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Analysis of enhanced transdermal transport by skin electroporation
journal o f
ELSEVIER
Journal of Controlled Release 34 (1995) 211-221
controlled release
Analysis of enhanced transdermal transport by skin electroporation David A. Edwards
a,*, Mark
R. Prausnitz
b, Robert Langer a, James C. Weaver c
a Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA b School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA Harvard-MlT Division of Health Sciences and Technology, Massachusetts Institute of Technologv Cambridge, MA 02139, USA
Received 23 March 1994; accepted 5 December 1994
Abstract The transport of charged molecules across human skin can be dramatically enhanced by application of high-strength, pulsed electric fields. This phenomenon is theoretically characterized here in terms of the electroporation of lipid bilayers within the stratum corneum above the transbilayer voltage for which electropores have been observed in single bilayer membranes. Accounting for the size, shape and charge of the transporting molecules, predictions of transdermal molecular flux are made in two electric field conditions. At small field strengths ( transdermal voltage << 100 V), representative of standard skin iontophoresis, charged molecules are modeled as transporting through the pre-existing shunt routes of the skin. At electric field strengths sufficiently large (transdermal voltage > 100 V) to electroporate lipid bilayers, a transcorneocyte pathway is accessible to charged molecules, with transbilayer transport occurring through electropores within the lipid bilayers. Experimental data of transdermal molecular flux compared favorably with the respective theoretical predictions in the small and large electric field strength limits. Predictions of the skin's electrical resistance are also found to be consistent with experimental data at small and large electric field strengths. In both limits, electrophoretic transport is shown to be predominantly convective (i.e., dominated by electric-field drift); however, a unique form of transport enhancement involving convective dispersion may be significant during skin electroporation.
I. Introduction The oral administration of many drugs is prevented by significant degradation in the stomach, intestine and liver [1]. While injections may reduce these effects, parenteral delivery is invasive and generally unpleasant. An attractive alternative to conventional methods is drug delivery across the skin, a noninvasive, userfriendly approach which reduces degradation by the stomach, intestine and liver [ 2,3 ]. However, transder* Correspondingauthor. Present address: Departmentof Chemical Engineering, The Pennsylvania State University, 158 Fenske Laboratory, University Park, PA 16802, USA. 0168-3659/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD10168-3659(94)00132-4
mal drug delivery is presently limited. Few drugs are able to cross the skin at therapeutic rates, due to the remarkable barrier properties of the skin's outermost, dead layer, the stratum corneum. The stratum corneum is composed of flattened cells (corneocytes) separated by narrow regions of intercellular lipids, arranged largely in bilayers [4,5]. Corneocytes are usually considered to be impenetrable, forcing drugs to cross the stratum corneum through the intercellular lipids. Recently, a novel transdermal drug delivery approach, believed to involve electroporation of stratum corneum lipids, has been shown [ 6 - 8 ] to dramatically increase drug transport across the skin. This phenomenon is believed to be distinct from the more commonly observed phenomenon of skin iontopho-
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D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
resis [2,3,9], whereby molecules are forced by application of an electric field through existing aqueous pathways of the skin. Electroporation involves the formation of transient aqueous pathways in lipid bilayers by the application of a brief electric field pulse [ 10-12]. This phenomenon occurs when the voltage across a lipid bilayer reaches approximately 0.5-1 V for short pulses [ 1315]. Typical electrical exposures last 10/.ts to 10 ms. Electropores are thought to be created on the submicrosecond time scale and, under reversible conditions, to disappear over time scales ranging from milliseconds to hours. Electroporation has been demonstrated in many different mammalian, plant, yeast, bacterial and other cells, as well as in artificial planar and spherical membranes [ 10,11 ]. It has found application as a method of introducing DNA into cells for gene transfection in vitro [ 10,11 ] and, more recently, for transporting drugs into tumor cells for improved chemotherapy in vivo [ 16-18]. This study seeks to determine if there is theoretical evidence supporting the electropore origin of skin electroporation. Transport of charged species through the skin is described on the basis of a recently derived theory [ 19], by considering three routes of transport through the skin (i.e., 'intercellular', 'shunt' and 'transcorneocyte' pathways). Predictions based upon the shunt route of transport are found to agree with iontophoretic data at low electric field strengths, whereas transcorneocyte route predictions agree with experimental data at high electric field strengths. These results are shown to be consistent (qualitatively as well as quantitatively) with single lipid bilayer electroporation at high electric field strengths.
2. Theory
2.1. Iontophoresis vs electroporation Experimental evidence [20,21] suggests that the transport of charged molecules through the stratum corneum in the presence of electric fields typical of iontophoresis occurs via pre-existing pathways, viz. either a 'shunt' (hair follicle and sweat duct) route or an intercellular route between corneocytes. This conclusion is supported by theoretical considerations as well [ 19,22]. However, if a suitably large electric field is
applied across the skin, new, perforating pathways through the intercellular lipid bilayers (and possibly through the comeocytes as well) may be created via bilayer electroporation. An estimation of the transdermal voltage A f' necessary to electroporate lipid bilayers within the stratum corneum may be made upon assuming lipid bilayers to be simple voltage dividers. That is, the voltage A 17' across the skin is taken to be the sum total of the individual voltage drops across the stratum comeum' s lipid bilayers. Given that there exist approximately 100 lipid bilayers between the upper and lower surfaces of the stratum corneum [ 5 ], and that electroporation of single bilayers occurs at a transbilayer voltage of approximately 1 V [ 13-15], we have that A I?<< 100 V skin iontophoresis
( 1)
typifies the transdermal voltage for which charged molecules may be expected to follow the standard intercellular and/or shunt routes of transport through the skin, whereas A I?> 100 V skin electroporation
(2)
characterizes the conditions for which electroporation of lipid bilayers may be expected to occur, possibly resulting in a transcorneocyte route of transport. (Note that since corneocytes constitute the primary source of water in the stratum corneum, we expect electropores formed within lipid bilayers to be comprised of water originating in the corneocytes.) In the remainder of this paper, theoretical expressions are developed for the transdermal flux of charged solute molecules in the low field-strength conditions of standard skin iontophoresis (cf. Eq. (1)) and in the high field-strength conditions of skin electroporation (cf. Eq. (2)). We begin by presenting general expressions for transdermal solute flux in terms of effective transport properties of the skin.
2.2. Transdermal flux formulas The steady-state, time-average, one-dimensional solute flux across the stratum corneum may be expressed as [ 19] T
(J)=l~jdt=Kl(U*)Cl, o
(3)
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
assuming transport by diffusion is negligible. These conditions are typical of electric-field mediated transport of charged molecules across the skin [21,22]. Here, ] is the solute flux normal to the skin surface, T the time period of any oscillatory process,/~ the skin/ donor-solution equilibrium partition coefficient, O* the mean solute velocity component normal to the skin surface ( with ( 0 " ) its time average), and Oi the timeindependent solute concentration in the donor compartment. The receptor solute concentration is taken to be zero. In the absence of convection (i.e. mean, electricfield drift), (0"> =0,
(4)
the diffusive contribution to (J), which is neglected in Eq. (3), predominates, and the time-average, steadystate flux of solute is given by 1 --
(J) = 7 K, (D)C,, n
(5)
with/)* the effective dispersivity of the solute in the stratum corneum and h the stratum corneum thickness. The formulas in Eqs. (3) and (5) may be used to offer predictions of steady-state, transdermal solute flux ( J ) data in the presence of an electric field given expressions for the mean solute velocity O* and dispersivity D* in terms of the geometrical and physicochemical properties of the specific transdermal pathways. These expressions are summarized below for the cases of skin iontophoresis (intercellular/shunt pathway) and skin electroporation (transcorneocyte pathway).
2.3. lontophoretic transport through unaltered tissue At low electric fields (cf. Eq. ( 4 ) ) , the structure of intercellular lipids is assumed to be unaltered, and the transport pathways of charged molecules through the skin are taken to be the standard pre-existing intercellular and/or shunt routes. These pathways of transport have been discussed previously [ 19], where it was predicted that the mean, transdermal velocity of charged solute in the presence of an electric field appro-
213
pilate to the combined intercellular and shunt routes of transport is given by j 0* = 0.02594( 4)SH+ O.042H~v)ZA ~"
(6)
Here, O* is given in units of cm/s, 4)sn denotes the area fraction of shunt pathways relative to the total skin surface area (for the abdomen region of human skin, 4)sn = 2.7 X 10-4: see Ref. [ 19] ), and H~v is a hydrodynamic hindrance factor characterizing hydrodynamic interactions between the convecting molecule (of valence z) and the lipid head groups between which it convects in an applied electrical field. The transdermal voltage A f' is expressed in units of volts. Intercellular and shunt routes are jointly considered in the preceding flux expression because both involve transport through the skin via aqueous pathways and each are accessed over a similarly small skin surface area fraction. The first term in Eq. (6) characterizes the flux through shunts. This route exhibits relatively large (/,m-size) pathways. Thus, hydrodynamic hindrance is negligible; this is reflected implicitly in the first term of Eq. (6) by a hydrodynamic hindrance coefficient of unity. The second term accounts for hindered transport through the lipid head group channels of the intercellular route. The factor 0.042 appearing in the second term in parenthesis in Eq. (6) represents an inverse tortuosity for intercellular transport [ 19]. The tortuous pathway between corneocytes is only slightly reduced by the creation of pores in intercellular lipid bilayers, owing to the fact that the lateral corneocyte dimension ( = 23/,m: Ref. [34] ) is much larger than the spacing between corneocytes ( = 0 . 0 5 /,m: Ref. [24] ). Thus, Eq. (6) can be used to describe intercellular transport during electroporation as well (as described in the next subsection). A characteristic value for the thickness (lw) of the bound-water layers between lipid head groups is 0.7 nm (Ref. [4] ). Because the molecules (i.e., calcein) considered in comparisons with experimental data (presented below) possess a Stokes-Einstein diameter 2a > 0.7 nm (cf. the discussion following Eq. (13)), the hindrance coefficient H~v appearing in Eq. (6) is n It is important to emphasize that the numerical values appearing in Eq. (6) have been obtained [ 19] by use of estimates [principally those reported following Eq. (10)] for geometrical and physicochemical properties of the stratum corneum. They have not been fitted to the data in this study.
