Endplate Topography is Associated with the Brittleness of Human Whole Vertebral Bodies

INTRODUCTION: Vertebral fractures are often the result of a progressive deformation process. Structural brittleness parameters should be considered relevant for such failure processes. Much of the previous work has been concerned with vertebral stiffness and strength but measures of brittleness such as work to fracture and failure displacement largely remained unexplored. In a previous study examining the relationships of local stress distribution properties with vertebral strength and brittleness, it was observed that the finite element (FE) calculated whole vertebral stiffness ratio from two different models of the same vertebra was highly correlated with experimental displacement and strain to maximum load [1]. Because the only difference between the two models was in the elastic properties of the filler material that was digitally added to the microcomputed tomography (μCT) image to create flat boundaries at the superior and inferior vertebral endplates, this result suggested that differences in the ability of vertebral endplates to distribute stresses are a major determinant of vertebral brittleness. Based on these observations, it was hypothesized that vertebral end-plate geometry is associated with structural brittleness of a vertebra. In order to test this hypothesis, the current study investigated the relationships of vertebral endplate topography with structural brittleness (viz., work to fracture, displacement and strain to maximum load) and stress distribution properties of human vertebral bodies. Our finding that endplate topography predicts vertebral brittleness is significant in that it offers a potential mechanism for disease progression in addition to loss of bone mass and cancellous bone microstructural integrity. METHODS: Eighteen thoracic and lumbar (T6-L3) vertebral bodies, extracted from 4 female and 5 male cadavers, aged 40-98 years were used for the study. The vertebral bodies were scanned using a μCT system. Details of the scans, axial compression testing using Wood's metal as filler material, construction of voxel-based FE models, assignment of element material modulus to cancellous bone based on image gray value, digital addition of filler material and subsequent calculation of FE results have been presented before [2, 3, 4]. Structural stiffness (S), strength (maximum load, Fmax), work to fracture, U, and displacement (∆u) and strain (εu) to maximum load were calculated from the load-displacement curves of axial compression tests. Average, standard deviation, and coefficient of variation of von Mises stress (VMExp, VMSD, VMCV respectively) in vertebral bone were calculated. Two sets of FE models simulating axial compression were constructed; one using stiffer filler material modulus of 12.7 GPa, simulating experiments that used Wood's metal (called W-layer models) and the other with a low filler material modulus of 8 MPa, to simulate the intervertebral disc (called D-layer models). Ratios of FE parameters from the W-layer models to those from the D-layer models were calculated for the same vertebrae as reported previously. Also, for comparison purposes, a μCT equivalent of bone mineral density (μCTBMD) was calculated. To investigate the role of endplate geometry, surface topographical distributions of both superior and inferior endplates for each vertebral body were determined using a custom-written code by calculating the depth of each surface voxel on the respective endplates with respect to a reference plane. Along with mean, standard deviation, and coefficient of variation, shape factors of inferior and superior endplate surface topographical distribution, viz., skewness (γ1) and kurtosis (γ2) were also determined for each vertebra according to the following equations [5]: