Voxel-based localization in frame-based and frameless stereotaxy and its accuracy

The problem of accurate stereotactic localization and registration of targets in computed tomography (CT) data sets is addressed, in particular the effect of using a single transformation matrix to map voxel coordinates onto stereotactic coordinates. An algebraic approach to the calculation of stereotactic target coordinates in tomographic data acquired with conventional stereotactic localizers is presented. The volume transformation matrix (VTM) is discussed, which is useful for the registration of volumetric data sets, and also corresponds to the rigid body transformation matrix used in many so-called frameless registration methods. The VTM can lead to accuracy degradation, in particular due to patient movement during scanning. Simulations were performed and CT data sets acquired with patients fitted with the CRW or the GTC stereotactic localizer were analyzed. Comparison of STM- and VTM-derived stereotactic coordinates shows an average overall registration error of 0.1 mm for anesthetized patients and in the range 0.6-1.4 mm for nonanesthetized patient. Accuracy maps are described that enable the user to visualize the registration error in relation to the data. It is shown that the effect of fiducial point localization error and patient movement for VTM-based localization is minimized when all available fiducials in the region of interest are used. The significance of these results is discussed, and methods are proposed to minimize these effects for frame-based and frameless registration methods.