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D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
expected to be negligibly small. Thus Eq. (6), with (bsH= 2.7 X 10 -4, simplifies to I_7"- 7 . 0 0 × IO-6EA V,
(7)
characterizing the mean iontophoretic velocity of solute species through the hair follicles and/or sweat ducts. In this case, the solute partition coefficient, which accounts for area exclusion effects, is simply /~'1-- ~bsH=2-7 × 10-4-
(8)
Thus, Eq. (3) may be expressed as (J) = 6.8z(A V)CI (nmol/cmZ/h),
(9)
with C1 given in units of mol/1.
M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) is the net area fraction of the lamellax layers accessible to ion transfer, h ( = 15/zm: Ref. [4] ) is the thickness of the stratum comeum, R is the gas constant, T is the absolute temperature and D w = 10 - 5 c m Z / s is the free-volume diffusion coefficient of the transporting substance. The hindrance factors H l, H 1 respectively characterize hydrodynamic hindrance coefficients in the aqueous channels of the comeocytes, and in the aqueous electropores in the lipid bilayers. The effective dispersivity for the transcomeocyte route is given by [ 19]
if)* [ZFRcAVe2
2.4. Electrophoretic transport through porated tissue For the electric-field conditions of Eq. (2), electroporation of intercellular lipid bilayers is assumed to permit transport of charged molecules across lipid bilayers and through the corneocytes of the stratum corneum. This pathway of transport is expected to predominate over the intercellular and shunt pathways since it is characterized by a significantly greater exposed surface area fraction than the latter pathways, which are essentially unaffected by the creation of electropores. Owing to the thinness of the intercellular regions relative to the thickness of corneocyte layers, electrophoretic transport of charged molecules is expected to be rate-limited by transport through the comeocytes, whence [ 19] U*=[ (lc+lL)2(lw+1°! ] klL(lo +/w4~) 4,c +/c(lw + lo) q~LJ (lo + lw4h.) (bLChcH[H1 XF LIcH[(lo~~+lo)~J
×(
3
(tw+_to)(_lc+tL) ]2
lo)] [ H 1 + 7 . 4 2 × 10 6H3c(RcZAf')2]X 10 -5, (11)
\lL4)c(lo + lw4~) + 1C4~(lw +
in units of cm2/s. Here, Rc is the radius of corneocyte channels (see below) expressed in units of nm, H i is a convective-dispersion transport coefficient, which depends upon molecular size and shape and the dimensions of the aqueous channels of the corneocytes. Aqueous channels within comeocytes can be characterized as circular cylinders of radius Rc. This idealization has frequently been used [25-27] to characterize pore spaces within biological porous media as it allows explicit analytical expressions to be developed for the hindrance coefficients H I, H 3. Characterizing solute molecules as hard spheres (of radius a), allows the calculation of the hindrance factors introduced above by [28]
] zFDw RT
1
1, 9a Rc
8
H1 × (-~h--~= 0.012H~zA l3.
Here, lL ( ~-0.05 /zm: Ref. [24] ) is the thickness of a single stratum comeum lamella, lc ( ~ 1.0 tzm: Ref. [24] ) is the characteristic thickness of a comeocyte, 1o ( ~ 5.8 nm: Ref. [4] ) and lw ( ~ 0.7 nm: Ref. [4] ) are the respective thicknesses of the lipid bilayer and bound-water layers within intercellular lamellae, ~bc ( ~ 0.5: Ref. [23] ) is the lateral area fraction of aqueous channels within the corneocytes, 4)L ( ~ 10-3;
(12a) a 2 (1-~c)
(10)
for small a/Ro
,
"1 _ a , 5 / 2 [ Rc/ [ a
for large a/Ro and
1)
D.A. Edwards et al. /Journal of Controlled Release 34 (1995) 211-221
(~c)2[0.158 lnZ(~a~)-0.901 1 ~ ) +
1.385]
1 --~-c)6 (13) For intermediate ratios o f a / R c (i.e., 0.2 < a / R c < 0.8) H~ can be determined by extrapolation, as shown in Fig. 2 of Ref. [36]. The characteristic radius Rc can be estimated upon noting that corneocytes are composed of cross-linked keratin fibers of radius = 7 nm [24] and contain approximately 50% water when fully hydrated [23]. Assuming a uniform distribution of keratin fibers within the corneocytes, Re = 1.8 nm is found from the geometric relationship [ 7 nm/(Rc + 7 rim) ] 3 = 0.5. The Stokes-Einstein radius of calcein (the molecule principally examined in subsequent comparisons with experiments) is estimated2 as a = 0.6 nm. Assuming calcein molecules to be hydrated by a uniform layer of water molecules (molecular diameter = 0.2 nm), suggests a hydrated calcein radius o f a = 0.8 nm. Thus, a~ Rc = 0.44 and Eqs. (12) and (13) give H1 = 0.20, H3 = 5.09, such that Eqs. (10) and ( 11 ) furnish 0* = 0.0024zA 1),
(14)
/)* = [0.20 + 0.0001 (zA I?) 2] × 10 -5.
(15)
The skin/donor compartment partition coefficient characterizing the transcorneocyte route is equivalent to the skin area fraction accessible to charged molecular transport during skin electroporation. Recent experiments involving skin electroporation (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) suggest a steady-state value for this calcein area fraction of /~l = 10-3,
(16)
2Use of Lyderson'smethod [29] for estimatingcriticalvolumes suggests an estimate for the criticalvolumeof calceinof Vc ~ 1260 cm3/gmOl. Combinationof the Stokes-Einsteinequationfor a spherical particle together with the Wilke-Chang and Tyn-Calmus relations [30] permits the hydrodynamicradius a (in nm) to be related to the criticalvolumeas, a = 0.00683Vc °'6288.
215
for skin voltages satisfying Eq. (2). For transdermal voltages on the order of 100 V or less, this value has been observed (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) to diminish sharply with skin voltage. It also depends strongly on the size of the transporting substance. It is interesting to observe that the partition coefficient (Eq. 16) is consistent with theoretical predictions made for single bilayer electroporation [ 15]. These calculations suggest a maximum aqueous area fraction of 10- 3, though the aqueous area fraction may be many orders of magnitude smaller than 10 - 3 , depending upon factors such as voltage pulse duration and magnitude. However, given that direct experimental evidence of aqueous pore area fraction in single lipid bilayers is presently lacking, and that experimental studies of multilipid bilayer electroporation have not been reported in the literature, the precise physical state and kinetics of stratum corneum lipid bilayers during skin electroporation is not well enough understood to make a clear physical interpretation of the partition coefficient value experimentally observed (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) and shown in Eq. (16). Upon combining Eqs. ( 14)-(16) with Eqs. (3) and (5) we have (J) = 8.64 × 103z(A V ) C 1 ( n m o l / c m 2 / h )
(17)
for convectively dominated transdermal transport, and (J) = 2 . 4 × 10410.20 + 0.0001((ZA V)2)] C1 (nmol/cm:/h)
(18)
in the conditions (Eq. 4) of zero time-average convection. For voltages characteristic of electroporation (cf. Eq. (2)), the dispersive flux (Eq. 18) is much smaller in magnitude than the purely convective (i.e., electricfield drift) flux (Eq. 17). This explains our neglect of the diffusional contribution in Eq. (17). (Similarly, the diffusion contribution to the iontophoretic flux (Eq. 9) is also negligible in conventional iontophoretic conditions.)
216
D,A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221 103
3. R e s u l t s
Here we compare theoretical predictions and experimental data for both small and large electric field strengths.
10 2
f
/ 101
3.1. Small/1 13: lontophoresis 10 0
In the experiments of Prausnitz et al. [ 7 ], a continuous dc voltage was applied across human epidermis. In these conditions,
(ag) =ag.
rO
Calcein molecules (MW = 623, z = -4) were placed in the donor compartment of an in vitro diffusion-cell apparatus at a concentration of C1 = 1 mM. The transdermal flux of calcein was measured for 'small' transdermal voltages (/113<2 V). For iontophoretic transport through unaltered tissue, Eq. (9) yields ( J ) = 1.7 × 10-2/19 (/xg/cmZ/h),
i
10-2
(20)
A comparison of the experimental data with the theoretical estimates based upon Eqs. (19) and (20) is made in Fig. 1. The shunt-route (nonporated) prediction (Eq. 19) nearly matches the experimental data over most of the voltage range considered. In contrast, the porated (transcorneocyte) formula (Eq. 20) overpredicts the transport of calcein by several orders of magnitude. This suggests that the hair follicle/sweat duct route is the most likely pathway for charged calcein transport through the skin, at least for A 13< 1 V. The poor correspondence between the shunt-route prediction ( Eq. 19) and the experimental data at the largest voltages examined (i.e., 1.5 V), and, particularly, the nonlinear dependence of the experimental flux values versus voltage, might be explained by an increase in the number of shunt pathways accessible by the iontophoresed molecules with increasing voltage, as described by Scott et al. [35].
3.2. Large A 13: Electroporation Transdermal calcein flux values were measured in a second set of experiments [7] at significantly larger
1
/
t
• /0 10-3
10 -4
1
Experimental data ] Theory / Shunt / (iontophoresis) / Transcorneocyte / (electroporation) ] /
•
I 0.5
I 1.0
(19)
whereas for electrophoretic transport through porated tissue, Eq. (17) gives (,J) ~ 2.5 × 101A I? (/zg/cm2/h).
