Smart Drug Delivery System Based on Magnetic-Responsive Hydrogel: Drug Diffusion Modelling and Mathematical Paradigm

In order to improve the efficacy of drug delivery system (DDS) and minimize the adverse effects on patients, a mathematical model was established to optimize the magnetic response hydrogel intelligent drug delivery system, the aim is to achieve precision administration with potential clinical applications, particularly in the treatment of cancer, chronic diseases, and sustained pain relief and anti-inflammation. Physical simulations are validated only by numerical simulations based on mathematical derivation. A mathematical model was developed to describe the diffusion and release of Fe3O4 nanoparticles by embedding them in a Polyethylene glycol matrix (PEG) with an external magnetic field. The model combines Fick's second law and Korsmeyer-Peppas model to quantitatively analyze the effects of magnetic field strength and FE3O4 content on drug diffusion coefficient and release rate. The numerical simulation shows that with the increase of magnetic field intensity and FE3O4 content, the drug release rate increases obviously and the diffusion coefficient increases linearly. In addition, the model fit confirmed that the drug release process was mainly controlled by diffusion, and the high content of Fe3O4 nanoparticles enhanced the magnetic response of hydrogels. This study provides a theoretical framework and optimization strategy for the design of intelligent DDS using magnetic response hydrogels, and highlights its potential in precision medicine and personalized therapy.