Mechanism of Percutaneous Absorption - CORE

Most students of skin permeability wouldagree that there are potentially three distinctroutes of penetration through the stratum eor-neum: (1) the follicular regions, (2) the sweatducts and (3) the unbroken stratum corneum inbetween these appendages. But which one is theprincipal route of penetration? This frequentlyposed question has resulted in a division of opin-ion, the one favoring percutaneous absorptionprimarily by diffusion via sweat ducts and hairfollicles and the other holding that diffusionthrough the unbroken stratum eorneum is theprincipal pathway. Rather interestingly there issubstantial confirmed data in the literature whichseemingly support both views. Those investiga-tors favoring appendageal diffusion cite the pref-erential staining of hair follicles (1), the forma-tion of perifollieular wheals (2) and the rapiddiffusion of charged dyes through sweat duetsunder a potential gradient (3). The proponentsof diffusion through the unbroken stratum eor-neum matrix (4) make us aware first of thevery small fractional surface area of the ap-pendages 10. They further demonstrate thatthe steady state diffusion rate into skin is es-sentially unchanged when more or fewer folli-also been shown that steady state diffusion ofmany small molecules through stratum eorneumoccurs with large activation energies = 10 — 15

Keal mole', which would be very unlikely forrelatively rapid appendageal diffusion (6). Areconciliation of these contrary theories and are-interpretation of the conflicting data is reallylong overdue and quite necessary if a useful link

between studies of skin permeability in the lab-oratory and their relevance to the topical appli-cation of a drug by the physician is to be ob-tained.

It seems to the author that attempts toanswer what is really a very bad scientificquestion have led to a misplacement of em-phasis and to an oversimplification of the stra-tum corneum membrane as a diffusion barrier.As the analysis given below will show, it isprobably wrong to assume that a principalroute of penetration exists without a require-ment to further specify other conditions,A mathematical analysis* of the skin as a com-posite membrane with the appendages in therole of diffusion shunts has been developed. It isshown that under the appropriate conditionseach one of the three contending routes of per-meability may be, in turn, overwhelminglydominant. In particular the transient diffusionwhich occurs shortly after the application of asubstance to the surface of the skin is shownto be potentially far greater through theappendages than through the matrix of the stra-tum corneum. After steady state diffusion hasbeen established the dominant diffusion modeis probably no longer intra-appendageal but oc-curs through the matrix of the stratum cor-neum.

THE EPIDERMIS AS A DIFFUSION BARaIER

While still somewhat simplified and ab-stract, the illustration in Figure 1 depicts in areasonably accurate way the great complexity ofthe epidermis as a diffusion barrier. The dia-gram is representative of human abdominalskin and the relative sizes and distances of theprincipal features have been faithfully ren-dered. Diffusion constants and geometrical datacorresponding to appendages and to various re-

* The author wishes to thank Professor KennethA. Smith of the Department of Chemical Engineer-ing, Massachusetts Institute of Technology forderiving the equations and for many helpful dis-cussions on the mathematical analysis of the skindiffusion problem.

THE JOURNAL OF JNVESTIOATIVE DERMATOLOOT

Copyright 1867 by The williams & wilkins Co.

MECHANISM OF PERCUTANEOUS ABSORPTION

II. TRANSIENT DIFFUSION AND THE RELATIVE IMPORTANCE OFVARIOUS ROUTES OF SKIN PENETRATION*

ROBERT J. SCHEUPLEIN, Pn.D.

vol. 48, No. IPrinted in U.S.A

This investigation was supported in part byUnited States Department of Defense ContractDA1S-B8-AMC-148 (A) CP3-18330 from U. S.Army Chemical Center, Edgewood Arsenal, Mary-land and in part by United States Public HealthService Research Grant GM-04760 from the Na-tional Institute of General Medical Sciences.

Presented at the Twenty-seventh Annual Meet-ing of The Society for Investigative Dermatology,Inc., Chicago, Illinois, June 27, 1966.

* From the Research Laboratories of the Depart-ment of Dermatology of the Harvard MedicalSchool at the Massachusetts General Hospital,Boston, Massachusetts 02114.

