RELATIONSHIP BETWEEN H-BONDING OFPENETRANTS TO STRATUM CORNEUM LIPIDS

AND DIFFUSION

William John Pugh

Welsh School of Pharmacy Cardiff University Cardiff Wales

I INTRODUCTION

It is generally accepted that the barrier to permeation is effectively the

outermost 10ndash15mm of the skin (1ndash3) To overcome this stratum corneum (SC)

obstacle a molecule must first enter and then cross it

Fickrsquos law relates the steady-state flux Js to the concentration gradient

across the SC If the viable dermis is regarded as a sink the gradient determining

the flux is Csch Since the partition coefficient K of a solute between the SC and

vehicle can be written as Csc Cv Js can be expressed as

Js frac14 ADKCv=h

The permeability coefficient kp is the steady-state flux per unit area divided by the

concentration of solute in solution so that

kp frac14Js

ACv

frac14 KD

h

Most reports on epidermal structure penetration relationships are based on

this composite quantity kp for aqueous vehicles This article concentrates mainly

on the diffusion step and examines the molecular features particularly H-bonding

that determine it To set this in context a very brief outline of the overall process is

given

303

Copyright q 2001 by Marcel Dekker Inc wwwdekkercom

Reprinted from Percutaneous Adsorption 3rd Ed Bronaugh RL Maibach HI Eds Marcel

Dekker Inc New York 1999 177ndash192

J TOXICOLmdashCUT amp OCULAR TOXICOL 20(2amp3) 303ndash317 (2001)

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II THE NATURE OF THE BARRIER

Absorption across the stratum corneum (SC) is a passive process of

diffusion The SC is composed of dead corneocytes in a lipid matrix pierced by

hair follicles and sweat glands In principle there are three routes for diffusion

intercellular diffusion through the lipid matrix transcellular diffusion through the

corneocytes and pilosebaceous diffusion along the sweat pores and hair follicles

Absorption via the pores and follicles is considered to be insignificant

because the orifices account for only 01 of skin area and diffusion along sweat

ducts is against an outward aqueous flow (4) Lauer et al (5) reviewed this

pathway recalling Scheupleinrsquos (67) proposal that the initial transient

penetration of steroids is consistent with diffusion through pores However

after the steady state is established bulk diffusion through the lipid region

accounts for most permeation Siddiqui et al (8) compared diffusion of steroids

across SC and a pore-free membrane (Silastic) and concluded that the penetration

kinetics could be explained without invoking the need for aqueous channels

Although the recent mathematical modeling work of Heisig et al (9) suggests that

permeation through the corneocytes cannot be ignored the barrier must be

essentially lipid in nature since its barrier function is lost after extracting the lipids

(1011) and the equations developed by Edwards and Langer (12) suggest that the

intercellular matrix is the significant route for diffusion of uncharged permeants

Roberts et al (13) propose a mixed model where transport occurs along a

continuous pathway but both the lipid and polar portions of the bilayer are used

depending on the polarity of the penetrant

The lipid composition of SC has been determined by Wertz et al (14) and the

major components are fatty acids ceramides and cholesterol Leickfeldt et al

consider that the precise molecular form of the lipids is unimportant to barrier

function Interaction between cholesterol and fatty acids produces an ordered

impermeable bilayer structure and the distinctive form of the ceramide molecules

enables solubilization of the cholesterol and prevents its separation into a separate

phase (15)

III DETERMINANTS OF THE PERMEABILITYCOEFFICIENT kp

The equation for Js suggests that partitioning into the SC is an important

determinant of permeability and correlations were sought between kp and K

between various model solvents and water The partition between octanol and

water Koctanol is as good as any other for this purpose (16)

Reasonable correlations between kp and Koctanol were obtained only for

families of similar compounds Thus Roberts et al (17) found for a set of phenols

log kp frac14 233 1 069 log Koctanol N frac14 19 r 2 frac14 72

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For hydrocortisone esters El Tayar et al (18) found

log kp frac14 253 1 080 log Koctanol N frac14 11 r 2 frac14 88

and for alkanols

log kp frac14 227 1 077 log Koctanol N frac14 8 r 2 frac14 89

Correlations on mixed datasets were unsuccessful For combined alkanols

and phenols El Tayar et al found

log kp frac14 236 1 016Koctanol N frac14 22 r 2 frac14 03

When plotted separately the data fall on two distinct lines and El Tayarrsquos group

attributed the difference in the gradients to penetration via intracellular and

transcellular routes

Kasting et al (19) appreciating that kp was the product of both partition and

diffusion terms included molecular weight (MW) as a size determinant of

diffusion and following on from this Potts and Guy (20) published their much

quoted relationship

log kpethcm=hTHORN frac14 2274 1 071 log Koctanol 2 00061MW N frac14 93

r 2 frac14 67

which encompassed the data set of diverse compounds collected by Flynn

Roberts et al (13) analyzed data for 91 of the compounds studied by Potts

and Guy and found a similar regression

log kpethcm=hTHORN frac14 2270 1 063 log Koctanol 2 00054MW N frac14 91

r 2 frac14 65

They suggested that interaction might occur between penetrant and both polar and

nonpolar components of SC and related kp to partition into dissimilar (polar and

nonpolar) solvents This enabled them to account for some of the 33 of the

variation in kp not explained by Potts and Guy

log kp frac14 2229 1 024 log Koctanol 1 040 log Khexane N frac14 24

r 2 frac14 88

Taft Kamlet Abraham and co-workers developed the solvatochromic

approach to determining permeability According to this the essential features of a

permeant molecule are its size (V) electronic charge distribution (p) and

hydrogen bonding donor and receptor capabilities (a and b )

PENETRANT BONDING TO STRATUM CORNEUM 305

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Abrahametal (21) found fora mixeddatasetofalcohols steroids andphenols

log kp frac14 2149 2 059p 2 063a2 348b1 00179V N frac14 46

r 2 frac14 96

and were thus able to explain permeation in terms of a single pathway model The

findings of Potts and Guy (20)

log kp frac14 2129 2 172a2 393b1 00256V N frac14 37 r 2 frac14 94

and Roberts et al (13)

log kp frac14 2135 2 137a2 453b1 00205V N frac14 24 r 2 frac14 93

confirm this observation and furthermore suggest that p is not a significant

predictor of kp

It seems then that permeation can be explained by a single pathway and is

chiefly determined by H-bonding properties and permeant size

It has already been noted that kp is a composite of two factors K and (Dh )

Principal component analysis (PCA) measures how data points in a matrix may be

related In essence it enables us to see how many processes or mechanisms are

involved in relating an outcome (log kp) and molecular properties (a b V ) of the

permeants (22)

If the data used by Roberts et al (13) are subjected to PCA (unpublished) the

variation in the matrix of four datasets (log kp a b V ) is described in terms of

four combinations (principal components) of the variables The output from the

Minitab statistical package (23) is

This output is interpreted as follows The sum of eigenvalues for four PCs is 4 The

eigenvalue for a particular PC is a measure of the amount of variation in the data

that can be explained by that PC Thus variation due to PC1 frac14 21352=5 frac14

0534 eth534THORN So we can explain 534 of the variation in the data by the

Eigenvectors

Variable PC1 PC2 PC3 PC4

log kp 0661 0197 20099 0718

a 20030 20880 0353 0318

b 20561 20096 20690 0448

V 0498 20422 20625 20429

Eigenvalue 21352 11808 06534 00306

Proportion explained 0534 0295 0163 0008

Cumulative proportion 0534 0829 0992 1000

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interrelationship between the four variables

eth0661 log kpTHORN2 eth0030 aTHORN2 eth0561 bTHORN1 eth0498 VTHORN

There is a mechanismprocess that accounts for 534 of the variation in the data

and the first two PCs mechanismsprocesses will together account for 829 of the

variation It is reasonable to speculate that these two processes are the partition and

diffusion processes that comprise kp

The importance of a variable in its PC is given by the square of its

eigenvector Thus in PC1 (process 1) a is unimportant since 999 that is

frac12frac121 2 eth20032THORN 100 of the variation due to this process can be explained

without it It is however very important in process 2

The importance of H-bonding had been recognized earlier when Roberts (24)

showed that kp was related to the number of H-bonding groups in the penetrant

Recently attempts were made (13) to quantify H-bonding as the difference in

partition from water into H-bonding and non-H-bonding solvents Anderson and

Raykar (25) suggested that the SC barrier resembled a hydrogen-bonding organic

solvent and El Tayar et al (18) concluded that the H-bond donor potential was

dominant However this differential partitioning approach has been shown to be

unreliable by the analyses of Roberts et al (13) and Pugh et al (16) and use of a

and b values as quantifiers of H-bonding seems to be the way forward The papers

of Abraham (26) and Abraham et al (21) are valuable data sources for the

solvatochromic parameters

IV DETERMINANTS OF DIFFUSION ACROSS THE SC

Potential factors reducing diffusion include molecular size interaction with

SC components and the obstructive effects of the corneocytes In principle it is

possible for penetrants to diffuse both along the lipid pathway and through the

corneocytes (12) but Potts and Francoeur (27) argue forcefully against diffusion

of water through corneocytes and it is unlikely that polar organic molecules

traverse them if water cannot Their reasoning may be summarized as follows

Corneocytes are covered by covalently bound highly nonpolar lipids with

exceptionally long (C30ndashC34) hydrocarbon chains (28) which are significantly

more hydrophobic than other SC lamellae (29) The presence of inert ldquoflakesrdquo in a

homogenous matrix reduces permeability (3031) by an obstruction effect and

water permeability falls with increasing corneocyte size (32) as predicted by flake

theory SC is 1000 times less permeable to water vapor than other lipid

membranes and Hadgraft and Ridout (33) found that the passage of drugs through

SC was about 1000 times slower than through films of isopropyl myristate Twenty

to 30 layers of corneocytes 05mm thick and 30mm square spaced 01mm apart

(34) would lower permeability by a factor of 1000 by an obstruction effect They

thus seem to act as mechanical barriers and increase the path length of diffusion

