficient Kow via a power-law relationship26,41 Kmw ) Kown
(7)
(8)
where Cb is the apparent concentration of active molecules in the “brick” of corneocytes and Db is the effective diffusivity. Keratin constitutes the main dry mass of corneocytes. The partition coefficient of corneocytes (brick) to water, Kbw, is related to the volume fraction of water in the corneocyte phase, µb, and the partition coefficient between keratin and water, Kkw, as follows: Kbw ) (1 - φb)Kkw + θb
(9)
Experimental values of Kkw were usually measured using delipidized SC.42,44-47 The reliability of these data relies on whether the delipidization processes alter the solute binding properties of keratin. There are significant variations in published results. The data of Anderson, Raykar, and co-workers42,44,45 are very different from those of Surber et al.46,47 The work of Anderson, Raykar, and co-workers indicated that the delipidization processes does not appreciably alter the solute binding properties of the keratin. These data were fitted with a power law in the following form:45 Kkw ) 5.6(Kow)0.27
(10)
This equation was derived by fitting the experimental data of the compounds with Kow g 10. For Kow < 10, however, the above equation predicts solute solubility in keratin much higher than those in water, octanol, and lipid matrix, which is very unlikely. In the absence of reliable experimental data on keratin/ water partition coefficient for solutes of Kow < 10, it is arbitrarily set to Kkw ) (1 + Kmw)/2. This is to ensure that for solutes in the range of 1 < Kow < 10 the solubility in keratin is less than that in lipid matrix and more than that in water, while for solutes of Kow < 1, the solute solubility in keratin is less than that in water and more than that in lipid matrix. In this study, the corneocytes are considered to be a gel phase and the diffusion coefficient is related to the hydration level, following the combined hydrodynamic/obstruction diffusion theory in gel networks.48 The following empirical equation proposed by Johnson et al.48 is used to predict solute diffusion in the corneocytes Db exp[-RSλ] ) Dw rs rs2 1+ + √k 3k
[
]
(11)
where S ) φf[(rs + rf)/rf]2, φf is the excluded volume and for corneocytes it is related to water content by φf ) 1 - θb, k is the hydraulic permeability of the medium and is estimated from the correlation derived by Jackson and James49 given as k ) βrf2(1 - θb)γ, rf is the radius of keratin microfibril (rf ) 3.5 nm20), and R, β, λ, and γ are model fitting parameters, respectively. Johnson et al.48 applied this model to macromo-
6468 Ind. Eng. Chem. Res., Vol. 47, No. 17, 2008
lecular (MW > 14 000 Da) diffusion in agarose gels and obtained the values R ) 0.84, β ) 0.31, λ ) 1.09, and γ ) -1.17. In this study, these values were set to λ ) 1.09, γ ) -1.17, R ) 9.47, and β ) 9.32 ×10-8. These were obtained by applying the model to fit the skin permeability data. The method had also been used by Wang et al.19 In eq 11, Dw is the diffusion coefficient of solute in water and can be predicted using the following Stokes-Einstein equation:50
are shown in Figure 1. For each SC lipid-corneocyte layer there are 10 grids. The total number of grids depends on the number of lipid-corneocyte layers simulated, and the relationship is Ngrids ) 10Nlayers + 5. According to mass conservation principles, concentration of each grid A satisfies the following equation
KT (12) 6πηrs where K is the Boltzmann constant, T is the temperature (309 K), and η is the viscosity of water (0.0071 P, 36 °C). Thus, for a given solute of known molecular weight MW and octanol-water partition coefficient Kow, calculation of its diffusion coefficient and partition coefficient in SC corneocytes of known water content becomes straightforward using eqs 9-12. Interfacial Mass Transfer. The mass transfer equation of solute in the heterogeneous SC lipids and corneocytes is solved by a finite difference scheme. The numerical scheme employed uses the grid structure shown by Figure 1. Since the side length of each grid is less than a few micrometers, the numerical scheme for the mass transfer between neighboring grids can be formulated using the interfacial mass transfer equation. In general, the equation that governs the interfacial mass transfer between two neighboring grids A and B can be written in the following form
where CA is the solute concentration in grid A, V is the grid volume, ts is time, and qAB is the mass of solute into/out of grid A from neighboring grid B per time unit. In total, Ngrids ordinary differential equations (ODEs) will be assembled for the mass balance equations of all grids. The ODEs are solved using MATLAB solver ode15s with variable time steps. The solver is based on the backward differentiation formula, also known as Gear’s method for stiff ordinary differential equations. At each time step, the solver estimates the local error e in the ith component of the solution, y(i). This error must be less than or equal to the acceptable error, which is a function of the specified relative tolerance, RelTol, and the specified absolute tolerance, AbsTol.
