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.

The N-localizer and the Sturm-Pastyr localizer are two technologies that facilitate imageguided stereotactic surgery. Both localizers enable the geometric transformation of tomographic image data from the two-dimensional coordinate system of a medical image into the three-dimensional coordinate system of the stereotactic frame. Monte Carlo simulations reveal that the Sturm-Pastyr localizer is less accurate than the N-localizer in the presence of image noise.

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.

BACKGROUND Efficacy in deep brain stimulation (DBS) is dependent on precise positioning of electrodes within the brain. Intraoperative fluoroscopy, computed tomography (CT), or magnetic resonance imaging are used for stereotactic intraoperative localization (StIL), but the utility of biplanar X-ray has not been evaluated in detail. OBJECTIVE To determine if analysis of orthogonal biplanar X-rays using graphical analysis (GA), ray tracing (RT), and/or perspective projection (PP) can be utilized for StIL. METHODS A review of electrode tip positions comparing postoperative CT to X-ray methods was performed for DBS operations containing orthogonal biplanar X-ray with referential spheres and pins. RESULTS Euclidean (Re) errors for final DBS electrode position on intraoperative X-rays vs postoperative CT using GA, RT, and PP methods averaged 1.58 mm (±0.75), 0.74 mm (±0.45), and 1.07 mm (±0.64), respectively (n = 56). GA was more accurate with a ventriculogram. RT and PP predicted positions that correlated with third ventricular structures on ventriculogram cases. RT was the most stable but required knowledge of the geometric setup. PP was more flexible than RT but required well-distributed reference points. A single case using the O-arm demonstrated Re errors of 0.43 mm and 0.28 mm for RT and PP, respectively. In addition, these techniques could also be used to calculate directional electrode rotation. CONCLUSION GA, RT, and PP can be employed for precise StIL during DBS using orthogonal biplanar X-ray. These methods may be generalized to other stereotactic procedures or instances of biplanar imaging such as angiograms, radiosurgery, or injection therapeutics.

All stereotactic neurosurgical procedures utilize coordinate systems to allow navigation through the brain to a target. During the surgical planning, indirect and direct targeting determines the planned target point and trajectory. This targeting allows a surgeon to precisely reach points along the trajectory while minimizing risks to critical structures. Oftentimes, once a target point and a trajectory are determined, a frame-based coordinate system is used for the actual procedure. Considerations include the use of various coordinate spaces such as the anatomical (), the frame (), the head-stage (), and an atlas. Therefore, the relationships between these coordinate systems are integral to the planning and implementation of the neurosurgical procedure. Although coordinate transformations are handled in planning via stereotactic software, critical understanding of the mathematics is required as it has implications during surgery. Further, intraoperative applications of these coordinate conversions, such as for surgical navigation from the head-stage, are not readily available in real-time. Herein, we discuss how to navigate these coordinate systems and provide implementations of the techniques with samples.