Sean McTavish^{1}, Anh Tu Van^{1}, Johannes Peeters^{2}, Tetsuo Ogino^{3}, Andreas Hock^{4}, Ernst Rummeny^{1}, Rickmer Braren^{1}, and Dimitrios 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 recently been 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 using asymmetric diffusion gradients for combined motion compensation and residual vessel signal suppression in liver DWI, optimized for short echo times.

*Partial optimized
asymmetric velocity-compensated diffusion encoding scheme (asym
vc-pgsep)*

The proposed diffusion encoding combines an
optimized asymmetric velocity-compensated diffusion encoding waveform (asym vc) on the M and S axes, and a traditional Stejskal-Tanner
diffusion encoding (pgse) waveform on the P axis. The velocity-compensated
diffusion waveform is asymmetric in order to reduce the
echo time, and the duration of each gradient lobe was found by running a
constrained optimization algorithm. Figure 1**a** shows the velocity compensated component of the proposed
diffusion encoding waveform, which was
assumed to have 2 lobes on either
side of the $$$180°$$$pulse. It was also assumed that each lobe would ramp up to the maximum gradient
strength at the maximum allowed slew rate. The constraints being applied to the
optimization procedure, given in Figure 1**c**,
were the M_{0} and M_{1} nulling, and the timing constraints for the 4 lobes. An
expression for the b-value was found for this configuration of gradient lobes,
and the echo time was minimized for a given target b-value. This
gave the analytical expressions for each lobe
plateau duration shown in Figure 1**d**. No correction was done for concomitant magnetic fields. Figure 2
shows the asym vc-pgsep waveform for all 3 axes.

*MR measurement*

In-vivo experiments were carried out in 5 subjects to assess the
performance of the proposed asym
vc-pgsep diffusion encoding scheme in motion resistance and vessel
signal suppression. For comparison, experiments with pgse in all three axes and
bipolar-vc in all three axes were also
performed. Imaging parameters included: acquisition voxel size $$$=3x3x6mm^3$$$; 10 slices placed in the upper part
of the liver; 3 orthogonal diffusion encoding directions at b-values of $$$[0,100,200,300,400]$$$s/mm^{2} and
averages of $$$[4,4,5,6,8]$$$;
TE=55/71/64ms for pgse, bipolar-vc and asym vc-pgsep; full Fourier encoding for pgse and a
partial Fourier encoding factor of 0.7 for bipolar-vc and
asym vc-pgsep. All experiments were
performed on a 3T scanner (Philips Ingenia Elition, Best, The Netherlands)
using anterior and posterior torso coils for receiving. ADC maps were
calculated from b-values of $$$200,300$$$ and $$$400$$$ in order to avoid including the
perfusion signal that can be detected at lower b-values.

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