Dw )
Ai (C - KABCB) (13) δA KABδB A + DA DB where qAB (mass/time) is the solute mass across the interface of grids A and B per time unit, Ai is the interfacial area, δA and δB are the respective half-side length of grids A and B in the direction normal to the interface, CA and CB are the concentrations of the solute in grids A and B, DA and DB are the diffusivities of the solute in grids A and B, and KAB () KAw/ KBw) is the partition coefficient between grids A and B. There are three cases for the determination of KAB including KAB ) 1 if grids A and B are the same material of lipids or corneocytes, KAB ) Kmw/Kbw if grid A is lipids and grid B is corneocytes, and KAB ) Kbw/Kmw if grid A is corneocytes and grid B is lipids. The general eq 13 also applies to the mass transfer between the vehicle and the SC lipids with KAB ) Kvw/Kmw, DA ) Dv, and DB ) Dm, where Dv is the solute diffusion coefficient in the vehicle and Kvw is the solute partition coefficient between the vehicle and the water. The lower boundary of the SC is the epidermis and dermis which is modeled as an infinite sink. Mass transfer between the continuous lipid matrix and sink is also modeled by the same eq 13 with KAB ) Kmw, DA ) Dm, and DB > Dm. With the above general-purpose “brick-and-mortar” model, there are two routes for the permeation of active molecules through the SC, that is, the continuous lipid route and the transcellular route. Both pathways are integrated into the effective transport properties of the “mortar” representing the lipid matrix and the “bricks” representing the corneocytes. Thus, the model presented in this study applies not only to lipophilic compounds but also to hydrophilic compounds. qAB )
Computer Simulation The above general-purpose 2-D “brick-and-mortar” model is implemented in Matlab. The grids used for numerical solution
dCA )dts
∑q
AB
B
V
(14)
|e(i)| e min(RelTol × abs(y(i)), AbsTol(i)) (15) The default values of RelTol () 1 × 10-3) and AbsTol () 1 × 10-6) are used in the current simulation. The resolution and accuracy of the current numerical grids can be compared with the example presented by Barbero and Frasch.12 The results are shown in Figure 2. With the same parameter ranges of diffusion ratios and partition coefficient ratios between the SC lipids and corneocytes, the predicted results of the current model agreed well with the finite element model of Barbero and Frasch.12 As it will be discussed later, further refinement of the grids did not improve the resolution of the simulated results. Initial Validation To test the predictive capability of the current model, the in vivo tape striping data of 4-cyanophenol presented by Stinchcomb et al.51 are simulated. Tape striping is an established in vivo method for obtaining transdermal permeation and absorption of topically applied actives. The tape striping data presented by Stinchcomb et al.51 involved topical application of 1.4 mL of saturated aqueous solution of 4-cyanophenol to a 20 cm2 area of skin in the ventral forearm of 25-30 years old health volunteers. In the simulation, the vehicle is simulated as an infinite source with a constant concentration of 4-cyanophenol at saturation of 0.11 mol/L. The initial concentration of 4-cyanophenol was 0.31 mol/L which is well above the saturation point. The vehicle thickness is 0.7 mm, and the experimental duration did not exceed 30 min. The 4-cyanophenol concentration during the experiment period did not drop below the saturation concentration of 0.11 mol/L. As a result, it is reasonable to consider the vehicle as an infinite source. The structural parameters of the “bricks and mortar” were set to the typical values used by others as shown in Table 1.24,26 The water content of the SC is set to 55% across the depth because the SC was likely to be hydrated under the occlusive experimental condition.31,32 The thickness of the aqueous boundary layer in the vehicle, δv, was set to 200 µm according to the data of Robert et al.52 and Anderson et al.53 The diffusion coefficient of 4-cyanophenol in water is calculated to be 9.12 ×10-10 m2/s using eq 12. Its octanol-water partition coefficient is log Kow ) 1.6.54 Using eqs 6, 7, and 9-11, the diffusion and
Ind. Eng. Chem. Res., Vol. 47, No. 17, 2008 6469
Figure 3. Model prediction (lines) compared with in vivo tape striping data of 4-cyanophenol permeation into the SC of the forearm of a health volunteer after exposure times of 1 min (b), 5 min (×), and 15 min (9) to a saturated aqueous solution. The in vivo experimental data is from Stinchcomb et al.51
