Motion Detection and Correction for Frame-Based Stereotactic Localization.

Frame-based stereotactic localization is an important step for targeting during a surgical procedure. The motion may cause artifacts in this step reducing the accuracy of surgical targeting. While modeling of motion in real-life scenarios may be difficult, herein we analyzed the case where motion was suspected to impact the localization step. In this case, a scan with and without motion was performed with a 3N localizer, allowing for a thorough analysis. Pseudo-bending of straight rods was seen when analyzing the data. This pseudo-bending appears to occur because head-frame motion during imaging acquisition decreases the accuracy of the subsequent reconstruction, which depends on Digital Imaging and Communications in Medicine (DICOM) metadata to specify the slice-to-slice location that assumes embedded object stability. Comparison of single-slice and multi-slice stereotactic localization allowed for comparative errors for each slice in a volume. This comparative error demonstrated low error when the patient was under general anesthesia and presumed not to have moved, whereas a higher error was present during the scan with motion. Pseudo-bending can be corrected by using only localizer fiducial-based information to reorient the pixels in the volume, thus creating a reoriented localizer scan. Finally, targeting demonstrated a low error of 0.1 mm (+/- 0.1 mm) using this reoriented localizer scan, signifying that this method could be used to improve or recover from motion problems. Finally, it is concluded that stability and elimination of motion for all images utilized for stereotactic surgery are critical to ensure the best possible accuracy for the procedure.

Stereotactic Localization: From Single-Slice to Multi-Slice Registration Including a Novel Solution for Parallel Bipanels.

Frame-based stereotactic localization generally assumes that all required fiducials are present in a single-slice image which can then be used to form targeting coordinates. Previously, we have published the use of novel localizers and mathematics that can improve stereotactic localization. As stereotactic procedures include numerous imaging slices, we sought to investigate, develop, and test techniques that utilize multiple slices for stereotactic localization and provide a solution for a parallel bipanel N-localizer.  Several multi-slice equations were tested. Specifically, multi-slice stereotactic matrices (ms-SM) and multi-slice normal to parallel planes (ms-nPP) were of particular interest. Bipanel (2N) and tripanel (3N) localizer images were explored to test approaches for stereotactic localization. In addition, combination approaches using single-slice stereotactic matrices (ss-SM) and multi-slice methods were tested. Modification of ss-SM to form ms-SM was feasible. Likewise, a method to determine ms-nPP was developed. For the special case of the parallel bipanel N-localizer, single-slice and multi-slice methods fail, but a novel non-linear solution is a robust solution for ms-nPP. Several methods for single-slice and multi-slice stereotactic localization are described and can be adapted for nearly any stereotactic system. It is feasible to determine ms-SM and ms-nPP. In particular, these methods provide an overdetermined means to calculate the vertical z, which is determined for a tripanel system using single-slice methods. In addition, the multi-slice methods can be used for extrapolation outside of the localizer space. Importantly, a novel non-linear solution can be used for parallel bipanel N-localizer systems, where other methods fail. Finally, multi-slice stereotactic localization assumes strict patient and imaging system stability, which should be carefully assessed for each case.

Improved Accuracy for the Sturm-Pastyr Localizer in the Presence of Image Noise.

Image guidance for frame-based stereotaxis is facilitated by incorporating three to four Sturm-Pastyr (SP) localizers into a stereotactic frame. Typically, each SP localizer enables the calculation of one set of [Formula: see text] coordinates in the three-dimensional coordinate system of the stereotactic frame, given three sets of [Formula: see text] coordinates created by the SP localizer in the two-dimensional coordinate system of a computed tomography (CT) image. Bouza and Brown propose formulas to calculate three sets of [Formula: see text] coordinates for each SP localizer. Monte Carlo (MC) simulation compares the accuracy of the new formulation to the accuracy of the original SP formulation that calculates only one set of [Formula: see text] coordinates for each SP localizer. Monte Carlo simulation reveals that the calculation of three sets of [Formula: see text] coordinates instead of only one set improves the accuracy of image guidance.

Novel Geometries for Stereotactic Localizers.

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) N-localizer 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 N-localizer 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 Z-localizer. 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.

Image-guidance for frame-based stereotaxis is facilitated by incorporating three to four N-localizers or Sturm-Pastyr localizers into a stereotactic frame. An extant frame that incorporates only two N-localizers violates the fundamental principle of the N-localizer, which requires three non-colinear points to define a plane in three-dimensional space. Hence, this two N-localizer configuration is susceptible to error. The present article proposes the V-localizer that comprises multiple diagonal bars to provide four or more non-colinear points to minimize error.

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

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 y-coordinates 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.

Comparative Accuracies of the N-Localizer and Sturm-Pastyr Localizer in the Presence of Image Noise.

The N-localizer and the Sturm-Pastyr localizer are two technologies that facilitate image-guided 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.

Coordinate Systems for Navigating Stereotactic Space: How Not to Get Lost.

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 ([Formula: see text]), the frame ([Formula: see text]), the head-stage ([Formula: see text]), 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.

Applied Mathematics of Ray Tracing and Perspective Projection in Fiducial-Based Registration of X-Ray Images.

Ray tracing (RT) and perspective projection (PP) using fiducial-based registration can be used to determine points of interest in biplanar X-ray imaging. We sought to investigate the implementation of these techniques as they pertain to X-ray imaging geometry. The mathematical solutions are presented and then implemented in a phantom and actual case with numerical tables and imaging. The X-ray imaging is treated like a Cartesian system in millimeters (mm) with a standard frame-based stereotactic system. In this space, the point source is the X-ray emitter (focal spot), the plane is the X-ray detector, and fiducials are in between the source and plane. In a phantom case, RT was able to predict locations of fiducials after moving the point source. Also, a scaled PP matrix could be used to determine imaging geometry, which could then be used in RT. Automated identification of spherical fiducials in 3D was possible using a center of mass computation with average Euclidean error relative to manual measurement of 0.23 mm. For PP, RT projection or a combinatorial approach could be used to facilitate matching 3D to 2D points. Despite being used herein for deep brain stimulation (DBS), utilization of this kind of imaging analysis has wide medical and non-medical applications.

Use of the Brown-Roberts-Wells Stereotactic Frame in a Developing Country.

Stereotactic surgery planning software has been created for use with the Brown-Roberts-Wells (BRW) stereotactic frame. This software replaces the Hewlett-Packard calculator originally supplied with the BRW frame and provides modern tools for surgery planning to the BRW frame, which facilitate its potential use as a low-cost alternative to the Cosman-Roberts-Wells (CRW) frame in developing countries.