The Mathematics of Three or More N- Localizers for Stereotactic Neurosurgery

The mathematics that were originally developed for the N-localizer apply to three N-localizers that produce three sets of fiducials in a tomographic image. Some applications of the Nlocalizer use four N-localizers; however, the mathematics that apply to three N-localizers do not apply to four N-localizers. One solution to this problem is to ignore one of the four Nlocalizers in order that the mathematics that apply to three N-localizers may be used. This article presents a novel solution that applies to three or more N-localizers without the requirement that any N-localizer be ignored. This solution provides a transformation matrix that transforms coordinates from the two-dimensional coordinate system of a tomographic image into the three-dimensional coordinate system of the stereotactic frame. In addition, this solution provides a statistical measure of the accuracy of the transformation that may be influenced by conditions, such as nonlinear distortion of the tomographic image. Categories: Medical Physics, Radiation Oncology, Neurosurgery