Preliminary Preparations

Before the µCT images could be converted into specimen-specific models, they were resampled to a lower resolution, assigned material properties through the use of thresholding operations and a mesh was created. The details of these procedures are presented in the following subsection.

Resampling

The images from the µCT scanner (*.DICOM) were converted at the same resolution (74 µm) to an alternative format (*.TIFF) using a custom written algorithm (Matlab 7.9, MathWorks, USA; Jones and Wilcox 2007). Conversion of the images to TIFF format reduced the number of greyscales present in the images from 64,000 Hounsfield units to 256 greyscale colours and made the images compatible with the

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commercial image processing software that was available (ScanIP v4.2, Simpleware, UK). Because the image processing software converted the images into a FE mesh with the same element size as the voxel spacing, the images were downsized in ScanIP to a resolution of 1 mm using the built-in algorithm based on partial volume interpolation. A resolution of between 1 – 2 mm has been shown to be appropriate for modelling intact human and porcine vertebra on a continuum level (Wijayathunga et al. 2008; Jones and Wilcox 2007). Since the information on mesh density already existed for models generated using the same process, no further mesh convergence analysis was conducted. The partial volume interpolation method of resampling assigned a new greyscale value to each downsampled voxel based on the proportion of greyscale the previous voxels occupied within that space. Downsizing the images in this manner caused the definition of individual trabeculae to be averaged to a greyscale value that represented the bone and surrounding trabecular spacing, as shown in Figure 4.1.

Figure 4.1 A single cycle specimen at a resolution of (a) 74 µm and (b) 1 mm.

Material Properties

Threshold operations were performed using ScanIP in order to assign masks to the regions corresponding to the bone, fracture, PMMA loading plates and radio-opaque marker. The radio-opaque marker was used experimentally as a reference point in order to apply a point load to the middle of the vertebral body (Section 2.3.1). It was necessary to apply a point load, computationally, to the same location; however, it was also necessary to remove the marker from the model in order to provide a

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smooth surface on the upper loading plate. Therefore, the mask of the radio-opaque marker was exported as a lone object, without material properties, to the FE software (Abaqus v6.8 – 6.9, Simulia, USA) where the coordinates of the midpoint were obtained. Following this, the mask corresponding to the marker was deleted from the image processing software. If necessary, additional voxels were added to the upper surface of the superior loading plate in order create a smooth surface for loading.

Homogenous material properties were assigned to the masks of the PMMA (Young‟s modulus = 2.45 GPa, Poisson‟s ratio = 0.3 (Wijayathunga et al. 2008)) and the fracture (Young‟s modulus = 1x10-9 _{GPa, Poisson‟s ratio = 0.3). A very low}

modulus was chosen for the fracture in order to simulate a void as previous work has shown this to be an appropriate approximation (Tarsuslugil 2011). The Young‟s modulus of the bone was based on the greyscale value of each individual voxel and tuned using a linear greyscale conversion value since the greyscale is related to the bone density and the density is related to the elastic modulus of bone. The optimised greyscale conversion value was obtained when the stiffness of a set of computational models was in closest agreement with the stiffness of the corresponding experimental set. For fractured porcine vertebra, the greyscale conversion value employed was 5.229 MPa/greyscale value and was obtained by another researcher using a set of 18 fractured, porcine specimens (Tarsuslugil 2011). Previous studies have shown that a linear relationship for the greyscale conversion factor provides a similar level of accuracy for intact human and porcine vertebra as a power law relationship (Tarsuslugil 2011; Jones and Wilcox 2007). It has also been shown that a Poisson‟s ratio of 0.3 is appropriate for modelling trabecular bone (Jones and Wilcox 2007).

Transverse and sagittal views of the thresholding used for the bone, fracture and PMMA loading plates of the specimen presented above in Figure 4.1 are shown in Figure 4.2.

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Figure 4.2 A specimen in the image processing software with masks in place for the bone (cream), fracture (red) and PMMA loading plates (green) in the (a) transverse and (b) sagittal

view.

Contact pairs were created between the masks that came into contact with each other. A contact was established between each of the loading plates and both the bone and the fracture masks. A final contact set was created between the bone and fracture.

Model Exportation

Once the material properties had been assigned, the built-in topology and volume preserving algorithm was used to pre-smooth the voxels of the specimen prior to the creation of a mesh. Pre-smoothing the specimen prior to mesh generation helped to create a more accurate mesh (ScanIP v4.2, Simpleware, UK). An image of a specimen following pre-smoothing is shown in Figure 4.3.

Figure 4.3 A Finite Element model of a single cycle specimen following pre-smoothing but prior to meshing and model exportation.

Once the specimen had been smoothed, a mixed mesh of hexahedral and tetrahedral elements was created based on the topology of the model using the in-

(a) (b)

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built meshing algorithm, +FE Grid. With an element edge length of 1 mm, the mesh was then smoothed; this has been shown previously to improve model accuracy (Zhao 2010). The smoothed models were exported from the commercial image processing software as FE input files.