10 - I
I 1.5
I 2.0
2.5
Transdermal voltage drop (volts)
Fig. 1. Calcein flux magnitude versus transdermal voltage drop in conditions of typical skin iontophoresis.The experimentaldata of Prausnitz et al. [7] are comparedwith theoreticalpredictionsbased upon shunt-route (Eq. 19) and transcorneocyte(Eq. 20) formulas. pulsed voltages (40 V < A13<500 V) across human epidermis. The electric field pulses exponentially decayed with a time constant, r, of approximately 1 ms. One pulse was applied every T = 5 s for 1 h (corresponding to a duty cycle of 0.02%). In the present notation, these conditions correspond to (A 17')= 2 X 10-4A I,3. Eq. (9) adopts the form ( J ) = 3.4X 10
6Ar~
(/xg/cm2/h)
(21)
characterizing the flux of calcein associated with the shunt (nonporated) route of transport, whereas, Eq. (17) gives ( ] ) = 4 . 4 X 10 3AI? (/xg/cm2/h)
(22)
characterizing transport through electroporated skin (transcorneocyte route). Fig. 2 provides a comparison of the theoretical estimates (Eq. 21) and (22) with the experimental data. At the lowest voltages examined (ALP'< 100 V), the data fall between the predictions based upon the shunt (nonporated) formula (Eq. 21 ) and the porated (trans-
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221 102
101 _
to each molecule its respective hindrance coefficient via Eq. (12) (for Lucifer yellow, H i = 0 . 2 ( a = 0 . 7 8 nm) ; for the erythrosin derivative, H~ --~0.17 (a -- 0.90 n m ) ) , Eqs. (3), (10) and (16) may be combined to give
•
1o°-
/
/
~ /
~
•
4.4× 10-3Al? (calcein) (Y) =~l.6X 10-3AV (Lucifer yellow) (1.5X 10-3AV (erythrosin derivative)
Experimentaldata Theory
i0 -1 _ I / ~
I
-- -- - Shunt
"'=8 "~
217
I
(23)
(iontophoresis) ]
Transcorneocyte (electroporation)
10-2 _ •
10 -3 --Q / 10 .4
/ 0
I 100
I
I
I
200
300
400
500
Transdermalvoltage drop(volts) Fig. 2~ Calcein flux magnitude versus transdermal voltage drop in the (high electric field strength) conditions of skin electroporation. The experimental data of Prausnitz et al. [ 7 ] are compared with theoretical predictions based upon shunt-route ( E q . 21 ) a n d transcorneocyte ( E q . 2 2 ) formulas.
corneocyte) formula (Eq. 22). However, as A9 increases beyond 100 V, predictions based upon the porated-route formula (Eq. 22) match the experimental data. At the highest voltages, the transcorneocyte route underpredicts the experimental data. While this discrepancy may owe to many factors, as discussed in the following section, it may be significant that for transdermal voltages exceeding 100 V, irreversible damage to the skin was observed [7]. In general, however, the several-fold enhancement of charged molecule transport associated with the porated, transcorneocyte route of transport appears to offer evidence that pores were created in the intercellular bilayers and that a transcorneocyte (rather than an intercellular or shunt) route of transport is followed by the calcein molecules at the highest voltage drops shown in Fig. 2. Further support of transcorneocyte transport through bilayers at high electric field strengths is provided by the comparisons made in Fig. 3. This figure supplements the calcein data of Fig. 2 with experimental data (collected by Prausnitz et al. [7] under identical conditions) for Lucifer yellow (MW = 457, z = -2) and an erytbrosin derivative (MW = 1025, z = - 1 ). Attributing
characterizing the transport rates (/xg/cm2/h) for the three different molecules according to the porated route through the stratum corneum. Predictions based upon the above equations are shown with the experimental data in Fig. 3. The convergence of experimental and theoretical results as A f'increases above 100 V is consistent with the comparisons made between theory and experiment in Fig. 2.
3.3. Large A (1 (Alternating Polarity): Electroporation Recently (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and ionto102
10 !
[] []
,oO 10 -1
/ / -
~
~
~
~
N
eory T . . . . . . . . . . . yte (electroporation)
I \ ]
•
calceln
rn
Luciferyellow
~
, [ Erythrosinderivativ~
10-2
10 3
10.4
Experimentaldata [] [] •
Calcein Lucifer yellow
I I
ErythrosinderivativeJ
I 100
I 200
[ 300
I 400
500
Transdermalvoltage drop (volts) Fig. 3. Molecular flux magnitude for three different compounds versus transdermal voltage drop in the (high electric field strength) conditions of skin electroporation. The experimental data of Prausnitz et al. [7] are compared with theoretical predictions based upon the transcorneocyte formula ( E q . 2 3 ) .
218
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221 102
101
•
Experimentaldata Theory Transcorneocyte (electroporation)
100 10-1
10-2
10-3
10-4
[ 100
I 200
I 300
i 400
500
Transdermalvoltagedrop (volts) (alternating polarity) Fig. 4. Calcein flux magnitude versus (alternating) transdermal voltage drop in the (high electric field strength) conditions of skin electroporation. The experimental data of Prausnitz et al. (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) are compared with theoretical predictions based upon the transcorneocyte formula (Eq. 24).
phoresis, submitted for publication), calcein flux was measured during skin electroporation due to electric field pulses, with r = 1 ms, T = 5 s, and Ct = 1 mM, but with the polarity alternating from one pulse to the next (Fig. 4); thus,
=0. These are the conditions of validity of Eq. (18); i.e., there is zero net convection (cf. Eq. (4)) across the skin. Even in the absence of net solute convection, a significant enhancement of transport was experimentally observed (see Fig. 4). This phenomenon cannot be explained in the standard electrophoresis (or electroosmosis) terms by which electric field enhancement of charged molecule transport across the skin has been explained in the past, since, on average, there is no net forced diffusion or convection. For zero net skin convection, Eq. (18) gives ( J ) = 3 . 0 × 10-3[0.20 + 0.0008A g 2] (/~g/cmZ/h).
(24)
The first term in brackets identifies the contribution arising from the purely diffusive transport of calcein in the conditions of skin electroporation. This term is seen to be of order 10 -4/xg/cm2/h, the order of the sensitivity of the experimental measurements. The second term in brackets identifies a convective-dispersive contribution, quantifying the (oscillatory) convective enhancement of net solute 'diffusion'. This contribution remains even in an alternating electric field because it depends upon the square of the transdermal voltage. The physical origin of convective dispersion is further discussed in the following section. Predictions based upon Eq. (24) are shown in Fig. 4 together with the experimental data. Very good agreement is found between the experimental data and the theoretical predictions for A f ' > 100 V. This appears to be strong evidence both for the validity of a porated, transcorneocyte route of transport in the ~onditions of Eq. (2) and for the occurrenceofconvectivedispersion in the skin.
4. Discussion
The theoretical/experimental comparisons made in Figs. 1-4 strongly suggest that charged molecules follow different pathways through the stratum corneum below and above a transdermal voltage of approximately 100 V. At transdermal voltages significantly less than 100 V, transport of charged calcein appears to occur through nonporated skin via a shunt route (Fig. 1). However, for A f ' > 100 V, the comparisons made in Figs. 2-4 indicate that transport through porated intercellular bilayers and corneocytes is preferred, consistent with the known characteristics (cf. Eqs. (2) as well as Eq. (16) ) of lipid bilayer electroporation. Additional evidence for the electroporation of stratum corneum bilayers can be offered on the basis of the electrical properties of skin. It has been found [22,35,39] that the specific electrical resistance of the skin exhibits a steady-state value of approximately 1000-10 000 g2.cm 2 following application of a lowstrength electric field for about 1 h. In the high-strength conditions of Eq. (2), the skin's electrical resistance can diminish up to three orders of magnitude, to a value of approximately 10-100 ~ . cm 2 ( [ 38 ] and U. Pliquett and J.C. Weaver, The change in the passive electrical properties of human stratum corneum due to electro-
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
poration, submitted for publication) . This drop in resistance is found to be consistent with the current analysis. Thus, the electrical resistance of unaltered skin has been estimated as [ 19] fi ~- 4000/2. c m 2,
( 25 )
with ions transporting through intercellular and shunt routes. As previously (cf. Eq. (10)), if we assume q~ = 10- 3 for the stratum comeum area fraction accessible to ion transfer in electroporation conditions, a value that has been experimentally observed (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication), it follows that the transport of ions through electropores and comeocytes causes a reduction of the skin's electrical resistance to approximately (cf. Eq. (31b) of Ref. [19]) f i = 6 ~ - c m 2.
