  Purpose: Simulation of motion in the frequency domain during the MRI
acquisition process is an important tool to study the effect of object motion.
It is natural in this context to rely on a voxel-to-voxel difference metric
between the original image and its motion-simulated version to quantify the
alteration. These metrics are very sensitive to any mis-coregistration between
the two images. As we observed global displacements of the corrupted image for
specific simulated motions, we focused this work on the critical choice of a
reference position of the object for the motion simulation that avoids any
global displacement. Methods: We used the motion simulation framework and we
studied the different proposed solutions. Classically, the position around the
k-space center is considered as a reference with two analytical solutions to
correct for global image shifts: demeaning the image in the Fourier domain
either using the exact position at k-space center or using a weighted average
around the center.
  Results: We demonstrated with motion simulated examples that these analytical
solutions did not yield the same results as a direct co-registration method.
Indeed, short transitions around the k-space center did not induce any global
displacement, in contrast with what both analytical solutions assumed. We also
observed a dependence of the global shift to both the motion amplitude and the
translation direction. Conclusion: In the absence of a theoretical solution, we
concluded that an extra co-registration step after motion simulation was needed
in order to compare the simulation with its reference image.
