The success of minimally invasive procedures under MR-guidance can be increased by the knowledge of the current needle pose. The difference of the magnetic susceptibility between an intervention needle and the surrounding tissue generates a large susceptibility artifact in magnetic resonance images. We hypothesize that a one-to-one mapping exists between the needle orientation with respect to the static magnetic field and the cross-sectional shape of the needle’s susceptibility artifact. Features are derived from the shape geometry, and significant features are identified that map the shape geometry onto the azimuth angle of the needle.
2 Material and methods
An amagnetic biopsy needle (SOMATEX®, MR Chiba Needle 20 G, dneedle = 0.95 mm, lneedle = 150 mm) has been inserted into a copper sulfate (CuSO4) solution. The needle orientations (inclination angle ϑNH and azimuth angle φNH) were predefined by a needle holder’s (NH) geometry parameters (fig. 1).
With a SIEMENS MAGNETOM Aera 1.5 T, coronal MR-images, which show the cross section of the susceptibility artifact, have been acquired for the needle orientations listed in table 1. The imaging sequence was a bSSFP (balanced Steady-State Free Precession)-sequence with TR = 5.01 ms, TE = 2.51 ms, a FOV of 230 mm × 230 mm, and a pixel spacing of .
For the purpose of deriving features from the shape geometry of the needle artifact, all points of the artifact boundary have to be determined. Therefore, a gray scale value based segmentation algorithm was applied to the MR-images. The segmentation results of one exemplary needle artifact for ϑNH = 0° and φNH = 0° is shown in fig. 2.
As can be seen from this image, for the chosen imaging sequence, the shape of the needle artifact is very characteristic. It can be described by 4 lobes, of which 2 are opposed.
2.2.1 Ellipse approximation
All points of the segmentation line are defined as a set x. The 2 pairs of opposed lobes of the needle artifact are roughly oriented horizontally and vertically. Let the set x consist of 2 disjoint sets ℋ (horizontal) and V (vertical) with ℋ∩ V = x and ℋ ∩ V = ∅.
The points of these sets shall be approximated by one ellipse each (EH, EV):12
with the rotation matrices3
and 0 ≤ β < 2π. The parameters of the ellipses are (cf. fig. 3)
Fitting is performed by non-linear least squares, optimizing the squared sums of orthogonal distances eH and eV from the points to the fitted ellipse EH and EV, respectively .
Since the membership of points to one of the sets ℋ or V is not known previously, a number of different constellations is assumed. These constellation distinguish in the number of points and their angle interval. For each constellation, the two ellipses EH and EV are approximated and their approximation errors eH, eV are determined. As the optimal membership distribution, that constellation is chosen, which leads to the lowest product J = eH · eV of over-all approximation errors for EH and EV.
For every imaged needle orientation, the needle’s artifact geometry has been approximated by two ellipses EH and EV. Figure 3 shows the optimal membership distribution ellipse approximations for ϑNH = 0° and φNH = 0°. The parameters of all optimal ellipse approximations for every imaged needle orientation are listed in tab. 2.
Figure 4a shows the relation between the inclination angles αH of the semi-major axis of the ellipse EH and the azimuth angle φNH of the needle. Figure 4b shows the relation between the length bH of the semi-minor axis of the ellipse EH and the azimuth angle φNH of the needle.
It can be seen that for these two parameters a linear regression is possible within certain ranges of φNH. For αH this range is −30° ≤ φNH ≤ 60° and for bH this range is 0° ≤ φNH ≤ 90°. Therefore, a combined analysis of the parameters gives an estimation of the needle’s azimuth angle within the range 0° ≤ φNH ≤ 60°.
The shape geometry of a needle’s susceptibility artifact in magnetic resonance images has been approximated by 2 ellipses EH and EV. It could be shown that the combination of the parameters αH and bH of the ellipse EH enables an estimation of the needle’s azimuth angle within the range 0° ≤ φNH ≤ 60°. This estimation is only valid, if both the values of the parameter αH and the values of the parameter bH are within the range in which both linear regressions are suitable.
Features for estimating the needle’s inclination angle ϑNH could not be derived with the presented method and the available data. For this purpose, further measurements are required, where the inclination angle needs to be varied.
If proper feature extraction from the shape geometry of the needle artifact is possible, an estimation of the current needle pose would be feasible by measuring only one coronal image slice. Therefore, the results of this estimation could be used for plausibility checks and mutual improvement of other – active or passive – needle tracking methods, which measure the pose of the needle.
This work was funded by Landesregierung Nordrhein-Westfalen in the IuK & Gender Med.NRW program, grant no. GW02-052.
About the article
Published Online: 2015-09-12
Published in Print: 2015-09-01
Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent has been obtained from all individuals included in this study. Ethical approval: The research related to human use has been complied with all the relevant national regulations, institutional policies and in accordance the tenets of the Helsinki Declaration, and has been approved by the authors’ institutional review board or equivalent committee.