(26)
This latter result is substantially lower than the experimental skin resistance data ( [38] and U. Pliquett and J.C. Weaver, The change in the passive electrical properties of human stratum corneum due to electroporation, submitted) at high electric field strengths. A potential explanation for this underprediction is that the result (Eq. 26) does not include the effect of (small) electrode area on measured skin resistances. However, the predicted diminution of skin resistance by several orders of magnitude appears to lend further support to a transcorneocyte route of transport in skin electroporation circumstances. The results of this study indicate that multiple lipid bilayers within the stratum corneum electroporate at conditions similar to those for which electroporation has been observed or predicted in single bilayer systems [ 10-15]. As in single bilayer systems, whether planar or spherical, electroporation of skin appears to give rise to a dramatic enhancement of transbilayer molecular flux, leading to pathways for molecular transport through the aqueous channels of the comeocytes. The successful description of key features of electric field-mediated transdermal transport, based upon the physical characteristics of the stratum corneum and the transporting molecules, constitutes an essential step toward understanding the mechanisms of transport and optimizing experimental protocols. However, the physical and geometrical complexity of the stratum cor-
219
neum, including its possible dependence upon applied (e.g., electric) fields, limits the scope of conclusions that may be drawn via each set of theoretical predictions until a broad range of experimental observations have been confirmed. In the current study, experimental flux data at relatively low transdermal voltages ( < 1 V) have been fairly well predicted (Fig. 1) on the basis of a shunt route of charged-molecule transport. Yet, the observed nonlinear dependence of molecular flux upon voltage is not predicted by the current theory. This may reflect the creation of new transport pathways through the skin with increasing applied voltage (as observed in Ref. [35] ). Nonlinear electrical properties of skin above 1 V are well documented (see, e.g., Refs. [22,35,37] ). Experimental transdermal flux values have been found (Fig. 2) to be approximated by theoretical predictions based upon an electroporated, transcomeocyte route of transport through the stratum corneum. However, the strong nonlinearities exhibited by the data over the entire range of voltages shown in Fig. 2 suggest a significant dependence of electropore area fraction upon voltage (a dependence not accounted for here), and perhaps irreversible skin damage at the very highest voltages. Moreover, Eqs. (10) and ( 11 ), which describe the transcorneocyte route of transport, apply to circumstances where transport across the intercellular lipids occurs relatively fast in comparison to transport across the corneocytes. It may occur, however, that at the intermediate voltages shown in Fig. 2, significant hindrance of transport across the intercellular lipids occurs, requiring modification of Eqs. (10) and (11). Other approximations made in the theory, such as the idealization of circular cylindrical aqueous pores within corneocytes, may give rise to significant errors in conditions other than have been examined here. For example, very large molecules (i.e., a > 1.8 nm), may potentially transport across corneocytes during electroporation. However, our assumption of a uniform pore size in the corneocytes (see following Eq. (13) ) would wrongly preclude this possibility because it does not account for the heterogeneous distribution of aqueous pathway dimensions within corneocytes. One of the striking features of skin electroporation is the observation (Fig. 4) that a dramatic enhancement of charged species is possible even in the absence of a net transdermal voltage. This has been explained here
220
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
by the convective dispersion of charged molecules within corneocytes-a phenomenon that appears not to have been discussed previously in the context of transdermal transport. Convective dispersion resulting from oscillating flow conditions has been observed in numerous practical capillary and porous media problems [28], such as human lungs (i.e., high-frequency ventilation schemes) [32], abdominal cavities [33] and river estuaries [ 31 ]. Physically, these phenomena occur because solute molecules instantaneously transport through porous media at significantly different rates depending upon their individual 'local' trajectories through the medium. In the case of skin, a charged molecule may transport (under the action of an oscillatory electric field) predominantly along the centerline through aqueous channels of the corneocytes, avoiding contact with keratin fibers, and thereby maximizing its speed through the skin. However, diffusion may cause another molecule to follow a trajectory that frequently brings it into contact with keratin fibers, so that it moves much more slowly through the skin than the 'centerline' molecule. On average, all molecules will move with a mean speed through the skin. In the case of oscillatory flow, this mean speed may even be zero. However, the dispersion - or spatial spread - of the solute molecules about this mean speed will be significantly enhanced (over that enhancement which normal molecular diffusion provides) owing to the interaction between convection and diffusion.
Acknowledgements This work has been supported in part by the National Institutes of Health Grants GM448884 (D.A.E. and R.L. ) and GM34077 ( J.C.W. ), by Cygnus Therapeutic Systems (M.R.P. and J.C.W.) and by the Army Research Office Grant DAAL03-90-G-0218 (J.C.W.), The authors are grateful for several helpful discussions with Mark E. Johnson and Russell O. Potts.
References [ 1] R. Langer, New methods of drug delivery. Science, 249 (1990) 1527-1533.
[2] R.L. Bronaugh and H.I. Maibach, (Eds.), Percutaneous Absorption, Mechanisms-Methodology-Drug Delivery. Marcel Dekker, New York, 1989, [ 3 ] J. Hadgraft and R.H, Guy, (Eds.), Transdermal Drug Delivery: Developmental Issues and Research Initiatives. Marcel Dekker, New York, 1989. [4] J.A. Bouwstra, M.A. de Vries, G.S. Gooris, W. Bras, J, Brussee and M. Ponec, Thermodynamic and structural aspects of the skin barrier. J. Control. Release 15 ( 1991 ) 209-220. [5] P.M. Elias, Epic)ermal barrier function: intercellular lamellar lipid structures, origin, composition and metabolism. J. Control. Release 15 ( 1991 ) 199-208. [6] M.R. Prausnitz, V.G. Bose, R. Langer and J.C. Weaver, Transdermal drug delivery by electroporation. Proc. Int. Symp. Control. Release Bioact. Mater. 19 (1992) 232-233. [7] M.R. Prausnitz, V.G. Bose, R. Langer and J.C. Weaver, Electroporation of mammalian skin: A mechanism to enhance transdermal drug delivery. Proc. Natl. Acad. Sci. USA 90 (1993) 10504-10508. [8] D. Bommannan, L. Leung, J. Tamada, J. Sharifi, W. Abraham and R. Potts, Transdermal delivery of luteinizing hormone releasing hormone: comparison between electroporation and iontophoresis in vitro. Proceed. Intern. Symp. Control Rel. Bioact. Mater. 20 (1993) 97-98. [ 9 ] C. Cullander and R.H. Guy, Transdermal delivery of peptides and proteins. Adv. Drug Deliv. Rev. 8 (1992) 291-329. [10]E. Neumann, A.E. Sowers and C.A. Jordan (Eds.), Electroporation and Electrofusion in Cell Biology. Plenum Press, New York, 1989. [ 11 ] D.C. Chang, B.M. Chassy, J.A, Saunders and A.E. Sowers, ( Eds. ), Guide to Electroporation and Electrofusion. Academic Press, New York, 1992. [12] J.C. Weaver, Electroporation: A general phenomenon for manipulating cells and tissues. J. Cell. Biochem. 51 (1993) 426-435. [13] I.G. Abidor, V.B. Arakelyan, L.V. Chernomordik, Y.A. Chizmadzhev, V.F. Pastushenko and M.R. Tarasevich, Electric breakdown of bilayer membranes, I. The main experimental facts and their qualitative discussion. Bioelectrochem. Bioenerget. 6 (1979) 37-52. [ 14] J.C. Weaver and A. Barnett, Progress towards a theoretical model for electroporation mechanism: membrane electrical behavior and molecular transport, in: D.C. Chang, B.M. Chassy, J.A. Saunders and A.E. Sowers, (Eds.), Guide to Electroporation and Electrofusion, Academic Press, New York, 1992, pp. 91-118. [15] S.A. Freeman, M.A. Wang and J.C. Weaver, Theory of electroporation of planar bilayer membranes: Predictions of the aqeuous area, change in capacitance and pore-pore separation. Biophys. J. (1994) in press. [ 16] M. Okino and J.H. Mohri, Effects of a high voltage electrical impulse and an anticancer drug on in vivo growing tumors. Jpn. J. Cancer Res. 78 (1987) 1319-1321. [17] L.M. Mir, S. Orlowski, J. Belehradek and C. Paoletti, Electrochemotherapy: potentiation of antitumor effect of bleomycin by local electric pulses. Eur. J. Cancer 27 ( 1991 ) 68-72.
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[18] L.G. Salford, B.R.R. Persson, A. Brun, C.P. Ceberg, P.C. Kongstad and L.M. Mir, A new brain tumor therapy combining bleomycin with in vivo electropermeabilization. Biochem. Biophys. Res. Commun. 194 (1993) 938-943. [ 19] D.A. Edwards and R. Langer, A linear theory of transdermal transport phenomena. J. Pharm. Sci. 83 (1994) 1315-1334. [ 20] C. Cullander, What are the pathways of iontophoretic current flow through mammalian skin? Adv. Drug Del. Rev. 9 (1992) 119-135. [21 ] J.B. Phipps and J.A. Gyory, Transdermal ion migration. Adv. Drug Del. Rev. 9 (1992) 137-176. [22] G.B. Kasting, Theoretical models for iontophoretic delivery. Adv. Drug Del. Rev. 9 (1992) 177-199. [23] S.D. Campbell, K.K. Kranino, E.G. Schibli and S.T. Momii, Hydration characteristics and electrical resistivity of stratum corneum using a noninvasive four-point microelectrode method. J. Invest. Dermatol. 89 (1977) 290-296, [24] R. Scheuplein, The skin as a barrier, in: The Physiology and Pathophysiology of the Skin, Vol. 5, Academic Press, New York, 1978. [25] W.M. Deen, Hindered transport of large molecules in liquidfilled pores. Am. Inst. Chem. Eng. J. 33 (1987) 1409-1425. [26] D.M. Malone and J.L. Anderson, Hindered diffusion of particles through small pores. Chem. Eng. Sci. 33 (1978) 1429-1444. [27] J. Frenkel, On the theory of seismic and seismoelectric phenomena in a moist soil. J. Phys. USSR 8 (1944) 230-241. [28] H. Brenner and D.A. Edwards, Macrotransport Processes, Butterworth-Heinemann, Boston, 1993. [29] Lyderson, A.L., Estimation of Critical Properties of Organic Compounds. Univ. Wisconsin Coll. Eng., Eng. Exp. Stn. Rep. 3, Madison, WI, April, 1955.
