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.

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.

The Invention and Early History of the N-Localizer for Stereotactic Neurosurgery.

Nearly four decades after the invention of the N-localizer, its origin and history remain misunderstood. Some are unaware that a third-year medical student invented this technology. The following conspectus accurately chronicles the origin of the N-localizer, presents recently discovered evidence that documents its history, and corrects misconceptions related to its origin and early history.

Retraction: The Origin of the N-Localizer for Stereotactic Neurosurgery.

[This retracts the article DOI: 10.7759/cureus.140.].

Retraction: The Mathematics of Three or More N-Localizers for Stereotactic Neurosurgery.

[This retracts the article DOI: 10.7759/cureus.218.].

Retraction: The Mathematics of the N-Localizer for Stereotactic Neurosurgery.

[This retracts the article DOI: 10.7759/cureus.142.].

Retraction: The N-Localizer and Volume Imaging.

[This retracts the article DOI: 10.7759/cureus.232.].

Retraction: The History and Mathematics of the N-Localizer for Stereotactic Neurosurgery.

[This retracts the article DOI: 10.7759/cureus.156.].

The Mathematics of Four or More N-Localizers for Stereotactic Neurosurgery.

The mathematics that were originally developed for the N-localizer apply to three N-localizers that produce three sets of fiducials in a tomographic image. Some applications of the N-localizer use four N-localizers that produce four sets of fiducials; however, the mathematics that apply to three sets of fiducials do not apply to four sets of fiducials. This article presents mathematics that apply to four or more sets of fiducials that all lie within one planar tomographic image. In addition, these mathematics are extended to apply to four or more fiducials that do not all lie within one planar tomographic image, as may be the case with magnetic resonance (MR) imaging where a volume is imaged instead of a series of planar tomographic images. Whether applied to a planar image or a volume image, the mathematics of four or more N-localizers provide a statistical measure of the quality of the image data that may be influenced by factors, such as the nonlinear distortion of MR images.

The Mathematics of Three N-Localizers Used Together for Stereotactic Neurosurgery.

The N-localizer enjoys widespread use in image-guided stereotactic neurosurgery and radiosurgery. This article derives the mathematical equations that are used with three N-localizers and provides analogies, explanations, and appendices in order to promote a deeper understanding of the mathematical principles that govern the N-localizer.

The Origin and History of the N-Localizer for Stereotactic Neurosurgery.

Nearly four decades after the invention of the N-localizer, its origin and history remain misunderstood. Some are unaware that a third-year medical student invented this technology. The following conspectus accurately chronicles the origin and early history of the N-localizer and corrects some misconceptions related to both.

Invention of the N-localizer for stereotactic neurosurgery and its use in the Brown-Roberts-Wells stereotactic frame.

The N-localizer, which facilitates computed tomography-guided stereotactic surgery, was invented in the late 1970s by a medical student who built a prototype stereotactic frame to test the concept. Initial experiments using the prototype frame were soon followed by surgery in humans using the Brown-Roberts-Wells stereotactic frame.

Second derivatives in generalized Born theory.

Generalized Born solvation models offer a popular method of including electrostatic aspects of solvation free energies within an analytical model that depends only upon atomic coordinates, charges, and dielectric radii. Here, we describe how second derivatives with respect to Cartesian coordinates can be computed in an efficient manner that can be distributed over multiple processors. This approach makes possible a variety of new methods of analysis for these implicit solvation models. We illustrate three of these methods here: the use of Newton-Raphson optimization to obtain precise minima in solution; normal mode analysis to compute solvation effects on the mechanical properties of DNA; and the calculation of configurational entropies in the MM/GBSA model. An implementation of these ideas, using the Amber generalized Born model, is available in the nucleic acid builder (NAB) code, and we present examples for proteins with up to 45,000 atoms. The code has been implemented for parallel computers using both the OpenMP and MPI environments, and good parallel scaling is seen with as many as 144 OpenMP processing threads or MPI processing tasks.