# Impedance-Controlled Molecular Transport Across Multilayer Skin Membranes

## TL;DR

This paper introduces a new model for drug delivery through skin layers that better captures how molecules move through different skin tissues over time.

## Contribution

The paper introduces an impedance-based analytical model for multilayer skin transport that preserves physical properties and replaces ad hoc boundary conditions.

## Key findings

- The model identifies distinct short- and long-time transport regimes in multilayer skin membranes.
- Common boundary conditions like Dirichlet and Robin cannot reproduce the regime-dependent behavior of a finite backing layer.
- The impedance framework allows for a unified and extensible analysis of multilayer transport systems.

## Abstract

Analytical models of transdermal drug delivery (TDD) often represent deeper skin layers using ideal sink assumptions or phenomenological interfacial resistances. While mathematically convenient, these approaches obscure the physical role of the dermis and hypodermis in controlling molecular transport. Here, we develop an impedance-based analytical 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. Diffusion impedance links transport conductivity, storage capacity, and layer thickness, while preserving continuity of concentration and flux at all interfaces. Closed-form expressions in the Laplace domain describe concentration fields and interfacial fluxes, and cumulative drug uptake is computed in the time domain via inverse Laplace transformation. The model identifies distinct short- and long-time transport regimes. Commonly used Dirichlet and Robin boundary conditions emerge as limiting cases but cannot reproduce the regime-dependent behavior of a backing layer. In particular, Robin formulations reduce the backing layer to a constant effective resistance, neglecting its storage capacity and time-dependent impedance. By replacing ad hoc boundary conditions with a physically grounded impedance framework, this approach provides a unified and extensible method for analyzing multilayer transport systems, including extensions to anomalous or memory-dependent diffusion.