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80 THE JOURNAL OF INVESTIGATIVE DERMATOLOGY

FIG. 1. Schematic scale drawing showing a crossection of human abdominal skin. (Hairdiameter equals 7Oc.) Sweat ducts, hair follicles and the stratum corneum are representedboth in size and distribution according to their average measured values given in Table I.

TABLE IStructural and diffusion data on epidermis. Average dimensions on the sweat ducts,

hair follicles and the surface layers of the skin are given

Appendage Density/cm2 sn Individual area fractional Nominal diffusion constant

Hair Follicles(Ref. 10, 11, 12,

13, 14)(Hair only)

40 (Abdo-men)

100 (Fore-arm)

2,200 j.s

1,400 )1

3.84 X 10—s cm

3.84 X 10 cm

1.5 X 10

3.8 X 1O

2 X 1O cm2 sec1

2 X 10T7 cm2 sec'1—8 X 108 cm2 sec

70 /L

70 z

Sweat Ducts(Ref. 10, 14, 15,

16)

Surface OpeningOuter DuctInner DuctCells

210 (Abdo-men)

220 (Fore-arm)

980

950 j.s

Abdo-men

Fore-arm

3.84 X 10 cm21.77 X 106 cm21.73 X 10 cm21.59 X 1O cm2

3.84 X 10—i cm21.77 X 1O cm21.73 X 1O cm21.59 X 10 cm2

8.1 X 10—i3.7 X 103.6 >< 103.3 X 10

8.4 X 103.9 )< 103.8 X 10—i3.5 X 10

2 X 1O cm2 sec10 cm2 sec'

2 X 1O cm2 sec1O6 cm2 sec1

704.7j

7On14hz

Stratum Corneum(Ref. 6, 8)Well HydratedEpidermis(Ref. 6, 7, 8)Dermis(Ref. 8)

Forearm andAbdomen

Forearm andAbdomen

Forearm andAbdomen

1.00

1.001.00

1.00

1.0 X 10b0 cm2 sec°

1.0 X 10 cm2 sec1.0 X 10—s cm2 sec1

1.0 X 1O6 cm2 sec1

13 ,

38 p110

O.Sp

S& t.P rids n1 iddi

MECHANISM OF PERCUTANEOUS ABSORPTION 81

gions near the surface of the skin are given inTable I. It will be helpful to keep in mind thefollowing particularly relevant dimensions whichare based upon reported values: thickness ofstratum eorneum, 14: thickness of epidermis,1 10: distance from surface to mieroeireulation,150—200g.

A consideration of the diffusibility, structureand geometry of the various surface regions andthe role of the microeireulatory system leads toan approximate diffusion model for the skinwhich is amenable to exact calculation.

The stratum eorneum, the epidermis and theuppermost part of the papillary layer of the der-mis (i.e., that portion subjacent to the basallayer of the epidermis and above the capillariesof the mieroeireulation) are together assumed tocomprise the effective composite layer throughwhich substances must diffuse to enter the bloodstream. We consider only the diffusion of lowmolecular weight molecules which readily pene-trate capillary walls and rapidly enter the sys-temic circulation. The rich vaseularity of the su-perficial layers of the dermis should drasticallylimit the number of molecules free to diffusedeeper into the dermis and for these reasonslower lying layers of the dermis would not be ex-pected to radically influence diffusion. (This con-clusion is supported by the work of Tregear (7)who applied high energy tracers to the flank epi-dermis of anesthetized pigs and showed that thecount stopped falling when the animal waskilled.) The skin is then assumed to be a com-posite membrane about 200 thick, with aconcentration at the average superficial termi-nus of the microcireulation maintained nearzero. This membrane is pierced at variousplaces by two types of potential diffusionshunts; follicles and duets each with a differentdiffusion constant. The aqueous cells and con-nective tissue of the dermis and the aqueouscells of the epidermis are both assumed to havea nominal diffusion constant of 10 em2 see°.This is a conservative value based on labora-tory permeability measurements by I. Blank(8). The detailed structure of the viable ep-idermal cells, notably the presence of cell mem-branes, cannot contribute significantly to thediffusion resistance of this layer owing to thevery small dimensions of the cell membranes

100, A in comparison with the thickness ofthe stratum eorneum 100,000 A. This is evi-

dent from the Einstein diffusion formula X)2 =2 Dt assuming comparable diffusion constants.This would also be true for the basement mem-brane. The stratum eorneum and the appendagesplay the significant role in the diffusion systemand the diffusibility and structure of each will beconsidered in turn.

