Novel Geometries for Stereotactic Localizers

Abstract

Introduction: The N-localizer is generally utilized in a 3-panel or, more rarely, a 4-panel system for computing stereotactic positions. However, a stereotactic frame that incorporates a 2-panel (bipanel) Nlocalizer system with panels affixed to only the left and right sides of the frame offers several advantages: improved ergonomics to attach the panels, reduced claustrophobia for the patient, mitigation of posterior panel contact with imaging systems, and reduced complexity. A bipanel system that comprises two standard N-localizer panels yields only two three-dimensional (3D) coordinates, which are insufficient to solve for the stereotactic matrix without further information. While additional information to determine the stereotactic positions could include scalar distances from Digital Imaging and Communications in Medicine (DICOM) metadata or 3D regression across the imaging volume, both have risks related to noise and error propagation. Therefore, we sought to develop new stereotactic localizers that comprise only lateral fiducials (bipanel) that leave the front and back regions of the patient accessible but that contain enough information to solve for the stereotactic matrix using each image independently.Methods: To solve the stereotactic matrix, we assumed the need to compute three or more 3D points from a single image. Several localizer options were studied using Monte Carlo simulations to understand the effect of errors on the computed target location. The simulations included millions of possible combinations for computing the stereotactic matrix in the presence of random errors of 1mm magnitude. The matrix then transformed coordinates for a target that was placed 50mm anterior, 50mm posterior, 50mm lateral, or 50mm anterior and 50mm lateral to the centre of the image. Simulated cross-sectional axial images of the novel localizer systems were created and converted into DICOM images representing computed tomography (CT) images.Results: Three novel models include the M-localizer, F-localizer, and Z-localizer. For each of these localizer systems, optimized results were obtained using an overdetermined system of equations made possible by more than three diagonal bars. In each case, the diagonal bar position was computed using standard Nlocalizer mathematics. Additionally, the M-localizer allowed adding a computation using the Sturm-Pastyr method. Monte Carlo simulation demonstrated that the Z-localizer provided optimal results. Conclusion:The three proposed novel models meet our design objectives. Of the three, the Z-localizer produced the least propagation of error. The M-localizer was simpler and had slightly more error than the Zlocalizer. The F-localizer produced more error than either the Z-localizer or M-localizer. Further study is needed to determine optimizations using these novel models.

The V-Localizer for Stereotactic Guidance

“…The error in the -coordinate provided by a diagonal bar is proportional to the slope of that bar [4]; hence, low-slope diagonal bars produce less error than high-slope diagonal bars. Therefore, the low-slope diagonal bars of the V-localizer decrease its RMSe compared to the RMSe of the M-localizer that includes only high-slope diagonal bars [7]. Fourth, in some CT images, the low-slope diagonal bars of the V-localizer extend farther anteriorly and posteriorly than any diagonal bars of the M-localizer, as discussed in the Appendices.…”

“…Fourth, in some CT images, the low-slope diagonal bars of the V-localizer extend farther anteriorly and posteriorly than any diagonal bars of the M-localizer, as discussed in the Appendices. Hence, these low-slope diagonal bars increase the area of the polygon enclosed by fiducials in the CT image and decrease the RMSe of the V-localizer compared to the RMSe of the M-localizer [4,7,9,10].…”

“…To enable the incorporation of only two localizers, wherein one localizer is attached to each lateral face of a rectangular stereotactic frame, several localizers that comprise two or more diagonal bars (instead of only one diagonal bar) have been proposed recently [7]. The most promising of these localizers are the Mlocalizer and Z-localizer.…”

“…(A) One V-localizer is affixed to each lateral face of a stereotactic frame. Each V-localizer is inverted top-tobottom relative to the opposite V-localizer, similar to the configuration proposed for two M-localizers [7]. (B) Two V-localizers are affixed to each lateral face of a stereotactic frame.…”

“…This article reports root mean square errors (RMSe) calculated via MC simulation for the two and four Vlocalizer configurations. These RMSe are compared to the RMSe for the M-localizer, the Z-localizer, a four Nlocalizer configuration, and the Brown-Roberts-Wells (BRW) localizer that embodies a three N-localizer configuration [1,4,7]. MC simulation models random fluctuations of the coordinates of the centroids of fiducials in a CT image.…”