Anh T Van^{1}, Barbara Cervantes^{1}, Tetsuo Ogino^{2}, Johannes M Peeters^{3}, Andreas Hock^{4}, Ernst J Rummeny^{1}, Rickmer Baren^{1}, and Dimitrios C Karampinos^{1}

Despite its strong clinical significance in lesion detection and tumor staging, liver DWI remains challenged by its strong sensitivity to motion effects. Motion-compensated diffusion encoding schemes have been recently proposed to improve DW liver signal homogeneity especially in the left liver lobe, a region typically affected by cardiac motion. However, motion-compensated diffusion encoding is associated with hyperintense vessel signal even at high b-values, which can obscure lesion detection. The present work proposes a partial velocity-compensated diffusion encoding for combined motion compensation and residual vessel signal suppression in liver DWI.

*Partial velocity-compensated diffusion encoding scheme (vmcpgse)*

The proposed diffusion encoding combines velocity-compensated diffusion encoding (vmc) on two axes and traditional Stejskal-Tanner diffusion encoding (pgse) on the third axis. The pgse waveform suppresses vessel signal and the proposed diffusion encoding scheme selects the pgse axis aiming to reduce sensitivity to motion based on the following two arguments.

1) The pgse waveform is applied along the direction that is least affected by cardiac motion, which has been shown by Kwee et al to be the A-P direction [4].

2) Partial Fourier encoding (PF) needs to be used to shorten the echo time. However, with PF, motion-induced k-space shifts can drive the k-space center outside of the acquired region, leaving unusable noisy data [9]. In the case of rigid body motion, the direction of k-space shift is the cross product between the axis of the rotation and the diffusion encoding direction [10, 11] and the k-space shift along the phase encoding direction (ky, or partial Fourier direction) is$${\Delta}k_y=\gamma\int{[G_z(t)\theta_x(t) - G_x(t)\theta_z(t)]dt} \ (1)$$

where $$$G_x, G_z$$$ are the diffusion encoding gradients along the x and the z direction, respectively and $$$\theta_x, \theta_z$$$ are the rotation angles around the x and the z axis, respectively. Equation (1) implies that the shift along the ky direction is independent of the diffusion encoding gradient Gy. Therefore, when PF is used, the pgse waveform should be applied along the phase encoding direction to minimize the probability of missing the k-space center.

Based on the above arguments the pgse waveform in the vmcgse scheme should be applied on the phase encoding axis. The proposed diffusion encoding scheme (vmcpgse-p) is thus depicted in Figure 1.

*MR measurement*

In-vivo experiments were carried out in 3 subjects to assess the performance of the proposed vmcpgse-p diffusion encoding scheme in motion resistance and vessel signal suppression. To show the benefits in terms of k-space shifts when the pgse waveform is applied along the phase encoding direction, acquisitions with three varieties of vmcpgse in which the pgse waveform is applied along the frequency (vmcpgse-m), phase (vmcpgse-p), and slice encoding (vmcpgse-s) directions were performed. For comparison, experiments with pgse in all three axes and vmc in all three axes were also performed. Imaging parameters included: acquisition voxel size = 3x3x6mm3, 6 slices in the upper part of the liver, 3 diffusion encoding directions ([-0.5 -1 -1], [1 0.5 -1], [1 -1 0.5]), b-value of 600s/mm2, 10 averages, TE=61/67ms for pgse/vmc and vmcpgse, full Fourier encoding for pgse and PF factor of 0.6 for vmc and vmcpgse. All experiments were performed on a 3T Ingenia system (Philips, Best, the Netherlands) using anterior and posterior torso coils for receiving.

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Figure 1: Proposed partial velocity-compensated
diffusion encoding in a single-shot EPI sequence combining velocity-compensated
diffusion gradient waveforms (vmc) on frequency encoding (M) and slice
selection (S) axes and the traditional Stejskal-Tanner diffusion encoding
(pgse) waveform in the phase encoding (P) axis.

Figure 2: In vivo DW images at two
different locations in the upper part of the liver. Pgse diffusion encoding
scheme shows signal loss on the left lobe locations of the liver (red arrows).
Vmc diffusion encoding restores the signal loss but suffers from hyperintense
vessel signals. Vmcpgse-p is a good
combination of vessels signal suppression and reduced signal loss.

Figure 3: k-space shifts along the phase
encoding axis in a subject using 4 diffusion encoding variants. The proposed
diffusion encoding vmcpgse-p shows lower k-space shifts than vmcpgse-m and
vmcpgse-s diffusion encodings.

Figure 4: Standard deviation of k-space
shifts for the 4 diffusion encoding variants in the 3 scanned subjects.
Velocity compensated diffusion encoding in all three axes (vmc) shows the
lowest k-space shift standard deviation and the proposed diffusion encoding
(vmcpgse-p) shows lower k-space shift standard deviation than vmcpgse-m and
vmcpgse-s.