Modeling of percutaneous drug transport in vitro using skin-imitating Carbosil membrane

Journal of Controlled Release 52 (1998) 25–40

Modeling of percutaneous drug transport in vitro using skin-imitating Carbosil membrane a, b c d Mikhail M. Feldstein *, Igor M. Raigorodskii , Alexey L. Iordanskii , Jonathan Hadgraft a

b

Lekbiotech R& D Center, ‘ Biotechnologia’ JSCo., 8 Nauchny Proezd, 117246 Moscow, Russia State Scientific Research Institute of Medical Polymers ( Medpolymer), 10 Nauchny Proezd, 117246 Moscow, Russia c N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia d The Welsh School of Pharmacy, University of Wales, Cardiff CF1 3 XF, UK Received 16 January 1997; received in revised form 29 August 1997; accepted 17 September 1997

Abstract A comparative study of the barrier function of human skin and polydimethylsiloxane–polycarbonate block copolymer Carbosil membrane was performed in vitro using 14 drugs spanning a wide range of structures and therapeutic classes. The drug permeability coefficients across the skin and the Carbosil membrane were examined as an explicit dependence of permeant molecular weight, melting point, solubility in aqueous solution and octanol–water partition coefficient. Owing to heterophase and heteropolar structure, Carbosil membranes and human skin epidermis share a common solubility–diffusion mechanism of drug transport. This synthetic membrane is shown to provide a mechanistically substantiated model for percutaneous drug absorption. Carbosil membranes can be used both for quantitative prediction of transdermal drug delivery rate and as a skin-imitating standard membrane in the course of in vitro drug delivery kinetics evaluation.  1998 Elsevier Science B.V. Keywords: Polydimethylsiloxane–polycarbonate membrane; Structure; Permeability; Prediction of percutaneous drug penetration; Transdermal drug delivery

1. Introduction The ultimate outcome of any model system is inevitably its ability to yield observations in agreement with the more complicated process that it is intended to mimic. For percutaneous penetration in man this means in vivo experiments in humans. These experiments are often morally undesirable (e.g. pesticide evaluations), expensive, and time *Corresponding author. Tel.: 17 095 3323408; fax: 17 095 3310101

consuming. Interpretation of the results is further complicated by the high inter- and intraindividual variability sometimes found in the data. Such experiments are certainly precluded when the compound of interest has known or uncharacterized toxicity. Alternatives to in vivo studies in humans include in vivo studies in animals and in vitro experiments using excised skin (human or animal). Correlation between excised human skin and penetration studies performed in vivo on human volunteers has been demonstrated in a limited number of studies reviewed in Ref. [1]. Human skin for in vitro studies is

0168-3659 / 98 / $19.00  1998 Elsevier Science B.V. All rights reserved. PII S0168-3659( 97 )00208-3

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M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

obtained from cadavers, or following cosmetic and plastic surgical procedures, and is subject to variability in the age, race, sex, anatomical site and general health of the donor. Extreme care is necessary in the preparation of human skin epidermal membranes. The length and method of skin storage may also introduce variability. The problems involved in working with real skin make simpler, better characterized membrane systems appear attractive as models for transdermal absorption [1]. It is conventional practice to use polymeric membranes as skin-imitating barriers in the evaluation of transdermal drug delivery systems (TDDS) both in batch-to-batch tests and for comparison of drug delivery rates between innovator, generic and competitor products [2,3]. Polymeric membranes differ advantageously from human skin epidermis due to their ready availability, uniformity, tensile strength and chemical purity. Although skin-imitating membranes will continue to be important in the future, model studies have not always considered the mechanistic relevance of the membrane system employed and do not indicate the utility of membrane transport as a model for transepidermal absorption [1]. Synthetic membranes will provide the most useful information about in vivo transdermal delivery process from a device when: (1) the passive diffusional barrier imposed by the stratum corneum is the major resistance to transport; (2) the drug of interest is known to be metabolically inert and not specifically bound in viable skin; (3) the formulation does not contain a permeability enhancer which can interact with skin but not the membrane; (4) in vivo experiments of similar design have been or can be performed and correlated with the in vitro results. The tests of in vitro drug release and transdermal delivery rates from TDDS are aimed at predicting the attainability of in vivo-required delivery rate and its dependence on time in advance of in vivo studies, so that the clinical studies of the developed patch may be held to a minimum. The correlation between in vitro and in vivo data serves to substantiate the predictive capability of the in vitro test results. In most instances, the membrane acts merely to separate physically the formulation from the receptor phase in diffusion cells. To allow the prediction of in vivo transdermal delivery rate, skin-imitating mem-

branes should be more or equally permeable than human skin. In many cases, therefore, a formulation that controls delivery through skin-imitating membrane will not necessarily control in vivo transdermal absorption. The complex mechanism of percutaneous drug transport involves both drug diffusion and partition between polar and lipophilic phases resulting from the complex heterophase and heteropolar structure of the stratum corneum. Various correlations have been found and explained between transdermal permeability and the permeant’s molecular size, structure, hydrogen bond activity, polarity and lipophilicity [4–14]. Could a synthetic polymer membrane provide a mechanistically substantiated model for transdermal drug absorption? The analysis of this question is the major objective of this paper. Does the obtained data of in vitro delivery through the model synthetic membrane have a definite predictive capacity for various drugs? Is it possible to predict in vitro / in vivo percutaneous drug absorption based on the results of drug transfer measurement across the model membrane? The answers not only are of an obvious practical value, but they also permit us to determine the common and distinguishing features in drug transport through such different permeation barriers as human skin epidermis and synthetic polymer membranes.

