A finite element rheological model for polymethylmethacrylate flow: analysis of the cement delivery in vertebroplasty

Polymethylmethacrylate (PMMA) is increasingly used in orthopaedics. Finite element (FE) modelling can play an important role in understanding the PMMA flow behaviour. However, FE models have not been used so far because conventional FE packages do not allow for the rheopectic and pseudoplastic behaviour of PMMA to be taken into consideration and because it requires multiple expertise to incorporate these behaviours into an FE package. The objectives of the present paper are to: (a) propose a rheological model that describes PMMA flow behaviour; (b) implement this model into ANSYS using FORTRAN; and (c) validate the implementation by comparing it with analytical solutions. After the validation showed good agreement, an FE model of PMMA delivery through an eight-gauge cannula was developed to examine the extra-vertebral flow conditions of vertebroplasty. The FE analysis showed a logarithmic increase of the injection pressure, where it almost doubled from 1.2 to 2.3 MPa over two minutes. This unanticipated non-linear increase is due to the highly nonuniform viscosity profile in the cannula. It can be concluded that: (a) the rheological model implemented in ANSYS can be used to analyse practical flow problems related to PMMA and (b) time and shear-rate effects of PMMA are crucial to estimate its flow behaviour accurately.