Abstract
The development of new drugs and drug delivery systems relies heavily on careful acquisition and interpretation of large amounts of experimental data to identify and select promising candidates for therapeutic and prophylactic use. Predictive mathematical modeling can expedite this process by capturing the complex interplay of physical, chemical, and biological factors that influence drug delivery. However, traditional compartmental models of pharmacokinetics and pharmacodynamics typically rely on oversimplified approximations of drug transport mechanisms and may fail to accurately represent the key deterministic processes that drive drug mass transport – particularly in complex delivery scenarios where the drug targets are close to the sites of drug administration. Here, we present a deterministic mathematical framework that addresses a challenging drug delivery modality: the injection of a fluid drug vehicle that undergoes phase separation upon entering poroelastic tissue. This phase change improves localized retention of the loaded drug in a finite volume near the injection site. Our model is directly relevant to in situ-gelling injections of chemotherapeutic agents into superficial tumors - a strategy gaining attention in the development of improved cancer therapeutics. Our approach uniquely incorporates both diffusion and convection, accounts for tissue poroelasticity, and uses Cahn-Hilliard theory to describe the phase separation behavior of the injected material. Simulations across a broad parameter space indicate that drug retention is enhanced in softer tissues and with high-rate, low-volume injections. This computational framework is currently being used to guide the design of improved therapeutic strategies for ethanol-based ablation, when co-injected with ethyl cellulose as a phase-transitioning agent for superficial tumors. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1038/s41598-026-40299-8.