Spinal fusion permanently connects two or more vertebrae in spine to improve stability, correct a deformity or reduce pain by immobilizing the vertebrae through pedicle screw fixation. Pedicle screws should be inserted very carefully to prevent possible irrecoverable damages to the spinal cord. Surgeons use CT/fluoroscopic images to find how to insert the screws safely. However, there is still human error, as determining precise trajectory in 3D space is difficult because of asymmetric structure of pedicle. In this study we attempt to propose a shape based method to help the surgeons to find the more accurate and safe path for screw insertion that minimizes the risk or invasiveness of the surgery using pre-operative CT images. We extracted two features for insertion paths from CT images, named "safety margin" and "pedicular screw fixation strength". By using weighted k-means different paths were clustered and compared with each other. Results of comparison between those paths obtained from surgeon's pre-operative planning, intra operative and the proposed method proves a great improvement on the rate of success in reaching a suitable insertion trajectory by using our method. It is observed that the risk of damage in intra operative stage can be potentially high and it can be reduced considerably by using the proposed planning approach.

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A new method for position determination of stationary targets from radio bearings, using triangulation, and based on the partial derivative analysis of bearing error has been proposed. Mathematical derivations have been carried out and a simulation illustrating the effectiveness of the method has been run. It turns out that, the method works best when the noise is excessively high and the traversed path is asymmetric. In such conditions, the method illustrates an error reduction of up to 5% with respect to the Least Square algorithm.

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