Szabolcs David^{1}, Anneriet Heemskerk^{1}, Max Viergever^{1}, and Alexander Leemans^{1}

^{1}Image Sciences Institute, UMC Utrecht, Utrecht, Netherlands

### Synopsis

**Subject
motion during diffusion weighted MRI acquisition is a well-known confounding
factor which can affect diffusion tensor metrics. In this simulation study, we investigated
whether this confound is related to the change in distribution of diffusion
gradient orientations due to the required “B-matrix rotation” during subject
motion. According to our findings, subject motion can indeed generate a
significant angular bias in addition to the noise bias, suggesting that subject
motion itself may cause group differences in diffusion metrics.**### Introduction

In many studies, diffusion tensor imaging (DTI)
measures, such as fractional anisotropy (FA), of white matter structures are compared
between groups, such as different age groups or healthy controls vs patients. The
observed differences in these measures, however, may not always be due to
biologically related processes, but may originate from group differences in
physiological characteristics during acquisition, something already
well-studied in the fMRI society [1]. While
for diffusion MRI several processing steps have been optimized [2] [3], a recent study with real data showed
that FA group differences could still be observed simply based on differences
in subject motion between the groups [4]. In this simulation study, we explored
whether this confound can be explained by the concomitant change in
distribution of diffusion gradient orientations due to the required “B-matrix
rotation” during subject motion [5]. We also investigated how the introduced
angular bias due to subject motion compares to another well-known confound, the
noise bias.

### Methods

Subject motion trajectories were simulated along all three coordinate
axes to mimic the slow drift of head motion. These trajectories were defined as
described previously in [5], where the average absolute angular difference (represented
by D), a measure that quantifies the amount of subject motion (rotation only), was
varied from 0° (i.e., no subject motion) to 5°
(typically considered as a lot of subject motion) and subsequently quantified
in steps of 0.5° (500 trajectories per step and per
axis). Other simulation settings were defined in line with current acquisition
settings for typical DTI studies: 60 diffusion gradient directions distributed
isotropically on the unit half-sphere [6]; the mean diffusivity (MD) of the
diffusion tensor is 0.7×10-3 mm2/s; the FA
was set between 0.2 to 0.8; and the b-value was set at 1000 s/mm2. For
each motion trajectory, Rician noise was added (100 instances) with SNR levels equal
to 10, 20, 30, 40, and 50. To investigate the relative contribution of the
noise bias with respect to the angular bias induced by subject motion, we also
simulated diffusion signals as described above, but then without adding this
angular bias (i.e., as if there was no subject motion). Mean, standard deviation,
coefficient of variation (COV), and percentage difference of FA estimates are
computed and evaluated as function of SNR level and amount of subject motion (D).

### Results

Figure 1 shows that for a small amount of subject
motion (average D = 1°), the introduced angular bias does not add significantly
to the noise bias, even at high SNR levels. By contrast, for higher degrees of
subject motion (average D = 4°) the angular bias becomes more apparent (Figure
2), especially at higher SNR levels (e.g., see Figure 2a and 2d). Figure 3
shows the estimated FA percentage difference as a function of D for a simulated
diffusion tensor with FA = 0.8. One can clearly appreciate that for higher
amounts of subject motion, the angular bias becomes more dominant, with a net
result of nearly 2% difference for the largest values of D compared to the case
without subject motion. Figure 4 shows the COV of the FA percentage difference demonstrating
the difference in relative variability between the estimated FA values with and
without the induced angular bias.

### Discussion and Conclusion

Our main finding is that the underestimation and
variance of FA due to motion depends on the underlying FA value and the SNR
level. At low SNR levels, the noise will swamp the effects of diffusion gradient
imperfections, whereas at higher SNR levels, these disturbances become more
apparent and will act as a confounding factor by introducing an additional increase
in bias and variability, becoming more dominant with larger amounts of subject motion.
Note that this finding is in line with a similarly observed underestimation of
FA as reported in work on non-perfect gradient distributions [7]. Our study demonstrates
that confounds in FA can be explained by associated changes in the distribution
of diffusion gradient orientations due to subject motion.

### Acknowledgements

This
research is supported by VIDI Grant 639.072.411 from the Netherlands
Organisation for Scientific Research (NWO).### References

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