Figure 2. Comparison of the numerical resolution of the current SC grids with the finite element model of Barbero and Frasch:12 Predicted lag time (a) and steady-state flux (b) using the same structure and property parameters as Barbero and Frasch (2005). Open squares (0) and open circles (O) indicate the predicted results of Barbero and Frash12 with Kmb ) 0.1 and Kmb ) 1000, respectively; line + closed squares and line + close circles indicate the predicted results of current model with Kmb ) 0.1 and Kmb ) 1000, respectively. Table 1. Structural and Compositional Properties of SC for “Brick-and-Mortar” Model parameter
value
layers of corneocytes, N width of corneocytes, d heigh of corneocytes, t thickness of intercellular lipid, g lateral spacing between keratinocytes, s offset ratio, w dry mass fraction of lipid, fl dry mass fraction of keratin, fk saturated water content of the SC, fSC water content of the first layer corneocyte, fw1 water content in the Nth layer corneocyte, fwN density of water, Fw density of lipid, Fl density of keratin, Fk
16 40 µm 0.8 µm 0.075 µm 0.075 µm 8 12.5% 87.5% 55% (w/w) 55% (w/w) 55% (w/w) 1000 kg/m3 1000 kg/m3 1200 kg/m3
partition properties of SC lipids and corneocytes are calculated directly without fitting to the in vivo data. This include the diffusion coefficient of 4-cyanophenol in the lipid matrix Dm ) 3.59 × 10-11 m2/s, its partition coefficient between lipid and water, Kmw ) 13.18, the diffusion coefficient in the corneocytes, Db ) 1.98 × 10-15 m2/s, and the partition coefficient between corneocytes and water, Kbw ) 6.23. The partition coefficient between the stratum corneum (SC) and water was derived to be approximately Kscw ) 6.83. This is comparable to the
experimental value of 6-11, as determined in vitro by equilibrating isolated sheets of human SC with aqueous 4-cyanophenol solutions of different concentrations.47 The vehicle/water partition coefficient, Kvw, is set to 1. Using the above parameters established separately, 4-cyanophenol permeation into the SC is predicted directly. Figure 3 shows the predicted concentration profile of 4-cyanophenol along the depth of the SC as a function of time, in comparison with the original experimental data. The predicted concentration value is the average concentration of each lipid-corneocyte layer in the SC, with corresponding depth value set at the center. The prediction agreed remarkably well with the experimental data. Stinchcomb et al.51 also tried to model the data using the simple diffusion equation, assuming the SC as a homogeneous medium, but did not obtain satisfactory agreement. From the computer simulation, the fluxes of the 4-cyanophenol that diffuses into the SC and across the SC into the epidermis and viable dermis can be obtained, as shown in Figure 4a. Here the results of two different grids are presented. Further refinement of the grid did not improve the simulation results, indicating the grid of Figure 1 is satisfactory. From the flux of 4-cyanophenol into the epidermis and viable dermis, the accumulative amount can be obtained by integration, the socalled area under the curve (AUC). This is presented in Figure 4b. Of practical interests of the accumulative curve is the socalled lag time. It is defined as the intercept of the linear portion of accumulative curve Qt with the positive side of the time axis. The lag time for 4-cyanophenol is obtained to be tlag ) 22 min, which is very short. The overall permeability of 4-cyanophenol through SC is Kp ) 1.30 × 10-6 cm/s. These values are reasonably consistent with those reported by Stinchcomb et al.51 and Pirot et al.55 Their reported values of tlag are 12 min and 30 min, respectively, and reported values of Kp are 1.67 × 10-6 cm/s and 1 × 10-6 cm/s, respectively. With the computer simulation, more detailed information of solute diffusion in the heterogeneous structures of the SC can be obtained. Figure 5 shows the predicted concentrations of 4-cyanophenol in the SC lipids and corneocytes. Solute 4-cyanophenol is a moderately hydrophobic molecule with Kow ) 40. It has been widely suggested that the intercellular lipid pathway is the primary permeation route for hydrophobic solutes. However, the computer simulation indicates that for moderately hydrophobic solute 4-cyanophenol, concentration in the corneocytes reached half of that in the lipid matrix.
