Dariya I Malyarenko^{1}, Yuxi Pang^{1}, Lisa J Wilmes^{2}, Ek T Tan^{3}, Johan Tondeur^{4}, Ajit Devaraj^{5}, Julien Sénégas^{6}, Johannes Peeters^{7}, John E Kirsch^{8}, Michael A Jacobs^{9}, David C Newitt^{2}, and Thomas L Chenevert^{1}

The most practical correction of nonuniform diffusion weighting due to gradient nonlinearity would use scanner-specific gradient design information similar to current mitigation of geometric image distortions. To check the feasibility of this approach in a multi-center, multi-scanner setting, longitudinal DWI quality control studies using a quantitative diffusion phantom were performed on representative MRI platforms in collaboration with three vendors. Here we report preliminary results for proposed descriptive metrics that adequately reflect the amount and source of deviations from system gradient design to guide implementation of comprehensive bias correction for quantitative DWI applications.

**Methods**

A quantitative diffusion phantom^{5}
was scanned on three clinical scanners (Sys1, Sys2 and Sys3 from three MRI
vendors) on two dates (“d1” and “d2”, > 6 months apart) using shared
protocol^{6}. For phantom orientations along right-left (RL) and
superior-inferior (SI) axes, axial and
sagittal single spin-echo (SSE) DWI scans were performed, respectively, on all
systems, with three diffusion gradient directions along primary magnet axes to
characterize individual gradient channels (G_{RL}, G_{AP}, G_{SI}). An additional double spin-echo (DSE) DWI
variant was acquired on two systems (Sys2 and Sys3) to suppress EC-distortions^{7} and
shim-induced gradient bias^{3}. B_{0}
maps were generated from multi-echo GRE scans with the same shim settings as
for DWI to independently characterize chronic shim gradients.

The ADC
mean and standard deviation (SD) were measured from circular regions-of-interest
(ROIs) placed along the phantom tube for offsets between -180 and 180 mm. The measured ADC dependence on offset from
magnet isocenter along RL and SI was fit to 4^{th} order polynomials. The
GNL-induced ADC bias with respect to the known ice-water value (ADC_{0}=1.1x10^{-3}
mm^{2}/s), was modeled using vendor-provided gradient field parameters.
Shim-gradient profiles were calculated as spatial derivatives of B_{0} maps
along RL and SI axes. “Alignment” between the ADC profiles of individual gradient
channels was quantified by Pearson correlation coefficient (R), and fractional “root-mean-square
distance” was quantified by fRMS = RMS/ADC_{0}.
All data analysis was performed in
Matlab (R2015b).

**Results and Discussion**

All
systems showed spatial bias patterns (e.g., Figure 1) consistent with their GNL
models for individual gradient channels (positive bias RL and negative bias SI)
with the highest DWI nonuniformity for G_{RL} and G_{AP} gradients
along SI direction (up to -45% absolute error). Platform-specific bias exhibited finite local
asymmetries (Figs.1,2, solid curves) that deviated from ideal gradient models
(Figs.1,2, dashed traces). Higher
absolute longitudinal variability and deviation was along SI (Fig.2, bottom
panes, lighter traces), while relative misalignment with respect to the model
was higher for RL offsets (Fig.1, dark traces). For all systems, differences between
longitudinal measurements (Fig.2, solid curves) did not exceed the deviations
from their models (Fig.2, dashed traces.)

The
offset dependence for ADC SD of Sys2 and Sys3 (Fig.1) correlated with the image
distortions due to localized eddy current (Fig.3). Alternative acquisitions
(DSE for Sys2 and Sys3) eliminated EC-induced distortions (Fig. 3) and uniformly
reduced the measurement SDs. For SSE DWI,
spatially localized EC led to artifactually
enhanced signal density counteracting positive GNL bias for right offset
position (Fig.1-3, Sys2) which was removed by DSE. Measured B_{0} gradients (sloped for
Sys2 and constant < 0.1 mT/m for Sys3) were consistent with observed
geometric distortions (“parabolic” for Sys2 and “linear” for Sys3, Fig.3) and
their longitudinal changes (e.g., Fig.3, Sys1).
Longitudinal changes in B_{0} shim gradients were higher than those
in EC-induced distortions, suggesting the object-dependent origin for the
former versus the system-dependent for the latter.

Consistent with Figures 1-3, higher correlation and lower fRMS were found between longitudinal measurements relative to the first (“d1”) measurement and the model (“m”). For each system, correlation with the model was higher for SI offsets, while fRMS was lower along RL (Table 1). Better alignment and smaller fRMS observed between longitudinal QC scans compared to the model confirmed repeatable measurements and suggested systematic sources for the residual deviations. Alternative (“d1a”) measurements (DSE for Sys2 and Sys3, and improved shim for Sys1) increased correlation and reduced fRMS to the model (Table 1). These improvements in R and fRMS metrics agreed with observed reduction of image distortions (Fig.3). Minor (order of SD) unexplained deviations persisted for “d1a” of Sys1 along RL and Sys2 along SI, while Sys3 SI deviation from model was in excess of longitudinal fRMS.

**Summary**

^{1}Bammer R, Markl
M, Barnett A, et.al. Magn. Reson. Med. 2003 50:560-569;

^{2}Malyarenko DI, Ross BD, Chenevert TL. Magn
Reson Med. 2014; 71(3):1312-1323;

^{3}Malyarenko DI,
Newitt D, Wilmes LJ, et.al. Magn Reson Med. 2016; 75(3):1312-23;

^{4}Tan ET, Marinelli
L, Slavens ZW, et.al.J Magn Reson Imaging. 2013; 38(2):448-453;

^{5}Chenevert TL, Craig JG, Ivancevic MK, et.al. J.
Magn Reson Imaging 2011; 34:983-987;

^{6}Chenevert TL and Malyarenko DI, “Longitudinal
quantitative diffusion phantom QC protocol” (2016) https://www.researchgate.net/publication/316932001;

^{7}Reese TG,
Heid O, Weisskoff RM, Wedeen VJ. Magn Reson Med 2003;49(1):177-182.

“R” – percent Pearson correlation; “fRMS” – percent fractional root-mean-square distance; “G_{RL}“–
right-left gradient; “RL” – right-left
offset direction; “ G_{SI}” – superior-inferior gradient; “SI” –
superior-inferior offset direction; “G_{AP}“–
anterior-posterior gradient;
“d1” and “d2” –
SSE data from two longitudinal QC time points; “d1a” – alternative DWI
for the first QC point (DSE for Sys2 and Sys3, and 2^{nd} order shim correction for Sys1); “m” -- model based on vendor-provided spherical
harmonics