PENETRANT BONDING TO STRATUM CORNEUM 307

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The lipids form the only continuous domain in the SC (3536) and their

removal increases water permeability (37) SC that has been reconstituted from

corneocytes and extracted SC lipids behaves similarly to intact SC (3839) and

Friberg et al (40) showed a variety of lipids could restore SC properties to isolated

corneocytes Rougier et al (32) showed that permeability of SC to water and

benzoic acid are highly correlated for a group of human subjects suggesting a

common pathway

All this evidence points to corneocytes having only a pathlength-increasing

effect and not providing a parallel pathway for watermdashand by inference

hydrophilicmdashmolecules

Early methods for finding D (41) involved measurement of the lag time t to

establish steady flux across the SC This is given (42) by

t frac14 h2=6D

The value of h is uncertain and estimation of t involves extrapolation of the

ldquolinearrdquo portion of the plot of amount transferred against time Curve-fitting

programs now make it possible to deconvolute the terms in the non-steady-state

equation (8)

C

Cm

frac14 1 24

p

X1nfrac140

eth21THORNn

2n 1 1exp

2Deth2n 1 1THORN2p2t

4h2

to find Dh 2

Robertsrsquos group went on to examine the influence of H-bonding on the

diffusion (16) using a different approach to find Dh Since log kp frac14

log Ksc 1 logethD=hTHORN and

log Ksc frac14 20024 1 059 log Koctanol N frac14 45 r 2 frac14 84

then

logethD=hTHORN frac14 log kp 2 059 log Koctanol 1 0024

V DIFFUSION OF MONOFUNCTIONAL COMPOUNDS

Using experimental values of Ksc Roberts et al (43) calculated log(Dh ) as

ethlog kp 2 log KscTHORN and used a and b values as measures of H-bonding potential A

good correlation was found

logethD=hTHORN frac14 2186 2 061a2 209b N frac14 37 r 2 frac14 90

but inclusion of p or MW did not improve the regression The major determinant

of diffusion is H-bonding implying that each substituent group on the permeant

retards diffusion to a characteristic degree Further the high coefficient of b shows

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that SC is predominantly an H-bond donor as proposed earlier by El Tayar et al

(18)

They next set out to quantify the H-bonding powers of various chemical

groups (16) first confirming that log(Dh ) as estimated from log Koctanol was

related to a and b

logethD=hTHORN frac14 2132 2 130a2 257b N frac14 29 r 2 frac14 85

and going on to regress log(Dh ) against the number (0 or 1) of each functional

group present

logethD=hTHORN frac14 2136 2 167 acid 2 141 alcohol 2 117 phenol

2 0986 carbonyl 2 0759 ether 2 00502C

where acid is the number of the acid groups (0 or 1) in permeant and C is the

number of C atoms not involved in CyO bonds The (negative) coefficients were

greater for strong H-bonding functions and were called retardation coefficients

(RCs) Thus the presence of an acid would reduce the diffusion across the SC by a

factor of about 50 and an ether by about 6 This multiplicative effect explained

their earlier observation that introduction of multiple groups caused a dramatic

decrease in diffusion

VI H-BONDING POTENTIAL OF THE SC

Using the lipid composition of the SC given by Wertz (44) and the a and

b values of Abraham (26) Pugh et al (16) calculated the H-bonding effects of

the SC to be in the ratio ascbscfrac14 0406 This would suggest that SC is

predominantly an H-bond acceptor environment and contradicted their earlier

conclusion and that of El Tayar et al The H-bonding for each functional

group g should be related to the quantity frac12ethagbscTHORN1 ethbgascTHORN but a plot of

RC against frac12ethagbscTHORN1 ethbgascTHORN did not pass through the origin as expected

The ascbsc value of 04060 was therefore considered dubious and the

H-bonding potential of the SC was reestimated indirectly from RC values as

follows

In the simplest case RC would be directly related to H-bonding between

penetrant and SC

RC frac14 X 1 Yfrac12ethapbscTHORN1 ethbpascTHORN

Since asc frac14 eth1 2 bscTHORN

RC frac14 X 1 Ybscethap 2 bpTHORN1 Ybp

The regression is

RC frac14 00024 1 136ethap 2 bpTHORN1 318bp r 2 frac14 99

PENETRANT BONDING TO STRATUM CORNEUM 309

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The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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II THE NATURE OF THE BARRIER

Absorption across the stratum corneum (SC) is a passive process of

diffusion The SC is composed of dead corneocytes in a lipid matrix pierced by

hair follicles and sweat glands In principle there are three routes for diffusion

intercellular diffusion through the lipid matrix transcellular diffusion through the

corneocytes and pilosebaceous diffusion along the sweat pores and hair follicles

Absorption via the pores and follicles is considered to be insignificant

because the orifices account for only 01 of skin area and diffusion along sweat

ducts is against an outward aqueous flow (4) Lauer et al (5) reviewed this

pathway recalling Scheupleinrsquos (67) proposal that the initial transient

penetration of steroids is consistent with diffusion through pores However

after the steady state is established bulk diffusion through the lipid region

accounts for most permeation Siddiqui et al (8) compared diffusion of steroids

across SC and a pore-free membrane (Silastic) and concluded that the penetration

kinetics could be explained without invoking the need for aqueous channels

Although the recent mathematical modeling work of Heisig et al (9) suggests that

permeation through the corneocytes cannot be ignored the barrier must be

essentially lipid in nature since its barrier function is lost after extracting the lipids

(1011) and the equations developed by Edwards and Langer (12) suggest that the

intercellular matrix is the significant route for diffusion of uncharged permeants

Roberts et al (13) propose a mixed model where transport occurs along a

continuous pathway but both the lipid and polar portions of the bilayer are used

depending on the polarity of the penetrant

The lipid composition of SC has been determined by Wertz et al (14) and the

major components are fatty acids ceramides and cholesterol Leickfeldt et al

consider that the precise molecular form of the lipids is unimportant to barrier

function Interaction between cholesterol and fatty acids produces an ordered

impermeable bilayer structure and the distinctive form of the ceramide molecules

enables solubilization of the cholesterol and prevents its separation into a separate

phase (15)

III DETERMINANTS OF THE PERMEABILITYCOEFFICIENT kp

The equation for Js suggests that partitioning into the SC is an important

determinant of permeability and correlations were sought between kp and K

between various model solvents and water The partition between octanol and

water Koctanol is as good as any other for this purpose (16)

Reasonable correlations between kp and Koctanol were obtained only for

families of similar compounds Thus Roberts et al (17) found for a set of phenols

log kp frac14 233 1 069 log Koctanol N frac14 19 r 2 frac14 72

PUGH304

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For hydrocortisone esters El Tayar et al (18) found

log kp frac14 253 1 080 log Koctanol N frac14 11 r 2 frac14 88

and for alkanols

log kp frac14 227 1 077 log Koctanol N frac14 8 r 2 frac14 89

Correlations on mixed datasets were unsuccessful For combined alkanols

and phenols El Tayar et al found

log kp frac14 236 1 016Koctanol N frac14 22 r 2 frac14 03

When plotted separately the data fall on two distinct lines and El Tayarrsquos group

attributed the difference in the gradients to penetration via intracellular and

transcellular routes

Kasting et al (19) appreciating that kp was the product of both partition and

diffusion terms included molecular weight (MW) as a size determinant of

diffusion and following on from this Potts and Guy (20) published their much

quoted relationship

log kpethcm=hTHORN frac14 2274 1 071 log Koctanol 2 00061MW N frac14 93

r 2 frac14 67

which encompassed the data set of diverse compounds collected by Flynn

Roberts et al (13) analyzed data for 91 of the compounds studied by Potts

and Guy and found a similar regression

log kpethcm=hTHORN frac14 2270 1 063 log Koctanol 2 00054MW N frac14 91

r 2 frac14 65

They suggested that interaction might occur between penetrant and both polar and

nonpolar components of SC and related kp to partition into dissimilar (polar and

nonpolar) solvents This enabled them to account for some of the 33 of the

variation in kp not explained by Potts and Guy

log kp frac14 2229 1 024 log Koctanol 1 040 log Khexane N frac14 24

r 2 frac14 88

Taft Kamlet Abraham and co-workers developed the solvatochromic

approach to determining permeability According to this the essential features of a

permeant molecule are its size (V) electronic charge distribution (p) and

hydrogen bonding donor and receptor capabilities (a and b )

PENETRANT BONDING TO STRATUM CORNEUM 305

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Abrahametal (21) found fora mixeddatasetofalcohols steroids andphenols

log kp frac14 2149 2 059p 2 063a2 348b1 00179V N frac14 46

r 2 frac14 96

and were thus able to explain permeation in terms of a single pathway model The

findings of Potts and Guy (20)

log kp frac14 2129 2 172a2 393b1 00256V N frac14 37 r 2 frac14 94

and Roberts et al (13)

log kp frac14 2135 2 137a2 453b1 00205V N frac14 24 r 2 frac14 93

confirm this observation and furthermore suggest that p is not a significant

predictor of kp

It seems then that permeation can be explained by a single pathway and is

chiefly determined by H-bonding properties and permeant size

It has already been noted that kp is a composite of two factors K and (Dh )

Principal component analysis (PCA) measures how data points in a matrix may be

related In essence it enables us to see how many processes or mechanisms are

involved in relating an outcome (log kp) and molecular properties (a b V ) of the

permeants (22)

