A user-defined element for simulating hydrogel injection into trabecular bone: Numerical simulations and experimental validation

In this study, we present a comprehensive numerical model to simulate the injection of hydrogel into femurs. The model is designed to capture the complex interactions between the hydrogel rheological properties and the biomechanical environment of the femur. The coupled mechanical-flow formulation, based on the Theory of Porous Media, is implemented in an open source Abaqus UEL subroutine, where displacements, pressure and saturation are the unknowns. The rheological properties of the hydrogel were calibrated against experimental augmentations in three femurs and the calibrated model was then applied to three different femurs where the hydrogel patterns were compared to experimental data. Furthermore, the simulations demonstrated the effect of injection flow rate and heterogeneous permeability on the hydrogel patterns and quantified the trabecular matrix's solid strains developed during the injection process. The simulations captured well the volume distribution with an average dice coefficient of 0.75 for the three tested specimens. In addition, the calculated solid strains were below the tensile yield limit for the tested flow rate range. A description of the constitutive equations and the implementation into an Abaqus user element subroutine is provided. Overall, our modeling methodology provides a computational tool that can be used to more accurately model bone augmentation and furthermore plan more safely the treatment of osteoporotic patients.