Biomechanical mechanism of swelling-induced pain in injectable hydrogels: a numerical simulation study aimed at optimizing low-pain delivery strategies

swelling of the hydrogel within the tissue post-injection. However, the complex biomechanical mechanisms underlying this process remain uncertain. This study utilized the COMSOL Multiphysics platform to construct a multiphysics model that couples the large-deformation swelling of the hydrogel with the poro-viscoelastic interactions of subcutaneous tissue, aiming to investigate the evolution of tissue stress during the quasi-static phase post-injection. The simulation results reproduce the characteristic rise-and-fall dynamics of tissue stress. The stress peaks at approximately 60-100 min post-injection, driven by hydrogel swelling, reaching a peak stress of approximately 10.8 kPa, a level clearly exceeding the reported ∼6-9 kPa threshold for activating nociceptors. Subsequently, it gradually decreased owing to the poro-viscoelastic relaxation effects of the tissue, reaching a stress equilibrium phase after approximately 400 min. Parametric studies further reveal two key design principles for low-pain formulations: (1) An optimal injection depth window exists (6-12 mm in this model) that effectively disperses stress and facilitates the formation of a morphologically regular drug depot, whereas injections that are too shallow or too deep lead to stress concentration due to boundary constraints; (2) A smaller hydrogel radius (volume) can trigger higher local peak stress due to a point-like pressure source effect. This study provided a theoretical foundation for the design of low-pain injectable formulations. By synergistically optimizing parameters such as injection depth and volume, the poromechanical microenvironment induced by hydrogel swelling can be actively managed, thereby enhancing patient comfort and compliance while ensuring therapeutic efficacy.