2. Materials Polydimethylsiloxane(PDMS)–polycarbonate(PC) block copolymers were synthesized at ‘Medpolymer’ by heterophase polycondensation of oligo-dioxiaryl carbonates with oligo-bis-chlorformate alkyl siloxanes as described earlier [15,16]. Carbosil membrane (0.04 mm in thickness) was produced in ‘Medpolymer’ by casting of 12–15 wt.% block copolymer solution in methylene chloride followed by drying. Carbosil-1 differs from Carbosil-2 by links R in PC block (see Scheme 1): oxyethylene for Carbosil-1 and methylene for Carbosil-2. For drug delivery kinetics the samples of Carbosil membrane contained 55 wt.% PDMS and 45 wt.% PC blocks. The Carbosil membrane of this composition has been approved in Russia as a standard gas-separating barrier in blood oxygenation

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

and as air-permeable non-occlusive backing materials in covers for treatment of burns and wounds. Human skin epidermis (inner thigh) was obtained from both male and female cadavers using heat separation (608C, 30 s) [17]. Hydrogel drug-containing pressure-sensitive adhesive TDDS matrices were used in the course of the drug-delivery kinetics study as donor vehicles. The TDDS were produced in JSCo. ‘Biotechnologia’ using bench-scale equipment. The hydrophilic matrices, based on a polycomplex between high molecular mass polyvinyl pyrrolidone (PVP) and polyethylene glycol of molecular weight 400 g / mol (PEG-400) [18], were combined with an occlusive metallized polyethyleneterephthalate backing film of 0.02 mm in thickness.

3. Methods In vitro drug delivery rate determination from water-soluble TDDS matrices was performed using human cadaver skin or the Carbosil membrane to protect the matrices from dissolving in the receptor solution. The TDDS was adhered to the center of a Carbosil membrane sheet of twice its area. The membrane margins were then wrapped around the sample. The back side of the packet was closely attached to a steel plate-holder to prevent a straightforward contact of the matrix with the receptor solution. In a similar fashion, cadaver skin epidermis can be used instead of the Carbosil membrane. The holder with the wrapped sample was then submerged into an aqueous sink and the following determination was based on the USP rotating cylinder paddle-overdisc method, as described earlier [19]. The measurement of drug appearance in receptor solution (0.15 M NaCl) at 35.060.58C and paddle rotation speed 10061 rpm was performed using an LKB Tablet Dissolution System combined with a UV-Spectrophotometer (Ultrospec 4052), a six-cell temperature-controlled bath (Sotax AT6), a multi-channel peristaltic pump (LKB), and a computer (Olivetti M-240). In experiments with cadaver skin epidermis the drug concentration in the receptor solution was measured manually by means of an Hitachi F-4000 spectrofluorimeter or by a gas chromatography method. The precision of the drug concentration measure-

27

ment was 60.002 mg / ml (UV spectrophotometry), 620 ng / ml (spectrofluorimetry) and 61.0 ng / ml (gas chromatography). Drug permeability coefficients through skin epidermis (Ps ) and Carbosil membrane (Pm ) were measured as flux normalized by the drug concentration in donor vehicle. In this work, Pm and Ps relate to the permeabilities of drugs delivered from the hydrophilic TDDS matrices. These were calculated taking into account the matrix density (1.1060.12 g / cm 3 ). Drug permeability coefficients through the Carbosil membrane and the skin, denoted by symbols P am and P as , were determined using stirred aqueous donor and receptor solutions in Franz-type diffusional cells [19]. Gas permeability through the Carbosil membrane was evaluated by gas chromatography in a special cell [16]. The membrane–matrix drug partition coefficient was measured as the ratio of steady-state drug concentrations in membrane and matrix after TDDS lamination with the Carbosil membrane at 258C and 48 h of contact. The solubility of drugs in 0.15 M NaCl (Cs ) w was assessed by equilibrating an excess amount of drug in an aqueous solution using a shaker. All measurements were performed at 358C. Octanol–water drug partition coefficients (Ko / w ) were obtained using the Medchem database (Biobyte) or estimated using group contributions and Hansch type analysis (for aminostigmine, foridon, cytisine, nifedipin, fluacizine and salbutamol). Multiple regression analysis was carried out using appropriate software.

4. Results and discussion

4.1. The structure of PDMS–PC block copolymers and the Carbosil membrane The Carbosil membrane was produced from PDMS–PC block copolymer based on 4,49-bisdiphenylol-2,29-propane carbonate ether [15,16].

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

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The PDMS–PC block copolymer films were shown to have a heterophase domain structure [15]. Homopolymers of PDMS and PC have different glass transition temperatures (T g ): 1498C for PC and 21238C for PDMS. Phase segregation in PDMS–PC block copolymers results in two T g values. The glass transition temperature of the PDMS block (T g1 ) ranges from 2110 to 21208C, decreasing with the PC block content increase, and practically independent of molecular weight of the PDMS block. In contrast, T g2 of the PC block depends very strongly on its MW. It increases from 55 to 1408C with PC block MW increase. Small-angle X-ray diffractometry shows glassy PC domain formation against a background of PDMS chains which appear in a viscous state. As the PDMS block content in the copolymer increases from 24 to 50 wt.%, the ratio of reflex–background intensity increases from 0.45 to 0.85. The reason is that the increase of flexible PDMS segments in the polymer promotes spatially the coupling of more rigid and polar PC segments into the domains. According to small-angle X-ray diffraction analysis data, elon˚ in length and 90 A ˚ gated PC domains of 150–160 A in diameter exist in copolymers containing 24 wt.% of PDMS blocks. Further increase of PDMS content in copolymers to 45 wt.% leads to compaction of the ˚ [16]. PC domains (110:60 A) The domain structure of PDMS–PC films is confirmed by gas permeability data. As is evident from Table 1, permeability coefficients of various gases are considerably higher through PDMS films as compared with PC membranes. It is possible to control the permeation of PDMS–PC block copolymer Carbosil membranes through the variation of block content in the copolymer (Fig. 1). The sigmoidal dependence of gas permeability Table 1 Permeability coefficients of gases (Kp , 10 28 cm 3 ?cm / cm 2 ?s?atm) through polydimethylsiloxane or polycarbonate films and PDMS– PC block copolymer Carbosil membrane Membrane

a

PDMS Carbosil PC a a

Data from Ref. [20].

Kp O2

CO 2

380 106 5.5

1635 570 1.14

Fig. 1. Relationship between gas (CO 2 and O 2 ) permeability coefficients through the PDMS–PC block copolymer membranes (P, 10 214 mol?m / m 2 ?s?Pa) and PDMS block content in the copolymer (%).