Stratum eorneum.—Steady state measure-ments have shown that diffusion through theintact hydrated membrane occurs essentiallyuniformly throughout the tissue (6, 9), with anaverage diffusion constant near S x 10°"cm° see°. This is based on measurements of hy-drated membrane thicknesses 1 of approxi-mately 40JL. It has also been shown that hydra-tion increases the steady state permeability ofthe membrane approximately by a factor oftwo. These two facts together with the plausibleassumption that hydration is at least equallyeffective in increasing the permeability of themembrane before the first steady state measure-ment can be taken (after 4 hours) lead to a dif-fusion constant near 1.0 x cm5 see_t for theunswollen membrane. In the theoretical compu-tation, 1 = 10t and D = 10_to em° see' are usedas normal values for the unswollen membrane.

Hair follicles —The densities of follicles onthe epidermis of the abdomen and forearm,Table I, are from Szabó (10). The region 200,afrom the surface is normally above the duet ofthe sebaeeous gland and the inner root sheath ofthe hair canal. Also, according to Odland (11),the stratum corneum disappears at nearwithin the follicle. Up to that point the stra-tum eorneum more or less effectively shroudsthe hair as shown in Figure 1. The diffusionconstants of wet hair (12) and wool (13, 14)have been extensively measured and valuesfrom 2 x 10° — 1 x 10 cm2 sect have been ob-tained for water and small molecular weightelectrolytes and non-electrolytes. The outer rootsheath, the vitreous membrane and any rem-nant of the connective tissue sheath still pres-ent around the follicle near the epidermis areall considered to have a diffusion constantequal to or greater than that of the hair. If thehair follicle is rich in lipid material due to se-baceous excretion, the permeability of lipidsoluble substances would be appreciably en-hanced. This possibility should be kept inmind, although it is not considered in thecomputations or suggested in Figure 1. In the


RESULTS

(1>

calculation d = 7Oy arid D = 10' — 10 em seewere used as normal values for the average di-

3. The principal rate determining step isdiffusion through the membrane, not adsorp-

ameter and diffusion constant of hair. tion of desorption at the interfaces. Hydrody-Sweat ducts—The densities and dimensions namic flow through pores is excluded, transport

of the sweat duets on the epidermis of the ab- occurs by diffusion only.domen and forearm, Table I, are from Szabó 4. The physical chameteristics of the barrier(10), Kuno (15) and Montagna (16). The lumenof the duet is about one third the diameter of the

are not rapidly and drastically altered upon ap-plieation of the solution. Hydration is permis-

duct per se; the walls are apparently composedof two layers of euboidal cells surrounded by a

sible, but solvents which destroy the stratumcorneum like chloroform-methanol are pre-

thin ring of keratinized cells similar to thekeratinized cells of the epidermis. Because of

eluded.Most of these assumptions are generally im-

the uncertainty and difficulty in wetting or plicitly or explicitly assumed in all discussionsfilling the lumen by the application of a solu-tion to the epidermis, the structural cells of theduet wall may be more important as a diffusionpathway than the lumen itself. Their similar-ity to the aqueous cells of the epidermis sug-gests a diffusion constant near 106 cm sec'. Ifthe lumen were filled, as in a sweating individ-

on percutaneous absorption.The appropriate differential equations have

been solved for the particular boundary condi-tions involved and are derived and discussedelsewhere (19). The equations are complex anda computer was used for the calculations. Mostof the data on Figures 4, 5 and 6 was obtained

ual, the pore itself would possess a diffusionconstant near 2 x 10 em2 sec1, i.e., the selfdiffusion constant for water,

from these equations.Solutions for the finite simple membrane are

given by Crank (14). The total amount ofBoth sweat ducts and hair follicles are closely substance Q, passing through such a membrane,

surrounded by dense capillary meshes. The sur- one lace of which x = 1 is maintained at zerolace area of the capillaries surrounding the concentration is given byduet to that of the duet itself is 1:2.2 accordingto Kuno (15). This strongly implies that themost molecules reaching the vaseularized re-

