Published: October 25, 2013 (see history)
DOI: 10.7759/cureus.142
Cite this article as: Brown R A (October 25, 2013) The Mathematics of the NLocalizer for Stereotactic Neurosurgery. Cureus 5(10): e142. doi:10.7759/cureus.142
Abstract
The Nlocalizer enjoys widespread use in imageguided stereotactic neurosurgery and radiosurgery. This paper derives the mathematical equations that are used with the Nlocalizer and provides analogies and explanations in order to promote an intuitive understanding of the mathematical principles.
Related articles
The Mathematics of the NLocalizer for Stereotactic Neurosurgery
Russell A. Brown ^{ }
Author Information
Russell A. Brown Corresponding Author
Principal Engineer, A9.com
Ethics Statement and Conflict of Interest Disclosures
Human subjects: This study did not involve human participants or tissue. Animal subjects: This study did not involve animal subjects or tissue. Conflicts of interest: The authors have declared that no conflicts of interest exist.
Article Information
DOI
10.7759/cureus.142
Cite this article as:
Brown R A (October 25, 2013) The Mathematics of the NLocalizer for Stereotactic Neurosurgery. Cureus 5(10): e142. doi:10.7759/cureus.142
Publication history
Received by Cureus: October 13, 2013
Peer review began: October 21, 2013
Published: October 25, 2013
Copyright
© Copyright 2013
Brown. This is an open access article distributed under the terms of the Creative Commons Attribution License CCBY 3.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
License
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The Mathematics of the NLocalizer for Stereotactic Neurosurgery
Russell A. Brown ^{ }
Figures etc.
Figure 1: Intersection of the scan section with the Nlocalizer
Figure 2: Calculation of the point of intersection between the rod \(\mathrm{\textbf{B}}\) and the central plane of the scan section
Figure 3: Representation of the central plane of the scan section in the threedimensional coordinate system of the stereotactic frame
Figure 4: Representation of the twodimensional coordinate system of the scan image
Figure 5: Three Nlocalizers are attached to the prototype stereotactic frame
Figure 6: Cranial computed tomography (CT) scan image of a patient surrounded by three Nlocalizers
Figure 7: Interpolation within the vector from \(P_Q\) to \(P_R\) in order to obtain the point \(P_S\) that appears in the scan image
Figure 8: Extrapolation beyond the vector from \(P_Q\) to \(P_R\) in order to obtain the point \(P_S\) that appears in the scan image
Retracted: The Mathematics of the NLocalizer for Stereotactic Neurosurgery

Author Information
Russell A. Brown Corresponding Author
Principal Engineer, A9.com
Ethics Statement and Conflict of Interest Disclosures
Human subjects: This study did not involve human participants or tissue. Animal subjects: This study did not involve animal subjects or tissue. Conflicts of interest: The authors have declared that no conflicts of interest exist.
Acknowledgements
Article Information
Published: October 25, 2013
DOI
10.7759/cureus.142
Cite this article as:
Brown R A (October 25, 2013) The Mathematics of the NLocalizer for Stereotactic Neurosurgery. Cureus 5(10): e142. doi:10.7759/cureus.142
Publication history
Received by Cureus: October 13, 2013
Peer review began: October 21, 2013
Published: October 25, 2013Copyright
© Copyright 2013
Brown. This is an open access article distributed under the terms of the Creative Commons Attribution License CCBY 3.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.License
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.


Figure 1: Intersection of the scan section with the Nlocalizer
Figure 2: Calculation of the point of intersection between the rod \(\mathrm{\textbf{B}}\) and the central plane of the scan section
Figure 3: Representation of the central plane of the scan section in the threedimensional coordinate system of the stereotactic frame
Figure 4: Representation of the twodimensional coordinate system of the scan image
Figure 5: Three Nlocalizers are attached to the prototype stereotactic frame
Figure 6: Cranial computed tomography (CT) scan image of a patient surrounded by three Nlocalizers
Figure 7: Interpolation within the vector from \(P_Q\) to \(P_R\) in order to obtain the point \(P_S\) that appears in the scan image
Figure 8: Extrapolation beyond the vector from \(P_Q\) to \(P_R\) in order to obtain the point \(P_S\) that appears in the scan image
Abstract
The Nlocalizer enjoys widespread use in imageguided stereotactic neurosurgery and radiosurgery. This paper derives the mathematical equations that are used with the Nlocalizer and provides analogies and explanations in order to promote an intuitive understanding of the mathematical principles.
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