An analysis of solute structure–human epidermal transport relationships in epidermal iontophoresis using the ionic mobility: pore model

Journal of Controlled Release 58 (1999) 323–333

An analysis of solute structure–human epidermal transport relationships in epidermal iontophoresis using the ionic mobility: pore model Pamela M. Lai, Michael S. Roberts* Department of Medicine, University of Queensland, Princess Alexandra Hospital, Brisbane, Queensland 4102, Australia Received 9 March 1998; accepted 22 September 1998

Abstract This study sought to examine the extent the ionic mobility–pore model, used to describe epidermal iontophoretic structure–permeability relationships, could describe a range of published iontophoretic data. The model incorporates, as determinants of iontophoretic transport, solute size, solute mobility, total current applied, presence of extraneous ions, determined by conductivities of both donor and receptor solutions, permselectivity of the epidermis, as well as a solute pore interaction term which together provided an excellent regression for iontophoretic permeability. The ‘pore’ radii for solute ˚ depending on the transport estimated from literature iontophoretic permeabilities using the model ranged from 6.8 to 17 A degree of hydration and conformation of solute assumed. The pore size range is consistent with transport through the polar intercellular and transappendageal pathway for transport. The pore restriction form of the model better describes the data obtained to date than other models described previously (Yoshida, N.H., Roberts, M.S., Solute molecular size and transdermal iontophoresis across excised human skin. J. Control. Release 25 (1993) 177–195).  1999 Elsevier Science B.V. All rights reserved. Keywords: Iontophoresis; Ionic mobility; Pore model; Hydration; Free volume

1. Introduction The potential of iontophoresis as a generalised transdermal drug delivery system is increasing with a better understanding of the mechanisms for iontophoretic transport. A number of models have been developed to predict iontophoretic solute flux [1–3]. The work to date suggests that ion composition, solute size and charge are all important factors.

*Corresponding author. Tel.: 161-7-32402546; fax: 161-732405806; e-mail: [email protected]

However, no single model has integrated all of the determinants of iontophoretic transport. In our initial attempt at creating a theoretical formula for an iontophoretic model, we made a number of assumptions, including: (i) a competitive ion model for ionic transport in solution under an electrical potential difference applies to iontophoresis of ions across the skin; (ii) the relative contribution of the anion and cation transport numbers in the iontophoretic process are fixed; and (iii) the ionic mobility of a given solute is identical to that of other co-ions [1]. The importance of competition between ions in the iontophoretic donor and receptor solutions

0168-3659 / 99 / $ – see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S0168-3659( 98 )00172-2

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was further examined by Phipps and Gyory [2], where a ‘binary mixture’ model based on Faraday’s law, Ohm’s law and the electroneutrality condition was used to predict the iontophoretic flux of an ion in a simple solution. The model was useful in predicting drug ion flux through a homogeneous non-ionic membrane in the presence of one type of co-ions and counter-ions. Given the complexity of the ion interactions and difficulty in predicting the effects of these interactions, we proposed the use of solution conductivity as a means of predicting the effects of solution composition on iontophoretic flux [4,5]. We also reported that the logarithm of the iontophoretic permeability coefficient could be related to solute molecular weight. This size determination of iontophoretic transport was then expressed in terms of ‘free volume’ and ‘pore-restriction’ models of iontophoretic transport [3]. There are a range of other factors to be considered in iontophoretic transport including the Nernst layer [6], interaction with the pore wall [7], permselectivity [8], charge of solute [9] and convective flux [10]. Recently, we have described an ionic mobility–pore model which integrates solute size, solution composition and other variables as determinants of iontophoretic transport [11]. The overall determinants described in the model were ion mobility, fraction of the solute ionized, total current applied, epidermal permselectivity, solute size, conductivity of both the donor and receptor compartments and a partitioning term for interaction of the solute with the pore walls [11]. We showed that this model adequately described the iontophoretic transport of a series of local anesthetics [12]. However, the extent to which this model can be applied to other solutes has not yet been examined. We therefore attempted to apply this model to describe the available published iontophoretic data for small cations, anions and uncharged solutes, as well as macromolecules.

