Factors Affecting Skin Flux

The key determinants of epidermal flux are solute concentration in the SC (Csc), the effective diffusivity in the SC, and the potential buildup of solute concentrations in the viable epidermis [see Eq. (28) and Fig. 7]. A maximum flux is attained, therefore, at the solubility of the solute in the SC [see Eq. (55)], recognizing that solubility may include the thermodynamically unstable potential supersaturation. The concentrations of solute in the SC may be related to those in the vehicle by a partition coefficient. Our analysis also shows that the apparent diffusivity is a function of both the diffusivity of unbound solute down the intercellular lipid pathway as well as the fraction of solute unbound in this pathway. Finally, solutes may be transported in the vapor phase as has been shown for the alcohols (5) and for a homologous series of acetate esters (122). In the latter, the vapor pressure of the pure solutes decreased as the alkyl chain was increased. The observed SC permeation rate decreased with the decrease in vapor pressure. We now consider factors affecting each determinant.

A. Solute Concentration in Vehicle

Equation (39) suggests that JZ should be linearly related to the concentration of solute in the vehicle Cv, up to the solute saturation solubility in the vehicle. Thereafter, at higher solute concentrations, a suspension exists and the solute flux is the maximal flux, which has been discussed earlier. Hence, Barry et al. (57) showed that benzyl alcohol vapor flux was linearly related to benzyl alcohol activity, suggesting that percutaneous absorption is controlled by thermodynamic activity when the vehicle has no effect on the SC barrier. It may be important to recognize that, if a solute activity is defined as fractional solubility (as implied by convention 1), then the flux from different vehicles will be the same for all fractional concentrations. Flux is not necessarily linear with fractional concentrations, as illustrated by the deviations from Raoult's law for benzyl alcohol vapor concentration versus mole fraction (57).

If, on the other hand, solute activities are those measured (as implied by convention 2), for a given concentration, the highest flux will be seen from the vehicle in which the solute is least soluble with identical fluxes being apparent when both vehicles are saturated. These deductions are based on the assumption that the effects of the two vehicles on the skin are the same and there is no nonlinearity in flux versus Cv profiles.

A nonlinearity in flux-convention profiles may also arise if the concentration of the solute used is sufficiently high to affect the integrity of the SC barrier, or if nonsink conditions preclude the attainment of equilibrium during the course of the experiment (90). Figure 18 shows three examples of nonlinearity. In Figure 18A a positive deviation from linearity can be shown to arise as a consequence of solute effects on SC permeability by comparison with a flux through an inert membrane. The proportionality of flux to vehicle concentration through the inert membrane is evidence that the effects do not arise from alterations in the activity coefficients of

Figure 18 (A) Penetration flux of phenol through rat skin (o) and polyethylene film (•) at 37°C for various concentrations of phenol in water; (B) Fluxes of octylsalicylate at various concentrations: (left-hand axis: polyethylene membrane (o) and nylon membrane filter (A); (right-hand axis) human epidermis (A) and dialysis membrane (•); (C) penetration flux of pentanol from an olive oil vehicle through human skin (o) and polyethylene film (•). (From Refs. 101[A,C]; 325[B].)

the solutes in the vehicle. The permeability coefficient is relatively constant; but increases abruptly at about 2% phenol as a result of several changes (123). Figure 18B shows a negative deviation from a linear flux versus concentration relation through membranes other than nylon. The negative deviation here arises from octyl salicylate self-association in the vehicle at high concentrations and is accounted for in Eq. (40) by a reduction in Ksc-v as a result of a decreased yv [see Eq. (7)]. The positive deviation from linearity for the nylon membrane suggests that octyl salic-ylate has increased flux by plasticization or other effects on the membrane. Figure 18C shows a negative deviation in flux from a linear flux concentration relation as a result of an effect such as dehydration and a reduction in Dsc, arising from the high concentration of solute in the vehicle.

Twist and Zatz (124) reported a parabolic relation between flux and solute concentration for methylparaben and propylparaben through polydimethylsiloxane membrane from 1-propanol. They proposed that the propanol vehicle is sorbed by the membrane and creates an environment ("clusters") in which the paraben can dissolve. The resultant paraben membrane concentration and flux is higher than if the propanol was not present in the membrane. At high paraben concentrations, the propanol activity in the vehicle is reduced: less partitions into the membrane. The paraben solubility and flux therefore decreases. Another nonlinearity that may arise is the nonlinear binding of components to SC. Bronaugh and Congdon (125) showed that hair dye binding to human epidermis could be described by a Scatchard plot, and that permeability values followed the rank order of dye permeability and paralleled the partition coefficients only when the binding sites were saturated. Wurster

(122) has reported the adsorption isotherm for sarin's uptake on ^-dioxane-condi-tioned callous tissue.

B. Drug-Vehicle Interactions

Figure 19A shows that the penetration flux of phenol decreases through both rat skin and polyethylene owing to a higher affinity of dimethyl sulfoxide (DMSO) than for water, even though DMSO is a very strong penetration enhancer. A similar profile is observed for glycerol, an agent that has less effect on the epidermis (see Fig. 19B)

(123). The effect of the DMSO and glycerol relative to water is simply a reduction in Ksc-v owing to a greater solubility [see Eq. (42)] or low-activity coefficient owing to the high affinity [see Eq. (40)] of phenol for these vehicles than for water. Indeed when the logarithm of the penetration flux is plotted against the percentage glycerol, a linear relation is observed (see Fig. 19C) consistent with the relation (126).

log Js = log Js water + (log Js (glycerol) - log Js (water))(1 - fg) (60)

Where (Js) is the penetration flux for a given binary composition, Js (glycerol) and Js(water) are the penetration fluxes of phenol from glycerol and water vehicles, respectively, and fg is the fraction of glycerol in the glycerol-water vehicle.

Vehicles may also affect drug release by a diffusion limitation in the vehicle with a range of expressions being presented (see Chap. 3). Other effects such as vehicle evaporation, dissolution kinetics, solvent flux through stratum corneum, and changes in vehicle composition with time are dealt with elsewhere in this book and the literature (83,126,127). In the present context, the shape of the cumulative amount versus time profile is often indicative of whether flux is membrane-limited as dis-

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