Abstract

Incorporating pharmaceutical benefits into cosmetic preparations has stimulated growing interest in transdermal delivery systems that enhance the penetration, stability, and activity of skin-active ingredients. This study presents a mathematical analysis of transdermal drug delivery in cosmetics with pharmaceutical function, with particular emphasis on the correlation between formulation properties, skin permeability, drug concentration, drug diffusion pattern, and therapeutic effect. Mathematical model for the transport of active pharmaceutical and cosmetic ingredients through the skin barrier is developed using Fick's laws of diffusion. The model includes parameters such as diffusion coefficient, partition coefficient, skin thickness, drug concentration gradient, and permeability coefficient to calculate transdermal flux and cumulative drug permeation. The second aspect of the model includes formulation variables, penetration enhancers, molecular characteristics of active ingredients, vehicle composition, and application duration that affect delivery efficiency. A pharmacodynamic component is added to define the concentration-therapeutic effect (or cosmetic effect) relationship for the delivered active compound. To evaluate concentration profiles in various skin layers, numerical simulations were conducted, along with an investigation of how skin permeability and formulation parameters influence systemic or localized exposure. The mathematical results show that improved permeability and optimized formulation conditions can significantly boost the transport rate of the active compound, but overly high permeability can reduce the controlled-delivery effect and increase the risk of unintended exposure. The quantitative analysis provides a rational basis for optimizing multifunctional cosmetic compositions containing compounds aimed at delivering pharmacological effects (antioxidant, anti-inflammatory, anti-microbial, photoprotective, and reparative action on the skin). The framework can help formulation scientists predict delivery performance before experimental testing, reducing formulation-development time and improving reproducibility.