Supervised learning for bone shape and cortical thickness estimation from CT images for finite element analysis.

Knowledge about the thickness of the cortical bone is of high interest for fracture risk assessment. Most finite element model solutions overlook this information because of the coarse resolution of the CT images. To circumvent this limitation, a three-steps approach is proposed. 1) Two initial surface meshes approximating the outer and inner cortical surfaces are generated via a shape regression based on morphometric features and statistical shape model parameters. 2) The meshes are then corrected locally using a supervised learning model build from image features extracted from pairs of QCT (0.3-1 mm resolution) and HRpQCT images (82 µm resolution). As the resulting meshes better follow the cortical surfaces, the cortical thickness can be estimated at sub-voxel precision. 3) The meshes are finally regularized by a Gaussian process model featuring a two-kernel model, which seamlessly enables smoothness and shape-awareness priors during regularization. The resulting meshes yield high-quality mesh element properties, suitable for construction of tetrahedral meshes and finite element simulations. This pipeline was applied to 36 pairs of proximal femurs (17 males, 19 females, 76 ± 12 years) scanned under QCT and HRpQCT modalities. On a set of leave-one-out experiments, we quantified accuracy (root mean square error = 0.36 ± 0.29 mm) and robustness (Hausdorff distance = 3.90 ± 1.57 mm) of the outer surface meshes. The error in the estimated cortical thickness (0.05 ± 0.40 mm), and the tetrahedral mesh quality (aspect ratio = 1.4 ± 0.02) are also reported. The proposed pipeline produces finite element meshes with patient-specific bone shape and sub-voxel cortical thickness directly from CT scans. It also ensures that the nodes and elements numbering remains consistent and independent of the morphology, which is a distinct advantage in population studies.