Jessica M Winfield^{1,2}, Nandita M deSouza^{1,2}, Veronica A Morgan^{1,2}, David J Collins^{1,2}, and Matthew R Orton^{1,2}

The influence of b-value selection on fitted parameters from the
stretched exponential model (distributed diffusion coefficient DDC, and ‘stretching
parameter’ α) and mono-exponential model (apparent diffusion
coefficient ADC) was investigated in a cohort of 42 patients with cervical tumours. Diffusion-weighted
images images were acquired using 9 b-values between 0 and 800smm^{-2}, and
fitted voxel-by-voxel using all b-values (0 to 800smm^{-2}) and
b-values n-to-800smm^{-2}
(where n is 20,40,60,80,100, or 300smm^{-2}).
ADC estimates are highly sensitive to b-value
selection, with reduction in ADC when low b-values are excluded, whereas DDC and α are
more robust to differences in b-value selection.

**Patients:** Patients with cervical cancer
were scanned after informed consent as part of a prospective single-centre study.
Forty-two consecutive patients with histologically-proven cervical tumours (24
squamous cell carcinomas, 15 adenocarcinomas, 3 rarer sub-types) and tumour
volume at least 50mm^{3} visible on DW-MRI were included in this
exploratory analysis.

**
Imaging:** Hyoscine
butylbromide (20 mg) i.m. was administered before scanning to reduce image
artefacts due to peristalsis. Patients were scanned on a Philips Achieva 3T MR
scanner using an endovaginal coil.^{4} Following T_{2}-weighted
and diffusion-weighted images acquired transversely, coronally and sagitally
through the cervix, a coronal DWI sequence with 9 b-values was acquired for
assessment of DW-MRI models (b-values 0,20,40,60,80,100,300,500,800smm^{-2}).

**Analysis:** Regions
of interest (ROIs) were drawn on computed diffusion-weighted images (b=800smm^{-2})
using in-house software, with reference to T_{2}-weighted images.^{5}
ROIs were drawn around the whole tumour on all slices on which the tumour
appeared. Mono-exponential $$$S(b)=S_0exp(-b\textrm{ADC})$$$ and stretched exponential $$$S(b)=S_0exp(-[b\textrm{DDC}]^α)$$$ models were fitted
voxel-by-voxel using least-squares fits (Matlab 2016a). The ‘stretching parameter’, α, was constrained to lie between 0 and 1. Pixels where the signal did
not decay montonically with increasing b-value and pixels with fitted S_{0}
below a background noise level in mono-exponential fits were excluded. Fitting
was repeated by excluding consecutive low b-values, specifically, fitting to
all points between 20 and 800smm^{-2}, 40 to 800smm^{-2},
60 to 800smm^{-2}, 80 to 800smm^{-2}, 100 to 800smm^{-2},
and 300 to 800smm^{-2}.

Cohort differences were investigated using paired t-tests to assess whether there were differences in parameters estimated by fitting the reduced b-value range compared with fitting the data from all b-values; the median value was used from each tumour. In order to correct for multiple comparisons in this exploratory analysis, p-values less than 0.05 were considered statistically significant, and p-values less than 0.0028 considered highly significant (0.0028=0.05/18, including a correction factor of 3 for three fitted parameters and a factor of 6 for multiple b-value ranges).

Individual differences were assessed by taking the difference voxel-by-voxel between parameters estimated by fitting the model to data from all b-values and parameters estimated by fitting the reduced b-value range.

*Cohort differences*: Median ADC estimates for the
cohort were reduced when low b-values were excluded, and were significantly
different from ADCs estimated from all b-values (Figure 1). DDC and α exhibited
less variation with b-value selection for their estimation. Highly significant
differences were seen only when comparing results of fitting from 20 to 800smm^{-2}
with results from all b-values, and for α when comparing results of fitting
300 to 800smm^{-2} with all b-values (Figure 1).

*Individual differences*: All tumours showed a reduction
in ADC when low b-values were excluded, for all reduced b-value ranges (Figure
2). DDC and α did not exhibit marked changes with b-value range, except when
fitting 300 to 800smm^{-2} (Figures 3 and 4).

1. Winfield J, Orton M, Collins D, et al. Separation of type and grade in cervical tumours using non-mono-exponential models of diffusion-weighted MRI. Eur Radiol 2016; DOI 10.1007/s00330-016-4417-0.

2. Winfield J, deSouza N, Priest A, et al. Modelling DW-MRI data from primary and metastatic ovarian tumours. Eur Radiol 2015;25:2033-2040.

3. Orton M, Messiou C, Collins D, et al. Diffusion-weighted MR imaging of metastatic abdominal and pelvic tumours is sensitive to early changes induced by a VEGF inhibitor using alternative diffusion attenuation models. Eur Radiol 2016;26:1412-1419.

4. deSouza N, Scoones D, Krausz T, et al. High resolution MR imaging of stage 1 cervical neoplasia with a dedicated transvaginal coil: MR features and correlation of imaging and pathologic findings. AJR Am J Roentgenol. 1996;166:553-559.

5. Blackledge M, Leach M, Collins D, et al. Computed diffusion-weighted MR imaging may improve tumor detection. Radiology. 2011;261(2):573-581.

**Figure 1:** Median ADC, DDC and α from voxel-by-voxel
fitting of all tumor voxels in 42 patients with cervical cancer. Paired t-tests
show cohort differences between fitting over the range *n*-to-800smm^{-2} (where *n*
is between 20 and 300smm^{-2}) and fitting from all b-values (0 to
800smm^{-2}). Models were fitted voxel-by-voxel in all tumour voxels and the median parameter estimate taken for each patient.

*denotes p-values less than 0.05.

**and **bold**-type denotes
p-values less than 0.0028 (=0.05/18).