= — — e1)m2r2t!UI0 l2 6 ir2 ,,i n2

gion of the duet below the epidermis would be.

swept into the systemic circulation before dif-.

fusing to lower layers of the dermis.

.where 1 = membrane thickness C,, = concen-.

tration at the entrance side of the membrane. -

(x = o) and D = diffusion constant. This rela-tion is strictly applicable a simple inert mem-brane but it is also a reasonably good approxi-

A mathematical model for the skin diffusion mation to the in vivo composite membranelayer.—Although these data on the diffusibility model of the skin presented above because ofand structure of the skin represent rather crude the rapid diffusion through the viable layersaverage values, their range of variation appears in comparison to the stratum corneum. Thisto be sufficiently narrow to justify and approxi- simple equation exhibits the essential qualita-mate mathematical treatment of the diffusion tive features of the more appropriate formulaeproblem based on the following assumptions. and can serve as a focus for our discussion.

1. The mathematical description of the sys- Steady state vs. transient diffusion.—Thetem (exclusive of the duets and follicles) is that left hand side of equation (1) is plotted againstof a finite composite membrane consisting of a t in Figure 2. Values of the diffusion coefficientthin (l0s) slab of low diffusibility (the stratum appropriate to dry and hydrated stratum cor-eorneum) over a thicker slab (2OOs) of higher neum were used and 1 = 20 . There is a "timediffusibility (the viable epidermis and papil- lag" until the diffusion of a species across thelary dermis), membrane attains a constant "steady state"

2. The concentration at one side of the mem- value. This initial transient diffusion eorre-brane is maintained effectively at zero concen- sponds to the exponential term in equationtration, the concentration at the other side is (1) and rapidly becomes small as t increases.maintained constant at C0. An unambiguous measure of this "hold-up"


t sec.FIG. 2. Quantity of diffusing species exhibiting membranes of different diffusion con-

stants and constant thickness, = 20M, plotted against time. The corresponding "hold-up"times are indicated by dotted lines. The line corresponding to D = 10-' cm' sec' (shuntdiffusion) has been scaled downward in proportion to a crossectional area appropriate tothe shunts.

time is given by the intercept of the curveon the t-axis, i.e.,

12 l

where k, is the permeability constant. Various"hold-up" times are indicated in Figure 2.True steady state diffusion is not achieveduntil at approximately 4r or after about 2—3hours for a membrane with D = 10'° cm' seC1.An examination of the curves shows that r de-creases with increasing D and for the muchlarger D = 10 cm' seC1, appropriate to diffu-sion within a hair follicle, the curve is linearalmost to the origin. The inset shows the inter-section of this latter curve with one appropri-ate to hydrated stratum corneum. The 10cm' sec curve has been scaled down by a factorof 10' corresponding to an approximate frac-tional area f of these diffusion shunts. It isimmediately evident that while diffusionthrough the bulk of the membrane is larger atlater times owing to the much larger fractional

area for this pathway, f = 0.9999, diffusionthrough the follicles (or sweat ducts) is muchlarger initially. This is a consequence of themuch larger "hold-up" time for the diffusionroute with the lower diffusion constant, inspite of a much larger area over which diffu-sion can occur. Moreover since the initialtransient diffusion depends exponentially onD, fluxes and concentration levels for the re-spective pathways may differ by many ordersof magnitude as shown below.