(Fig. 1) on block copolymer composition is the result of PDMS–PC phase inversion of between 35 and 70% of PDMS content in the copolymer. While permeable PDMS blocks form a continuous diffusion medium with dispersed PC domains within, the resulting membrane permeability is high. The structure of PC-overloaded block copolymers (more than 60 wt.% of PC in copolymer) is inverted: the impermeable PC blocks make up a continuous diffusion medium, whereas PDMS domains are dispersed in PC phase. Within the rather narrow intermediate range of copolymer composition (to which Carbosil membranes belong) PC and PDMS phases are deeply interpenetrated. The ratio between domain length (L) and thickness (W ) can be evaluated from the Nielsen equation [21], relating gas permeability coefficients through Carbosil (P) with those through pure PDMS membrane (PSi ) and with volume fractions of PDMS (FSi ) and PC (Fc ) in the copolymer: P/PSi 5 FSi [1 1 (L / 2W )Fc ]

(1)

Small-angle X-ray diffraction analysis permits direct measurement of the L /W value; gas permeability data enables estimation of this value through diffusion pathlength within the membrane. It was found that higher L /W values were obtained for the same domain structure from permeability data using Eq. (1) as compared to X-ray diffractometry. Considerably more elongated PC domains with L /W513–16

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

were observed for PDMS–PC block copolymer films containing 24–44 wt.% of PDMS block. As PDMS block content in copolymer increases to 50 wt.%, a decrease of diffusion pathlength occurs (L /W57). For the Carbosil membrane sample used in this work as a skin-imitating permeation barrier (PDMS block content in copolymer is around 55 wt%), further compaction of PC domains results in a decrease of diffusion pathway tortuosity within the membrane (L /W54). A further increase of PDMS block content in the copolymer leads to spherical PC domains (L /W51). As was shown in the course of finite-dose gas transfer through the Carbosil membrane, sorption of diffusing molecules occurs within the membrane. The increase of PDMS content in the copolymer decreases the time of permeant retention by the membrane. It follows that PC domains represent the permeant sorption centers within the membrane. PDMS chains were found to be around 1.6 times as lipophilic as PC domains. The water drop contact angles are 768 with PDMS and 478 with PC films, respectively. Relatively more polar PC domains are able to sorb polar permeant molecules diffusing within the non-polar PDMS matrix. Like human skin epidermis, the Carbosil membrane has a heterophase and heteropolar structure that might be easily controlled by varying of PDMS– PC block copolymer composition. Drug transport through the membrane has to involve, firstly, permeant partition between considerably more polar PC domains and hydrophobic PDMS medium and, secondly, drug diffusion transfer within the much more permeable PDMS matrix.

4.2. Drug delivery from hydrophilic TDDS matrices Matrix compatibility with various drugs has been examined by using the drugs in Table 2. The properties of drug-loaded hydrophilic matrices are presented in Table 3. The following discussion is intended to summarize the drug-delivery kinetics through the Carbosil membranes or the skin as a function of permeant molecular structure and properties, so that a general picture can emerge. For all the drugs, except fluacizine, the delivery rates from the hydrophilic matrices are significantly higher

29

through the Carbosil-1 and -2 membranes compared to transdermal delivery rates. The values of drug delivery rates increase in proportion to the drug concentration in the matrix, up to the solubility limit (24.3% for verapamil, 14–15% for propranolol) [19]. As is evident from the data obtained with the Carbosil membranes, even with minor variations in link R polarity of copolymer PC block (oxyethylene for Carbosil-1, methylene for Carbosil-2) changes in membrane permeability are noticeable. In the case of drugs containing highly polar and ionogenic groups (e.g. propranolol, phenazepam, salbutamol), the permeability reduces with decrease of PC domain polarity. In contrast, for non-ionic amphiphilic drug molecules (nitrates) the slight decrease in PC domain polarity has no obvious effect on drug permeability (glyceryl trinitrate) or leads to a permeability decrease (isosorbide dinitrate). Pm values are tabulated for Carbosil-2 if drug delivery rates are measured both across Carbosil-1 and -2. The delivery rates of various drugs spanning a wide range of molecular structures, physicochemical properties and therapeutic classes, from a universal hydrophilic matrix through human skin epidermis or skin-imitating Carbosil membrane, have been earlier shown to be enhanced compared to hydrophobic matrices [19,22,23] and controlled by these permeation barriers [19,24–28]. The fractional contributions of the Carbosil membrane and skin to drug delivery rate control [29] have been calculated for propranolol as a test representative of the drugs incorporated into hydrophilic TDDS matrix. These were 88% across Carbosil membrane in vitro and 98% across human skin epidermis both in vitro and in vivo [24]. The same general rules are valid for delivery kinetics of all the drugs examined (Table 2) from the universal hydrophilic TDDS matrix [26]. Using a mathematical simulation method drug diffusion within the barrier and barrier–matrix partition coefficients have been shown to be of primary importance for control of overall drug-delivery kinetics from the hydrophilic matrix through both the skin and Carbosil membrane [25,27,28]. The logarithms of normalized fluxes for various drugs from the hydrophilic matrix across the Carbosil membrane (log Pm ) or human skin epidermis (log Ps ) are presented in Table 4, together with appropriate physicochemical characteristics of the drugs, e.g. molecular weight (MW), melting

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M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

Table 2 Drugs delivered from the hydrophilic matrices

point (MP), octanol–water partition coefficient (log Ko / w ), solubility in water (log(Cs ) w ) and the logarithms of permeability coefficients through the Carbosil membrane (log P am ) or the human skin

epidermis (log P as ), measured under delivery from aqueous donor solutions. In accordance with delivery rates from the matrix all the drugs examined can be classified in two

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40 Table 2. Continued

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M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

32

Table 3 Properties of drug-loaded hydrophilic TDDS matrices Drug

Delivery rate in vitro (mg / cm 2 h) across:

Drug content in matrix (%)

(1) Anabasine (2) Isosorbide dinitrate (3) Aminostigmine

1.6 9.6

(4) Glyceryl trinitrate (5) Verapamil

(6) Propranolol

(7) Silabolin

8. Foridone

(9) Clonidine (10) Cytisine 11. Phenazepam (12) Nifedipin (13) Fluacizin (14) Salbutamol

14.3 7.6 4.0 7.3 1.9 39.1 24.3 13.8 3.9 13.8 11.4 7.4 6.0 3.1 1.6 13.9 10.8 7.2 13.8 10.8 7.4 3.1 7.7 1.4 7.4 7.4 6.8 15.4 13.8 13.8

Pm (10 4 cm / h)

