1 Department of Informatics and Mathematical Modeling, Technical University of Denmark
This thesis presents mathematical and computational techniques for three dimensional growth modeling applied to human mandibles. The longitudinal shape changes make the mandible a complex bone. The teeth erupt and the condylar processes change direction, from pointing predominantly backward to pointing more upward. The full dataset consists of 31 mandibles from six patients. Each patient is longitudinally CT scanned between three and seven times. Age range is 1 month to 12 years old for the scans. Growth modeling consists of three overall steps: 1.extraction of features. 2.registration of the common features. 3.model the process that moves the matched points (growth modeling). A local shape feature called crest line has shown itself to be structurally stable on mandibles. Registration of crest lines (from different mandibles) results in a sparse deformation field, which must be interpolated to yield a spatially dense field. Different methods for constructing the sparse field are compared. Adaptive Gaussian smoothing is the preferred method since it is parameter free and yields good results in practice. A new method, geometry-constrained diffusion, is used to simplify The most successful growth model is linear and based on results from shape analysis and principal component analysis. The growth model is tested in a cross validation study with good results. The worst case mean modeling error in the cross validation study is 3.7 mm. It occurs when modeling the shape and size of a 12 years old mandible based on the 3 month old scan. When using successively more recent scans as basis for the model the error drops to 2.0 mm for the 11 years old scan. Thus, it seems reasonable to assume that the mandibular growth is linear.