Yuan Li^{1,2}, Michelle Kim^{3}, Theodore Lawrence^{2}, Parmar Hemant^{3}, and Yue Cao^{1,2,3}

It is a challenge to differentiate non-enhanced solid tumor from edema in glioblastoma. This study applied the restricted diffusion model to high b-value diffusion weighted images to characterize glioblastoma. The formation of the restricted diffusion model was derived for bi-polar diffusion gradients. The parameters fitted by the restricted diffusion model can differentiate solid tumor from edema and normal-appearing white matter and grey matter, better than the conventional apparent diffusion coefficient and the bi-exponential model without accounting for diffusion restriction of intra-cellular water.

Restricted
water diffusion in glioblastoma (GBM) has been reported. However, the conventional apparent water
diffusion (ADC) is often elevated and cannot differentiate solid tumor from
edema in GBM.^{1-5} A recent study shows that cell sizes and
cellularity in three colon cancer cell lines estimated by a restricted
diffusion model (RDM) were correlated with histology.^{6} The RDM considers
intra-cellular water diffusion restricted in spherical cells and modulated by
diffusion gradients,^{6-8} and
its formulations are derived for the mono-polar pulse gradient spin echo and oscillating
gradient spin echo.^{6-7,9}

In this study, we extended the RDM formulation to a bi-polar pulse gradient spin echo (Figure 1) (that minimizes eddy-current caused artifacts in diffusion images). We characterized GBM using this model and compared to normal-appearing white matter (WM) and grey matte (GM), and edema.

*R*, *D _{ex}* and

This work is supported in part by a grant of NIH/NCI 1U01CA183848.

Thanks for Dr. Himanshu Bhat (Siemens Healthineers) for assistance of the project.

1. P. Pramanik, H. Parmar, A. Mammoser, L. Junck, M. Kim, C. Tsien, T. Lawrence and Y. Cao, "Hypercellularity Components of Glioblastoma Identified by High b-Value Diffusion-Weighted Imaging", International Journal of Radiation Oncology*Biology*Physics, vol. 92, no. 4, pp. 811-819, 2015.

2. T. Sugahara, Y. Korogi, M. Kochi, I. Ikushima, Y. Shigematu, T. Hirai, T. Okuda, L. Liang, Y. Ge, Y. Komohara, Y. Ushio and M. Takahashi, "Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas", Journal of Magnetic Resonance Imaging, vol. 9, no. 1, pp. 53-60, 1999.

3. T. Chenevert, "Diffusion Magnetic Resonance Imaging: An Early Surrogate Marker of Therapeutic Efficacy in Brain Tumors", Journal of the National Cancer Institute, vol. 92, no. 24, pp. 2029-2036, 2000.

4. H. Lyng, O. Haraldseth and E. Rofstad, "Measurement of cell density and necrotic fraction in human melanoma xenografts by diffusion weighted magnetic resonance imaging", Magnetic Resonance in Medicine, vol. 43, no. 6, pp. 828-836, 2000.

5. A. Guo, T. Cummings, R. Dash and J. Provenzale, "Lymphomas and High-Grade Astrocytomas: Comparison of Water Diffusibility and Histologic Characteristics", Radiology, vol. 224, no. 1, pp. 177-183, 2002.

6. X. Jiang, H. Li, J. Xie, E. McKinley, P. Zhao, J. Gore and J. Xu, "In vivo imaging of cancer cell size and cellularity using temporal diffusion spectroscopy", Magnetic Resonance in Medicine, vol. 78, no. 1, pp. 156-164, 2016.

7. J. Xu, M. Does and J. Gore, "Quantitative characterization of tissue microstructure with temporal diffusion spectroscopy", Journal of Magnetic Resonance, vol. 200, no. 2, pp. 189-197, 2009.

8. A. Ianuş, B. Siow, I. Drobnjak, H. Zhang and D. Alexander, "Gaussian phase distribution approximations for oscillating gradient spin echo diffusion MRI", Journal of Magnetic Resonance, vol. 227, pp. 25-34, 2013.

9. J. Stepišnik, "Time-dependent self-diffusion by NMR spin-echo", Physica B: Condensed Matter, vol. 183, no. 4, pp. 343-350, 1993.

Fig. 1 Bi-polar
diffusion gradients with pulse durations of δ_{1}, δ_{2},δ_{3},δ_{4} (δ_{1}+δ_{2}=δ_{3}+δ_{4}). Red boxes represent 180 degrees RF pulses. Black boxes
represent diffusion gradients.

Fig. 2: Volumes of
interest for DWI analysis. Solid tumor
(red), genu (Magenta), frontal white matter (yellow), head of caudate nucleus (deep
gray matter) (green), cortex (blue), and edema(cyan).

Fig. 3:* R*, *D*_{in}, *D*_{ex}, and *V*_{in}
in six tissue types fitted from the RDM. **: 0.001<p < 0.01; ***: p < 0.001.
Error bar is SEM of certain kind of tissue.

Fig.4:* D*_{1}, *D*_{2}, and* V*_{in}
in all tissue types fitted by a conventional bi-exponential model. *:
0.01<p<0.05; **: 0.001<p < 0.01; ***: p < 0.001. Error bar is
SEM of certain tissue type.

Fig. 5: ADC in all tissue types. Error bar is SEM of
each kind of tissue types.