Prediction of transdermal flux of prodrugs of 5-fluorouracil, theophylline, and 6-mercaptopurine with a series/parallel model

Multiple regression analysis of fluxes from suspensions in isopropyl myrist ate (J(M)) as a function of molecular weights (MW) and solubilities in isop ropyl myristate (S-IPM) and water (S-AQ) were performed on a data set of 41 compounds (n = 41) comprising 39 prodrugs of 5-fluorouracil (5-FU), theoph ylline (Th), and 6-mercaptopurine (6-MP), in addition to 5-FU and Th, using four models. Two series/parallel models have been developed that allow an aqueous-only path in parallel with a lipid-only path and with a lipid-aqueo us series path for the permeation of solutes through skin: log J(M) = log { 1/[1/(aS(LIPID) 10(phi MW)) + 1/(bS(AQ)/MW1/2)] + cS(LIPID)10L(phi MW) + dS (AQ)/MW1/2} where a, b, c, and d are coefficients for flux through the lipi d and aqueous portions of the series path, the lipid-only path, and the aqu eous-only path, respectively, and Phi, is the dependence of diffusivity in lipid on MW. In the first series/parallel model, S-LIPID was predicted by S -IPM, and in the second, solvatochromic series/parallel model, S-LIPID was predicted by S-IPM(k MW+Omegai) where Omega (i) is the sum of the solvatoch romic terms alpha, beta, pi, and R-2, and k is the coefficient for the depe ndence of partitioning on MW. Using the n = 41 solutions, the coefficients for the aqueous-only path were very small or not different from zero in the two series/parallel models, so only two-path series/parallel models were c ompared with the solvatochromic and transformed Potts-Guy models where a ho mogeneous barrier to permeation was assumed. For each model, one compound a t a time was omitted from the data set and new parameter estimates were obt ained for these 41-1 solutions and used to predict log J(M) for the omitted compound. The average errors of prediction of log J(M) (experimental log J (M) - predicted log J(M)) for the four models were 0.134 for the series/par allel (r(2) = 0.937), 0.127 for the solvatochromic series/parallel (r2 = 0. 967), 0.150 for the solvatochromic (r(2) = 0.950), and 0.134 log units for the transformed Potts-Guy model (r(2) = 0.944). Thus, the solvatochromic se ries/parallel model provides fit and predictive ability comparable to or sl ightly superior to previous models that assumed homogeneity of the diffusio nal barrier to flux in the rate-determining step, provides further theoreti cal support against the existence of a high capacity aqueous-only path, and provides further insight into the physicochemical properties that should b e incorporated into solutes to optimize their flux. Using the solvatochromi c series/parallel model, the parameter estimates for the n = 41 solution we re used to calculate the flux of each compound through the two paths. For c ompounds with log partition coefficients (K-IPM:AQ) of <0.8, permeation was mostly by the lipid-aqueous series path; for compounds with log K-IPM:AQ > 1.0, permeation was mostly by the lipid-only path; the lipid-aqueous series path exhibited the higher carrying capacity. (C) 2000 Wiley-Liss, Inc. and the American Pharmaceutical Association.