A Mechanistic Diffusion–Erosion Model for Drug Release from Shrinking Cylindrical Matrices

Drug release from long-acting intravitreal implants is governed by the coupled effects of diffusion, hydrolysis-driven erosion, and progressive shrinkage of the polymeric matrix. To capture these mechanisms, we solve the diffusion equation in a cylindrical domain whose radius decreases according to the hydrolytic degradation kinetics of PLGA, which follow a pseudo-first-order behaviour in aqueous excess. The resulting formulation combines a modal Bessel expansion with an erosion-controlled time transformation, allowing the evolving geometry and the attenuation of the diffusion modes to be incorporated in a fully mechanistic manner. Within this framework, the shrinkage parameter p quantifies the rate of erosion-induced geometric evolution and enables an accurate reconstruction of the experimental dexamethasone release profile. The solution reproduces both the initial fast-release phase and the extended depletion tail from which the characteristic times (Formula presented.) and (Formula presented.) are extracted, providing compact and physically meaningful indicators of the transition between early and late kinetic regimes. Overall, the approach offers a robust and interpretable description of drug release from shrinking polymeric systems and is directly applicable to the design of long-acting intravitreal therapies.