Guangyu Dan^{1,2}, Yuxin Zhang^{3,4}, Zheng Zhong^{1,2}, Kaibao Sun^{1}, M. Muge Karaman^{1,2}, Diego Hernando^{3,4}, and Xiaohong Joe Zhou^{1,2,5}

^{1}Center for Magnetic Resonance Research, University of Illinois at Chicago, Chicago, IL, United States, ^{2}Department of Bioengineering, University of Illinois at Chicago, Chicago, IL, United States, ^{3}Department of Medical Physics, University of Wisconsin-Madison, Madison, WI, United States, ^{4}Department of Radiology, School of Medicine and Public Health, University of Wisconsin-Madison, Madison, WI, United States, ^{5}Department of Radiology and Neurosurgery, University of Illinois at Chicago, Chicago, IL, United States

Parameters in many diffusion models depend on diffusion time. However, time-dependent diffusion behaviors in the long diffusion time regime have not been well studied because a longer diffusion time would lead to a longer TE, substantially reducing signal-to-noise ratio in conventional spin-echo diffusion pulse sequences. In this study, we employed a STEAM diffusion sequence to investigate the diffusion-time dependence of parameters in a fractional order calculus diffusion model. Our results showed substantial dependence of all diffusion parameters on diffusion times in the range of 100-1000 ms.

$$S = S_0exp[-D\mu^{2(\beta-1)}(\gamma G_d\delta )^{2\beta}(Δ- \frac{2\beta - 1}{2\beta + 1}\delta)],$$

where

$$Contrast = \mid\frac{\lambda _{GM} - \lambda _{WM}}{\lambda _{GM} + \lambda _{WM}}\mid,$$

where λ represents the mean parameter value of

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Fig.
1. (a): A diagram of single-shot STEAM-DW
imaging sequence used in the study. *δ* is diffusion gradient lobe duration, Δ is diffusion time, *G*_{ss}
is slice selection gradient, *G*_{diff} is diffusion gradient, and *G*_{TM}
is a spoiling gradient to crush the residual transverse magnetization. The
STEAM DW module is followed by an echo planar imaging (EPI) readout. (b): TM
and the corresponding Δ.

Fig.
2. Parametric
*D* map estimated from the FROC
diffusion model at different TM values.

Fig.
3. Parametric
*β* map estimated from the FROC
diffusion model at different TM values.

Fig.
4. Parametric
*μ* map estimated from the FROC
diffusion model at different TM values.

Fig.
5. (a): The mean
values of *D*, *β*, and *μ* in gray matter
(GM: red) and white matter (WM: blue) plotted against TM. (b): The GM/WM
contrast in *D*, *β*, and *μ* as a function of
TM.