Objective <p>A fundamental understanding of drug diffusion and binding processes is critical for the design and optimization of a wide variety of drug delivery devices. Most of the past literature assume binding to occur uniformly throughout the tissue, or, at best, in specific layers of a multilayer tissue.&#xa0;However, in many realistic scenarios,&#xa0;such as in cancer-targeting drugs, drug binding occurs in discrete irregularly shaped regions.</p> Methods <p>This work presents mathematical modeling of drug diffusion and binding in a Cartesian tissue containing a number of irregularly shaped drug binding regions. Based on linear irreversible binding, an exact expression for the transient concentration distribution in the tissue, and thus, the amount of bound drug is derived. A comprehensive verification of the theoretical model, including comparison with past work, is presented.</p> Results <p>The capability of the theoretical model to account for irregular non-Cartesian shapes of the drug binding regions is demonstrated by solving a number of illustrative problems. The impact of the location and size of a drug binding region on the extent of drug binding is determined. Comparison between a single large drug binding region and two smaller drug binding regions is carried out.</p> Conclusions <p>This work advances the literature on drug diffusion and binding by making it possible to account for realistic, irregular shapes of drug binding regions. The model may help design and optimize drug delivery processes and devices in the presence of realistic drug binding regions.</p>