If the data used by Roberts et al (13) are subjected to PCA (unpublished) the

variation in the matrix of four datasets (log kp a b V ) is described in terms of

four combinations (principal components) of the variables The output from the

Minitab statistical package (23) is

This output is interpreted as follows The sum of eigenvalues for four PCs is 4 The

eigenvalue for a particular PC is a measure of the amount of variation in the data

that can be explained by that PC Thus variation due to PC1 frac14 21352=5 frac14

0534 eth534THORN So we can explain 534 of the variation in the data by the

Eigenvectors

Variable PC1 PC2 PC3 PC4

log kp 0661 0197 20099 0718

a 20030 20880 0353 0318

b 20561 20096 20690 0448

V 0498 20422 20625 20429

Eigenvalue 21352 11808 06534 00306

Proportion explained 0534 0295 0163 0008

Cumulative proportion 0534 0829 0992 1000

PUGH306

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interrelationship between the four variables

eth0661 log kpTHORN2 eth0030 aTHORN2 eth0561 bTHORN1 eth0498 VTHORN

There is a mechanismprocess that accounts for 534 of the variation in the data

and the first two PCs mechanismsprocesses will together account for 829 of the

variation It is reasonable to speculate that these two processes are the partition and

diffusion processes that comprise kp

The importance of a variable in its PC is given by the square of its

eigenvector Thus in PC1 (process 1) a is unimportant since 999 that is

frac12frac121 2 eth20032THORN 100 of the variation due to this process can be explained

without it It is however very important in process 2

The importance of H-bonding had been recognized earlier when Roberts (24)

showed that kp was related to the number of H-bonding groups in the penetrant

Recently attempts were made (13) to quantify H-bonding as the difference in

partition from water into H-bonding and non-H-bonding solvents Anderson and

Raykar (25) suggested that the SC barrier resembled a hydrogen-bonding organic

solvent and El Tayar et al (18) concluded that the H-bond donor potential was

dominant However this differential partitioning approach has been shown to be

unreliable by the analyses of Roberts et al (13) and Pugh et al (16) and use of a

and b values as quantifiers of H-bonding seems to be the way forward The papers

of Abraham (26) and Abraham et al (21) are valuable data sources for the

solvatochromic parameters

IV DETERMINANTS OF DIFFUSION ACROSS THE SC

Potential factors reducing diffusion include molecular size interaction with

SC components and the obstructive effects of the corneocytes In principle it is

possible for penetrants to diffuse both along the lipid pathway and through the

corneocytes (12) but Potts and Francoeur (27) argue forcefully against diffusion

of water through corneocytes and it is unlikely that polar organic molecules

traverse them if water cannot Their reasoning may be summarized as follows

Corneocytes are covered by covalently bound highly nonpolar lipids with

exceptionally long (C30ndashC34) hydrocarbon chains (28) which are significantly

more hydrophobic than other SC lamellae (29) The presence of inert ldquoflakesrdquo in a

homogenous matrix reduces permeability (3031) by an obstruction effect and

water permeability falls with increasing corneocyte size (32) as predicted by flake

theory SC is 1000 times less permeable to water vapor than other lipid

membranes and Hadgraft and Ridout (33) found that the passage of drugs through

SC was about 1000 times slower than through films of isopropyl myristate Twenty

to 30 layers of corneocytes 05mm thick and 30mm square spaced 01mm apart

(34) would lower permeability by a factor of 1000 by an obstruction effect They

thus seem to act as mechanical barriers and increase the path length of diffusion

PENETRANT BONDING TO STRATUM CORNEUM 307

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The lipids form the only continuous domain in the SC (3536) and their

removal increases water permeability (37) SC that has been reconstituted from

corneocytes and extracted SC lipids behaves similarly to intact SC (3839) and

Friberg et al (40) showed a variety of lipids could restore SC properties to isolated

corneocytes Rougier et al (32) showed that permeability of SC to water and

benzoic acid are highly correlated for a group of human subjects suggesting a

common pathway

All this evidence points to corneocytes having only a pathlength-increasing

effect and not providing a parallel pathway for watermdashand by inference

hydrophilicmdashmolecules

Early methods for finding D (41) involved measurement of the lag time t to

establish steady flux across the SC This is given (42) by

t frac14 h2=6D

The value of h is uncertain and estimation of t involves extrapolation of the

ldquolinearrdquo portion of the plot of amount transferred against time Curve-fitting

programs now make it possible to deconvolute the terms in the non-steady-state

equation (8)

C

Cm

frac14 1 24

p

X1nfrac140

eth21THORNn

2n 1 1exp

2Deth2n 1 1THORN2p2t

4h2

to find Dh 2

Robertsrsquos group went on to examine the influence of H-bonding on the

diffusion (16) using a different approach to find Dh Since log kp frac14

log Ksc 1 logethD=hTHORN and

log Ksc frac14 20024 1 059 log Koctanol N frac14 45 r 2 frac14 84

then

logethD=hTHORN frac14 log kp 2 059 log Koctanol 1 0024

V DIFFUSION OF MONOFUNCTIONAL COMPOUNDS

Using experimental values of Ksc Roberts et al (43) calculated log(Dh ) as

ethlog kp 2 log KscTHORN and used a and b values as measures of H-bonding potential A

good correlation was found

logethD=hTHORN frac14 2186 2 061a2 209b N frac14 37 r 2 frac14 90

but inclusion of p or MW did not improve the regression The major determinant

of diffusion is H-bonding implying that each substituent group on the permeant

retards diffusion to a characteristic degree Further the high coefficient of b shows

PUGH308

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ORDER REPRINTS

that SC is predominantly an H-bond donor as proposed earlier by El Tayar et al

(18)

They next set out to quantify the H-bonding powers of various chemical

groups (16) first confirming that log(Dh ) as estimated from log Koctanol was

related to a and b

logethD=hTHORN frac14 2132 2 130a2 257b N frac14 29 r 2 frac14 85

and going on to regress log(Dh ) against the number (0 or 1) of each functional

group present

logethD=hTHORN frac14 2136 2 167 acid 2 141 alcohol 2 117 phenol

2 0986 carbonyl 2 0759 ether 2 00502C

where acid is the number of the acid groups (0 or 1) in permeant and C is the

number of C atoms not involved in CyO bonds The (negative) coefficients were

greater for strong H-bonding functions and were called retardation coefficients

(RCs) Thus the presence of an acid would reduce the diffusion across the SC by a

factor of about 50 and an ether by about 6 This multiplicative effect explained

their earlier observation that introduction of multiple groups caused a dramatic

decrease in diffusion

VI H-BONDING POTENTIAL OF THE SC

Using the lipid composition of the SC given by Wertz (44) and the a and

b values of Abraham (26) Pugh et al (16) calculated the H-bonding effects of

the SC to be in the ratio ascbscfrac14 0406 This would suggest that SC is

predominantly an H-bond acceptor environment and contradicted their earlier

conclusion and that of El Tayar et al The H-bonding for each functional

group g should be related to the quantity frac12ethagbscTHORN1 ethbgascTHORN but a plot of

RC against frac12ethagbscTHORN1 ethbgascTHORN did not pass through the origin as expected

The ascbsc value of 04060 was therefore considered dubious and the

H-bonding potential of the SC was reestimated indirectly from RC values as

follows

In the simplest case RC would be directly related to H-bonding between

penetrant and SC

RC frac14 X 1 Yfrac12ethapbscTHORN1 ethbpascTHORN

Since asc frac14 eth1 2 bscTHORN

RC frac14 X 1 Ybscethap 2 bpTHORN1 Ybp

The regression is

RC frac14 00024 1 136ethap 2 bpTHORN1 318bp r 2 frac14 99

PENETRANT BONDING TO STRATUM CORNEUM 309

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The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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Order now

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For hydrocortisone esters El Tayar et al (18) found

log kp frac14 253 1 080 log Koctanol N frac14 11 r 2 frac14 88

and for alkanols

log kp frac14 227 1 077 log Koctanol N frac14 8 r 2 frac14 89

Correlations on mixed datasets were unsuccessful For combined alkanols

and phenols El Tayar et al found

log kp frac14 236 1 016Koctanol N frac14 22 r 2 frac14 03

When plotted separately the data fall on two distinct lines and El Tayarrsquos group

attributed the difference in the gradients to penetration via intracellular and

transcellular routes

Kasting et al (19) appreciating that kp was the product of both partition and

diffusion terms included molecular weight (MW) as a size determinant of

diffusion and following on from this Potts and Guy (20) published their much

quoted relationship

log kpethcm=hTHORN frac14 2274 1 071 log Koctanol 2 00061MW N frac14 93

r 2 frac14 67

which encompassed the data set of diverse compounds collected by Flynn

Roberts et al (13) analyzed data for 91 of the compounds studied by Potts

and Guy and found a similar regression

log kpethcm=hTHORN frac14 2270 1 063 log Koctanol 2 00054MW N frac14 91

r 2 frac14 65

They suggested that interaction might occur between penetrant and both polar and

nonpolar components of SC and related kp to partition into dissimilar (polar and

nonpolar) solvents This enabled them to account for some of the 33 of the

variation in kp not explained by Potts and Guy

log kp frac14 2229 1 024 log Koctanol 1 040 log Khexane N frac14 24

r 2 frac14 88

Taft Kamlet Abraham and co-workers developed the solvatochromic

approach to determining permeability According to this the essential features of a

permeant molecule are its size (V) electronic charge distribution (p) and

hydrogen bonding donor and receptor capabilities (a and b )

PENETRANT BONDING TO STRATUM CORNEUM 305

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Abrahametal (21) found fora mixeddatasetofalcohols steroids andphenols

log kp frac14 2149 2 059p 2 063a2 348b1 00179V N frac14 46

r 2 frac14 96

and were thus able to explain permeation in terms of a single pathway model The

findings of Potts and Guy (20)

log kp frac14 2129 2 172a2 393b1 00256V N frac14 37 r 2 frac14 94

and Roberts et al (13)

log kp frac14 2135 2 137a2 453b1 00205V N frac14 24 r 2 frac14 93

confirm this observation and furthermore suggest that p is not a significant

predictor of kp

It seems then that permeation can be explained by a single pathway and is

chiefly determined by H-bonding properties and permeant size

It has already been noted that kp is a composite of two factors K and (Dh )

