This study developed software tools to analyze geometric distortions in MRI images compared to CT reference images of a fiducial phantom containing 5229 spheres. The software automatically located all fiducial markers in the CT data and most in the MRI data. Analysis found the MRI data exhibited distortions from gradient nonlinearities, visible as an outward radiating effect and bulging near the edges of the field of view compared to the CT data. The positions in the CT data agreed with specifications within 1.73mm root mean squared error, providing a reference for quantifying the geometric distortions in the MRI images.

1. Figure 5
Fiducial marker locations
identified from the CT
data (red) compared with
the locations specified by
the phantom manufacturer
(blue).
The locations that we
found were in close
agreement with the
vendor specifications.
© 2015 Mayo Foundation for Medical Education and Research
Brian McCollough1,2, Paul Weavers, Ph.D.3, Joshua Trzasko, Ph.D.3, Shengzhen Tao2, Matt A. Bernstein, Ph.D.3
1Bethel University, St. Paul, MN; 2Biomedical Engineering and Physiology Graduate Program,
Mayo Graduate School, Rochester, MN; 3Department of Radiology, Mayo Clinic, Rochester, MN
•Locations of the fiducial markers in the CT data are
consistent with phantom schematics
•Increasing distortion is observed within the MRI data
near the edges of the FOV
•GNL have a significant effect on MRI data and require
corrections
Conclusions
•Complete the MRI code, and find the isocenter of the
magnetic field and the center of the phantom.
•Compare CT and MRI data with the phantom
specifications and find the differences.
•Compare collected CT and MRI data and directly
calculate the distortions between the two data sets.
•Feed the results into an iterative corrective scheme.
Future Work
McRobbie, D.W., Moore, E.A., Graves, M.J., & Prince,
M.R. (2007). MRI From Picture to Proton: Cambridge:
University Press, Cambridge.
Bushberg, J.T., Seibert, J.A., Leidholdt, E.M., & Boone,
J.M. (2012). The Essential Physics of Medical Imaging.
Philadelphia: Lippincott Williams & Wilkins
J.D. Trzasko, S. Tao, J. Gunter, Y. Shu, J. Huston III,
and M.A. Bernstein, in ISMRM Annual Meeting
(Toronto, 2015), p. 3735.
S. Tao, J.D. Trzasko, Y. Shu, J. Huston III, and M.A.
Bernstein, Magn. Reson. Med. Early View. (2014).
References
Magnetic resonance imaging (MRI) is made possible
by subjecting protons (in water) to a static magnetic
field, exciting these protons with radio-frequency (RF)
energy, and monitoring the resulting RF
signal. Additional dynamic magnetic fields called
gradients are applied to spatially encode this RF
signal. These gradients are ideally linear, but can
suffer from gradient nonlinearity, especially at the
edges of the field-of-view (FOV). This work utilized a
fiducial phantom with computed tomography (CT)
reference data to map the effect of the gradient non-
linearity (GNL). A set of CT and MRI data were
analyzed to find the positions of several thousand
fiducial markers across a large FOV, and the
differences in position between the reference standard
(CT) and the MRI images were used to characterize
the GNL. The resulting information can be used to
generate an improved GNL correction.
In this work, software tools were developed to
automatically determine the locations of 5229 fiducial
markers in the CT and MRI data. Analysis of the CT
data demonstrated that the correct number of points
was found, with a root mean squared error of 1.73
mm. Most fiducial markers were located in the MRI
data, and the distortions from the GNL were evident.
Abstract
1. Locate and identify all 5229 fiducial points in both the CT and
MRI images sets.
2. Create a list of all points in the CT and MRI data
3. Determine the geometric distortions of the MRI data using the
CT data as the reference truth
Objectives
Develop software tools to evaluate and quantitatively
analyze the geometric distortions found in an Magnetic
Resonance Imaging (MRI) machine.
Study Aim
CT and MRI images of the same 5229-sphere fiducial phantom
were analyzed to determine the image distortion properties of the
GE MR750w MRI scanner (GE Healthcare, Waukesha,
Wisconsin). The CT data (1.2695 mm [left/right (L/R)] by 1.2695
mm [anterior/posterior (A/P)] by 0.6 mm [superior/inferior (S/I)]
voxel sizes) were taken as the reference to which the MRI data
were compared (1.1992 mm (L/R) by 1.1992 mm (A/P) by 1.2 mm
voxel sizes).
The MRI data were corrected with the vendor’s standard
gradient non-linearity correction.
The positions of the fiducial markers were determined from CT
and MRI data using a Hough transform. A Hough transform
locates the bright circular centers of the fiducial markers. First, a
template image was applied that contained all of the markers of
interest to exclude any points outside the desired region. Then,
using a distance function and the X and Y coordinates, the circles
belonging to a specific marker were linked together. Finally, the
centers of each marker were calculated by taking the mean
location from the top and bottom locations of the circles for a
given marker.
Methods
Using a Fiducial Phantom To Track Geometric Distortion in Large
Field of View MRI Imaging: Comparison Against CT Reference
Figure 2
Original CT Image CT Image After Transform
Points found by the Hough transform are displayed as blue circles.
Figure 4
Image data included multiple
views of each fiducial marker.
To determine the physical
location of the center of a specific
fiducial marker, individual images
were compared to adjacent
images by calculating the
distance between circles in
adjacent axial images. The Z-axis
location was determined by
taking the mean position from the
top and bottom positions of a
fiducial marker.
CT view of images (blue) with
fiducial centers (red)
A.CT axial view of the circles found
by the Hough transform
B.MRI axial view of the circles
displaying the outward-radiating
distortion caused by the gradient
non-linearity.
C.MRI sagittal view of half of the
circles displaying the bulging
distortion of the magnet.
Figure 3
A.
C.
B.
Z
Y Y
X
Y
X
•The developed software tools were able to
automatically determine the locations of all the fiducial
markers in the CT data and the locations of most of
the fiducial markers in the MRI data
•The determined positions in the CT data differed from
the manufacturer specifications by a root mean
squared error of 1.73 mm
Results
Figure 1
Fiducial Phantom set up inside CT scanner