xiaoyu jiang^{1}, hua li^{1}, zou yue^{1}, junzhong xu^{1}, and john Gore^{1}

The changes that occur over a cell cycle play a vital role in mediating a cell’s sensitivity towards radiation therapy. Radiation exposure is expected to arrest cells at a particular cell cycle phase which improves the effectiveness of subsequent doses of radiation/chemotherapy. Cells in different phases have different sizes that can be detected by diffusion MRI with appropriate diffusion times. In this study, we evaluate the hypothesis in a rat glioma model that measurements of mean tumor cell size provides a means to quantify changes of cell phase distributions, and hence is capable of monitoring tumor response to radiotherapy.

*Theory*: The diffusion weighted signals from tissues are assumed to be the sum of
signals arising from intra- and extracellular spaces, namely, S=V_{in}*S_{in}+(1-V_{in})*S_{ex},
where V_{in} is the water volume fraction of intracellular space, and Sin
and Sex are the signal magnitudes per volume from the intra- and
extracellular spaces, respectively. Cells are modeled as impermeable spheres of
diameter d. The analytical expression for the diffusion weighted signal for
water within an impermeable sphere of size d and intrinsic diffusion rate Din
has been reported previously and was assumed here. Sex=exp[−𝑏(D_{ex0}+𝛽_{ex}∙𝑓)], where D_{ex0} is the extracellular diffusion rate at
frequencies close to 0, and β_{ex} is the slope of extracellular
diffusion coefficient with respect to frequency f, which also contains
information on structural dimensions.

*In vivo experiments*: A rat glioma cell line (9L) was used
to create tumors in a total of 30 rats. Half of 9L-bearing rats were treated with a single
fraction of 20 Gy of x-ray radiation. Of all the 9L-bearing rats, 16 (8
irradiated and 8 non-irradiated) were used for survival studies, and 14 (8
irradiated and 6 non-irradiated) for the characterization of radiation
treatment response using the IMPULSED method. Diffusion-weighted images
covering the tumor region were collected before, and 1, 3, and 6 days post
irradiation. A region of temporal diffusion spectra with diffusion times
ranging from ≈ 3 to 48 ms were obtained at 9.4 T using a combination of PGSE
and OGSE acquisitions.

*Data analysis*: The survivals of animals were
represented on Kaplan-Meier curves. The diffusion MR signals were fit to
equations reported in our previous publication^{2} on a voxel-wise
basis to derive parametric images of the cell size d.