Introduction

Multi-shot interleaved EPI (msh-EPI) provides significant improvement for diffusion-weighted imaging (DWI) to allow images with higher spatial resolution and less geometric distortions¹. However, multi-shot acquisitions for DWI applications are susceptible to physiological motion-induced phase variations between the shots. This difficulty is usually addressed by 1) acquiring additional navigator images^1,2, or 2) employing self-navigation approaches^3,4. Moreover, residual fat artefacts represent another difficulty in DWI due to the large water-fat shift in phase-encoding direction. Fat suppression⁵ techniques, widely used for eliminating fat, often fail for large B₀ inhomogeneities. Moreover, they do not fully consider the multipeak nature of the fat spectrum (e.g., Olefinic peak, 0.61 ppm to water). Recently, chemical-shift encoding has been proposed to jointly separate water and fat images while estimating the B₀ inhomogeneities^6-8. Nevertheless, the need to acquire images at multiple TEs may limit its efficiency in clinical applications. Alternatively, Uecker et al. has proposed an approach exploiting the chemical-shift-induced spatial shift of fat using sensitivity encoding (SENSE) to disentangle water and fat signals. The method is validated with a single-peak fat model and single-shot EPI images.
In this work, we propose to include the multipeak nature of the fat spectrum into the approach by Uecker et al.⁹ to separate water and fat in EPI based on SENSE. This approach is extended to multi-shot, in-vivo DWI using a novel water-fat phase self-navigation method to compensate for motion-induced phase errors, making the need for measuring an extra-navigator echo obsolete.

Methods

The forward model of the DW msh-EPI data at a certain b-value can be written as:$$s=\sum_{n}^{N}Q_{n}\left(\hat{F}\hat{C}\hat{\Phi}_{w,n}\rho_{w}+\alpha_{m}\sum_{m=1}^{M}\hat{\Psi}_{f,m}\hat{F}\hat{C}\hat{\Phi}_{f,n}\rho_{f}\right)\tag{1}$$where $$$\hat{F}$$$ is the Fourier transform operator, $$$\hat{C}$$$ the SENSE operator, $$$\hat{\Phi}_{w,n}$$$ and $$$\hat{\Phi}_{f,n}$$$ the operators of motion-induced phase errors for water and fat, respectively. $$$\alpha_{m}$$$ is the relative amplitude weight, $$$\hat{\Psi}_{f,m}$$$ denotes the fat off-resonance operator for peak $$$m$$$, and $$$Q_{n}$$$ represents the k-space trajectory for each shot $$$n$$$. $$$s$$$ and $$$\rho_{w}/\rho_{f}$$$ are the vectorized representations of the measured multi-shot k-space signal and the target water/fat images. The water/fat images can be calculated by minimizing:$$\left\{\rho_{w},\rho_{f}\right\}=\underset{\rho_{w},\rho_{f}\in\mathbb{C}}{\operatorname{argmin}}\|\hat{A}X-s\|_{2}^{2}\tag{2}$$where $$$X=\left[\rho_{w},\rho_{f}\right]^{T}$$$ and $$$\hat{A}$$$ is the coefficient matrix, containing all the operators described above. For multi-shot acquisition, the relatively small spatial shift of fat compared to single-shot EPI makes the accuracy of coil-sensitivity maps (CSM) particularly important. Therefore, the advanced JSENSE described in Shin et al.¹⁰ is used to self-calibrate the CSM for b=0 s/mm². Two threshold water/fat masks can be calculated using the separated $$$\rho_{w}$$$ and $$$\rho_{f}$$$ images to mask the CSM and stabilize the phase estimation step.
For the diffusion-weighted cases, the SENSE-based water/fat separation is performed for each shot data to calculate motion-induced phase errors for water/fat individually. Inspired by MUSE³, the water/fat-adapted SENSE formalism is used to recover ghost-free images for each shot. First, this can be done by solving the equation:$$s_{n}=Q_{n}\left(\hat{F}\hat{C}\rho_{w,n}+\alpha_{m}\sum_{m=1}^{M}\hat{\Psi}_{f,m}\hat{F}\hat{C}\rho_{f,n}\right)\tag{3}$$using conjugate gradient (CG), to estimate $$$\rho_{w,n}$$$ and $$$\rho_{f,n}$$$ for each individual shot $$$n$$$ from the measured data. Then, the motion-induced phase $$${\Phi}_{w,n}$$$ and $$${\Phi}_{f,n}$$$ can be calculated separately for water and fat by:$$e^{i\phi_{w/f,n}}=\frac{\rho_{w/f,n}}{\left|\rho_{w/f,n}\right|}.\tag{4}$$In addition, k-space triangular window¹¹ is applied individually on $$$e^{i\phi_{w,n}}$$$ and $$$e^{i\phi_{f,n}}$$$ to enforce smoothness and construct the operators $$$\hat{\Phi}_{w,n}$$$ and $$$\hat{\Phi}_{f,n}$$$ in Eq.1. The window width is chosen to be half of the matrix size. Finally, the DW water/fat images can be calculated by solving Eq. 2 using CG. The whole pipeline is illustrated in figure 1.
DW msh-EPI spin-echo data of the lower leg of a normal volunteer was acquired using a 3T-MRI (Philips Healthcare, Best, Netherlands) with the following parameters: TR/TE=2000/60ms, resolution 1.5×1.5×4 mm³, three b-values (0, 300, 600 s/mm²), 3 shots, an 8-channel knee coil. For comparison, an extra-navigator² was acquired for each shot. In addition, another fat-suppressed DWI scan was acquired using SPIR⁵ and reconstructed through IRIS algorithm².

Results and Discussion

Figure 2 shows the non-diffusion dataset comparing the JSENSE-calibrated CSM with single-peak/multi-peak⁸ fat model and the SPIR scan. The result for a conventional pre-scan CSM with a multi-peak fat model is shown for comparison. The JSENSE results show improved water images compared to the pre-scan for both spectral fat models. This is mainly due to the geometric distortion mismatch between the EPI images and the reference scan. Besides, the water images with adjusted level/window show the capability of the algorithm to deal with the multi-peak fat spectrum, which is superior to fat suppression by SPIR. Figure 3 shows water images with different b-values and the associated ADC maps for (1) SPIR, (2) the SENSE-based water/fat separation with extra-navigators and (3) with self-navigation. SPIR shows an unsuppressed fat rim, probably arising from strong B₁⁺ inhomogeneities. Some artefacts can be seen in the SENSE-based water image with extra-navigators, which are not present for the self-navigated results. Figure 4 shows the estimated water/fat phases derived for self-navigation.

Conclusion

The proposed method allows for an efficient SENSE-based water/fat separation of non-DW and DW msh-EPI data. The SENSE-based solution requires only one acquisition for each b-value to separate water/fat with a multi-peak fat model. This directly increases the flexibility and is important when different b-values/diffusion directions are desired. Future studies will include undersampling for acceleration and use of phased array coils with more channels to support higher segmentation factors.

Acknowledgements

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