Synopsis

Keywords: Image Reconstruction, Diffusion/other diffusion imaging techniques

Multi-shot EPI readout-approaches provide high spatial resolution at reduced geometric distortions and improved SNR in diffusion weighted imaging (DWI). As a specific challenge, physiological motion induces shot-to-shot phase variations and needs specific handling, e.g., using additionally measured phase navigators, data-driven phase estimation and/or low-rank regularizations. Furthermore, good fat-suppression is also needed in DWI, making the use of chemical-shift encoding interesting. In this work, a structured low-rank-based water/fat separation pipeline is proposed to jointly estimate water/fat images while correcting motion-induced phase variations with improved time efficiency. In-vivo examples from different anatomies demonstrate improved water/fat separation compared to conventional approaches.

Introduction

In EPI-based diffusion-weighted imaging (DWI), fat is always a confounding factor, especially in regions of large B₀ inhomogeneities, where conventional fat-saturation is prone to failure. To address this challenge, chemical-shift encoding (Dixon) has been combined with DWI^1,2. Furthermore, multi-shot EPI has gained popularity in DWI to increase image resolution and reduce geometric distortions³. But at the same time, extra-navigation³, or self-navigation methods⁴ become necessary to cope with physiological motion-induced shot-to-shot phase variance. However, when combining multi-shot EPI DWI and Dixon, the fat signals present in the extra-navigators are not easily removed and may thus cause problems. Self-navigation/navigation-free methods can potentially solve this with reduced scan time. Inspired by MUSSELS⁵, we propose an iterative, model-based reconstruction pipeline with two individual structured low-rank regularizations acting respectively on water/fat channels to deal with the shot-to-shot phase variations while separating water/fat images. In-vivo experiments in different anatomies demonstrate its effectiveness compared to extra-navigated/SPIR results.