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[30] R.C. Reid, J.M. Prausnitz and T.K. Sherwood, The Properties of Gases and Liquids. 3rd ed., McGraw-Hill, New York, 1977. [31] H.B. Fisher, E.J. List, R.C.Y. Koh, J. Imberger and N.H. Brooks, Mixing in Inland and Coastal Waters. Academic Press, New York, 1979. [32] Y.C.B. Fung and S.S. Sabin. Mechanics of pulmonary circulation, in: Cardiovascular Flow Dynamics and Measurements N.H.C. Hwang and N.A. Norman (Eds.), pp. 665-730. University Park Press, Baltimore, 1977. [33] J. Rudoy, R. Kohan and J. Ben-Ari, Externally applied abdominal vibration as a mthod for improving efficiency in peritoneal dialysis. Nephron 46 (1987) 364-366. [ 34 ] A. Rougier, C. Lotte, P. Corcuff and H.I. Maibach, Relationship between skin permeability and corneocyte size according to anatomic site, age, and sex in man. J. Soc. Cosmet. Chem. 39 (1988) 15-26. [35] E.R. Scott, A.I. Laplaza, H.S. White and J. Phillips, Transport of ionic species in skin: contribution of pores to the overall skin conductance. Pharm. Res. 10 (1993) 1699-1709. [36] G.M. Mavrovouniotis and H. Brenner, Hindered sedimentation, diffusion and dispersion coefficients for Brownian spheres in cylindrical pores. J. Colloid Interface Sci. 124 (1988) 269-283. [37] W.G.S. Stephens, The current-voltage relationship in human skin. Med. Electron. Biol. Eng. 1 (1963) 389-399, [38] V.G. Bose, Electrical characterization of electroporation of human stratum corneum. MS thesis, Massachusetts Institute of Technology, 1994. [39] H. Inada, H.A.-H. Graham and W.I. Higuchi. Studies on the effects of applied voltage and duration on human epidermal membrane alteration/recovery and the resultant effects upon iontophoresis. Pharm. Res. 11 (1994), 687-697.
ELSEVIER
Journal of Controlled Release 34 (1995) 211-221
controlled release
Analysis of enhanced transdermal transport by skin electroporation David A. Edwards
a,*, Mark
R. Prausnitz
b, Robert Langer a, James C. Weaver c
a Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA b School of Chemical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA Harvard-MlT Division of Health Sciences and Technology, Massachusetts Institute of Technologv Cambridge, MA 02139, USA
Received 23 March 1994; accepted 5 December 1994
Abstract The transport of charged molecules across human skin can be dramatically enhanced by application of high-strength, pulsed electric fields. This phenomenon is theoretically characterized here in terms of the electroporation of lipid bilayers within the stratum corneum above the transbilayer voltage for which electropores have been observed in single bilayer membranes. Accounting for the size, shape and charge of the transporting molecules, predictions of transdermal molecular flux are made in two electric field conditions. At small field strengths ( transdermal voltage << 100 V), representative of standard skin iontophoresis, charged molecules are modeled as transporting through the pre-existing shunt routes of the skin. At electric field strengths sufficiently large (transdermal voltage > 100 V) to electroporate lipid bilayers, a transcorneocyte pathway is accessible to charged molecules, with transbilayer transport occurring through electropores within the lipid bilayers. Experimental data of transdermal molecular flux compared favorably with the respective theoretical predictions in the small and large electric field strength limits. Predictions of the skin's electrical resistance are also found to be consistent with experimental data at small and large electric field strengths. In both limits, electrophoretic transport is shown to be predominantly convective (i.e., dominated by electric-field drift); however, a unique form of transport enhancement involving convective dispersion may be significant during skin electroporation.
I. Introduction The oral administration of many drugs is prevented by significant degradation in the stomach, intestine and liver [1]. While injections may reduce these effects, parenteral delivery is invasive and generally unpleasant. An attractive alternative to conventional methods is drug delivery across the skin, a noninvasive, userfriendly approach which reduces degradation by the stomach, intestine and liver [ 2,3 ]. However, transder* Correspondingauthor. Present address: Departmentof Chemical Engineering, The Pennsylvania State University, 158 Fenske Laboratory, University Park, PA 16802, USA. 0168-3659/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSD10168-3659(94)00132-4
mal drug delivery is presently limited. Few drugs are able to cross the skin at therapeutic rates, due to the remarkable barrier properties of the skin's outermost, dead layer, the stratum corneum. The stratum corneum is composed of flattened cells (corneocytes) separated by narrow regions of intercellular lipids, arranged largely in bilayers [4,5]. Corneocytes are usually considered to be impenetrable, forcing drugs to cross the stratum corneum through the intercellular lipids. Recently, a novel transdermal drug delivery approach, believed to involve electroporation of stratum corneum lipids, has been shown [ 6 - 8 ] to dramatically increase drug transport across the skin. This phenomenon is believed to be distinct from the more commonly observed phenomenon of skin iontopho-
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resis [2,3,9], whereby molecules are forced by application of an electric field through existing aqueous pathways of the skin. Electroporation involves the formation of transient aqueous pathways in lipid bilayers by the application of a brief electric field pulse [ 10-12]. This phenomenon occurs when the voltage across a lipid bilayer reaches approximately 0.5-1 V for short pulses [ 1315]. Typical electrical exposures last 10/.ts to 10 ms. Electropores are thought to be created on the submicrosecond time scale and, under reversible conditions, to disappear over time scales ranging from milliseconds to hours. Electroporation has been demonstrated in many different mammalian, plant, yeast, bacterial and other cells, as well as in artificial planar and spherical membranes [ 10,11 ]. It has found application as a method of introducing DNA into cells for gene transfection in vitro [ 10,11 ] and, more recently, for transporting drugs into tumor cells for improved chemotherapy in vivo [ 16-18]. This study seeks to determine if there is theoretical evidence supporting the electropore origin of skin electroporation. Transport of charged species through the skin is described on the basis of a recently derived theory [ 19], by considering three routes of transport through the skin (i.e., 'intercellular', 'shunt' and 'transcorneocyte' pathways). Predictions based upon the shunt route of transport are found to agree with iontophoretic data at low electric field strengths, whereas transcorneocyte route predictions agree with experimental data at high electric field strengths. These results are shown to be consistent (qualitatively as well as quantitatively) with single lipid bilayer electroporation at high electric field strengths.
2. Theory
2.1. Iontophoresis vs electroporation Experimental evidence [20,21] suggests that the transport of charged molecules through the stratum corneum in the presence of electric fields typical of iontophoresis occurs via pre-existing pathways, viz. either a 'shunt' (hair follicle and sweat duct) route or an intercellular route between corneocytes. This conclusion is supported by theoretical considerations as well [ 19,22]. However, if a suitably large electric field is
applied across the skin, new, perforating pathways through the intercellular lipid bilayers (and possibly through the comeocytes as well) may be created via bilayer electroporation. An estimation of the transdermal voltage A f' necessary to electroporate lipid bilayers within the stratum corneum may be made upon assuming lipid bilayers to be simple voltage dividers. That is, the voltage A 17' across the skin is taken to be the sum total of the individual voltage drops across the stratum comeum' s lipid bilayers. Given that there exist approximately 100 lipid bilayers between the upper and lower surfaces of the stratum corneum [ 5 ], and that electroporation of single bilayers occurs at a transbilayer voltage of approximately 1 V [ 13-15], we have that A I?<< 100 V skin iontophoresis
( 1)
typifies the transdermal voltage for which charged molecules may be expected to follow the standard intercellular and/or shunt routes of transport through the skin, whereas A I?> 100 V skin electroporation
(2)
characterizes the conditions for which electroporation of lipid bilayers may be expected to occur, possibly resulting in a transcorneocyte route of transport. (Note that since corneocytes constitute the primary source of water in the stratum corneum, we expect electropores formed within lipid bilayers to be comprised of water originating in the corneocytes.) In the remainder of this paper, theoretical expressions are developed for the transdermal flux of charged solute molecules in the low field-strength conditions of standard skin iontophoresis (cf. Eq. (1)) and in the high field-strength conditions of skin electroporation (cf. Eq. (2)). We begin by presenting general expressions for transdermal solute flux in terms of effective transport properties of the skin.
2.2. Transdermal flux formulas The steady-state, time-average, one-dimensional solute flux across the stratum corneum may be expressed as [ 19] T
(J)=l~jdt=Kl(U*)Cl, o
(3)
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
assuming transport by diffusion is negligible. These conditions are typical of electric-field mediated transport of charged molecules across the skin [21,22]. Here, ] is the solute flux normal to the skin surface, T the time period of any oscillatory process,/~ the skin/ donor-solution equilibrium partition coefficient, O* the mean solute velocity component normal to the skin surface ( with ( 0 " ) its time average), and Oi the timeindependent solute concentration in the donor compartment. The receptor solute concentration is taken to be zero. In the absence of convection (i.e. mean, electricfield drift), (0"> =0,
(4)
the diffusive contribution to (J), which is neglected in Eq. (3), predominates, and the time-average, steadystate flux of solute is given by 1 --
(J) = 7 K, (D)C,, n
(5)
with/)* the effective dispersivity of the solute in the stratum corneum and h the stratum corneum thickness. The formulas in Eqs. (3) and (5) may be used to offer predictions of steady-state, transdermal solute flux ( J ) data in the presence of an electric field given expressions for the mean solute velocity O* and dispersivity D* in terms of the geometrical and physicochemical properties of the specific transdermal pathways. These expressions are summarized below for the cases of skin iontophoresis (intercellular/shunt pathway) and skin electroporation (transcorneocyte pathway).
