Especially in severe cases of craniofacial microsomia, as shown with the three examples in Fig. 1, the reconstruction of a normal shape of the mandible is a challenging task.

A mean mandibular shape model will be derived from a large set of normally developed mandibles being reconstructed from CT data. Each of the reconstructed mandible geometries is mapped onto a common reference shape to identify corresponding points, thus allowing the representation of each surface model in a common vector space (cf. Fig. 2b). This transformed training set is subject to subsequent statistical analysis via Principle Component Analysis. The essential degrees of freedom of the resulting statistical model enable us to explore characteristic mandibular shapes within a normal variation. Hence, a statistical 3D shape model of a normally developed human mandible is supposed to serve as a planning aid for surgical reconstruction. The shape model can be adapted to the individual anatomy under consideration of individual mandibular parts that are to be preserved.

Each of the mandible models is decomposed into a set of corresponding patches (Fig. 2c). We chose a separation of the condyles and the horizontal and vertical branches on each side. For symmetry aspects, the entire mandible is split into half, subdivided through the lower frontal incisors. In order to separate the variability of an individual dentition from the shape of the bone, the tooth region was assigned its own patch. Each pair of corresponding patches on two different surfaces is finally parameterized to a common base domain by minimizing metric distortion.

That way, a statistical model of a mean mandible can be constructed (cf. Fig. 3). First experiments with a rather small amount of mandibular shape samples already show a broad range of typical variations.

With only a few characteristic shape modes we are able to distinguish between the height of the rami mandibulae, the mandibular angle, the length of the vertical branches, the width of the entire mandible, the radius of the mandibular arch, the shape and the size of the condyles. In order to fit the statistical shape model to an individual malformed mandible, a rigid transformation is optimized in combination with the shape weights to minimize the distance between relevant parts of a patient's mandible that are to be preserved and the corresponding parts of the shape model. As a result a best matching candidate of the shape model, with normal proportions will be computed that can serve as a template for surgical reconstruction.

First preliminary results already demonstrate that a representative model might provide a reasonable basis for surgical reconstruction of distinct mandibular deformities (cf. Fig. 4).

With a best matching candidate of a mean shape model (within normal variation), regarding the size and the shape of available bone, a surgeon gets a good perception of the reconstruction that is to be performed. We expect, that with an increasing number of samples the shape model can be accurately adapted to any given mandibular substructure. Therefore, we are constantly extending our mandible atlas.

• H. Lamecker, S. Zachow, H. Haberl, M. Stiller. Medical Applications for Statistical Shape Models.. Computer Aided Surgery around the Head, volume 17 of Fortschritt-Berichte - Biotechnik/Medizintechnik, p. 61, 2005.
• S. Zachow, H. Lamecker, B. Elsholtz, M. Stiller. Reconstruction of mandibular dysplasia using a statistical 3D shape model. Computer Assisted Radiology and Surgery, p. 1238–1243, Chicago, 2005.
• A. Westermark, S. Zachow, B. Eppley. 3-D osteotomy planning in maxillofacial surgery, including soft tissue prediction.. Journal of Craniofacial Surgery, 16(1):100–104, 2005.