Effect of fabric on the accuracy of computed tomography-based finite element analyses of the vertebra

Abstract

Quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra are widely used in studying spine biomechanics and mechanobiology, but their accuracy has not been fully established. Although the models typically assign material properties based only on local bone mineral density (BMD), the mechanical behavior of trabecular bone also depends on fabric. The goal of this study was to determine the effect of incorporating measurements of fabric on the accuracy of FE predictions of vertebral deformation. Accuracy was assessed by using displacement fields measured via digital volume correlation-applied to time-lapse microcomputed tomography (μCT)-as the gold standard. Two QCT-based FE models were generated from human L1 vertebrae (n = 11): the entire vertebral body and a cuboid-shaped portion of the trabecular centrum [dimensions: (20-30) × (15-20) × (15-20) mm³]. For axial compression boundary conditions, there was no difference (p = 0.40) in the accuracy of the FE-computed displacements for models using material properties based on local values of BMD versus those using material properties based on local values of fabric and volume fraction. However, when using BMD-based material properties, errors were higher for the vertebral-body models (8.4-50.1%) than cuboid models (1.5-19.6%), suggesting that these properties are inaccurate in the peripheral regions of the centrum. Errors also increased when assuming that the cuboid region experienced uniaxial loading during axial compression of the vertebra. These findings indicate that a BMD-based constitutive model is not sufficient for the peripheral region of the vertebral body when seeking accurate QCT-based FE modeling of the vertebra.

Keywords: BMD; Elastic property; Fabric; Finite element analysis; Quantitative computed tomography; Vertebral body.

Fig. 1

For a representative specimen at the pre-yield increment: FE-computed axial displacement fields corresponding to the use of BMD- and fabric-based constitutive models for a, c the trabecular-cuboid model under Experimentally Matched boundary conditions; f, h the whole-vertebra model under Experimentally Matched boundary conditions and i, j the trabecular-cuboid model under Uniaxial boundary conditions; b, g show the experimentally measured displacement fields for comparison; in d, e two layers of finite elements have been removed from the superior, left, and anterior surfaces of a, c, respectively, so that the more of the interior displacements can be seen; in f–h, the white dotted lines delineate the location of the cuboid region; k, l FE-computed minimum principal strains and m, n FE-computed maximum principal strains for a representative specimen

Fig. 2

For the trabecular-cuboid models under Experimentally Matched boundary conditions: a comparison of the median percent error in displacement (obtained by comparing the measured and FE-computed displacements node by node) between BMD- and fabric-based constitutive relationships, at each loading increment (each pair of symbols connected by a line represents one specimen) and b scatter plot of experimentally measured and FE-computed displacements for a single, representative specimen, for each constitutive relationship and at the pre-yield increment; in a the horizontal arrows represent the median errors for specimen 6 when using the BMD-based constitutive relationship

Fig. 3

Comparison of the median percent error in displacement between BMD- and fabric-based constitutive relationships, at each loading increment for the whole-vertebra model along a X-axis, b Y-axis, c Z-axis; d comparison of the median percent error in displacement in the trabecular-cuboid models to that in the cuboidal and peripheral regions of the whole-vertebra models; in a–c, the symbols connected by a line represent one specimen; in d the data only shown are for the pre-yield increment; *p < 0.001. No effect of constitutive model was found for the median displacement error in any of the three directions (X: p = 0.44; Y: p = 0.54; Z: p = 0.4)

Fig. 4

Comparison of axial reaction forces predicted by the whole vertebral FE models to the experimentally measured values

Fig. 5

For the trabecular-cuboid FE models: a comparison of the median percent error in displacement for Experimentally Matched versus Uniaxial boundary conditions (each pair of symbols connected by a line represents one specimen) and b scatter plot of experimentally measured and FE-computed displacements for a single, representative cuboid model, for each boundary condition; all data shown are for the pre-yield increment; *p < 0.05

Fig. 6

Young’s moduli in the z-direction (superior-inferior direction) according to the two constitutive relationships: a data for all specimens and b data for the average value of Young’s moduli in z-direction for FE elements which surround the DVC element-containing nodes with experimentally measured displacement larger than the detection limit; in each of a and b, different symbols represent different specimens

Fig. 7

a Histogram showing the distribution of the angle between the superior–inferior direction and the principal fabric direction (data are pooled across all specimens) and b dot plots showing the angle distribution for each specimen