Dariya I Malyarenko^{1}, Yuxi Pang^{1}, Lisa J Wilmes^{2}, Ek Tsoon Tan^{3}, John E Kirsch^{4}, Julien Sénégas^{5}, Michael A Jacobs^{6}, David C Newitt^{2}, and Thomas L Chenevert^{1}

^{1}Radiology, University of Michigan, Ann Arbor, MI, United States, ^{2}Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, CA, United States, ^{3}GE Global Research, Niskayuna, NY, United States, ^{4}Siemens Healthcare, Malvern, PA, United States, ^{5}Philips Research Laboratories, Hamburg, Germany, ^{6}Radiology and Radiological Science, John Hopkins University School of Medicine, Baltimore, MD, United States

### Synopsis

System-specific gradient nonlinearity (GNL) causes
spatially nonuniform weighting in diffusion weighted imaging (DWI). This leads
to systematic bias and variability in derived apparent diffusion coefficient (ADC)
maps, diminishing their quantitative utility for multi-site, multi-platform
clinical trials. An ADC error correction methodology for three-direction DWI acquisition
was developed previously using an empiric system GNL approximation. Here we demonstrate implementation of
correction for three clinical scanners using the system-specific
gradient-channel fields derived from vendor-provided spherical harmonic tables.
Implemented correction substantially improves precision and removes ADC bias for
ice-water phantoms. Comparable accuracy and
performance is achieved across all gradient platforms.

### Introduction

Spatial nonuniformity of diffusion weighting (DW)
induced by system-specific gradient nonlinearity (GNL)^{1} confounds apparent diffusion coefficient (ADC) maps for
off-center anatomy. This platform-dependent bias causes significant errors and
variability in ADC measurements in multi-site, multi-platform clinical trials
that utilize quantitative DWI^{2,3}. Previously, a framework was developed^{4}
to correct for the bulk of systematic ADC bias error for a mono-exponential medium
of arbitrary anisotropy using three orthogonal DWI measurements. In the present
work, the proposed DW bias correction was implemented for three clinical
scanners using gradient channel design information provided by vendors.### Methods

Sagittal DWI scans of
a long-tube ice-water phantom^{2} (Figure1f, insert) were performed on Siemens
Espree, GE Signa, and Philips Ingenia 1.5T MRI scanners, using three b-values
(*b* = 0, 750, 1500), with three DWI gradient directions, *u*_{k}, along primary magnet axes. Scanner-specific
nonlinearity tensors, *L**(***r**),^{1} were calculated
numerically on a 4-5 mm 3D grid within the magnet bores (450-600 mm diameter) by
each site using shared Matlab libraries and gradient design (spherical
harmonics) coefficients^{1} provided by their vendors. Three-dimensional
bias corrector maps for each gradient direction were generated by the central
analysis site as, *C*^{k}(**r**) = Tr(*Lu*_{k}[*Lu*_{k}]^{T})^{4}. For experimental ice-water
DWI data, the directional-average correctors were 3D-spline interpolated according
to the DICOM header information for each imaged volume and resolution. The 3D corrector maps were then applied on a pixel-by-pixel
basis to yield corrected trace-DWI intensities and
*b*-maps to derive unbiased ADC^{4}.
ADC maps were obtained from the linear log-signal DWI fit for (*b* = 0, *b* > 0) pairs. The ADC bias, *%(ADC-
ADC*_{0})/ADC_{0},
was estimated as percent-deviation from the known
diffusion value of ice-water, *ADC*_{0} = 1.1 (x10^{-3}mm^{2}/s)^{5}.
ADC regions-of-interest (ROIs) were defined on
three slices of the phantom tube near zero right-left (RL) offset (Table 1) and
superior-inferior offset *SI * > 30mm. The correction performance was quantified by
reduction of percent-bias for ROI histogram metrics (median and range).### Results

The observed ADC bias was independent of
b-value, ranged from -43% to +9% and induced systematic variations across all systems:
e.g., about 9% at SI = 10cm (Table 1). The steep DW nonuniformity along SI phantom
tube, Fig.1 (a,d,g), resulted in systematic (skewed) broadening of the corresponding
ADC histograms, Fig.1 (c,f,i, magenta). Application of the system-specific corrector
maps substantially improved ADC uniformity, Fig.1 (b,e,h), and reduced the histogram
widths (down to ±5% range for 90th percentile, Fig.1 (c,f,i, green)).
The median bias error was effectively eliminated (<0.1%) and systematic cross-platform
variability along SI was reduced (e.g., about 2% at SI=10cm after correction,
Table 1) to below measurement noise <3%. Both original and residual
histogram widths depended on phantom volume and SI extent of the selected ROI
(Table 1).### Discussion

Consistent with previous observations,^{2,3}
uncorrected DW nonuniformity led to substantial errors both in absolute ADC
values at offset locations and technical cross-system variability. The GNL-bias
correction was clearly necessary to improve precision, uniformity and
reproducibility of ADC maps at off-center locations. Adequate correction
performance was achieved across all studied systems. The described results
confirmed theoretical prediction of static character for GNL-induced
nonuniformity bias in *b*-value^{1,4} determined primarily by the
gradient system design. As shown, once built for a specific gradient system,
the corrector maps can be applied to the DWI scans of arbitrary object and
geometry. Analogous to commonly-used correction of geometric distortion, the
prospective correction of GNL-induced DW bias can be implemented on-scanner
using gradient system design and DWI scan geometry information.### Conclusion

The vendor-provided gradient channel
descriptions adequately accounted for observed systematic b-value nonuniformity bias across the three studied clinical
scanner platforms. For a temperature-controlled phantom, implementation of GNL
bias correction substantially enhanced the accuracy of ADC map values and
eliminated systematic cross-platform variability. These results demonstrate
feasibility of prospective (on-scanner) correction for the system-specific GNL-induced
bias in diffusion weighting.### Acknowledgements

This research was supported by National Institutes of Health Grants: R01CA190299, U01-CA166104, U01CA151235, U01CA140204, 5P30CA006973.### References

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