SKIN PENETRATION 621 pointed out that the driving force behind the drug movement is the difference in the thermodynamic potential between the vehicle and the deeper tissues, and the direction of flow for systems is always from higher thermodynamic potential to lower thermodynamic potential. Wagner (53) has reviewed the thermodynamic considerations involved in vehicle-drug relationships. The positive penetrative effects of increased concentration have been particularly demonstrated using varied steroids (53-56). Skog and Wahlberg (57) have shown a definite increase in the absorption of various compounds with increasing concentration in guinea pigs. They noted increasing penetration up to a certain point at which a plateau was reached. This may indicate that the barrier layer may not be primarily influenced by diffusion gradients, but act by limiting the total amount of any substance passing through in unit time. When true steady-state diffusion is reached, the permeability constants are independent of con- centration. Dimethyl sulfoxide (DMSO) has an unusual concentration depen- dence. Low concentrations are virtually without effect. As the concen- tration is increased, there is a rapid enhancement of percutaneous pene- tration (58). A direct relationship was obtained between the concentra- ' tion of dimethyl sulfoxide and the rate of penetration of potassium methylsulfate (59). Solubility Characteristics of the Penetrant The aqueous solubility of a drug determines the concentration pre- sented to the absorption site, and the partition coefficient strongly in- fluences the rate of transport across the absorption site. Katz and Shaikh (60) indicate that the efficiency of percutaneous absorption may be a function of the product of the partition coefficient and the square root of the aqueous solubility, in agreement with theoretical considera- tions developed by Higuchi (11). The lipid/water partition coefficient per se is not as significant as the stratum corneum/vehicle partition coefficient (11, 28). If a substance is much more soluble in the stratum corneum than in the vehicle in which it is dissolved, the concentration in the first layers of the stratum corneum at equilibrium may be much higher than the concentration in the pre- senting solvent. The concentration in the lower layers of the stratum corneum will remain near zero, since these layers are in contact with a fluid which is being continuously replaced, or through which diffusion is relatively rapid. The flux, therefore, is more accurately related to the

622 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS difference in concentration in the top and bottom layers of the stratum comeurn. The concentration in the top layer of the stratum comeurn will be determined by the relative solubility of the penerrant in the stratum corneum and the vehicle, i.e., the partition coefficient (Kin), as shown in the expansion of Fick's law: - (2) where D,• is the diffusion constant, and the permeability constant now becomes: Kmf)m (3) k•- When kp and K• have been determined experimentally, and 3 is known, D,• can be calculated. The nonhomogeneous nature of the stratum comeurn and the complications and uncertainties attendant upon an accurate determination of Km and • pose serious limitations in develop- ing a satisfactory diffusion constant (61). Main factors in the physico-chemical relationship of the penerrant to vehicle appear to be the solubility of penetrant in the vehicles or a constituent of the vehicle, the rate of diffusion of penetrant within the vehicle, the rate of release of penerrant from the vehicle, and the possible release of penetrant in solubilized form together with a constituent of the vehicle. Blank and Scheuplein (25) consider that differences in penetration from vehicles can be explained by differences in stratum corneum/vehicle partition coefficient without assuming that one ve- hicle penetrates more readily than another. From the "model" work using receptor phases, it should be possible, with suitable models, to predict in vivo effects (62). Minato et al. (63) have reviewed the literature on the percutaneous absorption of various lipid-soluble substances. Tregear (16) has re- viewed the permeability of the skin to water, electrolytes, and organic solvents. Treherne (64) has related the permeability constants of a series of compounds to their ether/water partition coefficients and sug- gested that a partition coefficient of unity might favor skin penetration. A similar relationship between the vasodilator activity and lipid/water partition coefficient was demonstrated for a series of esters of nicotinic acid by Stoughton et al. (65). They also found a similar correlation be- tween the benzene/water partition coefficients and the penetration of the epidermis by a series of closely related boronic acid derivatives.