Relative amounts of shunt and bulk diffu-sion—Ratios of the total quantity of sub-stance carried through the membrane by eachdiffusion pathway are plotted against time inFigure 3. The ordinate

IQ SHUNT/1 = log BULK

and is equal to zero when the ratio is equal tounity. The various appendageal areas and diffu-sion constants used (Table I) are indicatedfor each curve. Owing to the difficulty of com-

(2)

0 500 1000 3000 4000SEC.

FIG. 3. The ratio of the total quantity of diffusing molecules transported across stratumcorneum by the various diffusion pathways indicated plotted against time. The ordinateR = logj Q j[SHIJNT]/Q, [BULK] . The curves drawn above the line R = 0 correspond toexcess shunt diffusion, those below the line to excess bulk diffusion.

pletely wetting the surface of the skin, as in-dicated in Figure 1, the invariable presenceof an irregular oil film partially covering thehairs, and the presence of an indefinite numberof layers of keratinized cells over the aqueouscells of the duct, our theoretical values are inreality heavily weighted in favor of the shunts.If the shunt pathways were as effective as in-dicated by their geometrical area and diffu-sion constants, appendageal diffusion woulddominate over the entire period, i.e., duringsteady state as well as during transient diffu-sion. More reasonable estimates for the effec-tive shunt areas are used for the lower twocurves. The curve labeled exp. is from an invitro membrane permeability experimentwhich was immersed in aqueous solution forseveral weeks until pores developed in the

membrane due to its partial dissolution. Thefractional pore area present was calculatedfrom an analysis of the temperature dependenceof the flux. It is probable that the actual in vivoepidermis falls somewhere between the in vitroexp. curve and the lower ones. It should benoted that the region of the curve accessible tomeasurement by the investigator of steadystate diffusion rates is only the horizontal seg-ment in each curve. The bulk of the work onsteady state transport through skin, supportsthe contention that in the steady state thebulk diffusion pathway through intact stratumcorneum predominates (4, 5, 6, 17). Howeverit is evident from these curves that diffusionthrough the follicles and sweat ducts can be sev-eral orders of magnitude greater in the initialperiod shortly after the application of the solu-


8.0

7.0

6.0

5.0 •

•

FOLLICLES / MATRIX • •

4

z0C,,

U-LI0

-J

0I.-

I-zx(I)

U-00F-

4.0

3.0

2,0

0.0

-1.0

DUCTS / MATRIX

ID

-2.0

5

EXPERIMENTAL — PORES / MATRIX

—3.0

-4.0 7


tion. The exact time at which the shunt: hulkratio equals unity depends upon the precisevalues of / and D which arc beyond our capac-ity to establish. But the conclusion that shuntdiffusion predominates for some time in theinitial transient stages appears unshakable inview of our reasonably accurate knowledge ofthe range of the critical parameters and theconservative bias of the calculations. A figure

about on the order of 300 sees may well be aconservative estimate.

The importance of the shunt pathways iseven more evident, particularly to localizedbiologic reactions when the actual concentra-tion levels present in the epidermis are consid-ered. The concentration levels in the neighbor-hood of the ducts and follicles may be verymuch higher than in the bulk of the epidermis

Fio. 4. Approximate transient concentration levels at the site of each kind of diffusionshunt at different times after the application of a solution at I 0. The drawing for a par-ticular shunt is discontinued for the sake of clarity after the concentration reaches l0 atthe corresponding capillaries.

I.

y --

I N/ // 1000 sec

160 s.c


in the early stages of diffusion. This is illus-trated schematically in Figure 4 which showsthe approximate time sequence of events inthe various diffusion pathways when a solu-tion is applied at t = 0. The dotted boundariesrepresent a relative concentration level of 10-v,the blackened areas a relative concentrationgreater than 10-s. The value of 10 correspondsto a concentration of approximately 108 molarwhen a 1% solution is applied to the skin.(This is approximately the threshold concen-tration of nicotinic acid necessary to inducevasodilatation) (18). Figure 4 is keyed toFigure 1 and shows extent of diffusion 10, 100,160, 300, and 1000 seconds after the applica-tion of the solution.

