Gabriel Nketiah^{1}, Kirsten M. Selnæs^{1,2}, Elise Sandsmark^{1}, Jose R. Teruel^{3}, Tone F. Bathen^{1,2}, and Mattijs Elschot^{1}

Tissue water diffusion (ADC) quantification through diffusion-weighted imaging (DWI) currently plays an integral clinical role in prostate cancer. The echo-planar imaging technique employed in DWI is however prone to geometric distortion due to static magnetic field (B0) inhomogeneity. We investigated the effect of the correction of this distortion on the quantification of ADC values in the prostate. Our study showed that there is a significant association between the amount of distortion (mm) and the difference between ADC values before and after correction, which implies that correction for this could be necessary, especially for voxel-based quantitative analysis.

As part of an overarching PET/MRI study, 3T multi-parametric
MR imaging (Biograph mMR; Siemens, Erlangen, Germany)
was performed on 28 biopsy-confirmed high-risk prostate cancer patients (Gleason score ≥ 7 and/or PSA > 20 and/or
clinical stage ≥ cT3) prior
to radical prostatectomy. The DWI was acquired in left-to-right phase
encoding direction, but included an extra b=0 s/mm^{2} image in the reverse (right-to-left) phase
encoding direction, solely
for distortion correction purposes (acquisition details in Table 1).

The preprocessing
algorithm for distortion correction proposed by Holland et al ^{}^{10} was applied to the DW image
data. Briefly, the symmetry of B0 inhomogeniety induced distortions in the forward
(Figure 1A) and reverse (Figure 1B) phase encoding directions were used to
iteratively calculate a deformation field map, which was subsequently employed
to correct for distortion in the complete DWI data set acquired in the forward direction (Figure
1C).

Whole prostate and tumor
volumes-of-interest (VOIs) were delineated on the T2W images (Figure 1D) by
spatial matching to whole-mount prostatectomy
histology slides using anatomical landmarks,
and then transformed to the respective DW via registration.^{11} ADC maps (Figures 1E and 1F) and distortion distance
per voxel were computed from the uncorrected and corrected DWI data sets. For
each tumor, the effect of distortion on ADC was investigated on the lesion
level by calculating the difference in mean ADC as $$$ \it abs\left(mean\left(uncorrected ADC\right)-mean\left(corrected ADC\right)\right)$$$ and on the voxel level by calculating the mean difference in ADC as $$$\it mean\left(abs\left(uncorrected ADC-corrected ADC\right)\right).$$$ Linear-mixed models were used for
statistical analysis. Matlab R2016a programming environment
(The Mathworks, Natick, MA, USA) was
used to perform all data computations and analysis.

A
total of 40 clinically significant tumor volumes (mean volume = 5.8 cm^{3};
range = 0.56–31.9 cm^{3}) were annotated. Thirty-four (85%) of the
tumors were located in the peripheral zone (PZ). An overview of the induced
distortion and the resulting differences in mean ADC are given in Table 2.

On both lesion-wise (Figure 2A) and voxel-wise (Figure
2B) analysis, the amount of distortion had significant effect on the difference in ADC
(p = 0.0002 and p < 0.0001, respectively), but the effect was more
pronounced on the voxel level. In the 6/40 tumors (from 3/28 patients) with mean distortion distance greater than 1 pixel (~2.5 mm), the median (range) difference in ADC
was 58 mm^{2}/s (4–330 mm^{2}/s) [or 5% (0–23%)] and 144 mm^{2}/s (126–337 mm^{2}/s)
[or 15% (11–24%)] on
the lesion and voxel level, respectively.

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**Figure 1:** Illustration
of magnetic field inhomogeneity induced geometric distortion
in diffusion-weighted imaging with EPI trajectory. Induced distortions in forward
(A) and reverse (B) b=0 image phase encoding directions. (C) Distortion
corrected b=0 s/mm^{2}
image. (D) Prostate anatomy on
T2-weighted image. Computed ADC maps before (E) and after (F) distortion
correction. The overlaid contours of the whole prostate (blue) and a peripheral
zone tumor (red) were delineated on the T2-weighted image and then transformed
via registration to the diffusion-weighted images.