Partial data reconstruction using statistical shape and material modelling for dental applications

Woods, Christopher and Dickinson, Alexander (2015) Partial data reconstruction using statistical shape and material modelling for dental applications. 21st Congress of the European Society of Biomechanics, , Prague, Czech Republic. 05 - 08 Jul 2015.

Abstract

Understanding concealed dental geometry and the position of teeth is essential for the effective implementation of many dental/orthodontic therapies. Statistical shape modelling (SSM) can predict missing information using a database of registered geometries [1]. Methodologies exist for the virtual reconstruction of geometry using SSM, but they do not distinguish between crown and root anatomy. The aim of this study was to predict missing crown data in teeth, including a material identification parameter to capture explicitly the cemento-enamel junction (CEJ). A digital (.stl) database of 15 undamaged mandibular canines was compiled from micro-CT. A binary material operator was assigned to each node. The data was registered to a baseline model using elastic mesh-morphing, and principle component analysis (PCA) was used to compile the SSM. Each tooth was artificially bruxed to the location of maximum distal crown width. A non-linear sum of least squares algorithm was used to minimise a non-rigid deformation objective function to predict tooth geometry from partial data (E) (Eq.1&2), where d and m are the target and the predicted shapes respectively. ρ is a vector containing the weightings (ω) for manipulating the eigenvectors (e) with respect to the mean tooth (ṁ) in rotation (R) and translation (T). A smoothing algorithm established the CEJ from a material probability parameter (Fig.1). Exhaustive modal analysis reconstructed each tooth in the dataset using an increasing number of modes (Fig.2a). It was seen that the median shape error reduced with each additional mode added. However, it was also seen that the range increased with the number of modes, possibly due to noise, which suggests that there may be an optimum number of modes. Also, it should be noted that additional modes incur time penalties. The number of modes which gave the minimum error range varied between reconstruction trials. This set of 15 trials indicated that if the target shape is not known, between 5 and 7 modes would give a satisfactory reconstruction. The Leave-One-Out (LOO) test reconstructed the shape of a bruxed tooth that was excluded from the training dataset. The size of the dataset was increased until all teeth were included (Fig.2b). From the LOO test it was seen that convergence was achieved at approximately 12 training samples. Convergence indicates that the dominant shape characteristics have been captured. The presented methodology was used to reconstruct dental geometry and material location from partial data. However, the optimisation strategy, size of training set, number of modes and computational resource must all be balanced against reconstruction quality. This methodology has the potential to improve prediction and analysis within dentistry, bioengineering, forensic medicine and osteo-archaeology, where dental wear is scored qualitatively.

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Contributors

Author: Alexander Dickinson

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