A probabilistic finite element analysis of the stresses in the augmented vertebral body after vertebroplasty

Abstract

Fractured vertebral bodies are often stabilized by vertebroplasty. Several parameters, including fracture type, cement filling shape, cement volume, elastic moduli of cement, cancellous bone and fractured region, may all affect the stresses in the augmented vertebral body and in bone cement. The aim of this study was to determine numerically the effects of these input parameters on the stresses caused. In a probabilistic finite element study, an osteoligamentous model of the lumbar spine was employed. Seven input parameters were simultaneously and randomly varied within appropriate limits for >110 combinations thereof. The maximum von Mises stresses in cancellous and cortical bone of the treated vertebral body L3 and in bone cement were calculated. The loading cases standing, flexion, extension, lateral bending, axial rotation and walking were simulated. In a subsequent sensitivity analysis, the coefficients of correlation and determination of the input parameters on the von Mises stresses were calculated. The loading case has a strong influence on the maximum von Mises stress. In cancellous bone, the median value of the maximum von Mises stresses for the different input parameter combinations varied between 1.5 (standing) and 4.5 MPa (flexion). The ranges of the stresses are large for all loading cases studied. Depending on the loading case, up to 69% of the maximum stress variation could be explained by the seven input parameters. The fracture shape and the elastic modulus of the fractured region have the highest influence. In cortical bone, the median values of the maximum von Mises stresses varied between 31.1 (standing) and 61.8 MPa (flexion). The seven input parameters could explain up to 80% of the stress variation here. It is the fracture shape, which has always the highest influence on the stress variation. In bone cement, the median value of the maximum von Mises stresses varied between 3.8 (standing) and 12.7 MPa (flexion). Up to 75% of the maximum stress variation in cement could be explained by the seven input parameters. Fracture shape, and the elastic moduli of bone cement and of the fracture region are those input parameters with the highest influence on the stress variation. In the model with no fracture, the maximum von Mises stresses are generally low. The present probabilistic and sensitivity study clearly showed that in vertebroplasty the maximum stresses in the augmented vertebral body and in bone cement depend mainly on the loading case and fracture shape. Elastic moduli of cement, fracture region and cancellous bone as well as cement volume have sometimes a moderate effect while number and symmetry of cement plugs have virtually no effect on the maximum stresses.