Meshless modeling of coupled transdermal pharmacokinetics with analytical validation

Abstract

An efficient localized collocation meshless computational approach is applied to the study of transdermal drug delivery (TDD). To validate the numerical technique, a one-dimensional analytical solution is first derived for the set of coupled differential equations that govern the pharmacokinetic process in the two-compartment compound diffusion model. These equations consist of one partial differential equation (PDE) and one ordinary differential equation (ODE). These equations are solved in one-dimensional space via superposition and separation of variables to arrive at the field solution for the compound concentration in the tissue. The convergence of the numerical result to the analytical result indicates the viability of the localized collocation meshless method (LCMM) as a valid approach to the solution of TDD problems. The analytical solution is used to benchmark the numerical technique for several cases with differing pharmacokinetic coefficients, demonstrating the robustness and accuracy of the meshless numerical technique. Furthermore, the highly efficient LCCM implementation is extended to address multi-dimensional TDD cases achieving stable and physically consistent results.