Mathematical Analysis of Drug Diffusion in Tissues

Abstract

A drug released at a tissue boundary may diffuse through extracellular space while simultaneously binding to tissue constituents, entering cells, undergoing metabolism or being removed by microvessels. Mathematical models link these processes to spatial concentration and exposure. This article develops a one-dimensional diffusion–reaction model from conservation of mass and Fick’s law, states its boundary conditions and analytical steady-state solution, and explains characteristic timescales and penetration length. A constructed example compares normalized concentration profiles under three first-order removal rates. With the same diffusivity and thickness, larger removal rates yield lower concentrations deeper in the modeled tissue. The illustration is not a fitted experiment and cannot determine any drug’s therapeutic dose or safety. Extensions cover reversible binding, vascular exchange, heterogeneous tissue and numerical solution. Reported data, tissue-specific parameters and validation are essential before translating such calculations to clinical use. Foundational diffusion theory and published drug-transport studies support the modeling framework [1–4].