Carbosil 1

Carbosil 2

human skin

279620

150620 384648

13.064.3

190627

260639 192621

625620 263610 6565 160640 45612 110620 110616 95619 7866 118625

106.3612.0 4465

Ps (10 4 ) cm / h

1.560.5

33.7612.0

12.464.0

25.661.4

1.960.5

21.461.5

0.460.1

10.661.1

2.160.2

662 26.0615.0

7966 135614 4066 3064

2163

1.560.3

131630 107621 65614 37.364.5 34.164.0 24.863.0 20.661.9 26.860.8 562 2163 1162 762 1963 561 0.1060.04

10.360.5

4.261.5

0.7560.04 0.7860.1 9.064.0

4.061.1

0.660.2

3.060.5 1.460.3

1.360.5

1.360.2 0.460.1 0.003

662

0.460.1

Table 4 The properties of drugs, delivered from the hydrophilic matrix, across human skin epidermis (Ps ) or the Carbosil membrane (Pm ) Drug

MW

MP (8C)

log Ko / w

log(Cs ) w (mg/ml)

(1) Anabasine (2) Isosorbide dinitrate (3) Aminostigmine (4) Glyceryl trinitrate (5) Verapamil (6) Propranolol (7) Silabolin (8) Foridone (9) Clonidine (10) Cytisine (11) Phenazepam (12) Nifedipin (13) Fluacizin (14) Salbutamol

162.24 236.14 223.26 227.09 454.59 259.34 345.58 367.35 230.10 190.24 348.61 346.34 394.46 239.31

9 70 ,0 13.5 245 96 120 153 130 155 227 173 164 151

0.97 1.31 20.005 0.981 3.79 2.98

.1 1.08 .1 0.097 20.027 20.28 20.44 21.96 ,21 0.89 21.85 21.16 20.90 1.00

2.91 1.57 20.939 3.30 2.353 0.111

log P am (cm/h)

log P as (cm/h)

0.35

21.58

20.81 20.57 20.70

21.32 22.08

23.93

223.55 23.10

log Pm (cm/h) 21.97 22.36 22.51 22.59 22.67 22.98 22.99 23.38 23.40 23.52 23.86 23.89 24.38 26.11

log Ps (cm/h) 23.82 23.72 24.30 23.68

24.19 23.89

24.36

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

groups [19]. The first seven tabulated drugs form the first group, whereas the last seven represent the second group. The first group consists mainly of water-soluble drugs with a solubility over 0.1 mg / ml and melting temperatures lower 1208C. As a rule, these exhibit high in vitro delivery rates across Carbosil membranes (over 100 mg / cm 2 h 21 ). Drugs of the second group have both low delivery rates across the membrane (,50 mg / cm 2 h 21 ), low solubility in water (,0.1 mg / ml) and high melting temperatures (over 1508C). Zero-order delivery kinetics have been observed for drugs of both groups. One notable feature of the hydrophilic matrix is its hygroscopicity and ability to absorb water from the receptor solution in vitro. The effect of hydrophilic matrix hydration on drug-delivery kinetics through the Carbosil membrane in vitro has been studied [30–37]. The hydrophilic matrix hydration does not affect in vitro delivery kinetics for the drugs of the first group, providing enhanced delivery rates. For the drugs of the first group the ratio between in vitro steady-state matrix hydration rate (0.31 mg / cm 2 h 21 ) and the rate of drug delivery ranges from 0.5 to 3.9. In contrast, for drugs of the second group, such as cytisine and clonidine, the alteration of the matrix composition owing to in vitro matrix hydration may produce a dramatic impact upon drug-delivery kinetics. For these drugs the hydration / delivery rate ratio is over 8.4. Extrapolation of the in vitro drug-delivery results to the in vivo situation may be reasonable only when the drug appearance in the receptor solution is controlled by the properties of the formulation or when membrane is a skin mimic. Taking into account the contributions of various physicochemical determinants to drug-delivery kinetics from the hydrophilic TDDS matrix in vitro and the knowledge of the matrix hydration kinetics both in vitro and in vivo, the prediction of in vivo skin-controlled drugdelivery kinetics from in vitro data may also be possible [19,36,37]. This prediction was confirmed by the data of TDDS pre-clinical and clinical trials [19,37]. To date, six hydrophilic transdermals based on this universal matrix have been developed and clinically evaluated with propranolol (Propercuten TDDS), isosorbide dinitrate (Nisopercuten TDDS), glyceryl trinitrate (Nitropercuten TDDS), cytisine

33

(Cypercuten TDDS), phenazepam (Phenopercuten TDDS) and clonidine (Clopercuten TDDS). Currently, Nisopercuten TDDS, Nitropercuten TDDS and the first nicotine-free TDDS for smoking cessation, Cypercuten TDDS, are approved for medical practice in Russia, whereas the clinical trials of the other three are in the final stage [19,23,37].

4.3. Carbosil membranes as skin-imitating permeation barriers The steady-state transport of molecules through both the stratum corneum and the Carbosil membrane is described as a solubility–diffusion process. The permeability coefficients (Pm , Ps ), relating permeant flux to the concentration gradient across the permeation barrier, was shown to be an explicit function of permeant molecular structure (size) and solubility (lipophilicity) [5,13]. Using log Ko / w , log(Cs ) w , MP and MW (Table 4), we now compare the manner in which these variables contribute to permeability coefficients across human skin or the Carbosil membrane in vitro.

4.3.1. Comparative contribution of drug solubility ( lipophilicity) to permeability across the skin or the Carbosil membrane Among 14 drugs examined, three persistent outliers have been found to occur throughout this study: cytisine, verapamil and salbutamol. An interpretation of the behaviour of the outliers is offered in the last section of this work. Figs. 2–9 exhibit complete data sets, while regression analysis has been performed separately both for the complete sets and omitting outliers. All the data points referring to the outliers are specified in the figures. While log P values for most of the tested drugs increase with (Cs ) w , cytisine and salbutamol deviate from this rule (Fig. 2). The plot of log P versus log(Cs ) w for the complete data set reveals no simple relation (r 2 50.1, n510), but omission of cytisine and salbutamol provides a linear correlation with very reasonable fit (r 2 50.79, n58). In accordance with their high solubility in water, both drugs belong to the first group and should exhibit enhanced drug delivery rates. The solubility of a drug is inversely related to its melting point. As is evident from Fig. 3, the relation-

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M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

Fig. 2. Relationship between the normalized fluxes (log P, cm / h) for the drugs, delivered from the hydrophilic matrix across Carbosil membrane or human skin epidermis, and their solubility in water solution (log(Cs ) w , mg / ml).

