Prediction of Transdermal Flux of Prodrugs of 5‐Fluorouracil, Theophylline, and 6‐Mercaptopurine with a Series/Parallel Model

Abstract

Multiple regression analysis of fluxes from suspensions in isopropyl myristate (JM) as a function of molecular weights (MW) and solubilities in isopropyl myristate (SIPM) and water (SAQ) 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 JM = log {1/[1/(aSLIPID 10ΦMW) + 1/(bSAQ/MW1/2)] + cSLIPID10ΦMW + dSAQ/MW1/2} 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 Φ is the dependence of diffusivity in lipid on MW. In the first series/parallel model, SLIPID was predicted by SIPM, and in the second, solvatochromic series/parallel model, SLIPID was predicted by SIPMk MW + Ωi where Ωi is the sum of the solvatochromic terms α, β, π, and R2, 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 JM for the omitted compound. The average errors of prediction of log JM (experimental log JM − predicted log JM) for the four models were 0.134 for the series/parallel (r2 = 0.937), 0.127 for the solvatochromic series/parallel (r2 = 0.967), 0.150 for the solvatochromic (r2 = 0.950), and 0.134 log units for the transformed Potts–Guy model (r2 = 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 (KIPM:AQ) of <0.8, permeation was mostly by the lipid–aqueous series path; for compounds with log KIPM:AQ >1.0, permeation was mostly by the lipid‐only path; the lipid‐aqueous series path exhibited the higher carrying capacity. © 2000 Wiley‐Liss, Inc. and the American Pharmaceutical Association J Pharm Sci 89: 1415–1431, 2000