Introduction

Recent interest in understanding the waste removal processes in the brain has highlighted the need for in vivo imaging of sub-millimeter/second flow^1-4. Diffusion imaging utilizes second-order water flow to characterize white matter microstructures and tractography. Conventional diffusion image processing relies on magnitude information; by using the remaining phase information, it becomes possible to simultaneously extract coherent motion profiles for the tissue, which can be related to CSF flow.
In this work, we present an analysis for the selection of timing parameters of a diffusion imaging pulse sequence to optimize the simultaneous collection of both magnitude and phase data. We also discuss the subsequent reconstruction for coherent motion that can run in parallel to existing diffusion imaging reconstruction.

Methods

Standard diffusion imaging uses a pair of trapezoidal pulses to encode a given b-value with minimum TE. We modified a single-spin echo diffusion imaging sequence to create the SCIMI (Simultaneous Coherent-Incoherent Motion Imaging) sequence, which allows setting a given b-value and an encoded velocity independently by appropriately tuning timing parameters. For a given b-value, minimum TE is achieved by varying $$$\delta$$$ while keeping the spacing between the two lobes of the encoding gradient fixed, $$$\Delta=\delta+t_{180}$$$, where $$$t_{180}$$$ is the minimum time needed for the refocusing pulse and crusher gradients surrounding it. By allowing $$$t_{180}$$$ to stretch, the sequence gains the flexibility to simultaneously choose a v_enc value, at the cost of lengthening TE. To encode for both a given b-value and v_enc, the timing for the diffusion-encoding trapezoids is modified using the roots $$$\delta$$$ in the following equation:
$$$c_2\delta^3+(\frac{c_2\zeta^2}{2}-3c_1)\delta+3c_1^2-c_2\zeta^3/10=0$$$
where $$$c_1=2bv_{enc}/\pi\gamma G$$$, $$$c_2=4bv_{enc}^2/\pi^2$$$, and $$$\zeta$$$ is the trapezoid ramp time. The combination of the values $$$c_1\propto bv_{enc}$$$ and $$$c_2\propto bv_{enc}^2$$$ encode the relevant parameters, while the ramp time can always be set using the maximum desired slew rate to keep TE as low as possible. The real positive values of are then used to determine the required $$$\Delta$$$ values according to
$$$\Delta=\frac{\delta^3-\zeta^3/10+\delta\zeta^2/2}{3\delta(\delta-c_1)}$$$
subject to $$$\Delta\ge\delta+t_{180,min}$$$ and $$$\delta\gt\zeta$$$.
Imaging with such a sequence allows for conventional diffusion image reconstruction while a separate phase-sensitive reconstruction pipeline is used to measure coherent motion. Figure 1 details the method to reconstruct velocity profiles in 3D from the images. Using this, we imaged 5 healthy volunteers on a GE Healthcare Discovery MR750 (Waukesha, WI) scanner using a custom high-performance gradient coil set for brain imaging⁵ with a gradient strength of 200 mT/m and slew rate of 500 T/m/s. We imaged with a 2-shell sequence (30 directions: 8 in inner shell, 22 in outer shell) with b_outer=2000sec/mm², b_inner=1400sec/mm², and v_enc=0.24mm/s. For each series of images, we varied the trigger delay (peripheral gating) to image axial slices containing the lateral ventricles at various phases in the cardiac cycle, using delay times of 14ms, 64ms, 114ms, 164ms, 214ms, and 514ms delays from the R-wave.

Results & Discussion

Figures 2 and 3 show some of the constraints when simultaneously setting the b-value and the v_enc. In Figure 2, several sample encoding pulses are shown for a variety of different v_enc values. As the v_enc decreases, the two lobes of the encoding pulses become narrower and further apart, increasing TE overall. The minimum TE sequence will always have the maximum v_enc allowed for a given b-value and gradient strength, as shown in Fig. 3. At higher b-values, the increase in TE is only nominal, while at low b-values and v_enc, this increase may make imaging impossible. With a stronger gradient coil, the maximum allowed v_enc increases and the effect of lowering the v_enc for a given b-value on TE is reduced.
Figures 4 and 5 show the result of the velocity profile reconstruction. In Fig. 4, the difference between gated and ungated acquisition clearly demonstrates that with gating, there is a net coherent motion with RMS 0.065 mm/s in the region of interest. In Fig. 5, the different trigger delays provide a sequence of motion at different phases in the cardiac cycle. Immediately after R-wave (systole phase), there is significant lateral motion around the ventricles. This motion fades, and a clear reversal is seen at 164 ms, demonstrating the expected brain pulsatility motion. This motion accounts for both tissue movement due to pulsation and CSF flow through the tissue. Both the motion sequence and the measured velocities agree with independent phase-contrast scans performed on the same volunteers.

Conclusion

Our method for simultaneous imaging of coherent and incoherent (diffusion) motion in vivo uses magnitude reconstruction of diffusion data and phase-sensitive reconstruction to image coherent motion. Adjusting timing parameters of a diffusion pulse sequence to set b-values and v_enc values independently allows low v_enc values on the order of 0.1-0.5 mm/s. This range is well suited to studying CSF pulsatile flow through brain parenchyma.
Analysis of this motion over the course of several hours, for example during a sleep study, may provide insight into the waste removal mechanisms of the brain. Slowly varying CSF mean velocity may be extracted by averaging the signal over multiple heartbeats to study CSF flow in interstitial spaces.