Fig. 4. Relationship between normalized drug fluxes (log P, cm / h) through human skin or Carbosil membrane and log Ko / w for a range of drugs delivered from the hydrophilic matrix.

ship between log P and reciprocal of the melting point has similar characteristics for the drugs delivered from the matrix across the Carbosil membrane or human skin. Besides salbutamol, the other noteworthy outlier is verapamil. With its high melting point, verapamil should be attributed to the second group, however it is representative of the first one according to its relatively high log P value. Omission of the both drugs from the regression analysis increases the fit from r 2 50.27, n512, to r 2 50.83, n510.

No obvious relationship was observed between log P and log Ko / w for the drugs delivered across epidermis or skin-imitating membrane (Fig. 4). Fig. 4 suggests that under these conditions the drug permeability through both the skin and the Carbosil membrane depends only marginally, if at all, on the Ko / w of the solute. The contribution of log Ko / w to drug permeability control is attenuated, compared to the Potts and Guy data [9].

4.3.2. Application of the Potts–Guy equation to the Carbosil membrane Percutaneous drug absorption is described by the equation of Potts and Guy [8], expressing permeability coefficients (log Ps ) simultaneously through the contributions of permeant lipophilicity (log Ko / w ) and molecular volume (MW): log Ps (cm / s) 5 log(D o / ≠) 1 f log Ko / w 2 b MW 5 2 6.3 1 0.71 log Ko / w 2 0.0061MW (2)

Fig. 3. Dependence between the normalized drug fluxes (log P, cm / h) and their melting points (T ) for a range of drugs, delivered from the hydrophilic matrix across the Carbosil membrane or human skin epidermis.

where D o represents the diffusivity of a hypothetical molecule having zero molecular volume (weight); ≠ is the diffusion pathlength; f is a coefficient accounting for the difference between the partitioning domain presented by octanol and that of stratum corneum lipids; and the reciprocal of b is a measure of the average free-volume available for diffusion within the stratum corneum.

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

Data for percutaneous drug delivery from the hydrophilic matrix are presented in Tables 3 and 4. Except for verapamil and cytisine, they are in reasonable correlation with Eq. (2) (r 2 50.94). The question arises as to whether the Potts–Guy relationship, established for a large set of various drugs delivered through human skin epidermis, is applicable also to the Carbosil membrane. Multiple regression analysis data obtained with the Carbosil membrane lie on a three-dimensional surface defined by log P, log Ko / w and MW (Figs. 5 and 6). For complete data set (n512) log(D o / ≠) value has been found to be 25.4, f 5 20.43 and b 5 0.0077. Omitting cytisine, verapamil and salbutamol from the regression analysis of log Pm data on log Ko / w and MW for the Carbosil membrane provides improving the fit from r 2 50.16, n512 to r 2 50.83, n59: log Pm 5 2 4.49 2 0.14 log Ko / w 2 0.0067MW

35

Fig. 6. Three-dimensional Potts–Guy plot for delivery of various drugs across the Carbosil membrane from hydrophilic polymeric matrices after rotation through 908. Drug permeability coefficients across Carbosil membrane, Pm in cm / s.

(3)

Contributions of drug molecular size (MW) and lipophilicity (log Ko / w ) to log Pm control are presented more graphically in two-dimensional Potts– Guy relationship plots (Figs. 7 and 8). Eq. (3) and Figs. 4–7 permit one to assess quantitatively the differences between the stratum corneum and the Carbosil membrane transport properties. The implication of the obtained f 5 20.14 value is that the Carbosil membrane is a considerably

Fig. 7. Plot of (log Pm (cm / s)10.14 log Ko / w ) versus MW.

Fig. 5. Three-dimensional Potts–Guy plot for delivery of various drugs across the Carbosil membrane from hydrophilic polymeric matrices. Drug permeability coefficients across the Carbosil membrane, Pm in cm / s.

Fig. 8. Plot of (log Pm (cm / s)10.0067MW) versus log Ko / w .

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M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

more polar diffusion medium compared to the stratum corneum. If stratum corneum is considered a lipophilic permeation barrier, the Carbosil membrane exhibits rather an amphiphilicity or very moderate hydrophilicity. For this reason, as is obvious from the data in Figs. 4 and 8, the octanol–water drug partition coefficient (log Ko / w ) does not have such a pronounced effect on drug absorption through the skin-imitating membrane. Both log Pm and (log Pm 1 0.0067MW) versus log Ko / w plots run practically parallel to the log Ko / w axis. An almost four-order variation in value of log Ko / w does not produce, as a rule, a change of (log Pm 10.0067MW) magnitude of over one order (Fig. 8). The use of Ko / w as a measure of the lipophilicity of the permeant was recently reported to disguise specific molecular details important to drug transport mechanism through the skin [9,10]. Similar findings are evident for the transport through the Carbosil membrane. The contribution of the permeant’s Ko / w to log P can be more explicitly represented in terms of the solute’s molecular size, polarity, hydrogen bond donor and acceptor activity within the permeation barrier [9,10]. However, the applicability of the approach based on hydrogen bonding activity to the Carbosil membrane is questionable due to the evident difference in the composition of epidermal and polymeric membranes. H-bonding of a permeant molecule depends on the content of complementary functional groups within a diffusion medium. The value of b characterizes the permeation barrier through the free-volume available for diffusion [8]. The obvious similarity of b for the skin and the membrane is indicative of an analogy between their domain structures. Both for the skin and the membrane, the average free-volume is about 30 cm 3 / mol. The main controlling factor of drug absorption through the penetration barrier is log(D o / ≠) value. For stratum corneum D o ¯10 27 cm 2 / s and ≠¯500 mm [8] (taking into account the tortuosity of the diffusion pathlength). Within the framework of the free-volume diffusion theory it is justified that the ratio between effective pathlengths through the skin ≠ s and the membrane ≠ m should be equal to the ratio between cube roots for the reciprocals of their freevolumes Vf : ≠ s / ≠ m 5 [V fm /V fs ] 1 / 3

(4)

where V sf and V m f are the free-volumes available for diffusion within the skin and membrane, respectively. The membrane and stratum corneum thicknesses and free volumes have been found to be close in their values. It is apparently reasonable to assume that diffusion pathlengths within these barriers should not differ markedly. However, the exceptionally low permeability of stratum corneum is shown to result rather from its unique morphology which creates a highly tortuous diffusion path via extracellular lipids than from low free-volume available for diffusion. Assuming similar pathlengths through epidermis and skin-mimetic membrane and comparing log(D o / ≠) values obtained for skin and Carbosil membrane, we are able to conclude that the logarithm of diffusivity within the membrane is 1.4 times higher than that within the skin.