PCj,iont,overall 2mj fi j Fz j IT V PRT j 5 ]]]]]]]]]]6(1 2 sj )nm (k s,a 1 k s,c )[1 1 fu juju 1 (1 2 fu j )uji ] (1) where mj is the ionic mobility of the solute, fi j and fu j is the fraction of the solute ionized and unionized, respectively, F is Faraday’s constant, z j is the charge of the solute, IT is the current, k s,a and k s,c is the conductivity of the solution in the anodal and cathodal chamber, respectively, uju and uji is a function of the interfacial clearance of the solute and other factors of unionized and ionized solutes, respectively, V is the permselectivity factor, PRT j is the pathway restriction term, sj is the reflection coefficient and is related to the electroosmotic component of iontophoretic transport, and nm is the velocity of flow across the membrane.

3. Membrane pathway restriction of iontophoretic transport. Fig. 1 shows the two forms of the pathway restriction term examined in this work, the free volume model and the pore–restriction model, together with modifications, as described later for macromolecules and partitioning into the pore wall. In the free volume model, the pathway restriction term (PRT j ) is defined by the negative exponent of the ratio of the solute molecular volume MV to an effective average ‘cage’ volume (V iav ) [11]:

S

MV PRT j 5 exp 2 ] V iav

D

The free volume form of the model can also be expressed in logarithmic form and MV can be approximated by MW [13]: log PCiont 5 A 1 B log mj 2 C MW

2. Theoretical considerations We recently derived a model to describe the overall iontophoretic permeability coefficient (PCj,iont,overall ) of a solute j during epidermal iontophoresis [11]:

(2)

(3)

where A is a constant defined by total current, epidermal cation permselectivity and solution conductivity, B is a correction factor associated with the use of deionized distilled water and conductivity for estimation of mobility (value should theoretically be unity) and C is the reciprocal of the average molecu-

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325

Fig. 1. Three submodels of the ionic mobility–pore model. (i) Free volume submodel, (ii) pore restriction submodel, and (iii) transport of macromolecules submodel.

lar weight associated with iontophoretic transport through a ‘free volume’ determined restricted pathway in the epidermis. In the pore–restriction form of the model, we defined PRT j terms of lj , the ratio of solute radius and pore radius, using either the approximate (Eq. (4)), or the full expression (Eq. (5)) [11]: PRT j 5 (1 2 lj )2 (1 2 2.10lj 1 2.09l 3j 2 0.95l 5j ) (4) for 0# lj ,0.4, or

4. Convective flow Electroosmotic flow is defined as the bulk fluid flow which occurs when a potential difference is applied across a charged membrane [10]. Whilst iontophoretic transport is dominant for small charged solutes, convective flow or electroosmotic flow is likely to be more significant for macromolecules [10]. For the free volume form of the model, (12 sj ) is also expressed as exp(2MV/V sav ). It is most likely i that V sav differs from that for iontophoresis V av [11]. The corresponding expressions for (12 sj ) for the pore restriction form of the model are [11]:

PRT j 5

2

6p (1 2 lj )2 ]]]]]]]]]]]]] 2 4

F O

3.18p 2 (1 2 lj )25 / 2 1 1

n51

an (1 2 lj )n

GO 1

(5) for 0# lj ,1, where the coefficients are a 1 5 21.22, a 2 51.53, a 3 5 222.51, a 4 5 25.61, a 5 5 20.34, a 6 5 21.22 and a 7 51.65. Roberts et al. [11] have developed PRT j further to include, (i) the shape of the solutes, and (ii) solute and membrane charge effects.

