SKIN PERMEATION MODELS 47 o o.ooo o.oo2 o.oo4 o.oo6 o.oo8 O.OLO SC AMOUNT Figure 10. Peak blood levels versus amount in the stratum corneum at 30 minutes, both following 30-minute application, for various values of PC. Parameter values are same as in Figure 9. inversely related to K. For three of the hypothetical permeants, the amounts excreted at four days were approximately the same, as would be expected. However, where the transport coefficient was very low (0.00125 or 0.0025 min- •), the amount excreted was significantly less than from the other applications. This is explained by deviation from two assumptions made in designing the experiment. One is that four days is sufficient to allow essentially complete absorption of whatever has been sorbed by the stratum corneum the second is that four days is long enough to allow essentially complete elimination of what has entered the blood. Either or both of these assumptions may be violated in situations in which the rate of transport across the stratum corneum is remarkably slow. A lack of correlation would also be expected if the elimination rate constant were extremely small. CONCLUSIONS While it is risky at the present time to model skin permeation without conducting preliminary experiments, simulations of the type described in this paper are a useful adjunct to the empirical information obtained in the laboratory. Using this approach, we can anticipate the effects of changing permeation parameters and/or pharmacokinetic characteristics of substances applied to the skin. While the quantitative differences

48 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS lO 8 6 4 2 o sc EXCR BLOOD [] 0.00125 ß 0.0025 ,[] o.oo5 [] 0.01 [] 0.02 Figure 11. Effect of K on relative value of amount in stratum corneum at 30 minutes, amount excreted at 96 hours, and peak blood concentration. (PC = 10 other parameter values are same as in Figure 9.) described above depend on the particular parameters employed in setting up the sim- ulations, the trends are quite general. The type of data presented in this paper helps to identify factors significantly affecting skin transport. REFERENCES (1) D. W. Osborne, "Computational Methods for Prodrug or Drug Analogue Selection Optimized for Percutaneous Delivery," in Topical Drug Delivery Formulations, D. W. Osborne and A. H. Amann, Eds. (Marcel Dekker, New York, 1990), pp. 109-126. (2) J. Hadgraft, The epidermal reservoir: A theoretical approach, Int. J. Pharm., 2, 265-274 (1979). (3) S. K. Chandrasekaran, W. Bayne, and J. E. Shaw, Pharmacokinetics of drug permeation through human skin, J. Pharm. Sci., 67, 1370-1374 (1978). (4) R. C. Wester, H. I. Maibach, D. A. W. Bucks, J. McMaster, and M. Mobayen, Percutaneous absorption and skin decontamination of PCBs: In vitro studies with human skin and in vivo studies in the rhesus monkey, J. Toxicol. Environ. Health, 31, 235-246 (1990). (5) J. L. Zatz, Influence of depletion on percutaneous absorption characteristics. J. Soc. Cosmet. Chem., 36, 237-249 (1985). (6) A. Rougier, D. Dupuis, C. Lotte, and H. I. Maibach, Stripping method for measuring percutaneous absorption in vivo, in Percutaneous Absorption, R. L. Bronaugh and H. I. Maibach, Eds. (Marcel Dekker, New York, 1989), pp. 415-434.