4.3.3. Using the Carbosil membrane for prediction of percutaneous drug permeability In developing transdermal systems, an in vitro delivery test is aimed at eliciting the information about the properties of device and, eventually, at predicting the attainability of therapeutic drug level in plasma. This section is intended to demonstrate a perspective in the application of the Carbosil membrane for this purpose. For all the drugs examined (Table 2), encompassing both groups, a linear relationship has been found between logarithms of drug permeability coefficients through the Carbosil membrane and the skin measured in the course of delivery from drugloaded hydrophilic matrices (Pm , Ps ) and mechania cally stirred aqueous donor solutions (P m , P sa ) (Fig. 9). The observed relationship proves that the delivery kinetics for various drugs examined are controlled by the penetration barrier [25]. Cytisine and verapamil do not deviate from this relationship. Similar rules are valid for the drug transport across such different penetration membranes as human skin epidermis or Carbosil. The relationships presented in Fig. 9 are described by the equations: a log Pm 5 0.26 log P m 2 2.53

(5)

for the Carbosil membrane (r 2 50.87, n55) and log Ps 5 0.17 log P as 2 3.46

(6)

for human skin epidermis (r 2 50.68, n55). The

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

37

Fig. 10. Relationship between log(Ps /Pm ) and log(P as /P am ). Fig. 9. Relationship between drug permeability coefficients (cm / h) within permeation barriers for various drugs of both groups, delivered across skin epidermis or skin-imitating Carbosil membrane from hydrophilic TDDS matrices (log Ps , log Pm ) and aqueous donor solutions (log P as , log P am ).

intercepts in Eq. (5) and Eq. (6) may be easily shown to relate to the logarithm of drug partition coefficients between the hydrophilic matrix and water. As is evident from the obtained intercept values, decreased drug solubility in the hydrophilic matrix under in vitro test with the Carbosil membrane compared to that with skin is most likely a result of membrane hydrophilicity causing enhanced water transfer from receptor solution into the matrix across the membrane and, consequently, enhanced matrix hydration [31,33,34]. The solubilities of the drugs in the hydrophilic matrix are 2–3 orders of magnitude higher compared with those in water. This fact is explainable, because PVP is known as a potent antinucleant agent causing enhanced drug solubilities and supersaturation in a donor vehicle [38], whereas liquid PEG is a good solvent for a wide range of drugs. Eq. (5) and Eq. (6) provide a way to estimate the percutaneous absorption of the drug based on the data obtained with the Carbosil membrane. A linear a relationship between log(Ps /Pm ) and log(P sa /P m ) (Fig. 10) is described by Eq. (7): a log(Ps /Pm ) 5 0.30 log(P sa /P m ) 2 0.69 (r 2 5 0.60)

(7) As was shown with propranolol as a test drug, the in vitro drug delivery rate from the hydrophilic matrix

across separated skin epidermis is the same as the input rate of propranolol into systemic circulation [19,39]. By combining Eq. (7) and in vitro / in vivo correlations of drug delivery from the hydrophilic matrix we are able to estimate in vivo percutaneous absorption and to predict attainable drug levels in plasma based on in vitro experiments with the Carbosil membrane and using Stella software [40– 43]. To enhance the accuracy of such a prediction, the coefficients in Eq. (7) have to be corrected for a much larger set of tested drugs. Skin permeability coefficients, P as , required for the calculations with Eq. (7), are currently determined for more than 100 drugs and available in a ready-to-use form, or can be predicted for other drugs using approaches based on group increments [7], H-bonding activity, polarity and molecular size [8–11]. Eq. (7) holds for the PVP–PEG matrix only. Similar equations are expected to be valid for membrane / skin-controlled drug delivery from other drug-loaded matrices. As is evident from the presented data, the similarity of correlation in barrier-controlled drug delivery through human skin epidermis or Carbosil membrane permits one to assume that these barriers share a common mechanism of drug transport. As a skinimitating permeation barrier, the Carbosil membrane appears to apply equally well for various compounds covering a wide range of physicochemical properties and structures.

4.3.4. Deviation analysis In order to interpret the abnormal log P values for a given drug it is necessary to explain its diffusivity within the permeation barrier. As is evident from the

38

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above data, salbutamol, cytisine and verapamil share an (apparently) abnormal mechanism of drug transport across the barriers. It is necessary to look at the structural characteristics of the outliers and see if there is any evidence of self-retardation or selfenhancement. The reason for the abnormally low salbutamol release rate from the PVP–PEG hydrophilic matrix lies most likely in the well-known capability of PVP to bind phenolic derivatives [44] to which salbutamol belongs (see Table 2). The reason for the enhanced verapamil and decreased cytisine permeability might be explained with the help of a model, based on permeant size. Although for many compounds molecular weight is often a reasonable approximation of molecular volume, it is not valid for verapamil and cytisine. As has been shown earlier [32,33], a decreased log P value for cytisine is the result of hydration of the drug molecules leading to the formation of an associated water cage around the drug molecule diffusing through highly hydrated hydrogel matrix or aqueous solution in the course of in vitro test. It is clear that such a complex particle has a lower diffusivity compared with a lone solute molecule. The oblong form of the verapamil molecule (see Table 2) facilitates its diffusivity by reptation-like translational motion along the direction of longitudinal molecular axis. Moreover, increasing molecular size of permeant increases the hydrophobic surface area. This latter feature will increase partitioning into (and, hence, permeability through) a heteropolar barrier, whether skin epidermis or the Carbosil membrane. Conversely, larger molecules diffuse more slowly since they require more ‘space’ to be created in the medium, and this in turn leads to diminished permeability. The partitioning effect was shown to dominate [9]. Thus, observed outliers lend support to the validity of the model.