6470 Ind. Eng. Chem. Res., Vol. 47, No. 17, 2008
Figure 4. (a) Predicted fluxes of 4-cyanophenol into and across the SC using the coarse gird of (2N + 1) × 5 as shown in Figure 1 (solid lines) and fine grids of (7N) × 11 (dotted lines). (b) The cumulative amount (Qt) of 4-cyanophenol permeated across the SC as a function of time after exposure to a saturated aqueous solution.
Corneocytes contribute more than 80% of mass of the SC. It follows that the actual amount of 4-CP stored in the corneocytes is more than twice of that stored in the lipid matrix. Uptake of moderately hydrophobic solutes (Kow < 1000) by the SC corneocyte phase has been also observed previously by Raykar et al.56 The absorption of 4-cyanophenol by corneocytes has the most significant effect on the overall concentration of the solute in the SC but only marginal influence on the rate of transdermal permeation. When the diffusion coefficient of 4-cyanophenol in the SC corneocytes is set to zero (impermeable), the overall concentration of 4-cyanophenol in the SC decreased by more than 2/3, and the rate of transdermal permeation of 4-cyanophenol only reduced by 10%. It appears that for 4-cyanophenol the intercellular lipid is still the main permeation pathway and the corneocytes serves as storage of the solute. Conclusion Transdermal permeation of solute through human stratum corneum depends not only on the cellular structure but also on the composition. Apart from lipid domain and keratin, water is also a major constituent substance of stratum corneum and exists in both the lipid matrix and the corneocytes. In this report, a general purpose model has been developed for predicting transdermal permeation of solute through human SC. Using the
Figure 5. Predicted concentration profiles of 4-cyanophenol concentration in the lipid matrix (a) and corneocytes (b) of the SC at 1 min (solid line), 5 min (dashed line), and 15 min (dotted line) of topical administration of saturated 4-CP aqueous solution as described by Stinchcomb et al.51
“brick-and-mortar” model for the cellular structure of human SC, the lipid matrix (mortar) has been further modeled as a bicontinuous phase consisting of lipid bilayers and water sandwiched between stacked lamellar structures of lipid bilayers. The corneocytes (brick) have been modeled as a gel phase filled with cross-linked soft keratin. Mathematical equations have been proposed to directly calculate the diffusion and partition properties of the SC lipids and corneocytes. These equations are established separately by considering their correlations with the fundamental physical-chemical properties of solutes and taking into account of their interactions with the hydration level. It is demonstrated that a major advantage of the general purpose model is that one can directly predict the transdermal permeation from the fundamental physical properties of solutes in terms of the octanol-water partition and the diffusion coefficients in water and lipid, without parameter fitting to the experimental data to be predicted. Initial validation of the model has been demonstrated by simulating the in vivo tape striping data of 4-cyanophenol presented by Stinchcomb et al.51 With the partition and diffusion properties of the SC lipids and corneocytes calculated using the equations established separately, the predicted dynamic profiles of 4-cyanophenol agreed very well with the experimental data. The model predicts that, for a moderately hydrophobic solute of 4-cyanophenol, more than 2/3 partitioned into the corneocytes which has important effect on percutaneous absorption. Clearly, the model not only can be used as a valuable tool for predicting transdermal permeation
Ind. Eng. Chem. Res., Vol. 47, No. 17, 2008 6471