Principal component analysis (PCA) measures how data points in a matrix may be

related In essence it enables us to see how many processes or mechanisms are

involved in relating an outcome (log kp) and molecular properties (a b V ) of the

permeants (22)

If the data used by Roberts et al (13) are subjected to PCA (unpublished) the

variation in the matrix of four datasets (log kp a b V ) is described in terms of

four combinations (principal components) of the variables The output from the

Minitab statistical package (23) is

This output is interpreted as follows The sum of eigenvalues for four PCs is 4 The

eigenvalue for a particular PC is a measure of the amount of variation in the data

that can be explained by that PC Thus variation due to PC1 frac14 21352=5 frac14

0534 eth534THORN So we can explain 534 of the variation in the data by the

Eigenvectors

Variable PC1 PC2 PC3 PC4

log kp 0661 0197 20099 0718

a 20030 20880 0353 0318

b 20561 20096 20690 0448

V 0498 20422 20625 20429

Eigenvalue 21352 11808 06534 00306

Proportion explained 0534 0295 0163 0008

Cumulative proportion 0534 0829 0992 1000

PUGH306

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interrelationship between the four variables

eth0661 log kpTHORN2 eth0030 aTHORN2 eth0561 bTHORN1 eth0498 VTHORN

There is a mechanismprocess that accounts for 534 of the variation in the data

and the first two PCs mechanismsprocesses will together account for 829 of the

variation It is reasonable to speculate that these two processes are the partition and

diffusion processes that comprise kp

The importance of a variable in its PC is given by the square of its

eigenvector Thus in PC1 (process 1) a is unimportant since 999 that is

frac12frac121 2 eth20032THORN 100 of the variation due to this process can be explained

without it It is however very important in process 2

The importance of H-bonding had been recognized earlier when Roberts (24)

showed that kp was related to the number of H-bonding groups in the penetrant

Recently attempts were made (13) to quantify H-bonding as the difference in

partition from water into H-bonding and non-H-bonding solvents Anderson and

Raykar (25) suggested that the SC barrier resembled a hydrogen-bonding organic

solvent and El Tayar et al (18) concluded that the H-bond donor potential was

dominant However this differential partitioning approach has been shown to be

unreliable by the analyses of Roberts et al (13) and Pugh et al (16) and use of a

and b values as quantifiers of H-bonding seems to be the way forward The papers

of Abraham (26) and Abraham et al (21) are valuable data sources for the

solvatochromic parameters

IV DETERMINANTS OF DIFFUSION ACROSS THE SC

Potential factors reducing diffusion include molecular size interaction with

SC components and the obstructive effects of the corneocytes In principle it is

possible for penetrants to diffuse both along the lipid pathway and through the

corneocytes (12) but Potts and Francoeur (27) argue forcefully against diffusion

of water through corneocytes and it is unlikely that polar organic molecules

traverse them if water cannot Their reasoning may be summarized as follows

Corneocytes are covered by covalently bound highly nonpolar lipids with

exceptionally long (C30ndashC34) hydrocarbon chains (28) which are significantly

more hydrophobic than other SC lamellae (29) The presence of inert ldquoflakesrdquo in a

homogenous matrix reduces permeability (3031) by an obstruction effect and

water permeability falls with increasing corneocyte size (32) as predicted by flake

theory SC is 1000 times less permeable to water vapor than other lipid

membranes and Hadgraft and Ridout (33) found that the passage of drugs through

SC was about 1000 times slower than through films of isopropyl myristate Twenty

to 30 layers of corneocytes 05mm thick and 30mm square spaced 01mm apart

(34) would lower permeability by a factor of 1000 by an obstruction effect They

thus seem to act as mechanical barriers and increase the path length of diffusion

PENETRANT BONDING TO STRATUM CORNEUM 307

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The lipids form the only continuous domain in the SC (3536) and their

removal increases water permeability (37) SC that has been reconstituted from

corneocytes and extracted SC lipids behaves similarly to intact SC (3839) and

Friberg et al (40) showed a variety of lipids could restore SC properties to isolated

corneocytes Rougier et al (32) showed that permeability of SC to water and

benzoic acid are highly correlated for a group of human subjects suggesting a

common pathway

All this evidence points to corneocytes having only a pathlength-increasing

effect and not providing a parallel pathway for watermdashand by inference

hydrophilicmdashmolecules

Early methods for finding D (41) involved measurement of the lag time t to

establish steady flux across the SC This is given (42) by

t frac14 h2=6D

The value of h is uncertain and estimation of t involves extrapolation of the

ldquolinearrdquo portion of the plot of amount transferred against time Curve-fitting

programs now make it possible to deconvolute the terms in the non-steady-state

equation (8)

C

Cm

frac14 1 24

p

X1nfrac140

eth21THORNn

2n 1 1exp

2Deth2n 1 1THORN2p2t

4h2

to find Dh 2

Robertsrsquos group went on to examine the influence of H-bonding on the

diffusion (16) using a different approach to find Dh Since log kp frac14

log Ksc 1 logethD=hTHORN and

log Ksc frac14 20024 1 059 log Koctanol N frac14 45 r 2 frac14 84

then

logethD=hTHORN frac14 log kp 2 059 log Koctanol 1 0024

V DIFFUSION OF MONOFUNCTIONAL COMPOUNDS

Using experimental values of Ksc Roberts et al (43) calculated log(Dh ) as

ethlog kp 2 log KscTHORN and used a and b values as measures of H-bonding potential A

good correlation was found

logethD=hTHORN frac14 2186 2 061a2 209b N frac14 37 r 2 frac14 90

but inclusion of p or MW did not improve the regression The major determinant

of diffusion is H-bonding implying that each substituent group on the permeant

retards diffusion to a characteristic degree Further the high coefficient of b shows

PUGH308

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that SC is predominantly an H-bond donor as proposed earlier by El Tayar et al

(18)

They next set out to quantify the H-bonding powers of various chemical

groups (16) first confirming that log(Dh ) as estimated from log Koctanol was

related to a and b

logethD=hTHORN frac14 2132 2 130a2 257b N frac14 29 r 2 frac14 85

and going on to regress log(Dh ) against the number (0 or 1) of each functional

group present

logethD=hTHORN frac14 2136 2 167 acid 2 141 alcohol 2 117 phenol

2 0986 carbonyl 2 0759 ether 2 00502C

where acid is the number of the acid groups (0 or 1) in permeant and C is the

number of C atoms not involved in CyO bonds The (negative) coefficients were

greater for strong H-bonding functions and were called retardation coefficients

(RCs) Thus the presence of an acid would reduce the diffusion across the SC by a

factor of about 50 and an ether by about 6 This multiplicative effect explained

their earlier observation that introduction of multiple groups caused a dramatic

decrease in diffusion

VI H-BONDING POTENTIAL OF THE SC

Using the lipid composition of the SC given by Wertz (44) and the a and

b values of Abraham (26) Pugh et al (16) calculated the H-bonding effects of

the SC to be in the ratio ascbscfrac14 0406 This would suggest that SC is

predominantly an H-bond acceptor environment and contradicted their earlier

conclusion and that of El Tayar et al The H-bonding for each functional

group g should be related to the quantity frac12ethagbscTHORN1 ethbgascTHORN but a plot of

RC against frac12ethagbscTHORN1 ethbgascTHORN did not pass through the origin as expected

The ascbsc value of 04060 was therefore considered dubious and the

H-bonding potential of the SC was reestimated indirectly from RC values as

follows

In the simplest case RC would be directly related to H-bonding between

penetrant and SC

RC frac14 X 1 Yfrac12ethapbscTHORN1 ethbpascTHORN

Since asc frac14 eth1 2 bscTHORN

RC frac14 X 1 Ybscethap 2 bpTHORN1 Ybp

The regression is

RC frac14 00024 1 136ethap 2 bpTHORN1 318bp r 2 frac14 99

PENETRANT BONDING TO STRATUM CORNEUM 309

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The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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Order now

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Abrahametal (21) found fora mixeddatasetofalcohols steroids andphenols

log kp frac14 2149 2 059p 2 063a2 348b1 00179V N frac14 46

r 2 frac14 96

and were thus able to explain permeation in terms of a single pathway model The

findings of Potts and Guy (20)

log kp frac14 2129 2 172a2 393b1 00256V N frac14 37 r 2 frac14 94

and Roberts et al (13)

log kp frac14 2135 2 137a2 453b1 00205V N frac14 24 r 2 frac14 93

confirm this observation and furthermore suggest that p is not a significant

predictor of kp

It seems then that permeation can be explained by a single pathway and is

chiefly determined by H-bonding properties and permeant size

It has already been noted that kp is a composite of two factors K and (Dh )

Principal component analysis (PCA) measures how data points in a matrix may be

related In essence it enables us to see how many processes or mechanisms are

involved in relating an outcome (log kp) and molecular properties (a b V ) of the

permeants (22)

