Reduced Basis Methods in Orthopedic Hip Surgery Planning
Statistical shape models (SSMs) prove to be an adequate prior in medical registration problems such as 3D segmentation of CT- and MRI data (Seim et al., 2008, see also Atlas-based 3D Image Segmentation). SSMs utilize the Principal Component Analysis (PCA) to express statistically significant anatomical variations within a training population. We enrich SSMs with volumetric bone-interior information learned from CT and utilize these Statistical Shape and Intensity Models (SSIMs) as a prior for the reconstruction process. A treatment plan in orthopaedics does often not only involve single bony anatomies, but rather whole joint structures (e.g. in total hip replacement). The individual components of the joint are oriented in various poses, depending on the patient's physical condition and pose in front of the X-ray scanner. To cope with different joint postures in the reference X-ray images, we further extend the SSIMs to articulated statistical shape and intensity models (ASSIMs). The ASSIM of the hip developed at ZIB represents the hip cup as a ball joint, in which each proximal femur (upper thigh bone) rotates with three degrees of freedom (see Fig. 1). The rotational center of the hip joint is part of the statistical analysis of the model and learned from the training population.
Upon moving the femur bones, possible collisions with other bone material, like the hip is detected and possible contact zones are displayed (see Fig. 2).
The project is done in collaboration with the "Numerics of Partial Differential Equations" group led by Dr. Ralf Kornhuber