Creating cranial prostheses with RBFs

Biomedical engineers at Christchurch Hospital's Department of Medical Physics have used Radial Basis Functions to smoothly interpolate the surface of the skull in order to create CAD models for the manufacture of titanium prostheses. These are used by neuro-surgeons to repair skulls damaged in accidents, by disease or through surgery.

Computer graphics are used to render a 3D image of the skull from X-ray CT data on which a clinician identifies the region of sound bone surrounding the defect. An RBF model is used to interpolate the shape of the skull from this region. A mold in the shape of the fitted function can be milled directly from the mathematical description. A titanium prosthesis is then produced by pressing flat titanium plate into the mold.

  • Smooth interpolation across large, irregular holes is required
  • Accurate fit at the existing bone is needed 
  • Data density varies widely
  • An analytic model allows evaluation of the surface on a grid suitable for CNC milling
  • The smooth extrapolation of the RBF to a plane far from the data points suits the manufacturing process
  • The thin-plate spline basis naturally models the deformation of the titanium plate 

New 3D RBF tools allow more complex defects to be modelled. 

An RBF smoothly interpolates the surface of a skull to form a CAD model for the manufacture of a precision-fit titanium prosthesis at Christchurch Hospital, NZ.
Incomplete cranial surface
Cranial surface interpolated with RBFs


Reference

Surface Interpolation with Radial Basis Functions for Medical Imaging
J. C. Carr, W. R. Fright and R. K. Beatson
IEEE Transactions on Medical Imaging, Vol. 16, No 1, pp 96-107, February 1997.

  • Download (gzipped postscript) [1.23 MB]

    Other medical applications

    •