Gregory Lemberskiy^{1}, Steven Baete^{1}, Dmitry S Novikov^{1}, Els Fieremans^{1}, Elcin Zan^{1}, Kenneth Hu^{2}, and Sungheon Gene Kim^{1}

Synopsis: The effect of chemo-radiation therapy on advanced head & neck squamous cell carcinoma was evaluated via diffusion and kurtosis time-dependence. We found opposing diffusion limiting regimes pre and post therapy, where prior to therapy the tissue was well described by the long-time limit (Karger Model applies), and where after therapy the tissue was well described by the short-time S/V limit. This reversal of imaging regimes can serve as a signature of the minimal effective dose required for treatment.

**Data
Acquisition: **HNSCC
patients (n=6) were imaged on a Siemens 3T PRISMA system using a 20-channel
head/neck coil. An in-house developed stimulated echo acquisition mode (STEAM)
EPI sequence was used to acquire 5 diffusion times, [t=100,200,300,500,700 ms], over 4 b-shells [b=500,1000,2000,3000
s/mm^{2}] with 3 diffusion directions along x, y, and z axes. The
mixing time, *t*_{m}, was [80,180,280,480,680]
ms varying with *t*. Other parameters
include, TR=5000 ms, TE=66 ms, resolution=1.5x1.5x4.0 mm^{3}, FOV=190 mm, partial
Fourier 6/8, and GRAPPA with *R*=2. Each patient was imaged twice: once before
initiating chemo-radiation therapy and then 4-weeks later after starting the therapy.

**Analysis: **Each set of images was denoised^{6}, de-Gibbsed^{7}, and affine registered^{8} over all *b* and *t*. The estimated noise-level^{9 }was then used to correct the signal for Rician bias. Following post-processing, diffusion and kurtosis
maps were generated via a weighted linear least square fit method^{10}. Due to the proximity of to the Rician floor, b=3000 was
discarded in the final analysis.

**Modeling D(t)
& K(t): **In
the solid part of HNSCC prior to therapy with small cell size (radius ~4 $$$\mu m$$$),
a dynamic range of

where$$$\,K_\infty\,$$$marks the floor of diffusion kurtosis pertaining to the intrinsic tissue heterogeneity.

Chemo-radiation is a radical and destructive process that can results
in a dramatic increase of diffusivities^{2}. This drastic increase in diffusivity due to the break down of cell walls indicates a change in volume fraction and length scale, where membrane-like debris serve as the occasional restriction. After successful therapy, *D*(*t*) is no longer in the long-time
limit, but may move towards the short time limit,^{13,14} which is characterized by t^{1/2}: $$D(t)=D_0\bigg(1-\frac{4}{3d\sqrt{\pi}}\frac{S}{V}\sqrt{D_0t}\bigg)\,\,[2]$$where the tissue length scale would be
determined by a=6/(S/V), since *d*=3. In
this regime, *K*(*t*) is expected to be constant.

Between the shortest and longest *t* used in this study, we observed the degree
of the time-dependence of *D* and *K* change substantially before and after
therapy [Fig.1,Fig2(A,B)]. For the preliminary analysis, *D*(*t*) and *K*(*t*) were calculated
from the tumor voxels pooled from all six subjects in Figure 2.

Prior to therapy, *D*(*t*) does not show
notable change (coefficient
of variation, CV=std(*D*(*t*))/mean(*D*(*t*))=0.016). However, after the
therapy, *D*(*t*) shows remarkable
time-dependency [Fig.2(C)] (CV(*D)*=0.065) and becomes highly linear as
function of t^{1/2}, with Pearson’s$$$\,\rho\,$$$(when excluding the outlier at *t* = 700 ms) [Fig.2(C)]. Hence, Eq.[2]
was fit to *D*(*t*), which provided a length scale of *a*=311.50 $$$\mu m$$$.
On the other hand, *K*(*t*) shows an opposite trend [Fig.2(D)]. *K*(*t*) varies noticeably (CV(*K*)=0.032) prior to therapy, but
remains largely constant after therapy (CV(*K*)=0.014). Hence, the Karger Model
(Eq.[1]) was applied only to the pre-therapy
*K*(*t*) data, which estimated an
exchange time of 76 ms.

1. Padhani AR and others. Diffusion-weighted magnetic resonance imaging as a cancer biomarker: consensus and recommendations. Neoplasia 2009;11(2):102-125.

2. Kim S and others. Diffusion-weighted magnetic resonance imaging for predicting and detecting early response to chemoradiation therapy of squamous cell carcinomas of the head and neck. Clinical cancer research : an official journal of the American Association for Cancer Research 2009;15(3):986-994. 3. Thoeny HC and others. Predicting and Monitoring Cancer Treatment Response with Diffusion-Weighted MRI. Journal of Magnetic Resonance Imaging 2010;32(1):2-16.

4. Jansen JF and others. Non-gaussian analysis of diffusion-weighted MR imaging in head and neck squamous cell carcinoma: A feasibility study. AJNR American journal of neuroradiology 2010;31(4):741-748.

5. Goshima S and others. Diffusion kurtosis imaging to assess response to treatment in hypervascular hepatocellular carcinoma. AJR American journal of roentgenology 2015;204(5):W543-549.

6. Veraart J and others. Denoising of diffusion MRI using random matrix theory. Neuroimage 2016;142:394-406.

7. Kellner E and others. Gibbs-ringing artifact removal based on local subvoxel-shifts. Magn Reson Med 2016;76(5):1574-1581.

8. Klein S and others. elastix: a toolbox for intensity-based medical image registration. IEEE Trans Med Imaging 2010;29(1):196-205.

9. Veraart J and others. Diffusion MRI noise mapping using random matrix theory. Magn Reson Med 2016;76(5):1582-1593.

10. Veraart J and others. Weighted linear least squares estimation of diffusion MRI parameters: strengths, limitations, and pitfalls. Neuroimage 2013;81:335-346.

11. Novikov DS and others. Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation. ArXiv e-prints. Volume 16122016.

12. Fieremans E and others. Monte Carlo study of a two-compartment exchange model of diffusion. NMR Biomed 2010;23(7):711-724.

13. Lemberskiy G and others. Validation of surface-to-volume ratio measurements derived from oscillating gradient spin echo on a clinical scanner using anisotropic fiber phantoms. NMR Biomed 2017;30(5).

14. Mitra PP and others. Short-time behavior of the diffusion coefficient as a geometrical probe of porous media. Phys Rev B Condens Matter 1993;47(14):8565-8574.