Damage-based finite-element vertebroplasty simulations

The objectives of this study were to quantify the efficacy of vertebroplasty according to: (1) damage and (2) cement quantity (fill) and modulus. Vertebral body damage was numerically simulated using a previously validated two-dimensional finite-element model coupled with an elasto-plastic modulus reduction (EPMR) scheme. The effects of cement fill (% marrow replaced by cement, % MRC) and cement modulus on vertebral apparent modulus and trabecular bone tissue stress concentrations were parametrically assessed for four EPMR damage models (19%, 33%, 60%, and 91% modulus reduction). For this analysis, the elastic modulus of the trabecular bone tissue and marrow elements were assumed to be 10 GPa and 10 kPa, respectively. The effect of cement modulus (varied in the range 1 GPa to 9 GPa) on vertebral apparent modulus was also examined for partial fill (39% MRC) and complete fill (100% MRC) using the 33% modulus reduction damage model. In the case of polymethylmethacrylate (PMMA cement modulus = 2.16 GPa), restoration of the thoracic vertebral body (T10) apparent modulus to undamaged levels required 71% and 100% cement fill for the 19-33% and 60-91% modulus reduction damage models, respectively. Variations in cement modulus had no appreciable effect on the recovery of vertebral apparent modulus to undamaged levels for simulations of partial cement fill (39% MRC). For complete cement fill, however, a PMMA cement modulus produced approximately a 2-fold increase (82%) in vertebral apparent modulus relative to the undamaged vertebral body. Increasing the cement modulus to 9 GPa increased the vertebral apparent modulus over 2.5-fold (158%) relative to the undamaged state. The EPMR damage scheme and repair simulations performed in this study will help clinicians and cement manufacturers to improve vertebroplasty procedures.