Nicholas Senn^{1}, Yazan Masannat^{2,3}, Ehab Husain^{3,4}, Bernard Siow^{5}, Steven D Heys^{2,3}, and Jiabao He^{1}

QSI was compared against conventional DWI and
non-Gaussian diffusion models, namely diffusion kurtosis imaging (DKI) and
stretched-exponential model (SEM) to evaluate diffusivity heterogeneity for
profiling breast tumour cell diversity. We
investigated whole breast tumours excised from surgery, with imaging performed overnight
on the same day
on a clinical system. Asymmetry in diffusivity distribution was quantified as
histogram skewness, median and 25^{th}-percentile. Correlation analysis
was performed to compare QSI against other models. The skewness of diffusivity
distribution derived from QSI was the highest among the models and provided a
wider spread of values across cohort, allowing more sensitive clinical
applications.

Twenty female patients (age 35-78 years, 10 grade II and 10 grade III) with invasive ductal carcinoma undergoing wide local excision surgery were enrolled. To ensure no delay to pathological reporting, formalin was added to the excised whole tumour specimens and imaged same day overnight. NHS Research Ethics Committee approved the study and prior written informed consent was obtained.

Image Acquisition: Images were acquired on a clinical 3T MRI
scanner (Achieva TX, Philips Healthcare, Netherlands) using body coil for
transmission and a 32-channel coil as receiver. Three diffusion acquisitions
were performed using multi-shot pulsed gradient spin echo sequence, averaged
over 3 orthogonal diffusion directions, with FOV of 141x141mm^{2}, 2.2mm
slice thickness, matrix size of 64x64, in plane resolution of 2.2x2.2mm^{2},
over 7–10 slices depending on tumour size and saturation bands to supress
adjacent formalin signal. Acquisition 1 (DWI) was performed over 2 b-values of
0-800s/mm^{2}, with diffusion time δ/Δ of 15.3/27.5ms, TR/TE of
3000/70ms, single average. Acquisition 2 (DKI and SEM) was performed over 16
equidistant b-values from 0-2400s/mm^{2}, δ/Δ of 18.7/31.5ms, TR/TE of
3100/82ms, 2 averages. Acquisition 3 (QSI) was performed over 32 equidistant
q-values from 10.4-655cm^{-1} (to b-value of 5,000s/mm^{2}), δ/Δ
of 24.9/37.8ms, TR/TE of 5900/94ms, single average.

Image Analysis: Diffusivity
images from DWI were calculated using logarithmic ratio (Acquisition 1).
Diffusivity, and respective AKC and ALPHA images were computed through fitting
DKI and SEM models (Acquisition 2)^{3,4}. Two QSI approaches
of Fourier transform (QSI PDF) and non-linear fitting approach (QSI FIT) were
used to derive diffusivity images converted from diffusion root-mean-squared displacement
(Acquisition 3)^{8,9}.

Statistical Analysis: Regions
of interest were drawn to delineate tumour core with reference to anatomical and
b=800s/mm^{2} DWI images in MRIcron (University of South Carolina, USA).
The asymmetry of diffusivity distribution of each model was quantified as
skewness, median and 25^{th}-percentile. Subsequently QSI FIT results were
compared against those from other models using paired t-test and correlation
analysis.

QSI provides a wider spread of skewness in diffusivity distribution, likely due to no prior assumptions of diffusion pattern.

1. Kim YJ, Kim SH, Lee AW, et al. Histogram analysis of apparent diffusion coefficients after neoadjuvant chemotherapy in breast cancer. Jpn J Radiol. 2016;34(10):657–66.

2. Just N. Improving tumour heterogeneity MRI assessment with histograms. Br J Cancer. 2014;111(12):2205–13.

3. Jensen JH, Helpern JA, Ramani A, et al. Diffusional kurtosis imaging: The quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med. 2005;53(6):1432–40.

4. Bennett KM, Schmainda KM, Bennett RT, et al. Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model. Magn Reson Med. 2003;50(4):727–34.

5. Sun K, Chen X, Chai W, et al. Breast Cancer: Diffusion Kurtosis MR Imaging-Diagnostic Accuracy and Correlation with Clinical-Pathologic Factors. Radiology. 2015;277(1):46–55.

6. Cohen Y, Assaf Y. High b-value q-space analyzed diffusion-weighted MRS and MRI in neuronal tissues - a technical review. NMR Biomed. 2002;15(7-8):516–42.

7. Yamada I, Hikishima K, Miyasaka N, et al. Esophageal carcinoma: Evaluation with q-space diffusion-weighted MR imaging ex vivo. Magn Reson Med. 2015;73(6):2262–73.

8. Ong HH, Wehrli FW. Quantifying axon diameter and intra-cellular volume fraction in excised mouse spinal cord with q-space imaging. Neuroimage. 2010;51(4):1360–6.

9. Farrell JAD, Smith SA, Gordon-Lipkin EM, et al. High b-value q-space diffusion-weighted MRI of the human cervical spinal cord in vivo: feasibility and application to multiple sclerosis. Magn Reson Med. 2008;59(5):1079–89.

Figure 1 shows the T1 weighted (T1W) image
of the central image slice of a typical tumour, along with diffusivity (D) maps
observed from diffusion model of DWI, DKI, SEM, QSI FIT and QSI PDF. Kurtosis
(AKC) and Stretch factor (ALPHA) maps are shown for the DKI and SEM models
respectively. Cohort mean ± standard deviation of tumour median AKC and ALPHA
is shown, whilst diffusivity averaged across cohort are contained in Table 1. AKC
> 0 and ALPHA < 1 indicates a deviation from the single component of unimpeded
diffusion assumed in DWI.

Table 1 contains mean ± standard deviation of the
skewness, median and 25^{th}-percentile of diffusivity distribution
over the entire cohort. P-value represents the paired t-test comparison between QSI
FIT against other models.

Figure 2 shows the diffusivity (D, x10^{-3}mm^{2}/s)
histogram distributions produced by each diffusion model for the typical tumour
shown in Figure 1 (upper panel). The dot plot representation of the diffusivity
skewness is shown with cohort mean ± standard deviation displayed as an error
bar and each dot representing a single tumour value (bottom panel).

Table 2 contains the cohort correlation analysis results
of skewness, median and 25^{th}-percentile of diffusivity distribution of
QSI FIT against those from other models. The Pearson’s correlation coefficient
(R) and associated P-value are shown. The slope and intercept from the linear
regression are also shown. The intercepts of median and 25^{th}-percentile
are given in units of (x10^{-3}mm^{2}/s) and marked by (^{†}).

Figure 3 shows the correlation across the cohort of
diffusivity skewness from QSI FIT against other models. Pearson’s correlation
coefficient (R) and linear regression line equation are shown, with significant
results of P-value ≤ 0.001 indicated by (*) (Table 2). Each dot in the scatter
plot corresponds to one tumour skewness value.