Diffusion-preparation (DPrep) is regaining popularity thanks to its compatibility with any type of readout [1-4]. However, motion during diffusion-encoding results in spatially varying spin phase that modulates the magnitude of both longitudinal and transverse magnetization after the tip-up RF pulse (Fig.1). To mitigate phase-induced magnitude modulation, previous studies added a dephase gradient before the tip-up RF pulse and a rephase gradient in the readout [1,2]. The goal of this work is to characterize the effectiveness of the dephase/rephase gradient in reducing the motion-induced signal modulation and to propose additional strategies for improving the motion insensitivity of DPrep sequences.

Letting $$$\phi_i$$$ be the spin phase after the diffusion encoding period, $$$\theta_i$$$ be the phase induced by the dephasing gradient, the longitudinal magnetization after the tip-up pulse is $$m_i^z=cos(\phi_i+\theta_i)=\frac{1}{2}(e^{j(\phi_i+\theta_i)}+e^{-j(\phi_i+\theta_i)})\ (1)$$ After the excitation, refocusing pulse, and the rephase gradient, the transverse magnetization of a spin is $$m_i^{xy}=\frac{1}{2}(e^{j(\phi_i+\theta_i)}+e^{-j(\phi_i+\theta_i)})e^{-j\theta_i}e^{-j\pi/2}$$ $$m_i^{xy}=\frac{1}{2}(e^{j\phi_i}+e^{-j(\phi_i+2\theta_i)})e^{-j\pi/2}$$ and the measured magnetization of a voxel is $$M^{xy}=\sum_{i \in voxel}\frac{1}{2}(e^{j\phi_i}+e^{-j(\phi_i+2\theta_i)})e^{-j\pi/2}\ (2)$$ Equation (2) implies that the resulted voxel signal depends on both the motion-induced spin phase $$$\phi_i$$$ and the phase added by the dephase/rephase gradients pairs $$$\theta_i$$$. Furthermore, with arbitrary varying $$$\phi_i $$$ it is almost impossible to design dephase/rephase gradients that can mitigate the phase-induced signal modulation. Consider the special case where $$$\phi_i$$$ varies slowly enough spatially so that over a voxel with small enough size it is approximately constant, meaning $$$\phi_i \approx \phi_{voxel}$$$ for all spins within this voxel (call Condition 1), Equation (2) can be rewritten as $$M^{xy} = \frac{1}{2}e^{j(\phi_{voxel}-\pi/2)}(1–e^{-j2\phi_{voxel}}\sum_{i \in {voxel}}e^{-j2\theta_i}) \ (3)$$ Assuming further that the dephase/rephase gradients are designed so that $$$\sum_{i \in voxel}e^{j2\theta_i} = 0$$$ (call Condition 2), the transverse magnetization of the voxel is $$M^{xy}=\frac{N_{spin}}{2}e^{j(\phi_{voxel}-\pi/2)}\ (4)$$ where $$$N_{spin}$$$ is the total number of voxel spins. Equation (4) implies that while transverse magnetization has magnitude that is independent of motion-induced phase, its phase depends on the motion-induced phase. There are two important points that Equation (4) and its associated necessary conditions implies on the phase sensitivity of the DPrep sequence: 1) When the voxel size decreases, Condition 1 can be met by more $$$\phi_i$$$ patterns and therefore the resulted signal is more robust in avoiding motion-induced magnitude modulation. 2) DPrep sequence is not readily applicable to multi-shot acquisition due to the motion-dependent magnetization phase. To enable multi-shot acquisition special diffusion-encoding schemes that reduce motion effects such as velocity-compensated or acceleration-compensated diffusion encoding [4-6] or phase navigation must be used.

Simulation: Bloch simulations were performed considering two types of motion-induced phase $$$\phi_i$$$: constant phase in $$$(-\pi, \pi)$$$ and linear phase across the voxel $$$\alpha x+\pi/4$$$ with $$$\alpha\in(-\pi/mm,\pi/mm)$$$. Different voxel sizes were simulated to show the dependence of motion robustness on voxel size.

In vivo experiment: Sagittal diffusion-weighted imaging of the upper knee of a healthy volunteer was conducted using a 16-channel knee coil on a 3 T system (Ingenia, Philips Healthcare) with a diffusion-prepared 3D TSE sequence, with sequence parameters: FOV=160×127×100 mm3, voxel=1.7×1.7×1.7mm3, TR/TE=1700/19, TSE factor =60, Nex=2, total scan duration = 3min40s, using both traditional and velocity-compensated diffusion preparation at b=400s/mm2.

Simulation: Without dephase/rephase gradients, magnitude of the simulated voxel at echo oscillates even when $$$\phi_i$$$ is constant over the voxel (Figure 2a). When $$$\phi_i \in (-\frac{\pi}{2}, \frac{\pi}{2})$$$, spins are tipped to +z, otherwise spins are tipped to -z, which results in the toggling of the signal phase between $$$-\pi/2$$$ and $$$\pi/2$$$ states. When dephase/rephase gradients are used, the signal magnitude is stable for all values of $$$\phi_i$$$ while the phase varies and equals to $$$-\pi/2+\phi_i$$$ (Figure 2b). Figure 3 shows higher robustness of smaller voxel size in mitigating magnitude modulation caused by linear phase across the voxel. Both magnitude and phase of the signal exhibit smaller change with respect to the slope of the linear phase as the voxel size decreases.

In-vivo: Diffusion-weighted images of the human knee are shown in Figure 4. Since the readout module is multishot, dephase/rephase gradients alone cannot help with the motion problem and velocity-compensated diffusion preparation is needed to recover the signal loss. When dephase/rephase gradients are not used, motion-induced signal loss occurs in localized area. Since the rephase gradient also has the capability to crush T1-recovered signal, using dephase/rephase gradients gives better fat suppression.

We have shown that in Dprep sequences, motion-induced magnitude modulation can be avoided when employing dephase/rephase gradients. However, the signal phase remains motion-dependent, which makes multishot acquisition possible only with motion-compensated Dprep. When the induced phase is not constant, smaller voxel size is more robust in stabilizing both magnitude and phase of the signal.