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

Feasibility of the prospective correction for non-uniform diffusion weighting due to gradient nonlinearity using scanner-specific gradient design information was previously demonstrated by our academic-industrial partnership (AIP). Here we report on the progress toward implementation of the prospective correction by leading MRI vendor participants of the AIP on their respective scanner platforms. The vendor-provided on-line correction is benchmarked by comparison to previously validated retrospective off-line processing for uniform gel and flood phantoms, and a human volunteer. Vendor efforts enable comprehensive bias correction for standardization of quantitative DWI applications in multi-center clinical trial environments.

**Methods**

Uniform (water-based) diffusion
phantoms at ambient temperature
and the brain of an IRB-consented volunteer were scanned on three clinical MRI
systems (Sys1, Sys2 and Sys3) representing different MRI manufacturers. Torso-size
flood phantom was made with water
added to polyester fiber (to prevent swirling) in a rectangular 490x400x100mm^{3}
plastic container. Head-size (170mm-diameter) fBIRN^{10} phantom was
also used, consisting of 1.5% agar (in water) gel. fBIRN phantom and volunteer
brain were scanned as previously described^{3,8} near isocenter (low GNL bias
reference) and at 120-130mm superior offset (>10% predicted GNL bias).

2D
DWI scans used large field-of-view (FOV=500-550mm) with 9 (flood) and 25 (fBIRN)
4-5mm-thick coronal slices for phantoms,
and a typical brain protocol with 25 oblique axial slices (FOV=255mm) for a human
volunteer. Quantitative DWI was acquired using *b* = 0 and 1000s/mm^{2}
with 8 (fBIRN), 4 (brain) and 1 (flood) excitations per *b*-value to ensure
high-*b* SNR>15. Repetition times were: TR = 3.7, 8.3, 10s, and
echo-times: TE = 70, 80, 95ms, for brain, fBIRN and flood phantoms,
respectively. Three orthogonal DWI gradients were applied along the primary patient axes
in vendor-specific order (DWI1, DWI2, DWI3).

The
DWI gradient directions, *b*-values and acquisition geometry were
extracted from DICOM image header. Voxel-wise ADC was fit as the slope of the mono-exponential log-DWI signal dependence
on *b*-values. Measured spatial ADC_{m}
bias was quantified as deviation from ADC_{iso} reference at isocenter.
For histogram analysis, volumes-of-interest (VOIs) were manually defined avoiding B_{1}
inhomogeneity and susceptibility artifacts. The prospective DWI bias correction
was performed using vendor-provided tools. The independent benchmark correction
was applied retrospectively to DICOM series for the individual DWI directions
as previously described^{2,5}. Benchmark correction utilized system GNL
tensors numerically modeled using spherical harmonic (SPH) expansion with
vendor-provided model coefficients^{9}. All data analysis was automated in MATLAB
R2015b (Mathworks, Natick MA).

Sys1 on-scanner implementation allowed correction of individual DWI directions, and DICOM export of corrected DWI intensities, ADC maps, and corrector maps. The latter were used for direct comparison of (noise-less) scanner-generated and off-line benchmark corrector maps shown in Figure 1. The scanner-generated Sys1 corrector maps properly reflected GNL bias patterns (Fig.1, maps) with expected 50% under-weighting superior-inferior and over-weighting right-left. Minor differences versus independent benchmark correctors were detected for >200mm offsets. Good agreement between predicted direction-specific bias histograms within the flood phantom VOI confirmed correction implementation consistent with the benchmark (Fig.1, histograms).

Figure
2 illustrates flood-phantom ADC correction for Sys2 DWI3 direction. SPH-model
for DWI3 GNL corrector (Fig.2, middle map) properly reflected observed
direction-dependent ADC non-uniformity pattern (Fig.2, top map) with bias ranging
from -28% to +7% (Fig.2, magenta vs. blue histograms) with respect to isocenter
reference (ADC_{iso}=2.08x10^{-3}mm^{2}/s). Model-based correction effectively restored DWI3
ADC uniformity within the flood phantom volume (Fig.2, bottom map). Figure
3 illustrates comparable efficiency achieved by vendor-provided Sys3 GNL bias correction
(implemented post-reconstruction based on DWI DICOM) and independent benchmark
for average (trace-DWI) correction of an isotropic fBIRN phantom. The original observed ADC histogram bias (-50%
to -5%) with respect to the isocenter reference (ADC_{iso}=1.85x10^{-3}mm^{2}/s)
was reduced down to measurement uncertainty (±5%).

Figure
4 illustrates results of Sys1 vendor-provided correction for non-uniform
diffusion weighting bias in brain ADC maps. Significant anatomy-specific ADC “attenuation”
(e.g., from 0.8 to 0.5 (x10^{-3}mm^{2}/s) for midbrain white
matter) evident for offset scan map (Fig.4E) compared to (low-bias) reference
near isocenter (Fig.4A) is effectively corrected in Fig.4F. Anatomic %bias differences observed in Fig.4G
for isotropic CSF (-20%) versus anisotropic white-matter regions (-30%)
indicate sensitivity to directional DWI correction that would be lost by average
correction of the trace-DWI. Coronal reformats in Fig.4D,H confirm characteristic
GNL bias patterns with small bias near isocenter (0% to -5%, Fig.4D) and large SI
non-uniform weighting gradient for offset location (-5% to -45%, Fig.4H)
removed by correction.

**Summary**

National Institutes of Health Grants: R01CA190299, U01CA166104, U01CA151235, U01CA140204, 5P30CA006973.

**Disclosure:** T..Chenevert and D.Malyarenko are co-inventors of intellectual property assigned
to and managed by the University of Michigan for the patented GNL-bias DWI correction technology (US9851426)
licensed to Philips Medical Systems. E.Tan and J.Tondeur are employees of General Electric and Siemens, respectively. A.Devaraj and J.Peeters are Philips employees.

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