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Diffusion Dispersion Imaging: Mapping OGSE Frequency Dependence in the In Vivo Human Brain
Aidin Arbabi1 and Corey A. Baron1

1Centre for Functional and Metabolic Mapping, Robarts research institute, Western university, London, ON, Canada

### Synopsis

Oscillating gradient spin-echo (OGSE) diffusion MRI allows measurement of the frequency dependence of the apparent diffusion coefficient (ADC), which gives insight into tissue microstructure. OGSE has been utilized in numerous animal models, but its application in the in vivo human brain is challenging. Further, a parameterization that allows visualization of maps of the frequency dependence of ADC throughout the human brain has thus-far not been demonstrated. In this work, we report on an efficient method to generate maps of diffusion dispersion (DD), which characterizes the frequency dependence of the ADC, and demonstrate full-brain DD mapping in vivo at 7T.

### Theory

To develop images reflecting ADC change with frequency, we define the diffusion dispersion (DD):$$DD=\frac{ADC_{f}-ADC_{f0}}{\sqrt{f}}$=\frac{-\ln(\frac{S_{f}}{S_{0}})+\ln(\frac{S_{f0}}{S_{0}})}{b\sqrt{f}}$=\frac{\ln(\frac{S_{f_{0}}}{S_{f}})}{b\sqrt{f}}$$where S0 is the b0 image, and Sf and Sf0 are the diffusion weighted images at frequency f>0 and f=0, respectively. The $\sqrt{f}$-dependence was assumed due to theoretical predictions11 and animal findings9. Notably, b=0 images are not required for DD computation, which has several advantages: (1) DD has a lower sensitivity to perfusion than ADC9,10. (2) CSF signal changes drastically between b=0 and b>0 scans, creating large errors from Gibbs ringing12. However, CSF signal is much more consistent between different frequencies, mitigating this effect for DD. (3) Reduced scan times, improving potential for clinical translation.

### Methods

OGSE diffusion encoding with single shot EPI was implemented in a healthy volunteer on a 7T head-only system (80 mT/m strength and 350 T/m/s slew rate). PGSE (diffusion time 55 ms) and cosine-modulated trapezoidal OGSE waveforms6 with frequencies of 30Hz and 60Hz were implemented (b=565 s/mm2, 4 direction tetrahedral encoding8 with 10 averages each, 15 b0 acquisitions, TE/TR=111/5500 ms, FOV=200x200 mm2, 2.5 mm isotropic in-plane resolution, 32 slices (3 mm), scan time 15 min). Registration between diffusion directions and frequencies was performed using FSL eddy.

### Results

Sample PGSE and OGSE ADC maps and DD maps are shown in Fig. 1, where uniform DD values are observed throughout the brain tissue. As expected, DD maps have much lower Gibbs ringing than ADC maps (Fig. 2), and ADC increases approximately linearly with $\sqrt{f}$ (Fig. 3a-c). Accordingly, DD measurements at both 30Hz and 60Hz are comparable to the result from regression across all frequencies (Fig. 3d).

### Discussion

Maps of diffusion dispersion (DD) were demonstrated for the first time in the in vivo human brain, with b=565 s/mm2 at the peak frequency of 60Hz. New clinical systems come equipped with 80mT/m gradients, and SNR advantages of 7T were modest at TE=111ms; accordingly, similar quality DD maps may be feasible on clinical systems. Notably, the scan time to create the 60Hz DD maps would have been only 7 minutes with no b=0 or 30Hz acquisitions. For DD to be insensitive to perfusion, the perfusion signal must be much less than the tissue signal at both frequencies used in Eq. 1. In mice, no dependence on perfusion was observed up to 200Hz for b>300 s/mm2 9; accordingly, this assumption was likely satisfied for our b-value of 565 s/mm2 and maximum frequency of 60Hz. The obtained results demonstrate the feasibility of robust, time-efficient acquisition of parameter maps characterizing OGSE frequency dependence of ADC.

### Acknowledgements

Canada First Research Excellence Fund to BrainsCAN

### References

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### Figures

Figure 1: Example ADC and DD maps acquired at b = 565 s/mm2, from top to bottom: PGSE ADC (diffusion time=55 ms), 30Hz OGSE ADC, 60Hz OGSE ADC, 30 Hz DD, and 60Hz DD. Uniform maps are observed throughout the brain tissue. CSF was masked in DD maps by setting to zero all voxels with PGSE ADC> 1.2 mm2/s.

Figure 2: Comparison of ADC and DD maps on two sample slices for the frequency of 60Hz acquired at b=565 s/mm2: (left) PGSE ADC, (middle) 60Hz OGSE ADC, and (right) 60Hz DD. Red rectangles depict areas affected by Gibbs ringing on ADC maps.

Figure 3: Mean ADC change and diffusion dispersion (DD) measured within example regions-of-interest (ROI) on two different slices for 30Hz and 60Hz: (A) ROI placements on 60Hz DD map, (B) ADC change with frequency, (C) ADC change with the square root of frequency, with solid lines indicating linear regression, and (D) Mean DD for 30Hz and 60Hz, with dashed lines indicating the mean DD for each ROI estimated from the linear regression in (C). As expected, ADC increases linearly with the square root of frequency for all ROIs. Error bars indicate the standard deviation of voxel values within each ROI.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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