Impedance-Controlled Molecular Transport Across Multilayer Skin Membranes

Analytical descriptions of transdermal drug delivery (TDD) commonly model deeper skin layers using ideal sink assumptions or phenomenological interfacial resistances. While mathematically convenient, such approaches obscure the physical role of the dermis and hypodermis in regulating molecular transport. Here, we develop an analytical impedance-based model for diffusion across multilayer skin membranes, in which the epidermal barrier is dynamically coupled to a finite diffusive backing layer representing the dermis–hypodermis composite. The influence of deeper layers is expressed through diffusion impedance, linking transport conductivity, storage capacity, and layer thickness, while enforcing continuity of concentration and diffusive flux at all internal interfaces. Closed-form analytical expressions are derived in the Laplace domain for concentration fields and interfacial fluxes, and the cumulative drug amount transmitted across the epidermal barrier is evaluated in the time domain via inverse Laplace transformation. The model distinguishes short- and long-time transport regimes. Analysis demonstrates that commonly used Dirichlet and Robin formulations arise as limiting cases but fail to capture regime-dependent backing-layer effects. By replacing ad hoc boundary conditions with a physically grounded impedance description, the proposed approach provides a unified and extensible basis for analyzing impedance-controlled transdermal transport, including extensions to anomalous and memory-dependent diffusion.