Supplementary material: Simulation of scaling and delay corrections
It is noted in the manuscript that the effects of eddy currents and system delays can be partly corrected
by shifting and scaling the k-space trajectories prior to reconstruction. However, these simple
corrections cannot fully account for the intensity modulations that arise due to the mismapping of
spatial frequencies when complex deviations from the nominal k-space trajectories occur. In this
supplementary material we demonstrate the effects of these corrections using the numerical phantom
described in the manuscript.
Delay correction
Figure S1 shows simulated FID images, R2* maps and AC maps reconstructed using the measured
trajectories and again with nominal trajectories, with shifts applied corresponding to system delays of 1, 0, 1 and 2 µs. Intensity profiles across the FID images are also shown. A shift corresponding to a 1 µs
delay can remove some hyper-intense artifact and corresponding misclassification on the air-soft tissue
boundary. However, considerable hypo-intense artefacts and misclassifications persist on simulated
bone-soft tissue boundaries. Inspection of the intensity profiles also shows that some hyper-intense
artifact on the soft-tissue bone interfaces remains. Increasing the delay to 2 µs reduces the hyperintensities further, at the expense of low frequency modulation of the air signal, which leads to
misclassification of air as bone.
Scaling correction
Eddy current effects often lead to additional distortions. For instance, eddy currents can also result in
changing the k-space sample spacing, which affects the resolution or field of view of an image. If the
change in sample spacing is uniform across k-space, then scaling the trajectories prior to reconstruction
can correct for this. Equivalently, the FID image can be aligned to the echo image with affine
registration, which would remove edge artifacts in R2* maps. However, since k-space is sampled in the
FID and echo images in different ways, a simple scaling cannot completely remove eddy current effects.
Figure S2 shows FID and echo images of the numerical phantom reconstructed with nominal and
measured trajectories, along with the corresponding R2* and AC maps. The bottom row of images shows
corresponding images following registration of the nominal FID and echo images. Registration was
performed using an affine registration algorithm.41 Corresponding intensity profiles across the FID and
echo images are also shown. It can be seen that although there is a slight reduction in the
misclassifications in the AC map using this approach, a ring of bone still appears on the air-soft tissue
border (white arrow) and a region of bone is also still misclassified as air (black arrow), which occur due
to intensity modulations of the FID image (black arrows in the intensity profile plots).
To further demonstrate the limitations of this approach, the same experiment was repeated for a
different object, i.e. a grid pattern (Fig. S3), for which the grid should be classified as soft tissue and the
background as air. It appears from the intensity profiles that there is a slight scaling between the
nominal FID and echo images, but it is clear that the differences are dominated by intensity modulations
in the FID image (arrows), which can result in a misclassification of tissue types. However, when the
nominal trajectories are used, the edges of the grid are classified as bone, with negligible improvement
following registration (arrows).
Supplementary Figure captions
Figure No.
S1
S2
S3
Captions
Images of a numerical phantom showing the effect of shifting the k-space trajectories to
account for system delays. Shifting the trajectories changes the appearance of the
artifacts but in all cases artifacts persist, leading to misclassifications in AC maps.
Images of numerical phantom showing artifacts when reconstruction is performed using
nominal trajectories. Registration between the FID and echo images in part corrects for
the artifacts in the R2* maps, but misclassifications persist in the AC maps due to the
intensity modulations of the FID images, which are clearly seen in the plotted intensity
profiles.
Images of numerical grid phantom showing artifacts when reconstruction is performed
using nominal trajectories. Registration between the FID and echo images in part
corrects for the artifacts, but misclassifications persist due to the intensity modulations
of the FID images seen in the plotted intensity profiles.