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# Current Directions in Biomedical Engineering

### Joint Journal of the German Society for Biomedical Engineering in VDE and the Austrian and Swiss Societies for Biomedical Engineering

Editor-in-Chief: Dössel, Olaf

Editorial Board: Augat, Peter / Buzug, Thorsten M. / Haueisen, Jens / Jockenhoevel, Stefan / Knaup-Gregori, Petra / Kraft, Marc / Lenarz, Thomas / Leonhardt, Steffen / Malberg, Hagen / Penzel, Thomas / Plank, Gernot / Radermacher, Klaus M. / Schkommodau, Erik / Stieglitz, Thomas / Urban, Gerald A.

CiteScore 2018: 0.47

Source Normalized Impact per Paper (SNIP) 2018: 0.377

Open Access
Online
ISSN
2364-5504
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Volume 1, Issue 1

# Measurement of needle susceptibility artifacts in magnetic resonance images

Sebastian Schmitt
/ Katharina Skopnik
/ Heinrich Martin Overhoff
Published Online: 2015-09-12 | DOI: https://doi.org/10.1515/cdbme-2015-0050

## Abstract

The success of minimally invasive procedures under MR-guidance can be increased by the knowledge of the current needle pose. We hypothesize that a one-toone mapping exists between the needle orientation with respect to the static magnetic field and the cross-sectional shape of the needle’s susceptibility artifact. For this purpose, we derived a mathematical model, which describes the cross sectional geometry of the needle artifact. It is approximated by two ellipses. Certain parameters of these ellipses can be utilized for mapping the geometry of the needle artifact onto the needle orientation. The relation between the two ellipse parameters α (inclination of the semi-major axis) and b (length of the semi-minor axis) and the needle’s azimuth angle can be approximated by linear regression in a certain angle interval. A combination of these two ellipse parameters is suitable for estimating the needle’s azimuth angle within a range between 0° and 60°.

## 1 Introduction

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.

## 2.1 Materials

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).

Figure 1

Needle holder for ϑNH = 30° and φNH = 90°. The angles can be varied in the intervals −60° ≤ ϑNH ≤ 60° and 0° ≤ φNH ≤ 360°.

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 $0.599\frac{\text{mm}}{\text{px}}$.

Table 1

The needle orientations were given by the needle holder’s geometry parameters φNH (azimuth angle) and ϑNH (inclination angle). For every orientation one coronal image has been acquired, which shows the cross-section of the artifact.

## 2.2 Methods

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.

Figure 2

Segmented cross-section of the needle artifact for ϑNH = 0° and φNH = 0°.

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):

$EH:[xy]=RH[aHcos⁡(β)bHsin⁡(β)]+[x¯Hy¯H]$1$EV:[xy]=RV[aVcos⁡(β)bVsin⁡(β)]+[x¯Vy¯V],$2

with the rotation matrices

$RH=[cos⁡(αH)−sin⁡(αH)sin⁡(αH)cos⁡(αH)]$3

and

$RV=[cos⁡(αV)−sin⁡(αV)sin⁡(αV)cos⁡(αV)],$4

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 [1].

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.

## 3 Results

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 3

Optimal membership distribution (ℋ, V) and ellipse approximations for ϑNH = 0° and φNH = 0°.

Table 2

Parameters of the optimal ellipse approximations.

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.

Figure 4

Relations between αH (the inclination angle of the semi-major axis) and bH (length 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°.

## 4 Discussion

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.

## Funding

This work was funded by Landesregierung Nordrhein-Westfalen in the IuK & Gender Med.NRW program, grant no. GW02-052.

## References

• [1]

Published Online: 2015-09-12

Published in Print: 2015-09-01

#### Author’s Statement

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.

Citation Information: Current Directions in Biomedical Engineering, Volume 1, Issue 1, Pages 198–200, ISSN (Online) 2364-5504,

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© 2015 by Walter de Gruyter GmbH, Berlin/Boston.