2

2 0.163l 3j )

an13 ( lj )n

n50

2

1 2 sj 5 (1 2 lj ) s2 2 (1 2 lj ) d(1 2 0.667l j

(6)

for 0# lj ,0.4 and 1 2 sj 5 (1 2 lj )2 f 2 2 (1 2 lj )2 g

S

3.18p 2 (1 2 lj )25 / 2

F

O b (1 2 l ) G 1 O b 2

11

4

n

n

j

n51

n50

D

n n13 l j

]]]]]]]]]]]]]]

S

2

3.18p 2 (1 2 lj )25 / 2

F

O a (1 2 l ) G 1 O a 2

11

4

n

n

n51

j

n50

D

n n13 l j

(7)

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326

for 0# lj ,1, where b 1 50.12, b 2 5 20.04, b 3 54.02, b 4 5 23.97, b 5 5 21.92, b 6 54.39, b 7 55.01.

d k5] G a

4.1. Membrane and solute charge effects on transport.

where d is the distance between the electrodes and a is the area of the electrodes, d /a corresponds to the cell constant and G is the conductivity in reciprocal ohms. The units of specific conductance is S (siemens) per cm. The specific conductance of deionised distilled water was 0.70–0.95 m S / cm. The apparent mobility of each ion in solution mj is then estimated from the specific conductance, the solute concentration used in the determination of the conductivity, z j and Faraday’s constant (9.648310 4 C / mol), using the following equation:

The pathway restriction term will be influenced by the charge of the solute itself, through electrostatic and dispersion forces. The effect of a Debye layer l D associated with charged surfaces on the effective radius of the moving charged solute to effective pore radius l *j can be defined by [14]: rj 1 lD l j* 5 ]] rp 2 lD

(8)

where l D is defined by: ]]]] e kT l D 5 ]]]] 2 2 8p z s e NA Cs

œ

(9)

where e is the solution dielectric constant, k is Boltzman’s constant, T is the absolute temperature, z s is the charge of the supporting solute, e is the fundamental charge of a proton, NA is Avogadro’s number, and Cs is the concentration of the supporting solute. Deen and Smith [15] have described a more complex model for the effect of the Debye layer on pore transport.

5. Materials and methods

5.1. Materials All compounds (benzoic acid (sodium salt), spiperone, HEPES (N-2-hydroxyethylpiperazine-N92-ethanesulphonic acid), phenylethylamine, indomethacin, salicylic acid, lidocaine HCl, diclofenac and naproxen) were purchased from Sigma. All solutions were prepared with deionised distilled water and adjusted to the appropriate pH with 1 M HCl or 1 M NaOH. The specific conductance of solutions was measured using a conductivity meter (Radiometer, Copenhagen, model CDM80). Specific conductance was measured by direct reading of the conductivity meter and given by:

k jw mj 5 ]] c j Fz j

(10)

(11)

5.2. Analysis of cations, anions and uncharged solutes Data was obtained from Yoshida and Roberts [3], Phipps et al. [9] and Sage et al. [16]. Ionic mobilities of each solute were calculated from conductivity using Eq. (11) or obtained from Hanai [17]. Tables 1–3 lists the solutes used in this study.

5.3. Solute size estimation The effective solute size was estimated from the radius of the solute based on MV and MW with corrections for the water of hydration of each solute and the presence of a Debye layer. MV of the solutes was derived from partial molal volumes of the fragments comprising the solute [18]. The radius r j , was estimated assuming the solutes to be spherical: ]]]] 3MV (or MW) r j 5 3 ]]]] (12) 4p NA

œ

The extent of hydration is based on data by Pau et al. [19] and references therein. The Debye layer thickness was estimated using Eq. (9).

5.4. Data analysis Minitab statistical software (Minitab Inc., PA) was used to perform stepwise regressions on various data sets. Nonlinear regressions were undertaken using

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327

Table 1 Cationic solutes iontophoretic and physicochemical data Solute

MW (Da)

Sodium

23

Phenylethylamine Lidocaine Propranolol Spiperone Magnesium Potassium Calcium Lithium

121 234 259 395 24.3 39.1 40.1 6.9

MV (cm 3 / mol)

PCj,iont (cm / h)

IT (mA / cm 2 )

Solute mobility (cm 2 / V/ s)

