Application of orthogonal collocation and regression techniques for recovering parameters of a two-pathway transdermal drug-delivery model

This work focuses on the estimation of model parameters for a two-pathway transdermal drug-delivery system in which molecules are allowed to transfer from one pathway to the other. Orthogonal collocation, implemented in Mathematica® (Wolfram Research Inc.), was used to reduce the original system into a set of ordinary differential equations (ODEs). After selecting the optimum number of internal collocation points, a sensitivity analysis was performed to determine the process parameters that significantly affected the cumulative amount of drug released. “In silico” experiments were conducted using randomly generated values of the key input variables. A study was designed to explore the ability of an orthogonal collocation-based optimization scheme to recover the true parameter values from simulation data. Although the solution of such an inverse problem is non-unique, the methodology was successful at identifying the process values, in most cases. This approach avoids the use of elaborate numerical inversion techniques of Laplace transforms, uses a single computational environment for generating the ODEs and estimating the parameters and does not require an analytical solution of the model. The computational approach was applied to elucidate the transport mechanism of caffeine through excised human skin in the presence of several permeation enhancers. The method shows that (i) the route of penetration of the drug across the skin is determined by the type of enhancers, (ii) the notable increase in steady-state transdermal flux, in comparison with control, is reflected in the estimated model parameters.