Measuring diffusion time dependence of pseudo-diffusion using flow compensated pulsed and oscillating gradient sequences

Dan Wu^{1} and Jiangyang Zhang^{1,2}

Theory: Two types of microcirculatory flow were brought up
by Le Bihan et al^{1}. When the diffusion time is long enough for
microcirculatory flow to pass through multiple vascular segments (type 1), the
signal attenuation can be modeled as *F*_{1} = *e*^{-D*·b}, where *D** is the pseudo-diffusion coefficient. When the diffusion time is
short enough such that microcirculatory flow does not pass through one vascular
segment (type 2), we have
*F*_{2} = |*sinc*(*cv*)|·*e*^{-Dblood·b}, where *c* is the first order moment of the diffusion gradient waveform and *D*_{blood }is the self-diffusion
of the water molecules in the blood^{8}. For flow compensated pulsed and oscillating gradient waveforms, the first order moment is zero (*c* = 0), and we have
*F*_{2} = *e*^{-Dblood·b} (*D*_{blood}
≈1.6 x 10^{-3} mm^{2}/s)^{4}, and the signal attenuations from
microcirculatory flow and diffusion become

$$$\frac{S}{S_{0}}=f_{1}\cdot e^{-D^{*}(\omega)\cdot b}+f_{2}\cdot e^{-D_{blood}\cdot b}+(1-f_{1}-f_{2})\cdot e^{-D(\omega)\cdot b}$$$ Equation 1

MRI experiments: Experiments
were performed on an 11.7T Bruker scanner. A flow phantom (water in a
thin tube connected to an infusion pump with flow rates at 0, 2, and 4 mm/s)
was used to test flow compensation. PGSE
and OGSE data of mouse brains (*n*=7) were acquired at 16 b-values (25-1000 s/mm^{2}) with the following parameters: single-shot EPI, TE/TR = 58/3000ms, NA=4, 5
slices with in-plane resolution = 0.2 x 0.2 mm^{2} and thickness of 1 mm. The OGSE data were acquired at 50Hz and 100Hz oscillating frequencies, and the FC-PGSE data were acquired with gradient duration (*T* in
Figure 1A) of 10 ms and 20 ms. A conventional PGSE was acquired at diffusion time
of 40 ms (assuming type 2 flow is negligible at 40 ms in the mouse brain). The model parameters [*f*1, *f*2, *D**(ω)]
were estimated in Matlab using non-linear fitting, while *D*(ω) was calculated by log-linear fit from data with b-values greater than 300 s/mm^{2}.

1. Le Bihan D, Breton E, Lallemand D, et al. MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders. Radiology. 1986;161(2):401-407.

2. Iima M, Reynaud O, Tsurugizawa T, et al. Characterization of Glioma Microcirculation and Tissue Features Using Intravoxel Incoherent Motion Magnetic Resonance Imaging in a Rat Brain Model. Invest Radiol. 2014;49(7):485-490.

3. Federau C, O'Brien K, Meuli R, et al. Measuring brain perfusion with intravoxel incoherent motion (IVIM): initial clinical experience. J Magn Reson Imaging. 2014;39(3):624-32.

4. Wetscherek A, Stieltjes B, Laun FB. Flow-compensated intravoxel incoherent motion diffusion imaging. Magn Reson Med. 2015;74(2):410-419.

5. Maki H, MacFall R, Johnson GA. The use of gradient flow compensation to separate diffusion and microcirculatory flow in MRI. Magn Reson Med. 1991;17(1):95-107.

6. Does D, Parsons C, Gore C. Oscillating gradient measurements of water diffusion in normal and globally ischemic rat brain. Magn Reson Med. 2003;49(2):206-215.

7. Van T, Holdsworth J, Bammer R. In vivo investigation of restricted diffusion in the human brain with optimized oscillating diffusion gradient encoding. Magn Reson Med. 2013;71(1):83-94.

8. Stanisz J, Li G, Wright A, et al. Water dynamics in human blood via combined measurements of T2 relaxation and diffusion in the presence of gadolinium. Magn Reson Med. 1998;39:223-233.

9. Henkelman M, Neil J, Xiang Q. A quantitative interpretation of IVIM measurements of vascular perfusion in the rat brain. Magn Reson Med. 1994;32(4):464-469.

10. Hardee E, Zagzag D. Mechanisms of glioma-associated neovascularization. Am J Pathol. 2012;181(4):1126-41.

Fig.
1: (A) Timing diagrams of the flow-compensated PGSE (FC-PGSE) and
cosine-trapezoid OGSE sequences. (B) ADCs measured along the direction of flow
(X-axis) in a flow phantom (B’) using conventional PGSE, OGSE, and FC-PGSE
sequences. The flow phantom consists of water in a tube flowing at three rates,
which is placed above a gel phantom and connected to a pump. The experiments were
repeated eight times.

Fig.
2: Fitting of the pseudo-diffusion fraction (*f*1 in Equation 1). (A) *f*1 map of a mouse brain at
five diffusion times. (B) *f*1
values averaged in three coronal slices, excluding the ventricle. (C) Diffusion
signal attenuation at different diffusion times at b-values of 50 and 100 s/mm^{2}. Data is represented as mean ±
standard deviation (*n*=7).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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