Yu Gao^{1}, Ziwu Zhou^{1}, Fei Han^{1}, Xiaodong Zhong^{2}, Yingli Yang^{1}, and Peng Hu^{1}

^{1}Radiological Sciences, University of California, Los Angeles, Los Angeles, CA, United States, ^{2}MR R&D Collaborations, Siemens Healthineers, Los Angeles, CA, United States

Strong spatial distortion of the DW-ssEPI sequence prevents its utilization in radiotherapy planning and treatment adaptation. In this work, a 3D diffusion-prepared magnitude-stabilized bSSFP sequence was developed and validated at 1.5T. A phase navigator was acquired during the catalyzation stage of the bSSFP readout to estimate the spatial variation of the signal phase, and a locally low-rank constrained reconstruction was developed to resolve the phase variation. The sequence was validated on a diffusion phantom and healthy volunteers. It provided submillimeter geometric fidelity and acceptable ADC accuracy, which makes it a promising candidate for treatment planning and adaptation of the brain.

$$min_x\sum_{j=1}^{n_c}\sum_{i=1}^L||D_iFS_jP_{ij}x_i-y_{ij} ||_2^2+\gamma \sum_{b\in\Omega} ||C_bx||_\ast$$

where $$$y_{ij}$$$ is the acquired k-space data from the $$$i^{th}$$$ shot and $$$j^{th}$$$ coil, $$$x_i$$$ is the coil-combined image reconstructed from the $$$i^{th}$$$ shot, $$$x$$$ is the matrix concatenating all images from different shots, $$$F$$$ is the Fourier transform, $$$D_i$$$ is the under-sampling operator for $$$i^{th}$$$ shot, $$$P_{ij}$$$ is the phase compensation matrix derived from the Gaussian-windowed phase of the built-in ramp-up navigator, $$$S_j$$$ is the $$$j^{th}$$$ coil sensitivity map. $$$\Omega$$$ is a set of small image blocks partitioned from $$$x$$$, $$$C_b$$$ is the operator that takes image block from the set $$$\Omega$$$ and forms its Casorati matrix, $$$||\cdot||_{\ast}$$$ is the nuclear norm, and $$$\gamma $$$ is the regularization parameter.

Figure 3 shows the phantom ADC results. There was a good agreement of ADC values measured from the two diffusion sequences. The percent difference was less than 7%.

An in-vivo comparison is shown in Figure 4. Distortion and signal pile-up were apparent on DW-ssEPI images, particularly at the base of the brain. DP-MS provided high-quality diffusion images with no observable distortion. The mean TRE of DW-ssEPI was over 2mm for all four volunteers, and the maximum displacement was almost 10mm. The mean TRE was less than 0.8mm for DP-MS.

The Bland-Altman plots of the mean diffusivity for selected ROIs on the white matter, cerebellum, and CSF were shown in Figure 5. Overall, there were good agreements of ADC between the two diffusion approaches, and the systematic biases were low (0.01x10

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Figure 1. Sequence diagram of an example imaging shot
of the proposed DP-MS sequence. Blue rectangles represent the magnitude
stabilizers. DG: diffusion gradient. SP: spoiler gradient. CP: catalyzation
pulses. The linear catalyzation pulses are mainly used to reduce signal
oscillation and to achieve a steady-state signal intensity during the image
acquisition. A 2D navigator is acquired for phase inconsistency estimation and
correction. This navigator is only phase-encoded to cover the central 16 ky
lines.

Figure 2: Phantom image comparison. Images from left
to right are: TSE, DW-ssEPI (b=800 s/mm^{2}), and DP-MS (b=800 s/mm^{2}).
As indicated by the blue dotted lines, the phantom shell was strongly distorted
using the DW-ssEPI approach. There was susceptibility related artifact as
pointed by the blue arrow. In addition, several diffusion vials were elongated
and were no longer in round shape. In comparison, no visible distortion or
artifact was present in DP-MS image.

Figure 3. ADC accuracy at room temperature. The x-axis
shows the labels of the thirteen vials. The number represents the percent
concentration of polyvinylpyrrolidone (PVP) solutions (higher PVP, lower
diffusivity), and c (center), i (inner), o (outer) represent the relative
location of the vial. The y-axis is the reference and measured ADC values in 10^{-3}mm^{2}/s.
The error bar represents the standard deviation.

Figure 4. Representative transversal plane images from
two volunteers. The anatomical reference image, images at b-value of 0 s/mm^{2}
and 800 s/mm^{2} from DW-ssEPI and DP-MS are shown. The blue triangles
point to distortion and signal pile-up
artifacts in DW-ssEPI.

Figure 5. Bland-Altman
plot of the white matter, cerebellum and CSF ADC between DW-ssEPI and DP-MS.
Good agreements were observed for the ADC values from the two sequences