Waldemar Zylka

A Gaussian approach for the calculation of the accuracy of stereotactic frame systems

Stereotactic frame systems are widely used in neurosurgery. The accuracy of frame devices is considered as a gold standard to which the accuracy of new frameless stereotactic navigation systems is compared. The purpose of this study is to develop a general approach for the prediction of the application accuracy of stereotactic systems. The approach will be applied to the frame-based biopsy performed with three frame devices: Leksell G, Cosman–Roberts–Wells (CRW), and Brown–Roberts–Wells (BRW). A work-flow analysis will be carried out demonstrating that the accuracy relevant for a clinical application comprises several error sources including imaging, target and entry point selection, image to frame coordinates registration, and the setting of mechanical parameters of the frame. These error sources will be postulated to obey a Gaussian distribution probability density. The linear, i.e., Gaussian, error propagation, will be used to link all error contributions thus to calculate the cumulative accuracy of the frame used in the application. Although the Gaussian approach is an approximation, it allows for an analytical treatment of the accuracy. Both the accuracy at the target point and the accuracy of the probe needle guidance along the planned trajectory have been investigated. Of great significance is the relationship found between accuracy, pixel dimension, and image slice thickness, the latter being the dominant factor for slices of more than 1.5 mm thickness, yielding inaccuracies larger than 1.5 mm. For target points the predictions for the application accuracy have been compared to the results of measurements, showing good agreement with the experimental data.

Effect of Localization Devices and Registration Methods on the Accuracy of Stereotactic Frame Systems Predicted by the Gaussian Approach

A qualitative work-flow analysis of a neurosurgical procedure indicates that the resolution of the image used to plan the intervention is the major source of inaccuracy. Quantitative experimental measurements confirm this observation. They fail, however, to explain the relationship between the accuracy of the frame components involved in a stereotactic procedure and the overall application accuracy. This investigation shows that the novel Gaussian approach is a flexible framework for the calculation of the application accuracy of frame systems. Therefore, the Gaussian approach provides a detailed understanding of the interplay between the various factors affecting accuracy. The basic ideas and limitations of the Gaussian approach are briefly explained. The effect of fiducial marker distribution and registration is investigated and shown to introduce a spatial dependence to the accuracy. The results of the Gaussian approach are compared with experimental data for three stereotactic frame devices: Leksell G, Cosman-Roberts-Wells, and Brown-Roberts-Wells. Although the Gaussian approach is an approximation, it reproduces the accuracy measured in the experiment within the statistical error of that experiment.