Donor conductivity (mS / cm)b

Receptor conductivity (mS / cm)b

Reference

25.7 a 88.06 c 117 218 235 318 592.4 c 27.8 c 418.4 c 192.2 c

0.178 0.0039 0.09 0.08 0.063 0.034 0.00157 0.0037 0.0017 0.0034

0.38 0.25 0.38 0.38 0.38 0.38 0.25 0.25 0.25 0.25

0.000519

1.3 50.1 1.3 1.3 1.3 1.3 106.1 73.5 119.1 38.7

12.2 12.0 12.2 12.2 12.2 12.2 12.0 12.0 12.0 12.0

[3] [9] [3] [3] [3] [3] [9] [9] [9] [9]

0.001 b 0.000801 b 0.001077 b 0.000028 b 0.00055 0.00076 0.00062 0.00040

a

Data from Yalkowsky and Zografi [18]. Measured from this work. c Hydrated MV data from Pau et al. [19]. d Data from Hanai [17]. b

Table 2 Anionic solutes iontophoretic and physicochemical data Solute

MW (Da)

MV (cm 3 / mol)

PCj,iont (cm / h)

IT (mA / cm 2 )

Solute mobility (cm 2 / V/ s)

Donor conductivity (mS / cm)b

Receptor conductivity (mS / cm)b

Reference

Chloride Salicylate Naproxen Diclofenac Indomethacin

36 138 230 295 357

22 c 105 196 201 270

0.08 0.04 0.02 0.014 0.012

0.38 0.38 0.38 0.38 0.38

0.000791 a 0.002280 b 0.000135 b 0.000500 b 0.000048 b

1.3 1.3 1.3 1.3 1.3

12.2 12.2 12.2 12.2 12.2

[3] [3] [3] [3] [3]

a

Data from Hanai [17]. Measured from this work. c Data from Mukerjee [28]. b

Table 3 Uncharged solutes iontophoretic and physicochemical data Solute

MW (Da)

MV (cm 3 / mol)

PCj,iont (cm / h)

IT (mA / cm 2 )

Donor conductivity (mS / cm)b

Receptor conductivity (mS / cm)b

Reference

Water Phenol 5-Fluorouracil Glucose Antipyrine Sucrose Progesterone Hydrocortisone Sulphated insulin Peptide 2 analog Peptide 1 Peptide 3 Peptide 4

18 94 130 180 188 342 314 362 5600 3800 3500 1000 1000

12 72 84 114 147 204 270 338

0.028 0.019 0.014 0.009 0.009 0.004 0.006 0.003 0.00097 0.00030 0.00014 0.00041 0.00030

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.20 0.20 0.20 0.20 0.20

1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 14.8 14.8 14.8 14.8 14.8

12.2 12.2 12.2 12.2 12.2 12.2 12.2 12.2 n/a n/a n/a n/a n/a

[3] [3] [3] [3] [3] [3] [3] [3] [16] [16] [16] [16] [16]

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328

Minim 3.0.9 [20]. The data was weighted 1 /y obs , consistent with the variance of associated with radiolabeled solutes used in the majority of the data studied. Regression lines for the pore restriction form of the model (in which Eq. (5) were substituted into Eq. (1)) and free volume models were simulated for the case when ionic mobilities were assumed to be constant. For simplicity of modelling, uji is assumed is to be very small. The model of Davidson and Deen [21] (Table 2, a 510) was applied in the analysis of macromolecule data from Sage et al. [16]. A nonlinear least squares fit of a fifth-order polynomial was used to estimate (12 sj ), and the data of Sage et al. [16] was fitted to the equation.

