Maria Giovanna Di Trani^{1,2}, Alessandra Caporale^{2}, Marco Nezzo^{3}, and Silvia Capuani^{2}

Since DKI and transient anomalous diffusion imaging (tADI) are based on statistical models, they can be performed without the need of a-priori hypothesis on tissue micro-structures. However, the relation between tissue micro-structure DKI and tADI derived parameters have not been clearly established yet. In this work, we evaluated DKI, tAD and DTI diffusion parameters in normal and high-grade cancer prostate, by MR microimaging at 9.4T with a 70μmx70μm in plane resolution. As prostate tissue is a complex tissue, composed by several micro-compartments that exhibit different diffusion behaviors, it is an ideal tissue to investigate the biophysical features of diffusion parameters.

Tissue samples were
obtained from radical prostatectomy specimens and kept in 4%
PBS formaldehyde at 4°C for conservation. An expert
uropathologist selected one normal and one cancer sample from 3
patients with high-grade Pca (Gleason Score ≥ 4+4).
Acquisition was
performed on a Bruker AV400 spectrometer operating at 9.4 T with
a micro-imaging probe
and maximum gradient strength of 1200mT/m. XWINNMR® and ParaVision® 3.0 software were
employed for data acquisition.
DWIs were acquired
with a Pulsed Gradient Stimulated Echo
(TE/TR=14,8/4500 (ms); resolution=70x70x1000μm^{3}; δ/Δ=3/40 (ms); NSA=8),
by varing diffusion gradient strengths; 9 b-values from 0 to
5000^{ }s/mm^{2} were applied along 6 non-collinear directions

DTI was performed
by FSL 5.0 software, with the b-value range
0-1500
s/mm^{2};
non-Gaussian parameters were calculated by a customized algorithm
developed in Matlab R2012b.
Mean Kurtosis
(MK) and kurtosis-derived mean diffusivity (MD_{k}) were calculated by
fitting DWI signal for each diffusion encoding direction, with the
following equation:

$$\frac{S}{S_0}=e^{-bMD_k + \frac{1}{6}b^2MD_k^2\cdot K}$$

in the b-value
range 0-2000 s/mm^{2}. Moreover, proxy Kurtosis Fractional
Anisotropy (KFA) was calculated as reported in [6].

tAD was
performed, as described in [7],
by fitting signal in the b-values range 0-5000s/mm^{2} with the
following equation:

$$\frac{S}{S_0}=\prod_1^3 e^{-A_ib^{\gamma_i} (V_{ix}G_x+V_{iy}G_y+V_{iz}G_z)^{\gamma_i}}$$

where
G_{x},G_{y},G_{z}
are the diffusion-encoding directions, A_{i}
are the generalized diffusion constants, γ_{i},
the three values of the anomalous exponent projected along the 3 main
axes of the DTI reference frame, individuated by the eigenvectors
V_{ix},V_{iy},V_{iz}. Mean γ (Mγ),
i.e. the mean values of the pseudo-superdiffusion γ-parameter,
was calculated as reported in [3].

Region of Interests (ROI) were manually drawn on DW-images in tumoral and normal tissue.

Diffusion derived
micro-images highlight tissue architecture and reflect structural
modifications occurring with tumor. Histopathological evidences
showed that Pca with Gleason Score (GS) ≥ 4+4 consists in a solid mass of
undifferentiated cells (Fig.3), indeed no glandular structure is
recognizable on DWIs or diffusion maps (Fig. 2). MD and MD_{k} are lower in PCa,
as a result of malignant cells proliferation that obstructs the
almost-free diffusion compartments (acini, ducts), leading to an
increase of tissue heterogeneity (K increases) and a reduction of
tissue susceptibility differences (Mγ decreases). As a
consequence of increasing cell density, FA and KFA are lower in
cancer tissue.

In conclusion, MR micro-imaging in healthy and cancer prostate tissue allows to investigate diffusion proprieties of micro-structures approaching the cellular scale. As a consequence, micro-imaging technique could be employed to elucidate the biophysical underpinning of non–Gaussian diffusion parameters and in particular of the tAD parameters.

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[2] Metzler R. and Klafter J., The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports, 2000.

[3] Palombo M. et al., Spatio-temporal anomalous diffusion in heterogeneous media by nuclear magnetic resonance. J Chem Phys, 2011.

[4] Capuani S. et al., Spatio-temporal anomalous diffusion imaging: results in controlled phantoms and in excised human meningiomas. Magn Reson Imaging, 2013.

[5] Bourne R.M. et al., Microscopic diffusivity compartmentation in formalin-fixed prostate tissue.Magnetic Resonance in Medicine, 2012.

[6] Hansen B. and Jespersen S.N., Kurtosis fractional anisotropy, its contrast and estimation by proxy. Sci. Rep., 2016.

[7] Caporale A. et al.,The γ-parameter of Anomalous Diffusion quantified in human brain by MRI depends on local magnetic susceptibility differences, NeuroImage, 2016.

[8] Xu J.Q., et al.,. Magnetic resonance diffusion characteristics of histologically defined prostate cancer in humans. Magn Reson Med, 2009.

Figure 1 - DWI and diffusion map derived from DTI (MD, FA), DKI (MK, MD_{k}) and tADI (Mγ) of a normal prostate sample.

Figure 2 - DWI and diffusion map derived from DTI (MD, FA), DKI (MK,
MD_{k}) and tADI (Mγ) of a prostate cancer sample with GS≥4+4.

Figure 3 - Histologies of a PCa with GS≥4+4 (left) and normal (right) specimen.

Figure 4 - Mean and standard deviation calculated in PCa and normal prostate tissue for each diffusion parameter.