2.3. lontophoretic transport through unaltered tissue At low electric fields (cf. Eq. ( 4 ) ) , the structure of intercellular lipids is assumed to be unaltered, and the transport pathways of charged molecules through the skin are taken to be the standard pre-existing intercellular and/or shunt routes. These pathways of transport have been discussed previously [ 19], where it was predicted that the mean, transdermal velocity of charged solute in the presence of an electric field appro-
213
pilate to the combined intercellular and shunt routes of transport is given by j 0* = 0.02594( 4)SH+ O.042H~v)ZA ~"
(6)
Here, O* is given in units of cm/s, 4)sn denotes the area fraction of shunt pathways relative to the total skin surface area (for the abdomen region of human skin, 4)sn = 2.7 X 10-4: see Ref. [ 19] ), and H~v is a hydrodynamic hindrance factor characterizing hydrodynamic interactions between the convecting molecule (of valence z) and the lipid head groups between which it convects in an applied electrical field. The transdermal voltage A f' is expressed in units of volts. Intercellular and shunt routes are jointly considered in the preceding flux expression because both involve transport through the skin via aqueous pathways and each are accessed over a similarly small skin surface area fraction. The first term in Eq. (6) characterizes the flux through shunts. This route exhibits relatively large (/,m-size) pathways. Thus, hydrodynamic hindrance is negligible; this is reflected implicitly in the first term of Eq. (6) by a hydrodynamic hindrance coefficient of unity. The second term accounts for hindered transport through the lipid head group channels of the intercellular route. The factor 0.042 appearing in the second term in parenthesis in Eq. (6) represents an inverse tortuosity for intercellular transport [ 19]. The tortuous pathway between corneocytes is only slightly reduced by the creation of pores in intercellular lipid bilayers, owing to the fact that the lateral corneocyte dimension ( = 23/,m: Ref. [34] ) is much larger than the spacing between corneocytes ( = 0 . 0 5 /,m: Ref. [24] ). Thus, Eq. (6) can be used to describe intercellular transport during electroporation as well (as described in the next subsection). A characteristic value for the thickness (lw) of the bound-water layers between lipid head groups is 0.7 nm (Ref. [4] ). Because the molecules (i.e., calcein) considered in comparisons with experimental data (presented below) possess a Stokes-Einstein diameter 2a > 0.7 nm (cf. the discussion following Eq. (13)), the hindrance coefficient H~v appearing in Eq. (6) is n It is important to emphasize that the numerical values appearing in Eq. (6) have been obtained [ 19] by use of estimates [principally those reported following Eq. (10)] for geometrical and physicochemical properties of the stratum corneum. They have not been fitted to the data in this study.
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D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
expected to be negligibly small. Thus Eq. (6), with (bsH= 2.7 X 10 -4, simplifies to I_7"- 7 . 0 0 × IO-6EA V,
(7)
characterizing the mean iontophoretic velocity of solute species through the hair follicles and/or sweat ducts. In this case, the solute partition coefficient, which accounts for area exclusion effects, is simply /~'1-- ~bsH=2-7 × 10-4-
(8)
Thus, Eq. (3) may be expressed as (J) = 6.8z(A V)CI (nmol/cmZ/h),
(9)
with C1 given in units of mol/1.
M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) is the net area fraction of the lamellax layers accessible to ion transfer, h ( = 15/zm: Ref. [4] ) is the thickness of the stratum comeum, R is the gas constant, T is the absolute temperature and D w = 10 - 5 c m Z / s is the free-volume diffusion coefficient of the transporting substance. The hindrance factors H l, H 1 respectively characterize hydrodynamic hindrance coefficients in the aqueous channels of the comeocytes, and in the aqueous electropores in the lipid bilayers. The effective dispersivity for the transcomeocyte route is given by [ 19]
if)* [ZFRcAVe2
2.4. Electrophoretic transport through porated tissue For the electric-field conditions of Eq. (2), electroporation of intercellular lipid bilayers is assumed to permit transport of charged molecules across lipid bilayers and through the corneocytes of the stratum corneum. This pathway of transport is expected to predominate over the intercellular and shunt pathways since it is characterized by a significantly greater exposed surface area fraction than the latter pathways, which are essentially unaffected by the creation of electropores. Owing to the thinness of the intercellular regions relative to the thickness of corneocyte layers, electrophoretic transport of charged molecules is expected to be rate-limited by transport through the comeocytes, whence [ 19] U*=[ (lc+lL)2(lw+1°! ] klL(lo +/w4~) 4,c +/c(lw + lo) q~LJ (lo + lw4h.) (bLChcH[H1 XF LIcH[(lo~~+lo)~J
×(
3
(tw+_to)(_lc+tL) ]2
lo)] [ H 1 + 7 . 4 2 × 10 6H3c(RcZAf')2]X 10 -5, (11)
\lL4)c(lo + lw4~) + 1C4~(lw +
in units of cm2/s. Here, Rc is the radius of corneocyte channels (see below) expressed in units of nm, H i is a convective-dispersion transport coefficient, which depends upon molecular size and shape and the dimensions of the aqueous channels of the corneocytes. Aqueous channels within comeocytes can be characterized as circular cylinders of radius Rc. This idealization has frequently been used [25-27] to characterize pore spaces within biological porous media as it allows explicit analytical expressions to be developed for the hindrance coefficients H I, H 3. Characterizing solute molecules as hard spheres (of radius a), allows the calculation of the hindrance factors introduced above by [28]
] zFDw RT
1
1, 9a Rc
8
H1 × (-~h--~= 0.012H~zA l3.
Here, lL ( ~-0.05 /zm: Ref. [24] ) is the thickness of a single stratum comeum lamella, lc ( ~ 1.0 tzm: Ref. [24] ) is the characteristic thickness of a comeocyte, 1o ( ~ 5.8 nm: Ref. [4] ) and lw ( ~ 0.7 nm: Ref. [4] ) are the respective thicknesses of the lipid bilayer and bound-water layers within intercellular lamellae, ~bc ( ~ 0.5: Ref. [23] ) is the lateral area fraction of aqueous channels within the corneocytes, 4)L ( ~ 10-3;
(12a) a 2 (1-~c)
(10)
for small a/Ro
,
"1 _ a , 5 / 2 [ Rc/ [ a
for large a/Ro and
1)
D.A. Edwards et al. /Journal of Controlled Release 34 (1995) 211-221
(~c)2[0.158 lnZ(~a~)-0.901 1 ~ ) +
1.385]
1 --~-c)6 (13) For intermediate ratios o f a / R c (i.e., 0.2 < a / R c < 0.8) H~ can be determined by extrapolation, as shown in Fig. 2 of Ref. [36]. The characteristic radius Rc can be estimated upon noting that corneocytes are composed of cross-linked keratin fibers of radius = 7 nm [24] and contain approximately 50% water when fully hydrated [23]. Assuming a uniform distribution of keratin fibers within the corneocytes, Re = 1.8 nm is found from the geometric relationship [ 7 nm/(Rc + 7 rim) ] 3 = 0.5. The Stokes-Einstein radius of calcein (the molecule principally examined in subsequent comparisons with experiments) is estimated2 as a = 0.6 nm. Assuming calcein molecules to be hydrated by a uniform layer of water molecules (molecular diameter = 0.2 nm), suggests a hydrated calcein radius o f a = 0.8 nm. Thus, a~ Rc = 0.44 and Eqs. (12) and (13) give H1 = 0.20, H3 = 5.09, such that Eqs. (10) and ( 11 ) furnish 0* = 0.0024zA 1),
(14)
/)* = [0.20 + 0.0001 (zA I?) 2] × 10 -5.
(15)
The skin/donor compartment partition coefficient characterizing the transcorneocyte route is equivalent to the skin area fraction accessible to charged molecular transport during skin electroporation. Recent experiments involving skin electroporation (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) suggest a steady-state value for this calcein area fraction of /~l = 10-3,
(16)
2Use of Lyderson'smethod [29] for estimatingcriticalvolumes suggests an estimate for the criticalvolumeof calceinof Vc ~ 1260 cm3/gmOl. Combinationof the Stokes-Einsteinequationfor a spherical particle together with the Wilke-Chang and Tyn-Calmus relations [30] permits the hydrodynamicradius a (in nm) to be related to the criticalvolumeas, a = 0.00683Vc °'6288.
215
for skin voltages satisfying Eq. (2). For transdermal voltages on the order of 100 V or less, this value has been observed (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) to diminish sharply with skin voltage. It also depends strongly on the size of the transporting substance. It is interesting to observe that the partition coefficient (Eq. 16) is consistent with theoretical predictions made for single bilayer electroporation [ 15]. These calculations suggest a maximum aqueous area fraction of 10- 3, though the aqueous area fraction may be many orders of magnitude smaller than 10 - 3 , depending upon factors such as voltage pulse duration and magnitude. However, given that direct experimental evidence of aqueous pore area fraction in single lipid bilayers is presently lacking, and that experimental studies of multilipid bilayer electroporation have not been reported in the literature, the precise physical state and kinetics of stratum corneum lipid bilayers during skin electroporation is not well enough understood to make a clear physical interpretation of the partition coefficient value experimentally observed (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) and shown in Eq. (16). Upon combining Eqs. ( 14)-(16) with Eqs. (3) and (5) we have (J) = 8.64 × 103z(A V ) C 1 ( n m o l / c m 2 / h )
(17)
for convectively dominated transdermal transport, and (J) = 2 . 4 × 10410.20 + 0.0001((ZA V)2)] C1 (nmol/cm:/h)
(18)
in the conditions (Eq. 4) of zero time-average convection. For voltages characteristic of electroporation (cf. Eq. (2)), the dispersive flux (Eq. 18) is much smaller in magnitude than the purely convective (i.e., electricfield drift) flux (Eq. 17). This explains our neglect of the diffusional contribution in Eq. (17). (Similarly, the diffusion contribution to the iontophoretic flux (Eq. 9) is also negligible in conventional iontophoretic conditions.)
216
D,A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221 103
3. R e s u l t s
Here we compare theoretical predictions and experimental data for both small and large electric field strengths.