6. Results and discussion

6.1. Iontophoresis of charged solutes Fig. 2 shows the cation data from Yoshida and Roberts [3] plotted as a function of solute MV and MW. Also shown in this figure are the predicted data obtained for the pore–restriction and free volume forms of the together with predictions for these models, when the ion mobilities were assumed to be constant. The regressions obtained for the pore restriction form of the model were: 35.9mj fi j z j PRT j PCj,iont 5 ]]]]]]]60.38(1 2 sj ) (k s,d 1 k s,r )(1 2 233.3fu j ) (r 2 5 0.97, n 5 5)

(13)

for calculations based on MV, where PRT j is defined ˚ and (12 sj ) by Eq. (5) in which r p (5 lj r j ) is 7.22 A is given by Eq. (7), and 49.5mj fi j z j PRT j PCj,iont 5 ]]]]]]]60.46(1 2 sj ) (k s,d 1 k s,r )(1 2 29.2fu j ) 2

(r 5 0.99, n 5 5)

Fig. 2. (A) Iontophoretic permeability coefficient (PCj,iont ) of cations versus MV. (B) Iontophoretic permeability coefficient (PCj,iont ) of cations versus MW (data from Ref. [3]). Solid line represents the ionic mobility–pore model when mobilities are assumed to be constant; the dotted line represents the free volume form of the model, (h) is the pore restriction form of the model with ionic mobility taken into account and (d) is the measured PCj,iont .

log PCj,iont 5 2 0.45 2 0.0025MV 1 0.02 log mi

(r 2 5 0.87, n 5 5) (15)

(14)

for calculations based on MW, where PRT j is defined ˚ The corresponding expressions for by a r p of 7.28 A. the free volume form of the model using MV and MW of the solute as variables are:

log PCj,iont 5 2 0.65 2 0.0018MW 1 0.01 log mi

(r 2 5 0.95, n 5 5) (16)

Fig. 3 shows the corresponding anion data from

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329

˚ for where PRT j is defined by a r p of 6.18 A calculations based on MV and 11.2mj fi j z j PRT j PCj,iont 5 ]]]]]]]60.15(1 2 sj ) (k s,d 1 k s,r )(1 1 2.1fu j ) (r 2 5 0.99, n 5 5)

(18)

˚ for where PRT j is defined by a r p of 6.90 A calculations based on MW. The corresponding expression for the free volume form of the model are: log PCj,iont 5 2 1.29 2 0.0040MV 1 0.099 log mi

(r 2 5 0.97, n 5 5) (19)

logPCj,iont 5 2 1.03 2 0.0028MW 1 0.038 log mi

2

(r 5 0.98, n 5 5) (20)

6.2. Iontophoresis of uncharged solutes For small uncharged solutes, the main mechanism of penetration through the membrane is by convective flow [10,11]. Fig. 4 shows the regressions of the two forms of the model, applied to the data of Yoshida and Roberts [3]. The regressions were: PCj,iont 5 0.037(1 2 sj ) Fig. 3. (A) Iontophoretic permeability coefficient (PCj,iont ) of anions versus MV. (B) Iontophoretic permeability coefficient (PCj,iont ) of anions versus MW (data from Ref. [3]). Solid line represents the ionic mobility–pore model when mobilities are assumed to be constant, the dotted line represents the free volume form of the model, (h) is the pore restriction from of the model with ionic mobility taken into account and (d) is the measured PCj,iont .

(r 2 5 0.96, n 5 8)

(21)

where (12 sj ) is given by Eq. (7) and is defined by a ˚ for calculations based on MV, and r p of is 6.97 A PCj,iont 5 0.038(1 2 sj )

(r 2 5 0.97, n 5 8)

(22)

for calculations based on MW and (12 sj ) is defined ˚ The corresponding expression for by a r p of 7.53 A. the free volume form of the model are: log PCj,iont 5 2 1.54

Yoshida and Roberts [3] plotted as a function of solute MV and MW, with predictions based on the pore–restriction and free volume forms of the model for variable and constant ion mobilities. The regressions obtained for the pore restriction form of the model were: 14.6mj fi j z j PRT j PCj,iont 5 ]]]]]]]60.18(1 2 sj ) (k s,d 1 k s,r )(1 1 4.0fu j ) (r 2 5 0.99, n 5 5)

2 0.0027MV

2

(r 5 0.91, n 5 5) (23)

log PCj,iont 5 2 1.48 2 0.004MW

(r 2 5 0.97, n 5 5) (24)

(17)

When Yoshida and Roberts [3] applied the same data to their model, they obtained an r 2 of 0.832 for the

330

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equivalent size, and water can flow through these macromolecules. The main mechanism of transport of macromolecules is by convective flow. In analysing the data of Sage et al. [16], a pore size of ˚ (n55, r 2 50.71) was estimated. This 17.0061.11 A ˚ estimated by Ruddy and Hadzija compares 18 A [22], in the analysis of their macromolecules.

