Dynamics and control of percutaneous drug absorption in the presence of epidermal turnover

The integration of epidermal turnover into the study of transdermal drug-delivery kinetics is addressed in light of classical control theory. A mathematical representation of the process, which includes Fickian diffusion and advection, was formulated in the frequency domain. This transformation facilitated a detailed analysis of the system dynamics and revealed the intricate relationships among a medicament transient absorption through the skin, the epidermal turnover rate, its physicochemical properties and the amount of drugs in a reservoir. The process, represented by transcendental transfer functions, was reduced to a second-order system with dead-time by minimizing the squared magnitude of the complex error between the original and simplified models. Clinically relevant parameters, such as the time to reach steady-state flux or drug concentration in the skin layers, are readily available from the low-order models. The time it takes to deliver a specified dose of drug to a particular depth in the skin is a function of the penetration depth and the diffusion coefficients of the drug molecules in the stratum corneum and the viable epidermis. An optimum administration protocol was developed for the transdermal delivery of chemicals when epidermal turnover is likely to affect their absorption into the systemic circulation.