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.