Xiaodong Zhong^{1,2}, Phil Young^{3}, Peter Kollasch^{4}, Venkata Chebrolu^{4}, and Brian M. Dale^{5}

In order to investigate the effects of b-value acquisition strategies on the stability and bias of the prostate DWI results, including calculated b-value images and ADC, a framework was developed. Using the DWI data from 8 prostate patients, this study revealed that acquiring many averages at a few b-values increases bias compared to acquiring few averages at many b-values, particularly when large numbers of averages have been removed. The framework and strategies proposed in this work may provide a useful tool to design b-value acquisition protocols to achieve the stability of prostate DWI results in clinic.

Prostate cancer is the leading malignancy
in males.^{1} Prostate diffusion weighted imaging (DWI) has been
utilized for prostate cancer assessment.^{2-5} High b-value images are
very important, but often suffer from low SNR. Multiple averages can be
performed to compensate this, at the cost of scan time. Alternatively, high
b-value images can be calculated after apparent diffusion coefficient (ADC) is
calculated. Given a certain scan time, the best strategies to determine
b-values and averages to achieve comparable results compared to an ideally long
scan are not clear. Different strategies also influence the stability of ADC.

The purpose of this work was to develop a framework to explore this topic, and apply it in vivo to investigate the effects of b-value acquisition strategies on the stability and bias of the prostate DWI results, including calculated b-value images and ADC.

A routine clinically-indicated multi-slice
spin-echo (SE) echo planar imaging (EPI) diffusion sequence was performed on 8 clinical
patients on a 3T scanner (Skyra, Siemens, Erlangen, Germany) using an 18-channel body array and a 32-channel spine array (both Siemens
coils). Parameters included TR = 3500 ms, TE = 88 ms,
pixel-size = 0.94×0.94 mm^{2}, slices = 16, slice thickness = 4 mm,
GRAPPA×2, b-value = 50/100/400/600/800/1200 s/mm^{2} with repetitions
of 2/4/4/7/13/13, directions = 3, acquisition time = 464 s. Anonymized raw data was saved for offline processing.

Acquired b-values/repetitions were sampled to form different subsets (Table 1). The strategies were based on two categories, namely “focus” and “spread”. Focus strategies involved saving time by removing some acquired b-values and acquiring many averages for remaining b-values, while spread strategies remove averages from each b-value relatively evenly.

Using a Matlab program (Mathworks, Natick, MA), S0 and ADC maps were calculated for each subset using a regular log-linear fitting method, and subsequently used to generate calculated b-value images of 50/100/400/600/800/1200, same as the acquired ones. The prostate peripheral and central regions were manually segmented on one representative slice, and their mean and standard deviation values on all images were exported.

Statistical analyses were performed using R (R
Core Team, Vienna, Austria). To investigate stability, the coefficient of
variation (CV) was calculated for each region. To investigate bias, the
complete dataset was used as a surrogate for the ground truth, and the
difference between the complete dataset and each subset was used as an estimate
of the bias introduced by using the partial data. A bias-adjusted CV was
calculated as $$$\sqrt{\sigma^{2}+\triangle^{2}}/\mu_{0}$$$, where *σ* was the standard deviation of the estimator, Δ was the bias in the estimator (*µ* - *µ*_{0}), *µ* was the mean from the estimator and *µ*_{0} was the ground truth. This value provided a sum of squares combination of both bias and variation. A linear model was fitted to the
bias-adjusted CV to determine the effects of strategy, time, region and
diffusion weighting (main effects plus interaction between strategy and time, p<0.05
as significantly different).

The overall linear model was highly significant
(p<0.0001) with an adjusted R^{2}=0.39. Tests of significance for the model
parameters showed that the acquisition time was significant (p<0.0001), as
was the acquisition strategy (p<0.0001) with the spread strategy having a
bias-adjusted CV that was 0.03 smaller than the focus strategy (see Figure 1). Their interaction was also significant (p=0.012),
but the uncorrected CV was not significantly dependent on time or strategy (see
Figure 2).

Bias-adjusted CV for the calculated b1600 images and ADC maps was highest when using any acquisition strategy which omitted either the highest b-values or the lowest b-values (see Figure 3 and 4). For the b1600 image the bias generally decreased as more data was sampled, and at any fixed sampling time the spread strategy resulted in the least absolute bias.

1. Siegel RL, Miller KD, Jemal A. Cancer statistics, 2016. CA Cancer J Clin 2016;66:7-30.

2. Hosseinzadeh K, Schwarz SD. Endorectal diffusion-weighted imaging in prostate cancer to differentiate malignant and benign peripheral zone tissue. J Magn Reson Imaging. 2004;20:654-661.

3. Vargas HA, Akin O, Franiel T, Mazaheri Y, Zheng J, Moskowitz C, Udo K, Eastham J, Hricak H. Diffusion-weighted Endorectal MR Imaging at 3 T for Prostate Cancer: Tumor Detection and Assessment of Aggressiveness. Radiology 2011;259:775-784.

4. Kobus T, Vos PC, Hambrock T, De Rooij M, Hulsbergen-Van de Kaa CA, Barentsz JO, Heerschap A, Scheenen TW. Prostate cancer aggressiveness: in vivo assessment of MR spectroscopy and diffusion-weighted imaging at 3 T. Radiology 2012;265:457-467.

5. Jung SI, Donati OF, Vargas HA, Goldman D, Hricak H, Akin O. Transition zone prostate cancer: incremental value of diffusion-weighted endorectal MR imaging in tumor detection and assessment of aggressiveness. Radiology 2013;269:493-503.

Table 1 The 20 sampling strategies tested in this work.

Figure 1 Absolute
value of the estimated bias. The spread
strategies have significantly lower bias (p<0.0001) than the focus
strategies. The bias is less sensitive to total acquisition time for spread
strategies.

Figure 2 Coefficient
of variation as a function of strategy and data acquisition time. The
differences in uncorrected CV are not significant for N=8 subjects.

Figure 3 Bias-adjusted
CV in the calculated b1600 images, using the mean of the full data set as the estimated
ground truth. For a given acquisition time, the spread strategies had lower
bias in the more substantially reduced data sets.

Figure 4 Bias-adjusted
CV in the calculated ADC images, using the mean of the full data set as the
estimated ground truth. The bias for ADC was not a strong function of
acquisition time or strategy, provided some data from the highest b-value was
included.