Concentration levels in the epidermis—Steady state concentration levels present in theepidermis corresponding to regions near andaway from the presence of a diffusion shunt(duct or follicle) are shown in Figure 5. Theordinate, log C/CO expresses the concentrationin the tissue relative to that on the surface. A

NO EFFECTIVE OTNATSO 0O'TESM STEADY STATEThRAIT

principal effect of the presence of the thin,relatively impermeable stratum corneum is thelarge concentration drop produced across itssurface. This results in a much lower concen-tration within the viable epidermis than thatwhich would exist in the absence of the stratumcorneum or in the case of a ruptured or dis-eased stratum corncum. Almost a thousand-folddecrease in the steady state concentration levelresults for a stratum corneum with D = 10°em2 sect overlaying an epidermis with D =10° cm2 sec:t This curve is compared withone corresponding to the predicted concentra-tion level for the skin without a stratum cor-neum. A larger concentration level would simi-larly be expected within the follicles and ductswhich are not protected by the full thicknessof a stratum corncum. In effect the stratumcorneum limits the accumulation of substanceswithin the viable epidermis by preventingtheir entrance except at rates so slow that therelatively rapid diffusion from the aqueousviable cells to the cutaneous microcirculationis adequate to maintain their concentration atvery low levels.

The way in which this effect is modifiedfor various composite media is graphicallyillustrated in Figure 6A and 6B. Concentra-tions of lipid soluble molecules can be larger inboth the transient and the steady state owingto their favorable solubility in the stratumcorncum. Figure 6C shows the large increase inboth the concentration gradient and the con-centration sustained in the viable epidermiswhen a solute with a membrane-solvent parti-tion coefficient of 10 is applied in solutionto the surface of the skin. This effect can bevery appreciable as partition coefficients ofthe order of 100 have been measured for aque-ous solutions of alcohols and fatty acids (17).

DISCUSSION

When the extant data on skin permeabilityare considered in the light of both steady stateand transient diffusion much apparently con-flicting data can be resolved. Measurements ofskin permeability done in vitro are invariablymeasurements of steady state rates, if for noother reason that it is usually impossible todetect concentrations within the first few min-utes. Thus the measurements of Treherne (4),Trcgear (5), Scheuplcin (6) and Blank (17)

0

—I

-2

-3

-4

-5

-s

-7

log *

-IS 0 50 (00 (50 200DISTANCE (MICRONS)

Fio. 5. Steady state and transient concentra-tion levels in the epidermis. The dotted line at110o corresponds to the location of the basal layer;the line at 200/h corresponds to the location of theaverage edge of the mierocirculation. A semi-in-finite approximation was used to obtain the valuesfor the transient eases.


FIG. 6. Concentration profiles at steady state for a finite composite slab. The first numberin each case is the diffusion constant in medium 1 (11 = l0); the second number is thediffusion constant in medium 2 (12 20O). The diffusion media correspond in thickness 1and partition coefficient K to the stratum corneum (1) and the viable underlying tissue (2).

are all measurements of steady state fluxes andall in agreement of the paramount role of bulkdiffusion through the unbroken stratum cor-neum. On the other hand, permeability measure-ments in vivo are commonly rapid measurementsand often depend of biological endpoints sensi-tive to extremely small concentrations. Shelleyand Melton observed perifollicular wheals fiveminutes after the application of 10% histamine-free base in water (2). Abramson and Gorin (3)demonstrated that penetration through sweatduets under a potential gradient could occurwithin 1—5 mm. with no comparable transportthrough the stratum corneum within this period.Histologic studies of percutaneous penetrationnotably those of MacKee, Sulzberger, Herrmannand Baer (1) have also demonstrated follicular

diffusion occurring within 5 minutes. These invivo results are also mutually consistent butshow only that shunt diffusion is predominantin the early transient stage of diffusion. Nei-ther group of investigators has actually demon-strated the constant predominance of a singlepermeability pathway. Re-interpreted in thisway, the work of these and other investigatorsbecomes mutually consistent, and in accord withthe observed structure and predicted physicalbehavior of the epidermis.

