Monte Carlo Simulation of Errors for N-localizer Systems in Stereotactic Neurosurgery: Novel Proposals for Improvements

Abstract

Introduction: Frame-based stereotaxis has been widely utilized for precise neurosurgical procedures throughout the world for nearly 40 years. The N-localizer is an integral component of most of the extant systems. Analysis of targeting errors related to the N-localizer has not been carried out in sufficient detail. We highlight these potential errors and develop methods to reduce them. Methods: N-localizer systems comprising three and four N-localizers of various geometries were analyzed using Monte Carlo (MC) simulations. The simulations included native and altered geometric dimensions (Width [W] x Height [H]). Errors were computed using the MC simulations that included the x-and y-axes of vertically oriented rods, that altered the W/H ratio, and that added a fourth N-localizer to a three N-localizer system. Results: The inclusion of an overdetermined system of equations and the geometries of the N-localizer systems had significant effects on target errors. Root Mean Square Errors (RMS-e) computed via millions of MC iterations for each study demonstrated that errors were reduced by (1) inclusion of the x-and ycoordinates of the vertically oriented rods, (2) a greater triangular area enclosed by the diagonal fiducials of the N-localizer system (stereotactic triangle), (3) a larger W/H ratio, and (4) an N-localizer system that comprised four N-localizers. Conclusion: Monte Carlo simulations of Root Mean Square error (RMS-e) is a useful technique to understand targeting while using N-localizer systems in stereotactic neurosurgery. The application of vertical rod positions enhances computational accuracy and can be performed on any N-localizer system. Keeping the target point within the stereotactic triangle enclosed by the diagonal rods can also reduce errors. Additional optimizations of N-localizer geometry may also reduce potential targeting errors. Further analysis is needed to confirm these findings which may have clinical importance.

Novel Geometries for Stereotactic Localizers

“…The novel bipanel systems give rise to an overdetermined set of equations that optimize the computations [3]. While the Z-localizer fared best in accuracy, this accuracy came at the cost of increased complexity.…”

“…Moreover, the Z-localizer has supporting vertical bars to which 10 diagonal bars abut; these supporting vertical bars are not intended for use in stereotactic calculations. All of these new localizer panels (M, F, and Z) are arranged in an "antiparallel" manner (i.e., one panel inverted compared to the opposite panel) that was found previously to minimize errors [3]. Each diagonal bar is bracketed by parallel, vertically oriented bars and can therefore exploit N-localizer mathematics to calculate the (x,y,z) coordinates of a point along a diagonal bar, given the (u,v) coordinates of 3 fiducials in a CT or MRI image [6].…”

“…This stereotactic matrix converts 3D coordinates to two-dimensional (2D) coordinates or 2D to 3D. It has been shown previously that the use of an overdetermined system of equations affords an incremental minimization of error at a given target [3]. However, with the introduction of a 2-panel (bipanel) localizer system, the ability to localize a single image yields insufficient information because only two of the three required 3D points are present (Figure 1).…”

“…Previously, Monte Carlo (MC) simulations were utilized to predict potential errors related to stereotactic localization [3]. These errors were reported as Root Mean Square Error (RMSE) and reflect millions of simulations for each system.…”

“…Four N-localizer panels affixed to its anterior, posterior, and lateral sides afford the smallest errors. Due to practical considerations, the posterior Nlocalizer panel is often omitted, resulting in a configuration that comprises three N-localizer panels [3]. In order to promote patient comfort, minimize claustrophobia, and simplify the design, the removal of the anterior and posterior N-localizer panels creates a configuration that comprises only two N-localizer panels, wherein one N-localizer panel is affixed to each lateral side of a rectangular frame [4].…”