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 vessels^2,3. 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 compensated^4,5 pulsed gradient spin-echo (PGSE) and oscillating gradient spin-echo (OGSE)^6,7 sequences.

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^-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 F₂ = |sinc(cv)|·e^-D_blood·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 blood⁸. For flow compensated pulsed and oscillating gradient waveforms, the first order moment is zero (c = 0), and we have F₂ = e^-D_blood·b (D_blood ≈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.

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.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.