6.4. Mobility of solutes

Fig. 4. (A) Iontophoretic permeability coefficient (PCj,iont ) of uncharged solutes versus MV. (B) Iontophoretic permeability coefficient (PCj,iont ) of uncharged solutes versus MW (data from Ref. [3]). Solid line represents the ionic mobility–pore model when mobilities are assumed to be constant; the dotted line represents the free volume form of the model and (d) is the measured PCj,iont .

pore–restriction form and 0.934 for the free volume form of the model for cations, 0.901 and 0.943 for the pore–restriction form and free volume form for anions and 0.92 and 0.896 for uncharged solutes. Clearly, the inclusion of the additional terms have improved the regression of the data.

6.3. Iontophoresis of macromolecules As noted by several authors [11,21,22], macromolecules are porous bodies, with their Stokes– Einstein radius smaller than a solid sphere solute of

As stated in Eq. (11) and shown in our previous work [11,12], ionic mobility of a solute is dependent on a number of factors, including concentration, interactions between the ions, interactions between the ions and solvent molecules, size of the solute, and polarity of the solvent, polarity of the solute, solvation of the solute, presence of hydrogen bonding, viscosity of the solvent and temperature. In our previous work [1], when ionic mobilities were unavailable, it was assumed that ionic mobilities for solutes were identical. However, later work [11] showed the importance of ionic mobilities in the prediction of PCiont for a group of similar compounds, such as local anesthetics. In this work, values of ionic mobility were either from direct measurements [17], or from conductivity measurements. One disadvantage of using conductivity as measurement of ionic mobility is that conductivity measures the movement of all ions (cations and anions) in the solution. However, our previous work [12] has shown that conductivity provides a good estimate of ionic mobility. The inclusion of ionic mobility in the present analysis significantly improved the regressions, relative to size alone, for both the cation and anion data in each forms of the model used (pore restriction and free volume).

6.5. Comparison of pore sizes From analysis of cations, anions and uncharged solutes, the pore size estimated by the pore restric˚ based on tion form of the model were 6.7960.44 A, ˚ MV calculations, and 7.2460.26 A, base on MW calculations. When the Debye layer was taken into consideration for the iontophoresis of charged solutes (anions and cations), the pore size was calculated to

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˚ This compares with 10 A, ˚ be from 8 to 10 A. ˚ estimated in our previous study [12], 8 A by Yoshida ˚ by Dinh et al. [6], 30 A ˚ by and Roberts [3], 25 A ˚ Yoshida and Roberts [13] and 18 A by Ruddy and Hadzija [22].

6.6. Ion hydration and solute transport The pore size estimated in this study and in our previous study [3,12] is comparable to that of other studies. As Yoshida and Roberts [3] noted in their analysis, one dilemma in using any model was the use of an appropriate definition of molecular size. In Figs. 2–4, hydrated ion radii, or ion with its hydration shell were used in the calculations of the pore radius. Fig. 5 shows that when solvated solute radii data from Pau et al. [19] were used with the iontophoretic pig epithelial data from Phipps et al. [9], a larger ˚ was obtained compared to pore radius (9.060.5 A) when an unhydrated solute size was assumed. Pau et al. [19] have shown that most monovalent cationic and anionic solutes above a MW of 135 tend to two water molecules for hydration. Regressions ignoring this hydration result in pore sizes for anions, cations and uncharged solutes of 8.7, 6.9 and

331

˚ respectively. Removal of the Debye layer 6.5 A, thickness did not greatly affect ‘pore’ size estimates.

