An Analytical Validation of the Localized Collocation Meshless Method Formulation for Transdermal Drug Delivery

Abstract

The Localized Collocation Meshless Method (LCMM) is applied to the solution of a set of partial differential equations describing the diffusive transport of a dermally injected compound. This efficient and accurate numerical technique then provides the framework for the estimation of pharmacokinetic (PK) parameters by the comparison of two models, both containing information derived from experimental results, using the iterative Golden Section search algorithm. This comparison is quantified using a norm between the two solution spaces. While this method does provide an estimate of the effective-diffusion coefficient, it ultimately demonstrates that a simple, free-diffusion model is inadequate for quantifying the spatial and temporal distribution of a dermally-injected compound if elimination effects are not accounted for properly.