5. Conclusion Carbosil membranes are composed of PDMS–PC block copolymers. Like human skin epidermis it has a heterophase and heteropolar structure. For this reason the Carbosil membrane and skin share a common mechanism of drug transport described by a solubility (partition)–diffusion process. The same

properties of permeant contribute to the drug permeability through both epidermis and the Carbosil membrane. The same rules are valid for the permeant transfer across the Carbosil or the human skin for drugs widely varied in their physicochemical properties, structures and therapeutic classes. Application of the Potts–Guy equation to the Carbosil membrane offers a clearer view of common and distinguishing features of drug transport within such different permeation barriers as stratum corneum and synthetic polymer membrane. Drug transfer across the Carbosil membrane imitates percutaneous drug absorption. In vivo transdermal penetration can be quantitatively evaluated through in vitro drug delivery using the Carbosil membrane as the skin-imitating permeation barrier. As the presented analysis demonstrates, different heterophase / heteropolar polymer membranes can also provide mechanistically based models of a good predictive capacity for percutaneous drug transport.

Acknowledgements The research described in this publication was made possible in part by Award No. RN2-409 of the US Civilian Research & Development Foundation for the Independent States of the Former Soviet Union (CRDF) and by Grant No. 97-03-32156a from the Russian Foundation of Basic Research. We express our appreciation to Professor Nicolai A. Plate´ for his valuable contribution to this work.

References [1] J. Houk, R.H. Guy, Membrane models for skin penetration studies, Chem. Rev. 88 (1988) 455–471. [2] V.P. Shah, N.W. Tymes, W. Ment, J.P. Shelly, Collaborative study results of a dissolution test procedure developed by FDA for nitroglycerin transdermal delivery systems, Pharmacopeial Forum 14 (1988) 3458–3462. [3] R.H. Guy, J. Hadgraft, On the determination of drug release rates from topical dosage forms, Int. J. Pharm. 60 (1990) R1–R3. [4] G.L. Flynn, Physicochemical determinants of skin absorption, in: T.R. Gerrity, C.J. Henry (Eds.), Principles of Routeto-route Extrapolation for Risk Assessment, Elsevier, NY, 1990, pp. 93–127. [5] J. Hadgraft, Physicochemical determinants in transdermal

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

[6]

[7]

[8] [9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

drug delivery, in: Proc. 2nd Transdermal Drug Delivery Symp., The Role of Skin in Transdermal Delivery, Nihon Toshi Center, Japan, 1993, pp. 31–43. M.H. Abraham, H.S. Chadha, R.C. Mitchell, The factors that influence skin penetration of solute, J. Pharm. Pharmacol. 47 (1995) 8–16. W.J. Pugh, J. Hadgraft, Ab initio prediction of human skin permeability coefficients, Int. J. Pharm. 103 (1994) 163– 168Y. R.O. Potts, R.H. Guy, Predicting skin permeability, Pharm. Res. 9 (1992) 663–669. R.O. Potts, R.H. Guy, The effects of the permeant’s molecular size and hydrogen bound activity on skin transport, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4b, STS Publishing, Cardiff, 1996, pp. 45–47. W.J. Pugh, M.S. Roberts, J. Hadgraft, T. Degim, Relationship between H-bonding of penetrants to stratum corneum lipids and diffusion within the stratum corneum, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4b, STS Publishing, Cardiff, 1996, pp. 48–51. T. Degim, W.J. Pugh, J. Hadgraft, M.S. Roberts, Prediction of skin permeability using partial charge calculations, in: I.W. Kellaway, J. Hadgraft (Eds.), Proc. 4th UKaps Annual Conference, STS Publishing, Cardiff, 1995, pp. 49–53. A.S. Michaels, S.K. Chandrasekaran, J.E. Show, Drug permeation through human skin: theory and in vitro experimental measurements, Am. Inst. Chem. Eng J. 21 (1975) 985–996. G.B. Kasting, R.L. Smith, E.R. Cooper, Effect of lipid solubility and molecular size on percutaneous absorption in: B. Shroot, H. Schaefer (Eds.), Skin Pharmacokinetics, Karger, Basel, 1987, pp. 138–153. W.J. Pugh, K.R. Brain, J. Hadgraft, The prediction of skin permeability ab initio, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 3b, STS Publishing, Cardiff, 1993, pp. 49–53. I.M. Raigorodskii, V.S. Rabkin, V.V. Kireev, Polyorganopolysiloxane copolymers, Vysokomolec. Soed. (Polymer Sci. Russ.) 37A(3) (1995) 445–469. G.I. Listvoib, Polycarbonate-polysiloxane block copolymers and membranes, Ph.D. Thesis, D.I. Mendeleev Moscow Chemical and Technological Institute, Moscow, 1992, p. 177. M. Katz, B.J. Poulsen, Absorption of drugs through the skin, in: B.B. Brodie, J.R. Gillet (Eds.), Handbook of Experimental Pharmacology, vol. 26 Springer Verlag, Berlin–NY, 1971, pp. 103–105. ´ M.M. Feldstein, V.E. Igonin, T.E. Grokhovskaya, N.A. Plate, Structure of hydrogels for transdermal drug delivery based on interpolymeric complexes between macromolecules of incommensurable length, Proc. Int. Symp. Control. Release Bioactive Mater. 23 (1996) 749–750. M.M. Feldstein, V.N. Tohmakhchi, L.B. Malkhazov, A.E. ´ Hydrophilic polymeric matrices for Vasiliev, N.A. Plate, enhanced transdermal drug delivery, Int. J. Pharm. 131(2) (1996) 229–242.