6.7. Cation permselectivity The isoelectric point of human skin is between 3 and 4 [23]. At physiological pH, the stratum corneum is permselective to cations, due to the amino acid residues of proteins found on the membrane. From analysis of the ‘A’ constant in each equation, the permselectivity ratio of cation to anion was 0.54:0.46, which is similar to that of 0.6:0.4 reported by Burnette and Ongpipattanakul [8].

6.8. Other factors 6.8.1. Charge In the work of Phipps et al. [9], it was shown that solutes with a divalent charge had only approximately half the delivery efficiency of monovalent solutes, despite having similar molecular weight, e.g. sodium (MW 23.0) has a delivery efficiency of 42.563.1% compared with magnesium (MW 24.3) which has a delivery efficiency of 16.861.3%. According to Phipps et al. [9], this suggests that the divalent ions interact more strongly with charged sites in the skin than monovalent ions. It is well known that, in some instances, divalent metal ions can bind more tightly to proteins than monovalent ions [24]. Fig. 5 suggests that the difference in the transport of monovalent ions and divalent ions may be better explained by size (hydrated molecular volume of the ions) considerations than by charge interactions. 6.8.2. Current PCj,iont,overall has been shown by several studies to be proportional to the total current, as defined in Eq. (1) [1,9,13,25–27].

Fig. 5. Iontophoretic permeability coefficient (PCj,iont ) of inorganic ions (data from Ref. [9]) versus MV of hydrated ion (d), and MV on unhydrated ion (m) (data from Ref. [19]). Also shown are the regression lines obtained for the pore restriction (solid line) and free volume (dotted line) forms with (h) constant ionic mobility and predicted PCj,iont based on the two forms of the model.

6.8.3. Conductivity of solutions It has previously been demonstrated that the conductivity of donor solution and receptor solution has an effect on iontophoretic transport [4,5,11]. Yoshida and Roberts [4,5] have shown differing solute concentrations, pHs, and buffer concentrations have an effect on the conductivities of the donor and receptor solutions, and hence affect the iontophoretic transport. Differences in solution conductivities used

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in several studies precluded a comparison of all PCiont data reported in some studies with the data in this work.

[6]

[7]

7. Conclusion [8]

In this work, we attempted to apply the ionic mobility–pore model [11] using a range of data from published studies. This model incorporates solute size, solute mobility, total current applied, presence of extraneous ions and epidermal permselectivity as determinants of iontophoretic flux. The inclusion of these additional factors in the model resulted in improved regressions relative to our earlier work based on size alone [3]. The pore radius estimated from analysis of cations, anions and uncharged ˚ A permselectivity solutes ranged from 6.8 to 17 A. of the skin was estimated to be 0.54:0.46 (cations / anions).

[9]

[10] [11]

[12]

[13]

[14]

Acknowledgements The authors wish to acknowledge the financial support of the National Health and Medical Research Council of Australia, the Princess Alexandra Hospital Foundation and the Queensland and Northern New South Wales Lions Medical Research Foundation.

References [1] M.S. Roberts, J. Singh, N. Yoshida, K.I. Currie, Iontophoretic transport of selected solutes through human epidermis, in: R.C. Scott, J. Hadgraft, R. Guy (Eds.), Prediction of Percutaneous Absorption, IBC, London, 1990, pp 231– 241. [2] J.B. Phipps, J.R. Gyory, Transdermal ion migration, Adv. Drug Deliv. Rev. 9 (1992) 137–176. [3] N.H. Yoshida, M.S. Roberts, Solute molecular size and transdermal iontophoresis across excised human skin, J. Control. Release 25 (1993) 177–195. [4] N.H. Yoshida, M.S. Roberts, Role of conductivity in iontophoresis. 2. Anodal iontophoretic transport of phenylethylamine and sodium across excised human skin, J. Pharm. Sci. 83 (1994) 344–350. [5] N.H. Yoshida, M.S. Roberts, Prediction of cathodal iontophoretic transport of various anions across excised skin

[15]

[16]

[17] [18]

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