Abstract
Principal components analysis is a powerful technique which can be used to reduce data dimensionality. With reference to three-dimensional bone shape models, it can be used to generate an unlimited number of models, defined by thousands of nodes, from a limited (less than twenty) number of scalars. The full procedure has been here described in detail and tested. Two databases were used as input data: the first database comprised 40 mandibles, while the second one comprised 98 proximal femurs. The “average shape” and principal components that were required to cover at least 90% of the whole variance were identified for both bones, as well as the statistical distributions of the respective principal components weights. Fifteen principal components sufficed to describe the mandibular shape, while nine components sufficed to describe the proximal femur morphology. A routine has been set up to generate any number of mandible or proximal femur geometries, according to the actual statistical shape distributions. The set-up procedure can be generalized to any bone shape given a sufficiently large database of the respective 3D shapes.
Highlights
Great emphasis has been given in recent years to the possibility of producing patientspecific devices
The regression of each mandible versus the respective Principal Components” (PCs) has resulted in a root mean square error below 1.13 mm, while the same error has resulted to be below 1.09 mm for the proximal femurs
The different PCs describing the main shape variations with reference to the average shape are illustrated in Figures 3 and 4 for the mandible and for the femur, respectively
Summary
Great emphasis has been given in recent years to the possibility of producing patientspecific devices. In this context, the subject’s geometry is generally obtained through reconstruction from Computed Tomography (CT) scans or Magnetic Resonance (MR). CT and MR exams are often confined to a limited number of applications on a restricted cluster of patients [4]. This is due to the limited availability of the respective scanners, high exam costs and the radiation considerations of X-ray.
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