Introduction and evaluation of a gray-value voxel conversion technique

In micro finite element analyses (microFEA) of cancellous bone, the 3D-imaging data that the FEA-models are based on, contain a range of gray-values. In the construction of the eventual FEA-model, these gray-values are commonly thresholded. Although thresholding is successful at small voxel sizes, at larger voxel sizes there is substantial loss of trabecular connectivity. We propose a new method: the gray-value method, where the microFEA-models use the information within the 3D-imaging data directly, without prior thresholding. Our question was twofold. First, how does the gray-value method compare to both plain and mass-compensated thresholding? Second, what is the effect of element size on the results obtained with the gray-value method? We used nine microCT-scans of human vertebral cancellous bone. These were degraded to represent different resolutions, and converted into microFEA-models using plain thresholding, mass-compensated thresholding, and the gray-value method. The apparent elastic moduli of the specimens were determined using microFEA. The different methods were compared on the basis of the apparent elastic moduli, compared to those calculated for a 28 microm reference model. The results showed that the gray-value method greatly improves the results relative to other methods. The gray-value method gives accurate predictions of the apparent elastic moduli, for voxel sizes up to one trabecular thickness (Tb.Th.). For voxel sizes greater than one Tb.Th. the accuracy, although still better than for both thresholding methods, becomes increasingly worse.