Methods

The cost function of the chemical-shift encoded multi-shot DWI-EPI can be written as:$$\left\{\bar{x}_w,\bar{x}_f\right\}=\underset{x_w,x_f\in\mathbb{R}^Q}{\operatorname{argmin}}\|A{P}{x}-d\|_2^2+\lambda_1\left\|H\left(P_w{x_w}\right)\right\|_*+\lambda_2\left\|H\left(P_f{x_f}\right)\right\|_*,\qquad\qquad{(1)}$$where $$$Q$$$ is the number of voxels, $$$P$$$ contains $$$P_w$$$ and $$$P_f$$$ on its diagonal blocks adding the diffusion phase for individual water/fat shots, $$$x=\left[x_w,x_f\right]^T$$$ the joint water/fat magnitude images, $$$d$$$ the vectorized k-space data for N Dixon points, L shots, and J coils, $$$\lambda_1/\lambda_2$$$ the regularization factors for water/fat channels. $$$\left\|H\left(P_{w/f}x_{w/f}\right)\right\|_*$$$ are the block-Hankel regularization terms similar as introduced in the MUSSELS⁵ which enforce the low-rankness between different shots of the water/fat channels, separately, through the nuclear norm. The low-rank constraint leverages the redundancy across shots by assuming that their underlying magnitude components are equal despite their different phases. It should be noted that water/fat signals are assumed to have one joint phase, after correcting for the spatial displacement of fat for each shot. This joint, but shot-specific phase, is described by the phase operator $$$P$$$ (shape $$$2\times{N}\times{L}\times{Q},2\times{Q}$$$), which also introduces the Dixon dimension into the cost function. The matrix $$$A$$$ can be expressed as:$$A=K\left[\begin{array}{ll}I&I\end{array}\right]\left[\begin{array}{cc}F{S}{\Psi_B}&0\\0&\Psi_f{F}S\Psi_B\end{array}\right],\qquad\qquad{(2)}$$where $$$K$$$ indicates the shot-specific k-space undersampling, $$$I$$$ is the identity matrix, $$$\Psi_f$$$ adds fat off-resonance, $$$S$$$ adds the coil sensitivity weighting, $$$\Psi_B$$$ adds the B₀ inhomogeneity-induced phase, which are implemented through linear operators. For the DWI reconstruction, the B₀ map prior (and two thresholding water/fat masks) and coil-sensitivity maps can be calculated/calibrated using an image-based water/fat decomposition approach for EPI (IDE)² and ESPIRiT⁷ as described in ref.⁶ from the b = 0 s/mm² data. For all reconstructions, a multi-peak fat model was used. The general reconstruction pipeline is shown in Figure 1. The water/fat images were initialized by first minimizing:$$\left\{\bar{m}_w,\bar{m}_f\right\}=\underset{m_w,m_f\in\mathbb{C}^{N\times{L}\times{Q}}}{\operatorname{argmin}}\|A{m}-d\|_2^2+\lambda_3\left\|H\left(m_w\right)\right\|_*+\lambda_4\left\|H\left(m_f\right)\right\|_*,\qquad\qquad{(3)}$$where $$${m}=\left[m_w,m_f\right]^T$$$ is the collection of all complex water/fat shot images (L$$$\times$$$N). In this case, since the operator $$$P$$$ is dropped in Eq.3, the water/fat separation for each l and n can be treated as a SENSE-based separation scenario (water-fat SENSE^6-9), benefiting from the chemical-shift-induced spatial displacement of fat, using SENSE to disentangle water and fat. In Eq.3, this step is also guided by structured low-rank regularization.
Experiments were conducted in healthy volunteers (after informed consent was obtained) in brain, knee and head-neck regions at 3T (Philips, Best, The Netherlands), using chemical-shift encoded spin-echo DW four-shot-EPI^2,6, with b-values of 0,1000s/mm² for brain and 0,300,600s/mm² for other anatomies. A 16-channel head-neck and 8-channel knee coil were used, resolution: 1×1×4mm³ (brain), 1.4×1.5×4 mm³ (head-neck/knee) with TE=120ms/TR=5000ms or TE=70/TR=5000ms (no partial-Fourier). For water/fat encoding, three echoes of $$$\Delta{TE}$$$ were chosen as 0.2/1.0/1.8ms with respect to the spin echo, enabled by shifting the msh-EPI sampling window back and forth. An extra-navigator was acquired for each diffusion shot for comparison^2,6. One scan in the head-neck was repeated with conventional fat suppression (SPIR¹⁰). Moreover, fully sampled data were retrospectively undersampled. All hyper parameter tuning and the implementation of Hankel-matrices were done as in ref.¹¹ with filter size of 8×8. Eq. 1 and Eq. 3 were solved using 20 iterations of each.

Results

Figure 2 shows water/fat, magnitude/phase shot-images of one Dixon point, comparing water-fat SENSE separation without (A) and with (B) low-rank-regularization, and (C) the structured low-rank-regularized full-model Dixon-based water/fat separation. Figure 3 shows water/fat images comparing reconstruction without navigation (phase-blind), with extra-navigators, and with the proposed structured low-rank full-model reconstruction. An example navigator image of the leg slice, which has shifted fat present, was also shown to compare with the fat-displacement-corrected phase map from the proposed method. Figure 4 shows a comparison between water/fat images from SPIR and from the proposed approach in a B₀ critical region, with corresponding ADC maps. Figure 5 shows reconstruction results of the proposed approach using different k-space undersampling patterns for the Dixon/multi-shot dimensions.

Discussion and conclusion

In this work, we used low-rank regularizations to enable navigator-free water/fat separation for multi-shot diffusion-weighted EPI. The results showed that this approach produces superior image quality with shorter scan times compared to both extra-navigation and SPIR techniques. Although Dixon is a smart way of signal averaging, it is also demanding for robust water/fat separation and scanning time. However, in this work, we showed the ability of the proposed approach to support k-space undersampling, when covering the full k-/Dixon-space extent. Thus, no scan time penalty has to be paid, allowing to get Dixon-based water/fat separation in ms-DWI-EPI for “free”.

Acknowledgements

The authors would like to acknowledge NWO-TTW (HTSM-17104).