Damage-based finite-element vertebroplasty simulations

Abstract

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.

Fig. 1

A μCT image of a T10 vertebral body was volumetrically rendered (left) and projected to create an anatomically accurate 2D structural finite element (FE) model (center). Load-induced damage of the vertebral body was simulated using a modulus reduction scheme (elasto-plastic modulus reduction; EPMR) [18, 19]. Simulation of vertebroplasty was then performed by replacing bone-marrow elements with cement elements (right). The resulting FE damage-repair model was uniformly loaded and simply supported. IVD intervertebral disc, Marrow bone marrow, Bone trabecular bone, Cement bone cement, Pos posterior, Ant anterior, Sup superior, Inf inferior

Fig. 2

Non-linear stress-strain response of the T10 vertebral body predicted by the elasto-plastic modulus reduction (EPMR) scheme

Fig. 3

Left The T10 vertebral apparent modulus decreases with increasing amount of trabecular bone damage (apparent modulus reduction) and increases with increasing marrow replaced by cement (% MRC). Right Stress concentrations (% Bone Elements with Stress Concentrations >6) increase with increasing amount of trabecular bone damage and decrease with increasing marrow replaced by cement (% MRC). The solid black line shown is representative of the undamaged untreated vertebral model

Fig. 4

Tissue element stress concentrations (tissue stress/apparent stress) decrease with increasing marrow replaced by cement (% MRC). Stress concentrations are color coded over a range from 0 (low) to 10 (high). Results shown are for the 91% apparent modulus reduction damage model

Fig. 5

Relationship between vertebral apparent modulus and cement modulus for partial (39% MRC) marrow replacement with cement (dashed line) and complete (100% MRC) marrow replacement with cement (solid line). The square and circle symbols show results representative of PMMA (E_cement=2.16 GPa) and Orthocomp (E_cement=5.8 GPa), respectively. Results shown are for the 33% apparent modulus reduction damage model

Fig. 6

Magnified anterior-inferior regions, for the 91% apparent modulus reduction damage model, around the cement augmentation showing the increased tissue stress concentrations around the boundaries of the cement. Stress concentrations are color coded over a range from 0 (low) to 10 (high)