If the data used by Roberts et al (13) are subjected to PCA (unpublished) the

variation in the matrix of four datasets (log kp a b V ) is described in terms of

four combinations (principal components) of the variables The output from the

Minitab statistical package (23) is

This output is interpreted as follows The sum of eigenvalues for four PCs is 4 The

eigenvalue for a particular PC is a measure of the amount of variation in the data

that can be explained by that PC Thus variation due to PC1 frac14 21352=5 frac14

0534 eth534THORN So we can explain 534 of the variation in the data by the

Eigenvectors

Variable PC1 PC2 PC3 PC4

log kp 0661 0197 20099 0718

a 20030 20880 0353 0318

b 20561 20096 20690 0448

V 0498 20422 20625 20429

Eigenvalue 21352 11808 06534 00306

Proportion explained 0534 0295 0163 0008

Cumulative proportion 0534 0829 0992 1000

PUGH306

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interrelationship between the four variables

eth0661 log kpTHORN2 eth0030 aTHORN2 eth0561 bTHORN1 eth0498 VTHORN

There is a mechanismprocess that accounts for 534 of the variation in the data

and the first two PCs mechanismsprocesses will together account for 829 of the

variation It is reasonable to speculate that these two processes are the partition and

diffusion processes that comprise kp

The importance of a variable in its PC is given by the square of its

eigenvector Thus in PC1 (process 1) a is unimportant since 999 that is

frac12frac121 2 eth20032THORN 100 of the variation due to this process can be explained

without it It is however very important in process 2

The importance of H-bonding had been recognized earlier when Roberts (24)

showed that kp was related to the number of H-bonding groups in the penetrant

Recently attempts were made (13) to quantify H-bonding as the difference in

partition from water into H-bonding and non-H-bonding solvents Anderson and

Raykar (25) suggested that the SC barrier resembled a hydrogen-bonding organic

solvent and El Tayar et al (18) concluded that the H-bond donor potential was

dominant However this differential partitioning approach has been shown to be

unreliable by the analyses of Roberts et al (13) and Pugh et al (16) and use of a

and b values as quantifiers of H-bonding seems to be the way forward The papers

of Abraham (26) and Abraham et al (21) are valuable data sources for the

solvatochromic parameters

IV DETERMINANTS OF DIFFUSION ACROSS THE SC

Potential factors reducing diffusion include molecular size interaction with

SC components and the obstructive effects of the corneocytes In principle it is

possible for penetrants to diffuse both along the lipid pathway and through the

corneocytes (12) but Potts and Francoeur (27) argue forcefully against diffusion

of water through corneocytes and it is unlikely that polar organic molecules

traverse them if water cannot Their reasoning may be summarized as follows

Corneocytes are covered by covalently bound highly nonpolar lipids with

exceptionally long (C30ndashC34) hydrocarbon chains (28) which are significantly

more hydrophobic than other SC lamellae (29) The presence of inert ldquoflakesrdquo in a

homogenous matrix reduces permeability (3031) by an obstruction effect and

water permeability falls with increasing corneocyte size (32) as predicted by flake

theory SC is 1000 times less permeable to water vapor than other lipid

membranes and Hadgraft and Ridout (33) found that the passage of drugs through

SC was about 1000 times slower than through films of isopropyl myristate Twenty

to 30 layers of corneocytes 05mm thick and 30mm square spaced 01mm apart

(34) would lower permeability by a factor of 1000 by an obstruction effect They

thus seem to act as mechanical barriers and increase the path length of diffusion

PENETRANT BONDING TO STRATUM CORNEUM 307

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The lipids form the only continuous domain in the SC (3536) and their

removal increases water permeability (37) SC that has been reconstituted from

corneocytes and extracted SC lipids behaves similarly to intact SC (3839) and

Friberg et al (40) showed a variety of lipids could restore SC properties to isolated

corneocytes Rougier et al (32) showed that permeability of SC to water and

benzoic acid are highly correlated for a group of human subjects suggesting a

common pathway

All this evidence points to corneocytes having only a pathlength-increasing

effect and not providing a parallel pathway for watermdashand by inference

hydrophilicmdashmolecules

Early methods for finding D (41) involved measurement of the lag time t to

establish steady flux across the SC This is given (42) by

t frac14 h2=6D

The value of h is uncertain and estimation of t involves extrapolation of the

ldquolinearrdquo portion of the plot of amount transferred against time Curve-fitting

programs now make it possible to deconvolute the terms in the non-steady-state

equation (8)

C

Cm

frac14 1 24

p

X1nfrac140

eth21THORNn

2n 1 1exp

2Deth2n 1 1THORN2p2t

4h2

to find Dh 2

Robertsrsquos group went on to examine the influence of H-bonding on the

diffusion (16) using a different approach to find Dh Since log kp frac14

log Ksc 1 logethD=hTHORN and

log Ksc frac14 20024 1 059 log Koctanol N frac14 45 r 2 frac14 84

then

logethD=hTHORN frac14 log kp 2 059 log Koctanol 1 0024

V DIFFUSION OF MONOFUNCTIONAL COMPOUNDS

Using experimental values of Ksc Roberts et al (43) calculated log(Dh ) as

ethlog kp 2 log KscTHORN and used a and b values as measures of H-bonding potential A

good correlation was found

logethD=hTHORN frac14 2186 2 061a2 209b N frac14 37 r 2 frac14 90

but inclusion of p or MW did not improve the regression The major determinant

of diffusion is H-bonding implying that each substituent group on the permeant

retards diffusion to a characteristic degree Further the high coefficient of b shows

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ORDER REPRINTS

that SC is predominantly an H-bond donor as proposed earlier by El Tayar et al

(18)

They next set out to quantify the H-bonding powers of various chemical

groups (16) first confirming that log(Dh ) as estimated from log Koctanol was

related to a and b

logethD=hTHORN frac14 2132 2 130a2 257b N frac14 29 r 2 frac14 85

and going on to regress log(Dh ) against the number (0 or 1) of each functional

group present

logethD=hTHORN frac14 2136 2 167 acid 2 141 alcohol 2 117 phenol

2 0986 carbonyl 2 0759 ether 2 00502C

where acid is the number of the acid groups (0 or 1) in permeant and C is the

number of C atoms not involved in CyO bonds The (negative) coefficients were

greater for strong H-bonding functions and were called retardation coefficients

(RCs) Thus the presence of an acid would reduce the diffusion across the SC by a

factor of about 50 and an ether by about 6 This multiplicative effect explained

their earlier observation that introduction of multiple groups caused a dramatic

decrease in diffusion

VI H-BONDING POTENTIAL OF THE SC

Using the lipid composition of the SC given by Wertz (44) and the a and

b values of Abraham (26) Pugh et al (16) calculated the H-bonding effects of

the SC to be in the ratio ascbscfrac14 0406 This would suggest that SC is

predominantly an H-bond acceptor environment and contradicted their earlier

conclusion and that of El Tayar et al The H-bonding for each functional

group g should be related to the quantity frac12ethagbscTHORN1 ethbgascTHORN but a plot of

RC against frac12ethagbscTHORN1 ethbgascTHORN did not pass through the origin as expected

The ascbsc value of 04060 was therefore considered dubious and the

H-bonding potential of the SC was reestimated indirectly from RC values as

follows

In the simplest case RC would be directly related to H-bonding between

penetrant and SC

RC frac14 X 1 Yfrac12ethapbscTHORN1 ethbpascTHORN

Since asc frac14 eth1 2 bscTHORN

RC frac14 X 1 Ybscethap 2 bpTHORN1 Ybp

The regression is

RC frac14 00024 1 136ethap 2 bpTHORN1 318bp r 2 frac14 99

PENETRANT BONDING TO STRATUM CORNEUM 309

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The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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ORDER REPRINTS

interrelationship between the four variables

eth0661 log kpTHORN2 eth0030 aTHORN2 eth0561 bTHORN1 eth0498 VTHORN

There is a mechanismprocess that accounts for 534 of the variation in the data

and the first two PCs mechanismsprocesses will together account for 829 of the

variation It is reasonable to speculate that these two processes are the partition and

diffusion processes that comprise kp

The importance of a variable in its PC is given by the square of its

eigenvector Thus in PC1 (process 1) a is unimportant since 999 that is

frac12frac121 2 eth20032THORN 100 of the variation due to this process can be explained

without it It is however very important in process 2

The importance of H-bonding had been recognized earlier when Roberts (24)

showed that kp was related to the number of H-bonding groups in the penetrant

Recently attempts were made (13) to quantify H-bonding as the difference in

partition from water into H-bonding and non-H-bonding solvents Anderson and

Raykar (25) suggested that the SC barrier resembled a hydrogen-bonding organic

solvent and El Tayar et al (18) concluded that the H-bond donor potential was

dominant However this differential partitioning approach has been shown to be

unreliable by the analyses of Roberts et al (13) and Pugh et al (16) and use of a

and b values as quantifiers of H-bonding seems to be the way forward The papers

of Abraham (26) and Abraham et al (21) are valuable data sources for the

solvatochromic parameters

IV DETERMINANTS OF DIFFUSION ACROSS THE SC

Potential factors reducing diffusion include molecular size interaction with

SC components and the obstructive effects of the corneocytes In principle it is

possible for penetrants to diffuse both along the lipid pathway and through the

corneocytes (12) but Potts and Francoeur (27) argue forcefully against diffusion

of water through corneocytes and it is unlikely that polar organic molecules

traverse them if water cannot Their reasoning may be summarized as follows

Corneocytes are covered by covalently bound highly nonpolar lipids with

exceptionally long (C30ndashC34) hydrocarbon chains (28) which are significantly

more hydrophobic than other SC lamellae (29) The presence of inert ldquoflakesrdquo in a

homogenous matrix reduces permeability (3031) by an obstruction effect and

water permeability falls with increasing corneocyte size (32) as predicted by flake

theory SC is 1000 times less permeable to water vapor than other lipid

membranes and Hadgraft and Ridout (33) found that the passage of drugs through

SC was about 1000 times slower than through films of isopropyl myristate Twenty

to 30 layers of corneocytes 05mm thick and 30mm square spaced 01mm apart

(34) would lower permeability by a factor of 1000 by an obstruction effect They

thus seem to act as mechanical barriers and increase the path length of diffusion

PENETRANT BONDING TO STRATUM CORNEUM 307

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The lipids form the only continuous domain in the SC (3536) and their

removal increases water permeability (37) SC that has been reconstituted from

corneocytes and extracted SC lipids behaves similarly to intact SC (3839) and

Friberg et al (40) showed a variety of lipids could restore SC properties to isolated

corneocytes Rougier et al (32) showed that permeability of SC to water and

benzoic acid are highly correlated for a group of human subjects suggesting a

common pathway

All this evidence points to corneocytes having only a pathlength-increasing

effect and not providing a parallel pathway for watermdashand by inference

hydrophilicmdashmolecules

Early methods for finding D (41) involved measurement of the lag time t to

establish steady flux across the SC This is given (42) by

t frac14 h2=6D

The value of h is uncertain and estimation of t involves extrapolation of the

ldquolinearrdquo portion of the plot of amount transferred against time Curve-fitting

programs now make it possible to deconvolute the terms in the non-steady-state

equation (8)

