## Calibration Error Due to Different Motion-Encoding Gradient Strength on Two Scanners

In this study, displacements of brain tissue in six human subjects and one gelatin “phantom” were measured by MR elastography on two MR scanners. Both were Siemens Trio 3T MRI scanners. One Trio scanner was located at the Beckman Institute at University of Illinois in Urbana-Champaign (UIUC; four subjects) and the other Trio scanner was at the Center for Clinical Imaging Research at Washington University in St. Louis (WU; two subjects and gel phantom). After publication, we discovered that the default motion-encoding gradient strength was not identical on the two scanners, but was lower on the WU scanner than on the UIUC scanner (20 mT/m versus 26 mT/m on the UIUC scanner). Thus, in two subjects and the gel phantom, the estimated displacement amplitudes should be higher by a factor equal to $26/20$ (1.3).

Correcting this error changes estimates of mean and standard deviation of brain displacement, curl, and strain values in the human brain by about 10% (due to 30% error in 2/6 subjects). Corresponding measurements in a gel phantom are also affected; these were included solely for qualitative comparison to the behavior of the brain. In rechecking calculations four other errors were discovered: (1) a small error in the location of the brain origin, which affected brain rotation/translation estimates (Fig. 8); (2) an error in presenting the scaled displacements of the gel container (Fig. 7); (3) a calculation error in the relative temporal phase and spatial angle between case and gel motion in the gel phantom; and (4) a calculation error in the relative temporal phase and spatial angle between skull and brain motion for two human subjects. No statistical comparisons were affected by these errors. The main conclusions of the study are unchanged.

Fig. 8
Fig. 8
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The following corrections are thus necessary:

• (i)

Text of Methods section (underlined): “Imaging parameters included motion-encoding gradient strength of 20 mT/m (WU) or 26 mT/m (UIUC), 6 k-space interleaves, ….”

• (ii)

Figures 5–7: Gel (not case) displacements should be multiplied by 1.3. (Note that this will improve agreement between the estimated motions of the gel and the case in Fig. 6).

• (iii)

Caption of Fig. 7 (underlined): “For comparison to curl and strain (dimensionless measures of displacement/length) displacement magnitude is normalized by R/10, where R is the radius of the case.”

• (iv)

Figure 8: The revised panels show slightly different mean and standard deviation values for rigid-body displacements of the brain.

• (v)

Figure 9: The revised figure shows slightly different mean and standard deviation values for wave-induced brain displacement, curl, and strain.

• (vi)

Table 2: Values of spatial angle and temporal phase between gel and case motion in the gel phantom are slightly different than reported.

• (vii)

Table 3: Values of spatial angle and temporal phase between skull and brain motion in the six human subjects have slightly different means and standard deviations.

Fig. 9
Fig. 9
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Table 2

caption (unchanged): Spatial angle $(β)$ and temporal phase delay ($ϕ$) between harmonic motion of the gelatin phantom case and harmonic, rigid-body motion of gelatin

as published
PositionPhantom case/gelatin
$β$ (rad)$ϕ$ (rad)
Anterior0.500.03
Right0.300.17
Left0.340.04
Posterior0.110.17
as published
PositionPhantom case/gelatin
$β$ (rad)$ϕ$ (rad)
Anterior0.500.03
Right0.300.17
Left0.340.04
Posterior0.110.17
corrected
Phantom case/gelatin
Position$β$ (rad)$ϕ$ (rad)
Anterior0.500.26
Right0.270.22
Left0.320.14
Posterior0.050.12
corrected
Phantom case/gelatin
Position$β$ (rad)$ϕ$ (rad)
Anterior0.500.26
Right0.270.22
Left0.320.14
Posterior0.050.12
Table 3

caption (unchanged): Spatial angle $(β)$and temporal phase delay ($ϕ$) between harmonic motion of the human skull and harmonic, rigid-body motion of brain tissue

as published
PositionHuman skull/brain (n = 6)
$β$ (rad)$ϕ$ (rad)
Anterior0.76 $±$ 0.483.97 $±$ 0.95
Right0.63 $±$ 0.403.91 $±$ 0.96
Left0.75 $±$ 0.514.01 $±$ 0.85
Posterior1.19 $±$ 0.373.94 $±$ 0.91
as published
PositionHuman skull/brain (n = 6)
$β$ (rad)$ϕ$ (rad)
Anterior0.76 $±$ 0.483.97 $±$ 0.95
Right0.63 $±$ 0.403.91 $±$ 0.96
Left0.75 $±$ 0.514.01 $±$ 0.85
Posterior1.19 $±$ 0.373.94 $±$ 0.91
corrected
Human skull/brain (n = 6)
Position$β$ (rad)$ϕ$ (rad)
Anterior0.55 $±$ 0.305.16 $±$ 1.12
Right0.59 $±$ 0.325.13 $±$ 1.22
Left0.69 $±$ 0.515.13 $±$ 1.13
Posterior0.97 $±$ 0.375.09 $±$ 1.18
corrected
Human skull/brain (n = 6)
Position$β$ (rad)$ϕ$ (rad)
Anterior0.55 $±$ 0.305.16 $±$ 1.12
Right0.59 $±$ 0.325.13 $±$ 1.22
Left0.69 $±$ 0.515.13 $±$ 1.13
Posterior0.97 $±$ 0.375.09 $±$ 1.18