SUMMARY AND CONCLUSIONS

1. The structure and diffusion parametersof epidermis have been measured and employedin a mathematical analysis of skin diffusion.

2. The ratio of the total amount of material

C

CONCENTRATION PROFILES

(STEADY STATE)

A B

KI K.I

6

N to-60 Iota

to6

to-,


capable of diffusing through the follicles andsweat ducts to the amount through the stratumcorneum has been computed.

3. Shunt diffusion (through ducts and fol-licles) was found to be overwhelmingly domi-nant in the initial transient stage of diffusion.Bulk diffusion through the intact stratum cor-neum was found to be dominant in the steadystate stage.

4. Concentration levels in the stratum cor-neum and in the viable epidermis have beencomputed for steady state and for the transientperiod. The effect of the composite nature ofthe skin diffusion barrier and of the partitioncoefficient are included.

5. The recognition of transient diffusion oc-curring primarily via follicles and duets andsteady state diffusion primarily through theintact stratum eorneum has been shown to re-sult in a considerably more self-consistent andorderly treatment of the process of pereutane-ous absorption.

REFERENCES1. Mackee, C. M., Sulzberger, M. B., Herrmann,

F. and Baer, R. L.: Histologic studies on per-cutaneous penetration with special referenceto the effect of vehicles. J. Invest. Derm., 6:43, 1945.

2. Shelley, W. B. and Milton, F. M.: Factors ac-celerating the penetration of histaminethrough normal intact human skin. J. In-vest. Derm., 13: 61, 1949.

3. Abramson, H. A. and Gorin, M. H.: Skin Re-actions IX. The electrophoretic demonstra-tion of the patent pores of living humanskin; its relation to the charge on theskin. J. Phys. Chem. 44: 1094, 1940.

4. Treherne, J. E.: The permeability of the skin

to some non-electrolytes. J. Physiol., 133:171, 1956.

5. Tregear, R. T. :• Epidermis as a thick mem-brane. J. Physiol. 153: 54, 1960.

6. Seheuplein, R. J.: Mechanism of percutaneousadsorption. I. Routes of penetration and theinfluence of solubility. J. Invest. Derm., 45:334, 1966.

7. Tregear, R. T.: Relative penetrability of hairfollicles and epidermis. J. Physsol. 156: 307,1961.

S. Blank, I. H.: priv. comm. 1965.9. Blank, I. H.: Further observations on factors

which influence the water content of thestratum corneum. J. Invest. Derm., 36: 337,1953.

10. Szabó, G.: The number of eccrine sweat glandsin human skin. Chapter I in "advances inBiology of Skin" Vol. III, London, Per-gamon Press, 1962.

11. Odland, C. F.: Skin. Chapter 17 in "histology"edited by Roy 0. Creep. 2nd ed. New York,McGraw-Hill Book Company, 1966.

12. Reese, C. E. and Eyring, H.: Mechanical prop-erties and structure of hair. Tex. Res. J.,XX: 743, 1950.

13. Alexander, P. and Hudson, R. F.: Wool ItsChemistry and Physics. 2nd ed. by C. Ear-land, Chapman and Hall, 1963. London, GB.

14. Crank, J.: Simultaneous diffusion of heat andmoisture. Chapter XIII in "The Mathe-matics of Diffusion" P. 303. Oxford Univer.sity Press, Inc., 1956. London G.B.

15. Kuno, Y.: Human Perspiration. Springfield,Charles C Thomas, publisher, 1956.

16. Montagna, W.: The Structure and Function ofSkin. New York, Academic Press, 1962.

17. Blank, I. H.: Penetration of low-molecularweight alcohols into skin. I. Effect of con-centration of alcohol and type of vehicle.J. Invest. Derm., 43: 415, 1964.

18. Stroughton, R. B., Clendenning, W. E. andKruse, D.: Percutaneous absorption of nico-time acid and Derivatives. J. Invest. Derm.,35: 337, 1960.

19. Scheuplein, R. J.: The permeability of theskin. To be submitted to the J. Gen. Physiol.,1966.

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