C

Cm

frac14 1 24

p

X1nfrac140

eth21THORNn

2n 1 1exp

2Deth2n 1 1THORN2p2t

4h2

to find Dh 2

Robertsrsquos group went on to examine the influence of H-bonding on the

diffusion (16) using a different approach to find Dh Since log kp frac14

log Ksc 1 logethD=hTHORN and

log Ksc frac14 20024 1 059 log Koctanol N frac14 45 r 2 frac14 84

then

logethD=hTHORN frac14 log kp 2 059 log Koctanol 1 0024

V DIFFUSION OF MONOFUNCTIONAL COMPOUNDS

Using experimental values of Ksc Roberts et al (43) calculated log(Dh ) as

ethlog kp 2 log KscTHORN and used a and b values as measures of H-bonding potential A

good correlation was found

logethD=hTHORN frac14 2186 2 061a2 209b N frac14 37 r 2 frac14 90

but inclusion of p or MW did not improve the regression The major determinant

of diffusion is H-bonding implying that each substituent group on the permeant

retards diffusion to a characteristic degree Further the high coefficient of b shows

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ORDER REPRINTS

that SC is predominantly an H-bond donor as proposed earlier by El Tayar et al

(18)

They next set out to quantify the H-bonding powers of various chemical

groups (16) first confirming that log(Dh ) as estimated from log Koctanol was

related to a and b

logethD=hTHORN frac14 2132 2 130a2 257b N frac14 29 r 2 frac14 85

and going on to regress log(Dh ) against the number (0 or 1) of each functional

group present

logethD=hTHORN frac14 2136 2 167 acid 2 141 alcohol 2 117 phenol

2 0986 carbonyl 2 0759 ether 2 00502C

where acid is the number of the acid groups (0 or 1) in permeant and C is the

number of C atoms not involved in CyO bonds The (negative) coefficients were

greater for strong H-bonding functions and were called retardation coefficients

(RCs) Thus the presence of an acid would reduce the diffusion across the SC by a

factor of about 50 and an ether by about 6 This multiplicative effect explained

their earlier observation that introduction of multiple groups caused a dramatic

decrease in diffusion

VI H-BONDING POTENTIAL OF THE SC

Using the lipid composition of the SC given by Wertz (44) and the a and

b values of Abraham (26) Pugh et al (16) calculated the H-bonding effects of

the SC to be in the ratio ascbscfrac14 0406 This would suggest that SC is

predominantly an H-bond acceptor environment and contradicted their earlier

conclusion and that of El Tayar et al The H-bonding for each functional

group g should be related to the quantity frac12ethagbscTHORN1 ethbgascTHORN but a plot of

RC against frac12ethagbscTHORN1 ethbgascTHORN did not pass through the origin as expected

The ascbsc value of 04060 was therefore considered dubious and the

H-bonding potential of the SC was reestimated indirectly from RC values as

follows

In the simplest case RC would be directly related to H-bonding between

penetrant and SC

RC frac14 X 1 Yfrac12ethapbscTHORN1 ethbpascTHORN

Since asc frac14 eth1 2 bscTHORN

RC frac14 X 1 Ybscethap 2 bpTHORN1 Ybp

The regression is

RC frac14 00024 1 136ethap 2 bpTHORN1 318bp r 2 frac14 99

PENETRANT BONDING TO STRATUM CORNEUM 309

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The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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Order now

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The lipids form the only continuous domain in the SC (3536) and their

removal increases water permeability (37) SC that has been reconstituted from

corneocytes and extracted SC lipids behaves similarly to intact SC (3839) and

Friberg et al (40) showed a variety of lipids could restore SC properties to isolated

corneocytes Rougier et al (32) showed that permeability of SC to water and

benzoic acid are highly correlated for a group of human subjects suggesting a

common pathway

All this evidence points to corneocytes having only a pathlength-increasing

effect and not providing a parallel pathway for watermdashand by inference

hydrophilicmdashmolecules

Early methods for finding D (41) involved measurement of the lag time t to

establish steady flux across the SC This is given (42) by

t frac14 h2=6D

The value of h is uncertain and estimation of t involves extrapolation of the

ldquolinearrdquo portion of the plot of amount transferred against time Curve-fitting

programs now make it possible to deconvolute the terms in the non-steady-state

equation (8)

C

Cm

frac14 1 24

p

X1nfrac140

eth21THORNn

2n 1 1exp

2Deth2n 1 1THORN2p2t

4h2

to find Dh 2

Robertsrsquos group went on to examine the influence of H-bonding on the

diffusion (16) using a different approach to find Dh Since log kp frac14

log Ksc 1 logethD=hTHORN and

log Ksc frac14 20024 1 059 log Koctanol N frac14 45 r 2 frac14 84

then

logethD=hTHORN frac14 log kp 2 059 log Koctanol 1 0024

V DIFFUSION OF MONOFUNCTIONAL COMPOUNDS

Using experimental values of Ksc Roberts et al (43) calculated log(Dh ) as

ethlog kp 2 log KscTHORN and used a and b values as measures of H-bonding potential A

good correlation was found

logethD=hTHORN frac14 2186 2 061a2 209b N frac14 37 r 2 frac14 90

but inclusion of p or MW did not improve the regression The major determinant

of diffusion is H-bonding implying that each substituent group on the permeant

retards diffusion to a characteristic degree Further the high coefficient of b shows

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that SC is predominantly an H-bond donor as proposed earlier by El Tayar et al

(18)

They next set out to quantify the H-bonding powers of various chemical

groups (16) first confirming that log(Dh ) as estimated from log Koctanol was

related to a and b

logethD=hTHORN frac14 2132 2 130a2 257b N frac14 29 r 2 frac14 85

and going on to regress log(Dh ) against the number (0 or 1) of each functional

group present

logethD=hTHORN frac14 2136 2 167 acid 2 141 alcohol 2 117 phenol

2 0986 carbonyl 2 0759 ether 2 00502C

where acid is the number of the acid groups (0 or 1) in permeant and C is the

number of C atoms not involved in CyO bonds The (negative) coefficients were

greater for strong H-bonding functions and were called retardation coefficients

(RCs) Thus the presence of an acid would reduce the diffusion across the SC by a

factor of about 50 and an ether by about 6 This multiplicative effect explained

their earlier observation that introduction of multiple groups caused a dramatic

decrease in diffusion

VI H-BONDING POTENTIAL OF THE SC

Using the lipid composition of the SC given by Wertz (44) and the a and

b values of Abraham (26) Pugh et al (16) calculated the H-bonding effects of

the SC to be in the ratio ascbscfrac14 0406 This would suggest that SC is

predominantly an H-bond acceptor environment and contradicted their earlier

conclusion and that of El Tayar et al The H-bonding for each functional

group g should be related to the quantity frac12ethagbscTHORN1 ethbgascTHORN but a plot of

RC against frac12ethagbscTHORN1 ethbgascTHORN did not pass through the origin as expected

The ascbsc value of 04060 was therefore considered dubious and the

H-bonding potential of the SC was reestimated indirectly from RC values as

follows

In the simplest case RC would be directly related to H-bonding between

penetrant and SC

RC frac14 X 1 Yfrac12ethapbscTHORN1 ethbpascTHORN

Since asc frac14 eth1 2 bscTHORN

RC frac14 X 1 Ybscethap 2 bpTHORN1 Ybp

The regression is

RC frac14 00024 1 136ethap 2 bpTHORN1 318bp r 2 frac14 99

PENETRANT BONDING TO STRATUM CORNEUM 309

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The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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Order now

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ORDER REPRINTS

that SC is predominantly an H-bond donor as proposed earlier by El Tayar et al

(18)

They next set out to quantify the H-bonding powers of various chemical

groups (16) first confirming that log(Dh ) as estimated from log Koctanol was

related to a and b

logethD=hTHORN frac14 2132 2 130a2 257b N frac14 29 r 2 frac14 85

and going on to regress log(Dh ) against the number (0 or 1) of each functional

group present

logethD=hTHORN frac14 2136 2 167 acid 2 141 alcohol 2 117 phenol

2 0986 carbonyl 2 0759 ether 2 00502C

where acid is the number of the acid groups (0 or 1) in permeant and C is the

number of C atoms not involved in CyO bonds The (negative) coefficients were

greater for strong H-bonding functions and were called retardation coefficients

(RCs) Thus the presence of an acid would reduce the diffusion across the SC by a

factor of about 50 and an ether by about 6 This multiplicative effect explained

their earlier observation that introduction of multiple groups caused a dramatic

decrease in diffusion

VI H-BONDING POTENTIAL OF THE SC

Using the lipid composition of the SC given by Wertz (44) and the a and

b values of Abraham (26) Pugh et al (16) calculated the H-bonding effects of

the SC to be in the ratio ascbscfrac14 0406 This would suggest that SC is

predominantly an H-bond acceptor environment and contradicted their earlier

conclusion and that of El Tayar et al The H-bonding for each functional

group g should be related to the quantity frac12ethagbscTHORN1 ethbgascTHORN but a plot of

RC against frac12ethagbscTHORN1 ethbgascTHORN did not pass through the origin as expected

The ascbsc value of 04060 was therefore considered dubious and the

H-bonding potential of the SC was reestimated indirectly from RC values as

follows

In the simplest case RC would be directly related to H-bonding between

penetrant and SC

RC frac14 X 1 Yfrac12ethapbscTHORN1 ethbpascTHORN

Since asc frac14 eth1 2 bscTHORN

RC frac14 X 1 Ybscethap 2 bpTHORN1 Ybp

The regression is

RC frac14 00024 1 136ethap 2 bpTHORN1 318bp r 2 frac14 99

PENETRANT BONDING TO STRATUM CORNEUM 309

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The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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ORDER REPRINTS

