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Towards a definition of the biophysical bases of transient Anomalous Diffusion (tAD) parameters. Evaluation of tAD, DKI and DTI in normal and cancer prostate tissue with Magnetic Resonance micro-imaging at 9.4 Tesla
Maria Giovanna Di Trani1,2, Alessandra Caporale2, Marco Nezzo3, and Silvia Capuani2

1SAIMLAL Dept., Sapienza University of Rome, Rome, Italy, 2CNR-ISC Physics Dept., Sapienza University of Rome, Rome, Italy, 3Diagnostic and Interventional Radiology Dept., Tor Vergata University, Rome, Italy

### Synopsis

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.

### Introduction

In this work Diffusion Kurtosis Imaging (DKI) and transient Anomalous Diffusion Imaging (tADI) were performed on ex-vivo prostate specimens, in addition to the conventional DTI. Kurtosis is the fourth-order term of the NMR signal cumulant expansion, it quantifies the signal deviation from the mono-exponential decay, providing a measure of tissue heterogeneity [1]. tADI derived from Continuous Time Random Walk model introduced by Metzler and Klafter [2], a generalization of the basic random walk theory, developed with the purpose to investigate heterogeneous and complex media. tADI allows to measure the γ-parameter that is sensitive to tissue susceptibility differences and multi-compartmentalization [3,4]. Since DKI and tADI are based on statistical models, they can be performed without needing a-priori hypothesis on tissue micro-structures. However, the relation between tissue micro-modifications and DKI- and tADI-derived parameters must be investigated and established. In this preliminary work, we evaluated DKI, tAD and DTI diffusion parameters in normal and high-grade PCa, by MR microimaging at 9.4T and with a resolution of 70x70μm2 in the plane. Prostate tissue is composed by several micro-compartments that exhibit different diffusion behaviors [5]. Therefore, as prostate is a complex tissue, consisting of structures with length scale from 100 μm to less than 1 μm, it is an ideal tissue to investigate the biophysical features of diffusion parameters.

### Methods

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=70x70x1000μm3; δ/Δ=3/40 (ms); NSA=8), by varing diffusion gradient strengths; 9 b-values from 0 to 5000 s/mm2 were applied along 6 non-collinear directions

DTI was performed by FSL 5.0 software, with the b-value range 0-1500 s/mm2; non-Gaussian parameters were calculated by a customized algorithm developed in Matlab R2012b. Mean Kurtosis (MK) and kurtosis-derived mean diffusivity (MDk) 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/mm2. 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/mm2 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 Gx,Gy,Gz are the diffusion-encoding directions, Ai are the generalized diffusion constants, γi, the three values of the anomalous exponent projected along the 3 main axes of the DTI reference frame, individuated by the eigenvectors Vix,Viy,Viz. 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.

### Results

The glandular structure of prostate is visible in DWIs and diffusion parameters maps of normal samples, except for FA-map; MDk seems to better describe the tissue architecture (Fig. 1 and 2). MD, MDk and Mγ are lower in PCa, while FA, KFA and MK are higher; DTI-parameters show mean values comparable with other ex-vivo studies [5,8].

### Discussion and Conclusions

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 MDk 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.

### Acknowledgements

No acknowledgement found.

### References

[1] Jensen J.H. and Helpern J.A., MRI quantification of Non-Gaussian water diffusion by Kurtosis Analysis. NMR Biomed, 2010.

[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.

### Figures

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

Figure 2 - DWI and diffusion map derived from DTI (MD, FA), DKI (MK, MDk) 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.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)
3205