and absorption without parameter fitting but also has great potential to provide much insight into how the SC structure, composition, and property influence the dynamic process of transdermal permeation. Literature Cited (1) Albery, W. J.; Hadgraft, J. Percutaneous absorption in-vivo experiments. J. Pharm. Pharmacol. 1979, 31, 140–147. (2) Langelieckfeldtr, R.; Lee, G. Use of a model lipid matrix to demonstrate the dependence of the stratum-corneums barrier properties on its internal geometry. J. Controlled Release 1992, 20, 183–194. (3) Michaels, A. S.; Chandrasekaran, S. K.; Shaw, J. E. Drug permeation through human skin-theory and in-vitro experimental measurement. AIChE J. 1975, 21, 985–996. (4) Potts, R. O.; Francoeur, M. L. The influence of stratum-corneum morphology on water permeability. J. InVest. Dermatol. 1991, 96, 495– 499. (5) Frasch, H. F.; Barbero, A. M. Steady-state flux and lag time in the stratum corneum lipid pathway: Results from finite element models. J. Pharm. Sci. 2003, 92, 2196–2207. (6) Moghimi, H. R.; Williams, A. C.; Barry, B. W. A lamellar matrix model for stratum corneum intercellular lipids. 2. Effect of geometry of the stratum corneum on permeation of model drugs 5-fluorouracil and oestradiol. Int. J. Pharm. 1996, 131, 117–129. (7) Kruse, J.; Golden, D.; Wilkinson, S.; Williams, F.; Kezic, S.; Corish, J. Analysis, interpretation, and extrapolation of dermal permeation data using diffusion-based mathematical models. J. Pharm. Sci. 2007, 96, 682–703. (8) Potts, R. O.; Guy, R. H. Predicting skin permeability. Pharm. Res. 1992, 9, 663–669. (9) Tang, H.; Blankschtein, D.; Langer, R. S. Prediction of steady-state skin permeabilities of polar and nonpolar permeants across excised pig skin based on measurements of transient diffusion: characterization of hydration effects on the skin porous pathway. J. Pharm. Sci. 2002, 91, 1891–1907. (10) Heisig, M.; Lieckfeldt, R.; Wittum, G.; Mazurkevich, G.; Lee, G. Non steady-state descriptions of drug permeation through stratum corneum 0.1. The biphasic brick-and-mortar model. Pharm. Res. 1996, 13, 421– 426. (11) Tojo, K. Random brick model for drug transport across stratum corneum. J. Pharm. Sci. 1987, 76, 889–891. (12) Barbero, A. M.; Frasch, H. F. Modeling of diffusion with partitioning in stratum corneum using a finite element model. Ann. Biomed. Eng. 2005, 33, 1281–1292. (13) Barbero, A. M.; Frasch, H. F. Transcellular route of diffusion through stratum corneum: Results from finite element models. J. Pharm. Sci. 2006, 95, 2186–2194. (14) Hansen, S.; Henning, A.; Naegel, A.; Heisig, M.; Wittum, G.; Neumann, D.; Kostka, K.-H.; Zbytovska, J.; Lehr, C.-M.; Schaefer, U. F. In-silico model of skin penetration based on experimentally determined input parameters Part I. Experimental determination of partition and diffusion coefficients. Eur. J. Pharm. Biopharm. 2008, 68, 352–367. (15) Hansen, S.; Henning, A.; Naegel, A.; Heisig, M.; Wittum, G.; Neumann, D.; Kostka, K.-H.; Zbytovska, J.; Lehr, C.-M.; Schaefer, U. F. In-silico model of skin penetration based on experimentally determined input parameters Part II. Mathematical modelling of in-vitro diffusion experiments. Identification of critical input parameters. Eur. J. Pharm. Biopharm. 2008, 68, 368–379. (16) Kushner, J.; Deen, W.; Blankschtein, D.; Langer, R. First-principles, structure-based transdermal transport model to evaluate lipid partition and diffusion coefficients of hydrophobic permeants solely from stratum corneum permeation experiments. J. Pharm. Sci. 2007, 96, 3236–3251. (17) Rim, J. E.; Pinsky, P. M.; van Osdol, W. W. Using the method of homogenization to calculate the effective diffusivity of the stratum corneum. J. Membr. Sci. 2007, 293, 174–182. (18) Wang, T.-F.; Kasting, G. B.; Nitsche, J. M. A multiphase microscopic diffusion model for stratum corneum permeability. I. Formulation, solution, and illustrative results for representative compounds. J. Pharm. Sci. 2006, 95, 620–648. (19) Wang, T.-F.; Kasting, G. B.; Nitsche, J. M. A multiphase microscopic diffusion model for stratum corneum permeability. II Estimation of physicochemical parameters and application to a large permeability database. J. Pharm. Sci. 2007, 96, 3024–3051. (20) Kasting, G. B.; Barai, N. D.; Wang, T. F.; Nitsche, J. M. Mobility of water in human stratum corneum. J. Pharm. Sci. 2003, 92, 2326–2340. (21) Bodde, H. E.; Van, D.; Koerten, H. K.; De, H. Visualization of in vitro percutaneous penetration of mercuric chloride transport through intercellular space versus cellular uptake through desmosomes. J. Controlled Release 1991, 15, 227–236.
