Measuring diffusion time dependence of pseudo-diffusion using flow compensated pulsed and oscillating gradient sequences
Dan Wu1 and Jiangyang Zhang1,2

1Radiology, Johns Hopkins University School of Medicine, BALTIMORE, MD, United States, 2Radiology, New York University School of Medicine, New Yourk, NY, United States

### Synopsis

Intravoxel incoherent motion (IVIM) in the capillaries reflects capillary geometry and flow velocity, which may be probed by diffusion MRI measured at varying diffusion times. In this study, we employed flow-compensated pulsed and oscillating gradient sequences to investigate the diffusion time dependence of pseudo-diffusion in the mouse brain with diffusion times ranging from 2.5 ms to 40 ms. We used a simplified IVIM model to characterize the pseudo-diffusion compartment and flow compartment based on the relation between capillary segments and diffusion time/distance. Our results clearly demonstrated diffusion time dependence and suggested that the pseudo-diffusion fraction increased with increasing diffusion time.

### Introduction

Diffusion MRI signals acquired from biological tissues reflect intra-cellular and extra-cellular water diffusion as well as certain microcirculatory flow that mimics diffusion. The latter, commonly called pseudo-diffusion, is a major focus of intra-voxel incoherent motion (IVIM) imaging1, which provides unique information about blood perfusion in the capillaries and small vessels2,3. It is also suggested1 that the observed IVIM signals may be linked to the relation between the vascular segment length and the diffusion distance/time. Recently, Wetscherek et al. demonstrated diffusion time dependency of pseudo-diffusion in the liver and pancreas4. In this study, we investigated the contribution of pseudo-diffusion on diffusion MRI signals in the brain over a relatively wide range of diffusion times using flow compensated4,5 pulsed gradient spin-echo (PGSE) and oscillating gradient spin-echo (OGSE)6,7 sequences.

### Methods

Theory: Two types of microcirculatory flow were brought up by Le Bihan et al1. 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 F1 = e-Db, 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 F2 = |sinc(cv)|·e-Dblood·b, where c is the first order moment of the diffusion gradient waveform and Dblood is the self-diffusion of the water molecules in the blood8. For flow compensated pulsed and oscillating gradient waveforms, the first order moment is zero (c = 0), and we have F2 = e-Dblood·b (Dblood ≈1.6 x 10-3 mm2/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/mm2) with the following parameters: single-shot EPI, TE/TR = 58/3000ms, NA=4, 5 slices with in-plane resolution = 0.2 x 0.2 mm2 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 [f1, f2, 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/mm2.

### Results

We implemented flow compensated PGSE4 (FC-PGSE) sequence and cosine-trapezoid OGSE7 sequence (Fig. 1A) to measure IVIM at a range of diffusion times. Phantom data (Fig. 1B) showed that FC-PGSE and OGSE ADC measurements at b = 200 s/mm2 remained unchanged as flow rate increased from 0 to 4 mm/s, whereas conventional PGSE ADC measurements increased rapidly. Based on Equation 1, non-linear fitting was performed at five diffusion times (Δ=2.5ms and 5ms from OGSE at frequencies of 50Hz and 100Hz, FC-PGSE with durations of T=10 ms and 20ms, and Δ=40ms from conventional PGSE). The fitting results showed the pseudo-diffusion fraction (f1) from IVIM model 1 increased with increasing diffusion time (Fig. 2A-B). The average f1 (n=7) in the center slices (three slices as shown Fig. 2A, excluding the ventricle) increased from 0.037±0.002 to 0.049±0.005 as the diffusion time increased from 2.5ms to 40ms. The difference associated with diffusion times was significant with p-value=5.3x10-7 based on one-way ANOVA. In low b-value regime, the overall diffusion signals decreased as diffusion time increased (Fig. 3C), consistent with the increase of f1.

### Discussion and conclusion

In this study, we investigated the diffusion time dependency of pseudo-diffusion in the mouse brain. We adopted a compartmental IVIM model considering both types of microcirculatory flow1. By employing flow compensated PGSE and OGSE sequences, the model can be simplified (Equation 1) with c=0, and a series of measurements from very short to long diffusion times can be acquired. The fitting results support our hypothesis that as the diffusion time increases, higher fraction of microcirculatory flow falls into type1 (flow across several segments) rather than type2 (flow within one segment). More sophisticated models may be needed for microcirculatory flow in the transit state between type 1 and type 2. The changes in IVIM signals with diffusion time potentially reflects the micro-vasculature geometry9, and could be useful to study change in capillary segments and associated vasculature pathology, e.g., abundant and aberrant vasculature in tumor10.

### Acknowledgements

No acknowledgement found.

### References

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.

### Figures

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 (f1 in Equation 1). (A) f1 map of a mouse brain at five diffusion times. (B) f1 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/mm2. Data is represented as mean ± standard deviation (n=7).

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