Skull deformities can lead to increased intracranial pressure, vision, hearing, and breathing problems. Since research on the correction of underlying disorders on the cellular level is still being carried on patients with craniosynostosis depend on surgical intervention for preventing or reducing functional impairment and improving their appearance. The most commonly used surgical procedure consists of bone fragmentation, deformation (reshaping) and repositioning based on standards developed by Paul Tessier and refined by Daniel Marchac and Dominique Renier. A major problem is the evaluation of the aesthetic results of reshaping the cranial vault in small children as the literature does not provide sufficient criteria for assessing skull shape during infancy. A definition of the correct target shape after surgery is missing. The most important and in many cases only indication of the best possible approximation of the skull shape to the unknown healthy shape is left to the subjective aesthetic assessment of the surgeon. This prevents impartial control of therapeutic success and aggravates guidance and instruction of the remodelling process for inexperienced surgeons.

Statistical models of shapes offer the possibility for automated reconstruction of unknown shapes. In order to establish objective criteria for the reshaping process, we propose to perform statistical analysis of normally developed cranial shapes, c.f. Seg3D project. This information can then be used to map pathological shapes onto the statistical ensemble of the healthy shapes. The result provides a patient-specific basis for the remodeling process.

The samples for the statistical analysis are generated on the basis of MRT data of normally developed skulls. First, the relevant region for the surgical intervention is determined. To this end, some landmarks for defined on the reconstructed skull surfaces:

• meatus acusticus externus: the entries to the auditory canals.
• nasion: foremost point of the sutura naso-frontalis in the mid-sagittal plane.
• sella: center of the sella turcica (hypophysis)
• occiput: palpable elevation of the os occipitale in the mid-sagittal plane.

These are used to generate corresponding regions for the statistical analysis. Using the methods developed in the Seg3D-project, an average shape plus the main modes of variation within the sample are computed.

The 3D cranial model serves as a template for the reshaping process, by finding an optimal fit of any of its variations to a given malformed skull. Usually, no pre-operative MRI scan is available for the infant patients (mostly under the age of one year) in order to avoid unnecessary anaesthesia. Hence the matching of the model towards the pathological skull of the patient is performed by non-invasively measuring anthropometric distances that are not affected by the surgical intervention:

• width between both entries of the auditory canals
• distance from nasion to occiput
• height between vertex and the midpoint of the line between the auditory canals

These distances are extrapolated to the skull surface by approximating the skin and skull thickness. The shape model instance that best fits these measurements is selected as a template for the reconstruction process. The resulting shape instance represents an individual interpolation of all shapes contained in the training set.

A statistical shape model was created from 21 MRI data sets (patient age: 3 to 10 months). The completeness of the model was tested in a leave-one-out experiment on all 21 data sets available: on average the model is capable of approximating any other arbitrary skull shape with an error of 0.7 +/- 0.2 mm (mean symmetric surface distance). The size of the training set shall be enlarged in the future.

In a first clinical application, the statistical model was pre-operatively matched to a patient using the method described above. From this computed shape model instance a life-size facsimile of the skull was built and taken to the operating room to guide the reshaping process. The following figure illustrate the surgical procedure and the role of the statistical skull model (photos taken by F. Hafner, Charité Berlin):

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