Accuracy of stereotactic coordinate transformation using a localisation frame and computed tomographic imaging Part II. Analysis of matrix-based coordinate transformation

Authors
Citation
P. Grunert, Accuracy of stereotactic coordinate transformation using a localisation frame and computed tomographic imaging Part II. Analysis of matrix-based coordinate transformation, NEUROSURG R, 22(4), 1999, pp. 188-203
Citations number
24
Language
INGLESE
art.tipo
Review
Categorie Soggetti
Neurology
Journal title
NEUROSURGICAL REVIEW
ISSN journal
0344-5607 → ACNP
Volume
22
Issue
4
Year of publication
1999
Pages
188 - 203
Database
ISI
SICI code
0344-5607(199912)22:4<188:AOSCTU>2.0.ZU;2-1
Abstract
The accuracy of coordinate transformation from a CT image to a stereotactic frame was investigated for stereotactic systems using a localisation frame and matrix-based coordinate transformation. The main source of error influ encing calculation was input data, due to inaccurate calculation of the cen tres of the rods of the localisation frame in the CT image, and the propaga tion of this input error during subsequent matrix calculation. Systemic err ors during matrix calculation do not exist, and rounding off errors were of subordinate importance compared to the input data error. The influence of input data error on coordinate transformation was studied by geometric meth ods, computer simulation, and numerical analysis. In the geometric model, i nput data errors affected the calculation of the centres of the three obliq ue rods in the frame space and shifted them three points upwards or downwar ds on the axis of each rod. The three centres of the oblique rods defined t he "CT plane" in the 3D space of the stereotactic frame. Displacements of t hese three centres caused a characteristic tilting of the CT plane. The pos itions of the correct and tilted CT planes defined the spatial error proper ties for all target points on the CT plane. The computer simulation investi gated the effects on matrix-based transformation of all possible displaceme nt combinations on the three oblique rods by 1 pixel (1.16 mm) in the x and y directions. A characteristic, space-dependent distribution of the frame- related coordinates was obtained for each target point. In the centre of th e frame, we found a maximal deviation of 1.0 mm in the xy direction and 2 m m in the z direction. This corresponded to an error amplification of 0.73 i n the xy direction and 1.22 in the z direction relative to the error at the centres of the rods. The maximum deviation (found in the periphery) for al l combinations on the three oblique rods was 1.7 mm in the xy direction and 3.3 mm in the z direction. This resulted in an amplification of 1.03 in th e xy direction and 2.01 in the z direction. This results had to be multipli ed by 2 to obtain a maximal error estimate for displacements including all nine rods of the localisation frame. Numerical analysis showed stable solut ions with low error amplification for hexagonal frame arrangements.