10 2
f
/ 101
3.1. Small/1 13: lontophoresis 10 0
In the experiments of Prausnitz et al. [ 7 ], a continuous dc voltage was applied across human epidermis. In these conditions,
(ag) =ag.
rO
Calcein molecules (MW = 623, z = -4) were placed in the donor compartment of an in vitro diffusion-cell apparatus at a concentration of C1 = 1 mM. The transdermal flux of calcein was measured for 'small' transdermal voltages (/113<2 V). For iontophoretic transport through unaltered tissue, Eq. (9) yields ( J ) = 1.7 × 10-2/19 (/xg/cmZ/h),
i
10-2
(20)
A comparison of the experimental data with the theoretical estimates based upon Eqs. (19) and (20) is made in Fig. 1. The shunt-route (nonporated) prediction (Eq. 19) nearly matches the experimental data over most of the voltage range considered. In contrast, the porated (transcorneocyte) formula (Eq. 20) overpredicts the transport of calcein by several orders of magnitude. This suggests that the hair follicle/sweat duct route is the most likely pathway for charged calcein transport through the skin, at least for A 13< 1 V. The poor correspondence between the shunt-route prediction ( Eq. 19) and the experimental data at the largest voltages examined (i.e., 1.5 V), and, particularly, the nonlinear dependence of the experimental flux values versus voltage, might be explained by an increase in the number of shunt pathways accessible by the iontophoresed molecules with increasing voltage, as described by Scott et al. [35].
3.2. Large A 13: Electroporation Transdermal calcein flux values were measured in a second set of experiments [7] at significantly larger
1
/
t
• /0 10-3
10 -4
1
Experimental data ] Theory / Shunt / (iontophoresis) / Transcorneocyte / (electroporation) ] /
•
I 0.5
I 1.0
(19)
whereas for electrophoretic transport through porated tissue, Eq. (17) gives (,J) ~ 2.5 × 101A I? (/zg/cm2/h).
10 - I
I 1.5
I 2.0
2.5
Transdermal voltage drop (volts)
Fig. 1. Calcein flux magnitude versus transdermal voltage drop in conditions of typical skin iontophoresis.The experimentaldata of Prausnitz et al. [7] are comparedwith theoreticalpredictionsbased upon shunt-route (Eq. 19) and transcorneocyte(Eq. 20) formulas. pulsed voltages (40 V < A13<500 V) across human epidermis. The electric field pulses exponentially decayed with a time constant, r, of approximately 1 ms. One pulse was applied every T = 5 s for 1 h (corresponding to a duty cycle of 0.02%). In the present notation, these conditions correspond to (A 17')= 2 X 10-4A I,3. Eq. (9) adopts the form ( J ) = 3.4X 10
6Ar~
(/xg/cm2/h)
(21)
characterizing the flux of calcein associated with the shunt (nonporated) route of transport, whereas, Eq. (17) gives ( ] ) = 4 . 4 X 10 3AI? (/xg/cm2/h)
(22)
characterizing transport through electroporated skin (transcorneocyte route). Fig. 2 provides a comparison of the theoretical estimates (Eq. 21) and (22) with the experimental data. At the lowest voltages examined (ALP'< 100 V), the data fall between the predictions based upon the shunt (nonporated) formula (Eq. 21 ) and the porated (trans-
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221 102
101 _
to each molecule its respective hindrance coefficient via Eq. (12) (for Lucifer yellow, H i = 0 . 2 ( a = 0 . 7 8 nm) ; for the erythrosin derivative, H~ --~0.17 (a -- 0.90 n m ) ) , Eqs. (3), (10) and (16) may be combined to give
•
1o°-
/
/
~ /
~
•
4.4× 10-3Al? (calcein) (Y) =~l.6X 10-3AV (Lucifer yellow) (1.5X 10-3AV (erythrosin derivative)
Experimentaldata Theory
i0 -1 _ I / ~
I
-- -- - Shunt
"'=8 "~
217
I
(23)
(iontophoresis) ]
Transcorneocyte (electroporation)
10-2 _ •
10 -3 --Q / 10 .4
/ 0
I 100
I
I
I
200
300
400
500
Transdermalvoltage drop(volts) Fig. 2~ Calcein flux magnitude versus transdermal voltage drop in the (high electric field strength) conditions of skin electroporation. The experimental data of Prausnitz et al. [ 7 ] are compared with theoretical predictions based upon shunt-route ( E q . 21 ) a n d transcorneocyte ( E q . 2 2 ) formulas.
corneocyte) formula (Eq. 22). However, as A9 increases beyond 100 V, predictions based upon the porated-route formula (Eq. 22) match the experimental data. At the highest voltages, the transcorneocyte route underpredicts the experimental data. While this discrepancy may owe to many factors, as discussed in the following section, it may be significant that for transdermal voltages exceeding 100 V, irreversible damage to the skin was observed [7]. In general, however, the several-fold enhancement of charged molecule transport associated with the porated, transcorneocyte route of transport appears to offer evidence that pores were created in the intercellular bilayers and that a transcorneocyte (rather than an intercellular or shunt) route of transport is followed by the calcein molecules at the highest voltage drops shown in Fig. 2. Further support of transcorneocyte transport through bilayers at high electric field strengths is provided by the comparisons made in Fig. 3. This figure supplements the calcein data of Fig. 2 with experimental data (collected by Prausnitz et al. [7] under identical conditions) for Lucifer yellow (MW = 457, z = -2) and an erytbrosin derivative (MW = 1025, z = - 1 ). Attributing
characterizing the transport rates (/xg/cm2/h) for the three different molecules according to the porated route through the stratum corneum. Predictions based upon the above equations are shown with the experimental data in Fig. 3. The convergence of experimental and theoretical results as A f'increases above 100 V is consistent with the comparisons made between theory and experiment in Fig. 2.
3.3. Large A (1 (Alternating Polarity): Electroporation Recently (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and ionto102
10 !
[] []
,oO 10 -1
/ / -
~
~
~
~
N
eory T . . . . . . . . . . . yte (electroporation)
I \ ]
•
calceln
rn
Luciferyellow
~
, [ Erythrosinderivativ~
10-2
10 3
10.4
Experimentaldata [] [] •
Calcein Lucifer yellow
I I
ErythrosinderivativeJ
I 100
I 200
[ 300
I 400
500
Transdermalvoltage drop (volts) Fig. 3. Molecular flux magnitude for three different compounds versus transdermal voltage drop in the (high electric field strength) conditions of skin electroporation. The experimental data of Prausnitz et al. [7] are compared with theoretical predictions based upon the transcorneocyte formula ( E q . 2 3 ) .
218
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221 102
101
•
Experimentaldata Theory Transcorneocyte (electroporation)
100 10-1
10-2
10-3
10-4
[ 100
I 200
I 300
i 400
500
Transdermalvoltagedrop (volts) (alternating polarity) Fig. 4. Calcein flux magnitude versus (alternating) transdermal voltage drop in the (high electric field strength) conditions of skin electroporation. The experimental data of Prausnitz et al. (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication) are compared with theoretical predictions based upon the transcorneocyte formula (Eq. 24).
phoresis, submitted for publication), calcein flux was measured during skin electroporation due to electric field pulses, with r = 1 ms, T = 5 s, and Ct = 1 mM, but with the polarity alternating from one pulse to the next (Fig. 4); thus,
(24)
The first term in brackets identifies the contribution arising from the purely diffusive transport of calcein in the conditions of skin electroporation. This term is seen to be of order 10 -4/xg/cm2/h, the order of the sensitivity of the experimental measurements. The second term in brackets identifies a convective-dispersive contribution, quantifying the (oscillatory) convective enhancement of net solute 'diffusion'. This contribution remains even in an alternating electric field because it depends upon the square of the transdermal voltage. The physical origin of convective dispersion is further discussed in the following section. Predictions based upon Eq. (24) are shown in Fig. 4 together with the experimental data. Very good agreement is found between the experimental data and the theoretical predictions for A f ' > 100 V. This appears to be strong evidence both for the validity of a porated, transcorneocyte route of transport in the ~onditions of Eq. (2) and for the occurrenceofconvectivedispersion in the skin.
4. Discussion
The theoretical/experimental comparisons made in Figs. 1-4 strongly suggest that charged molecules follow different pathways through the stratum corneum below and above a transdermal voltage of approximately 100 V. At transdermal voltages significantly less than 100 V, transport of charged calcein appears to occur through nonporated skin via a shunt route (Fig. 1). However, for A f ' > 100 V, the comparisons made in Figs. 2-4 indicate that transport through porated intercellular bilayers and corneocytes is preferred, consistent with the known characteristics (cf. Eqs. (2) as well as Eq. (16) ) of lipid bilayer electroporation. Additional evidence for the electroporation of stratum corneum bilayers can be offered on the basis of the electrical properties of skin. It has been found [22,35,39] that the specific electrical resistance of the skin exhibits a steady-state value of approximately 1000-10 000 g2.cm 2 following application of a lowstrength electric field for about 1 h. In the high-strength conditions of Eq. (2), the skin's electrical resistance can diminish up to three orders of magnitude, to a value of approximately 10-100 ~ . cm 2 ( [ 38 ] and U. Pliquett and J.C. Weaver, The change in the passive electrical properties of human stratum corneum due to electro-
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
poration, submitted for publication) . This drop in resistance is found to be consistent with the current analysis. Thus, the electrical resistance of unaltered skin has been estimated as [ 19] fi ~- 4000/2. c m 2,
( 25 )
with ions transporting through intercellular and shunt routes. As previously (cf. Eq. (10)), if we assume q~ = 10- 3 for the stratum comeum area fraction accessible to ion transfer in electroporation conditions, a value that has been experimentally observed (M.R. Prausnitz et al., Transdermal transport efficiency during skin electroporation and iontophoresis, submitted for publication), it follows that the transport of ions through electropores and comeocytes causes a reduction of the skin's electrical resistance to approximately (cf. Eq. (31b) of Ref. [19]) f i = 6 ~ - c m 2.
