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Trabecular bone is made up of an irregular, interconnecting framework of rod- and plate-like struts [1], therefore the mechanical properties of the bone may only be determined through experimental testing or detailed Finite Element modelling. Experimental testing requires a sample to be removed from the body, which is not possible in living patients. As such, there is a drive to move away from experimental testing and focus instead on creating accurate patient-specific Finite Element models from CT scans of the bone. The computational “gold-standard” Finite Element model used for trabecular bone, namely the voxel-based method, uses solid tetrahedral elements, which are extremely resource intensive. Vanderoost, et al [2] developed an alternative Finite Element code which discretises the structure into a series of beams and shells. This beam-shell approach vastly reduces the size of the mesh and, consequently, the processing time required for the simulation. In this work, an analysis cycle was developed to determine the apparent modulus of a structure using the beam-shell Finite Element model [2]. The cycle imports micro-CT scans of a structure, discretises the structure into a beam-shell mesh, performs a Finite Element simulation and outputs the apparent modulus of the structure along with a reconstructed image. The analysis cycle was validated by analysing over 3000 artificially generated images, comprising various configurations of cubic lattices, Kelvin cell lattices and octet truss lattices, and comparing the modulus output by the analysis cycle to baseline results obtained through the simulation of known node and element data. The analysis cycle provided predictions within 10% of the baseline value for most lattices, however there were issues associated with the rasterisation of the input images and postprocessing which caused variation in the results. Overall, it was determined that the analysis cycle is capable of capturing the apparent modulus of a variety of different structures. Micro-CT scans of 127 bone specimens were run through the analysis cycle. The results from the beam-shell analysis were compared to results from experimental testing [3] and an equivalent voxel-based analysis. There was a clear trend in both the beam-shell and voxel-based data, however the voxel-based method produced stiffer results than the beam-shell method overall. The beam-shell method showed more scatter than the voxel-based method, but contained less significant outliers. The effective modulus, i.e. the modulus of an inner core region, was determined for 17 of the bone specimens and compared to equivalent experimental results. The beam-shell method captured the increase in stiffness between the apparent modulus and the effective modulus as regularly as the voxel-based method, given appropriate boundary conditions were applied. The results produced by both methods can be improved by the removal of machining artifacts and improved segmentation of the micro-CT scans. This work confirms that the beam-shell method is capable of capturing the apparent modulus of a trabecular bone sample, however the scatter in the data must be reduced for it to be considered a viable alternative to the voxel-based method. It was found that the beamshell method is equally capable of predicting the relationship between apparent modulus and effective modulus as the voxel-based method. In both the beam-shell results and voxel-based results, the accuracy of a particular data point could only be determined by considering the results in reference to additional simulation and experimental data points. In light of these results, researchers should be cautious in reporting simulation results for trabecular bone without additional verification. |