(22) Elias, P. M. Epidermal lipids, membranes, and keratinisation. Int. J. Dermatol. 1981, 20, 1–19. (23) Talreja, P. S.; Kasting, G. B.; Kleene, N. K.; Pickens, W. L.; Wang, T. F. Visualization of the lipid barrier and measurement of lipid pathlength in human stratum corneum. AAPS PharmSci 2001, 3, 1–9. (24) Johnson, M. E.; Blankschtein, D.; Langer, R. Evaluation of solute permeation through the stratum corneum: Lateral bilayer diffusion as the primary transport mechanism. J. Pharm. Sci. 1997, 86, 1162–1172. (25) Downing, D. T. Lipid and protein structures in the permeability barrier of mammalian epidermis. J. Lipid Res. 1992, 33, 301–313. (26) Mitragotri, S. Modeling skin permeability to hydrophilic and hydrophobic solutes based on four permeation pathways. J. Controlled Release 2003, 86, 69–92. (27) Forslind, B. A domain mosaic model of the skin barrier. Acta Derm. Venereol. 1994, 74, 1–6. (28) Lampe, M. A.; Burlingame, A. L.; Whitney, J. Human stratum corneum lipids: characterization and regional variations. J. Lipid Res. 1983, 24, 120–130. (29) Caspers, P. J.; Lucassen, G. W.; Bruining, H. A.; Puppels, G. J. Automated depth-scanning confocal Raman microspectrometer for rapid in vivo determination of water concentration profiles in human skin. J. Raman Spectrosc. 2000, 31, 813–818. (30) Warner, R. R.; Myers, M. C.; Taylor, D. A. Electron-probe analysis of human skin: Determination of the water concentration profile. J. InVest. Dermatol. 1988, 90, 218–224. (31) Graves, C. J.; Edwards, C.; Marks, R. The effects of protective occlusive gloves on stratum corneum barrier properties. Contact Dermatitis 1995, 33, 183–187. (32) Held, E.; Jorgensen, L. L. The combined use of moisturizers and occlusive gloves: An experimental study. Am. J. Contact Dermatitis 1999, 10, 146–152. (33) Bouwstra, J. A.; de Graaff, A.; Gooris, G. S.; Nijsse, J.; Wiechers, J. W.; van Aelst, A. C. Water distribution and related morphology in human stratum corneum at different hydration levels. J. InVest. Dermatol. 2003, 120, 750–758. (34) Barai, N. D. Effect of hydration on skin permeability. Master Thesis, University of Cincinnati, Cincinnati, OH, 2001. (35) Trommer, H.; Neubert, R. H. H. Overcoming the stratum corneum: The modulation of skin penetration. Skin Pharmacol. Physiol. 2006, 19, 106–121. (36) Blank, I. H.; Moloney, J. I.; Emslie, A. G.; Simon, I.; Apt, C. The diffusion of water across the stratum corneum as a function of its water content. J. InVest. Dermatol. 1984, 82, 188–194. (37) Bouwstra, J. A.; Gooris, G. S.; Ponec, M. The lipid organisation of the skin barrier: liquid and crystalline domains coexist in lamellar phases. J. Biol. Phys. 2002, 28, 211–223. (38) Mitragotri, S. A theoretical analysis of permeation of small hydrophobic solutes across the stratum corneum based on scaled particle theory. J. Pharm. Sci. 2002, 91, 744–752. (39) Bondi, A. van der Waals volumes and radii. J. Phys. Chem. 1964, 68, 441–451. (40) Mitragotri, S.; Johnson, M. E.; Blankschtein, D.; Langer, R. An analysis of the size selectivity of solute partitioning, diffusion, and permeation across lipid bilayers. Biophys. J. 1999, 77, 1268–1283. (41) Johnson, M. E. Bio physical aspects of transdermal drug delivery and chemical enhancement. