Abstract
The N-localizer enjoys widespread use in image-guided stereotactic neurosurgery and radiosurgery. This paper derives the mathematical equations that are used with the N-localizer and provides analogies and explanations in order to promote an intuitive understanding of the mathematical principles.
Highlights
The mathematical treatment of the N-localizer has been discussed previously [1]
This N-shaped structure produces two circles and one ellipse in sectional images that are obtained via medical imaging technologies, such as computed tomography or magnetic resonance imaging [1,2]
Equation 3 is derived as follows: Transformation of coordinates from one three-dimensional coordinate system into another three-dimensional coordinate system may be accomplished via matrix multiplication that operates in a four-dimensional space [5]
Summary
The mathematical treatment of the N-localizer has been discussed previously [1]. The Nlocalizer comprises a diagonal rod that extends from the top of one vertical rod to the bottom of another vertical rod (Figure 1). Proceeding sequentially around the circumference of the stereotactic frame in the same direction as the direction from rod to rod , the remaining rods that were encountered in sequence were labeled , , , , , and This ordering for the rods permitted unambiguous labeling of the three diagonal rods , and and thereby permitted assignment of the three respective points of intersection , and between the long axes of these rods and the central plane of the scan section. The vertical rod at the right rear of the prototype stereotactic frame is larger in diameter than the other rods This large rod facilitates unambiguous pairing of each of the centroids , and in the scan section (Figure 4) with the correct one of the points of intersection , , and between the long axes of the three diagonal rods and the central plane of the scan section (Figure 3). This extrapolant is used to calculate the in the scan image
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