(26)
This latter result is substantially lower than the experimental skin resistance data ( [38] and U. Pliquett and J.C. Weaver, The change in the passive electrical properties of human stratum corneum due to electroporation, submitted) at high electric field strengths. A potential explanation for this underprediction is that the result (Eq. 26) does not include the effect of (small) electrode area on measured skin resistances. However, the predicted diminution of skin resistance by several orders of magnitude appears to lend further support to a transcorneocyte route of transport in skin electroporation circumstances. The results of this study indicate that multiple lipid bilayers within the stratum corneum electroporate at conditions similar to those for which electroporation has been observed or predicted in single bilayer systems [ 10-15]. As in single bilayer systems, whether planar or spherical, electroporation of skin appears to give rise to a dramatic enhancement of transbilayer molecular flux, leading to pathways for molecular transport through the aqueous channels of the comeocytes. The successful description of key features of electric field-mediated transdermal transport, based upon the physical characteristics of the stratum corneum and the transporting molecules, constitutes an essential step toward understanding the mechanisms of transport and optimizing experimental protocols. However, the physical and geometrical complexity of the stratum cor-
219
neum, including its possible dependence upon applied (e.g., electric) fields, limits the scope of conclusions that may be drawn via each set of theoretical predictions until a broad range of experimental observations have been confirmed. In the current study, experimental flux data at relatively low transdermal voltages ( < 1 V) have been fairly well predicted (Fig. 1) on the basis of a shunt route of charged-molecule transport. Yet, the observed nonlinear dependence of molecular flux upon voltage is not predicted by the current theory. This may reflect the creation of new transport pathways through the skin with increasing applied voltage (as observed in Ref. [35] ). Nonlinear electrical properties of skin above 1 V are well documented (see, e.g., Refs. [22,35,37] ). Experimental transdermal flux values have been found (Fig. 2) to be approximated by theoretical predictions based upon an electroporated, transcomeocyte route of transport through the stratum corneum. However, the strong nonlinearities exhibited by the data over the entire range of voltages shown in Fig. 2 suggest a significant dependence of electropore area fraction upon voltage (a dependence not accounted for here), and perhaps irreversible skin damage at the very highest voltages. Moreover, Eqs. (10) and ( 11 ), which describe the transcorneocyte route of transport, apply to circumstances where transport across the intercellular lipids occurs relatively fast in comparison to transport across the corneocytes. It may occur, however, that at the intermediate voltages shown in Fig. 2, significant hindrance of transport across the intercellular lipids occurs, requiring modification of Eqs. (10) and (11). Other approximations made in the theory, such as the idealization of circular cylindrical aqueous pores within corneocytes, may give rise to significant errors in conditions other than have been examined here. For example, very large molecules (i.e., a > 1.8 nm), may potentially transport across corneocytes during electroporation. However, our assumption of a uniform pore size in the corneocytes (see following Eq. (13) ) would wrongly preclude this possibility because it does not account for the heterogeneous distribution of aqueous pathway dimensions within corneocytes. One of the striking features of skin electroporation is the observation (Fig. 4) that a dramatic enhancement of charged species is possible even in the absence of a net transdermal voltage. This has been explained here
220
D.A. Edwards et al. / Journal of Controlled Release 34 (1995) 211-221
by the convective dispersion of charged molecules within corneocytes-a phenomenon that appears not to have been discussed previously in the context of transdermal transport. Convective dispersion resulting from oscillating flow conditions has been observed in numerous practical capillary and porous media problems [28], such as human lungs (i.e., high-frequency ventilation schemes) [32], abdominal cavities [33] and river estuaries [ 31 ]. Physically, these phenomena occur because solute molecules instantaneously transport through porous media at significantly different rates depending upon their individual 'local' trajectories through the medium. In the case of skin, a charged molecule may transport (under the action of an oscillatory electric field) predominantly along the centerline through aqueous channels of the corneocytes, avoiding contact with keratin fibers, and thereby maximizing its speed through the skin. However, diffusion may cause another molecule to follow a trajectory that frequently brings it into contact with keratin fibers, so that it moves much more slowly through the skin than the 'centerline' molecule. On average, all molecules will move with a mean speed through the skin. In the case of oscillatory flow, this mean speed may even be zero. However, the dispersion - or spatial spread - of the solute molecules about this mean speed will be significantly enhanced (over that enhancement which normal molecular diffusion provides) owing to the interaction between convection and diffusion.
Acknowledgements This work has been supported in part by the National Institutes of Health Grants GM448884 (D.A.E. and R.L. ) and GM34077 ( J.C.W. ), by Cygnus Therapeutic Systems (M.R.P. and J.C.W.) and by the Army Research Office Grant DAAL03-90-G-0218 (J.C.W.), The authors are grateful for several helpful discussions with Mark E. Johnson and Russell O. Potts.
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[2] R.L. Bronaugh and H.I. Maibach, (Eds.), Percutaneous Absorption, Mechanisms-Methodology-Drug Delivery. Marcel Dekker, New York, 1989, [ 3 ] J. Hadgraft and R.H, Guy, (Eds.), Transdermal Drug Delivery: Developmental Issues and Research Initiatives. Marcel Dekker, New York, 1989. [4] J.A. Bouwstra, M.A. de Vries, G.S. Gooris, W. Bras, J, Brussee and M. Ponec, Thermodynamic and structural aspects of the skin barrier. J. Control. Release 15 ( 1991 ) 209-220. [5] P.M. Elias, Epic)ermal barrier function: intercellular lamellar lipid structures, origin, composition and metabolism. J. Control. Release 15 ( 1991 ) 199-208. [6] M.R. Prausnitz, V.G. Bose, R. Langer and J.C. Weaver, Transdermal drug delivery by electroporation. Proc. Int. Symp. Control. Release Bioact. Mater. 19 (1992) 232-233. [7] M.R. Prausnitz, V.G. Bose, R. Langer and J.C. Weaver, Electroporation of mammalian skin: A mechanism to enhance transdermal drug delivery. Proc. Natl. Acad. Sci. USA 90 (1993) 10504-10508. [8] D. Bommannan, L. Leung, J. Tamada, J. Sharifi, W. Abraham and R. Potts, Transdermal delivery of luteinizing hormone releasing hormone: comparison between electroporation and iontophoresis in vitro. Proceed. Intern. Symp. Control Rel. Bioact. Mater. 20 (1993) 97-98. [ 9 ] C. Cullander and R.H. Guy, Transdermal delivery of peptides and proteins. Adv. Drug Deliv. Rev. 8 (1992) 291-329. [10]E. Neumann, A.E. Sowers and C.A. Jordan (Eds.), Electroporation and Electrofusion in Cell Biology. Plenum Press, New York, 1989. [ 11 ] D.C. Chang, B.M. Chassy, J.A, Saunders and A.E. Sowers, ( Eds. ), Guide to Electroporation and Electrofusion. Academic Press, New York, 1992. [12] J.C. Weaver, Electroporation: A general phenomenon for manipulating cells and tissues. J. Cell. Biochem. 51 (1993) 426-435. [13] I.G. Abidor, V.B. Arakelyan, L.V. Chernomordik, Y.A. Chizmadzhev, V.F. Pastushenko and M.R. Tarasevich, Electric breakdown of bilayer membranes, I. The main experimental facts and their qualitative discussion. Bioelectrochem. Bioenerget. 6 (1979) 37-52. [ 14] J.C. Weaver and A. Barnett, Progress towards a theoretical model for electroporation mechanism: membrane electrical behavior and molecular transport, in: D.C. Chang, B.M. Chassy, J.A. Saunders and A.E. Sowers, (Eds.), Guide to Electroporation and Electrofusion, Academic Press, New York, 1992, pp. 91-118. [15] S.A. Freeman, M.A. Wang and J.C. Weaver, Theory of electroporation of planar bilayer membranes: Predictions of the aqeuous area, change in capacitance and pore-pore separation. Biophys. J. (1994) in press. [ 16] M. Okino and J.H. Mohri, Effects of a high voltage electrical impulse and an anticancer drug on in vivo growing tumors. Jpn. J. Cancer Res. 78 (1987) 1319-1321. [17] L.M. Mir, S. Orlowski, J. Belehradek and C. Paoletti, Electrochemotherapy: potentiation of antitumor effect of bleomycin by local electric pulses. Eur. J. Cancer 27 ( 1991 ) 68-72.
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[30] R.C. Reid, J.M. Prausnitz and T.K. Sherwood, The Properties of Gases and Liquids. 3rd ed., McGraw-Hill, New York, 1977. [31] H.B. Fisher, E.J. List, R.C.Y. Koh, J. Imberger and N.H. Brooks, Mixing in Inland and Coastal Waters. Academic Press, New York, 1979. [32] Y.C.B. Fung and S.S. Sabin. Mechanics of pulmonary circulation, in: Cardiovascular Flow Dynamics and Measurements N.H.C. Hwang and N.A. Norman (Eds.), pp. 665-730. University Park Press, Baltimore, 1977. [33] J. Rudoy, R. Kohan and J. Ben-Ari, Externally applied abdominal vibration as a mthod for improving efficiency in peritoneal dialysis. Nephron 46 (1987) 364-366. [ 34 ] A. Rougier, C. Lotte, P. Corcuff and H.I. Maibach, Relationship between skin permeability and corneocyte size according to anatomic site, age, and sex in man. J. Soc. Cosmet. Chem. 39 (1988) 15-26. [35] E.R. Scott, A.I. Laplaza, H.S. White and J. Phillips, Transport of ionic species in skin: contribution of pores to the overall skin conductance. Pharm. Res. 10 (1993) 1699-1709. [36] G.M. Mavrovouniotis and H. Brenner, Hindered sedimentation, diffusion and dispersion coefficients for Brownian spheres in cylindrical pores. J. Colloid Interface Sci. 124 (1988) 269-283. [37] W.G.S. Stephens, The current-voltage relationship in human skin. Med. Electron. Biol. Eng. 1 (1963) 389-399, [38] V.G. Bose, Electrical characterization of electroporation of human stratum corneum. MS thesis, Massachusetts Institute of Technology, 1994. [39] H. Inada, H.A.-H. Graham and W.I. Higuchi. Studies on the effects of applied voltage and duration on human epidermal membrane alteration/recovery and the resultant effects upon iontophoresis. Pharm. Res. 11 (1994), 687-697.