(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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ORDER REPRINTS

Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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onal

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ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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Order now

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ORDER REPRINTS

The high r 2 value and the insignificant value of the constant 00024 imply a

satisfactory relationship Solving Ybsc frac14 136 Y frac14 318 gives asc frac14 0573 and

bsc frac14 0427 implying that SC is predominantly an H-bond donor with a and b

binding strengths in the approximate ratio 0604

VII DIFFUSION OF POLYFUNCTIONAL COMPOUNDS

For polyfunctional compounds a plot of Dh against number of H-bonding

groups shows the dramatic effect of introducing more than one group (16) The

curve (Fig 1) resembles a Langmuir adsorption plot and shows that maximal

retardation is quickly reached These polyfunctional compounds have a large MW

range and a size effect is seen

logethD=hTHORN frac14 2150 2 091a2 158b2 0003MW N frac14 53

r 2 frac14 94

Figure 1 Effect of number of hydrogen-bonding groups on diffusion across stratum corneum

PUGH310

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ORDER REPRINTS

The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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ORDER REPRINTS

adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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ORDER REPRINTS

(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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ORDER REPRINTS

Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

Cut

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ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

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nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

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ORDER REPRINTS

26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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Order now

Reprints of this article can also be ordered at

httpwwwdekkercomservletproductDOI101081CUS120001862

Request Permission or Order Reprints Instantly

Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

Cut

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ORDER REPRINTS

The intercept (D0=h frac14 0032 cm=h 95 confidence interval 002ndash005)

represents an intrinsic diffusion term describing the diffusion of an infinitely

small nonbonding molecule The regression shown earlier enables the relative

importance of a and b to be estimated by comparison of the coefficients 2091

and 2158 The relative importance of the H-bonding parameters and size is more

difficult to assess since the magnitudes of the predictors are so different The

values of a and b are typically between 0 and 1 while MW ranges from 50 to 500

Thus the low coefficient of the MW term might still result in a large contribution to

log(Dh ) when multiplied by a large MW

Comparison of the importance of such diverse predictors requires that their

magnitudes be similar This standardization of the data can be achieved by

subtracting the predictor mean from each value and dividing by the predictor

standard deviation The standardized predictors thus all have means of zero and

standard deviations of 1

Regression of these standardized data (a etc) gives

logethD=hTHORN frac14 2378 2 0239a 2 0752b 2 0521MV N frac14 53

r 2 frac14 94

indicating that in practice variations in H-bonding and MW have comparable

effects on diffusion

Principal component analysis gives

The PCA output shows that two processes account for 963 of the variation in

data relating diffusion the H-bonding parameters and size b is probably more

important than a

VIII MODEL OF THE H-BONDING PROCESS

The plot of (Dh ) against number of H-bonding groups (Fig 1) is a curve

resembling an inverted Langmuir adsorption isotherm (43) which describes

Eigenvectors

Variable PC1 PC2 PC3 PC4

log(Dh ) 0584 0070 0235 0774

a 20099 20979 20035 0174

b 20569 0181 20552 0582

MW 20570 0061 0799 0182

Eigenvalue 28371 10130 01149 00350

Proportion explained 0709 0253 0029 0009

Cumulative proportion 0709 0963 0991 1000

PENETRANT BONDING TO STRATUM CORNEUM 311

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ORDER REPRINTS

adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

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ORDER REPRINTS

(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

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ORDER REPRINTS

Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

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ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

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ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

Cut

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nd O

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olog

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Com

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For

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onal

use

onl

y

ORDER REPRINTS

26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

Cut

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Com

mon

wea

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nive

rsity

on

100

113

For

pers

onal

use

onl

y

Order now

Reprints of this article can also be ordered at

httpwwwdekkercomservletproductDOI101081CUS120001862

Request Permission or Order Reprints Instantly

Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

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oade

d fr

om in

form

ahea

lthca

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Com

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100

113

For

pers

onal

use

onl

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ORDER REPRINTS

adsorption as an equilibrium between binding and debinding at an interface The

position of equilibrium is determined by the relative affinities of the adsorbate for

the surface and the support phase The general form of the isotherm is

w frac14wmax

ethK=cTHORN1 1

where wmax is the amount needed to saturate the surface w is the amount adsorbed

at concentration c in the support phase and K is the ratio between the rates of

desorption and adsorption kdka c can be considered as the force driving

adsorption In diffusion across the SC the effect analogous to w is the reduction in

diffusion ethDo 2 DTHORN=h and the saturation effect is ethDo 2 DmTHORN=h where Dm is the

minimum diffusion coefficient relating to an infinitely hindered penetrant Pugh

et al proposed that the driving force causing binding of the permeant to SC

(corresponding to c ) is the retardation coefficient or more precisely

ethRC 2 RCoTHORN where RCo represents the binding of a compound with no

H-bonding groups (Fig 2)

Substituting these values into Langmuirrsquos equation and rearranging gives

D=h frac14 Do=h 2 frac12ethDo=h 2 Dm=hTHORNethRC 2 RCoTHORN=ethK 1 RC 2 RCoTHORN

and nonlinear curve fitting enables estimation of the parameters

The high standard deviation for Dmh suggests it is indistinguishable from zero as

expected but all the other parameters are statistically valid The low value for K

(the equilibrium constant for debinding) shows that H-bonding is a highly favored

process in the SC

IX EFFECT OF PENETRANT SIZE ON DIFFUSION

Diffusion is related to size (42) by

D frac14 DoethMWTHORNb

where Do refers to diffusion of an infinitely small molecule Scheuplein and Blank

Parameter Final Value SD

Doh 0192 0009

Dmh 66E2 5 124E2 5

RCo 0222 0004

K 00053 00002

N frac14 53 r 2 frac14 98

PUGH312

Cut

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ORDER REPRINTS

(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

Cut

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ORDER REPRINTS

Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

Order now

Reprints of this article can also be ordered at

httpwwwdekkercomservletproductDOI101081CUS120001862

Request Permission or Order Reprints Instantly

Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

(37) and Roberts (24) used values of b of 205 and 2033 but this assumes the SC

is an isotropic fluid medium that does not interact apart from by physical

obstruction with the diffusant In fact the SC is an anisotropic liquid crystalline

structure and the evidence already described suggests powerful interaction via

H-bonding Diffusion should be more accurately written as

D frac14 D0ethbindingTHORNaethMWTHORNb

If RC is used as a measure of the binding term then

logethD=hTHORN frac14 2162 2 26 logethRCTHORN2 22 logethMWTHORN n frac14 53 r 2 frac14 87

and the higher size dependency ethb frac14 222THORN is consistent with nonfluidity andor

anisotropy

Figure 2 Analogy between retardation coefficientndashdiffusion relationship and Langmuirrsquos

adsorption isotherm

PENETRANT BONDING TO STRATUM CORNEUM 313

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

Order now

Reprints of this article can also be ordered at

httpwwwdekkercomservletproductDOI101081CUS120001862

Request Permission or Order Reprints Instantly

Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

Regression of the standardized data

logethD=hTHORN frac14 2381 2 0647 logethRCTHORN 2 0633 logethMWTHORN

confirms the equal importance of permeant binding to the SC and molecular size in

determining the diffusion process

Therefore 939 of the variation relating diffusion overall H-bonding measured

as RC and size can be accounted for by a single mechanism In this mechanism

(PC1) the equality of the eigenvectors (0587 20576 20568) indicates equal

importance of H-bonding and size and there are negative relationships between

these factors and diffusion as expected

X SUMMARY

The permeability coefficient kp quantifying the flow of a permeant across

the stratum corneum barrier is the product of two terms Kscvehicle (transfer from

vehicle into the outermost layer) and Dh (diffusion across the SC) The general

opinion is that diffusion occurs through the intercellular lipids with the

corneocytes acting as a staggered mechanical barrier giving a high value to the

pathlength h Both steps are determined by the affinity between the permeant and

the SC The partitioning step from aqueous vehicles can be quantified by

Koctanolwater The lipid lamellae in the SC form a liquid crystalline anisotropic

barrier and H-bond to functional groups on the permeant The effects that these

groups have on diffusion can be quantified as characteristic retardation

coefficients Diffusion is reduced dramatically if multiple groups are present

with the effect being modeled by an equation analogous to Langmuirrsquos adsorption

isotherm The H-bond acceptor potential (b ) of a group has a greater effect on

diffusion than its a potential implying that SC is overall an H-bond donor barrier

Regression of diffusion against standardized H-bonding and size data suggests that

in practice both H-bonding interaction and size are equally important in retarding

diffusion

Eigenvectors

Variable PC1 PC2 PC3

log(Dh ) 0587 20166 0792

RC 20576 0601 0554

MW 20568 20782 0257

Eigenvalue 28172 01451 00377

Proportion explained 0939 0048 0013

Cumulative proportion 0939 0987 1000

PUGH314

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

Order now

Reprints of this article can also be ordered at

httpwwwdekkercomservletproductDOI101081CUS120001862

Request Permission or Order Reprints Instantly

Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

XI GLOSSARY

A area (cm2)

C concentration in receptor cell at time t

Cm maximal concentration in receptor cell

Csc concentration in outermost layer of the stratum corneum

Cv concentration in vehicle

D diffusion coefficient (cm2h)

Dm minimum diffusion coefficient attainable by powerfully H-bonding

molecule

Do diffusion coefficient of infinitely small non-H-bonding molecule

h pathlength of diffusion (cm)

Js flux (molcm2h) at the steady state

K rate of desorptionrate of adsorption at an interface

Kab partition coefficient in phases a b

kp permeability coefficient (cmh)

