Modelling material injection into porous structures under non-isothermal conditions

In this work, the Theory of Porous Media (TPM) is employed to model percutaneous vertebroplasty, a medical procedure in which acrylic cement is injected into cancellous vertebral bone. Previously, isothermal macroscale models have been derived to describe this material injection and the arising mechanical interactions. However, the temperature of the injected cement is typically below the human body temperature, necessitating the extension of these existing models to the non-isothermal case. Following the modelling principles of the TPM and considering local thermal non-equilibrium conditions, our model introduces three energy balances as well as constitutive relations for thermal conduction and heat transfer. If restricted to local thermal equilibrium conditions, our model equations are in agreement with other TPM-based models. We observe that our model elicits physically reasonable behaviour in numerical simulations that employ parameter values and initial and boundary conditions relevant for our application. We claim our model to be thermodynamically consistent despite the employment of the Coleman and Noll procedure.