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 myristate (J(M)) as a function of molecular weights (MW) and solubilities in isopropyl 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), theophylline (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-aqueous series path for the permeation of solutes through skin: log J(M) = log ¿1/[1/(aS(LIPID) 10(PhiMW)) + 1/(bS(AQ)/MW(1/2))] + cS(LIPID)10(PhiMW) + dS(AQ)/MW(1/2)¿ where a, b, c, and d are coefficients for flux through the lipid and aqueous portions of the series path, the lipid-only path, and the aqueous-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 solvatochromic terms alpha, beta, pi, and R(2), and k is the coefficient for the dependence 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 compared with the solvatochromic and transformed Potts-Guy models where a homogeneous barrier to permeation was assumed. For each model, one compound at a time was omitted from the data set and new parameter estimates were obtained 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/parallel (r(2) = 0.937), 0.127 for the solvatochromic series/parallel (r(2) = 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 series/parallel model provides fit and predictive ability comparable to or slightly superior to previous models that assumed homogeneity of the diffusional barrier to flux in the rate-determining step, provides further theoretical support against the existence of a high capacity aqueous-only path, and provides further insight into the physicochemical properties that should be incorporated into solutes to optimize their flux. Using the solvatochromic series/parallel model, the parameter estimates for the n = 41 solution were used to calculate the flux of each compound through the two paths. For compounds 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.