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 1996. (42) Raykar, P. V.; Fung, M. C.; Anderson, B. D. The role of protein and lipid domains in the uptake of solutes by human stratum corneum. Pharm. Res. 1988, 5, 140–150. (43) Mitragotri, S. In situ determination of partition and diffusion coefficients in the lipid bilayers of the stratum corneum. Pharm. Res. 2000, 17, 1024–1027. (44) Anderson, B. D.; Higuchi, W. I.; Raykar, P. V. Heterogeneity effects on permeability-partition coefficient relationships in human stratum corneum. Pharm. Res. 1988, 5, 566–573. (45) Anderson, B. D.; Raykar, P. V. Solute structure-permeability relationships in human stratum corneum. J. InVest. Dermatol. 1989, 93, 280–286. (46) Surber, C.; Wilhelm, K. P.; Hori, M.; Maibach, H. I.; Guy, R. H. Optimization of topical therapy: partitioning of drugs into stratum corneum. Pharm. Res. 1990, 7, 1320–1324. (47) Surber, C.; Wilhelm, K. P.; Maibach, H. I.; Hall, L. L.; Guy, R. H. Partitioning of chemicals into human stratum corneum: implications for risk assessment following dermal exposure. Fundam. Appl. Toxicol. 1990, 15, 99–107. (48) Johnson, E. M.; Berk, D. A.; Jain, R. K.; Deen, W. M. Hindered diffusion in agarose gels: test of effective medium model. Biophys. J. 1996, 70, 1017–1026.
6472 Ind. Eng. Chem. Res., Vol. 47, No. 17, 2008 (49) Jackson, G. W.; James, D. G. The permeability of fibrous porous media. Can. J. Chem. Eng. 1986, 64, 362–374. (50) Einstein, A. Uber die von der molekular-kineticshen theorie der warme geforderte bewegung von in ruhenden flussigkeiten suspendierten teilchen. Ann. Physik. 1905, 17, 549–560. (51) Stinchcomb, A. L.; Pirot, F.; Touraille, G. D.; Bunge, A. L.; Guy, R. H. Chemical uptake into human stratum corneum in vivo from volatile and non-volatile solvents. Pharm. Res. 1999, 16, 1288–1293. (52) Roberts, M. S.; Anderson, R. A.; Swarbrick, J.; Moore, D. E. The percutaneous absorption of phenolic compounds: the mechanism of diffusion across the stratum corneum. J. Pharm. Pharmacol. 1978, 30, 486–490. (53) Anderson, B. D.; Higuchi, W. I.; Raykar, P. V. Heterogeneity effects on permeability-partition coefficient relationships in human stratum corneum. Pharm. Res. 1988, 5, 566–573.
(54) Hansch, C.; Leo, A.; Hoekman, D. Exploring QSAR: Hydrophobic, electronic, and steric constants; American Chemical Society: Washington, DC, 1995. (55) Pirot, F.; Kalia, Y. N.; Stinchcomb, A. L.; Keating, G.; Bunge, A.; Guy, R. H. Characterization of the permeability barrier of human skin in vivo. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 1562–1567. (56) Raykar, P. V.; Fung, M. C.; Anderson, B. D. The role of protein and lipid domains in the uptake of solutes by human stratum corneum. Pharm. Res. 1988, 5, 140–150.
ReceiVed for reView December 15, 2007 ReVised manuscript receiVed June 17, 2008 Accepted June 26, 2008 IE701711V