39

[20] S.A. Reitlinger, Permeability of Polymeric Materials, Moscow, Khimia, 1974, p. 66. [21] H. Hopfenberg, D. Paul, Transfer processes in polymeric mixtures, in: D. Paul, M. Newman (Eds.), Polymer Blends, MIR, Moscow, 1981, p. 494. ´ Enhanced drug [22] M.M. Feldstein, A.E. Vasiliev, N.A. Plate, delivery from transdermal therapeutic systems with hydrophilic polymeric matrix, Proc. Int. Symp. Control. Release Bioactive Mater. 21 (1994) 423–424. ´ [23] A.E. Vasiliev, M.M. Feldstein, M.E. Pudel, N.A. Plate, Universal hydrophilic drug-containing adhesive matrix for systemic and topical transdermal drug delivery, in: Proc. 1st World Meeting APGI /APV, Budapest, 1995, pp. 683–684. [24] R.H. Guy, J. Hadgraft, Rate control in transdermal drug delivery?, Int. J. Pharm. 82 (1992) R1–R6. [25] M.M. Feldstein, J. Hadgraft, Interrelationship between diffusivity and tack of pressure-sensitive adhesives: Significance for transdermal drug delivery, Proc. Int. Symp. Control. Relase Bioactive Mater. 24 (1997) 21–22. [26] M.M. Feldstein, Skin-controlled drug delivery from the hydrophilic matrices, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4a, STS Publishing Ltd, Cardiff, 1995, C15. ´ [27] M.M. Feldstein, J. Hadgraft, A.L. Iordanskii, N.A. Plate, General rules for drug delivery from a hydrophilic polymeric matrix across skin or skin-imitating Carbosil membrane, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4b, STS Publishing Ltd, Cardiff, 1996, pp. 56–60. [28] V.S. Markin, A.L. Iordanskii, M.M. Feldstein, A.E. Vasiliev, ´ Diffusion model of drug delivery from hydroN.A. Plate, philic polymeric matrices across skin-imitating polymeric membrane in vitro, Khim.-Farm. Zh. (Chem.-Pharm. J. Russ.) 28(10) (1994) 38–45. [29] M.M. Feldstein, V.S. Markin, A.L. Iordanskii, J. Hadgraft, ´ Rate-controlling device contributions to overall N.A. Plate, skin-controlled transdermal drug delivery, in: Abstract Book of the IV Eur. Symp. Control. Drug Delivery, Noordwijk aan Zee, The Netherlands, 1996, pp. 158–162. [30] M.M. Feldstein, I.F. Dlickman, S.V. Pavperova, M.E. Pudel, ´ In vitro and in vivo hydration A.E. Vasiliev, N.A. Plate, kinetics of the hydrophilic polymer matrices for transdermal drug delivery, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4a, STS Publishing Ltd, Cardiff, 1995, C16. [31] M.M. Feldstein, I.F. Dlickman, S.V. Pavperova, I.V. Pariy, ´ Effect of hydrophilic M.E. Pudel, A.E. Vasiliev, N.A. Plate, matrix hydration on transdermal drug delivery kinetics: I. Matrix hydration in vivo and in vitro, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4b, STS Publishing Ltd, Cardiff, 1996, pp. 61–64 [32] M.M. Feldstein, I.V. Pariy, I.F. Dlickman, L.B. Malkhazov, V.N. Tohmakhchi, N.M. Petukhova, A.E. Vasiliev, N.A. ´ Influence of matrix hydration on cytisine in vitro Plate, delivery from Cypercuten TTS, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4a, STS Publishing Ltd, Cardiff, 1995, C17.

40

M.M. Feldstein et al. / Journal of Controlled Release 52 (1998) 25 – 40

[33] M.M. Feldstein, I.V. Pariy, I.F. Dlickman, L.B. Malkhazov, V.N. Tohmakhchi, N.M. Petukhova, A.E. Vasiliev, N.A. ´ Effect of hydrophilic matrix hydration on transdermal Plate, drug delivery kinetics: II. In vitro cytisine delivery from Cypercuten TTS, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4b, STS Publishing Ltd, Cardiff, 1996, pp. 65–67. [34] M.M. Feldstein, N.M. Petukhova, I.F. Dlickman, L.B. Mal´ Effect of khazov, I.B. Kadenatsi, A.E. Vasiliev, N.A. Plate, matrix hydration on clonidine in vitro delivery from Clopercuten TTS, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4a, STS Publishing Ltd, Cardiff, 1995, C18. [35] M.M. Feldstein, N.M. Petukhova, I.F. Dlickman, L.B. Mal´ Effect of khazov, I.B. Kadenatsi, A.E. Vasiliev, N.A. Plate, hydrophilic matrix hydration on transdermal drug delivery kinetics: III. In vitro clonidine delivery from Clopercuten TTS, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4b, STS Publishing Ltd, Cardiff, 1996, pp. 68–70. ´ In vitro–in vivo [36] M.M. Feldstein, A.E. Vasiliev, N.A. Plate, correlations for cytisine and clonidine transdermal delivery from hydrophilic matrices of drug delivery systems in the course of matrix hydration, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 4a, STS Publishing Ltd, Cardiff, 1995, C19. ´ Effect of hydro[37] M.M. Feldstein, A.E. Vasiliev, N.A. Plate, philic matrix hydration on transdermal drug delivery kinetics: IV. In vitro–in vivo correlation, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous

[38]

[39]

[40]

[41]

[42]

[43]

[44]

Penetration, vol. 4b, STS Publishing Ltd, Cardiff, 1996, pp. 71–73. M.A. Pellet, A.F. Davis, J. Hadgraft, Effect of supersaturation on membrane transport: 2. Piroxicam, Int. J. Pharm. 111 (1994) 1–6. M.M. Feldstein, J. Hadgraft, A.L. Iordanskii, A.E. Vasiliev, ´ Assessment of inter-subject variability in perN.A. Plate, cutaneous drug absorption using skin-controlled drug delivery from hydrophilic matrix in vitro, Proc. Int. Symp. Control. Release Bioactive Mater. 22 (1995) 638–639. V.M. Knepp, R.H. Guy, J. Hadgraft, Transdermal drug delivery: problems and possibilities, CRC Crit. Rev. Ther. Drug Carriers Syst. 4(1) (1987) 13–37. J. Hadgraft, S. Hill, M. Himpel, L. Johnson, L.R. Lever, R. Marks, T.M. Murphy, C. Rapier, Investigation on the percutaneous absorption of the antidepressant Rolipram in vitro and in vivo, Pharm. Res. 7(12) (1990) 1307–1312. V. Koprda, H. Balgova, J. Hadgraft, Blood levels of nitroglycerin modelled using liberation rates of the drug from matrix type transdermal delivery devices, in: K.R. Brain, V.J. James, K.A. Walters (Eds.), Prediction of Percutaneous Penetration, vol. 3b, STS Publishing Ltd, Cardiff, 1993, pp. 568–575. J. Hadgraft, G. Gordes, H.M. Wolff, Prediction of the transdermal delivery of b-blockers, in: N. Rietbrock (Ed.), Die Haut als Transportorgan fur Arzneistoffe, Steinkopf Verlag, Darmstadt, 1990, pp. 133–143. K.H. Fromming, W. Ditter, D. Horn, Sorption properties of cross-linked insoluble polyvinylpyrrolidone, J. Pharm. Sci. 70(7) (1981) 738–743.