PC principal component

PCA principal component analysis

r 2 coefficient of determination adjusted for degrees of freedom

RCx retardation coefficient of H-bonding group x

SC stratum corneum

V intrinsic molar volume (dm3mol)

a scaled H-bonding donor (acid) potential

b scaled H-bonding acceptor (base) potential

d Hildebrand solubility parameter

p dipole momentpolarizability

REFERENCES

1 Albery WJ Hadgraft J Percutaneous Absorption Theoretical Description

J Pharm Pharmacol 1979 31 129ndash139

2 Albery WJ Hadgraft J Percutaneous Absorption In Vivo Experiments J Pharm

Pharmacol 1978 31 140ndash147

3 Bouwstra JA De Vries MA Gooris GS Bras W Brussee J Ponec M

Thermodynamic and Structural Aspects of the Skin Barrier J Controlled Release

1991 15 209ndash219

4 Schaefer H Watts J Illel B Follicular Penetration In Prediction of Percutaneous

Penetration Methods Measurements and Modeling Scott RC Guy RH

Hadgraft J Eds IBC Technical Services London 1990 163ndash173

5 Lauer A Lieb LM Ramachandran C Flynn GL Weiner ND Transfollicular

Drug Delivery Pharm Res 1995 12 179ndash186

6 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

PENETRANT BONDING TO STRATUM CORNEUM 315

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

Order now

Reprints of this article can also be ordered at

httpwwwdekkercomservletproductDOI101081CUS120001862

Request Permission or Order Reprints Instantly

Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

7 Scheuplein RJ Mechanism of Percutaneous Adsorption II Transient Diffusion

and the Relative Importance of Various Routes of Skin Penetration J Invest

Dermatol 1967 48 79ndash88

8 Siddiqui O Roberts MS Polack AE Percutaneous Absorption of Steroids

Relative Contributions of Epidermal Penetration and Dermal Clearance

J Pharmacokinet Biopharm 1989 17 405ndash424

9 Heisig M Lieckfeldt R Witturn G Mazurkevich G Lee G Non Steady-State

Descriptions of Drug Permeation Through Stratum Corneum I The Biphasic Brick-

and-Mortar Model Pharm Res 1996 13 421ndash426

10 Scheuplein R Ross L J Soc Cosmet Chem 1970 21 853ndash873

11 Anderson BD Higuchi WI Raykar PV Heterogeneity Effects on

PermeabilityndashPartition Coefficient Relationships in Human Stratum Corneum

Pharm Res 1988 5 566ndash573

12 Edwards DA Langer R A Linear Theory of Transdermal Transport Phenomena

J Pharm Sci 1994 83 1315ndash1334

13 Roberts MS Pugh WJ Hadgraft J Watkinson AC Epidermal Permeabilityndash

Penetrant Structure Relationships 1 An Analysis of Methods of Predicting

Penetration of Monofunctional Solutes from Aqueous Solutions Int J Pharm 1995

126 219ndash233

14 Wertz PW Miethke MC Long SA Strauss JS Downing DT The

Composition of the Ceramides from Human Stratum Corneum and from

Comedones J Invest Dermatol 1985 84 410ndash412

15 Lieckfeldt R Villalain J Gomez Fernandez JC Lee G Diffusivity and

Structural Polymorphism in Some Model Stratum Corneum Lipid Systems

Biochim Biophys Acta Biomembr 1993 1150 182ndash188

16 Pugh WJ Roberts MSR Hadgraft J Epidermal PermeabilityndashPenetrant

Structure Relationships 3 The Effect of Hydrogen Bonding Interactions and

Molecular Size on Diffusion Across the Stratum Corneum Int J Pharm 1996 138

149ndash167

17 Roberts MS Anderson RA Swarbrick J Permeability of Human Epidermis to

Phenolic Compounds J Pharm Pharmacol 1977 29 677ndash683

18 El Tayar N Tsai R-S Testa B Carrupt P-A Hansch C Leo A Percutaneous

Penetration of Drugs A Quantitative StructurendashPermeability Relationship Study

J Pharm Sci 1991 80 744ndash749

19 Kasting GB Smith RL Cooper ER Effect of Lipid Solubility and Molecular

Size on Percutaneous Absorption Pharmacol Skin 1987 1 138ndash153

20 Potts RO Guy RH Predicting Skin Permeability Pharm Res 1992 9 663ndash669

21 Abraham MH Chadha HS Mitchell RC The Factors That Influence Skin

Penetration of Solutes J Pharm Pharmacol 1995 47 8ndash16

22 Armstrong NA James KC Pharmaceutical Experimental Design and

Interpretation in Pharmaceutics Taylor and Francis London 1996

23 Minitab Release 10Xtra Minitab Inc Reading MA 1995

24 Roberts MS Percutaneous Absorption of Phenolic Compounds PhD Thesis

University of Sydney 1976

25 Anderson BD Raykar PV Solute StructurendashPermeability Relationships in

Human Stratum Corneum J Invest Dermatol 1989 93 280ndash286

PUGH316

Cut

aneo

us a

nd O

cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

form

ahea

lthca

rec

om b

y V

irgi

nia

Com

mon

wea

lth U

nive

rsity

on

100

113

For

pers

onal

use

onl

y

ORDER REPRINTS

26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

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26 Abraham MH Scales of Solute Hydrogen-Bonding Their Construction and

Application to Physicochemical and Biochemical Processes Chem Soc Rev 1993

22 73ndash83

27 Potts RO Francoeur ML The Influence of Stratum Corneum Morphology on

Water Permeability J Invest Dermatol 1991 96 495ndash499

28 Swartzendruber DC Wertz PW Madison KC Downing DT Evidence That

the Corneocyte Has a Chemically Bound Lipid Envelope J Invest Dermatol 1987

88 709ndash713

29 Rehfeld SJ Plachy WZ Hou SYE Elias PM Localization of Lipid

Microdomains and Thermal Phenomena in Murine Stratum-Corneum and Isolated

Membrane ComplexesmdashAn Electron-Spin-Resonance Study J Invest Dermatol

1990 95 217ndash223

30 Michaels AS Chandrasekaran SK Shaw JE Drug Permeation Through Human

Skin Theory and In Vitro Experimental Measurement AIChE J 1975 21 985ndash996

31 Cussler EL Hughes SE Ward WJ Aris R Barrier Membranes J Membr Sci

1988 86 161ndash174

32 Rougier A Lotte C Corcuff P Maibach HI Relationship Between Skin

Permeability and Corneocyte Size According to Anatomic Site Age and Sex in Man

J Soc Cosmet Chem 1988 39 15ndash26

33 Hadgraft J Ridout G Development of Model Membranes for Percutaneous

Absorption Measurements I Isopropyl Myristate Int J Pharm 1987 39 149ndash156

34 Elias PM Friend DS The Permeability Barrier in Mammalian Epidermis J Cell

Biol 1975 65 180ndash191

35 Williams ML Elias PM The Extracellular Matrix of Stratum Corneum Role of

Lipids in Normal and Pathological Function CRC Crit Rev Ther Drug Carrier

Syst 1987 3 95ndash112

36 Wertz PW Swartzendruber DC Abraham W Madison K Downing DT

Essential Fatty Acids and Epidermal Integrity Arch Dermatol 1987 123

1381ndash1384

37 Scheuplein RJ Blank IH Permeability of the Skin Physiol Rev 1971 51

702ndash747

38 Smith WP Christensen MS Nacht S Gans EH Effect of Lipids on the

Aggregation and Permeability of Human Stratum Corneum J Invest Dermatol

1982 78 7ndash11

39 Kock WR Berner B Burns JL Bissett DL Preparation and Characterisation

of a Reconstituted Stratum Corneum Membrane Film as a Model Membrane for Skin

Transport Arch Dermatol Res 1988 280 252ndash256

40 Friberg SE Kayali I Beckerman W Rhein DL Simion A Water Permeation

of Reaggregated Stratum Corneum with Model Lipids J Invest Dermatol 1990 94

377ndash380

41 Scheuplein RJ Blank IH Brauner GJ MacFarlane DJ Percutaneous

Absorption of Steroids J Invest Dermatol 1969 52 63ndash70

42 Crank J The Mathematics of Diffusion Clarendon Press Oxford 1975 Chs 1 2 4

43 Roberts MS Pugh WJ Hadgraft J Epidermal PermeabilityndashPenetrant Structure

Relationships 2 The Effect of H-Bonding Groups in Penetrants on Their Diffusion

Through the Stratum Corneum Int J Pharm 1996 132 23ndash32

44 Wertz PW Epidermal Lipids Semin Dermatol 1992 11 106ndash113

PENETRANT BONDING TO STRATUM CORNEUM 317

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For

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onal

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Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

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r T

oxic

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om in

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Com

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100

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For

pers

onal

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Order now

Reprints of this article can also be ordered at

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Request Permission or Order Reprints Instantly

Interested in copying and sharing this article In most cases US Copyright Law requires that you get permission from the articlersquos rightsholder before using copyrighted content

All information and materials found in this article including but not limited to text trademarks patents logos graphics and images (the Materials) are the copyrighted works and other forms of intellectual property of Marcel Dekker Inc or its licensors All rights not expressly granted are reserved

Get permission to lawfully reproduce and distribute the Materials or order reprints quickly and painlessly Simply click on the Request PermissionReprints Here link below and follow the instructions Visit the US Copyright Office for information on Fair Use limitations of US copyright law Please refer to The Association of American Publishersrsquo (AAP) website for guidelines on Fair Use in the Classroom

The Materials are for your personal use only and cannot be reformatted reposted resold or distributed by electronic means or otherwise without permission from Marcel Dekker Inc Marcel Dekker Inc grants you the limited right to display the Materials only on your personal computer or personal wireless device and to copy and download single copies of such Materials provided that any copyright trademark or other notice appearing on such Materials is also retained by displayed copied or downloaded as part of the Materials and is not removed or obscured and provided you do not edit modify alter or enhance the Materials Please refer to our Website User Agreement for more details

Cut

aneo

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cula

r T

oxic

olog

y D

ownl

oade

d fr

om in

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Com

mon

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For

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